Internal_Erosion_Toolbox.pdf

INTERNAL EROSION TOOLBOX

A Method for Estimating Probabilities of Failure of Embankment Dams due to Internal Erosion Best Practices Guidance Document

4 August 2009

Credits

USACE “Best Practices” Authors:

Jeff Schaefer US Army Corps of Engineers, ERRDX Noah Vroman US Army Corps of Engineers, ERDC Tim O’Leary US Army Corps of Engineers, ERRDX

Date: Status:

4 August 2009 Final Draft

USACE-USBR “Unified Method” Authors:

Robin Fell School of Civil and Environmental Engineering University of New South Wales, Sydney Mark Foster URS Australia John Cyganiewicz US Bureau of Reclamation George Sills US Army Corps of Engineers, ERDC Noah Vroman US Army Corps of Engineers, ERDC Richard Davidson URS Corporation

Date: Status:

21 August 2008 Delta Version, Issue 2

Table of Contents

i

1 Introduction ------------------------------------------------------------------------------------------------- 1-1

1.1 General 1-1 1.2 Terminology to Describe Embankment Types 1-1 1.3 Terminology 1-2

2 Methodology------------------------------------------------------------------------------------------------ 2-1

2.1 Introduction 2-1 2.2 General Process 2-1 2.3 Information Review 2-2

3 Failure Modes and Load Partitioning--------------------------------------------------------------- 3-1

3.1 Generic Event Tree 3-1 3.2 General Failure Modes 3-3

3.2.1 Internal Erosion through the Embankment 3-3 3.2.2 Internal Erosion through the Foundation 3-4 3.2.3 Internal Erosion of the Embankment into or at the Foundation 3-4

3.3 Identification of Failure Paths 3-5 3.3.1 Overview 3-5 3.3.2 Examples 3-6

3.4 Failure Path Screening 3-9 3.4.1 Overview 3-9 3.4.2 Internal Erosion through the Embankment 3-10 3.4.3 Internal Erosion through the Soil Foundation 3-17 3.4.4 Internal Erosion of the Embankment into or at the Foundation 3-19

3.5 Partitioning of the Reservoir Levels 3-20 3.5.1 Pool of record level 3-20 3.5.2 Partitioning of reservoir levels 3-20 3.5.3 Assessing frequencies of reservoir loading 3-21

3.6 Earthquake Load Partitioning 3-21

4 Application of Tables for Estimating Conditional Probabilities--------------------------- 4-1

4.1 General Approach 4-1 4.2 Historical Frequencies of Cracks and Poorly Compacted or High Permeability

Zones in Embankments 4-1 4.3 Historical Frequencies for Internal Erosion in and into the Foundation 4-3 4.4 Estimating Conditional Probabilities 4-3

4.4.1 Estimating conditional probabilities using relative importance factors and likelihood factors 4-3

4.4.2 Estimating conditional probabilities using scenario tables 4-4 4.4.3 Estimating conditional probabilities using probability estimate tables 4-4

4.5 Length Effects 4-5 4.6 Nature of the Estimates of Probabilities Given by the Toolbox 4-13

4.6.1 The toolbox gives “best estimate” probabilities 4-13

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4.6.2 Adjusting the toolbox best estimates 4-13 4.6.3 Limitations of the methods used in the toolbox 4-14 4.6.4 Assessment of probabilities of failure for failure modes which are not

covered by the toolbox 4-15 4.7 Modeling Uncertainty in the Estimates of Conditional Probabilities 4-15

4.7.1 Purpose of this section 4-15 4.7.2 Sensitivity analysis 4-16 4.7.3 Uncertainty analysis 4-16

4.8 Summarizing (Making the Case) 4-21 4.9 Development of System Response Curves 4-21 4.10 Combining Probabilities 4-23

5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment ------ 5-1

5.1 Overall Approach 5-1 5.2 Probability of Transverse Cracking in the Embankment 5-3

5.2.1 Transverse cracking due to cross valley differential settlement (IM1) 5-3 5.2.2 Transverse cracking due to differential settlement adjacent to a cliff at the

top of the embankment (IM2) 5-5 5.2.3 Transverse cracking due to cross section settlement due to poorly

compacted shoulders (IM3) 5-7 5.2.4 Transverse cracking due to differential settlement in the foundation soil

beneath the core (IM4) 5-9 5.2.5 Transverse cracking due to differential settlement due to embankment

staging (IM5) 5-11 5.2.6 Transverse cracking due to desiccation (IM6 and IM7) 5-11 5.2.7 Transverse cracking due to an earthquake (IM8) 5-15

5.3 Probability of Hydraulic Fracturing in the Embankment 5-18 5.3.1 Hydraulic fracturing due to differential settlement causing cross valley

arching (IM9) 5-18 5.3.2 Hydraulic fracturing due to differential settlement causing arching of the

core onto the embankment shoulders (IM10) 5-20 5.3.3 Hydraulic fracturing due to differential settlement in the soil foundation

beneath the core (IM11) 5-21 5.3.4 Hydraulic fracturing due to differential settlement over small-scale

irregularities in the foundation profile beneath the core (IM12) 5-21 5.4 Factors to Account for Observations and Measured Settlements 5-23 5.5 Probability of Initiation of Erosion in a Transverse Crack or Hydraulic Fracture in

the Embankment 5-26 5.5.1 Overall approach 5-26 5.5.2 Details of the method 5-28

6 Probability of Initiation of Erosion in Poorly Compacted or High Permeability Zones in the Embankment ---------------------------------------------------------- 6-1

6.1 Overall Approach 6-1 6.2 Probability of Continuous Poorly Compacted or High Permeability Zones in the

Embankment or on the Core-Foundation/Abutment Contact 6-2

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6.2.1 Poorly compacted or high permeability zones within the core (IM13) 6-2 6.2.2 Poorly compacted or high permeability zones at the core-

foundation/abutment contact (IM14) 6-7 6.2.3 High permeability zones in the embankment due to freezing (IM15 and

IM16) 6-8 6.3 Probability of Continuous Poorly Compacted or High Permeability Zones adjacent

to a Conduit or Features Allowing Erosion into the Conduit 6-13 6.3.1 Poorly compacted or high permeability zones adjacent to a conduit (IM17) 6-13 6.3.2 Features allowing erosion into a conduit (IM18) 6-14

6.4 Probability of Continuous Poorly Compacted or High Permeability Zones or Gaps adjacent to a Spillway or Abutment Wall 6-15 6.4.1 Approach 6-15 6.4.2 Poorly compacted or high permeability zones adjacent to a spillway or

abutment wall (IM19) 6-16 6.4.3 Crack or gap adjacent to a spillway or abutment wall (IM20) 6-17 6.4.4 Transverse cracking due to differential settlement adjacent to a spillway or

abutment wall (IM21) 6-19 6.4.5 Special considerations for wrap-around details for connection of

embankment dam to concrete gravity dam (IM19 and IM21) 6-20 6.5 Factors to Account for Observations 6-22 6.6 Probability of Initiation of Erosion in Poorly Compacted or High Permeability

Zones in the Embankment or adjacent to a Conduit or Wall 6-24 6.6.1 Screening of erosion mechanism based on soil classification 6-24 6.6.2 Assessment of the probability of initiation of backward erosion in a layer

of cohesionless soil or soil with Plasticity Index ≤ 7 6-25 6.6.3 Probability of initiation of erosion by suffusion in a layer of cohesionless

soil or soil with Plasticity Index ≤ 7 (PI ≤ 12 for seepage gradients > 4) 6-33 6.6.4 Probability of initiation of erosion in a poorly compacted or high

permeability cohesive soil layer and in silt-sand-gravel soils in which collapse settlement may form a crack or flaw (IM13 and IM14) 6-35

6.6.5 Probability of initiation of erosion in a high permeability soil due to frost action (IM15 and IM16) 6-37

6.6.6 Probability of initiation of erosion in a poorly compacted or high permeability cohesive soil layer adjacent to a conduit (IM17) 6-38

6.6.7 Probability of initiation of erosion into a conduit (IM18) 6-39 6.6.8 Probability of initiation of erosion in a poorly compacted or high

permeability cohesive soil layer adjacent to a wall (IM19) 6-39

7 Probability of Initiation of Erosion in a Soil Foundation------------------------------------- 7-1

7.1 Screening Check on Soil Classification 7-1 7.2 Probability of Initiation of Backward Erosion in a Layer of Cohesionless Soil or

Soil with Plasticity Index ≤ 7 in the Foundation (IM22) 7-1 7.2.1 Overall approach 7-1 7.2.2 Probability of a continuous layer of cohesionless soil (Pexit) 7-2 7.2.3 Probability of a seepage exit (Pexit) 7-2 7.2.4 Probability of initiation of backward erosion given a seepage exit exists 7-6

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7.3 Probability of Initiation of Suffusion in a Cohesionless Layer in the Foundation (IM23) 7-9

7.4 Probability of Initiation of Erosion in a Crack in Cohesive Soil in the Foundation (IM24) 7-9 7.4.1 Overall approach 7-9 7.4.2 Some factors to consider in this assessment and suggested method for

estimating the probability of a continuous crack 7-10

8 Probability of Continuous Open Defects in the Rock Foundation ----------------------- 8-1

8.1 Overall Approach 8-1 8.2 Probability of Continuous Defects in the Rock Foundation due to Stress Relief in

the Valley Sides 8-4 8.2.1 Overview of method 8-4 8.2.2 Probability of continuous rock defects due to stress relief in the valley

sides based on geologic and topographic data (PGT) 8-4 8.2.3 Probability of continuous rock defects due to stress relief in the valley

sides based on site investigations, construction, and performance data (PSC) 8-7

8.2.4 Effects of blasting on the foundation 8-8 8.3 Probability of Continuous Defects in the Rock Foundation due to Valley Bulge or

Rebound 8-8 8.3.1 Overview of method 8-8 8.3.2 Probability of continuous rock defects due to valley bulge or rebound

based on geologic and topographic data (PGT) 8-9 8.3.3 Probability of continuous rock defects due to valley bulge or rebound

based on site investigations, construction, and performance data (PSC). 8-11 8.4 Probability of Continuous Defects in the Rock Foundation due to Solution Features 8-12

8.4.1 Overview of method 8-12 8.4.2 Probability of continuous rock defects due to solution features based on

geologic and topographic data (PGT) 8-13 8.4.3 Probability of continuous rock defects due to solution features based on

site investigations, construction, and performance data (PSC) 8-15 8.5 Probability of Continuous Defects in the Rock Foundation due to Other Geological

Features such as Landslides, Faults, or Shears 8-16 8.5.1 Overview of method 8-16 8.5.2 Probability of continuous rock defects due to landslides, faults, or shears

based on geologic and topographic data (PGT) 8-17 8.5.3 Probability of continuous rock defects due to landslides, faults, or shears

based on site investigations, construction, and performance data (PSC) 8-19 8.6 Weighted Averages of Estimated Probability of Continuous Rock Defects 8-20 8.7 Probability of Grouting Being Ineffective in Cutting Off Rock Defects (PGI) 8-21 8.8 Probability of Cut-Off Walls Being Ineffective in Cutting Off Rock Defects (PCI) 8-23 8.9 Probability of Rock Surface Treatment Being Ineffective at Preventing Contact of

the Core with Open Rock Defects (PTI) 8-25 8.10 Probability of Continuous Rock Defects (PCR) 8-25 8.11 Describing the Defects 8-26

8.11.1 Extent of features associated with stress relief in the valley sides 8-26

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8.11.2 Extent of features associated with valley bulge or rebound 8-29 8.11.3 Extent of solution features 8-29 8.11.4 Extent of other geological features such as landslides faults and shears 8-29

9 Probability of Initiation of Erosion from the Embankment into or at the Foundation -------------------------------------------------------------------------------------------------- 9-1

9.1 General Principles 9-1 9.2 Overall Approach 9-1

9.2.1 Rock Foundations 9-1 9.2.2 Open-Work Granular Foundations 9-4

9.3 Probability of a Continuous Pathway of Coarse-Grained Layers in Soil Foundations 9-6 9.4 Probability of Initiation of Scour at the Core-Foundation Contact 9-8 9.5 Probability of Soil Transport through Defects 9-8

10 Probability of Continuation ---------------------------------------------------------------------------10-1

10.1 Probability of Continuation for Internal Erosion through the Embankment 10-1 10.1.1 Overall Approach 10-1 10.1.2 Probability of continuation (PCE) – Scenario 1 (homogeneous zoning) 10-3 10.1.3 Probability of continuation (PCE) – Scenario 2 (downstream shoulder can

hold a crack or pipe) 10-3 10.1.4 Probability for continuation – Scenario 3 (filter/transition zone is present

downstream of the core or a downstream shoulder zone which is not capable of holding a crack/pipe) 10-4

10.1.5 Probability of continuation (PCE) – Scenario 4 (internal erosion into open defects, joints, or cracks in conduits, walls, toe drains, or rock foundations) 10-16

10.2 Probability of Continuation for Internal Erosion through Soil Foundations 10-17 10.2.1 Overall approach 10-17

10.3 Probability of Continuation for Internal Erosion of the Embankment into or at the Foundation 10-18 10.3.1 Scour along rock defects or erosion into rock defects 10-18 10.3.2 Scour along the contact or erosion into open-work granular foundations 10-18

11 Probability of Progression----------------------------------------------------------------------------11-1

11.1 Overall Approach 11-1 11.2 Probability of Forming a Roof 11-1

11.2.1 Internal erosion through the embankment 11-1 11.2.2 Internal erosion through a soil foundation 11-1

11.3 Probability of Crack Filling Action Being Ineffective 11-4 11.3.1 Internal erosion through the embankment 11-4 11.3.2 Internal erosion through the foundation 11-4 11.3.3 Internal erosion of the embankment into or at the foundation 11-4

11.4 Probability for Limitation of Flows 11-6 11.4.1 Flow limitation by upstream zone 11-6 11.4.2 Flow into/out of open joint in conduits 11-6

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11.4.3 Flow into jointed bedrock 11-6

12 Probability of Unsuccessful Intervention--------------------------------------------------------12-1

12.1 General Principles 12-1 12.2 Some Information on the Rate of Internal Erosion and Piping 12-2 12.3 Detection 12-5

12.3.1 Some general principles 12-5 12.3.2 Probability of not detecting internal erosion (Pndi) 12-6

12.4 Intervention and Repair 12-10 12.5 Probability of Unsuccessful Intervention 12-12

13 Probability of Breach -----------------------------------------------------------------------------------13-1

13.1 Overall Approach and Screening 13-1 13.1.1 Overall approach 13-1 13.1.2 Screening of breach mechanisms 13-1

13.2 Probability of Breach by Gross Enlargement (Pge) 13-3 13.2.1 Screening for internal erosion through the embankment, through the soil

foundation, and from the embankment into or at the foundation 13-3 13.2.2 Assessment for internal erosion through the embankment, through the soil

foundation, and from the embankment into or at the foundation 13-4 13.3 Probability of Breach by Slope Instability (Psi) 13-5

13.3.1 Approach 13-5 13.3.2 Probability of slope instability initiates for internal erosion through the

embankment, through the soil foundation, and from the embankment into or at the foundation (Psi-i) 13-6

13.3.3 Probability of slope instability of the embankment initiates for internal erosion in a rock foundation (Psi-i) 13-8

13.3.4 Loss of freeboard due to slope instability (Psi-lf) 13-12 13.4 Estimation of the Probability of Breach by Sloughing or Unraveling (Psu) 13-13 13.5 Probability of Breach by Sinkhole Development (Psd) 13-16

13.5.1 Approach 13-16 13.5.2 Probability of sinkhole formation (Ps-f) 13-16 13.5.3 Probability of loss of freeboard due to sinkhole formation (Ps-lf) 13-16

14 References -------------------------------------------------------------------------------------------------14-1

Appendices

Appendix A Navigation Tables for Internal Erosion through the Embankment Appendix B Navigation Tables for Internal Erosion in Soil Foundations Appendix C Navigation Tables for Continuous Rock Defects Appendix D Navigation Tables for Internal Erosion of the Embankment into or at the Foundation

List of Tables and Figures

vii

Tables

Table 3.1 – Screening of initiating mechanisms for internal erosion through the embankment due to concentrated leaks in transverse cracks ......................................................................... 3-10

Table 3.2 – Screening of initiating mechanisms for internal erosion through the embankment due to concentrated leaks in hydraulic fractures....................................................................... 3-13

Table 3.3 – Screening of initiating mechanisms for internal erosion through the embankment due to concentrated leaks in poorly compacted or high permeability zones ............................ 3-14

Table 3.4 – Screening of initiating mechanisms for internal erosion through the foundation ................ 3-17 Table 3.5 – Screening of initiating mechanisms for internal erosion of the embankment into or at the

foundation...................................................................................................................... 3-19 Table 3.6 – Example of earthquake load partitions................................................................................. 3-21 Table 4.1 – Estimated historical frequencies of cracking, hydraulic fracture or poorly compacted or

high permeability zones in embankment dams................................................................ 4-2 Table 4.2 – Historical frequencies for cracking or poorly compacted zone in the embankment dam

body ................................................................................................................................. 4-2 Table 4.3 – Length effects for internal erosion through the embankment due to concentrated leaks in

transverse cracks.............................................................................................................. 4-6 Table 4.4 – Length effects for internal erosion through the embankment due to concentrated leaks in

hydraulic fractures ........................................................................................................... 4-8 Table 4.5 – Length effects for internal erosion through the embankment due to poorly compacted or

high permeability zones................................................................................................... 4-9 Table 4.6 – Length effects for internal erosion through the soil foundation and into or at the foundation4-11 Table 4.7 – Best estimate, likely high, and likely low equivalence table................................................ 4-18 Table 5.1 – Factors influencing the likelihood of transverse cracking in the embankment due to cross

valley differential settlement (IM1)................................................................................. 5-3 Table 5.2 – Probability of transverse cracking in the embankment dams due to cross valley differential

settlement (IM1) versus ∑(RFxLF) ................................................................................. 5-4 Table 5.3 – Factors influencing the likelihood of transverse cracking in the embankment due to

differential settlement adjacent a cliff at the top of the embankment (IM2) ................... 5-5 Table 5.4 – Probability of transverse cracking in the embankment due to differential settlement

adjacent to a cliff at the top of the embankment (IM2) versus ∑(RFxLF) ...................... 5-6 Table 5.5 – Factors influencing the likelihood of transverse cracking in the embankment due to cross

section settlement due to poorly compacted shoulders (IM3) ......................................... 5-7 Table 5.6 – Probability of transverse cracking in the embankment due to cross section settlement due to

poorly compacted shoulders (IM3) versus ∑(RFxLF) .................................................... 5-8 Table 5.7 – Factors influencing the likelihood of transverse cracking in the embankment due to

differential settlement in the foundation soil beneath the core (IM4) ............................. 5-9 Table 5.8 – Probability of transverse cracking due to differential settlement in the foundation soil

beneath the core (IM4) versus ∑(RFxLF) ..................................................................... 5-10 Table 5.9 – Factors influencing the likelihood of transverse cracking due to desiccation at the

embankment crest (IM6) ............................................................................................... 5-12 Table 5.10 – Probability of transverse cracking due to desiccation at the embankment crest (IM6)

versus ∑(RFxLF)........................................................................................................... 5-13 Table 5.11 – Factors influencing the likelihood of transverse cracking due to desiccation at seasonal

shutdown layers during construction or staged construction surfaces (IM7) ................ 5-14


viii

Table 5.12 – Probability of transverse cracking due to desiccation versus at seasonal shutdown layers during construction or staged construction surfaces (IM7) versus ∑(RFxLF) .............. 5-14

Table 5.13 – Damage classification system (Pells and Fell, 2002, 2003) ............................................... 5-15 Table 5.14 – Probability of transverse cracking and maximum likely crack width at the top of the core

due to an earthquake (IM8)............................................................................................ 5-17 Table 5.15 – Factors influencing the likelihood of hydraulic fracturing in the embankment due to

differential settlement causing cross valley arching (IM9) ........................................... 5-18 Table 5.16 – Probability of hydraulic fracturing in the embankment due to differential settlement

causing cross valley arching (IM9) versus ∑(RFxLF) .................................................. 5-19 Table 5.17 – Factors influencing the likelihood of hydraulic fracturing in the embankment due to

differential settlement causing arching of the core onto the embankment shoulders (IM10)............................................................................................................................ 5-20

Table 5.18 – Probability of hydraulic fracturing in the embankment due to differential settlement causing arching of the core onto the embankment shoulders (IM10) versus ∑(RFxLF)5-21

Table 5.19 – Factors influencing the likelihood of hydraulic fracturing in the embankment due to differential settlement over small-scale irregularities in the foundation profile beneath the core (IM12).............................................................................................................. 5-22

Table 5.20 – Probability of hydraulic fracturing in the embankment due to differential settlement over small-scale irregularities in the foundation profile beneath the core (IM12) versus ∑(RF x LF) .................................................................................................................... 5-22

Table 5.21 – Settlement multiplication factors versus observed settlements .......................................... 5-24 Table 5.22 – Cracking observation factors (applies to upper embankment only) ................................... 5-25 Table 5.23 – Maximum likely width of cracking at the top of the core for transverse cracking in the

embankment (IM1 through IM7 and IM21) versus ∑(RFxLF) ..................................... 5-28 Table 5.24 – Maximum likely depth of cracking from the top of the core for transverse cracking in the

embankment (IM1 through IM5 and IM8) .................................................................... 5-29 Table 5.25 – Maximum likely depth of desiccation cracking based on climate (IM6 and IM7) ............ 5-29 Table 5.26 – Maximum likely width of cracking for hydraulic fracturing in the embankment (IM9 and

IM20) versus ∑(RFxLF)................................................................................................ 5-30 Table 5.27 – Maximum likely width of cracking in the embankment for hydraulic fracturing in the

embankment (IM10 through IM12) versus ∑(RFxLF).................................................. 5-30 Table 5.28 – Examples of estimated maximum likely depths below the top of the core and widths of

cracking formed by hydraulic fracture in the embankment (IM9) ................................ 5-31 Table 5.29 – Representative erosion rate index (IHET) versus soil classification for non-dispersive soils

based on Wan and Fell (2002, 2004) ............................................................................. 5-31 Table 5.30 – Estimation of probability of initiation in a crack for ML or SM with < 30% fines soil

types............................................................................................................................... 5-33 Table 5.31 – Estimation of probability of initiation in a crack for SC with <40% fines or SM with >

30% fines soil types....................................................................................................... 5-33 Table 5.32 – Estimation of probability of initiation in a crack for SC with > 40% fines or CL-ML soil

types............................................................................................................................... 5-34 Table 5.33 – Estimation of probability of initiation in a crack for CL or MH soil types........................ 5-34 Table 5.34 – Estimation of probability of initiation in a crack for CL-CH or CH with LL < 65 soil types5-35 Table 5.35 – Estimation of probability of initiation in a crack for CH with LL > 65 soil types ............. 5-35 Table 5.36 – Estimation of probability of initiation in a crack for dispersive soils (CL, CH, CL-CH) . 5-36 Table 5.37 – Estimated hydraulic shear stress (N/m2) from water flowing in an open crack, versus

crack width and flow gradient ....................................................................................... 5-36 Table 5.38 – Initial shear stress assumed for Table 5.30 to Table 5.36 .................................................. 5-37


ix

Table 6.1 – Factors influencing the likelihood of poorly compacted or high permeability zones within the core for cohesive soils (IM13) ................................................................................... 6-3

Table 6.2 – Factors influencing the likelihood of poorly compacted or high permeability zones within the core for cohesionless soils (IM13)............................................................................. 6-5

Table 6.3 – Probability of poorly compacted or high permeability layers within the core (IM13) versus ∑(RFxLF) ........................................................................................................................ 6-6

Table 6.4 – Factors influencing the likelihood of poorly compacted or high permeability zones at the core-foundation/abutment contact (IM14)....................................................................... 6-7

Table 6.5 – Probability of a poorly compacted or high permeability zones at the core-foundation/abutment contact (IM14) versus ∑(RFxLF).................................................. 6-8

Table 6.6 – Factors influencing the likelihood of high permeability zones due to freezing at the embankment crest (IM15)................................................................................................ 6-9

Table 6.7 – Probability of high permeability zones due to freezing at the embankment crest (IM15) versus ∑(RFxLF)........................................................................................................... 6-10

Table 6.8 – Factors influencing the likelihood of high permeability zones due to freezing at seasonal shutdown layers during construction or staged construction surfaces (IM16) .............. 6-11

Table 6.9 – Probability of high permeability zones due to freezing at seasonal shutdown layers during construction or staged construction surfaces (IM16) versus ∑(RFxLF) ....................... 6-12

Table 6.10 – Factors influencing the likelihood of poorly compacted or high permeability zones adjacent to a conduit through the embankment (IM17)................................................. 6-13

Table 6.11 – Probability of poorly compacted or high permeability zones adjacent to a conduit through the embankment (IM17) versus ∑(RFxLF) ................................................................... 6-14

Table 6.12 – Factors influencing the likelihood of an open joint or crack allowing erosion into a non-pressurized conduit when the internal condition is known............................................ 6-15

Table 6.13 – Factors influencing the likelihood of poorly compacted or high permeability zones adjacent to a spillway or abutment wall (IM19) ............................................................ 6-16

Table 6.14 – Probability of poorly compacted or high permeability zones adjacent to a spillway or abutment wall (IM19) versus ∑(RFxLF)....................................................................... 6-16

Table 6.15 – Factors influencing the likelihood of a crack or gap adjacent to a wall (IM20)................. 6-17 Table 6.16 – Probability of a gap or crack adjacent to a wall (IM20) versus ∑(RFxLF)........................ 6-17 Table 6.17 – Factors influencing the likelihood of transverse cracking in the embankment due to

differential settlement adjacent a spillway or abutment wall (IM21) ............................ 6-19 Table 6.18 – Probability of cracking due to differential settlement adjacent a spillway or abutment wall

(IM21) versus ∑(RFxLF) .............................................................................................. 6-19 Table 6.19 – Factors to be considered in assessing seepage gradients on wrap-around ......................... 6-20 Table 6.20 – Seepage observation factors ............................................................................................... 6-23 Table 6.21 – Suggested locations for determination of average gradients .............................................. 6-24 Table 6.22 – Time to develop seepage gradient in cohesionless soils .................................................... 6-30 Table 6.23 – Probability of initiation of backward erosion in cohesionless soils and soils with PI ≤ 7 for

compacted layers ........................................................................................................... 6-32 Table 6.24 – Probability of initiation of backward erosion in cohesionless soils and soils with PI ≤ 7 for

uncompacted layers ....................................................................................................... 6-33 Table 6.25 – Probability of initiation of erosion by suffusion................................................................. 6-35 Table 6.26 – Amount of collapse settlement which may occur on saturation versus compaction

properties ....................................................................................................................... 6-36 Table 6.27 – Width of frost-induced flaw versus ∑(RFxLF) .................................................................. 6-37 Table 7.1 – Probability of a seepage exit through the confining layer (Pexit) versus calculated factor of

safety against heave ......................................................................................................... 7-4


x

Table 7.2 – Factors influencing the likelihood of a seepage exit due to defects in the confining layer.... 7-5 Table 7.3 – Probability of a seepage exit due to defects in the confining layer (Pexit) versus ∑(RFxLF) . 7-6 Table 7.4 – Probability of initiation of backward erosion in the foundation given a seepage exit is

predicted .......................................................................................................................... 7-8 Table 8.1 – Geologic and topographic factors influencing the likelihood of continuous rock defects due

to stress relief in the valley sides ..................................................................................... 8-5 Table 8.2 – Factors influencing likelihood for topography ....................................................................... 8-6 Table 8.3 – Probability of continuous rock defects due to stress relief in the valley sides based on

geologic and topographic data (PGT) versus ∑(RFxLF)................................................... 8-6 Table 8.4 – Site investigation, construction, and performance factors influencing the likelihood of

continuous rock defects due to stress relief in the valley sides........................................ 8-7 Table 8.5 – Probability of continuous rock defects due to stress relief in the valley sides based on site

investigation, construction, and performance data (PSC) versus ∑(RFxLF) .................... 8-8 Table 8.6 – Geologic and topographic factors influencing the likelihood of continuous rock defects due

to valley bulge or rebound ............................................................................................. 8-10 Table 8.7 – Probability of continuous rock defects due to valley bulge or rebound based on geologic

and topographic data (PGT) versus ∑(RFxLF) ............................................................... 8-10 Table 8.8 – Site investigation, construction, and performance factors influencing the likelihood of

continuous rock defects due to valley bulge or rebound ............................................... 8-11 Table 8.9 – Probability of continuous rock defects due to valley bulge or rebound based on site

investigation, construction, and performance data (PSC ) versus ∑(RFxLF).................. 8-12 Table 8.10 – Geologic and topographic factors influencing the likelihood of continuous rock defects

due to solution features.................................................................................................. 8-14 Table 8.11 – Probability of continuous rock defects due to solution features based on geologic and

topographic data (PGT) versus ∑(RFxLF) ...................................................................... 8-14 Table 8.12 – Site investigation, construction, and performance factors influencing the likelihood of

continuous rock defects due to solution features ........................................................... 8-15 Table 8.13 – Probability of continuous rock defects due to solution features based on site investigation,

construction, and performance data (PSC) versus ∑(RFxLF)......................................... 8-16 Table 8.14 – Geologic and topographic factors influencing the likelihood of continuous rock defects

due to landslides, faults, or shears ................................................................................. 8-18 Table 8.15 – Probability of continuous rock defects due to landslides, faults, or shears based on

geologic and topographic factors (PGT) versus ∑(RFxLF) ............................................ 8-18 Table 8.16 – Site investigation, construction, and performance factors influencing the likelihood of

continuous rock defects due to landslides, faults, or shears .......................................... 8-19 Table 8.17 – Probability of continuous rock defects due to landslides, faults, or shears based on site

investigation, construction, and performance data (PSC) versus ∑(RFxLF) .................. 8-20 Table 8.18 – Weighting factors for assessing probabilities of open or in-filled rock defects ................. 8-20 Table 8.19 – Factors influencing the likelihood of grouting not being effective in cutting off rock

defects............................................................................................................................ 8-21 Table 8.20 – Probability of grouting not being effective for continuous rock defects (PGI) versus

∑(RFxLF) ...................................................................................................................... 8-22 Table 8.21 – Factors influencing the likelihood of a cut-off in the foundation not being effective for

continuous defects ......................................................................................................... 8-24 Table 8.22 – Probability of a cut-off not being effective for continuous defects (PCI) versus ∑(RFxLF)8-25 Table 8.23 – Probability of rock surface treatment being ineffective at preventing contact of the core

with open rock defects (PTI)........................................................................................... 8-25 Table 9.1 – Probability of a continuous pathway (PCP) for erosion into soil foundation .......................... 9-7


xi

Table 9.2 – Probability of soil transport through defects .......................................................................... 9-8 Table 10.1 – Probability of continuation (Scenario 2) ............................................................................ 10-4 Table 10.2 – Likelihood for filters with excessive fines holding a crack.............................................. 10-10 Table 10.3 – Potential for segregation of filtering materials ................................................................. 10-10 Table 10.4 – Gradation limits to prevent segregation (USDA SCS 1994, USBR 1987, US Corps of

Engineers 1994)........................................................................................................... 10-11 Table 10.5 – Susceptibility of filter/transition zones to segregation versus ∑(RFxLF)........................ 10-11 Table 10.6 – No erosion boundary for the assessment of filters of existing dams (after Foster and Fell

2001)............................................................................................................................ 10-12 Table 10.7 – Excessive and continuing erosion criteria (Foster 1999; Foster and Fell 1999, 2001)..... 10-12 Table 10.8 – Aid to judgment for estimation of probability of continuing erosion (PCE) when the actual

filter grading is finer than the continuing erosion boundary ....................................... 10-13 Table 10.9 – Example of estimating probabilities for no erosion, some erosion, excessive erosion, and

continuing erosion for the example shown in Figure 10.6 .......................................... 10-15 Table 10.10 – Probability of continuation for open defects, joints, or cracks....................................... 10-16 Table 11.1 – Probability of a soil being able to support a roof to an erosion pipe (PPR) ......................... 11-3 Table 11.2 – Probability for crack filling action not stopping pipe enlargement for internal erosion

through the embankment (PPC) ...................................................................................... 11-5 Table 11.3 – Probability that flow in the developing pipe will not be restricted by an upstream zone,

cut-off wall or a concrete element in the erosion path (PPL).......................................... 11-6 Table 12.1 – A method for the approximation estimation of the time for progression of piping and

development of a breach, for breach by gross enlargement, and slope instability linked to development of a pipe (Fell et al 2001, 2003) ........................................................... 12-3

Table 12.2 – Rate of erosion of the core or soil in the foundation .......................................................... 12-4 Table 12.3 – Influence of the material in the downstream zone of the embankment on the likely time

for development of a breach .......................................................................................... 12-4 Table 12.4 – Qualitative terms for times of development of internal erosion, piping and breach (Fell et

al 2001, 2003) ................................................................................................................ 12-4 Table 12.5 – Factors influencing the likelihood of not observing a concentrated leak ........................... 12-8 Table 12.6 – Probability of not observing a concentrated leak (Pnol) versus ∑(RFxLF) for internal

erosion in an embankment ............................................................................................. 12-9 Table 12.7 – Probability that given the leak is observable it is not detected given the time between the

first appearance of the concentrated leak, and the frequency of inspections and/or reading of monitoring instruments (Pnd) ........................................................................ 12-9

Table 12.8 – Assessment of the probability that given the concentrated leak is detected, intervention and repair is not successful (Pdui)................................................................................. 12-11

Table 13.1 – Screening of breach mechanisms for internal erosion through the embankment, internal erosion through soil foundations, and of the embankment into the foundation............. 13-2

Table 13.2 – Screening for probability of breach by gross enlargement of the pipe: ability to support a pipe ................................................................................................................................ 13-3

Table 13.3 – Probability of breach by gross enlargement of the pipe (Pge)............................................. 13-5 Table 13.4 – Factors influencing the likelihood of breach by instability of the downstream slope: slide

initiates for internal erosion through the embankment, through the soil foundations, and from the embankment into or at the foundation ............................................................ 13-7

Table 13.5 – Probability of breach by slope instability: slide initiates for internal erosion through the embankment, through soil foundations, and from the embankment into or at the foundation (Psi-i) versus ∑(RFxLF)................................................................................ 13-8


xii

Table 13.6 – Probability of seepage exits from defects or solution features in a rock foundation into the downstream shell (PS).................................................................................................... 13-9

Table 13.7 – Assessment of size of leak in defect or solution feature in a rock foundation relative to discharge capacity of foundation drains and downstream shell .................................. 13-10

Table 13.8 – Factors influencing the likelihood of breach by instability of the downstream slope: slide initiates for internal erosion in rock foundation........................................................... 13-11

Table 13.9 – Estimation of the probability of breach by slope instability: slide initiates for internal erosion in rock foundations (Psi-i) versus ∑(RFxLF) ................................................... 13-12

Table 13.10 – Factors influencing the likelihood of breaching by instability of the downstream slope: loss of freeboard .......................................................................................................... 13-12

Table 13.11 – Probability of breach by loss of freeboard (Psi-lf) versus ∑(RFxLF) .............................. 13-13 Table 13.12 – Factors influencing the likelihood of breaching by sloughing: dams with an earthfill

downstream zone ......................................................................................................... 13-14 Table 13.13 – Probability of breach by sloughing (earthfill) for internal erosion through the

embankment, through soil foundations, and from the embankment into the foundation (Psl) versus ∑(RFxLF) ................................................................................................. 13-14

Table 13.14 – Factors influencing the likelihood of breaching by unraveling: dams with a rockfill downstream zone ......................................................................................................... 13-15

Table 13.15 – Probability of breach by unraveling (rockfill) for internal erosion through the embankment, through soil foundations, and from the embankment into the foundation (Pun) versus ∑(RFxLF)................................................................................................. 13-15

Table 13.16 – Probability of a sinkhole or crest settlement developing (Ps-f) ....................................... 13-16 Table 13.17 – Factors influencing the likelihood of breaching by sinkhole development: loss of

freeboard given sinkhole develops .............................................................................. 13-17 Table 13.18 – Probability of breach by sinkhole development: loss of freeboard given sinkhole

develops (Ps-lf) versus ∑(RFxLF)................................................................................. 13-17

Figures

Figure 1.1 – Dam zoning categories.......................................................................................................... 1-1 Figure 1.2 – Soil types which are subject to internal instability and suffusion ........................................ 1-3 Figure 1.3 – Gradation of broadly graded soils with poor self-filtering characteristics (Sherard 1979)... 1-3 Figure 3.1 – Typical embankment dam showing some key features associated with potential internal

erosion failure paths......................................................................................................... 3-7 Figure 3.2 – Examples of embankment crest details which may result in relatively high likelihood of

internal erosion ................................................................................................................ 3-8 Figure 3.3 – Example of an embankment with significantly different probabilities of internal erosion

above and below the top of the downstream berm .......................................................... 3-9 Figure 4.1 – Example system response curve ......................................................................................... 4-22 Figure 4.2 – Examples of multiple flow paths ........................................................................................ 4-23 Figure 5.1 – Definition of terms used to describe cross valley geometry ................................................. 5-4 Figure 5.2 – Cracking adjacent to cliffs due to differential settlement of the embankment...................... 5-6 Figure 5.3 – Sloping core dam (a) Definitions of terms (b) Limit of what constitutes a sloping core dam5-8 Figure 5.4 – Typical scenarios which may lead to differential settlement in the foundation.................. 5-10 Figure 5.5 – Longitudinal section through staged embankment ............................................................. 5-11 Figure 5.6 – Incidence of transverse cracking versus seismic intensity and damage class contours for

earthfill dams (Pells and Fell 2002, 2003)..................................................................... 5-16


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Figure 5.7 – Incidence of transverse cracking versus seismic intensity and damage class contours for earthfill and rockfill dams (Pells and Fell 2002, 2003) ................................................. 5-16

Figure 5.8 – Longitudinal profiles of the dam showing the definition of terms for cross valley arching5-19 Figure 5.9 – Examples of the estimation of crack width and flow gradient in the crack ........................ 5-32 Figure 6.1 – Example of poor detailing of seepage collars around a conduit (FEMA 2005).................. 6-14 Figure 6.2 – Situations where a gap may form between the dam fill and spillway wall (a) Steep

foundation adjacent spillway wall; (b) Change in slope of the retaining wall (Fell et al. 2004).............................................................................................................................. 6-18

Figure 6.3 – Wrap-around details for connection of embankment dam to concrete gravity dam ........... 6-21 Figure 6.4 – Underlayer factor CZ versus D/r (Schmertmann 2000)....................................................... 6-27 Figure 6.5 – Graph to obtain ipα from ipo and α (Schmertmann 2000) .................................................... 6-29 Figure 6.6 – Maximum point gradient (ipmt) needed for complete piping (initiation and progression for

an unfiltered exit) versus uniformity coefficient of soil (Schmertmann 2000) ............. 6-31 Figure 6.7 – Backward erosion piping layer and path geometry............................................................. 6-32 Figure 6.8 – Contours of the probability of internal instability for silt-sand-gravel soils and clay-silt-

sand-gravel soils of limited clay content and plasticity (PI ≤ 12) (Wan and Fell 2004)6-34 Figure 6.9 – Contours of the probability of internal instability for sand-gravel soils with less than 10%

non-plastic fines passing 0.075 mm (Wan and Fell 2004) ............................................ 6-34 Figure 6.10 – Map showing the maximum depth of frost penetration from Sowers (1970) ................... 6-38 Figure 7.1 – An example of a situation where there is no continuous layer of cohesionless soil in the

foundation and backward erosion cannot occur .............................................................. 7-2 Figure 7.2 – Cross section of an embankment and foundation showing seepage flow net and definition

of terms ............................................................................................................................ 7-3 Figure 7.3 – Section through embankment and foundation showing definition of terms to estimate the

average gradient in the foundation sand .......................................................................... 7-7 Figure 8.1 – Flow chart for estimating the probability, width, depth and spatial distribution of

continuous open defects and solution features in rock foundations ................................ 8-3 Figure 8.2 – Definition of Δhp and hp ...................................................................................................... 8-22 Figure 8.3 – Computation of probability of a continuous open defect below the embankment.............. 8-26 Figure 8.4 – Assumed distribution of defect depths for defects related to stress relief effects in the

valley sides (Figures from Fell et al. 2004) ................................................................... 8-27 Figure 10.1 – Examples of scenarios for evaluation of probability of continuation ............................... 10-2 Figure 10.2 – Flow chart for evaluating the probabilities of no erosion, some erosion, excessive

erosion, and continuing erosion..................................................................................... 10-7 Figure 10.3 – Example of the selection of representative grading curves (fine, average, and coarse) for

the assessment of filter compatibility ............................................................................ 10-9 Figure 10.4 – Approximate method for estimating DF15 after washout of the erodible fraction from a

suffusive soil or for soils susceptible to segregation ..................................................... 10-9 Figure 10.5 – Criteria for excessive erosion boundary.......................................................................... 10-13 Figure 10.6 – Example of filter/transition gradings compared to filter erosion boundaries determination

of the filter erosion boundaries for the representative fine, average, and coarse gradings of the core material ...................................................................................................... 10-14

Figure 10.7 – Example of unfiltered exits in the soil foundation .......................................................... 10-17 Figure 10.8 – Example of an unfiltered exit in the soil foundation due to daylighting of the foundation

sand layer downstream of the dam .............................................................................. 10-18 Figure 11.1 – Scenarios for holding a roof of a pipe for internal erosion through the foundation.......... 11-2 Figure 12.1 – Sub-event tree for calculating the probability of unsuccessful intervention................... 12-12

Introduction Section 1

1-1

1 Introduction

1.1 General

This document was prepared by the USACE Risk and Reliability Directory of Expertise (ERRDX) to summarize USACE best practices for estimating probabilities of failure of embankment dams by internal erosion. This document was developed by incorporating USACE best practices into the original guidance document entitled “A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping” Delta Version, Issue 2, dated August 2008 developed by U.S Bureau of Reclamation, USACE, University of New South Wales, and URS Corporation. Much of this document is similar to the original guidance document except for changes made here in.

1.2 Terminology to Describe Embankment Types

In several of the tables provided to assist in assessing probabilities, the probability is linked to embankment type. The terms shown in Figure 1.1 have been adopted.

0. Homogeneous earthfill

Foundation filter

Embankment filter and/or

1. Earthfill with filter

Rock toe

Max 0.2H

2. Earthfill with rock toe

corecore downstream zoneof sand/gravel

3. Zoned earthfill

corecore downstream zoneof rockfill

4. Zoned earth and rockfill

core

rockfillrockfill

5. Central core earth and rockfill

concretefacing

earthfill

6. Concrete face earthfill

concretefacing

rockfill

7. Concrete face rockfill

Puddle core

8. Puddle core earthfill

concrete corewall

earthfill

9. Earthfill with corewall

concrete corewall

rockfill

10. Rockfill with corewall

hydraulic fill core

11. Hydraulic fill

Figure 1.1 – Dam zoning categories


1-2

1.3 Terminology

The methodology uses the following terminology:

Internal erosion. Internal erosion occurs when soil particles within an embankment dam or its foundation, are carried downstream by seepage flow. Internal erosion can initiate by concentrated leak erosion, backward erosion, suffusion and soil contact erosion.

Concentrated leak erosion. Erosion in a concentrated leak may occur in a crack in an embankment or its foundation, caused by differential settlement, desiccation, freezing and thawing, or hydraulic fracture; or it may occur in a continuous permeable zone containing coarse and/or poorly compacted materials which form an interconnecting system of voids. The concentration of flow causes erosion (sometimes called scour) of the walls of the crack or interconnected voids.

Flaw. A continuous crack, gap, or poorly compacted or high permeability layer in which a concentrated leak may form.

Backward erosion. Backward erosion involves the detachment of soils particles when the seepage exits to a free unfiltered surface, such as the ground surface downstream of a soil foundation or the downstream face of a homogeneous embankment or a coarse rockfill zone immediately downstream from the fine grained core. The detached particles are carried away by the seepage flow and the process gradually works its way towards the upstream side of the embankment or its foundation until a continuous pipe is formed.

Piping. Piping is the form of internal erosion which initiates by backward erosion, or erosion in a crack or high permeability zone, and results in the formation of a continuous tunnel called a “pipe” between the upstream and the downstream side of the embankment or its foundation.

Suffusion and internal instability. Suffusion is a form of internal erosion which involves selective erosion of fine particles from the matrix of coarser particles (coarse particles are not floating in the fine particles). The fine particles are removed through the constrictions between the larger particles by seepage flow, leaving behind an intact soil skeleton formed by the coarser particles. Soils which are susceptible to suffusion are internally unstable. Coarse graded and gap graded soils, such as those shown schematically in Figure 1.2, are susceptible to suffusion. In these soils the volume of fines is less than the volume of voids between the coarse particles.


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0

1020

30

40

50

60

70

8090

100

0.001 0.01 0.1 1 10 100 1000

Particle size (mm)

% P

assi

ngCLAY TO SILT SAND GRAVEL

GAP GRADED SOIL

COARSELY GRADED SOIL WITH A FLAT TAIL OF FINES

Figure 1.2 – Soil types which are subject to internal instability and suffusion

Self-filtering. In soils which self-filter, the coarse particles prevent the internal erosion of the medium particles, which in turn prevent erosion of the fine particles. Soils which potentially will not self-filter include those which are susceptible to suffusion (internally unstable), and very broadly graded soils such as those which fall into the grading envelope shown in Figure 1.3 (Sherard 1979). The soils had particle size distributions which plotted nearly as a straight line, were typically of glacial origin, and the dams from which the soils were taken had all exhibited signs of internal erosion. The soils have a volume of fine particles greater than the volume of voids between the coarse sand and gravel fraction, and the coarser particles are “floating” in the finer particles. The figure is not meant to define the boundary of such soils, only examples.

Figure 1.3 – Gradation of broadly graded soils with poor self-filtering characteristics (Sherard 1979)


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Continuation. Continuation is the phase where the relationship of the particle size distribution between the base (core) material and the filter controls whether or not erosion will continue. Foster and Fell (1999, 2001) and Foster (1999) define four levels of severity of continuation from “no erosion” to “continuing erosion.”

No erosion. The filtering material stops erosion with no or very little erosion of the material it is protecting. The increase in leakage flows is so small that it is unlikely to be detectable.

Some erosion. The filtering material initially allows erosion from the soil it is protecting, but it eventually seals up and stops erosion.

Excessive erosion. The filter material allows erosion from the material it is protecting, and in the process permits large increases in leakage flow, but the flows are self healing. The extent of erosion is sufficient to cause sinkholes on the crest and erosion tunnels through the core.

Continuing erosion. The filtering material is too coarse to stop erosion of the material it is protecting and continuing erosion is permitted. Unlimited erosion and leakage flows are likely.

Progression. Progression is the third phase of internal erosion, where hydraulic shear stresses within the eroding soil may or may not lead to the enlargement of the pipe. Increases of pore pressure and seepage occur. The main issues are the likelihood of and rate of pipe enlargement and whether the pipe will collapse, whether upstream zones may control the erosion process by flow limitation, and whether a pipe will extend through the low permeability zones of the embankment.

Breach. Breach is the final phase of internal erosion. It may occur by one of the following four phenomena (listed below in order of their observed frequency of occurrence).

• Gross enlargement of the pipe (which may include the development of a sinkhole from the pipe to the crest of the embankment).

• Slope instability of the downstream slope.

• Unraveling of the downstream face.

• Overtopping (e.g., due to settlement of the crest from suffusion and/or due to the formation of a sinkhole from a pipe in the embankment).

Annual exceedance probability (AEP). The estimated probability that an event of specified magnitude will be exceeded in any year.

Frequency. A measure of likelihood expressed as the number of occurrences of an event in a given time or in a given number of trials (see also likelihood and probability).

Likelihood. Conditional probability of an outcome given a set of data, assumptions and information. Also used as a qualitative description of probability and frequency.


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Probability. A measure of the degree of certainty. This measure has a value between zero (impossibility) and 1.0 (certainty). It is an estimate of the likelihood of the magnitude of the uncertain quantity, or the likelihood of the occurrence of the uncertain future event.

There are two main interpretations:

Statistical (frequency or fraction) – The outcome of a repetitive experiment of some kind like flipping coins. It includes also the idea of population variability. Such a number is called an “objective” or relative frequentist probability because it exists in the real world and is in principle measurable by doing the experiment.

Subjective probability (degree of belief) – Quantified measure of belief, judgment, or confidence in the likelihood of an outcome, obtained by considering all available information honestly, fairly, and with a minimum of bias. Subjective probability is affected by the state of understanding of a process, judgment regarding an evaluation, or the quality and quantity of information. It may change over time as the state of knowledge changes.

Failure Path. A sequence of potential events starting from an initiating mechanism, such as a defect, flaw or seepage path in the dam or its foundation, and which may lead to an uncontrolled release of the reservoir.

Methodology Section 2

2-1

2 Methodology

2.1 Introduction

Risk is defined as the probability of a loss occurring in a given time period (annually). The equation for risk is:

Risk = [Probability of the loading] × [Probability of adverse response given the loading] × [Adverse consequence given the failure].

The first two components of this equation, when multiplied, produce the Annual Probability of Failure (APF) and are the main topic of this document.

2.2 General Process

The process for estimating the annual probability of failure by piping and internal erosion includes the following general steps:

Step 1: Review all information pertinent to internal erosion and piping (refer to Section 2.3 as an aid).

Step 2: Identify all potential failure paths associated with internal erosion and piping, considering each of the failure locations:

• Internal erosion through the embankment;

• Internal erosion through the foundation; and

• Internal erosion of the embankment into or at the foundation.

Screen those failure paths that are assessed to have negligible contribution to the annual probability of failure and document the reasons for their exclusion. Develop detailed descriptions and sketches of all realistic failure paths. Guidance is provided in Sections 3.3 and 3.4.

Step 3: Decompose each of the potential failure paths into event trees. Generic event trees have been developed for each general failure mode the navigation tables in Appendices A to D. Select the event tree and associated navigation table that best fits the failure path being considered.

Step 4: Select the loading partitions for each of the load conditions (hydrologic and seismic) as described in Sections 3.5 and 3.6.

Step 5: Estimate the conditional probabilities for each node on the event tree, fully documenting the rationale. Specific guidance is given for estimating the conditional probabilities for various initiating mechanisms and failure locations in Sections 5 to 13. Navigation tables are provided in

Methodology Section 2

2-2

Appendices A to D to assist the user to find the location of the guidance tables for each node of the event tree.

Step 6: Calculate the probability of failure for each load condition and failure path.

Step 7: Develop system response curves for use in follow-on risk analysis and assessment.

2.3 Information Review

The quality and credibility of a risk estimate will suffer unless the risk assessor is fully aware of all pertinent information about internal erosion. Typical information to review includes characteristics of the constructed project (e.g., embankment geometry, zoning, materials, construction methods, and seepage cut-off and control features) and characteristics of the setting (e.g., site geology and stratigraphy, and foundation material characteristics). Additional site information is provided by documented performance history.

To the maximum extent practicable, existing data from design and construction records, performance history, and post-construction investigations need to be reviewed. At preliminary stages of risk analysis, existing data supplemented by engineering judgment provide a sufficient basis for evaluation. If significant risk for the project is indicated including consideration of uncertainty, field investigations, laboratory testing, and additional analyses may be warranted. In some cases, however, it may be less expensive to simply fix the structure for the failure mode of concern.

A site examination has been found to provide valuable input into the risk analysis process. Typically, the site examination is performed as part of the PFMA process. It consists of a physical review of the dam site and appurtenant structures to better understand the layout of the dam and to help visualize potential failure modes as well as structural and geologic conditions. During the site visit, it is also essential to discuss the site, performance, and project operations with field personnel in their own environment and to obtain their opinion of potential vulnerabilities.

Failure Modes and Load Partitioning Section 3

3-1

3 Failure Modes and Load Partitioning

3.1 Generic Event Tree

The following generic sequence of events has been developed for internal erosion failure modes:

Reservoir Rises

Initiation – Flaw exists (1) (2)

Initiation – Erosion starts

Continuation – Unfiltered or inadequately filtered exit exists

Progression – Roof forms to support a pipe

Progression – Upstream zone fails to fill crack

Progression – Upstream zone fails to limit flows

Intervention fails

Dam breaches (consider all likely breach mechanisms)

Consequences occur

(1) A “flaw” is a continuous crack or gap, poorly compacted or high permeability zone in which a concentrated leak may form.

(2) For Backward Erosion Piping (BEP), no flaw is required, but a continuous zone of cohesionless soil in the embankment or foundation is required.

Generic event tree structures have been developed based on this sequence of events, and these are presented in the navigation tables in Appendices A to D for each of the general failure modes.

Initiation is the first phase and considers the existence of a flaw such as a continuous crack or poorly compacted layer in which a concentrated leak may form. If a flaw exists, erosion must start to initiate for internal erosion to develop. There are several processes by which erosion can initiate in the embankment or foundation as follows:

• Concentrated leak erosion. Erosion can commence from the walls of a crack within the soil or within a poorly compacted layer.

• Scour at the embankment-foundation contact. Erosion of the soil may occur where it is in contact with seepage passing through the foundation either through a coarse-grained soil or open joints in rock.


3-2

• Backward erosion. Backward erosion involves the detachment of soils particles when the seepage exits to a free unfiltered surface. The detached particles are carried away by the seepage flow, and the process gradually works its way towards the upstream side of the embankment or its foundation until a continuous pipe is formed.

• Suffusion. This is a form of internal erosion which involves selective erosion of fine particles from the matrix of coarser particles (coarse particles are not floating in the fine particles). The fine particles are removed through the constrictions between the larger particles by seepage flow, leaving behind an intact soil skeleton formed by the coarser particles.

Continuation is the phase where the relationship of the particle size distribution between the base (core) material and the filter controls whether or not erosion will continue. Foster and Fell (1999, 2001) and Foster (1999) define four levels of severity of continuation: no erosion, some erosion, excessive erosion and continuing erosion. In this document, only continuing erosion is considered since it indicates the base soil could be eroded through the filter without plugging off.

Progression is the third phase of internal erosion, where hydraulic shear stresses within the eroding soil may or may not lead to the enlargement of the pipe. Increases of pore pressure and seepage occur. The main issues are whether the pipe will collapse and whether upstream zones may control the erosion process by flow limitation or crack filling.

Intervention fails is the fourth phase of the event tree, and this considers whether the internal erosion failure mechanism will be detected and whether intervention and repair will successfully stop the failure process.

Dam breaches is the final phase of internal erosion. It may occur by one of the following four phenomena (listed below in order of their observed frequency of occurrence):

• Gross enlargement of the pipe;

• Instability of the downstream slope;

• Unraveling of the downstream face; and

• Sinkhole collapse resulting in overtopping.


3-3

3.2 General Failure Modes

Failure by internal erosion of embankment dams is categorized into three general failure modes:

• Internal erosion through the embankment;

• Internal erosion through the foundation; and

• Internal erosion of the embankment into or at the foundation.

3.2.1 Internal Erosion through the Embankment

In this failure mode, internal erosion occurs solely within the embankment. This includes internal erosion associated with through-penetrating structures, such as an outlet works, spillway, or adjoining a concrete gravity structure. The initiating mechanisms for these failure modes are listed below.

Transverse cracking of the embankment (Section 5.2)

• Cross valley differential settlement (IM1)

• Differential settlement adjacent to a cliff (IM2)

• Cross section settlement due to poorly compacted shoulders (IM3)

• Differential settlement in the foundation soil beneath the core (IM4)

• Differential settlement due to embankment staging (IM5)

• Desiccation (IM6 and IM7)

• Earthquake (IM8)

Hydraulic fracturing of the embankment (Section 5.3)

• Differential settlement causing cross valley arching (IM9)

• Differential settlement causing arching of the core onto the shoulders (IM10)


• Differential settlement due to small scale irregularities in the foundation profile (IM12)

A more detailed description of the entire process and a generic event tree is given in the navigation tables in Appendix A.


3-4

3.2.2 Internal Erosion through the Foundation

This general failure mode involves internal erosion occurring solely within the foundation until the later stages of the breach process where the embankment starts to collapse. The initiating mechanisms for these failure modes are as follows:

• Poorly compacted or high permeability layer during construction within the core (IM13) using Section 6.2.1.

• Poor compacted or high permeability layer on the foundation or abutment contact (IM14) using Section 6.2.2.

• High permeability layer due to freezing (IM15 and IM16) using Section 6.2.3.

• Poorly compacted or high permeability layer associated with a conduit (IM17 and IM18) using Sections 6.3.1 and 6.3.2, respectively.

• Poorly compacted or high permeability layer associated with other structures penetrating the core (IM 19 through IM21) using Section 6.4.

More detailed descriptions of the process are given in the navigation tables given in Appendix B for internal erosion in a soil foundation.

3.2.3 Internal Erosion of the Embankment into or at the Foundation

Internal erosion initiates at the contact between the embankment and foundation owing to: i) seepage through the embankment eroding material into the foundation; or ii) seepage in the foundation at the embankment contact, eroding the embankment material. The initiating mechanisms for these failure modes are:

• Scour along rock defects in the foundation (IM25) using Section 9.2.1

• Erosion into rock defects in the foundation (IM 26) using Section 9.2.1

• Scour along the contact with open-work granular soils (IM27) using Section 9.2.2

• Erosion into open-work granular soils (IM28) using Section 9.2.2

A more detailed description of the process is given in the navigation tables given in Appendix D.


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3.3 Identification of Failure Paths

3.3.1 Overview

A potential failure path is a sequence of events starting from an initiating mechanism, such as a defect, flaw or seepage path in the dam or its foundation, and which may lead to an uncontrolled release of the reservoir. The risk analysis team should go through a discussion of all potential failure paths and develop a thorough understanding of the sequence of events and the potential location of seepage and erosion paths through the embankment and foundation. The sequence of events and seepage pathways should be documented by annotating cross sections and longitudinal sections of the embankment and its foundation to help visualize the failure path. An example is given in Section 3.3.2. The development of the failure paths should consider the following:

• The general event tree structure as described in Section 3.1;

• Potential initiating mechanisms, as summarized in Table 3.1 to Table 3.5;

• Zoning of the embankment, including the configuration of internal filter and drainage measures;

• Foundation geology and stratigraphy; and

• Filtered and unfiltered exit points of seepage.

The possibility of overlooking potentially important failure modes is reduced by considering the particular details if the dam and it’s appurtenant structures, such as details of walls retaining the embankment, conduits through the embankment, by assembling construction photographs and reports and inspecting the dam as part of the failure modes assessment. It is also reduced by having the failure modes assessment done by a team which includes the engineer and geologist most familiar with the dam, dam operating and surveillance staff, and facilitated by a person experienced in failure modes analysis.

The development team has strived to address all failure modes that, in their experience, occur in embankment dams. Procedures are also suggested to handle failure modes not well covered in this methodology. However, in the end, as pointed out by the late Ralph Peck in his paper “The Risk of the Oddball”, there remains the potential that even with the “… efforts of even the most experienced engineers the most significant potential failure mode may occasionally be overlooked.”


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3.3.2 Examples

The following sketch depicts an example of the description of a failure path for an initiating event involving seepage through a poorly compacted layer in the embankment. It is followed by a description of the failure mode for seepage path A.

A

B

CZone 1(SC)

Zone 2(SM)

Zone 2(SM)

Drainage Blanket

Riprap onGravel Bedding El. 500

El. 460Downstream Slope

Protection (Cobbles)

“Initiating event: Poorly compacted layer

Failure Path Description: The reservoir rises to elevation 466 feet, which is 1 foot above the historic high reservoir elevation. A low density zone exists in the Zone 2 at this elevation due to a thick lift being placed during original construction of the embankment that was not compacted well by the equipment being used. Upon saturation from the reservoir, the bottom of this layer settles and separates from the upper portion of the layer leaving a gap (i.e., as a result of collapse settlement of the poorly compacted layer). Seepage flows through this gap achieve sufficient velocity (i.e., sufficient gradient and gap width) to initiate erosion and begin a concentrated leak erosion process. The downstream cobble layer (slope protection) does not filter the Zone 2 material or the material does not have sufficient overburden and the slope protection layer blows off from reservoir pressure reaching the layer. A roof forms through the Zone 2 material. The riprap bedding layer does not function as a crack stopping material because it does not have sufficient volume due to its limited thickness or it is not of the proper gradation to be filtered by the downstream slope protection material. There is no upstream zone of material to limit flows. Wet spots and flowing water appear on the downstream face of the embankment, but these seepage expressions are not seen by either the public or project personnel. If the seepage expressions are seen and reported, intervention efforts are unsuccessful because the efforts simply do not stop the erosion process or the erosion progresses too rapidly allow meaningful intervention efforts to be implemented. The gap widens which leads to increased seepage velocities and more erosion of the Zone 2 material. Eventually this process of increasing seepage velocities and erosion progresses to full breach. The breach occurs by mechanisms typical for this type of embankment (i.e., gross enlargement of the developing pipe, slope instability, or sinkhole development).”


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Spillwaycrest CrestCrest

Spillwaywalls

Outletconduit

Intaketower

A B

C

D

E

FG

FSLNo filters above FSLFilters

Rockfill

Alluvium

Rock

Earthfill core

A, BCD,E

FG

Adjacent spillway walls.Adjacent outlet conduit.Related to irregularitiesin the foundation profile.In the foundation.From embankment tofoundation.

LEGEND

PLAN

ELEVATION

SECTION

Rockfill

Figure 3.1 – Typical embankment dam showing some key features associated with potential internal erosion failure paths


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Figure 3.1 shows a fairly typical embankment dam, with a concrete spillway structure. Failure paths that could be considered for this dam include:

a) Internal erosion adjacent the spillway walls at A and B.

b) Internal erosion adjacent to and into the outlet conduit ©.

c) Internal erosion over irregularities in the foundation (e.g., at D for piping in the upper part of the embankment, and E for piping in the lower part, where there are likely to be low stresses and a potential for cracking and hydraulic fracture due to differential settlement).

d) Internal erosion for the remainder of the embankment (e.g., in high permeability layers).

e) Internal erosion in the alluvium foundation (F).

f) Internal erosion from the embankment to foundation at G.

For many dams, it is likely that features that lead to initiation of internal erosion are in the upper part of the dam. This is because cracking due to differential settlement over large scale irregularities in the foundation profile is more likely to be present near the crest. Continuation is also more likely because often the detailing of the dam design, or as-built, will give no or little filter protection. Figure 3.2 gives examples of this with increased likelihood of flood loading near the crest of the dam.

Figure 3.2 – Examples of embankment crest details which may result in relatively high likelihood of internal erosion


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Figure 3.3 is an example where there is a significantly different probability of internal erosion above the berm than below because the upper part is essentially a homogeneous dam while the sandy gravel in zone 2 may act as a filter. This is best managed in the analysis by considering internal erosion above the berm (the upper part of the embankment) separately to below the berm (the middle and lower parts of the embankment).

Figure 3.3 – Example of an embankment with significantly different probabilities of internal erosion above and below the top of the downstream berm

While considering failure paths in this amount of detail may seem to be a lot of extra work, experience shows that it is necessary to do the analysis in this detail to allow proper consideration of the probability of failure, and in reality it makes assessment of conditional probabilities easier because factors are not being lumped together.

3.4 Failure Path Screening

3.4.1 Overview

The purpose of the failure path screening process is to systematically review the potential failure paths/modes that have been identified and eliminate those from further consideration that are assessed to have negligible contribution to risk.

The failure path is evaluated by listing the adverse factors that make the failure mode “more likely” and the favorable factors that make the failure mode “less likely”. These are based on the team’s understanding of the dam and background material.

Flow path B

Flow path A


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Screening of the failure paths is also evaluated using the screening criteria for the various initiating mechanisms which are summarized in Table 3.1 to Table 3.5.

Each failure path is then screened by the analysis team based on the consideration of the list of the more likely and less likely factors, and using the initiating mechanism screening criteria. The primary intent is to identify those failure paths that are clearly so remote as to be negligible or non-credible. These screened failure paths are not carried forward into the risk analysis. The rationale for the inclusion or exclusion of each potential failure path should be fully documented.

3.4.2 Internal Erosion through the Embankment

Table 3.1 – Screening of initiating mechanisms for internal erosion through the embankment due to concentrated leaks in transverse cracks

Failure path/location Exclude the failure path if the following conditions are satisfied Reference

IM1 – Transverse cracking due to cross valley differential settlement

Exclude if:

(1) The abutment profile is uniform without benches.

OR (2) The abutment slope is gentle (β2 < 25°, refer to Figure 5.1).

OR

(2) The reservoir stage being considered is below the likely maximum depth of cracking.

Section 5.2.1, Table 5.1

IM2 – Transverse cracking due to differential settlement adjacent to a cliff at the top of the embankment

Exclude if:

(1) There is no vertical cliff in contact with the embankment.

OR

(2) A wide bench is present at the base of the cliff (Wb/Hw > 2.5, refer to Figure 5.2).

OR

(3) The abutment slope below the cliff is gentle (β1 < 25°, refer to Figure 5.2).

OR




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IM3 – Transverse cracking due to cross section settlement due to poorly compacted shoulders

Exclude if:

(1) The dam is zoning type homogeneous earthfill, earthfill with filter drains, or zoned earthfill.

OR

(2) Evidence from relative settlements of core and shoulders indicate the materials have a similar modulus.

OR



IM4 – Transverse cracking due to differential settlement in the foundation soil beneath the core

Exclude if:

(1) There is no compressible soil in the foundation beneath the core.

OR



IM5 – Transverse cracking due to differential settlement due to embankment staging

Exclude if:

(1) The embankment construction was not staged.

OR

(2) There is little or no difference in the modulus of the different stages.

OR

(3) The existing embankment slope is gentle (β2 < 25°, refer to Figure 5.6). OR


Section 5.2.5 (and 5.2.1), Table 5.1


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IM6 – Transverse cracking due to desiccation at the embankment crest

Exclude if:

(1) The crest is paved with concrete, asphalt or bitumen seal with a base layer at least 12 in (300 mm) thick and/or rockfill or non-plastic granular layer at least 3 ft (1 m) thick.

OR

(2) The soils are not susceptible to desiccation in the climatic conditions at the site.

OR



IM7 – Transverse cracking due to desiccation at seasonal shutdown layers during construction or staged construction surfaces

Exclude if:


OR

(2) The soils are not susceptible to desiccation in the climatic conditions at the site.

OR

(3) Very good control and clean-up practices were used (e.g., desiccated layers were removed from the embankment and replaced with new soil or adequately reworked to specified moisture content).

OR



IM8 – Transverse cracking due to earthquake

Exclude if:

(1) The joint probability of the earthquake and reservoir level is at least 2 orders of magnitude less than the tolerable risk guidelines.

OR


Section 5.2.7


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Table 3.2 – Screening of initiating mechanisms for internal erosion through the embankment due to concentrated leaks in hydraulic fractures


IM9 – Hydraulic fracturing due to cross valley arching

Exclude if:

(1) The valley is very wide (Wv/H > 2, refer to Figure 5.8).

OR

(2) The reservoir stage being considered is below the likely location of hydraulic fracturing.


IM10 – Hydraulic fracturing due to differential settlement causing arching of the core onto the shoulders of the embankment

Exclude: (1) For all dam zoning types other than central core earth and rockfill (or gravel shells) and puddle core earthfill dams. OR

(2) The embankment has a wide core (W/H > 1), OR

(3) The core has a higher modulus than the shells. Shoulders poorly compacted or dumped. Core compacted >98% SMDD. OR (4) The reservoir stage being considered is below the likely location of the phreatic surface.


IM11 – Hydraulic fracturing in the lower part of the embankment due to differential settlement in the foundation soil beneath the core

Exclude if:

(1) There is no compressible soil in the foundation beneath the core.

Sections 5.3.3 (and 5.2.4), Table 5.7

IM12 – Hydraulic fracturing due to small-scale irregularities in the foundation/abutment profile beneath the core

Exclude if:

(1) The persistency of the irregularity is less than 50% across the base width of the core.



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Table 3.3 – Screening of initiating mechanisms for internal erosion through the embankment due to concentrated leaks in poorly compacted or high permeability zones


IM13 – Poorly compacted or high permeability zone within the embankment

Exclude if:

(1) All soils are very well-compacted with suitable equipment, suitable lift thicknesses, around optimum moisture content, and with good documentation and records. OR (2) For cohesive soils (PI > 7), compacted to ≥98% SMDD at -2% to +1% of OWC.

OR (3) For cohesionless soils and soils with PI ≤ 7, compacted to >85% relative density or SPT (N1)60 > 42 bpf.

Section 6.2.1

Table 6.1 for cohesive soils (PI > 7)

Table 6.2 for cohesionless soils or soils with PI ≤ 7

IM14 – Poorly compacted or high permeability layer on the core-foundation/abutment contact

Exclude if: (1) Contact soils are well-compacted on a regular foundation surface with good documentation and records OR

(2) Uniform or regular rock surface, or rock surface was treated with shotcrete or concrete to correct slope irregularities, and soils well compacted (contact soil compacted using special compaction methods (e.g., rubber tires, use more plastic material, compaction wet of OWC). OR

(3) Uniform well-compacted soil foundation, with good mixing, bonding and compaction of contact fill. OR (4) Compacted soil foundation


IM15 – High permeability zone due to freezing at the embankment crest

Exclude if:

(1) The climate is such that temperatures do not fall below freezing point except possibly overnight or for a day or two. OR




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IM16 – High permeability zone due to freezing at seasonal shutdown layers during construction or staged construction surfaces

Exclude if:


OR

(2) The climate is such that temperatures do not fall below freezing point except possibly overnight or for a day or two. OR (3) Very good control and clean-up practices were used (e.g., frozen layers were removed from the embankment and replaced with new soil or adequately reworked to specified moisture content). OR



IM17 – Poorly compacted or high permeability zone adjacent to a conduit through the embankment

Exclude if:

(1) There is no conduit passing through the embankment. OR (2) The conduit is totally embedded in a trench excavated in non-erodible rock and backfilled to the surface with concrete.


IM18 – Features allowing erosion into a conduit

Exclude if: (1) There is no conduit passing through the embankment. OR (2) Careful internal inspection of conduit shows no evidence of open joints or cracks.


IM19 – Poorly compacted or high permeability zone associated with a spillway or abutment wall

Exclude if: (1) There is no spillway or abutment wall in contact with the embankment.


IM20 – Crack or gap adjacent to a spillway or abutment wall

Exclude if: (1) There is no spillway or abutment wall in contact with the embankment. OR (2) The reservoir stage being considered is below the likely maximum depth of cracking.



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IM21 – Transverse cracking due to differential settlement adjacent to a spillway or abutment wall

Exclude if:

(1) There is no spillway or abutment wall in contact with the embankment.

OR

(2) A wide bench is present at the base of the wall (Wb/Hw > 2.5, refer to Figure 5.2).

OR

(3) The abutment slope below the wall is gentle (β1 < 30°, refer to Figure 5.2).

OR




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3.4.3 Internal Erosion through the Soil Foundation

Table 3.4 – Screening of initiating mechanisms for internal erosion through the foundation

Initiating mechanism Exclude the failure path if the following conditions are satisfied Reference

All modes of internal erosion through the foundation (backward erosion, suffusion, or erosion in a crack)

Exclude if:

(1) The foundation is rock. OR

(2) The soil layer beneath the dam is cut-off.

Section 7

IM22 – Backward erosion in a cohesionless foundation soil

Exclude if: (1) The foundation soil has a PI > 7. OR

(2) The layer of cohesionless soil or soil with PI ≤ 7 is not continuous below the embankment (i.e., it terminates beneath the dam, refer to Figure 7.1) OR

(3) The factor of safety against heave of the confining layer is greater than 1.3, or the thickness of the confining layer (for consideration of defects in the confining layer) is greater than 25 feet. OR

(4) The factor of safety for the exit gradient is greater than 1.3.

Section 7.2

IM23 – Suffusion in a cohesionless foundation soil

Exclude if: (1) The foundation soil has a PI > 7.

OR (2) The soil is not gap-graded. For gap-graded or broadly graded soils, the proportion of the finer fraction is less than 40% of the total mass. OR

(3) The layer of cohesionless soil or soil with PI ≤ 7 is not continuous below the embankment (i.e., it terminates beneath the dam, refer to Figure 7.1). OR (4) The factor of safety against heave of the confining layer is greater than 1.3, or the thickness of the confining layer (for consideration of defects in the confining layer) is greater than 25 feet. OR

Section 7.3


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(5) The factor of safety for the exit gradient is greater than 1.3.

IM24 – Erosion in a crack in a cohesive foundation soil due to differential settlement or desiccation

Exclude if: (1) The foundation soil is cohesionless.

OR (2) The layer of cohesive soil or soil with PI > 7 is not continuous below the embankment

OR

(3) There is no compressible soil in the foundation to cause cracking due to differential settlement.

OR

(4) The foundation soils are not susceptible to desiccation in the climatic conditions at the site. OR (4) Very good construction practices were used to strip zones of desiccation from the foundation.

Section 7.4

(Section 5.2.4, Table 5.7)

(Section 5.2.6, Table 5.9)


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3.4.4 Internal Erosion of the Embankment into or at the Foundation

Table 3.5 – Screening of initiating mechanisms for internal erosion of the embankment into or at the foundation


IM25 – Scour along defects in rock foundation < 25 mm

Exclude if:

(1) Rock foundation below the core is comprised of rock containing closed defects (<1 mm wide) or open defects less than 3D95 of fine limit of the core OR (2) Rock foundation below the core has been adequately treated (e.g., shotcrete, slush grouting mortar treatment, concrete cut-off wall)

Section 9

IM26 – Erosion into defects in rock foundation > 25 mm

Exclude if: (1) Rock foundation below the core is comprised of rock containing closed defects (<1 mm wide) or open defects less than 3D95 of fine limit of the core OR

(2) Rock foundation below the core has been adequately treated (e.g., shotcrete, slush grouting mortar treatment, concrete cut-off wall)

Section 9

IM27 – Scour along contact with open-work granular foundation

Exclude if:

(1) Foundation soil is fine-grained with FC > 12%, and the soil does not contain macrostructure such as root holes, relic joints, or solution features. OR (2) Soil foundation below the core is comprised of sands (SP or SW) which are filter-compatible with the embankment materials (i.e., satisfy the “no erosion” criteria in Section 10.1.4).

Section 9

IM28 – Erosion into open-work granular foundation

Exclude if:

(1) Foundation soil is fine-grained with FC > 12%, and the soil does not contain macrostructure such as root holes, relic joints, or solution features. OR

(2) Soil foundation below the core is comprised of sands (SP or SW) which are filter-compatible with the embankment materials (i.e., satisfy the “no erosion” criteria in Section 10.1.4).

Section 9


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3.5 Partitioning of the Reservoir Levels

3.5.1 Pool of record level

The pool of record (POR) level is the maximum level the reservoir has reached during its operation. It is also known as “historic high reservoir level” and “water surface of record.” It is an important level because the embankment and its foundations have been tested up to this level.

3.5.2 Partitioning of reservoir levels

For each failure path under consideration, the risk assessor must establish load increments for evaluation. These will be used in developing system response curves that relate the probability of failure to the reservoir level. The evaluation points must be carefully selected to define the shape of the system response curve, especially at elevations where significant changes in the probabilities will occur. Two pool elevations will be required to define significant changes in probabilities (e.g., at the location of the bottom of a know defect or crack and at the pool of record). It is important to capture the full range of loading so extrapolation outside of the defined system response curve will not be necessary with performing follow on risk analysis.

The reservoir levels should be partitioned to coincide with:

• Elevation of the maximum annual pool or the highest elevation where the probability of initiation becomes equal to zero (e.g., bottom of transverse crack, elevation of defect in rock, etc.)

• Geological features which occur above a particular level in the foundation (e.g., a highly permeable gravel layer).

• Elevations where there is a documented change in performance (e.g., boils, high piezometric levels)

• Topographic features such as major changes in foundation profile if these are above the pool of record.

• Changes in design such as the top of the filter or top of the core as shown in Figure 3.2(a) and Figure 3.2(b) or the top of downstream berms as shown in Figure 3.3.

• Pool of record level.

• Pool of record plus 1 foot (required for failure modes through the embankment, except IM17, and intervention if inspection frequency changes).

• Elevation equivalent to 20 percent increase in previously recorded hydraulic head (for IM17 only).

• Elevation equivalent to 20 percent increase in previously recorded hydraulic head, plus 1 foot (for IM17 only).


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• Bottom of transverse of crack (required for failure modes through the upper part of the embankment).

• Embankment crest level.

The reservoir levels do not have to be consistent between failure modes or with the reservoir frequency curve as long as the full range of loading is covered and the shape of the system response curve is adequately defined.

3.5.3 Assessing frequencies of reservoir loading

For internal erosion, use the annual probability that the level in the partition is exceeded regardless of how long, not the proportion of time the reservoir is above the level. This is because internal erosion often develops quite quickly and may go from initiation to breach in hours or days.

3.6 Earthquake Load Partitioning

Evaluate the peak ground bedrock acceleration and earthquake magnitude versus Annual Exceedance Probability (AEP) for the site. Partition the loads to form a table as shown in Table 3.6.

Table 3.6 – Example of earthquake load partitions

Earthquake peak ground acceleration

Representative earthquake moment

magnitude

Annual exceedance probability of the

earthquake loading

Probability/annum the loading is in this stage

0.99

< 0.10g 6.0 0.01

0.009

0.20g 6.0 0.001

0.0009

0.30g 7.0 0.0001

0.0001

Seismic loading data can be obtained from the U.S. Geological Survey (USGS) banded ground motion deaggregation web site:

http://eqint.cr.usgs.gov/deaggband/2002/index.php

The web site provides the mean annual rate of occurrence of peak ground acceleration (PGA) within pre-defined acceleration partitions and the relative contribution for different moment magnitude-distance combinations for a given location (latitude and longitude), frequency, and site condition. The earthquake load


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partition size varies: 0.05g (from 0 to 0.3g), 0.1g (from 0.3g to 1.0g), 0.25g (from 1.0g to 2.5g), 0.5g (from 2.5g to 3.0g), and 1.0g (from 3.0g to 5.0g). The magnitudes obtained from the USGS banded deaggregations are in moment magnitude scale (Mw). The most likely magnitude (mode) is suggested for the representative earthquake magnitude for risk assessments. The mode represents a relatively likely source, whereas the mean may represent an unlikely or even unconsidered source.

Probabilities of failure should be developed for each of the earthquake loading ranges. The first node in the main event tree will be the earthquake loading (annualized), and the second node will be the proportion of the time (in a given year) that the reservoir level is exceeded.

In some situations the reservoir may rise to higher levels before repairs to cracks caused by seismic loading can be affected, or cracking may be undetected. The possibility of these scenarios should be assessed.

Application of Tables for Estimating Conditional Probabilities

Section 4

4-1

4 Application of Tables for Estimating Conditional Probabilities

4.1 General Approach

For each failure mode the conditional probabilities at each node in the event tree are estimated for each reservoir and earthquake load partition. They are used in the event trees to calculate probabilities of failure for each load partition. These probabilities are conditional on the reservoir or earthquake loading and are known as the “system response.”

The estimation of conditional probabilities is covered in Sections 5 to 13, with Sections 5 to 9 covering Initiation, Section 10 Continuation, Section 11 Progression, Section 12 Intervention, and Section 13 Breach.

Tables are presented within the sections to provide guidance on the estimation of conditional probabilities. These tables have been developed to model the physical processes so far as practical. The probabilities have been assessed using the expert judgment of the workshop attendees. Where practical, the probabilities have been anchored to historic data. This has mainly been possible in the estimation of the probability of initiation of erosion in concentrated leaks and is discussed further in Section 4.2 and in the Supporting Document.

4.2 Historical Frequencies of Cracks and Poorly Compacted or High Permeability Zones in Embankments

Concentrated leak erosion may occur in cracks caused by differential settlement, desiccation, or in poorly compacted zones. In poorly compacted zones initiation of erosion may be a result of the voids between aggregated soil particles giving higher permeability and continuous open paths, or collapse settlement of the poorly compacted layer leading to a flaw or continuous open path in which water can flow and erode the sides of the flaw as happens in a crack.

Estimated frequencies of the occurrence of cracking, hydraulic fracture or poorly compacted or high permeability zones in embankments are presented in Table 4.1. They have been determined from analysis of historic dam accidents and failures, allowing for under reporting of the incidents in the database, cracking which may have been present in the dams in the database but were sufficiently resistant to erosion for erosion not to initiate, the cracks sealed by swelling, were above the Pool of Record (POR) of the dams, or erosion was stopped by filters. Details of the database and the analysis are given in the Supporting Document.

The frequencies in Table 4.1 are for a crack, hydraulic fracture or poorly compacted or high permeability zone being present, and do not include the assessment of whether erosion initiates in the crack, hydraulic fracture or poorly compacted or high permeability zone. These historic frequencies have been used as a basis for anchoring the estimated probabilities of a flaw being present in which erosion may initiate.

When applying the historic frequencies to predict future behavior it is assumed that the “Above POR” values apply when the reservoir level exceeds the pool of record level by at least one foot (0.3 meters). This is so the “Above POR” frequencies apply when the reservoir is testing significant new areas of the dam.


Section 4

4-2

Table 4.1 – Estimated historical frequencies of cracking, hydraulic fracture or poorly compacted or high permeability zones in embankment dams

Estimated historical frequencies of cracking, hydraulic fracture or poorly compacted or high permeability zones Location of cracking,

poorly compacted or high permeability zone First filling Reservoir level above

pool of record Reservoir level below

pool of record

In embankment (dam body) 0.014 0.014 0.001

Associated with conduit 0.01 0.01 0.0007

Associated with concrete wall or structure through embankment

0.004 0.004 0.0003

The historical frequencies for cracking or poorly compacted or high permeability zone in the dam body were further subdivided into the various mechanisms of crack formation. This was necessary so as to avoid the double counting of the historical frequencies when the probabilities for each initiating mechanism are added together. Table 4.2 presents the estimated historical frequencies for each of the mechanisms.

Table 4.2 – Historical frequencies for cracking or poorly compacted zone in the embankment dam body

Estimated historical frequencies of cracking, hydraulic fracture or poorly compacted or high permeability zones

Mechanism for cracking or poorly compacted or high permeability zone Proportion of

cases

Reservoir level above pool of

record

Reservoir level below pool of

record

All incidents (cracking, hydraulic fracture and poorly compacted or high permeability zone)

100% 0.014 0.001

Cracking and hydraulic fracture 63% In upper part (47%) 0.007 0.0005

In middle/lower part (16%) 0.002 0.0002

Poorly compacted or high permeability zone in upper and lower parts (total) 37% 0.005 0.0004

As described in the Supporting Document, the historical frequencies presented in Table 4.1 and Table 4.2 represent the average frequencies for cracks, hydraulic fracture, and poorly compacted or high permeability zones across the population of dams in the database. These represent a large number of dams of varying age and varying levels of engineering design and construction practice. They do not represent the historical


Section 4

4-3

frequencies for the “average dam” a term which has been applied previously (e.g., Fell et al 2003, 2004). It would be expected that a portfolio of well engineered Reclamation, USACE and Australian dams would have average probabilities estimated based on these historical data less than the average historical frequencies presented in the tables.

The historical frequencies have been determined for a load cycle. For “Above POR” case, the frequencies were not adjusted because the incidents were related to one load cycle. For the “Below POR” case, the frequencies have been adjusted by dividing by the average age of the dams before the incident occurred. It was assumed that a loading cycle was equivalent to one year of operation including a seasonal fluctuation below the pool of record.

The database of incidents is relatively small, and because of this, there should be no further subdivision of the failure and accident statistics.

4.3 Historical Frequencies for Internal Erosion in and into the Foundation

The conditions in the foundations of dams are inherently more complex and varied than in the dam body, and hence historic frequencies for internal erosion in and into the foundation are more difficult to interpret and apply. One of the key issues for these modes of internal erosion is whether continuous seepage paths or open defects are present, and historic performance data provides very little information to aid in the assessment. For this reason, the use of historic performance data for anchoring the conditional probabilities for internal erosion through the foundation and internal erosion from the embankment into the foundation has not been done.

4.4 Estimating Conditional Probabilities

4.4.1 Estimating conditional probabilities using relative importance factors and likelihood factors

Most of the sections for estimation of conditional probabilities are structured so there is a table of factors affecting the likelihood. These tables are structured to show:

• The factors;

• The relative importance of this factor (RF) with numeric weightings (usually three factors with relative importance weightings of 3, 2, and 1); and


Section 4

4-4

• Likelihood factors (LF) for which there are descriptions. Generally there are four for each factor, with likelihood weightings of 4, 3, 2 and 1.

There is then a second table which links ∑(RFxLF) to the conditional probability. Where there is historic data to “anchor” the probabilities these are shown in brackets (e.g., [0.0005] for Table 5.2, “Below POR”). The tables have two or more sets of probabilities. Where the “anchor” probabilities are estimated by expert judgment of the toolbox development team they are shown with rounded brackets: e.g., (0.003). The conditional probabilities on these tables are on a log scale, and interpolation between the bracketed probability values should be based on log interpolation.

The “Below POR” figures are for reservoir level stages with a representative level up to and 1 foot (0.3 meter) above the historic high reservoir pool level (POR). The “Above POR” figures are for representative reservoir level stages at least 1 foot (0.3 meter) above this historic high reservoir pool level.

These anchor probabilities are a form of a “base rate frequency” and the approach used in the tables is a base rate frequency approach.

Those carrying out the risk analysis are required to choose which of the descriptors for each factor best reflects conditions at the dam. Where there is little data this assessment should be made on the best available information and using judgment based on geological conditions and experience elsewhere on dams of similar age and design.

For some conditional probability estimates it has been necessary to modify the format of the table to better model relative importance or likelihood distributions.

In the tables the term “negligible” means that the contribution to the probability of failure would be very small indeed, insufficient to affect the outcome.

4.4.2 Estimating conditional probabilities using scenario tables

Where the number of factors affecting the estimation of conditional probabilities is few or to be based on limited data, “scenario tables” are used. These have been developed by the toolbox development team based on published information, and the experience of the team members.

These tables present ranges of conditional probabilities within which the risk analysis team are to select their best estimate based on the details of the dam they are analyzing.

4.4.3 Estimating conditional probabilities using probability estimate tables

In some sections, e.g., those describing the assessment of the probability of initiation of erosion in a crack, (Section 5.4.2) and initiation and progression of backward erosion in cohesionless soils (Section 6.6.2), the


Section 4

4-5

toolbox development team have carried out analyses to simplify the estimation of conditional probabilities from input data which itself has significant uncertainty, and the analysis methods themselves have uncertain outputs.

The assumptions made to develop these tables are described in the Supporting Document.

4.5 Length Effects

The effect of the length of the embankment being considered may have an influence on the assessed probability of internal erosion and piping. The effect is dependent on the failure mode, how the embankment is partitioned for the analysis, and how the conditional probabilities are assessed.

Many failure modes are independent of length because they are related to specific features in the embankment, such as a conduit, contact with a wall, and differential settlement of a major change in foundation profile. In many embankments, these failures modes contribute most to the likelihood of internal erosion and piping.

The failure modes which are potentially affected by length are cracking due to desiccation (either by drying and/or freezing), high permeability zones in the embankment (e.g., due to poorly compacted layers in the core), high permeability layer on the core-foundation contact, internal erosion of the embankment into or at a rock or soil foundation, and backward erosion in cohesionless soils in the foundations of dams. For these failure modes it is the likelihood of initiation of erosion for which length may be a factor. The length can be accounted for by considering it in determination of the probability: e.g., “what is the probability of a through going crack in the core due to desiccation in this 1000 feet length of embankment which so far as can be ascertained all has the same geometry, zoning and material properties?”

In statistical terms if all sections of the embankment are exactly the same, then they are perfectly correlated and the probability of at least one crack in the whole of the embankment is the same as for one section regardless of length. If each section is completely independent of the others (i.e., different construction materials, different specifications and construction methods, different cover (e.g., road pavement) over the core), then each section should be considered separately and the probabilities added using DeMorgan’s rule:

P = 1 – (1-P1) x (1-P2) x (1-P3)…etc.

The following tables describe whether length effects are applicable to each of the internal erosion failure paths/location, and if so, the method of accounting for length effects. The notes for all of the tables are located after Table 4.6.


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Table 4.3 – Length effects for internal erosion through the embankment due to concentrated leaks in transverse cracks

Initiating Mechanism Sketch of Failure Mode Effect of length on

failure probability Comments

IM1 – Transverse cracking due to cross valley differential settlement

Crack

Long Section

Crack

Long Section

No length effect but consider each abutment and add the calculated probabilities

In most cases one abutment or change in foundation profile will be much larger than the other, so it will be sufficient to calculate for this case only

IM2 – Transverse cracking due to differential settlement adjacent to a cliff at the top of the embankment

Crack/Gap

Long Section

Crack/Gap

Long Section

No length effect but consider each abutment and add the calculated probabilities

In most cases one abutment cliff will be much larger than the other, so it will be sufficient to calculate for this case only

IM3 – Transverse cracking due to cross section settlement due to poorly compacted shoulders

Long Section

Long Section (a)

(b)Long Section

Long Section (a)

(b)

No length effect for case (a)

No length effect for case (b) but each part contributes and add the calculated probabilities

In most cases one part of the embankment will be larger than the other, so it will be sufficient to calculate for this part only

IM4 – Transverse cracking due to differential settlement in the foundation soil beneath the core

Long Section

Compressible soil

Long Section

Long Section

(a)

(b)

(c)

Long Section

Compressible soil

Long Section

Compressible soil

Long Section

Long Section

(a)

(b)

(c)

No length effect for cases (a) and (b). No length effect for case (c) but each part contributes and add the calculated probabilities

IM5 – Transverse cracking due to differential settlement due to embankment staging

Crack

Stage 2

Long Section

Stage 1

Crack

Stage 2

Long Section

Stage 1

No length effect. If more than one staging surface add the probabilities


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Initiating Mechanism Sketch of Failure Mode Effect of length on

failure probability Comments

IM6 – Transverse cracking due to desiccation at the embankment crest

IM7 – Transverse cracking due to desiccation at seasonal shutdown layers during construction or staged construction surfaces

Long SectionLong Section

Length effects may apply. See Notes (1) and (2)

In many cases the nature of the embankment design and construction materials will be such that all sections are the same. Then the correlated condition exists, so length effects will be negligible.

IM 8 – Earthquake No length effect

Note: Refer to the end of Table 4.6 for notes.


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Table 4.4 – Length effects for internal erosion through the embankment due to concentrated leaks in hydraulic fractures

Initiating Mechanism Sketch of Failure Mode Effect of length

on failure probability

Comments

IM9 – Hydraulic fracturing due to cross valley arching Crack

Long Section

Crack

Long Section

No length effect

IM10 – Hydraulic fracturing due to differential settlement causing arching of the core onto the shoulders of the embankment

Long Section

Long Section (a)

(b)Long Section

Long Section (a)

(b)

No length effect for case (a)

No length effect for case (b) but each part contributes and add the calculated probabilities

In most cases one part of the embankment will be larger than the other, so it will be sufficient to calculate for this part only

IM11 – Hydraulic fracturing in the lower part of the embankment due to differential settlement in the foundation soil beneath the core

Long Section

Compressible soil

Long Section

Long Section

(a)

(b)

(c)

Long Section

Compressible soil

Long Section

Compressible soil

Long Section

Long Section

(a)

(b)

(c)

No length effect for cases (a) and (b).No length effect for case (c) but each part contributes and add the calculated probabilities

IM12 – Hydraulic fracturing due to small-scale irregularities in the foundation/ abutment profile beneath the core


No length effect, but allow for the number of irregularities and add the calculated probabilities.

See Note (3)

Note: Refer to the end of Table 4.6 for notes.


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Table 4.5 – Length effects for internal erosion through the embankment due to poorly compacted or high permeability zones

Initiating Mechanism Sketch of Failure Mode Effect of length on failure probability Comments

IM13 – Poorly compacted or high permeability zone within the embankment

Long SectionPoorly compacted layers

Long SectionPoorly compacted layers


In many cases the nature of the embankment design and construction materials will be such that all sections are the same. Then the correlated condition exists, so length effects will be negligible

IM14 – Poorly compacted or high permeability layer on the core-foundation/abutment contact

Long SectionPoorly compacted layer



IM15 – High permeability zone due to freezing at the embankment crest IM16 – High permeability zone due to freezing at seasonal shutdown layers during construction or staged construction surfaces



In many cases the nature of the embankment design and construction materials will be such that all sections are the same. Then the correlated condition exists, so length effects will be negligible

IM17 – Poorly compacted or high permeability zone adjacent to a conduit through the embankment

Long Section High Permeability Zone


No length effect. If there is more than one conduit treat each separately and add the probabilities

IM18 – Features allowing erosion into a conduit

Long Section Erosion into Conduit

Long Section Erosion into Conduit

No length effect. If there is more than one conduit treat each separately and add the probabilities


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IM19 – Poorly compacted or high permeability zone associated with a spillway or abutment wall IM20 – Crack or gap adjacent to a spillway or abutment wall IM21 – Transverse cracking due to differential settlement adjacent to a spillway or abutment wall

Crack/Gap

Long Section

Crack/Gap

Long Section

No length effect. If there is more than one wall treat each separately and add the probabilities

Notes. Refer to the end of Table 4.6 for notes.


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Table 4.6 – Length effects for internal erosion through the soil foundation and into or at the foundation


IM22 – Backward erosion in a cohesionless foundation soil IM23 – Suffusion in a cohesionless foundation soil


Length effects may apply. See Notes (1) and (7).

See Note 7

IM24 – Erosion in a crack in a cohesive foundation soil due to differential settlement or desiccation


Depends on the cause of the cracking. For desiccation induced cracking see IM6; for settlement induced cracking see IM9 or IM11

IM25 – Scour along defects in rock foundation < 25 mm IM26 – Erosion into defects in rock foundation > 25 mm



IM27 – Scour along contact with open-work granular foundation

IM28 – Erosion into open-work granular foundation



See Note 7

Notes for Table 4.3 to Table 4.6: (1) If all sections of the embankment are exactly the same, then they are perfectly correlated and the probability of cracking in the whole of the embankment is the same as for one section regardless of length. If each section is completely independent of the others, i.e., different construction materials, different specifications and construction methods, different cover (e.g., road pavement) over the core, each section should be considered separately and the probabilities added using DeMorgan’s rule. (2) The probabilities in Table 5.10 are determined by expert judgment and are for an embankment about 1600 feet (500 meters) long. The spacing of the cracks is likely to be about 5X crack depth, so there will be many cracks of maximum depth within the 500 meters. These probabilities will apply for embankments shorter than 1600 feet (500 meters) without adjustment for length. (3) The probabilities in Table 5.20 are anchored against historic data, for which there were between 2 and 5 small scale irregularities. Use these figures unless there are greatly more than 5 small scale irregularities. (4) The probabilities in Table 6.3 are anchored on historic data and are for an embankment about 1600 feet (500 meters) long. There are likely to be a number of sections within 500 meters which have the conditions


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potentially leading to a flaw. These probabilities will apply for embankments shorter than 1600 feet (500 meters) without adjustment for length. (5) The probabilities in Table 6.5 are anchored by relation to historic data and are for an embankment about 1600 feet (500 meters) long. There are likely to be a number of sections within 1600 feet (500 meters) which have the conditions potentially leading to a flaw. These probabilities will apply for embankments shorter than 1600 feet (500 meters) without adjustment for length. (6) The probabilities in Table 6.7 and Table 6.9 are determined by expert judgment and are for an embankment about 1600 feet (500 meters) long. There are likely to be a number of sections within 1600 feet (500 meters) which have the conditions potentially leading to a flaw. These probabilities will apply for embankments shorter than 1600 feet (500 meters) without adjustment for length. (7) The foundation should be partitioned so that geotechnical conditions are essentially the same within a section. Within a section the correlated condition exists, regardless of its length. Estimate the probability of backward erosion or suffusion for each section and add the probabilities using DeMorgan’s rule. Any section may have experience one or more sand boils. If these occurred at the same reservoir level for dams, the number of boils is not a factor in assessing the probability as one boil or many boils both mean initiation has occurred at that level. DeMorgan’s rule is P = 1 – (1-P1) x (1-P2) x (1-P3)…etc.


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4.6 Nature of the Estimates of Probabilities Given by the Toolbox

4.6.1 The toolbox gives “best estimate” probabilities

The methods in the toolbox provide “best estimates” of the conditional probabilities and hence “best estimate” probabilities of failure.

The estimates are determined by expert judgment based on analyses and laboratory tests modeling the physical processes. They are designed to avoid systematic bias towards conservative or non-conservative probabilities.

Probabilities for some of the most important initiating modes within the embankment are calibrated against historic performance of dams from a large database of around 10,000 dams in the ICOLD (1986) survey of failures and accidents. This is discussed in detail in Section 4.2. Where this has not been possible, expert judgment of the team developing the toolbox based on extensive experience in dams and risk assessment has been used, taking into account the feedback from trials and reviews of the toolbox by Reclamation and USACE.

The methods in the toolbox are likely to be more reliable in assessing relative probabilities between failure modes and between dams than assessing absolute values.

4.6.2 Adjusting the toolbox best estimates

Allowance for factors not included in the toolbox methods

It is recommended that the toolbox estimate be adopted except where there are factors not covered in the toolbox tables which the risk analysis team believe affect the estimate of the conditional probability for the node in question. These factors may include observations or monitoring data, or physical factors not allowed for in the toolbox. In these cases, the best estimate should be determined by adjusting the toolbox estimate to allow for the additional factors. It would not be expected that this would generally result in conditional probabilities greatly different to those estimated by the toolbox.

The additional factors should be described and the reasoning for the revised estimate provided in the risk analysis report.

What to do if the toolbox estimates seem incorrect

There may be cases where the toolbox estimates of failure probabilities are significantly different to what the risk analysis team would have expected. This may be due to 1) the logic (i.e., construction of the event tree)


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does not well match the perceived failure mode for the dam being analyzed, 2) the RF and LF factors do not well represent what the team originally thinks are the key factors or actual observances, or 3) the probability value suggested in the toolbox does not well represent what the risk assessor thinks is appropriate. The suggested steps to follow for each of these situations are:

a) If the issue appears to be in the logic, look carefully at the failure mode being modeled to identify where the perceived difference has occurred. Experience has shown that the logic presented in the toolbox has stood the test of time and is normally considered appropriate. Issues with the logic are typically due to a less-than-full understanding of what is already presented in the toolbox. If there is still perceived to be an error in the toolbox logic, check with USACE personnel familiar with the toolbox to ascertain that a problem still exists. If in the end there still is an issue, then the failure mode could be developed into its own event tree or adjustments made to the portion of the toolbox event tree in question followed by assigning probabilities using Expert Opinion Elicitation. In this case the issue should also be referred to one of the current toolbox developers for consideration in future updates.

b) If there seems to be an issue in the RF and/or LF factors, fully discuss the factors presented to ascertain that the proposed new factors are indeed more important. Be sure that the failure mode is well understood and that the risk assessor has a good understanding of the available case histories upon which the toolbox has been built around. If in the end, it appears that the factors should be adjusted or changed, make the changes/adjustments and document well what was done and why. The USACE person who manages the toolbox should oversee the corrections/adjustments.

c) If there seems to be an issue with the probabilities assigned, the risk assessor should be sure they are well aware of the database of historic precedent and experienced judgment that has been extensively used in the development of the method’s probabilities. Once the risk assessor is well-armed with this information, the risk assessor is then equipped to assess the appropriateness of the prescribed probabilities and attempt an adjustment. The adjustment should be made, using Expert Opinion Elicitation, and then fully documented. In this case the issue should also be referred to one of the current toolbox developers for consideration in future updates.

4.6.3 Limitations of the methods used in the toolbox

The toolbox is based on the (2007) state of the art on modeling the mechanics of initiation of internal erosion in cracks and other flaws, by backward erosion and suffusion. The methods available are sufficient to form the basis of the toolbox, and are to be preferred to methods based only on historic data, or expert judgment anchored on historic data such as those detailed in Fell et al (2003, 2004).

The mechanics of continuation (filter action) are fundamentally simpler, more extensively researched and the methods are less subjective than for initiation, provided the data to do the analyses is available.


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The modeling of progression, detection and intervention, and breach are more subjective and largely based on case studies and expert judgment.

The methods used here are a significant improvement on the methods described in Fell et al (2003, 2004) which have been used in Australia and as input to the Reclamation methods.

It is recommended that those using Fell et al (2003, 2004) now use the methods described in this Guidance Document.

Most of the logic, modeling, analysis, laboratory testing, expert elicitation techniques used in this document continues to be actively researched and/or studied. Case histories continue to occur that give more insight to the process involved. It is likely that these developments in understanding will result in improved methods for assessing probabilities of initiation, continuation, and progression of internal erosion, and breach mechanics. When this occurs, it will be necessary to revise the toolbox.

4.6.4 Assessment of probabilities of failure for failure modes which are not covered by the toolbox

In some dams, there may be failure modes which are not well modeled by the toolbox. For these failure modes the risk analysis team should develop an event tree to model the failure mode. Conditional probabilities within the event tree should be estimated using the toolbox where the nodes are common to the toolbox event tree, and by expert judgment for the other nodes. When expert judgment is required, use the current version of the Dam Safety Risk Management Center Training Document: “Technical Guide for the Use of Expert Opinion Elicitation for U.S. Army Corps of Engineers Risk Assessments.”

4.7 Modeling Uncertainty in the Estimates of Conditional Probabilities

4.7.1 Purpose of this section

The toolbox has been developed to provide “best estimate” values of conditional probabilities for the nodes in the event trees for all failure modes. Sometimes where there is considerable uncertainty or contradictory information in the data being used for the risk analysis a sensitivity analysis to gauge the effect of the likely range of estimates of conditional probability on one or two of the most critical nodes on the event tree may be modeled.

In some more detailed risk analyses, it may be required that the uncertainty which is inherent in such estimates is modeled. This uncertainty may arise from limitations in the toolbox methods used to estimate probabilities (a type of model uncertainty), the data available for the dam being analyzed (epistemic uncertainty) and uncertainty associated with unpredictable variations of a random nature in data relied on for the risk analysis (aleatory uncertainty), uncertainty about the true accuracy and/or applicability of an


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analytical model used to assess the data, and measurement and parameter uncertainty of properties of materials in the dam and its foundation.

The effects of uncertainty in the estimates of conditional probability can be examined either with sensitivity analysis or modeling uncertainty in the event tree. Both approaches are described in this section. Reference should be made to Reclamation (2001b), Dam Safety Risk Analysis Methodology, Appendix T, Handling Uncertainty.

4.7.2 Sensitivity analysis

There will be some cases where the quality and quantity of data available to do the risk analysis is limited, and/or is somewhat contradictory. For example, data on filters or transition zones may be limited. In these cases, it is recommended that the best estimate and the range of the best estimate for the node probability is calculated from this data and carried forward in the risk analysis as a sensitivity analysis. This means that there will be a best estimate and two other estimates representing the range of estimates of the frequency of failure to be reported for this failure mode. Alternatively, only the upper and lower estimates are carried through so decision makers can gauge the importance of this data on the risk analysis.

This approach should be adopted when uncertainty is not being modeled as detailed in Section 4.7.3.

4.7.3 Uncertainty analysis

In some situations, uncertainty of the estimate of conditional probability in each node of the event tree may need to be modeled. This uncertainty would then be used in Monte Carlo analyses to determine the distribution of estimates of the probability of failure.

The following sections provide some information on how uncertainty may be modeled.

Modeling uncertainty for event tree nodes where relative importance factors and likelihood factors tables are used to estimate conditional probabilities.

This covers the probability versus ∑(RFxLF) tables. In these tables there is:

i) Uncertainty in the historic data “anchor” probabilities, and in the minimum and maximum probabilities (e.g., negligible, [0.005], and 0.2 in Table 5.4). These in turn affect the values in the tables in between. Where there are no historic data to “anchor” the probabilities there is uncertainty in the estimates based on the expert judgment of the toolbox development team.

ii) Uncertainty in the ability of these tables and the factors they are based on to model the relative probabilities.


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iii) Uncertainty in the analysis and laboratory testing data upon which the methods may be based. An example would be the numerical analysis upon which Table 5.3 is largely based.

iv) Uncertainty resulting from limitations of the available investigations, design, construction and monitoring data relating to the probability being assessed. An example would be limitations of knowledge of the degree of compaction and borrow area variability in Table 6.1 and Table 6.2.

(a) Model uncertainty Uncertainties (i) (ii) and (iii) are model uncertainties.

Table 4.7 shows best estimate and equivalent likely low and likely high probabilities. This can be used to develop likely minimum and likely maximum probability versus ∑(RFxLF) tables. Table 4.7 is based on a dissection of the basis upon which the historic probabilities anchor points and the minimum and maximum values were determined. Details of how this was done are given in Section S4.7 of the Supporting Document. If the probability for ∑(RFxLF) = 6 is less than or equal to 0.0001, then the likely low probability should equal the best estimate.

Table 4.7 allows definition of the anchor point, minimum and maximum probability values. The risk assessor should then interpolate to determine the intermediate values on the ∑(RFxLF) table. An example is given in the Section S4.6 of the Supporting Document.

Reclamation Risk Analysis Methodology –Appendix T, Handling Uncertainty, uses the terms “reasonable low” to represent the 10th percentile bound, and “reasonable high” to represent the 90th percentile bound. The range of 0.2x (likely low) to 5x (likely high) represents more stringent percentiles, possibly < 1% to >99%. It is for the agency doing the uncertainty analysis to judge what range the model uncertainty represents and to decide what range to adopt.


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Table 4.7 – Best estimate, likely high, and likely low equivalence table

Best Estimate Probability Likely High Probability Likely Low Probability

0.0001 0.0005 0.0001

0.001 0.005 0.0002

0.01 0.05 0.002

0.02 0.1 0.004

0.05 0.2 0.01

0.1 0.4 0.02

0.2 0.6 0.04

0.3 0.8 0.07

0.5 0.95 0.15

0.9 0.999 0.4

Note. Likely high probabilities are assumed to be 5 times best estimate, and likely low probabilities 0.2 times best estimate. See Section S4.7 of the Supporting Document for details of the calculations to develop the values in the table.

(b) Data uncertainty The uncertainty in the probability estimate resulting from limitations in the data (factor (iv) above) should be assessed by assessing the likely low and likely high ∑(RFxLF) values from the table, and using these in the Probability versus ∑(RFxLF) tables to estimate the range of probabilities resulting from data uncertainty.

(c) Combining the model and data uncertainty. To combine the model and data uncertainty, use the likely low, best estimate and likely high probability from the relevant probability versus ∑(RFxLF) table. An example is given in Section S4.6 of the Supporting Document.

This is a severe test of overall uncertainty and Agencies will need to develop their policy on how to combine these components of uncertainty.

Modeling uncertainty for event tree nodes where scenarios and examples are described, and a range of probabilities provided

This covers the tables where scenarios are described, examples are given, and a range of probabilities provided from which the risk assessor makes a selection based on the available information, and the risk assessor’s degree of belief.

Examples are Table 11.1, Table 11.2, Table 11.3, Table 12.8, and Table 13.6.


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For these cases it is recommended that:

• The risk analysis team estimate is taken as the best estimate.

• The likely low and likely high probability is estimated by the analysis team, within the range shown in the table.

Where the toolbox table indicates a probability of 1.0, this should generally be adopted for best estimate and likely low and likely high estimates. These are only used in the toolbox where there is very high degree of confidence based on physical factors that a probability of 1.0 is applicable.

In cases where the information available to the risk analysis team strongly supports adopting best estimate and/or likely low or likely high probabilities outside the range in the tables, the risk analysis team may adopt this value, but it would not be expected that this would result in probabilities greatly different to those estimated by the toolbox.

The factors leading to this probability estimate should be described and the reasoning for the revised estimate provided in the risk analysis report.

Modeling uncertainty for event tree nodes where single value estimates of probability are provided

This covers tables where analysis has been carried out to combine a number of input variables, and the toolbox development team have allowed for uncertainty in the input variables to allow for uncertainty. This includes Table 5.30 to Table 5.36, Table 6.23 to Table 6.25, and Table 7.4.

i) Probability of initiation of erosion in concentrated leaks, Table 5.30 to Table 5.36

As described in Section S5.4.2.4 of the Supporting Document, these tables have been developed allowing for:

• Probability distributions in the maximum crack width and crack width at depth versus crack width at the surface.

• The initial shear stress of the soil.

• Using these to run Monte Carlo analyses.

The values in Table 5.30 through Table 5.36 are median values. Tables in S5.4.2.4 of the Supporting Document have the equivalent tables for the 10% and 90% values, representing the likely minimum and likely maximum probabilities.


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ii) Probability of initiation of erosion in cohesionless soils, Table 6.23 to Table 6.25 and Table 7.4

As described in Section S6.6.2.7 of the Supporting Document, these probabilities are obtained by comparing the actual average seepage gradient to that required to initiate and progress backward erosion. The probabilities were assessed by expert judgment allowing for the uncertainty in the method used to assess whether backward erosion would initiate and progress.

Table 6.23, Table 6.24, Table 6.25, and Table 7.4 are best estimate values. Tables in Section S6.6.2.7, S7.3.2 and S7.3.3 of the Supporting Document have the equivalent tables for the likely minimum and likely maximum probabilities. These have been developed by expert judgment.

Selection of the Probability Distribution

The risk analysis team should select the probability distribution they believe best fits their best estimate, likely low and likely high probability estimates. The alternatives which may be considered are explained in Reclamation (2001b). For many cases, a triangular distribution is likely to be suitable.

4.8 Summarizing (Making the Case)

Once a risk estimate is prepared with the use of this toolbox, the risk assessor needs to make summary of the key factors that generated the estimates of probability of failure. An exercise of “making the case” is important so that reviewers and decision makers can quickly focus on the story being told. This can be done relatively easily by reviewing each of the components of the estimate and select those that drive most of the final estimate. Once these are determined, they should be reviewed and the main factors that contribute most to the actual estimate of this component should be brought forward into an engineering summary of the failure mode. This engineering summary should normally only focus on those factors key to the overall estimate.

By doing this the redundancy, or lack thereof, in the design can be demonstrated. In the case with much redundancy (i.e., dams with many components that contribute to the overall risk being low), it is important to highlight this. For example, dams with a low chance for concentrated leakage; a non-erodible core; some filtering components should be viewed as an overall robust situation with reasonable redundancy. In contrast, a homogenous dam with an erodible core where the risk is low due almost solely to a low probability of a concentrated leak is a case with little redundancy. It is important to summarize this situation for reviewers and decision makers.

4.9 Development of System Response Curves

The following guidelines have been developed for users who intend to use system response curves to quantify the risk. The probabilities of failure estimated for each of the reservoir level and earthquake can be used as


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point estimates for developing system response curves. Separate system response curves should be developed for each of the potential failure modes identified in the screening process.

The process to develop system response curves for reservoir level loading is summarized as follows:

• Select the reservoir level partition points as described in Section 3.5.

• Estimate the conditional probabilities of failure for each step of the event tree developed for each failure path at each reservoir level of interest.

• Plot the conditional probabilities versus reservoir level on a semi-logarithmic scale. Join the individual point estimates using straight lines. An example is shown in Figure 4.1.

90

110

130

150

170

190

210

230

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

Conditional Probabilty of Failure

Res

ervo

ir Le

vel (

ft)

Annual Pool

Abutment Defect

Pool of Record Embankment Crest

Figure 4.1 – Example system response curve

• For a given initiating mechanism, if the dam profile is divided into segments or different cross-sections are evaluated (e.g., due to physical differences in geology, geometry, treatment, etc.), the individual system response curves should be combined into a single system response curve by selecting the maximum probability of failure at each reservoir level.

• For a given initiating mechanism (e.g. transverse cracking through the embankment), develop system response curves for each failure path (e.g. above and below a filter, above and below the top of a berm, etc.). The individual system response curves should be combined into a single system response curve by


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selecting the maximum probability of failure at each reservoir level. Examples of multiple flow paths are shown in Figure 3.2, Figure 3.3, and Figure 4.2.

Partial Core Partial Filter

Partial Filter Stability Berm

Flow Path A

Flow Path B

Flow Path A

Flow Path B

Flow Path A

Flow Path B

Flow Path A

Flow Path C

Flow Path B

Partial Core Partial Filter

Partial Filter Stability Berm

Flow Path A

Flow Path B

Flow Path A

Flow Path B

Flow Path A

Flow Path B

Flow Path A

Flow Path C

Flow Path B

Figure 4.2 – Examples of multiple flow paths

4.10 Combining Probabilities

Risk is computed by finding the product of probabilities and consequences for each path of the event tree.

The principles for combining the probabilities on the event trees and for the different failure paths are as follows:

• For mutually exclusive failure paths, as occurs on a specific event tree, the conditional probabilities of failure should be added.

• For failure paths that are not mutually exclusive, the total probabilities of failure from the event trees should be calculated using DeMorgan’s rule:

P = 1 – (1-PIM1) x (1-PIM2) x (1-PIM3)…etc.

Failure path probabilities should only be combined in cases where the mechanisms are very similar and all possible risk reduction remedial measures will have the same influence on the failure paths that were combined.

Probability of Initiation of Erosion in Transverse Cracks in the Embankment

Section 5

5-1

5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment

5.1 Overall Approach

a) Estimate the probability of a crack (PC.xx) for each of the initiating mechanisms that can lead to transverse cracking and low stress zones in which hydraulic fracture can occur. These are:

Transverse cracking of the embankment (Section 5.2)

• Cross valley differential settlement (IM1)

• Differential settlement adjacent to a cliff (IM2)

• Cross section settlement due to poorly compacted shoulders (IM3)


• Differential settlement due to embankment staging (IM5)

• Desiccation (IM6 and IM7)

• Earthquake (IM8)

Hydraulic fracturing of the embankment (Section 5.3)

• Differential settlement causing cross valley arching (IM9)

• Differential settlement causing arching of the core onto the shoulders (IM10)


• Differential settlement due to small scale irregularities in the foundation profile (IM12)

This is done using Table 5.1 to Table 5.14 in Section 5.2 for cracking and Table 5.15 to Table 5.20 in Section 5.3 for hydraulic fracturing. The probabilities obtained from these tables are modified for observed settlement and cracking using Table 5.21 and Table 5.22 in Section 5.4 to obtain Pflaw. Modifications are not applicable to all mechanisms.

For most dams not all mechanisms will be present, and those mechanisms are assigned a probability of zero. The details for screening the mechanisms are described in Section 3.4.

b) If grouting was performed within the maximum depth of likely cracking in the embankment, evaluate the likelihood of the grouting being ineffective at cutting off the cracking using Table 8.19 and Table 8.20 in Section 8.7. If a cut-off wall was installed through the maximum depth of likely cracking in the embankment, evaluate the likelihood of grouting being ineffective at cutting off the cracking using Table Table 8.21 and Table 8.22 in Section 8.8.

c) Estimate the maximum likely crack width at the surface of the core for each of the initiating mechanisms which apply as described in Section 5.5.


Section 5

5-2

d) Estimate the maximum likely crack depth as described in Section 5.5.

e) Estimate the likely crack width at the reservoir level under consideration assuming a uniformly tapered crack.

f) Estimate the probability of initiation of erosion for this mechanism given this estimated crack width, seepage gradient across the core, and the properties of the soil in the core (PI) using Section 5.5.

g) The estimated probabilities of a flaw and initiation of erosion for each initiating mechanism are not added together, but are carried through the event trees for each failure path. For many dams, one or more of the mechanisms will not be present.


Section 5

5-3

5.2 Probability of Transverse Cracking in the Embankment

5.2.1 Transverse cracking due to cross valley differential settlement (IM1)

Table 5.1 – Factors influencing the likelihood of transverse cracking in the embankment due to cross valley differential settlement (IM1)

Likelihood Factor (LF)

Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Cross valley profile under embankment core (a)

(3) Uniform abutment profile without benches

Note: Probability is zero if this condition is present. Narrow bench very low in the abutment b/h2 <0.5 h2/h1 >1.5

Wide bench low in the abutment b/h2 > 1

h2/h1 > 1

Wide bench in upper half to one-third of the abutment b/h2 > 1 0.5 < h2/h1 < 1 or narrow bench in upper half to one-third of the abutment b/h2 > 0.5 h2/h1 < 0.25

Wide bench near the crest in the abutment b/h2 > 1 0 < h2/h1 < 0.5

Slope of abutments under embankment core (a)

(2)

Gentle abutment slopes

β2 < 25°

Note: Probability is zero if this condition is present.

Moderate abutment slopes

25° < β2 < 45°

Steep abutment slopes

45° < β2 < 60°

Very steep abutment slopes

β2 > 60°

Height of embankment

(1) Dams less than 50 ft (15 m) high

Dams 50 to 100 ft (15 to 30 m) high


Very high dams > 200 ft (60 m)

Note: Select LF=5 for dams higher than 400 ft (120 m).

Notes: (a) See Figure 5.1 for definitions of b, h1, h2, and β2.


Section 5

5-4

Table 5.2 – Probability of transverse cracking in the embankment dams due to cross valley differential settlement (IM1) versus ∑(RFxLF)

negligible negligible 0.00005 0.00015 [0.0005] 0.005 0.02 Below POR

negligible negligible 0.0005 0.002 [0.007] 0.05 0.2 Above POR

6 7 8 11 13 18 24 RFxLF

Figure 5.1 – Definition of terms used to describe cross valley geometry

bH

h2

h1

β1

β2

Valley Centerline

Dam crest

Abutment


Section 5

5-5

5.2.2 Transverse cracking due to differential settlement adjacent to a cliff at the top of the embankment (IM2)

Table 5.3 – Factors influencing the likelihood of transverse cracking in the embankment due to differential settlement adjacent a cliff at the top of the embankment (IM2)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)


(3) Wide bench

Wb/Hw > 2.5


Bench adjacent to cliff 1.0 < Wb/Hw <2.5

Narrow bench adjacent to cliff 0.25 < Wb/Hw < 1.0

No or very narrow bench adjacent to cliff Wb/Hw < 0.25


(2) Gentle abutment slopes

β 1 < 25°



25° < β 1 < 45°


45° < β 1 < 60°

Very steep abutment slope

β 1 > 60°






Note: (a) See Figure 5.2 for definitions of Wb, Hw, β1.


Section 5

5-6

Table 5.4 – Probability of transverse cracking in the embankment due to differential settlement adjacent to a cliff at the top of the embankment (IM2) versus ∑(RFxLF)

negligible negligible negligible negligible [0.0005] 0.002 0.02 Below POR

negligible negligible negligible negligible [0.005] 0.02 0.2 Above POR

6 9 11 13 14 19 24 RFxLF

Figure 5.2 – Cracking adjacent to cliffs due to differential settlement of the embankment

β1


Section 5

5-7

5.2.3 Transverse cracking due to cross section settlement due to poorly compacted shoulders (IM3)

Table 5.5 – Factors influencing the likelihood of transverse cracking in the embankment due to cross section settlement due to poorly compacted shoulders (IM3)


Factor Relative

Importance Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

EITHER Embankment zoning and Compaction of outer zone Excluding sloping core earth and rockfill dams

(3) Zoned earthfill, earthfill with filter drains, or homogeneous (all materials have a similar modulus)

Note: Probability is zero if there is evidence that the materials have a similar modulus.

Zoned earthfill, earthfill with filter drains, modulus of outer zones lower than core

Central core earth and rockfill (or “gravel fill”), with well compacted shoulders and core

Central core earth and rockfill (or “gravel fill”), rockfill or “gravel fill” compacted by dozer tracking or by small rollers in thick layers

Central core earth and rockfill, uncompacted (dumped)

Rockfill

OR Embankment zoning and Compaction of outer zone Sloping core earth and rockfill dams (b)

(3) Core sloped steeper than 45° but within limits of sloping core embankment

Rockfill (or ”gravel fill”), and core well compacted, and with similar moduli

Core sloped flatter than 45°

Rockfill (or “gravel fill”), and core well compacted


Rockfill (or “gravel fill”), rockfill or “gravel fill” compacted by dozer tracking or by small rollers in thick layers


Construction staged with rockfill in the lower part of the dam compacted to a higher modulus than the upper part

OR

Uncompacted (dumped) rockfill

Core geometry (b)

(2) W/H > 3 1.5 < W/H < 3 0.5 < W/H < 1.5 W/H < 0.5






Note: (a) See Figure 5.3 for definition of core slope. (b) Average width (W) of core within the zone of cracking and height (H) of the embankment.


Section 5

5-8

Table 5.6 – Probability of transverse cracking in the embankment due to cross section settlement due to poorly compacted shoulders (IM3) versus ∑(RFxLF)

0.00001 0.00002 0.00005 0.0002 [0.0005] 0.002 Below POR

0.0001 0.0002 0.0005 0.002 [0.007] 0.02(a) Above POR

6 9 11 13 18 24 RFxLF

Note: (a) If there is a large difference in modulus between the core and shoulders, a probability of cracking between 0.02 and 0.2 may be applied.

Figure 5.3 – Sloping core dam (a) Definitions of terms

(b) Limit of what constitutes a sloping core dam

core slope β1


Section 5

5-9

5.2.4 Transverse cracking due to differential settlement in the foundation soil beneath the core (IM4)

Table 5.7 – Factors influencing the likelihood of transverse cracking in the embankment due to differential settlement in the foundation soil beneath the core (IM4)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Foundation geology and geometry (a)

(3) Rock foundations or uniform soil foundations

Note: Probability is zero if there is no compressible soil in the foundation.

Shallow soils or soils with gradual variation in depth and compressibility sufficient to cause differential settlement of less than 0.2% of the embankment height

Moderate depth of compressible soil in the foundation sufficient to cause differential settlement of 0.2% to 0.5% of the embankment height

Deep compressible soil in the foundation, including soils which collapse on saturation and which have not been treated or removed during construction, sufficient to cause differential settlement of >0.5% of embankment height

Slope of the sides of the compressible zones (b)

(2) Gentle

α < 30°

Moderate

30° < α < 45°

Steep

45° < α < 60°

Very steep

α > 60°






Notes: (a) See Figure 5.4 for typical scenarios which may lead to differential settlement. (b) See Figure 5.4 for definition of slope α.


Section 5

5-10

Table 5.8 – Probability of transverse cracking due to differential settlement in the foundation soil beneath the core (IM4) versus ∑(RFxLF)



6 8 9 11 13 18 24 RFxLF

Figure 5.4 – Typical scenarios which may lead to differential settlement in the foundation

α

α

α


Section 5

5-11

5.2.5 Transverse cracking due to differential settlement due to embankment staging (IM5)

This mode does not apply if the embankment construction was not staged. If the embankment was staged during construction, there is a potential for differential settlement to occur if the “existing” (first stage) embankment is a significantly higher modulus than the remainder of the embankment. If this is the situation, use the method described in Section 5.2.1 for IM1 to assess the likelihood of cracking. If there is no or little difference in the modulus, this mode may be ignored. In most cases, the latter will apply.

Figure 5.5 – Longitudinal section through staged embankment

5.2.6 Transverse cracking due to desiccation (IM6 and IM7)

At the embankment crest (IM6)

This mechanism only applies if the crest is not paved with concrete, asphalt or bitumen seal. If the crest is paved with concrete, asphalt or bitumen seal, the probability of cracking due to desiccation can be assumed to be zero. Where the mechanism applies, estimate the probability of desiccation cracking using Table 5.9 and Table 5.10.

Final embankment crest level

b

h1

h2

Existing Embankment β2


Section 5

5-12

Table 5.9 – Factors influencing the likelihood of transverse cracking due to desiccation at the embankment crest (IM6)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Crest zoning and surface layer over core

(3) Road pavement cover(a) with base layer at least 12 in (300 mm) thick

and/or Rockfill or non-plastic granular layer at least 3 ft (1 m) thick


No road pavement cover(a) with non-plastic granular layer 6 to 12 in (150 to 300 mm) thick

No pavement cover(a) with non-plastic granular layer less than 3 in (75 mm) thick or

Low plasticity granular transition layer over core

No surface layer; dam core extends to crest level

Climate (2) Temperate climate with uniform rainfall throughout the year

Seasonal climate with annual rainfall greater than 20 in (500 mm) and no prolonged hot dry periods

Monsoonal or other distinct wet and dry periods in the year with summer maximum temperatures >85°F (>30°C)

Arid climate with less than 10 in (250 mm) rainfall and high summer temperatures

Plasticity of core material

(1) Low plasticity to non-plastic (LL < 20)

Medium to low plasticity (20 < LL < 40)

Medium to high plasticity (40 < LL < 50)

High plasticity

(LL > 50)

Note: (a) Road pavement cover may comprise concrete, asphalt or bitumen seal.


Section 5

5-13

Table 5.10 – Probability of transverse cracking due to desiccation at the embankment crest (IM6) versus ∑(RFxLF)

0.0001 0.001 0.01 0.1 0.5 0.9

6 9 11 16 20 24 RFxLF

On seasonal shutdown layers or on the surface of staged embankments (IM7)

This mechanism only applies where there has been a seasonal shutdown during construction or the embankment construction was staged. If there was no seasonal shutdown layer during construction or the embankment construction was not staged, this mode can be ignored.

This mechanism only applies above the level of saturation of the core. Below that any desiccation cracks should have swelled and closed. If the seasonal shutdown layer is below the Pool of Record, use the “Below POR” probabilities in Table 5.15.

Where the mechanism applies, estimate the probability of desiccation cracking using Table 5.11 and Table 5.12. The descriptions in Table 5.11 are to be assessed according to the conditions across the width of the core.


Section 5

5-14

Table 5.11 – Factors influencing the likelihood of transverse cracking due to desiccation at seasonal shutdown layers during construction or staged construction surfaces (IM7)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Construction practices regarding clean-up of desiccated layers after construction shutdowns or the surface of the earlier stage of the dam

(4)

Very good control and clean-up practices.

Desiccated layers removed from embankment and replaced with new soil or adequately reworked to specified moisture content.


Good control and practices.

Surfaces scarified; moisture adjusted to specified range; and surface re-compacted.

Moderate control.

Attempts to scarify desiccated layers, but depth of scarifying insufficient or difficulties with moisture control

Poor control.

No attempt to scarify or remove desiccated layers, poor moisture control practices

Climate (2) Temperate climate with uniform rainfall throughout the year




Plasticity of core material

(1) Low plasticity to non-plastic (LL < 20)

Medium to low plasticity (20 < LL < 40)

Medium to high plasticity (40 < LL < 50)

High plasticity

(LL > 50)

Table 5.12 – Probability of transverse cracking due to desiccation versus at seasonal shutdown layers during construction or staged construction surfaces (IM7) versus ∑(RFxLF)

negligible negligible negligible 0.0001 0.001 0.01 0.1 Below POR

negligible negligible negligible 0.001 0.01 0.1 0.9 Above POR

7 10 12 13 18 22 28 RFxLF


Section 5

5-15

5.2.7 Transverse cracking due to an earthquake (IM8)

FIRST Determine the earthquake hazard for the site (refer to Section 3.6 for details).

SECOND Estimate the likely damage class which the embankment may experience as a result of the earthquake based on the peak ground acceleration (PGA) on bedrock at the dam site and the moment magnitude (Mw) using Figure 5.6 for earthfill dams or Figure 5.7 for earth and rockfill dams. Do this for each earthquake load partition.

THIRD Estimate the probability of transverse cracking from the damage class and Table 5.14.

This procedure applies to situations where liquefaction does not occur in the dam or its foundations. If flow liquefaction occurs assume the damage is class 4. For cases where liquefaction occurs but it is not flow liquefaction, assume damage class 3.

Table 5.13 – Damage classification system (Pells and Fell, 2002, 2003)

Damage Class

Number Description

Maximum Longitudinal Crack Width (a)

(mm)

Maximum Relative Crest Settlement (b)

(%)

0 No or Slight < 10 < 0.03

1 Minor 10 - 30 0.03 - 0.2

2 Moderate 30 - 80 0.2 - 0.5

3 Major 80 - 150 0.5 - 1.5

4 Severe 150 - 500 1.5 - 5

5 Collapse > 500 > 5

Notes: (a) Maximum crack width is taken as the maximum width of any longitudinal cracking that occurs. (b) Maximum relative crest settlement is expressed as a percentage of the structural dam height.


Section 5

5-16

Figure 5.6 – Incidence of transverse cracking versus seismic intensity and damage class contours for earthfill dams (Pells and Fell 2002, 2003)

Figure 5.7 – Incidence of transverse cracking versus seismic intensity and damage class contours for earthfill and rockfill dams (Pells and Fell 2002, 2003)


Section 5

5-17

Table 5.14 – Probability of transverse cracking and maximum likely crack width at the top of

the core due to an earthquake (IM8)

For cases where cracking assessment from Table 5.1, Table 5.3 or Table 5.7

results in ∑(RFxLF) ≤ 13

For cases where cracking assessment from Table 5.1, Table 5.3 or Table 5.7

results in ∑(RFxLF) > 13 Damage class Probability of

transverse cracking

Maximum likely crack width

mm (in)

Probability of transverse cracking

Maximum likely crack width

mm (in)

0 0.001 5 0.01 20

1 0.01 20 0.05 50 (2)

2 0.05 50 (2) 0.10 75 (3)

3 0.2 100 (4) 0.25 125 (5)

4 0.5 150 (6) 0.6 175 (7)


Section 5

5-18

5.3 Probability of Hydraulic Fracturing in the Embankment

5.3.1 Hydraulic fracturing due to differential settlement causing cross valley arching (IM9)

Table 5.15 – Factors influencing the likelihood of hydraulic fracturing in the embankment due to differential settlement causing cross valley arching (IM9)


Factor Relative


Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)


(3) Moderate abutment slope

β 1 ,β 2 < 45°

Moderate steep abutment slopes

45° < β1, β2 < 60°

Steep abutments

60° < β 1 ,β 2 < 75°

Very steep abutments,

β 1 ,β 2 > 75°

β 1 near vertical,

β 2 > 60°

Cross valley geometry under embankment core (a)

(2) Wv/H > 0.75

Note: Probability is zero if Wv/H > 2.

0.4< Wv/H <0.75

Narrow deep valley 0.25< Wv/H <0.4

Very narrow deep valley Wv/H < 0.25






Note: (a) See Figure 5.8 or definitions of Wv, H, β 1 and β 2

(b) If the soil in the lower part of the core is poorly compacted or subject to collapse compression on saturation, and the upper part is not, increase weighted factor ∑(RFxLF) by 1 or 2.


Section 5

5-19

Table 5.16 – Probability of hydraulic fracturing in the embankment due to differential settlement causing cross valley arching (IM9) versus ∑(RFxLF)

negligible negligible 0.00005 0.0001 0.0005 0.004 0.02 Below POR

negligible negligible 0.0005 0.001 0.007 0.05 0.2 Above POR

6 9 10 13 17 21 24 RFxLF

Figure 5.8 – Longitudinal profiles of the dam showing the definition of terms for cross valley arching

β1

β1 β1

β1

β2 β2

β2 β2


Section 5

5-20

5.3.2 Hydraulic fracturing due to differential settlement causing arching of the core onto the embankment shoulders (IM10)

This mode is applicable to central core earth and rockfill (or gravel shells) dams and puddle core earthfill dams. It is not applicable to all other the following dam types (including dams with a sloping core). The most likely location for arching to occur is in the upper to middle part of the dam. The mechanism is considered to be significant only for reservoir levels above the pool of record. Finite element analyses which properly model the history of the dam, and its properties including collapse on saturation may be used to assess the likelihood of hydraulic fracture.

Table 5.17 – Factors influencing the likelihood of hydraulic fracturing in the embankment due to differential settlement causing arching of the core onto the embankment shoulders

(IM10)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Core geometry (a)

(3) W/H > 1.0


0.5 < W/H < 1.0 Narrow core

0.25 < W/H < 0.5

Very narrow core

W/H < 0.25

Relative stiffness of core and shells

(2) Core has higher modulus than shells

Shoulders poorly compacted or dumped

Core compacted >98% SMDD

Note: Probability is zero if these conditions are present.

Modulus of core same or marginally lower than shoulders

Shoulders well compacted and high modulus

Core compacted to >98% SMDD at a moisture content between -2% and +1% of standard OWC

Core lower modulus than outer stiffness


Either core compacted 0% to 2% wet of OWC and between 95% and 98% SMDD or 2% to 3% dry of OWC and <95% SMDD (b)

Core much lower modulus than outer shoulders or subject to collapse compression


Either core compacted >2% wet of OWC, or more than 3% dry of OWC and <95% SMDD (b)






Notes: (a) Width (W) of the core at the phreatic line and height (H) of the embankment. (b) In core materials compacted dry of optimum moisture and to a density ratio less than about 95%, collapse

compression of the core may occur. This may lead to arching and low stresses. It may also lead to softened zones and even a crack in the vicinity of the contact between the saturated and unsaturated parts of the core (i.e., at the phreatic surface).


Section 5

5-21

.

Table 5.18 – Probability of hydraulic fracturing in the embankment due to differential settlement causing arching of the core onto the embankment shoulders (IM10) versus

∑(RFxLF)


6 9 11 12 13 18 24 RFxLF

Notes: The probability for this initiating mechanism is assumed to be negligible for the Below POR cases.

5.3.3 Hydraulic fracturing due to differential settlement in the soil foundation beneath the core (IM11)

Hydraulic fractures may occur in low stress or tension zones at the base of the embankment due to differential settlement in the soil foundation as shown in Figure 5.4b. Refer to the likelihood factors in Table 5.7 in Section 5.2.4 which covers this mode as well as cracking in the embankment.

5.3.4 Hydraulic fracturing due to differential settlement over small-scale irregularities in the foundation profile beneath the core (IM12)

Small-scale irregularities in the foundation profile under the core may comprise steps, benches or depressions in the foundation rock. Small scale irregularities include those features which have heights less than 10% of the embankment height. Larger irregularities are covered in Section 5.3.2.


Section 5

5-22

Table 5.19 – Factors influencing the likelihood of hydraulic fracturing in the embankment due to differential settlement over small-scale irregularities in the foundation profile beneath

the core (IM12)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Persistence of the irregularity across the core

(3) Persistent across less than 50% of the width of the core


Persistent 50% to 75% across the width of the core



Small-scale irregularities in abutment profile (a)

(2) Uniform abutment profile or irregularities treated by slope modification

Steps, benches, or depressions in rock foundations less than 3% of the embankment height

Steps, benches, or depressions in rock foundations 3% to 5% of the embankment height

Steps, benches, or depressions in rock foundation 5% to 10% of the embankment height (a)

Core geometry (b)

(1) Wide core W/H > 1.5

0.5 < W/H < 1.5

Narrow core 0.25 < W/H < 0.5

Very narrow core W/H < 0.25

Notes: (a) Larger irregularities are covered in Section 5.3.2. (b) Width (W) of the core at the base of the embankment and height (H) of the embankment.

Table 5.20 – Probability of hydraulic fracturing in the embankment due to differential settlement over small-scale irregularities in the foundation profile beneath the core (IM12)

versus ∑(RF x LF)

negligible negligible negligible 0.0002 [0.0007] 0.002 0.01 Below POR

negligible negligible negligible 0.002 [0.005] 0.02 0.1 Above POR

6 9 11 12 13 18 24 RFxLF


Section 5

5-23

5.4 Factors to Account for Observations and Measured Settlements

Settlement Observations

Where there are settlement observations for the dam, these can be used to modify the results of Sections 5.2 and 5.3. The probability from the relevant table is multiplied by the factor from Table 5.21. For dams which have experienced settlements larger than the average population of that class of dam, the probabilities of cracking or hydraulic fracturing will be increased, and for those which have experienced settlements smaller than the average population of that class of dams, the probability of cracking or hydraulic fracturing will be reduced. The multiplication factor should be selected taking account of what data is available, allowing for the quantity and quality of the data, and the relative importance of the observations. Table 5.21 applies to the assessment of transverse cracking in the upper part of the embankment, but lower corrections apply to the middle and lower parts of the embankment.

Select the likelihood column in Table 5.21 which corresponds to the maximum settlement measured anywhere in the embankment expressed as a ratio of the maximum embankment height. Then, obtain the settlement multiplication factors for the upper part and middle and lower parts from the corresponding bottom four rows of Table 5.21 depending on whether the dam has poorly compacted rockfill shells or not.

If there is significant differential settlement across the valley greater than expected from the mechanisms present, an additional increase in probabilities may be applied. The maximum multiplier should be less than 10 times and should not “double up” on the factors listed in Table 5.21.


Section 5

5-24

Table 5.21 – Settlement multiplication factors versus observed settlements

Influence on Likelihood Factor

Less Likely Neutral More Likely Much More Likely

Observed maximum settlements as percentage of embankment height

- Core settlement during construction

< 1.5% 1.5% to 3% 3% to 4% > 4%

- Post construction crest settlement at 10 years after construction dams with poorly compacted shoulders

<0.5% 0.5% to 1.0%

1.0% to 1.5%

> 1.5%

- Post construction crest settlement at 10 years after construction other dams

<0.25% 0.25% to 0.5%

0.5% to 1% > 1%

- Long term settlement rates(% per log time cycle in years) dams with poorly compacted shoulders

< 0.15% 0.15% to 0.4%

0.4% to 0.7%

> 0.7%

- Long term settlement rates(% per log time cycle in years)-other dams

< 0.1% 0.1% to 0.25%

0.25% to 0.5%

> 0.5%

Dams with poorly compacted rockfill (b)

0.05 to 0.2 0.2 to 0.5 1.0 2 to 5 Settlement multiplication factors for cracking or hydraulic fracture in the upper part (a) of the embankment based on observed maximum settlements

All other dams

0.2 to 0.5 1.0 2 to 10 10 to 20

Dams with poorly compacted rockfill (b)

0.2 0.2 to 0.5 1.0 2 to 5 Settlement multiplication factors for cracking or hydraulic fracture in the middle and lower parts (c)(d) of the embankment All other

dams 0.5 1.0 2 to 5 5 to 10

Notes: (a) Settlement multiplication factors to be applied to the probabilities for IM1 through IM5 and IM9. These factors are not applicable to IM6, IM7 and IM8.

(b) Includes dumped rockfill, and rockfill and other granular zones compacted by tracking with bulldozers and by small rollers in thick layers

(c) Settlement multiplication factors to be applied to the probabilities for IM10 and IM11. These factors are not applicable to IM12.

(d) Multiplication factors assumed to be half those for cracking in the upper part.


Section 5

5-25

Cracking Observations

Where there are observations of cracking for the dam these can be used to modify the results of Sections 5.2 and 5.3. The probability is multiplied by the factor from Table 5.22.

Table 5.22 – Cracking observation factors (applies to upper embankment only)

Influence on Likelihood Factor

Less Likely Neutral More Likely Much More Likely

Cracking observed in test pits to the top of or into the core

No cracking observed when large areas of the top of the core are exposed.

No test pits Transverse cracks persistent across the top of the core and/or, extensive, open longitudinal cracking

Transverse cracks which pits show persist across the core, and extend below reservoir water level in the reservoir level partition being considered

Cracking Factor (A)

0.5 to 0.1 depending on the extent of exposure and how relevant the exposure is to the possible mechanism of cracking

1.0 5 to 100 depending on width(2) of cracking and whether they are in locations in which cracking might be expected

Probability of transverse crack = 1.0

Cracking in the surface of the crest, no test pits

No cracking observed, core exposed on the surface, careful inspection for cracking

No cracking observed, core covered with road pavement or other granular material

Narrow (<10mm) transverse cracks persistent across the crest and/or, extensive, narrow longitudinal cracking

Transverse cracks which persist across the crest and/or, extensive, wide longitudinal cracking.

Cracking Factor (B)

0.5 to 0.2 depending on the quality of exposure and whether they are in locations in which cracking might be expected

1.0 2 to 5 depending on and whether they are in locations in which cracking might be expected

2 to 20 depending on the width(2) of cracking and whether they are in locations in which cracking might be expected

Notes: (1) Apply either Cracking Factor (A) or Cracking Factor (B) for IM1 through IM6 and IM9, whichever gives greatest probability of cracking. These factors are not applicable to IM7, IM8, and IM10 through IM12.

(2) The greater the crack width the more likely it represents cracking in the core.

Evaluate the Cracking Factors (A) and (B) from Table 5.22 and then multiply the largest value of (A) or (B) to the probabilities of transverse cracking in the upper part of the dam. For dams which display cracking the probabilities will be increased. For those which do not display cracking the probabilities may remain the same, or are reduced depending on how extensive the investigations to locate cracking have been. The multiplication factor should be selected taking account of what data is available, allowing for the relative importance of the observations. This factor only applies to the assessment of transverse cracking in the upper part of the embankment. Cracking in the middle and lower parts will generally not be observed.


Section 5

5-26

5.5 Probability of Initiation of Erosion in a Transverse Crack or Hydraulic Fracture in the Embankment

5.5.1 Overall approach

(a) For cracking in the embankment

The method to be followed is:

• Estimate the maximum likely crack width at the top of the core from Table 5.23 for IM1 through IM7 and from Table 5.14 for IM8.

• Estimate the maximum likely crack depth using Table 5.24 for IM1 through IM5 and IM8 and Table 5.25 for IM6 and IM7. The maximum likely crack depth for IM1 though IM6 and IM8 is measured from the top of the core, whereas the maximum likely crack depth for IM7 is measured from the seasonal shutdown layer during construction or staged construction surface.

• Consider flow paths based on embankment zoning and seepage exit conditions as shown in Figure 5.9 and perform a separate evaluation for each flow path.

• Estimate the likely crack width at the reservoir level stage under consideration using Figure 5.9 and assuming a uniformly tapered crack from the top of the core to the base of the crack.

• Estimate the average gradient of flow through the crack at the mid-level of the flow path for the reservoir level under consideration using Figure 5.9.

• Assess the soil classification and whether the soils are dispersive. Dispersive soils are soils with Sherard Pinhole test D1 or D2. While reservoir water salinity will affect dispersion, the salt content of the reservoir water will in most cases reduce with flood inflows and unless laboratory testing is carried out to assess the initial shear stress with the same reservoir water salts content it should be assumed soils which test dispersive in the laboratory will be so in the dam. Where there are signs of dispersive soils in field performance (e.g., severe gully erosion, sinkholes, and tunneling), soils should be assumed dispersive regardless of laboratory test results.

• Based on the soil classification and estimated crack width, estimate the probability of initiation of erosion in the crack (P IC ) using Table 5.30 to Table 5.36, depending on the gradient across the crack. If

there are hole erosion tests available assess which classification should apply to best reflect this value when using Table 5.30 to Table 5.36. Use approximate interpolation between values where necessary. These tables only apply to soil compacted to 95% to 98% of Standard Proctor maximum dry density at a moisture content between -1% to +2% of optimum moisture content. For saturated soils, soils


Section 5

5-27

significantly dry of optimum moisture content, and poorly compacted soils, Hole Erosion Tests should be carried out to determine the initial shear stress, and the method detailed in (c) below followed.

(b) For hydraulic fracturing in the embankment

The method to be followed is:

• Estimate the maximum likely crack width from Table 5.27 for IM9 and from Table 5.28 for IM10, IM11 and IM12.

• Assess the likely location for the hydraulic fracture. For IM9, estimate the location at which hydraulic fracture may occur using the ratio of approximate maximum depth at which hydraulic fracture may occur to embankment height at the abutment in Table 5.28. For IM10, assume the hydraulic fracture occurs in the core at the phreatic line. For IM11, assume the hydraulic fracture occurs at the base of the embankment. For IM12, assume the hydraulic fracture occurs at the core-foundation/abutment contact.

• Assess the soil classification and whether the soils are dispersive. Dispersive soils are soils with Sherard Pinhole test D1 or D2. While reservoir water salinity will affect dispersion, the salt content of the reservoir water will in most cases reduce with flood inflows and unless laboratory testing is carried out to assess the initial shear stress with the same reservoir water salts content it should be assumed soils which test dispersive in the laboratory will be so in the dam. Where there are signs of dispersive soils in field performance (e.g., severe gully erosion, sinkholes, and tunneling), soils should be assumed dispersive regardless of laboratory test results.

• Based on the soil classification and estimated crack width, estimate the probability of initiation of erosion in the hydraulic fracture (P IC ) using Table 5.30 to Table 5.36, depending on the gradient across

the crack. If there are hole erosion tests available assess which classification should apply to best reflect this value when using Table 5.30 to Table 5.36. Use approximate interpolation between values where necessary. These tables only apply to soil compacted to 95% to 98% of Standard Proctor maximum dry density at a moisture content between -1% to +2% of optimum moisture content. For saturated soils, soils significantly dry of optimum moisture content, and poorly compacted soils, Hole Erosion Tests should be carried out to determine the initial shear stress, and the method detailed in (c) below followed.

(c) Procedure to be followed where Hole Erosion Test data is available

In cases where Hole Erosion tests are available for the dam core soil, the following procedure should be followed:

• Estimate the crack width and hydraulic flow gradient as detailed in (a) or (b), whichever is applicable.

• EITHER Calculate the hydraulic shear stress in the crack for the reservoir stage under consideration using Table 5.37.


Section 5

5-28

• AND Compare this hydraulic shear stress to the initial shear stress of the soil at the compaction and moisture conditions it exists in the core. Based on this comparison estimate the probability of initiation of erosion. In doing this calculation, take account of the uncertainty in the crack width and initial shear stress as detailed in Section S5.4.2.4 of the Supporting Document.

• OR/AND Use Table 5.38 to determine which of Table 5.30 to Table 5.36 best fits the initial shear stress of the soil tested in the HET and use that table to estimate the probability of initiation of erosion.

5.5.2 Details of the method

Table 5.23 – Maximum likely width of cracking at the top of the core for transverse cracking in the embankment (IM1 through IM7 and IM21) versus ∑(RFxLF)

Maximum likely crack width (mm) versus ∑(RFxLF) Crack formation mechanism

6 to 9 9 to 11 11 to 13 13 to 18 18 to 24

Cross valley differential settlement (IM1 and IM5) Table 5.1

1 20 50 75 100

Differential settlement adjacent to a cliff or wall Table 5.3 (IM2)

Table 6.17 (IM21)

1 10 25 37 50

Cross section settlement due to poorly compacted shoulders (IM3) Table 5.5

1 20 50 75 100

Differential settlements in the soil foundation (IM4) Table 5.7

1 20 50 100 150

Desiccation cracking at the crest (IM6) Table 5.9

2 5 20 50 75

Desiccation cracking on seasonal shutdown layer (IM7) Table 5.11

2 5 20 50 75


Section 5

5-29

Table 5.24 – Maximum likely depth of cracking from the top of the core for transverse cracking in the embankment (IM1 through IM5 and IM8)

Maximum likely crack width at the top of the core (from Table 5.23)

mm (in)

Maximum likely crack depth from the top of the

core

ft (m) 10 (0.5) 5 (1.5) 25 (1) 10 (3) 50 (2) 15 (4.5) 75 (3) 25 (7.5) 100 (4) 30 (10)

250 (10) 75 (22.5)

Table 5.25 – Maximum likely depth of desiccation cracking based on climate (IM6 and IM7)

Climate

Maximum likely crack depth with gravel layer and no road

pavement cover (a)

(IM6 only) ft (m)

Maximum likely crack depth with no gravel layer or

pavement road cover (a) (i.e., dam core extends to the crest )

(IM6 or IM7) ft (m)


15 (4.5)

23 (7)

Monsoonal or other distinct wet and dry periods in the year with summer maximum temperatures >85°F (>30°C )

13 (4)

20 (6)


10 (3)

16 (5)

Temperate climate with uniform rainfall throughout the year

6 (2)

15 (4.5)

Note: (a) Road pavement cover may comprise concrete, asphalt or bitumen seal.


Section 5

5-30

Table 5.26 – Maximum likely width of cracking for hydraulic fracturing in the embankment (IM9 and IM20) versus ∑(RFxLF)

Maximum likely crack width (mm) ∑(RFxLF)

from Table 5.15 (IM9) and Table 6.15 (IM20) IM9 IM20

10 to 13 2 5

14 to 19 5 5

>19 10 10

Table 5.27 – Maximum likely width of cracking in the embankment for hydraulic fracturing in the embankment (IM10 through IM12) versus ∑(RFxLF)

Maximum likely crack width (mm) relative to ∑(RFxLF) Crack formation mechanism

6 to 9 9 to 11 11 to 13 13 to 18 18 to 24

Differential settlement causing arching of the core onto the shoulders (IM10) Table 5.17

0 0 1 2 10

Differential settlement in the foundation soil beneath the core (IM11) Table 5.7

0 0 2 10 20

Differential settlement over small-scale irregularities in the foundation/abutment beneath the core (IM12) Table 5.19

0 0 1 2 10


Section 5

5-31

Table 5.28 – Examples of estimated maximum likely depths below the top of the core and widths of cracking formed by hydraulic fracture in the embankment (IM9)

Abutment slope

degrees

Ratio of bench width to

embankment height

Ratio of depth of zero stress to embankment height at the

abutment

Ratio of approximate maximum depth at which

hydraulic fracture may occur to embankment height at the abutment

Likely crack width formed by hydraulic

fracture (mm)

15 0.67 <0.01 0.05 2

25 No bench 0.02 0.05 2

45 No bench 0.12 0.3 5

45 0.2 0.12 0.3 5

45 0.4 0.09 0.25 5

45 1.0 0.10 0.25 5

60 No bench 0.35 0.5 10

Table 5.29 – Representative erosion rate index (IHET) versus soil classification for non-dispersive soils based on Wan and Fell (2002, 2004)

Representative Erosion Rate Index (IHET)

Soil Classification Likely Minimum Best Estimate Likely Maximum

SM with < 30% fines 1 <2 2.5

SM with > 30% fines <2 2 to 3 3.5

SC with < 30% fines <2 2 to 3 3.5

SC with > 40% fines 2 3 4

ML 2 2 to 3 3

CL-ML 2 3 4

CL 3 3 to 4 4.5

CL-CH 3 4 5

MH 3 3 to 4 4.5

CH with Liquid Limit < 65 3 4 5

CH with Liquid Limit > 65 4 5 6

Notes: (1) Use best estimate value for best estimate probabilities. Check sensitivity if the outcome is strongly dependent on the results.

(2) For important decisions carry out Hole Erosion Tests, rather than relying on this table which is approximate (3) The Representative Erosion Rate index is for soils compacted to 95% standard (Proctor) maximum dry density at

optimum moisture content. (4) See Supporting Information Report for information regarding the Representative Erosion Rate index for soils which

are significantly drier than optimum moisture content or saturated.


Section 5

5-32

a) Homogeneous embankment

b) Embankment with a partial filter

Figure 5.9 – Examples of the estimation of crack width and flow gradient in the crack

( ) 2/1max

P

d

dDC

DC

−=

⎟⎠⎞

⎜⎝⎛ −

=DdDCC P

d 2max1

Base of Cracking

D

Cmax

dP d1

Cd1

Flow Path

1d

Pavg L

dDi −=

Ld1

11,

d

PFavg L

ddi −=

D

Cmax

dP d1Cd1

Flow Path 1

Ld1

22,

d

Pavg L

dDi −=

d2Cd2

( ) 2/2max

F

d

dDC

DC

−= ⎟

⎠⎞

⎜⎝⎛ −

=DdDCC F

d 2max2

dF

Base of Cracking

Flow Path 2

Ld2

Filter

( ) 2/1max

PF

d

ddDC

DC

+−= ⎟

⎠⎞

⎜⎝⎛ +

−=D

ddCC PFd 2

1max1


Section 5

5-33

Table 5.30 – Estimation of probability of initiation in a crack for ML or SM with < 30% fines soil types

Probability of initiation of erosion for different seepage gradients

Average Hydraulic Gradient

Estimated likely crack width in core for reservoir

stage being considered (mm) 0.1 0.25 0.5 1.0 2.0 5.0

1 0.05 0.2 0.6 0.95 1.0 1.0

2 0.1 0.6 0.9 1.0 1.0 1.0

5 0.6 1.0 1.0 1.0 1.0 1.0

10 0.9 1.0 1.0 1.0 1.0 1.0

25 1.0 1.0 1.0 1.0 1.0 1.0

50 1.0 1.0 1.0 1.0 1.0 1.0

75 1.0 1.0 1.0 1.0 1.0 1.0

100 1.0 1.0 1.0 1.0 1.0 1.0

Note: The gradient is the average hydraulic gradient from the upstream to the downstream of the core at the level of the assumed crack under the reservoir level under consideration. No allowance is made for seepage head losses in the zones upstream or downstream of the core.

Table 5.31 – Estimation of probability of initiation in a crack for SC with <40% fines or SM with > 30% fines soil types





1 0.02 0.2 0.6 0.9 0.95 1.0

2 0.1 0.6 0.9 0.95 1.0 1.0

5 0.6 0.95 0.99 1.0 1.0 1.0

10 0.9 1.0 1.0 1.0 1.0 1.0

25 0.95 1.0 1.0 1.0 1.0 1.0

50 1.0 1.0 1.0 1.0 1.0 1.0

75 1.0 1.0 1.0 1.0 1.0 1.0

100 1.0 1.0 1.0 1.0 1.0 1.0



Section 5

5-34

Table 5.32 – Estimation of probability of initiation in a crack for SC with > 40% fines or CL-ML soil types





1 0.02 0.1 0.4 0.8 0.9 0.95

2 0.1 0.5 0.7 0.9 0.95 1.0

5 0.4 0.8 0.9 0.95 1.0 1.0

10 0.7 0.9 0.95 1.0 1.0 1.0

25 0.9 0.95 1.0 1.0 1.0 1.0

50 0.95 1.0 1.0 1.0 1.0 1.0

75 1.0 1.0 1.0 1.0 1.0 1.0

100 1.0 1.0 1.0 1.0 1.0 1.0


Table 5.33 – Estimation of probability of initiation in a crack for CL or MH soil types





1 0.01 0.03 0.1 0.2 0.3 0.7

2 0.02 0.1 0.2 0.5 0.6 0.9

5 0.1 0.3 0.5 0.7 0.9 1.0

10 0.2 0.5 0.7 0.95 1.0 1.0

25 0.4 0.7 0.95 1.0 1.0 1.0

50 0.7 1.0 1.0 1.0 1.0 1.0

75 0.9 1.0 1.0 1.0 1.0 1.0

100 0.95 1.0 1.0 1.0 1.0 1.0



Section 5

5-35

Table 5.34 – Estimation of probability of initiation in a crack for CL-CH or CH with LL < 65 soil types





1 0.005 0.02 0.05 0.1 0.2 0.6

2 0.01 0.05 0.1 0.3 0.5 0.9

5 0.05 0.2 0.3 0.6 0.8 1.0

10 0.1 0.3 0.6 0.9 0.95 1.0

25 0.3 0.6 0.9 1.0 1.0 1.0

50 0.6 0.95 1.0 1.0 1.0 1.0

75 0.8 1.0 1.0 1.0 1.0 1.0

100 0.9 1.0 1.0 1.0 1.0 1.0


Table 5.35 – Estimation of probability of initiation in a crack for CH with LL > 65 soil types





1 0.001 0.002 0.005 0.01 0.05 0.1

2 0.002 0.005 0.01 0.02 0.1 0.4

5 0.005 0.01 0.05 0.1 0.3 0.95

10 0.01 0.04 0.1 0.4 0.6 1.0

25 0.02 0.1 0.4 0.8 0.95 1.0

50 0.1 0.5 0.95 1.0 1.0 1.0

75 0.3 0.8 1.0 1.0 1.0 1.0

100 0.4 0.95 1.0 1.0 1.0 1.0



Section 5

5-36

Table 5.36 – Estimation of probability of initiation in a crack for dispersive soils (CL, CH, CL-CH)





1 0.02 0.1 0.3 0.6 0.8 1.0

2 0.05 0.3 0.6 0.9 1.0 1.0

5 0.3 0.7 1.0 1.0 1.0 1.0

10 0.5 1.0 1.0 1.0 1.0 1.0

25 1.0 1.0 1.0 1.0 1.0 1.0

50 1.0 1.0 1.0 1.0 1.0 1.0

75 1.0 1.0 1.0 1.0 1.0 1.0

100 1.0 1.0 1.0 1.0 1.0 1.0


Table 5.37 – Estimated hydraulic shear stress (N/m2) from water flowing in an open crack, versus crack width and flow gradient

Flow Gradient in Crack Crack Width (mm) 0.1 0.25 0.5 1.0 2.0 5.0

1 0.5 1.25 2.5 5 10 25

2 1 2.5 5 10 20 50

5 2.5 6 12 25 50 125

10 5 12 25 50 100 250

20 10 25 50 100 200 500

50 25 60 125 250 500 1250

100 50 125 250 500 1000 2500


Section 5

5-37

Table 5.38 – Initial shear stress assumed for Table 5.30 to Table 5.36

Table Soil types Initial shear stress assumed for

assessing probabilities of initiation of erosion

Table 5.30 ML and SM with < 30% fines 2 Pa

Table 5.31 SC with < 40% fines, SM with > 30% fines 2 Pa

Table 5.32 SC with > 40% fines, and CL-ML 4 Pa

Table 5.33 CL and MH 5 Pa

Table 5.34 CL-CH and CH with LL < 65 25 Pa

Table 5.35 CH with LL > 65 60 Pa

Table 5.36 Dispersive soils 2 Pa

Probability of Initiation of Erosion in Poorly Compacted or High Permeability Zones in the Embankment

Section 6

6-1

6 Probability of Initiation of Erosion in Poorly Compacted or High Permeability Zones in the Embankment


a) Estimate the probability of a continuous poorly compacted or high permeability zone (PP.xx) for each of the mechanisms which can lead to a poorly compacted or high permeability zone. These are:

• Poorly compacted or high permeability layer during construction within the core (IM13) using Section 6.2.1.

• Poor compacted or high permeability layer on the foundation or abutment contact (IM14) using Section 6.2.2.

• High permeability layer due to freezing (IM15 and IM16) using Section 6.2.3.

• Poorly compacted or high permeability layer associated with a conduit (IM17 and IM18) using Sections 6.3.1 and 6.3.2, respectively.

• Poorly compacted or high permeability layer associated with other structures penetrating the core (IM 19 through IM21) using Section 6.4.

This is done using Table 6.1 to Table 6.9 in Section 6.2 for zones within the embankment or at the core-foundation/abutment contact, Table 6.10 and Table 6.11 in Section 6.3 for zones and features associated with a conduit, and Table 6.13 to Table 6.19 in Section 6.4 for zones adjacent to a spillway or abutment walls. The probabilities obtained from these tables are modified for observed seepage using Table 6.20 in Section 6.5 to obtain Pflaw. Modifications are not applicable to all mechanisms.

For most dams not all mechanisms will be present, and those mechanisms are assigned a probability of zero. The details for screening the mechanisms are described in Section 3.4.

b) If grouting was performed within the poorly compacted or high permeability zone in the embankment, evaluate the likelihood of the grouting being ineffective at cutting off the poorly compacted or high permeability zone using Table 8.19 and Table 8.20 in Section 8.7. If a cut-off wall was installed through the poorly compacted or high permeability zone in the embankment, evaluate the likelihood of grouting being ineffective at cutting off the cracking using Table Table 8.21 and Table 8.22 in Section 8.8.

c) Assess the erosion mechanism(s) which will apply. This will be one or more of the following:

• Backward erosion

• Suffusion

• Erosion in a crack or flaw resulting from the poor compaction.


Section 6

6-2

Backward erosion and suffusion will apply to cohesionless soils and as discussed in Section 6.6.1, to soils with a plasticity index ≤ 7. For cohesive soils, erosion will occur in cracks or continuous open flow paths formed by collapse of the soil on saturation, or between aggregated particles of the soil, and can be considered as equivalent to erosion in a crack. Even low plasticity soils may form a crack so soils with a plasticity index between zero and 7 should be considered for both erosion in a crack and backward erosion and suffusion and the highest probability of initiation carried forward in the analysis.

d) Assess the probability of erosion in the poorly compacted or high permeability zone (PI) for the mechanism using the relevant method described in Section 6.6.

e) The estimated probabilities of a flaw and initiation of erosion for each initiating mechanism are not added together, but are carried through the event trees for each failure path. For many dams, one or more of the mechanisms will not be present.

6.2 Probability of Continuous Poorly Compacted or High Permeability Zones in the Embankment or on the Core-Foundation/Abutment Contact

6.2.1 Poorly compacted or high permeability zones within the core (IM13)

The scenarios may lead to poorly compacted or high permeability zones within the core of an embankment:

• Poorly compacted layers in the core

• A segregated layer in the core due to the presence of coarser particles and poor construction practices

• Coarser soil layers in the core due to variability in particle size and soil type in the borrow areas. This can result in a cohesionless layer within a cohesive core, or a coarser cohesionless layer within a finer cohesionless soil.

The effect of these factors on the likelihood of a poorly compacted or high permeability zone is different for cohesive and cohesionless soils so they are treated separately. For these purposes, a cohesionless soil is non-plastic.


Section 6

6-3

Table 6.1 – Factors influencing the likelihood of poorly compacted or high permeability zones within the core for cohesive soils (IM13)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

METHOD BASED ON COMPACTION EQUIPMENT, LAYER THICKNESS, AND MOISTURE CONTENT (a)

EITHER Compaction equipment and

(3) As for “neutral” but with good documentation and records

Note: Probability is zero if the soils are well-compacted.

Soil compacted by suitable rollers in suitable layer thicknesses

Soil placed and compacted by bulldozer, no compaction by rollers, or rolled in thick layers beyond the capability of the roller

Soil placed with no formal compaction (e.g., by horse and cart in old dams or by pushing into place by excavator or bulldozer, or in very thick layers)

Layer thickness and

Layer thickness 6 to 10 in (150 to 250 mm) after compaction

Layer thickness at or beyond the limit of compaction equipment (e.g., > 12 to 18 in (300 to 450 mm) after compaction)

No control on layer thickness, often > 18 to 24 inches (450 to 600 mm) loose

Moisture content

Around OWC (b) Dry of OWC (b) Well dry of OWC

(b)

METHOD BASED ON COMPACTION EQUIPMENT, LAYER THICKNESS AND MOISTURE, CONTENT (a)

OR Measured or estimated compaction density ratio and moisture content

(3) All very well-compacted to e.g., ≥ 98% SMDD, moisture content 2% dry of OWC to 1% wet of OWC


Well-compacted to e.g., 95-98% SMDD, moisture content 2% dry of OWC to 1% wet of OWC

Layers of poorly compacted, dry of standard OWC e.g., < 93% SMDD, 2% to 3% dry of OWC

Layers of very poorly compacted

Dry of standard OWC

e.g., < 90% SMDD, 3% dry of OWC


Section 6

6-4


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

FACTORS APPLYING TO BOTH ALTERNATIVES

Borrow area variability and

(2) Uniform soils in the borrow areas

Uniform or minor variability in the borrow areas

Variable soils in the borrow areas

Very variable soils in borrow areas including gravely soils

Site supervision

Good site supervision documented with laboratory tests

Good site supervision

Moderate site supervision

Poor site supervision

Core geometry (b)

(1) Wide core W/H >1.5

0.5 < W/H < 1.5

Narrow core 0.25 < W/H < 0.5

Very narrow core W/H < 0.25

Note: (a) Make an assessment based on a combination of available data. (b) Average width (W) of core at poorly compacted or highpermeability layer and height (H) of the embankment.


Section 6

6-5

Table 6.2 – Factors influencing the likelihood of poorly compacted or high permeability zones within the core for cohesionless soils (IM13)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

METHOD BASED ON COMPACTION EQUIPMENT, LAYER THICKNESS, AND MOISTURE CONTENT (a)

EITHER Compaction equipment and

(3) As for “neutral” but with good documentation and records


Soil compacted by suitable rollers in suitable layer thicknesses


Soil placed with, no formal compaction ( e.g., by horse and cart in old dams, or by pushing into place by excavator or bulldozer or in very thick layers

Layer thickness and

Layer thickness 8 to 12 in (200 to 300 mm) after compaction

Layer thickness at or beyond the limit of compaction equipment (e.g., > 12 to 18 in (300 to 450 mm) after compaction)

No control on layer thickness, often > 24 to 36 in (600 to 900 mm) loose

Moisture content

Around OWC (a) Dry of OWC (a) Well dry of OWC (a)

OR Measured or estimated compaction density ratio and moisture content

(3) All very well- compacted (e.g., very dense, >85% relative density with good documentation and records, SPT (N1)60 > 42 bpf)


All well-compacted (e.g., dense, 66% to 85% relative density, SPT (N1)60 26 to 42 bpf)

Layers moderately compacted (e.g., medium dense, 36% to 65% relative density, SPT (N1)60 9 to 25 bpf)

Layers very poorly compacted (e.g., very loose to loose, <35% relative density, SPT (N1)60 < 8 bpf)


Section 6

6-6


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

FACTORS APPLYING TO BOTH ALTERNATIVES

Borrow area variability and

(2) Uniform soils in the borrow areas

Uniform or minor variability in the borrow areas

Variable soils in the borrow areas

Very variable soils in borrow areas including gravely soils

Site supervision

Good site supervision documented with laboratory tests

Good site supervision

Moderate site supervision

Poor site supervision

Core geometry (b)

(1) Wide core

W/H > 1.5

0.5<W/H<1.5

Narrow core

0.25 < W/H < 0.5

Very narrow core

W/H < 0.25

Note: (a) Make an assessment based on a combination of available data. (b) Average width (W) of core at poorly compacted or highpermeability layer and height (H) of the embankment.

Table 6.3 – Probability of poorly compacted or high permeability layers within the core

(IM13) versus ∑(RFxLF)



6 8 9 11 13 18 24 RFxLF


Section 6

6-7

6.2.2 Poorly compacted or high permeability zones at the core-foundation/abutment contact (IM14)

Table 6.4 – Factors influencing the likelihood of poorly compacted or high permeability zones at the core-foundation/abutment contact (IM14)


Factor Relative


Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

EITHER Rock foundation preparation below the core (a)

(3) Uniform rock surface or surface treated with shotcrete, or concrete to correct slope irregularities Note: Probability is zero if this condition is present.

Regular rock surface, or rock surface treated with shotcrete or concrete to correct slope irregularities Note: Probability is zero if this condition is present.

Irregular rock surface, with minimal slope correction or treatment or irregular or benched soil with no compaction

Very irregular rock surface, overhangs with no slope correction, shotcrete or concrete treatment

OR Soil foundation preparation below the core (a)

(3) Uniform well compacted soil foundation


Compacted soil foundation


Irregular or benched soil with no compaction

Poor stripping of soil foundation leading to poor compaction of first lift

Compaction methods for contact zone

(2) As for “neutral” but with good documentation and records (b)

Soil compacted using special compaction methods (rubber tires, use more plastic materials, compaction wet of OWC)

Soil placed and compacted by bulldozer, no compaction by rollers

Layer thickness at the limit of compaction equipment (e.g., > 12 to 18 in (c)

Poor compaction methods used, soil poorly compacted or allowing segregation against foundation surface.

Thick layer thickness, often > 18 to 24 in, loose

Core geometry, continuity of features

(1) Wide core

W/H > 1.5

Core wall or grout cap cutoff present

0.5 < W/H < 1.5

Narrow core

0.25 < W/H < 0.5

Very narrow core

W/H < 0.25

Notes: (a) For homogeneous earthfill dams, assess foundation preparation and compaction methods for the central portion of the section.

(b) Even situations where soil is well-compacted can soften or loosen if the contact is irregular. (c) Smaller thicknesses are for cohesive soil, larger thicknesses for cohesionless soil. (d) Width (W) of the core at the base of the embankment and height (H) of the embankment.


Section 6

6-8

Table 6.5 – Probability of a poorly compacted or high permeability zones at the core-foundation/abutment contact (IM14) versus ∑(RFxLF)



6 8 9 11 13 18 24 RFxLF

6.2.3 High permeability zones in the embankment due to freezing (IM15 and IM16)

Freezing conditions can result in frost heave and formation of ice lenses in the crest of dams. When the ice thaws, loosened and/or cracked soil may be present in which internal erosion may initiate if the reservoir rises sufficiently high. The following sections describe how to assess the probability of the presence of such features at the crest of the dam and on seasonal shutdown layers during construction and staged construction surfaces. The method for estimating the probability of initiation of erosion is detailed in Section 6.6.5.


Section 6

6-9

At the embankment crest (IM15)

Table 6.6 – Factors influencing the likelihood of high permeability zones due to freezing at the embankment crest (IM15)


Factor Relative


Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Climate (3) Other climates where temperatures do not fall below freezing point except possibly overnight or for a day or two.


Temperate climate where temperatures may remain below freezing point for up to 1 month

Sub arctic or alpine climates where temperatures remain below freezing point for 1 to 3 months

Sub arctic or alpine climates where temperatures remain below freezing point for 3 months or more

Classification of core material

(2) Clean gravel (GP, GW) and sand (SP, SW), less than 3% finer than 0.02 mm

Gravely (GP, GW) and sandy (SP, SW) soils with between 3% and 6% finer than 0.02mm

High plasticity clays (CH)

Silty gravely (GM, GW-GM, GP-GM) and silty sandy soils (SM, SW-SM, SP-SM) with 6% to 15% finer than 0.02mm

Clayey sands and gravels (SC, GC), clays with PI < 12

Silts (ML, MH), silty sands (SM) with > 15% finer than 0.02mm, and clayey silts (ML-CL)

Crest zoning-surface layer over core

(1) Greater than 6 ft (2 m) of rockfill over the core

Gravely material or rockfill 3 to 6 ft (1 to 2 m) thick over the core

Gravel material or rockfill 18 in to 3 ft (0.45 to 1 m) thick over the core

No surface layer with dam core extending to crest level or thin (< 3 in (75 mm)) road pavement or gravely material


Section 6

6-10

Table 6.7 – Probability of high permeability zones due to freezing at the embankment crest (IM15) versus ∑(RFxLF)

negligible negligible 0.0001 0.001 0.1 0.3 0.9

6 10 11 12 16 21 24 RFxLF

On seasonal shutdown layers or on the surface of staged embankments (IM16)

This mechanism only applies where there has been a seasonal shutdown during construction or the embankment construction was staged. If there was no seasonal shutdown layer during construction or the embankment construction was not staged, this mode can be ignored.

Where the mechanism applies, estimate the probability of a freezing layer using Table 6.8 and Table 6.9. The descriptions in Table 6.8 are to be assessed according to the conditions across the width of the core.


Section 6

6-11

Table 6.8 – Factors influencing the likelihood of high permeability zones due to freezing at seasonal shutdown layers during construction or staged construction surfaces (IM16)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Construction practices regarding clean-up of frozen layers after construction shutdowns or the surface of the earlier stage of the dam

(4)

Very good control and clean-up practices.

Frozen layers removed from embankment and replaced with new soil or adequately reworked to specified moisture content.


Good control and practices, surfaces scarified, moisture adjusted to specified range, surface re-compacted.

Moderate control. Attempts to scarify frozen layers, but depth of scarifying insufficient or difficulties with moisture control on re-compacting the soil

Poor control. No attempt to scarify or remove frozen layers, poor moisture control on re-compacting the soil

Climate (2) Other climates where temperatures do not fall below freezing point except possibly overnight or for a day or two.


Temperate climate where temperatures may remain below freezing point for up to 1 month

Sub arctic or alpine climates where temperatures remain below freezing point for 1 to 3 months

Sub arctic or alpine climates where temperatures remain below freezing point for 3 months or more

Classification of core material

(1) Clean gravel (GP, GW) and sand (SP, SW), less than 3% finer than 0.02 mm

Gravely (GP, GW) and sandy (SP, SW) soils with between 3% and 6% finer than 0.02mm

High plasticity clays (CH)

Silty gravely (GM, GW-GM, GP-GM) and silty sandy soils (SM, SW-SM, SP-SM) with 6% to 15% finer than 0.02mm

Clayey sands and gravels (SC, GC), clays with PI < 12

Silts (ML, MH), silty sands (SM) with > 15% finer than 0.02mm, and clayey silts (ML-CL)


Section 6

6-12

Table 6.9 – Probability of high permeability zones due to freezing at seasonal shutdown layers during construction or staged construction surfaces (IM16) versus ∑(RFxLF)

negligible negligible negligible 0.0001 0.001 0.01 0.1 Below POR

negligible negligible negligible 0.001 0.01 0.1 0.9 Above POR

7 10 12 13 18 22 28 RFxLF


Section 6

6-13

6.3 Probability of Continuous Poorly Compacted or High Permeability Zones adjacent to a Conduit or Features Allowing Erosion into the Conduit

6.3.1 Poorly compacted or high permeability zones adjacent to a conduit (IM17)

Table 6.10 – Factors influencing the likelihood of poorly compacted or high permeability zones adjacent to a conduit through the embankment (IM17)


Factor

Relative Importance of Factor

(RF) Less Likely

(1) Neutral

(2) More Likely

(3)

Much More Likely

(4)

Conduit type and surround

(3) Concrete encased round pipe, concrete precast or cast in situ, sloping sides

Concrete encased round pipe, concrete precast or cast in situ, vertical sides. Flowable fill (CLSM)

Masonry, brick Any round pipe (including corrugated metal pipe), not concrete encased

Cut-off collars

(2) No cut-off collars

Well detailed cut-off collars

Poorly detailed cut-off collars, widely spaced

Poorly detailed cut-off collars, close spacing

Compaction of earthfill around the conduit

(2)

Compaction by rollers to >98% SMDD at -1% to +2% OWC

Compaction by hand and mechanical equipment to >95% SMDD at -1% to 2% OWC

Compaction by hand equipment, thick layers, dry of optimum moisture content

No formal compaction, or poor compaction practices used (e.g., thick layers inappropriate for equipment)

Conduit trench details

(2)

Trench totally in non-erodible rock, backfilled to the surface with concrete


Wide, slopes flatter than 1H:1V, base width not less than conduit width plus 2 meters either side.

No desiccation of sides of trench

Medium width, depth, and slope; and/or sides of trench desiccated and cracked

Narrow, deep, near vertical sides in soil or rock, backfilled with soil; and/or sides of trench highly desiccated and cracked


Section 6

6-14

Table 6.11 – Probability of poorly compacted or high permeability zones adjacent to a conduit through the embankment (IM17) versus ∑(RFxLF)

0.0001 0.0002 0.0005 [0.0009] 0.005 0.02 Below 1.20 x hPOR

0.0003 0.0006 0.0015 [0.003 0.02 0.1 Above 1.20 x hPOR

0.001 0.002 0.005 [0.01] 0.05 0.5 First Fill (untested)

9 12 16 20 26 36 RFxLF

Note: Above POR probabilities apply where the reservoir rise is greater than 20% increase in previously recorded hydraulic head (e.g. for flood protection dams).

Figure 6.1 – Example of poor detailing of seepage collars around a conduit (FEMA 2005)

6.3.2 Features allowing erosion into a conduit (IM18)

For non-pressurized conduits, assess the probability of a feature being present in the conduit which would allow erosion of the surrounding soil into the conduit.

a) For cases where the internal condition of the conduit is regularly inspected and there is good documentation of the inspections: If open joints are cracks are documented, then estimate the probability of having a feature allowing erosion into the conduit using Table 6.12.

b) For cases where the internal condition of the conduit is not known, use the appropriate structural toolbox to assist in assessing the probability of having a feature allowing erosion into the conduit.


Section 6

6-15

Table 6.12 – Factors influencing the likelihood of an open joint or crack allowing erosion into a non-pressurized conduit when the internal condition is known

Observed Condition Probability of an Open Joint or Crack

Careful inspection showing no evidence of open joints or cracks Negligible Careful inspection showing no evidence of open joints, but cracks < 5 mm are present

0.001 to 0.005

Open joints or cracks ≥ 5 mm present with no evidence of flowing seepage 0.05 to 0.3 Open joints or cracks ≥ 5 mm present with evidence of flowing seepage through joint/crack, or evidence of erosion of soil into the conduit

1.0

It should be noted that this mechanism can apply for erosion into the conduit from the foundation and from the embankment. The probability of initiation of erosion into the conduit is assessed using the method detailed in Section 6.6.7. Whether erosion continues (continuation) into the conduit will be assessed in Section 10.1.5. When evaluating continuation, the defect size measured from careful inspection should be used. If defect size and location are unknown, assume a 5 mm defect located at the center of the core.

For pressurized conduits, recalculate the gradients for IM17 assuming full reservoir head at the known crack location along conduit. Otherwise, assume the crack is located at the center of the core. Recalculate the gradient using the shortened seepage path from the crack to the downstream exit.

6.4 Probability of Continuous Poorly Compacted or High Permeability Zones or Gaps adjacent to a Spillway or Abutment Wall

6.4.1 Approach

• Assess the probability of a poorly compacted or high permeability zone or gap for each of the three mechanisms for a spillway or abutment wall:

1) Poorly compacted or high permeability zone associated with the wall (IM19) using Table 6.13 and Table 6.14 in Section 6.4.2.

2) Crack/gap adjacent to the wall (IM20) using Table 6.15 and Table 6.16 in Section 6.4.3.

3) Differential settlement adjacent to the wall (IM21) using Table 6.17 and Table 6.18 in Section 6.6.4.

• For IM19, estimate the probability erosion will initiate in the high permeability zone using the methods detailed in Section 6.6.


Section 6

6-16

• For IM20 and IM21, estimate the probability erosion will initiate in the crack or gap using the methods detailed in Section 5.5.

6.4.2 Poorly compacted or high permeability zones adjacent to a spillway or abutment wall (IM19)

Table 6.13 – Factors influencing the likelihood of poorly compacted or high permeability zones adjacent to a spillway or abutment wall (IM19)


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Compaction of earthfill adjacent to the wall

(3)

Compaction by rollers to >98% SMDD at a moisture content between -2% and +2% of standard OWC

Compaction by hand and mechanical equipment to >95% SMDD at a moisture content between -2% and +2% of standard OWC

Compaction by hand equipment, thick layers, dry of optimum moisture content

No formal compaction, or poor compaction practices (e.g., placed in very thick lifts or allowing segregation against wall)

Concrete buttresses

(2) None

Single but with good compaction around the buttress

Single with poor details such as vertical sides, little evidence of good compaction

Several close together preventing good compaction

Finish on wall

(1) Smooth planar coupled with flat slope (flatter than 0.5H:1V)

Smooth, planar Rough and irregular

Vertical and horizontal steps (e.g., masonry or brick walls)

Table 6.14 – Probability of poorly compacted or high permeability zones adjacent to a spillway or abutment wall (IM19) versus ∑(RFxLF)

0.00005 0.0001 0.0002 [0.0003] 0.002 0.02 Below POR

0.001 0.002 0.005 [0.01] 0.05 0.5 Above POR

6 9 11 13 18 24 RFxLF


Section 6

6-17

6.4.3 Crack or gap adjacent to a spillway or abutment wall (IM20)

Table 6.15 – Factors influencing the likelihood of a crack or gap adjacent to a wall (IM20)


Factor


(RF) Less Likely

(1) Neutral

(2) More Likely

(3)

Much More Likely

(4)

Slope of wall (3) Sloping, flatter than 0.5H to 1V

Sloping, 0.1H to 1V to 0.5H to 1V

Vertical, or Vertical with flatter slope on lower part

Overhanging over the core width.

Wall type, wall stiffness

(2) Very stiff gravity wall or counterfort wall

Thin gravity wall

Cantilever wall (short wall)

Cantilever wall, (tall slender wall)

Cyclic loading conditions

(1) Wall not subject to cyclic reservoir level conditions

Wall rarely subject to cyclic reservoir level conditions

Wall frequently subject to cyclic reservoir level conditions

Wall subject to cyclic reservoir level conditions

Table 6.16 – Probability of a gap or crack adjacent to a wall (IM20) versus ∑(RFxLF)

0.00005 0.0001 0.0002 [0.0004] 0.002 0.02 Below POR

0.001 0.002 0.005 [0.01] 0.05 0.3 Above POR

6 9 11 13 18 24 RFxLF


Section 6

6-18

Figure 6.2 – Situations where a gap may form between the dam fill and spillway wall (a) Steep foundation adjacent spillway wall;

(b) Change in slope of the retaining wall (Fell et al. 2004)


Section 6

6-19

6.4.4 Transverse cracking due to differential settlement adjacent to a spillway or abutment wall (IM21)

Table 6.17 – Factors influencing the likelihood of transverse cracking in the embankment due to differential settlement adjacent a spillway or abutment wall (IM21)


Factor


(RF) Less Likely

(1) Neutral

(2) More Likely

(3)

Much More Likely

(4)


(3) Wide bench Wb/Hw > 2.5


Bench adjacent to wall 1.0 < Wb/Hw <2.5

Narrow bench adjacent to wall 0.25 < Wb/Hw < 1.0

No or very narrow bench adjacent to wall

Wb/Hw < 0.25


(2) Gentle abutment slopes

β 1 < 25°



25° < β 1 < 45°


45° < β 1 < 60°

Very steep abutment slope

β 1 > 60°






Note: (a) See Figure 5.2 for definitions of Wb, Hw, β1.

Table 6.18 – Probability of cracking due to differential settlement adjacent a spillway or abutment wall (IM21) versus ∑(RFxLF)

negligible negligible negligible negligible [0.0005] 0.002 0.02 Below POR


6 9 11 13 14 19 24 RFxLF


Section 6

6-20

6.4.5 Special considerations for wrap-around details for connection of embankment dam to concrete gravity dam (IM19 and IM21)

Figure 6.3 shows typical details of the connection of an embankment dam to a concrete gravity dam with a potential seepage path along PQRS. The seepage path length and hence the gradient varies with the reservoir level. However, there is a potential for the embankment to move away from the concrete dam at PQ and particularly at RS due to settlement of the embankment. There is also a potential for poorly compacted zone to exist along PQ or RS. It is recommended that this situation be assessed as follows:

• The primary control on seepage and initiation of erosion is considered to be along QR. When assessing the seepage gradient along QR, the likelihood there will be gaps or poorly compacted soil along PQ and RS should be assessed taking account of the factors in Table 6.19. For the worst scenarios, there will be no benefit from the seepage path on PQ and RS if there is a gap there which can be seen on inspection.

• Estimate the probability of a poorly compacted zone for IM19 (Section 6.4.2) and for a crack (or gap) being present for IM21 (Section 6.4.4). IM20 does not apply to long concrete sections or monoliths.

• However, when assessing the probability of initiation of erosion for both mechanisms (IM19 and IM21), use the “unpeeled” seepage path length. If a gap is likely as shown in Figure 6.3 (plan), the length at the mid-level of the flow path should be measured from Point Q to Point R rather than Point P to Point S.

• Combine the crack geometry and use the maximum probability of initiation for each reservoir level under consideration.

• The effect is likely to be most important for reservoir level stages nearing dam crest level. For evaluating the seepage path length, the crack width at the mid-level of the flow path or average gradients for the reservoir level under consideration.

Table 6.19 – Factors to be considered in assessing seepage gradients on wrap-around

Factors which make it likely there is a good seepage contact along PQ and RS, and

gradients will be lower )1(

Factors which make it likely there is a poor seepage contact along PQ and RS, and

gradients will be higher )1(

Uniform slope with no overhangs

Well compacted embankment shoulders or zoning with all materials having a similar and high modulus Uniform concrete slopes with at least 0.1H:1V slope Low embankments

Reservoir level at least 20 feet below dam crest level so there is a lesser likelihood a crack will persist to reservoir level

Overhangs in the concrete

Poorly compacted shoulders leading to large settlements during and post construction Change in slope of concrete such as shown in Figure 6.2 allowing a gap to form as the embankment settles High embankment Reservoir level approaching dam crest level


Section 6

6-21

Figure 6.3 – Wrap-around details for connection of embankment dam to concrete gravity dam


Section 6

6-22

6.5 Factors to Account for Observations

Seepage observations

Where there are observations of seepage for the dam these can be used to modify the results of Sections 6.2, 6.3 and 6.4. The probabilities obtained from Sections 6.2, 6.3, and 6.4 are multiplied by the factor from Table 6.20. The multiplication factor should be selected taking account of what data is available, allowing for the relative importance of the observations.

This factor applies to the assessment of poorly compacted or high permeability zones in the embankment, around conduits and adjacent walls. In addition, the seepage observations and observation factor must be associated with the initiating mechanism of interest. For example, seepage observations at the toe are not related to high permeability zones near the crest of the dam. Thus, a different seepage observation factor should be applied.


Section 6

6-23

Table 6.20 – Seepage observation factors

Influence on Likelihood Factor Less Likely

(1) Neutral

(2) More Likely

(3) Much More Likely

(4)

Observed seepage No seepage observed for dams where there is no potential for seepage to be hidden, careful inspection for seepage

Seepage observed at toe of dams with permeable downstream zone or internal drainage systems, or potential for hidden seepage

Wet areas on the downstream slope

Concentrated seepage is present on the downstream slope

Seepage Adjustment Factor (A)

Multiplier = 0.9 to 0.5 Multiplier = 1.0 Probability of high permeability zone = 0.5 to 1.0

Probability of high permeability zone = 1.0

Observations in drill holes/CPT in the core

Multiple drill holes or CPT tests indicate no evidence of high permeability or softened zones

No drill holes or CPT tests in core

Drill holes or CPT tests indicate softened zones in the core

Multiple drill holes or CPT tests indicate persistent high permeability zones are likely to be present

Drill Hole/CPT Adjustment Factor (B)

Multiplier = 0.1 to 0.5 depending on quantity and quality of the investigations

Multiplier = 1.0 Multiplier = 5 to 10 Probability of high permeability zone = 0.5 to 1.0

Drilling/grouting practices inducing defects in the core

Drilling through the core with water causing excessive water losses in the core

High pressure grouting was carried out through the core

Adjustment Factor for Induced Core Defects (C)

Neglect this adjustment factor if no water drilling or pressure grouting through the core

Multiplier = 2 to 5 Multiplier = 5 to 10

Notes: (a) Seepage observation factors do not apply to IM18, IM20, and IM21. (b) Apply either Seepage Adjustment Factor (A), Drill Hole/CPT Factor (B) or Induced Defect Factor (C), whichever

gives greatest probability of high permeability zones. (c) Use multipliers towards the lower of the range for reservoir level below POR and towards the upper of the range for

reservoir levels above POR.


Section 6

6-24

6.6 Probability of Initiation of Erosion in Poorly Compacted or High Permeability Zones in the Embankment or adjacent to a Conduit or Wall

6.6.1 Screening of erosion mechanism based on soil classification

If the soil is cohesionless or has a Plasticity Index ≤ 7, follow the procedures in Sections 6.6.2 and 6.6.3 to assess the probability of backward erosion and suffusion, respectively.

If the soil is cohesive with a Plasticity Index > 7, then the likelihood of backwards erosion and suffusion is negligible under the seepage gradients which occur in a conventional dam. Consider if erosion may occur through a crack in the soil using the procedure detailed in Sections 6.6.4 to 6.6.7. If the seepage gradients are greater than 4, consider suffusion for soils with a Plasticity Index ≤ 12.

For all erosion mechanisms, the location of the poorly compacted or high permeability zone is needed in order to estimate the average hydraulic gradient. Table 6.21 provides some suggested guidance for performing the gradient calculations.

Table 6.21 – Suggested locations for determination of average gradients

Initiating Mechanism Suggested Location(s)

IM13 Use specific layer identified from PFMA; or select critical location for given pool that maximizes gradient or has different filter characteristics

IM14 At the core-foundation/abutment contact

IM15 Use full depth of frost penetration, measured from the crest (or top of pavement)

IM16 Use full depth of frost penetration, measured from the elevation of the seasonal shutdown layer during construction or staged construction surface

IM17 Use specific layer identified from PFMA; or use conduit invert or bottom of trench

IM18 Use location along conduit if known from inspections; otherwise, assume open joint or crack beneath the center of the core

IM19 Assume a 5 mm crack full-height of the wall (UNO)

IM20 Assume depth of gap based on monolith geometry using Figure 6.2 as a guide

IM21 See IM2 for depth of transverse crack


Section 6

6-25

6.6.2 Assessment of the probability of initiation of backward erosion in a layer of cohesionless soil or soil with Plasticity Index ≤ 7

The steps to be followed are:

• Estimate the average seepage gradient (iave) through the dam (or in the continuous cohesionless layer) at the level of the high permeability layer for the reservoir stage under consideration.

• Estimate the time it will take to develop a seepage gradient in the layer from the estimated permeability of the soil, allowing for potential collapse of the layer on saturation if the soil is not well-compacted. Use Table 6.22 to assist in this estimate. From this and the time the reservoir will be above this stage, assess whether there is sufficient time to develop the seepage gradient in the layer. For layers below the normal operating pool level, the layer will be saturated and the seepage gradient will develop as the reservoir rises.

• From the particle size distribution of the core material, estimate a representative uniformity coefficient cu = D60/D10.

• For 1 ≤ cu ≤ 6, estimate the average gradient (ipmt) required to initiate backward erosion from Figure 6.6. This is the gradient that is required to initiate backward erosion at the downstream end of the layer and also to progress the pipe by backward erosion to the upstream end of the layer.

• Correct this average gradient for the geometry, horizontal to vertical permeability ratio of the zone subject to backward erosion, and grain size as detailed in the following step and in Section S6.6.2.4 of the Supporting Document. This gives (ipmt)corrected where

(ipmt)corrected = [(CD CL CS CK CZ Cγ Cα) / CR] ipmt (6.6a)

where ipmt = Maximum point seepage gradient needed for complete piping in the flume test based on the soil coefficient of uniformity cu (from Figure 6.6)

CD = Correction factor for (D/L)

CL = Correction factor for total pipe length L

CS = Correction factor for grain size

CK = Correction factor, for permeability anisotropy. This is for the anisotropy of the soil layer subject to backward erosion, not the embankment core as a whole.

CZ = Correction factor for high-permeability under layer

Cγ = Correction factor for density

Cα = Adjustment for pipe inclination


Section 6

6-26

CR = Correction factor for dam axis curvature

D = Depth of piping sand layer, in direction perpendicular to α (m)

L = Direct (not meandered) length between ends of a completed pipe path, from downstream to upstream exit, measured along the pipe path (m)

• Calculate the correction factors in the following steps:

o Determine the angle of the pipe exit from horizontal in the direction of the pipe formation (α). See Figure 6.7. For a horizontal exit α = 0° and for a vertical exit α = –90°

o Determine the average thickness of the piping layer being evaluated (D).

o Determine the relative density of the piping layer (Drf).

o Determine the ratio of the horizontal to vertical permeability (Rkf) of the piping soil as v

hkf k

kR = .

o Determine the length of the piping path in the field normal to the axis of the dam (L) transformed to

isotropic homogeneous conditions (Lf) as vh

f kkLL/

= .

o Calculate CD = Correction factor for (D/Lf)

4.1

1

2.02

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

=fL

D

fD

LD

C (6.6b)

o Calculate CL = Correction factor for total pipe length L

2.0

5⎟⎟⎠

⎞⎜⎜⎝

⎛=

fL L

C (6.6c)

o Calculate CS = Correction factor for grain size

2.0

10

20.0⎟⎠⎞

⎜⎝⎛=

dCs (6.6d)


Section 6

6-27

o Calculate CK = Correction factor, for permeability anisotropy. This is for the anisotropy of the soil layer subject to backward erosion, not the embankment core as a whole.

5.

5.1⎟⎟⎠

⎞⎜⎜⎝

⎛=

kfK R

C (6.6e)

o Calculate CZ = Under-layer factor. If the layer susceptible to piping is underlain by a more permeable “under-layer” of thickness d meters, and permeability ku (m/sec), CZ is calculated from Figure 6.4. In this figure, kp is the permeability of the piping layer (m/sec) and r is the equivalent radius of the tunnel developing as piping progresses (meters). For practical purposes, r is very small and D/r very large, so it is suggested that CZ = 1. If very thin erodible layers is being considered, use r = 2.5 to 10 mm. For thin alternating layers of erodible and non-erodible soil modelled as a homogenous layer with high anisotropy and use CZ = 1 as Schmertmann recommends in his paper (Schmertmann 2000).

Figure 6.4 – Underlayer factor CZ versus D/r (Schmertmann 2000)

o Calculate Cγ = Correction factor for density

⎟⎟⎠

⎞⎜⎜⎝

⎛−+= 6.0

1004.01 rfD

Cγ (6.6f)

CZ


Section 6

6-28

o Calculate Cα = Pipe inclination adjustment. This is based on the inclination α of the piping tunnel (the flow line) estimated on the true (not transformed) section. When α is zero (flow line horizontal), there is no correction. In Figure 6.5, ipo is obtained by making all the other corrections to ipmt using Equation 6.9h. In Figure 6.5, ipα is found on the graph by inputting ipo and α.

Cα = ipα/ipo (6.6g)

ipo = [(CD CL CS CK CZ Cγ) / CR] ipmt (6.6h)

o Calculate CR = Convergent or divergent flow factor. This factor is mainly used to correct for 3-D effects when there is significant convergence or divergence in flow as when there is significant curvature in the dam alignment. Divergent flow is flow from the center outward and convergent flow is flow towards the center. If the dam alignment is straight, CR = 1. For curved embankments, CR is estimated from

R2RRC 01

R+

= (6.6i)

where R = radius to point on the pipe path in a dam with curved axis (ft) (or radius of curvature in the dam)

R1 = shortest radius to an end of completed pipe path (ft) (i.e., distance from the center of curvature to the upstream toe)

R0 = longest radius to an end of completed pipe path (i.e., distance from the center of curvature to the downstream toe)

Note that a 3-D seepage analysis can also be used to determine the correction factor by comparing the gradients from a 2-D to a 3-D.


Section 6

6-29

Figure 6.5 – Graph to obtain ipα from ipo and α (Schmertmann 2000)

• If cu > 6, estimate the critical gradient (icr) from icr = (γsat – γw)/γw for vertical exits or icr = [(γsat – γw)/γw] tan(φ) for horizontal exits.

• Estimate the probability of initiation of backward erosion from Table 6.23 for compacted layers and Table 6.24 for poorly compacted layers. Use iave and (ipmt)corrected or (icr) as inputs. The table allows for gradients potentially being higher than the average at the downstream side as has been observed on many dams, and case study data from Sweden which shows erosion may occur at average gradients less than 1.0, at least if the layers are poorly compacted. It also allows for application of corrections recommended by Schmertmann (2000) which for a thin layer of permeable soil indicate gradients higher than those from Figure 6.6 are required to initiate erosion. These probabilities apply for reservoir levels up to and above the pool of record.

• For poorly compacted silt/sand/gravel soils which are subject to collapse settlement on saturation, assess the likelihood of initiation of erosion using Section 6.6.4.

ipα


Section 6

6-30

Table 6.22 – Time to develop seepage gradient in cohesionless soils

Method of compaction (see Table 6.1 and Table 6.2 for detailed descriptions

Time for developing seepage gradient with

collapse settlement

Time for developing seepage gradient if there is

no collapse settlement

No formal compaction Minutes Not applicable. Collapse settlement is highly likely.

Tracking by dozer or rolled in layers too thick for the equipment

Minutes to a few hours Not applicable. Collapse settlement is highly likely.

Compacted by rollers in suitable layer thicknesses to normal compaction standards

Not applicable. Collapse settlement is highly unlikely.

Hours to days for silty sands and sands

Compacted by rollers in suitable layer thicknesses to normal compaction standards with well-documented compaction records

Not applicable. Collapse settlement is highly unlikely.

Hours to days for silty sands and sands


Section 6

6-31

Figure 6.6 – Maximum point gradient (ipmt) needed for complete piping (initiation and progression for an unfiltered exit) versus uniformity coefficient of soil (Schmertmann 2000)

Note: This relationship applies for 1 ≤ cu ≤ 6. For cu > 6, calculate the critical gradient using icr = (γsat – γw)/ γw for horizontal exits or icr = [(γsat – γw)/γw] tan(φ) for vertical exits.


Section 6

6-32

Figure 6.7 – Backward erosion piping layer and path geometry

Table 6.23 – Probability of initiation of backward erosion in cohesionless soils and soils with PI ≤ 7 for compacted layers

Average seepage gradient across embankment core (iave) Average seepage gradient required to initiate and progress

backward erosion (ipmt)corrected or icr

0.05 0.1 0.25 0.5 1.0 2.0

0.05 0.9 0.95 0.99 0.99 0.99 0.99

0.1 0.2 0.9 0.95 0.99 0.99 0.99

0.25 0.01 0.2 0.9 0.95 0.99 0.99

0.5 0.001 0.01 0.2 0.9 0.95 0.99

1.0 0.0001 0.001 0.01 0.2 0.9 0.95

−α

α=0

α=0

+α −α D

L

+α


Section 6

6-33

Table 6.24 – Probability of initiation of backward erosion in cohesionless soils and soils with PI ≤ 7 for uncompacted layers

Average seepage gradient across embankment core (iave) Average seepage gradient required to initiate and progress

backward erosion (ipmt) corrected or icr

0.05 0.1 0.25 0.5 1.0 2.0

0.05 0.9 0.95 0.99 0.99 0.99 0.99

0.1 0.5 0.9 0.95 0.99 0.99 0.99

0.25 0.2 0.5 0.9 0.95 0.99 0.99

0.5 0.05 0.2 0.5 0.9 0.95 0.99

1.0 0.02 0.05 0.2 0.5 0.9 0.95

6.6.3 Probability of initiation of erosion by suffusion in a layer of cohesionless soil or soil with Plasticity Index ≤ 7 (PI ≤ 12 for seepage gradients > 4)

Check if the soil is potentially internally unstable

From the particle size distribution for the soil, determine the finer fraction which is defined by the point of inflection of broadly graded or gap-graded soils. This is a check on whether the coarser particles will form a matrix into which the finer particles will fit. If the proportion of the finer fraction is less than 40% of the total mass of the soil, continue to assess the probability of the soil being internally unstable as described in the following steps. If the proportion of the finer fraction is more than 40% of the total mass of the soil, the coarse particles will “float” in the finer particles, and suffusion is not possible. These soils may experience backward erosion. If the soil is likely internally unstable, the probability of initiation of erosion by suffusion, PI = (PIUS) x (PSI).

Assess the probability the soil is internally unstable (PIUS)

From the particle size distribution for the soil, determine the d15, d60 and d90 sizes (the particle size for which 15%, 60% and 90% are finer). The grading curve is not adjusted for this procedure. Then estimate the probability the soil is internally unstable (PIUS) from Figure 6.8 for soils with more than 10% fines passing 0.075 mm (#200 sieve), and Figure 6.9 for soils with less than 10% fines passing 0.075 mm.


Section 6

6-34

1 10 100 1000

2

4

6

8

10

[woSUNBD2.GRF]

h' =

d90

/d60

h" = d90 /d15

1 10 100 1000 4000

D1

Data source:Kenney et al. (1983)Kenney et al. (1984)Kenney & Lau (1984, 85)Lafleur et al. (1989)Burenkova (1993)Skempton & Brogan (1994)Chapuis et al. (1996)UNSW

Internally stable soil samples arerepresented by hollow symbols(e.g. , , etc.), andinternally unstable soil samples arerepresented by solid symbols(e.g. , , etc.).

Data point (447, 17.2)plotted out of range

B10.050.100.300.500.70

0.900.95

is the probability, predicted by logisticregression, that a soil is internally unstableif it is plotted along the respectivedotted line .

P

P = exp(Z)/[1 + exp(Z)]Z = 2.378 LOG(h") - 3.648 h' + 3.701

Sun (1989) data and UNSW data points B1,D1 not included in the logistic regression.

P

Figure 6.8 – Contours of the probability of internal instability for silt-sand-gravel soils and clay-silt-sand-gravel soils of limited clay content and plasticity (PI ≤ 12) (Wan and Fell

2004)

1 10 100

2

4

6

8

10

h' =

d90

/d60

h" = d90 /d15

1 10 100 200

0.950.90

0.700.500.30

0.100.05

4R

A3C1

Data source:Kenney et al. (1983)Kenney et al. (1984)Kenney & Lau (1984, 85)Lafleur et al. (1989)Burenkova (1993)Skempton & Brogan (1994)Chapuis et al. (1996)

Internally stable soil samples arerepresented by hollow symbols(e.g. , , etc.), andinternally unstable soil samples arerepresented by solid symbols(e.g. , , etc.).

UNSW (only data points 4R,A3 and C1)

is the probability, predicted by logisticregression, that a soil is internally unstableif it is plotted along the respectivedotted line .

P

P = exp(Z)/[1 + exp(Z)]Z = 3.875 LOG(h") - 3.591 h' + 2.436

Sun (1989) data are not included inthe logistic regression.

P

Figure 6.9 – Contours of the probability of internal instability for sand-gravel soils with less than 10% non-plastic fines passing 0.075 mm (Wan and Fell 2004)


Section 6

6-35

Assess the probability that given the soil is internally unstable erosion by suffusion will begin (PSI)

Assess the probability that given the soil is internally unstable suffusion will begin under the seepage gradient in the highly permeable layer using Table 6.25. The probability of suffusion and backward erosion should both be assessed and carried forward in the analysis.

Table 6.25 – Probability of initiation of erosion by suffusion

Average seepage gradient across embankment core (i) Porosity (volume of voids/total volume of

soil) 0.05 0.1 0.25 0.5 1.0 2.0

<0.20 0.01 0.02 0.05 0.2 0.9 0.99

0.20 to 0.25 0.02 0.05 0.1 0.5 0.95 0.99

0.25 to 0.30 0.05 0.1 0.2 0.9 0.99 0.99

0.30 to 0.35 0.1 0.2 0.5 0.95 0.99 0.99

>0.35 0.2 0.5 0.9 0.99 0.99 0.99

6.6.4 Probability of initiation of erosion in a poorly compacted or high permeability cohesive soil layer and in silt-sand-gravel soils in which collapse settlement may form a crack or flaw (IM13 and IM14)

This section only applies to such zones within the embankment (IM13) and on the embankment-foundation/abutment contact (IM14). It is well-documented that internal erosion and piping occurs in poorly compacted cohesive soils. This is particularly so for dispersive soils. The mechanism is potentially of two types:

• The soil behaves as a series of clods with openings between the clods in which water passes.

• The soil collapses on saturation forming a crack or flaw in which the water flows. This is most likely where there is poorly compacted soil against a pipe but is possible within layers of soil.

To model this it is most practical to assume a crack is formed and to assess the likelihood of erosion initiating in the crack. The procedure is:

• Assess the thickness of the layer of soil which is poorly compacted. (Tp). There may be a single layer or several layers. The minimum layer thickness adopted should be 300 mm (12 in).


Section 6

6-36

• Estimate the amount by which the layer may collapse (CF) using Table 6.26 as a guide. Then, estimate the height of the gap which could result, G = (Tp) x (CF). This represents the scenario with the weight of the soil above being supported on non-collapsed soil adjacent.

• Assume G is the height of the crack which is formed, and use the method outlined in Section 5.5 to estimate the probability of initiation of erosion given this width crack, the average gradient through the core at the level of the high permeability layer, and the soil properties.

This method should be also applied to silty sands, and silty sandy gravel soils which may be subject to collapse settlement even if the soils are non plastic, since they will erode rapidly in a crack.

Table 6.26 – Amount of collapse settlement which may occur on saturation versus compaction properties

Description of the method and degree of compaction of the core

Amount of collapse settlement as a

proportion of the layer thickness

Soil placed with, no formal compaction ( e.g., by horse and cart in old dams, or by pushing into place by excavator or bulldozer or in very thick layers)

No control on layer thickness,

Well dry of optimum moisture content.

Layers very poorly compacted, dry of standard optimum

moisture content e.g., < 90% standard dry density ratio, 3%

dry of standard OWC

0.02 to 0.05


Layer thickness at or beyond the limit of compaction equipment

Dry of optimum moisture content

Layers poorly compacted, dry of standard optimum moisture

content e.g., < 93% standard dry density ratio, 2% to 3% dry

of standard OWC

0.01 to 0.02

Soil rolled in layers near the limit of the capability of the rollers, at moisture contents dry of standard OWC

Compacted to e.g., 93-95% standard dry density ratio,

moisture content 2% to 3% dry of standard OWC

0.005

Soil compacted by suitable rollers in suitable layer thickness

Around optimum moisture content

Well compacted to e.g., 95-98% standard dry density ratio, moisture content 2% dry of

optimum to 1% wet of standard OWC

Will not collapse, but for the poorly compacted layer

within

0.005

As above but with good documentation and records. All very well compacted to e.g., ≥ 98% standard dry density ratio, moisture content 2% dry of optimum to 1% wet of standard OWC

Will not collapse, but for the poorly compacted layer

within

0.005


Section 6

6-37

6.6.5 Probability of initiation of erosion in a high permeability soil due to frost action (IM15 and IM16)

This section only applies to IM15 and IM16. The effects of frost action are complex and include formation of cracks due to heave and formation of ice lenses. The latter may melt in summer months and leave pathways in which erosion may initiate. The procedure is:

• Where there is specific information about frost effects for the dam being assessed, that information should be used by the risk analysis team to assess likely defect widths. In the absence of such data, assess the width of the frost-induced crack using Table 6.27. The selected width should be applied to the full depth of frost penetration since evidence shows ice lenses may be as thick at the base of freezing as at the surface. If the reservoir level under consideration is below the likely depth of freezing, the probability of a crack or poorly compacted zone due to freezing can be assumed to be zero.

• Assess the maximum likely depth of freezing for the soil in the core of the dam based on the frost depth of locality as determined by local building code (preferred method) or from the frost contour map (Sowers 1970) shown in Figure 6.10. The frost depth should be measured from the top of pavement, if present.

• For cases where the reservoir stage is above the base of potential freezing, use the method outlined in Section 5.5 to estimate the probability of initiation of erosion given this width crack or flaw, the average gradient through the core at the level of the high permeability layer, and the soil properties.

Table 6.27 – Width of frost-induced flaw versus ∑(RFxLF)

∑(RFxLF)

from Table 6.6 (IM15)

∑(RFxLF)

from Table 6.8 (IM16) Width of Flaw

(mm)

24 28 20

21 22 10

16 18 5

12 13 2

10 12 0


Section 6

6-38

Figure 6.10 – Map showing the maximum depth of frost penetration from Sowers (1970)

6.6.6 Probability of initiation of erosion in a poorly compacted or high permeability cohesive soil layer adjacent to a conduit (IM17)

This section only applies to section IM17. The method assumes that the critical case is where poorly compacted soil surrounding the conduit collapses on saturation and a gap is formed.

The procedure is:

• Assess the thickness of the layer of soil which is poorly compacted. (Tp). There may be a single layer or several layers.

• Estimate the amount by which the layer may collapse (CF) using Table 6.26 as a guide. Then, estimate the height of the gap which could result, G = (Tp) x (CF). To do this, take account of the dimensions of the conduit and the trench in which it is placed.

• For cases where it appears that the soil around the conduit is well compacted and where crack widths less than 5 mm are calculated, assume a crack width of 5 mm to allow for possible shrinkage of the soil


Section 6

6-39

from the pipe during construction or in service. For poorly compacted soil around the conduit, the minimum layer thickness adopted should be 300 mm (12 in).

• Assume G is the height of the crack which is formed, and use the method outlined in Section 5.5 to estimate the probability of initiation of erosion given this width crack, the average gradient through the core at the level of the high permeability layer, and the soil properties.

6.6.7 Probability of initiation of erosion into a conduit (IM18)

Given an open joint or crack is present, assume a probability of initiation = 1.0.

6.6.8 Probability of initiation of erosion in a poorly compacted or high permeability cohesive soil layer adjacent to a wall (IM19)

If the crack width is unknown from inspection, assume a 5 mm wide crack full-height of the wall and use the method outlined in Section 5.5 to estimate the probability of initiation of erosion given this width crack, the average gradient through the core at the level of the high permeability layer, and the soil properties.

Probability of Initiation of Erosion in a Soil Foundation

Section 7

7-1

7 Probability of Initiation of Erosion in a Soil Foundation

7.1 Screening Check on Soil Classification

If the soil is cohesionless or has a Plasticity Index ≤ 7, then follow the procedures in Section 7.2 to assess the probability of backward erosion and Section 7.3 for suffusion.

If the soil is cohesive with a Plasticity Index > 7, then the likelihood of backwards erosion and suffusion is zero under the seepage gradients which occur in foundations of a conventional dam. Consider if erosion may occur through a crack in the soil using the procedure detailed in Section 7.4. If the seepage gradients are > 4, consider suffusion for soils with a Plasticity Index ≤ 12.

7.2 Probability of Initiation of Backward Erosion in a Layer of Cohesionless Soil or Soil with Plasticity Index ≤ 7 in the Foundation (IM22)



a) Estimate the probability there is a continuous layer of cohesionless soil or soil with PI ≤ 7 across the core from upstream to downstream. The layer does not have to be exposed to the ground surface downstream of the embankment. That is, it may be overlain by a layer of cohesive soil or a confining layer. Assess the probability of a continuous layer (PCL) using subjective estimation methods.

b) If grouting was performed in the cohesionless foundation, evaluate the likelihood of the grouting being ineffective at cutting off the layer using Table 8.19 and Table 8.20 in Section 8.7. If a cut-off wall was installed through the cohesionless layer, evaluate the likelihood of grouting being ineffective at cutting off the layer using Table Table 8.21 and Table 8.22 in Section 8.8.

c) Estimate the probability a seepage exit (Pexit) occurs for the cohesionless layer. Three scenarios are possible. A seepage exit can occur if the cohesionless layer daylights downstream of the dam (e.g., daylights in a toe ditch). The likelihood of this exit condition should be determined using subjective estimation methods. If the cohesionless layer is overlain by a cohesive layer, a seepage exit can occur through the overlying confining layer. A seepage exit through the overlying confining layer can occur through either “heave” of the overlying confining layer or through defects in the confining layer (e.g., animal burrows, roots, etc). Details of assessing the probability of a seepage exit (Pexit) due to heave or defects in the confining layer are given in Section 7.2.3.

d) Calculate the probability of a continuous path with a seepage exit (Pflaw) from the results of the above assessments: (Pflaw) = (PCL) x (Pexit).


Section 7

7-2

e) Estimate the probability of initiation backward erosion given a seepage exit occurs (PI) using Section 7.2.4. For situations where sand boils have been observed, the probability of initiation (PI) for the reservoir level at which sand boils have been observed and above is assumed to be 1.0.

7.2.2 Probability of a continuous layer of cohesionless soil (Pexit)

This section assesses the probability of a continuous cohesionless layer (Pexit) associated with depositional conditions in which the soils were deposited. If there is no continuous layer such as shown in Figure 7.1, then backward erosion is not possible and the probability of backward erosion may be taken as zero. In some situations there will be some uncertainty and the probability of a continuous layer should be assessed from the geotechnical borehole data, understanding of the depositional conditions in which the soils were and deposited, piezometer data, including response of the piezometers to changes in reservoir level. Pexit is likely to be between 0.1 and 1.0 for most situations.

Figure 7.1 – An example of a situation where there is no continuous layer of cohesionless soil in the foundation and backward erosion cannot occur

7.2.3 Probability of a seepage exit (Pexit)

A seepage exit in the cohesionless layer can occur through either an exposed exit (e.g., daylights in a toe ditch, at the toe of the dam, or downstream of the dam) or through an overlying confining layer by heave or through defects. If the cohesionless layer daylights a considerable distance downstream of the dam, then the gradient along the pipe path would be lower and possibly less likely for backward erosion to initiate. However, if a seepage exit occurs through the confining layer at the toe of the dam then the gradients along the pipe path would be higher and more likely for backward erosion to initiate. Thus, it is necessary to evaluate the probability of initiation of backward erosion (PI) for each complete seepage path.

SAND

CLAY

CLAY

3 1 3


Section 7

7-3

No confining layer or cohesionless layer daylights downstream

If the cohesionless layer daylights downstream, assess the probability of a seepage exit (Pexit) using subjective estimation methods. If there is no confining layer or a known location where the cohesionless layer daylights, then Pexit will be 1.0.

Through heave of the confining layer

To determine probability of a seepage exit occurring through heaving of the confining layer, calculate the factor of safety against heave, and then use Table 7.1 to determine Pexit. This method applies to soil confining layers. If the confining layer is hard pan or rock, then the following procedure may not be appropriate.

a) The factor of safety against heave can be determined from the following equations:

FUT = σv/u (1)

where σv = total vertical stress at any point in the foundation, psf (kN/m2)

u = pore pressure at the same point, psf (kN/m2) or

FUT = (h γsat) / (hp γw) (2)

where γsat = unit weight of saturated foundation soil, pcf (kN/m3)

γw = unit weight of water, pcf (kN/m3)

hp = piezometric head, ft (m)

Figure 7.2 – Cross section of an embankment and foundation showing seepage flow net and definition of terms

b) Estimate the probability of a seepage exit occurring through the confining layer from heave (Pexit) using FUT from Table 7.1. If piezometric data is available in the cohesionless layer, this data can be


Section 7

7-4

used to determine the factor of safety against heave for recorded reservoir levels. If possible, the piezometric data may be extrapolated for higher unrecorded reservoir levels. If the factor of safety against heave is greater than 1.3, then the heave is not likely.

Table 7.1 – Probability of a seepage exit through the confining layer (Pexit) versus calculated factor of safety against heave

Factor of safety against heave Probability of a seepage exit through the confining layer

FUT Pexit

> 1.3 Negligible

1.3 0.005

1.23 0.02

1.12 0.05

1.05 0.1

1.0 0.9

0.92 0.99

0.80 0.999

Note: The selected probability should take account of the quality of the data on which the factors of safety are based.

Due to defects in the confining layer

The probability of a seepage exit occurring through defects in a confining layer is mostly governed by the thickness of the confining layer and other factors such as animal burrows, vegetation, utilities, desiccation cracks, etc which may cause defects. If the confining layer is hard pan or rock layer then considerations should given to formation and potential openings in the layer. Due to the complex nature of such layers, this should be handled on a case by case basis.

Generally, for soil confining layers (cohesive layers), the thinner the layer, the more likely these defects penetrate through the layer providing a seepage exit. If the layer thickness is greater than 25 feet, the probability of a seepage exit occurring through defects is negligible. The probability of a seepage exit occurring through defects in a soil confining layer should be assessed using Table 7.2 and Table 7.3. If concentrated seeps have been observed downstream of the dam, it should be assumed that the probability of a seepage exit through defects in the confining layer (Pexit) will be 1.0


Section 7

7-5

Table 7.2 – Factors influencing the likelihood of a seepage exit due to defects in the confining layer


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Confining layer thickness

(3) Thick layer (>25 ft)


Layer thickness 15 to 25 ft

Layer thickness 5 to 15 ft

Thin layer (<5 ft)

Vegetation downstream of the dam (b)

(1) No trees Small woody vegetation (i.e., small trees, bushes)

Small trees with very shallow root systems compared to the layer thickness (layer thickness 10 X depth of root system)

Large trees with shallow root systems compared to layer thickness (layer thickness 5 x depth of root system)

Numerous large trees with deep root systems/tap roots

Numerous downed trees with rotting stumps/root system

Desiccation cracking (b)

(1) Temperate climate with uniform rainfall throughout the year




Low plasticity to non-plastic

(LL < 20)

Medium to low plasticity

(20 < LL < 40)

Medium to high plasticity

(40 < LL < 50)

High plasticity

(LL > 50)

Animal burrows (b)

(1) Very little to no animals burrows found in the area

Few animal burrows found; burrows relatively shallow.

Some animal burrows found in area; burrows moderately deep compared to the layer thickness

Extensive animal burrows found in area; burrows moderately deep compared to the layer thickness

Note: (a) If concentrated seeps are observed downstream of the dam, it is likely that defects exist through the confining layer, and the probability = 1.0.

(b) Other considerations for sources of defects are utilities (buried lines, poles, etc), and an assessment should be made relative to the blanket thickness for these sources.


Section 7

7-6

Table 7.3 – Probability of a seepage exit due to defects in the confining layer (Pexit) versus ∑(RFxLF)

0.0001 0.0005 0.002 0.01 0.1 0.9

6 12 15 18 21 24 RFxLF

7.2.4 Probability of initiation of backward erosion given a seepage exit exists

Given sand boils have been observed

If sand boils have been observed it should be assumed that the probability of initiation of backward erosion will be 1.0 for reservoir levels at or above the level at which sand boils have been observed. For lower reservoir levels use the procedure given below for when a seepage exit is predicted. This applies to sand boils with moving sand but not pin boils.

In these sections the probability of initiation of backward erosion only covers whether the backwards erosion process will progress within the developing pipes. It does not include assessment of whether a roof will form and whether flow limitation may occur. These are covered in Section 11.

Given a seepage exit is predicted

Whether backwards erosion will progress to develop a pipe all the way from the downstream toe to upstream of the dam depends on the gradients along the pipe path. For practical purposes, in most cases, this can be taken as the average seepage gradient (iavf) in the foundation layer beneath the dam at the midpoint of the pipe path at the reservoir stage under consideration.

The average seepage gradient (iavf) is defined as the hydraulic head difference divided by the seepage path length. However, if there is upstream blanketing with lower permeability soil, much of the head may be lost in seepage through this “blanket.” If in doubt, neglect the blanketing effect. For cases, where a seepage exit is likely at the toe of the dam (either through heave or defects), this gradient may be estimated as (H2 – H3)/L in Figure 7.3. This allows for the head losses through the upstream clay layer.


Section 7

7-7

Figure 7.3 – Section through embankment and foundation showing definition of terms to estimate the average gradient in the foundation sand

If there is a sheet pile, soil-bentonite or concrete cut-off wall, the gradient of interest is the average gradient in the soil subject to backward erosion from downstream of the cut-off wall to the toe of the embankment allowing for the effectiveness of the cut-off wall. This is discussed further in Section S7.3.2 of the Supporting Document.

As discussed previously, the location of the seepage exit is important to determine the pipe path and average seepage gradient at the midpoint of the path. Typically, for heave the critical locations exists where the confining layer is the thinnest, and the uplift pressures are the highest. This occurs typically at the toe of the dam or at a near by toe ditch.

For seepage exits through defects using Table 7.2 and Table 7.3, the assumption is made that these defects occur at the toe of the dam. The gradients are calculated along the midpoint of pipe path where the path extends from the upstream toe of the dam to the downstream toe of the dam. For seepage exits where the cohesionless layer daylights downstream of the dam, the pipe path extends from upstream toe of the dam to point where the cohesionless layer daylights downstream of the dam.

Once the average seepage gradient has been determined, other factors such as particle size characteristics, permeability of the soil, and the geometry of the embankment and the foundation are considered. In the absence of more definite methods, the following procedure is used to determine the probability of initiation of backwards erosion given a seepage exit is predicted:

• Estimate the average seepage gradient (iavf) through the cohesionless soil layer in the foundation beneath the dam at the midpoint of the pipe path (not at the toe where there are likely to be locally higher gradients) for the level for the reservoir stage under consideration.

L (to downstream exit location)

H1

Reservoir level Piezometric surface at base of clay layer

Sand

ClayH2

Piezometric surface at base of clay layer

H3

Note heave is calculated at the base of the clay layer here

T


Section 7

7-8

• From the particle size distribution of the foundation material, estimate a representative uniformity coefficient, cu = D60/D10.


• Correct this average gradient for the geometry, horizontal to vertical permeability ratio of the zone subject to backward erosion, and grain size as detailed in Section 6.6.2 to obtain (ipmt)corrected.

• If cu > 6, estimate the critical gradient (icr) from icr = (γsat – γw)/ γw for vertical exits (e.g., heave or defects in the confining layer) or icr = [(γsat– γw)/ γw] tan(φ) for horizontal exits (e.g., cohesionless layer daylights into a toe ditch).

• Estimate the exit gradient for the seepage path under consideration. If the layer is exposed at the ground surface downstream of the embankment, estimate the exit gradient from a seepage analysis. For seepage exits through the overlying confining layer due to heave or defects, assume a continuous column of sand from the base of the confining layer to the ground surface, and estimate the exit gradient by ie = (H3 – T)/T. Calculate the factor of safety for the exit gradient, FSe = [icr or (ipmt)corrected)]/ie. If the factor of safety is greater than 1.3, then the probability of initiation is negligible.

• Estimate the probability of initiation of backward erosion given a seepage exit occurs from Table 7.4.

Table 7.4 – Probability of initiation of backward erosion in the foundation given a seepage exit is predicted

Average seepage gradient in the foundation (iavf) Average seepage gradient required

to initiate and progress

backward erosion (i pmt) corrected or icr

0.05

0.1

0.25

0.5

0.75

1.0

2.0

0.05 0.62 0.9285 0.9987 1.0000 1.0000 1.0000 1.0000

0.1 0.19 0.62 0.9671 0.9987 0.9999 1.0000 1.0000

0.25 0.008 0.11 0.62 0.93 0.98 0.9958 0.9999

0.5 0.0002 0.008 0.19 0.62 0.84 0.93 0.9958

0.75 0.00001 0.001 0.06 0.35 0.62 0.78 0.97

1.0 0.000001 0.0002 0.02 0.19 0.43 0.62 0.93


Section 7

7-9

7.3 Probability of Initiation of Suffusion in a Cohesionless Layer in the Foundation (IM23)


a) Use the methods outlined in Section 7.2.1 and 7.2.3 to estimate the probability of a continuous path with a seepage exit (Pflaw) = (PCL) x (Pexit).

b) Use the method outlined in Section 7.2.4 to estimate the factor of safety for the exit gradient. If the factor of safety is greater than 1.3, then the probability of initiation is negligible.

c) Use the method outlined in Section 6.6.3 to estimate the probability the soil is internally unstable (PIUS) and the probability that given the soil is internally unstable erosion by suffusion will begin (PSI). Table 6.25 should to determine PSI using the average gradient in the foundation layer.

d) Estimate the probability of initiation of erosion by suffusion by (PI) = (PIUS) x (PSI).

7.4 Probability of Initiation of Erosion in a Crack in Cohesive Soil in the Foundation (IM24)



a) Estimate the probability (PCL) of a layer of cohesive soil containing a continuous crack or interconnected pattern of cracks across the core from upstream to downstream. Cracking may be the result of differential settlement in the foundation, or desiccation cracks in the foundation soil which was not stripped from the foundation, or other causes.

b) If Scenario (b) in Figure 5.4 is applicable, estimate the probability of cracking due to differential settlement using Table 5.7 and Table 5.8 in Section 5.2.4. The probabilities obtained are modified for observed settlement using Table 5.21 (factors for lower part of the embankment) in Section 5.4 to obtain Pflaw.4. If the cracking is due to desiccation, estimate the probability of cracking using Table 5.11 and Table 5.12 (Below POR only) in Section 5.2.7 to obtain Pflaw.7. If the cracking is due to other causes, assess the probability of a flaw using subjective estimation methods.

c) If grouting was performed within the maximum depth of likely cracking in the foundation, evaluate the likelihood of the grouting being ineffective at cutting off the cracking using Table 8.19 and Table 8.20 in Section 8.7. If a cut-off wall was installed through the maximum depth of likely cracking in the foundation, evaluate the likelihood of grouting being ineffective at cutting off the cracking using Table 8.21 and Table 8.22 in Section 8.8.


Section 7

7-10

d) Calculate the probability of a flaw (Pflaw) from the results of the above assessments: (Pflaw) = (PCL) x (Pflaw.4 or Pflaw.7 or Pflaw.other).

e) Estimate the probability erosion will initiate in the cracks (PI) using Section 5.5. Unless crack widths are documented, assumed a 5 mm wide crack.

7.4.2 Some factors to consider in this assessment and suggested method for estimating the probability of a continuous crack

For cracking due to differential settlement

The situations which are likely to result in cracking in the foundation soils are essentially the same as those causing cracking low in the embankment due to differential settlement in the foundation. An example is shown in Figure 5.5(b). Given this, it is suggested that if in using Section 5.2.4 to assess the probability of cracking in the embankment due to differential settlement in the foundation, the presence of cracking in the embankment is likely to be on the foundation/embankment contact, then this probability also be assigned to the probability of cracking in the cohesive soil in the foundation beneath the embankment.

If the assessment of cracking in Section 5.2.4 is for features such as those in Figure 5.5(a) and (c) which will cause cracking near the crest of the dam, then cracking in the foundation due to differential settlement may be assumed to be negligible.

For cracking due to desiccation

Some factors to consider in assessing the likelihood of continuous or interconnected cracking include:

• Whether desiccation cracking is evident in the soil surrounding the dam.

• Whether the foundation soil is susceptible to desiccation in the climatic conditions at the site

• Whether good construction practices regarding clean-up of desiccated layers were used before embankment fill placement

Assess the likelihood of desiccation cracking using Section 5.2.7 and Table 5.11 and Table 5.12 considering the foundation soil as the “core material” and using “Below POR” values for all pools.

For cracking due to other causes

For cracking due to other causes, use subjective estimation methods to estimate the likelihood of cracking.

Probability of Continuous Open Defects in the Rock Foundation

Section 8

8-1

8 Probability of Continuous Open Defects in the Rock Foundation


The overall approach to determine the probability of continuous defects in rock is primarily based on judgment (degree of belief). When using the judgment tables included in this chapter it is critical that the risk assessor perform a complete evaluation of the available data and summarize the factors from the data that support their selections. The factors should be list under factors that make the item more likely and factors that make the item less likely.

The framework considers the geological processes which can lead to the formation of defects in rock. The geological processes considered are:

• Defects related to stress relief effects in the valley sides (Section 8.2).

• Defects related to stress relief effects in the valley floor – valley bulge and rebound (Section 8.3).

• Solution features for rock subject to solution such as limestone, dolomite, gypsum and salt (Section 8.4).

• Defects associated with landslides and faults and shear zones.(Section 8.5)

Tables have been produced to evaluate the probabilities for assessing the presence of continuous defects caused by these geological processes. For each applicable geological process four defect width ranges should be evaluated:

• <5 mm

• 5 to 25 mm

• 25 to 100 mm

• >100 mm

An outline of the overall approach is summarized in the flow chart shown in Figure 8.1.

The steps to assess the probability such defects and solution features exist in the dam foundation below the core are as follows:

a) Evaluate the geological profile through the dam and abutments. Determine if the profile should be divided up into separate segments based on differences in geology or foundation treatment.

b) Assess the probability of one or more continuous defects in the rock in the foundation beneath the core of the embankment for each type of applicable geological feature.

c) For each type of geological feature, there are two parts to the assessment. The first is based on the geology and topography of the dam site (PGT). This information will be available for all dam sites. The


Section 8

8-2

second is based on observations and site investigation data (PSC) of which there will be greatly varying amounts for different dams. It is anticipated that for some older dams there may be virtually no such data.

d) The two estimates are combined by a weighted average (Pw) depending on the detail of the investigation and construction data that is available with greater weighting to the second method where there is good quality data available (Section 8.6). The relative importance factors are selected taking account of the data which is likely to be available.

e) Assess the probability that grouting has not been effective (PGI) in cutting off the open defects (Section 8.7).

f) Assess the probability of cut-off walls not being effective (PCI) in cutting off defects (Section 8.8).

g) Assess the probability that foundation surface treatment (PTI) has not been effective in preventing contact of the core with the defects (Section 8.9).

h) Calculate the probability of a continuous rock defect (PCR) by multiplying the probabilities from the previous steps. If more than one geological process applies, then combine the probabilities for each defect size using DeMorgan’s Rule.

i) Describe the defects, their width, depth, spatial distribution in the foundation, and how these relate to the cut-off and general foundation of the embankment beneath the core. In particular identify features which will be in contact with the core at the base of the cut-off and in the sides of the cut-off trench.


Section 8

8-3

Figure 8.1 – Flow chart for estimating the probability, width, depth and spatial distribution of continuous open defects and solution features in rock foundations

Probability of one or more continuous defect (stress relief in the valley sides, valley bulge or rebound, solution features, and other geological features)

Make estimates based on: • Geologic/topographic factors; and • Site investigation/construction/performance factors

Probabilities are estimated for four widths <5 mm, 5 to 25 mm, 25 to 100 mm, and >100 mm).

Combine the estimates using a weighted average. (Pw)

Is grouting ineffective? (PGI)

Calculate the probability estimates for continuous rock defects. PCR= (Pw) (PGI) (PCI) (PTI)

Prepare a summary of the probability of occurrence of open defects categorized by width, depth and spatial occurrence in the embankment foundation. Prepare sketches showing the defects in relation to the cut-off foundation beneath the core, general foundation under the shoulders, foundation grouting and cut-off foundation surface treatment. Identify the failure modes and breach mechanisms which may develop from the presence of these features.

Is a cutoff wall ineffective? (PCI)

Is rock surface treatment ineffective? (PTI)

If more than one geologic process applies then combine the probabilities for each defect size using DeMorgan’s Rule.


Section 8

8-4

8.2 Probability of Continuous Defects in the Rock Foundation due to Stress Relief in the Valley Sides

8.2.1 Overview of method

This section assesses the probability of a stress relief feature in the valley sides such as a joint or joint set or bedding surface being continuous in the dam foundation from upstream of the core of the embankment to downstream of the core. It does not consider whether these are cut-off by the foundation excavation, grouting or other treatment. That is considered later.

Estimate the probabilities of features of all 4 defect sizes. Defects of each width may all be present, and each should be considered because of their likely impact on the probability of breach of the embankment. The widths for stress relief features are at the ground surface, not accounting for the depth of the cut-off of the embankment.

This is done in two ways:

• Based on the geology and topography of the site. This data will be available for all dams.

• Based on observations during site investigations, construction, and performance monitoring. There will be varying amounts of this data for each dam.

The weighted average of these estimates is carried forward in the analysis. The weighting relates to the detail of the investigations and construction data available.

8.2.2 Probability of continuous rock defects due to stress relief in the valley sides based on geologic and topographic data (PGT)

The defects are stress relief joints, sheet joints, and bedding surface partings. The major variables affecting the likelihood of these being in the dam foundation, and their relative importance are:

• Geological environment. It is known that interbedded weak and strong rocks such as interbedded shale and sandstone commonly result in open joints due to differential strains due to stress relief on valley formation with these strains being concentrated in bedding surface shears in the weaker rock. The other geological environments where stress relief defects are common are massive rocks such as granite. These are commonly called sheet joints.

• Topography. The topography which is likely to lead to stress relief features. This is dependent on the depth of valley and steepness of valley sides.

• Continuity of mapped defects in the exposure of rock in the abutments or regional outcrops.


Section 8

8-5

Use Table 8.1 to Table 8.3 to estimate the probability of one or more continuous stress relief features in the rock in the foundation beneath the embankment. In Table 8.3, the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total greater than 1.0 because they are not conditional probabilities. Where the geology of the site is not covered in Table 8.1, the risk analysis team should assess which of the descriptions in Table 8.1 best suits the geology of the site.

Table 8.1 – Geologic and topographic factors influencing the likelihood of continuous rock defects due to stress relief in the valley sides


Factor

Relative Importance

of Factor (RF)

Less Likely

(1)

Neutral

(2)

More Likely

(3)

Much More Likely

(4)

Geological environment likely to give features related to stress relief in the valley sides

(3) Shale not containing other rocks (sub-horizontal bedded)

Uniform sandstone (sub-horizontal bedded)

Schistose, steeply dipping

Granite

Basalt(a) columnar

Rhyolite, ignimbrite(a)

Schistose parallel to abutment

Thinly inter-bedded sedimentary

Sedimentary – inter-bedded thin beds of mud rocks and thick beds of sandstone or limestone/dolomite or conglomerate

Volcanics, inter-bedded thin beds of tuff or other soft rocks, with thick beds of hard rocks

Topography of the dam site (steepness and valley depth)

(2)

LL from Table 8.2 matrix

N from Table 8.2 matrix

ML from Table 8.2 matrix

MML from Table 8.2 matrix

Continuity (b) of defects from surface mapping or regional outcrops

(1) Discontinuous Possible interconnectivity

Interconnected defects

Continuous defects

Notes: (a) Some basalts (e.g., if interbedded with weak tuff, and some ignimbrites) may classify as MML. (b) Continuity should be judged based on a length equivalent to the width of the core in the upstream-downstream

direction.


Section 8

8-6

Table 8.2 – Factors influencing likelihood for topography

Average Abutment Slope (degrees) (a) (b) Valley Depth

<20 20 to 45 45 to 60 >60

<100 ft (<30 m)

LL LL N ML

100-300 ft (30-100 m)

LL N ML MML

300-1000 ft (100 – 300 m)

LL ML MML MML

>1000 ft (>300 m)

N ML MML MML

Notes: (a) Use average overall slope except for slopes with large colluvium deposits overlying the rock surface, in which case use the slope of the rock surface.

(b) For slopes with more than 20 ft (6 m) high cliffs, adopt a category not lower than ML.

Table 8.3 – Probability of continuous rock defects due to stress relief in the valley sides based on geologic and topographic data (PGT) versus ∑(RFxLF)

Defect width

<5 mm 0.005 0.01 0.05 0.1 0.9 1.0

5-25 mm 0.001 0.005 0.01 0.05 0.5 0.9

25-100 mm 0.0005 0.001 0.005 0.01 0.1 0.5

>100 mm 0.0001 0.0002 0.001 0.005 0.02 0.2

RFxLF 6 9 11 13 18 24


Section 8

8-7

8.2.3 Probability of continuous rock defects due to stress relief in the valley sides based on site investigations, construction, and performance data (PSC)

The evaluation will determine the likelihood that the defects are present and the likelihood that the defects are continuous across the core from upstream to downstream.

Review all available data from site investigation, construction records, and performance monitoring. This data can include: records/photographs from excavations, tunnels, down hole imaging, high water losses in drilling, high grout takes, core loss, drill rods dropping, high leakage rate in dam foundation, seepage observations, abnormal piezometric levels in the abutments.

The data should be summarized in a format that will support the selection made from Table 8.4. List the factors that make it “more likely” and “less likely” that defects are present. Do the same for the factors the make it “more likely” and “less likely” the defects are continuous.

Estimate the probability of one or more continuous defects from Table 8.4 and Table 8.5. Do this for each defect width. It is expected that there will be different probabilities for each defect size. Note that in Table 8.5 the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total greater than 1.0 because they are not conditional probabilities.

Table 8.4 – Site investigation, construction, and performance factors influencing the likelihood of continuous rock defects due to stress relief in the valley sides


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Data indicating defects of this size are/are not present

(3)

Good quality data indicates defects of this size are very unlikely to be present

Data indicates circumstantial evidence that defects of this size are unlikely to be present

Data indicates circumstantial evidence that defects of this size are present

Good quality data indicates defects of this size are present

Data indicating defects of this size are continuous across the core

(3) Good quality data indicates that defects of this size are isolated and/or discontinuous

Data indicates circumstantial evidence that defects of this size are isolated and/or discontinuous

Data indicates circumstantial evidence one or more defect of this size could be continuous

Good quality data indicates defects of this size are continuous


Section 8

8-8

Table 8.5 – Probability of continuous rock defects due to stress relief in the valley sides based on site investigation, construction, and performance data (PSC) versus ∑(RFxLF)

0.001 0.01 0.1 0.2 0.5 0.99

RFxLF 6 9 11 13 18 24

8.2.4 Effects of blasting on the foundation

The potential for blasting of the rock foundation to lead to open defects should be assessed (e.g., for the cut-off or to form a trench into which the diversion conduit is placed). This can only be assessed on a case by case approach. Construction photographs are the best guide as to whether such features may exist, and their likely continuity and opening.

8.3 Probability of Continuous Defects in the Rock Foundation due to Valley Bulge or Rebound


This section assesses the probability of an open or in-filled valley bulge or rebound feature such as a joint or joint set, thrust fault, or bedding surface being continuous in the foundation from upstream of the core of the embankment to downstream of the core. It does not consider whether these are cut-off by the foundation excavation, grouting or other treatment. That is considered later.

Estimate the probabilities of features of all 4 defect sizes. Defects of each width may all be present, and each should be considered because of their likely impact on the probability of breach of the embankment. The widths are at the ground surface not accounting for the depth of the cut-off of the embankment.






Section 8

8-9

8.3.2 Probability of continuous rock defects due to valley bulge or rebound based on geologic and topographic data (PGT)

The major variables and their relative importance are:

• Geological environment. Valley bulge or rebound features only occur in near horizontally bedded sedimentary rocks, and in particular where there are interbeds of strong rock such as sandstone, with weaker rocks such as shale or claystone on which differential movements due to stress relief are concentrated. For other geological environments assume the probability of valley bulge or rebound defects is negligible.

• Potential for buckling or strut shear. The presence of beds of stronger rock underlain by weaker rock in the valley floor and the slenderness of the strut as characterized by the relative thickness of the strong rock bed compared to the valley width.

• Topography. The topography which is likely to lead to stress relief features. This is dependent on the depth of valley and steepness of valley sides.

These assessments do not rely on mapping of the dam foundation during site investigations and construction.

Use Table 8.6 and Table 8.7 to estimate the probability of one or more continuous valley bulge or rebound features in the rock in the foundation beneath the embankment. In Table 8.7, the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total greater than 1.0 because they are not conditional probabilities.


Section 8

8-10

Table 8.6 – Geologic and topographic factors influencing the likelihood of continuous rock defects due to valley bulge or rebound

Influence on Likelihood

Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Geological environment likely to give valley bulge or rebound features

(3) Shale or siltstone not containing other rocks

Uniform sandstone

Note: If this condition is present, the probability is zero.

Thick beds of siltstone or shale inter-bedded with massive beds of sandstone, limestone, dolomite or conglomerate

Thin beds of siltstone inter-bedded with massive beds of sandstone, limestone, dolomite or conglomerate

Thin beds of claystone or shale inter-bedded with massive beds of sandstone, limestone, dolomite or conglomerate

Potential for buckling or strut failure relating to slenderness of the strut

(2)

(Valley floor width) / (strut thickness) <1

(Valley floor width) / (strut thickness) >2



Topography of the dam site (steepness and valley depth)

(1) LL from Table 8.2 matrix

N from Table 8.2 matrix

ML from Table 8.2 matrix

MML from Table 8.2 matrix

Table 8.7 – Probability of continuous rock defects due to valley bulge or rebound based on geologic and topographic data (PGT) versus ∑(RFxLF)

Defect width

<5 mm 0.005 0.01 0.05 0.1 0.9 1.0

5-25 mm 0.001 0.01 0.1 0.2 0.5 0.9

25-100 mm 0.0005 0.001 0.005 0.02 0.2 0.5

>100 mm 0.0001 0.0002 0.001 0.005 0.05 0.2

RFxLF 6 9 11 14 18 24


Section 8

8-11

8.3.3 Probability of continuous rock defects due to valley bulge or rebound based on site investigations, construction, and performance data (PSC).





Table 8.8 – Site investigation, construction, and performance factors influencing the likelihood of continuous rock defects due to valley bulge or rebound


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)


(3)











Section 8

8-12

Table 8.9 – Probability of continuous rock defects due to valley bulge or rebound based on site investigation, construction, and performance data (PSC ) versus ∑(RFxLF)

0.001 0.01 0.1 0.2 0.5 0.99

RFxLF 6 9 11 13 18 24

8.4 Probability of Continuous Defects in the Rock Foundation due to Solution Features


Screening

This Section applies only to rock foundations subject to solution such as limestone, dolomite, gypsum and salt.

Approach

This section assesses the probability of a solution feature in the dam foundation being continuous from upstream of the core of the embankment to downstream of the core. It does not consider whether these are cut-off by the foundation excavation, grouting or other treatment. That is considered later.







Section 8

8-13

8.4.2 Probability of continuous rock defects due to solution features based on geologic and topographic data (PGT)


• Geological environment. The presence or absence in the region and dam site of karst and solution features. This is based on geologic literature related to the formations present in the dam’s foundation and abutments.

• The topography which is likely to lead to the presence or absence of regional defects such as sinkholes, caves, pinnacled rock outcrops. This is based on topographic mapping, aerial photographs, and observations of rock outcrops.

• Continuity of regional defects relative to the width of the core in the upstream-downstream direction.

These assessments do not rely on mapping of the dam foundation during investigations and construction.

Use Table 8.10 to Table 8.11 to estimate the probability of one or more continuous solution features in the rock foundation beneath the embankment. In Table 8.11, the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total greater than 1.0 because they are not conditional probabilities.


Section 8

8-14

Table 8.10 – Geologic and topographic factors influencing the likelihood of continuous rock defects due to solution features


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Geological environment relating to development of solution features

(3) Regional geologic documentation indicates rock formations in the dam foundation or abutments do not contain solution features

Regional geologic documentation on the rock formations in the dam foundation or abutments does not mention the presence or absence of solution features

Regional geologic documentation indicates rock formations in the dam foundation or abutments contain occasional solution features

Regional geologic documentation indicates rock formations in the dam foundation or abutments contain numerous solution features

Regional defects observable on topographic mapping, aerial photographs or outcrops

(2) High quality evidence of no sinkholes, caves, or pinnacled rock in the region

No good quality mapping, photos, or outcrops available

Good quality evidence of occasional sinkholes, caves, or pinnacled rock

Good quality evidence of numerous sinkholes, caves, or pinnacled rock

Continuity (a) of defects from surface mapping or regional outcrops



Continuous defects

Note: (a) Continuity should be judged based on a length equivalent to the width of the core in the upstream-downstream direction.

Table 8.11 – Probability of continuous rock defects due to solution features based on geologic and topographic data (PGT) versus ∑(RFxLF)

0.001 0.01 0.1 0.2 0.5 0.99

RFxLF 6 9 11 13 18 24


Section 8

8-15

8.4.3 Probability of continuous rock defects due to solution features based on site investigations, construction, and performance data (PSC)





Table 8.12 – Site investigation, construction, and performance factors influencing the likelihood of continuous rock defects due to solution features


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)


(3)











Section 8

8-16

Table 8.13 – Probability of continuous rock defects due to solution features based on site investigation, construction, and performance data (PSC) versus ∑(RFxLF)

0.001 0.01 0.1 0.2 0.5 0.99

RFxLF 6 9 11 13 18 24

8.5 Probability of Continuous Defects in the Rock Foundation due to Other Geological Features such as Landslides, Faults, or Shears


Approach

This section assesses the probability of a feature associated with geological processes other than stress relief or solution features. These include defects related to landslides in rock, such as joints and bedding surface partings, and fault or shear zones. This section assesses the probability of a defect in the dam foundation continuous from upstream of the core of the embankment to downstream of the core. It does not consider whether these are cut-off by the foundation excavation, grouting or other treatment. That is considered later.







Section 8

8-17

8.5.2 Probability of continuous rock defects due to landslides, faults, or shears based on geologic and topographic data (PGT)


• Geological environment. The presence or absence in the region and dam site of rock slides or faulting. This is based on geologic literature related to the formations present in the dam’s foundation and abutments.

• The topography which is likely to lead to the presence or absence of regional defects such as rock slides or faults. This is based on topographic mapping, aerial photographs, and observations of rock outcrops.

• Continuity of regional defects relative to the width of the core in the upstream-downstream direction.

These assessments do not rely on mapping of the dam foundation during investigations and construction.

Use Table 8.14 to Table 8.15 to estimate the probability of a continuous defect in the rock foundation beneath the embankment. Note that in Table 8.14 the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total > 1.0 because they are not conditional probabilities.


Section 8

8-18

Table 8.14 – Geologic and topographic factors influencing the likelihood of continuous rock defects due to landslides, faults, or shears


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Geological environment relating to development of landslides, faults, or shears

(3) Regional geologic documentation indicates rock formations in the dam foundation or abutments do not contain defects due to rock slides, faults or shears

Regional geologic documentation on the rock formations in the dam foundation or abutments does not mention the presence or absence of rock slides, faults or shears

Regional geologic documentation indicates rock formations in the dam foundation or abutments contain occasional defects due to rock slides, faults or shears

Regional geologic documentation indicates rock formations in the dam foundation or abutments contain numerous defects due to rock slides, faults or shears

Regional defects observable on topographic mapping, aerial photographs or outcrops

(2) High quality evidence of no rock slides, faults, or shears

No good quality mapping, photos, or outcrops available

Good quality evidence of occasional defects due to rock slides, faults or shears

Good quality evidence of numerous defects due to rock slides, faults or shears

Continuity (a) of defects from surface mapping or regional outcrops



Continuous defects

Note: (a) Continuity should be judged based on a length equivalent to the width of the core in the upstream-downstream direction.

Table 8.15 – Probability of continuous rock defects due to landslides, faults, or shears based on geologic and topographic factors (PGT) versus ∑(RFxLF)

0.001 0.01 0.1 0.2 0.5 0.99

RFxLF 6 9 11 13 18 24


Section 8

8-19

8.5.3 Probability of continuous rock defects due to landslides, faults, or shears based on site investigations, construction, and performance data (PSC)





Table 8.16 – Site investigation, construction, and performance factors influencing the likelihood of continuous rock defects due to landslides, faults, or shears


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)


(3)











Section 8

8-20

Table 8.17 – Probability of continuous rock defects due to landslides, faults, or shears based on site investigation, construction, and performance data (PSC) versus ∑(RFxLF)

0.001 0.01 0.1 0.2 0.5 0.99

RFxLF 6 9 11 13 18 24

8.6 Weighted Averages of Estimated Probability of Continuous Rock Defects

In Sections 8.2 to 8.5, two estimates are made of the probability of the presence of defects. The first is based on geologic and topographic information (PGT) which should be available for all dam sites. The second (PSC) depends on having more detailed site investigations and construction records, which for some dams will be not available, or there will be limited data. The weighted estimate of the probability (Pw) should be estimated:

Pw = w PGT + (1 – w) PSC

where w = weighting factor to be assessed based on the quantity and quality of the available data. Table 8.18 provides some guidance in assessing the weighting factor.

Table 8.18 – Weighting factors for assessing probabilities of open or in-filled rock defects

Information Available Weighting Factor (w)

No site investigations or construction mapping or other records 1.0

Limited site investigations data (e.g., small number of boreholes, no or poor quality water pressure testing data, no mapping of the embankment cut-off foundation or grouting records, no foundation treatment information or photographs of foundations)

0.7 to 0.9

Some site investigations data (e.g., small number of boreholes or larger number but poor quality boreholes, Sparse or poor quality water pressure testing data, no mapping of the embankment cut-off foundation or grouting records, no foundation treatment information or photographs of foundations)

0.6 to 0.8

Some good quality site investigations data and water pressure testing, limited mapping of the embankment cut-off foundation, basic grouting records, no records of foundation treatment some photographs of foundations

0.4 to 0.6

Extensive good quality site investigations data and water pressure testing, reasonable quality mapping of the embankment cut-off foundation, and grouting records, some records of foundation treatment and photographs of foundations

0.2 to 0.4

Very detailed and good quality site investigations data, good quality mapping of the embankment cut-off foundation, grouting records, foundation treatment and photographs of foundations

0.1 to 0.2


Section 8

8-21

8.7 Probability of Grouting Being Ineffective in Cutting Off Rock Defects (PGI)

Evaluate the likelihood of grouting not being effective in cutting off the potential defect using Table 8.19 and Table 8.20. If no grouting was performed assume PGI = 1.0.

Table 8.19 – Factors influencing the likelihood of grouting not being effective in cutting off rock defects


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4) Orientation of grout holes compared with the open defects(a)

(3) (c)

Grout holes at a wide angle to the dip of the open defect (45 to 90 degrees)

Grout holes at an acute angle to dip of open defects (30 to 45 degrees)

Grout holes at an acute angle to dip of open defects (10 to 30 degrees)

Grout holes parallel or near parallel to dip of open defects (<10 degrees)

Quality of grouting (closure, number of lines, spacing, grout takes, w/c ratio)

(2)

Three or more lines of grout curtain, with primary holes 6m (20ft) or less spacing, secondary, tertiary etc holes to close to < 10 lugeons or <25 kg cement /meter (15lb/ft) take, W/C ratio < 3

Single line grout curtain with primary holes 6m (20ft) or less spacing, secondary, tertiary etc holes to close to < 10 lugeons or <25 kg cement /meter (15lb/ft) take, W/C ratio < 3

Single line curtain 5m to 6m (15 ft to 20 ft) spacing, no check of closure, high (>5:1 ) W/C ratio

Single line curtain, > 10m (30ft) spacing, single stage, no secondary holes to check closure, high (>10:1 ) W/C ratio

Note: Select LF=4 if in-filled or partially in-filled defects are present.

Performance (pore pressures and leakage) (b)

(1) (c)

Significant reduction in foundation pore pressures across the grout curtain (Δhp/hp >60%) Very low leakage in the foundation(c)

Moderate reduction in pore pressures across grout curtain (Δhp/hp = 30% to 60%) Low leakage in the foundation

Minor reduction in pore pressures across grout curtain (Δhp/hp = 10% to 30%) Moderate to high leakage in the foundation

No or very little reduction in pore pressures across grout curtain (Δhp/hp <10%) High leakage in the foundation OR No performance data available at all


Section 8

8-22

Notes: (a) The dip of the open defect will depend on the type of defect:

• For stress relief defects in the valley wall in inter-bedded sedimentary rock, these defects are likely to be near vertical and parallel to the valley walls (refer to Figure 8.4a). For stress relief defects associated with massive rocks, these are likely to be parallel to the valley slopes (refer to Figure 8.4b).

• Defects associated with valley bulge are likely to be horizontal or near horizontal. • Solution features are more likely to develop along the predominant defects sets.

(b) Refer to Figure 8.2 for definition of Δhp and hp. When making this assessment takes account of the amount and quality of the instrumentation, the duration and range of reservoir levels of the observations.

(c) If there is very good instrumentation which can measure the effectiveness of the grouting to a high degree of confidence, and there is a large drop in pore pressure across the grouting, use LF=3 for performance factor and LF=1 for orientation factor.

Figure 8.2 – Definition of Δhp and hp

Table 8.20 – Probability of grouting not being effective for continuous rock defects (PGI)

versus ∑(RFxLF)

<5 mm 0.0005 0.005 0.03 0.1 0.4 0.85

5-25 mm 0.001 0.01 0.05 0.2 0.5 0.9

25-100 mm 0.002 0.02 0.1 0.3 0.6 0.95

>100 mm 0.005 0.05 0.2 0.5 0.8 0.99

RFxLF 6 9 11 13 18 24

hp Δhp

Piezometer Rock Foundation

Grout curtain


Section 8

8-23

8.8 Probability of Cut-Off Walls Being Ineffective in Cutting Off Rock Defects (PCI)

Where a cut-off has been excavated and backfilled in the rock foundation to intercept the continuous defects, use Table 8.21 and Table 8.22 to assess the probability the cut-off has not been successful and a continuous open defect or solution feature remains. If no cut-off wall is present assume PCI = 1.0.

In assigning the weightings it is assumed that for such cut-offs there will be good quality monitoring of the pore pressure drop across the cut-off.


Section 8

8-24

Table 8.21 – Factors influencing the likelihood of a cut-off in the foundation not being effective for continuous defects


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Extent and depth of the cut-off relative to the defects

(3) Extent and depth of the defects well defined and cut-off extends sufficiently wide and deep

Extent and depth of the defects not well defined cut-off may or may not extend sufficiently wide and deep

Extent and depth of the defects not well defined and cut-off probably does not extend sufficiently wide and deep

Extent and depth of the defects well defined and cut-off does not extend sufficiently wide and deep

Performance (pore pressures and leakage) (a)

(2) Significant reduction in foundation pore pressures across the cut-off wall (Δhp/hp >60%)

Very low leakage in the foundation

Moderate reduction in pore pressures across cut-off wall (Δhp/hp = 30% to 60%)

Low leakage in the foundation

Minor reduction in pore pressures across cut-off wall (Δhp/hp = 10% to 30%)

Moderate to high leakage in the foundation

No or very little reduction in pore pressures across cut-off wall (Δhp/hp <10%)

High leakage in the foundation

OR

No performance data

Quality of the cut-off

(1) Excavated open hole or under water, borehole camera inspection to confirm defects are intercepted

and

Concrete, or bentonite, cement, sand gravel backfill

Excavated under bentonite, good clean-up of the base of the excavation, and overlap between panels or piers

and/or

Concrete, or bentonite, cement, sand gravel backfill

Excavated under bentonite, moderate clean-up of the base of the excavation, and overlap between panels or piers

and/or

Bentonite cement or poorly controlled concrete or cement, sand gravel backfill

Excavated under bentonite, poor clean-up of the base of the excavation, poor overlap between panels or piers

and/or

Bentonite cement or soil bentonite backfill

Note: (a) Refer to Figure 8.2 for definition of Δhp and hp. When making this assessment taking into account of the amount and quality of the instrumentation, the duration and range of reservoir levels of the observations.


Section 8

8-25

Table 8.22 – Probability of a cut-off not being effective for continuous defects (PCI) versus ∑(RFxLF)

0.001 0.005 0.02 0.1 0.5 0.9

6 9 11 14 18 24 RFxLF

8.9 Probability of Rock Surface Treatment Being Ineffective at Preventing Contact of the Core with Open Rock Defects (PTI)

Use Table 8.23 to assess the probability that the rock surface treatment is ineffective and fails to prevent contact of the core with continuous rock defects. Do this for each defect width, for the base and the sides of the cut-off trench, and for the various parts of the foundation (e.g., each abutment and the river section).

Table 8.23 – Probability of rock surface treatment being ineffective at preventing contact of the core with open rock defects (PTI)

Scenarios Probability of the treatment not preventing contact

Well-documented evidence that there was no treatment of the cut-off foundation

1.0

No construction records available, the design and construction organization not known or known but likely to have not paid much attention to inspecting foundations and carrying out surface treatment

0.3 to 0.9

No construction records available, but knowledge that the practice of the design and construction authority was to inspect foundations and carry out surface treatment

0.1 to 0.5

Evidence that the foundations were mapped, but not in detail. Some evidence that defects and solution features were covered with concrete or shotcrete

0.05 to 0.2

Well-documented evidence that the foundations were carefully mapped, and all defects and solution features were covered with at least 100 mm (4 in) of concrete or good quality shotcrete, or that they were cleaned out to at least 3 times the surface width and treated with slush grout

0.01 to 0.001

8.10 Probability of Continuous Rock Defects (PCR)

The probability of a continuous defect in rock foundation below the embankment can be calculated using the a sub-event tree as shown in Figure 8.3. This is to be done for each defect width for each applicable geologic


Section 8

8-26

process. If more than one geologic process applies, then combine the probability of each defect size using DeMorgan’s rule.

P TI Probability of 5-25mm Defect

P CI Rock Surface Treatment Ineffective?

P GI Cutoff Wall Ineffective?

Pw Is Grouting ineffective?

Continuous Defect?Valley Stress Relief 5-25mm

Yes

No

Yes

No

Yes

No

Yes

No

Evaluate:Regional Geology and Topographic DataSite Investigations, Construction, and Performance Data

Repeat for each defect range size

Figure 8.3 – Computation of probability of a continuous open defect below the embankment

8.11 Describing the Defects

It is essential that the risk analysis team document with sketch diagrams (plans and sections) of the spatial distribution of the defects which have been assessed potentially present in the foundation. This should show the features superimposed on the foundation drawings and showing the cut-off and general foundations beneath the core of the embankment so the relationship between the defects and the base of the cut-off trench, and sides of the cut-off trench is clear. The extension of the defects upstream and downstream of the core, including under the shoulders of the embankment, and beyond the embankment should also be shown. Any foundation grouting, surface treatment of the cut-off foundation, and cut-off walls (if constructed) should also be shown. These are required so that the potential failure modes can be clearly visualized for the assessment of progression, detection, intervention and repair, and breach probabilities. The following sections can be used to aid in judging the extent of the defects for each geological mechanism.

8.11.1 Extent of features associated with stress relief in the valley sides

For stress relief defects in valley sides, estimate the extent of the defects below the original ground surface based the available site investigations data, and construction mapping and grouting records. If there is little or no such data make the assessment based on the assumed geometry of stress relief defects shown in Figure 8.4. This may also be used to supplement the site investigations and construction data.


Section 8

8-27

(a) Horizontally bedded sedimentary rocks

Figure 8.4 – Assumed distribution of defect depths for defects related to stress relief effects in the valley sides (Figures from Fell et al. 2004)

Stress relief joints open for 3 or 4 joints or for a width of up to 30% of valley depth whichever is larger

Stress relief joints open for 3 or 4 joints or for a width of up to 30% of valley depth whichever is larger


Section 8

8-28

(b) Uniform jointed rock such as thinly bedded sandstone, jointed granites and basalt (see supporting document for explanation of numbers)

(c) Massive rocks such as some granite

Figure 8.4 (cont.) – Assumed distribution of defect depths for defects related to stress relief effects in the valley sides (Figures from Fell et al. 2004)

Stress relief joints to a distance normal to the ground surface of up to 30% of the valley depth.

Stress relief joints (sheet joints) to a distance normal to the slope of up to 30% of the valley depth


Section 8

8-29

8.11.2 Extent of features associated with valley bulge or rebound

For stress relief effects associated with valley bulge or rebound, the extent and depth to which the features may occur should be assessed based on the available information from construction and investigations.

In the absence of other information it should be assumed these features exist to below the level of the strut (massive stronger bed). It should be noted that these features are known to have occurred to depths of up to 50 feet (15 meters) below the valley floor.

8.11.3 Extent of solution features

For solution defects, the depth and spatial distribution of solution features should be assessed based on the following factors:

• How the solution features were formed – stress relief effects or regional effects and the extent these can be expected to occur.

• The geological history of the valley, particularly in relation to the historical groundwater levels which may have been lower in the geological history of the valley.

• Observational data – Observations from boreholes including in-filled features, voids, water losses and water pressure testing and grouting records.

It is not practical to develop any general rules for these assessments.

8.11.4 Extent of other geological features such as landslides faults and shears

For these features, the depth and spatial distribution of solution features should be assessed based on the following factors:

• How the features were formed – The faulting mechanism should be evaluated to assess the expected special distribution and depth.

• The geologic history of the valley including mapping and of known faults and shears.

• Observational data – Observations from boreholes including in-filled features, voids, water losses and water pressure testing and grouting records. Observations in foundation excavations and nearby rock cuts can be used to assess the extent and possibly spacing.

Probability of Initiation of Erosion from the Embankment into or at the Foundation

Section 9

9-1

9 Probability of Initiation of Erosion from the Embankment into or at the Foundation

9.1 General Principles

This section is concerned with assessing the failure path where initiation of internal erosion of the embankment into or at the foundation by backward erosion piping or scour is followed by gross enlargement, slope instability, unraveling or sinkhole development in the embankment. For erosion to initiate from the embankment into the foundation, open joints in rock or coarse-grained soils in the base or sides of the cut-off trench are required. For cases where a cut-off trench is not present, then the issue is whether erosion can occur along the core-foundation contact.

Internal erosion may initiate by:

• Scour at the core – foundation contact by water flowing in joints in the rock foundation or through open-work gravels

• Backward erosion of cohesionless soils or stoping of cohesive soils into rock defects or open-work gravels


9.2.1 Rock Foundations

Determine the probability of a continuous pathway of open joints in rock in the base or sides of the core trench or core-foundation contact. For rock defects the probability of continuous pathways (PCR) is determined in Section 8. For each defect size range use the corresponding evaluation size for the remaining steps.

Defect Size Ranges Defect Evaluation Size

0-5 mm 2.5 mm

5-25mm 15 mm

25-100mm 62.5 mm

>100 mm 300 mm


Section 9

9-2

Scour along rock defects < 25 mm (IM25)

a) Determine the probability of 2.5 mm and 15 mm defects (PCR) from Section 8.

b) Assess the probability of a seepage exit. Three scenarios are possible: 1) the rock defects daylight downstream with an unprotected exit; 2) the network of rock defects has a large void capacity below or downstream of the core; and 3) the exit is soil-covered. A review of all relevant data is required to determine the exit conditions that may be present. The likelihood of each exit condition should be determined using subjective estimation methods. In some cases, it will be obvious (e.g., a known rock outcrop with seepage exiting a defect).

c) Calculate the probability of a continuous path with a seepage exit (Pflaw) from the results of the above assessments: (Pflaw) = (PCR) x (Pexit).

d) Assess the probability of initiation (PI) of scour using the procedure described in Section 5.5. Evaluate for each reservoir level under consideration.

e) Assess the probability of continuation (PCE) by evaluating the exit conditions downstream of the core of the dam to determine if the soil can exit the rock defects. Three scenarios are possible:

• If the rock defects daylight downstream with an unprotected exit, then the probability of continuation is 1.0. The exit can be above or below the tailwater surface.

• If the network of rock defects has enough capacity below or downstream of the core to accept enough material to allow erosion to continue, then the probability of continuation is 1.0.

• If the exit is covered by soil, then use the methods described in Section 10.1.4 (Scenario 3) to determine the probability of continuation.

f) Assess the probability of progression (Section 11).

g) Assess the probability of unsuccessful intervention (Section 12).

h) Assess the probability of breach (Section 13).

Erosion into rock defects > 25 mm (IM26)

a) Determine the probability of 62.5 mm and 300 mm defects (PCR) from Section 8.

b) Assess the probability of a seepage exit. Three scenarios are possible: 1) the rock defects daylight downstream with an unprotected exit; 2) the network of rock defects has a large void capacity below or downstream of the core; and 3) the exit is soil-covered. A review of all relevant data is required to determine the exit conditions that may be present. The likelihood of each exit condition should be


Section 9

9-3

determined using subjective estimation methods. In some cases, it will be obvious (e.g., a known rock outcrop with seepage exiting a defect).

c) Calculate the probability of a continuous path with a seepage exit (Pflaw) from the results of the above assessments: (Pflaw) = (PCR) x (Pexit).

d) Assess the probability of the initiation (PI) of internal erosion given there is a continuous path, PI = PIC x PCED x PSTD.

• Given there are continuous open defects in the rock foundation, the probability of initiation (PIC) should be assumed to be 1.0 for both cohesionless soils (backward erosion) and for cohesive soils (sinkhole stoping).

• Assess the probability of continuation into the rock defect (PCED) using the procedures described in Section 10.1.5 (Scenario 4).

• Assess the probability that the average hydraulic gradient along the rock defect is sufficient to cause transport of soils through the defects (PSTD) using Table 9.2 in Section 9.5.

e) Assess the probability of continuation (PCE) by evaluating the exit conditions downstream of the core of the dam to determine if the soil can exit the rock defects. Three scenarios are possible:

• If the rock defects daylight downstream with an unprotected exit, then the probability of continuation is 1.0. This exit can be above or below the tailwater surface.

• If the network of rock defects has enough capacity below or downstream of the core to accept enough material to allow erosion to continue, then the probability of continuation is 1.0.



g) Assess the probability of detection, intervention, and repair (Section 12)


9.2.2 Open-Work Granular Foundations

Scour along the contact with open-work coarse-grained foundation soil (IM27)

a) Assess the probability of a continuous pathway (PCP) into an open-work coarse-grained foundation soil using Section 9.3.


Section 9

9-4

b) Assess the probability of a seepage exit. Three scenarios are possible: 1) the open-work soil daylights downstream with an unprotected exit; 2) the open-work soil has a large void capacity below or downstream of the core; and 3) the exit is soil-covered. A review of all relevant data is required to determine the exit conditions that may be present. The likelihood of each exit condition should be determined using subjective estimation methods. In some cases, it will be obvious (e.g., a known location where the open-work soil daylights with seepage exiting).

c) Calculate the probability of a continuous path with a seepage exit (Pflaw) from the results of the above assessments: (Pflaw) = (PCP) x (Pexit).

d) Assess the probability of initiation (PI) of scour using the procedure described in Section 0. Evaluate for each reservoir level under consideration.

e) Assess the probability of continuation (PCE) by evaluating the exit conditions downstream of the core of the dam to determine if the soil can exit the open-work coarse-grained foundation soil. Three scenarios are possible:

• If the open-work coarse-grained foundation soil daylights downstream with an unprotected exit, then the probability of continuation is 1.0. This exit can be above or below the tailwater surface.

• If the open-work coarse-grained foundation soil has enough capacity below or downstream of the core to accept enough material to allow erosion to continue, then the probability of continuation is 1.0.



g) Assess the probability of detection, intervention, and repair (Section 12).

h) Assess the probability of Breach (Section 13).

Erosion into open-work coarse-grained foundation soil (IM28)

a) Assess the probability of a continuous pathway (PCP) into an open-work coarse-grained foundation soil using Section 9.3.

b) Assess the probability of a seepage exit. Three scenarios are possible: 1) the open-work soil daylights downstream with an unprotected exit; 2) the open-work soil has a large void capacity below or downstream of the core; and 3) the exit is soil-covered. A review of all relevant data is required to determine the exit conditions that may be present. The likelihood of each exit condition should be


Section 9

9-5

determined using subjective estimation methods.In some cases, it will be obvious (e.g., a known location where the open-work soil daylights with seepage exiting).

c) Calculate the probability of a continuous path with a seepage exit (Pflaw) from the results of the above assessments: (Pflaw) = (PCP) x (Pexit).

d) Assess the probability of the initiation (PI) of internal erosion given there is a continuous path, PI = PIP x PCED x PSTD.

• Given there are continuous open defects in the open-work coarse-grained foundation soil, the probability of initiation (PIP) should be assumed to be 1.0 for both cohesionless soils (backward erosion) and for cohesive soils (sinkhole stoping).

• Assess the probability of continuation into the open-work coarse-grained foundation soil (PCED) using Section 10.1.4 (Scenario 3).

• Assess the probability that the average hydraulic gradient along the core-foundation contact is sufficient to cause transport of soils through the defects (PSTD) using Section 9.5.

e) Assess the probability of continuation (PCE) by evaluating the exit conditions downstream of the core of the dam to determine if the soil can exit the open-work coarse-grained foundation soil. Three scenarios are possible:

• If the open-work coarse-grained foundation soil daylights downstream with an unprotected exit, then the probability of continuation is 1.0. This exit can be above or below the tailwater surface.

• If the open-work coarse-grained foundation soil has enough capacity below or downstream of the core to accept enough material to allow erosion to continue, then the probability of continuation is 1.0.



g) Assess the probability of unsuccessful intervention (Section 12).



Section 9

9-6

9.3 Probability of a Continuous Pathway of Coarse-Grained Layers in Soil Foundations

This should be assessed from the geology of the foundation, mapping and, photographs taken during construction, the depth of general foundation and cut-off excavation, and whether there are filters between the core and trench side. In many cases it will become apparent at this stage that there is little or no likelihood of such features being present and the probability of internal erosion into the foundation may be assessed as negligible.

Guidance on estimating the probability is given for a range of scenarios for soil foundations in Table 9.1.


Section 9

9-7

Table 9.1 – Probability of a continuous pathway (PCP) for erosion into soil foundation

Scenarios Examples Range of probabilities for

continuous pathway of coarse-grained soils

Adequate treatment of soil foundation contact

Filter protection provided on downstream side of cut-off trench

Negligible

Assume probability = 0

Site investigations indicate continuous coarse-grained foundation soil layers are very unlikely to be present

No evidence of open-work gravel layers

Negligible

Assume probability = 0

Site investigation data is not available, but circumstantial evidence indicates coarse-grained foundation soils are unlikely to be present

Circumstantial evidence might include;

Observations of cuts in foundation soil;

Geological environments where coarse grained soils are unlikely to be present (e.g., residual soils, aeolian, lacustrine, volcanic ash)

0.0001 to 0.001

Depending on the quality of the available data. In some cases

negligible.

Site investigation data is not available, but circumstantial evidence indicates coarse-grained foundation soils maybe present

Circumstantial evidence might include;

Observations of cuts in foundation soil;

Geological environments where coarse grained soils maybe present (e.g., alluvium, colluvium, glacial, lateritic profiles)

0.001 – 0.01

Depending on level of confidence in assessment and degree of continuity

of features

Site investigation or construction data indicates coarse-grained foundation soils are likely to be in contact with the core, no or inadequate treatment

Evidence from drill holes, excavation logs, construction photographs

0.05 – 0.5

Depending on extent and degree of continuity of soils

Well-documented evidence confirming the presence of coarse-grained foundation soils are in contact with the core with no or inadequate treatment

Evidence from drill holes, excavation logs, construction photographs

1.0


Section 9

9-8

9.4 Probability of Initiation of Scour at the Core-Foundation Contact

This considers the likelihood that seepage flows within a continuous pathway in a rock or an open granular soil may initiate erosion of the core material at the core-foundation contact.

The steps in the assessment are as follows:

• Estimate the probability of erosion of the core material at the core-foundation contact (PI) using the method for erosion in a crack in the core as described in Section 5.5. The hydraulic gradient used in the assessment should be based on the estimated seepage gradient on the core-foundation contact. Assume that the hydraulic shear stresses imposed on the core by the water flowing in the open joints is equivalent to those for a crack width equal to the rock defect width. For open granular soils, assume a crack width equal to the D15/4.

• Do this for each of the potential defect openings (2.5 mm and 15 mm for rock) and soil type in contact with the defects.

9.5 Probability of Soil Transport through Defects

This section considers the likelihood that the average gradient through the rock defects or the open-work gravel is sufficient to transport the soils that have piped into the voids from above. The average gradient along the defect or core-open gravel contact should be estimated for each pool under consideration. Use Table to estimate the probability of soil transport though the defect PSTD. The probabilities in the table were estimated based on the assumption that the soils that are washed into the defects will be very loose and will essentially behave similar to a very uniform sand. This was then related to the testing done by Schmertmann that determined gradients required for complete backward erosion piping.

Table 9.2 – Probability of soil transport through defects

Average gradient along rock defect or core–open-work gravel contact

Probability of soil transport through defects, PSTD

0.01 0.002 0.025 0.02 0.05 0.2 0.1 0.6 0.25 0.97

0.5 or greater 1.0

Probability of Continuation Section 10

10-1

10 Probability of Continuation

10.1 Probability of Continuation for Internal Erosion through the Embankment

10.1.1 Overall Approach

Step 1: Assess which of the following five scenarios is most applicable to the dam section and failure path that is under consideration:

• Scenario 1: Homogeneous zoning with no fully intercepting filter.

• Scenario 2: Downstream shoulder of fine grained cohesive material which is capable of holding a crack/pipe. Soils which are capable of holding a crack or pipe are:

– well compacted shoulder (shell), containing > 5% plastic fines; or

– poorly compacted shoulder (shell), containing >15% plastic fines

– well compacted shoulder, containing > 30% non plastic fines

– poorly compacted shoulder, >30% non plastic

• Scenario 3: Filter/transition zone is present downstream of the core or a downstream shoulder zone which is not capable of holding a crack/pipe. This includes earthfill dams with a chimney filter.

• Scenario 4: Erosion into an open defect, joint, or crack (e.g., in a conduit, wall, toe drain, or rock foundation).

The example sketches shown in Figure 10.1 can be used to help evaluate the most applicable scenario.

Step 2: For Scenarios 1 and 2, estimate the probability of continuing erosion based on the guidance given in Sections 10.1.2 and 10.1.3, respectively.

For Scenario 3, estimate the probability of continuing erosion based on the guidance given in Section 10.1.4. If more than one filter/transition zone exists, evaluate the probability of continuing erosion for each material boundary, and then select the maximum probability of continuation for the system response curve.

For Scenario 4, estimate the probability of continuing erosion based on the guidance given in Section 10.1.5.


10-2

1

HOMOGENEOUS EARTHFILL

3

2

13

INTERNAL EROSION ABOVE CORE AND FILTERS

1

EARTHFILL WITH TOE DRAIN, INTERNAL EROSION ABOVE TOE DRAIN

1


1


3

2

13


3

2

13


1


1


1


a) Scenario 1 – Homogeneous zoning with no fully intercepting filter

11A

ZONED EARTHFILL WITH COHESIVE SHELLS

1A2

1

INTERNAL EROSION ABOVE FILTER ZONE, COHESIVE DOWNSTREAM SHELL

1A1A11A


1A11A


1A2

1


1A1A 21


1A1A

b) Scenario 2 – Downstream shoulder of fine grained cohesive material which is capable of holding a crack/pipe

1

21 3

2

13

31

3

EARTHFILL WITH CHIMNEY FILTER ZONED EARTHFILL WITH CHIMNEY FILTER

ZONED EARTHFILL WITH GRANULAR SHELLS

1

21

1

21 3

2

13 3

2

13

31

3 31

3

EARTHFILL WITH CHIMNEY FILTER ZONED EARTHFILL WITH CHIMNEY FILTER

ZONED EARTHFILL WITH GRANULAR SHELLS c) Scenario 3 – Filter/transition zone is present downstream of the core or a downstream shoulder zone which is not capable of holding a crack/pipe

SOIL

CONDUIT

EROSION INTO OPEN JOINTS IN ROCK FOUNDATION

SOIL

OPEN JOINTED ROCK

EROSION INTO AN OPEN CRACK OR JOINT IN A CONDUIT OR WALL

SOIL

CONDUIT

EROSION INTO OPEN JOINTS IN ROCK FOUNDATION

SOIL

OPEN JOINTED ROCK

EROSION INTO AN OPEN CRACK OR JOINT IN A CONDUIT OR WALL

1

INTERNAL EROSION THROUGH THE EMBANKMENT INTO A TOE DRAIN

1

INTERNAL EROSION THROUGH THE EMBANKMENT INTO A TOE DRAIN

d) Scenario 4 – Piping into an open defect, joint, or crack

Figure 10.1 – Examples of scenarios for evaluation of probability of continuation


10-3

10.1.2 Probability of continuation (PCE) – Scenario 1 (homogeneous zoning)

There is no potential for filtering action for this scenario. Adopt a probability of continuation, PCE = 1.0.

10.1.3 Probability of continuation (PCE) – Scenario 2 (downstream shoulder can hold a crack or pipe)

The issue for this scenario is whether the crack or high permeability feature that is present through the core is continuous through the downstream shoulder, or if not, whether it can find an exit. This depends on the following factors:

• The mechanism causing the concentrated leak, in particular whether it also causes cracking in the shoulder.

• The material characteristics and width of the downstream shoulder zone.

Use Table 10.1 to evaluate the conditional probability of continuation.


10-4

Table 10.1 – Probability of continuation (Scenario 2)

Predominant Mode of Concentrated Leak

Characteristics of downstream shoulder zone

Range of Probabilities of Continuing Erosion

Well compacted, cohesive materials. Material likely to hold a crack.

1.0 Cracking due to differential settlement (cross valley, foundation, embankment staging). Mechanism causing cracking in the core is also likely to cause cracking of the downstream shell (e.g., common cause cracking).

Poorly compacted, low plasticity materials. Material may collapse on wetting.

0.5 – 0.9

Similar plasticity to core 0.5 - 1.0 Desiccation cracking near crest, or on construction layer Lower plasticity than core, less prone to

desiccation cracking 0.1 – 0.5

High permeability feature also likely to be present across the shoulder zone (e.g., shutdown surface)

0.5 - 1.0

Leak unlikely to find an exit through the shoulder (e.g., very wide downstream shoulder, well compacted, low gradients, low erodibility, different compaction methods and lift thicknesses used in core and downstream shoulder)

0.01 – 0.1

High permeability zone in the core or along the foundation contact, or

Cracking due to differential settlement, features causing cracking in the core are not present below the downstream shell.

Leak likely to find an exit through the shoulder (e.g., narrow downstream shoulder, high gradient across shoulder, high erodibility, similar compaction methods and lift thicknesses used in core and downstream shoulder, materials placed in upstream/downstream orientation, feature extends part way through the shoulder)

0.1 – 0.5

Along outside of conduits passing through the dam

Leak also likely to be common cause through downstream shoulder (e.g., desiccation cracking on sides of excavation, poor compaction, arching in trench backfill)

0.5 - 1.0

10.1.4 Probability for continuation – Scenario 3 (filter/transition zone is present downstream of the core or a downstream shoulder zone which is not capable of holding a crack/pipe)

The method of assessing the probability for continuation depends on the information that is available on the particle size distributions of the core and filter/transition/shoulder materials. The two approaches are as follows:

• If particle size distribution information is available for the core and filter/transition/shoulder materials (either from construction, specifications and/or borrow area investigations), then use the approach described in 10.1.4(a).


10-5

• If particle size distribution information is not available for the core and filter/transition/shoulder materials, then use the approach described in 10.1.4(b).

(a) Particle size distribution information is available

The recommended procedure is shown as a flowchart in Figure 10.2 and involves the following steps:

Step 1: Check for the blow out condition for each reservoir level. In cases where there is limited depth of cover over the filter/transition zone, assess the potential for blow out by comparing the seepage head at the downstream face of the core to the weight of soil cover. This is calculated as the ratio of the total stress from the vertical depth of soil (and rockfill) over the crack exit to the potential reservoir head. If the factor of safety is greater than about 0.5 three dimensional effects will be sufficient to make this a non-issue. If the factor of safety is less than about 0.1 it should be assumed the filter/transition will not be effective and probability of continuation PCE = 1.0. Between these limits a probability of continuation between 0.1 and 0.9 should be applied. Blow out condition is a function of reservoir level and should be assessed accordingly. If the factor of safety for blow out is greater than 0.5, then follow the proceeding steps.

Step 2: Check if the filter/transition zone will hold an open crack. If the filter/transition zone contains an excess of silty or clayey fines, assess the potential for them to hold an open crack using Table 10.2. If the probability of the filter/transition holding a crack from Table 10.2 is ≥ 0.1, then evaluate the remaining steps by considering the cracked filter/transition zone as the base soil and the zone downstream of the cracked filter as the filter material. This assumes the cracked filter zone will also erode. If the filter is cemented, then the cracked filter zone should be ignored, and the core should be evaluated against the zone downstream of the cracked filter. Use the average grading when checking if the filter/transition zone will hold a crack.

Step 3: Adjust and select base soil gradings. Plot the particle size distributions for the core material and the filters or transitions which are protecting the core. If the maximum particle size of the core material is greater than 4.75 mm, then regrade the core grading such that the maximum size is 4.75 mm. If the base soil is gap graded, then regrade the base soil grading on the particle size that is missing (i.e., at the point of inflection of the grading curve). Select representative gradings of the regraded base soil which are indicative of the finer 5% of the base soil gradings (fine base soil grading), the average grading (average base soil grading) and the coarser 5% of the base soils (coarse base soil grading). Figure 10.3 shows an example.

Step 4: Check if the filter/transition zone is segregated. Assess the potential for segregation of the filter/transition/shoulder materials using Table 10.3, Table 10.4 and Table 10.5. If a continuous segregated layer is likely to be present, then estimate the grading of the segregated layer assuming that 50% of the finer soil fraction is segregated out leaving the remaining 50% of coarser fraction. Figure 10.4 shows a graphical method for adjusting the gradation curve to allow for segregation. Use the DF15 values from the adjusted grading curves for estimating the conditional probabilities of no erosion, some erosion, excessive erosion, and continuing erosion in the remaining steps. Use the average grading when checking if the filter/transition zone is segregated.


10-6

Step 5: Check if the filter/transition zone is internally unstable. Evaluate the probability that the filter or transition zone materials are internally unstable (PIUS) using Figure 6.8 for materials with >10% fines or Figure 6.9 for materials with <10% fines. If the probability of internal instability (PIUS) is ≥ 0.3, then adjust the grading curve assuming that 50% of the unstable soil fraction is washed out. Figure 10.2 shows a graphical method for adjusting the gradation curve to allow for suffusion. Use the DF15 values from the adjusted filter grading curves for assessing the probability of no erosion, some erosion, excessive erosion, and continuing erosion in Step 7. If the probability of internal instability is < 0.3, then do not adjust the filter grading curves. Note only the average grading should used when checking if the filter/transition zone is internally unstable.

Step 6: Evaluate the DF15 values for the no erosion, excessive erosion, and continuing erosion boundaries using Table 10.6 and Table 10.7 for the fine base soil grading, the average base soil grading and the coarse base soil grading. Plot the DF15 values for these boundaries on the grading curve limits of the filter/transition material (see Figure 10.6 for an example). Use the adjusted grading curves for the filter/transition zone if required to do so by the preceding Steps 4 or 5.

Step 7: Estimate the probabilities for no erosion, some erosion, excessive erosion, and continuing erosion for each representative base soil grading. Estimate the proportion of the actual (or adjusted) filter/transition gradings that fall into each of the particular erosion categories based on the plot of filter/transition grading curves versus filter erosion boundaries (an example is shown in Figure 10.6). If there are no filter/transition gradings that fall into the continuing erosion category, then use Table 10.8 to aid judgment in assigning probabilities for continuing erosion. This allows for the possibility of the gradations being coarser than indicated by the available information and depends on how much finer the gradings are to the continuing erosion boundary. The suggested approach is to estimate the proportions for the some, excessive, and continuing erosion categories first (PSE, PEE , and PCE ) and then calculate PNE = 1- (PSE + PEE + PCE). Do this for each of the representative base soil gradings (fine, average and coarse gradings) as follows:

• For the fine base soil grading: PNE fine, PSE fine, PEE fine, and PCE fine

• For the average base soil grading: PNE avg., PSE avg., PEE avg., and PCE avg.

• For the coarse base soil grading: PNE coarse, PSE coarse, PEE coarse, and PCE coarse

Make an initial estimate of the probabilities of no erosion, some erosion, excessive erosion, and continuing erosion by the sum-product of the percentage of base soil gradings and the percentage of no erosion, some erosion, excessive erosion, and continuing erosion for each representative base soil grading. The calculations are as follows:

• PNE = (5% x PNE fine) + (90% x PNE avg.) + (5% x PNE coarse)

• PSE = (5% x PSE fine) + (90% x PSE avg.) + (5% x PSE coarse)

• PEE = (5% x PEE fine) + (90% x PEE avg.) + (5% x PEE coarse).

• PCE = (5% x PCE fine) + (90% x PCE avg.) + (5% x PCE coarse).


10-7

Figure 10.2 – Flow chart for evaluating the probabilities of no erosion, some erosion, excessive erosion, and continuing erosion


10-8

An example of summing of the probabilities is shown in Table 10.9 for the example shown in Figure 10.6.

Use judgment to adjust the calculated percentages to take into account the effects of other factors such as the distribution of the core and filter gradations in the fill, borrow area variability and selective placement of materials.

(b) Particle size distribution information is not available

• Estimate the particle size distribution of the core materials based on the likely source of materials. The gradation of the soils may be able to be estimated based on the likely geological origin of the materials (e.g. decomposed granitic soils, residual soils, alluvial fine clays and silts, etc).

• Estimate the particle size distribution of the filter/transition/shoulder materials based on the likely source of the materials and whether they were processed or not (e.g. run-of-pit alluvial sands and gravels, unprocessed quarry fines or tunnel spoil, processed sand and gravels, etc). Estimate the DF15 of the filter/transition/downstream shoulder materials.

• Evaluate the DF15 values for the no erosion, excessive erosion, and continuing erosion boundaries for the estimated gradation of the core materials using Table 10.6 and Table 10.7.

• Estimate the probabilities for no erosion, some erosion, excessive erosion, and continuing erosion based on the estimated proportion of the filter/transition gradings that is likely to fall into each of the particular filter erosion categories. The suggested approach is to estimate the probabilities for some, excessive, and continuing erosion (PSE, PEE, and PCE) and calculate PNE = 1 – (PSE + PEE + PCE).


10-9

Figure 10.3 – Example of the selection of representative grading curves (fine, average, and coarse) for the assessment of filter compatibility

Figure 10.4 – Approximate method for estimating DF15 after washout of the erodible fraction from a suffusive soil or for soils susceptible to segregation

15%

(1) Select the point of maximum inflexion of the grading curve (2) Locate the mid point below the point of inflection

% P

assi

ng

Particle size

Original gradation

Estimated gradation curve after washout or segregation

Equal distance

(4) Estimate the D15 after washout or segregation

(3) Estimate the shape of the gradation curve passing through the mid point

Particle Size (mm)

Envelope of Base Soil Gradings

Average Grading

Representative Fine Grading Curve

Representative Coarse Grading Curve

% P

assi

ng


10-10

Table 10.2 – Likelihood for filters with excessive fines holding a crack

Probability of holding a crack Fines Plasticity

Fines Content

% Passing 0.075 mm Compacted Not compacted

5% 0.001 0.0002

7% 0.005 0.001

12% 0.05 0.01

15% 0.1 0.02

Non plastic (and no cementing present)

>30% 0.5 0.1

5% 0.05 0.02

7% 0.1 0.05

12% 0.5 0.3

Plastic

(or fines susceptible to cementing)

≥15% 0.9 0.7

Note: Fines susceptible to cementing for filters having a matrix predominately of sand sized particles (e.g., filters derived from crushed limestone).

Table 10.3 – Potential for segregation of filtering materials


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Construction practices

(3) Good construction and stockpiling practices used

Fair construction and stockpiling practices

Poor construction or stockpiling practices

Very poor construction and stockpiling practices with no regard for segregation effects

Placed in thin lifts < 2 ft (< 0.6 m), careful control during construction

End dumping from trucks, spread by dozer in thin lifts < 2 ft (< 0.6 m)

End dumping from trucks, spread by dozer in thick lifts > 2 ft (> 0.6 m)

Filters/transitions constructed by pushing material over the edge of the core

Gradation comparison to USACE filter criteria

(2) Meets segregation criteria in Table 10.4

Borderline segregation criteria in Table 10.4

Fails segregation criteria in Table 10.4

Significant departure from segregation criteria in Table 10.4

and %passing No. 4 sieve

>50% passing 4.75 mm sieve

40-50% passing 4.75 mm sieve

25-40% passing 4.75 mm sieve

<25% passing 4.75 mm sieve

Width of zone (1) Wide zone, >20 ft (>6 m)

10-20 ft (3-6 m) Narrow zone, 5-10 ft (1.5-3 m)

Narrow zone, <5 ft (<1.5 m)


10-11

Table 10.4 – Gradation limits to prevent segregation (USDA SCS 1994, USBR 1987, US Corps of Engineers 1994)

D10 (mm) Maximum D90 (mm)

<0.5 20

0.5 – 1.0 25

1.0 – 2.0 30

2.0 – 5.0 40

5.0 – 10 50

10 – 50 60

Note: D10 and D90 are based on the average filter gradation.

Table 10.5 – Susceptibility of filter/transition zones to segregation versus ∑(RFxLF)

∑(RFxLF) from Table 10.3 Segregation Assessment Consideration of Segregation Effects for

Filter/Transition Assessment

6 – 12 Low potential for segregation Segregation of filter/transition materials do not need to be considered

13 – 17 Moderate potential for segregation Segregation of filter/transition materials should be considered, unless investigations show otherwise.

18 – 24 High potential for continuous segregated layers

Segregation should be assumed to be present, unless investigations show otherwise.

Note: If ∑(RFxLF) ≥ 13, then segregation should be considered unless investigations show otherwise.


10-12

Table 10.6 – No erosion boundary for the assessment of filters of existing dams (after Foster and Fell 2001)

Base Soil

Category

Fines content

(1)

Design Criteria of Sherard and Dunnigan

(1989)

Range of DF15 for No Erosion Boundary

From Tests

Criteria for No Erosion Boundary

1 ≥85% DF15 ≤ 9 DB85 6.4 - 13.5 DB85 DF15 ≤ 9 DB85 (2)

2 40 - 85% DF15 ≤ 0.7 mm 0.7 - 1.7 mm DF15 ≤ 0.7 mm (2)

3 15 - 40% DF15 ≤ (40-pp% 0.075 mm) x (4DB85-0.7)/25 +

0.7

1.6 - 2.5 DF15 of Sherard and Dunnigan design

criteria

DF15 ≤ (40-pp% 0.075 mm) x (4DB85-0.7)/25 +

0.7

4 <15% DF15 ≤ 4 DB85 6.8 - 10 DB85 DF15 ≤ 4 DB85

Notes: (1) The fines content is the % finer than 0.075 mm after the base soil is adjusted to a maximum particle size of 4.75 mm.

(2) For highly dispersive soils (pinhole classification D1 or D2 or Emerson Class 1 or 2), it is recommended to use a lower DF15 for the no erosion boundary. For soil group 1 soils, suggest use the lower limit of the experimental boundary, i.e. DF15 ≤ 6.4 DB85. For soil group 2 soils, suggest use DF15 ≤ 0.5 mm. The equation for soil group 4 would be modified accordingly.

Table 10.7 – Excessive and continuing erosion criteria (Foster 1999; Foster and Fell 1999, 2001)

Base Soil Proposed Criteria for Excessive Erosion Boundary

Proposed Criteria for Continuing

Erosion Boundary

Soils with DB95 < 0.3 mm DF15 > 9 DB95

Soils with 0.3 < DB95 < 2 mm DF15 > 9 DB90

Soils with DB95 >2 mm and fines content > 35%

DF15 > the DF15 value which gives an erosion loss of 0.25g/cm2 in the CEF test (0.25g/cm2 contour line in Figure 10.5)

For all soils:

DF15 > 9 DB95

Soils with DB95 > 2 mm and fines content < 15%

DF15 > 9 DB85

Soils with DB95 > 2 mm and fines content 15-35%

DF15 > 2.5 DF15 design, where DF15 design is given by:

DF15 design = (35-pp%0.075 mm)(4DB85-0.7)/20+0.7

Notes: Criteria are directly applicable to soils with DB95 up to 4.75 mm. For soils with coarser particles determine DB85 and DB95 using grading curves adjusted to give a maximum size of 4.75 mm.


10-13

0

5

10

15

0 5 10 15 20 25 30 35 40 45 50 55 60Core material % fine - medium sand (0.075 - 1.18mm)

Filte

r D

F15

(mm

)

No Erosion Boundaryfor Soil Group 2DF15=0.7mm

0.25g/cm2

Contour of Erosion Loss

EXCESSIVE EROSION

SOME EROSION

Figure 10.5 – Criteria for excessive erosion boundary

Table 10.8 – Aid to judgment for estimation of probability of continuing erosion (PCE) when the actual filter grading is finer than the continuing erosion boundary

Comparison of Actual DF15 of the Filter/Transition Zone to the Continuing Erosion boundary Probability for Continuing Erosion (PCE)

DF15 in dam < 0.1x DF15,CE 0.0001

DF15 in dam < 0.2 x DF15,CE 0.001

DF15 in dam < 0.5 x DF15,CE 0.01 – 0.05

Notes: DF15,CE = DF15 for continuing erosion boundary from Table 10.7. For this comparison of actual DF15 to the CE boundary, use the coarse filter/transition gradation.


10-14

Assessment of Zone 1 core against no erosion, excessive erosion and continuing erosion criteriaNo Erosion Excessive

ErosionContinuing

Erosion

DB85 (mm) DB95 (mm)% passing 0.075mm

% fine-medium sand (0.075 - 1.18mm) DF15 (mm) DF15 (mm) DF15 (mm)

Fine Grading 1.9 3.3 50 25 0.7 2 30Average 2.4 4 41 29 0.7 2.5 36Coarse Grading 2.5 4.2 35 30 0.7 2.6 38

Base soil sizes (mm)Core Gradation

0

10

20

30

40

50

60

70

80

90

100

0.001 0.01 0.1 1 10 100 1000

Seive Size (mm)

Perc

ent P

assi

ng

Filter erosion boundaries for the Average core grading

Filter erosion boundaries for the Fine core grading

Filter erosion boundaries for the Coarse core gradingZone 1 - Core Materialre-graded to maximum size of 4.75 mm

Zone 3- FilterTransition

0.7 2.5 36

No Erosion

SomeErosion

Excessive Erosion

ContinuingErosion

0.7 2.0 30

Zone 1- Fine Grading

Zone 1 - Average Grading

Zone 1 - Coarse Grading

38

Figure 10.6 – Example of filter/transition gradings compared to filter erosion boundaries determination of the filter erosion boundaries for the representative fine, average, and

coarse gradings of the core material


10-15

Table 10.9 – Example of estimating probabilities for no erosion, some erosion, excessive erosion, and continuing erosion for the example shown in Figure 10.6

Estimated Proportion of Filter Gradings falling into each Filter Erosion category (from Figure 10.6) Representative

Base Soil Grading No Erosion (NE) Some Erosion

(SE) Excessive

Erosion (EE) Continuing

Erosion (CE) Sum PXX

Fine Base Soil Grading (represents 5% of finest grading curves)

PNE fine = 20%

PSE fine = 60%

PEE fine = 20%

PCE fine = 0%

100%

Average Base Soil Grading (represents 90% of grading curves)

PNE avg. = 20%

PSE avg. = 70%

PEE avg. = 10%

PCE avg. = 0%

100%

Coarse Base Soil Grading (represents 5% of coarsest grading curves)

PNE coarse = 20%

PSE coarse = 70%

PEE coarse = 10%

PCE coarse = 0%

100%

Calculation of Probabilities for No, Some, Excessive and Continuing Erosion (Pxx)

PNE = (5% x PNE fine) + (90% x PNE avg.) + (5% x PNE coarse)

PSE = (5% x PSE fine) + (90% x PSE avg.) + (5% x PSE coarse)

PEE = (5% x PEE fine) + (90% x PEE avg.) + (5% x PEE coarse)

PCE = (5% x PCE fine) + (90% x PCE avg.) + (5% x PCE coarse)

Calculation Result

20% 69.5% 10.5% 0% 100%

Assigned Probabilities

PNE = 0.20 PSE = 0.69 PEE = 0.11 PCE = 0.0001(a) 1.000

Notes: (a) Even though there are no filter gradings falling into the continuing erosion category in this example, a probability of 0.0001 was assigned for continuing erosion based on the guidance given in Table 10.8. This takes into account the possibility of the materials in the dam being coarser than indicated by the gradation curves. In this example, the filter gradation envelope is significantly finer than the continuing erosion boundary, and hence a very low probability is assigned based on Table 10.8.


10-16

10.1.5 Probability of continuation (PCE) – Scenario 4 (internal erosion into open defects, joints, or cracks in conduits, walls, toe drains, or rock foundations)

For erosion to continue through an open defect, the defect needs to be sufficiently open to allow the soil surrounding the defect to pass through it. The recommended procedure is as follows:

1. Compare the D95 of the coarse soil grading of the soil in contact with the open defect, joint, or crack to the JOS. If the D95,coarse ≤ JOS, then PCE = 1.0.

2. Compare the D95 of the fine soil grading of the soil in contact with the open defect, joint, or crack to the JOS. If the D95,fine > JOS, then determine PCE by interpolation using D95,fine in Table 10.10.

3. Estimate PCE by estimating the proportion of the soil grading at 95% passing finer than the JOS

For conduits, walls, or toe drains, use the JOS determined from inspection. If there is no inspection, assume a JOS of 5 mm. The supporting document gives additional details into the assessment of erosion into a toe drain and considers the observed condition of the toe drain (from video or external inspections) and the design and construction details of the toe drain. For rock defects, use the midpoint of the defect size range for the JOS.

Table 10.10 – Probability of continuation for open defects, joints, or cracks

Comparison of joint opening in the dam (JOS) to the Continuing Erosion criteria

Joint Opening in the dam Probability for Continuing Erosion (PCE)

JOS < 0.1x D95 0.0001

JOS < 0.2 x D95 0.001

JOS < 0.5 x D95 0.01

JOS = D95 0.1

JOS > D95 Estimate based on the proportion of the base soil grading (at 95% passing) finer than the JOS


10-17

10.2 Probability of Continuation for Internal Erosion through Soil Foundations


Given the exit condition is unfiltered, the probability of continuation will be 1.0. Given the exit is filtered, estimate the probability for continuing erosion using the method described in Section 10.1.4.

When considering seepage parths in the foundation, it needs to be recognized that low permeability strata beneath horizontal drains may prevent them working effectively. Figure 10.7 shows an alluvial foundation where the lower permeability strata (A and E) will prevent the seepage in the most permeable sand and gravel strata (B and D) from flowing into a filtered exit in the horizontal drain. For the situation of backward erosion piping or suffusion within a foundation sand layer which has an overlying low permeability (confining) layer, an unfiltered exit is implicit if a heave condition or a sand boil is present, or if there is a defect in the confining layer. In Figure 10.7, the possible seepage paths include through the confining layer (stratum E) due to heave or defects and an unfiltered exit for strata B and D if they daylight downstream of the dam. Figure 10.8 shows a foundation sand layer daylighting at an unfiltered exit downstream of the dam.

Figure 10.7 – Example of unfiltered exits in the soil foundation


10-18

Foundation filter

Sand layer

Unfiltered exit

Figure 10.8 – Example of an unfiltered exit in the soil foundation due to daylighting of the foundation sand layer downstream of the dam

10.3 Probability of Continuation for Internal Erosion of the Embankment into or at the Foundation

10.3.1 Scour along rock defects or erosion into rock defects

Assess the probability of continuation (PCE) by evaluating the exit conditions downstream of the core of the dam to determine if the soil can exit the rock defects. Three scenarios are possible:

• If the rock defects daylight downstream with an unprotected exit, then the probability of continuation is 1.0. The exit can be above or below the tailwater surface.

• It is also possible that the network of rock defects has enough capacity below or downstream of the core to accept enough material to allow erosion to continue. If this condition exists, then the probability of continuation is 1.0.


10.3.2 Scour along the contact or erosion into open-work granular foundations

The process for evaluating continuing erosion for open-work granular foundations is basically the same as for rock defects. Assess the probability of continuation (PCE) by evaluating the exit conditions


10-19

downstream of the core of the dam to determine if the soil can exit the open granular foundation. Three scenarios are possible:

• If the open granular soils daylight downstream with an unprotected exit, then the probability of continuation is 1.0. The exit can be above or below the tailwater surface.

• It is also possible that the void space in open-work coarse-grained foundation soil has enough capacity below or downstream of the core to accept enough material to allow erosion to continue. If this condition exists, then the probability of continuation is 1.0.


Probability of Progression Section 11

11-1

11 Probability of Progression


Step 1: Estimate the probability that the soil will “hold a roof” over a pipe (Section 11.2).

Step 2: Estimate the probability that “crack filling” action will not stop the erosion process (Section 11.3).

Step 3: Estimate the probability that flow in the developing pipe will not be restricted by an upstream zone (or for example a concrete face slab) so the erosion process continues to develop (Section 11.4).

11.2 Probability of Forming a Roof

11.2.1 Internal erosion through the embankment

For internal erosion and piping through the dam or piping from the embankment into a rock foundation, the core must be capable of holding the roof of a pipe. Assess the probability of the soil forming a roof of a pipe using Table 11.1.

11.2.2 Internal erosion through a soil foundation

For internal erosion and piping through a soil foundation, the roof of a pipe will be formed by layers of soil in the foundation which are cohesive or have high fines content, or by the core of the embankment. Other geological conditions which may form a roof within a soil foundation include where basalts overly the soil layer.

Assess the probability of the embankment and foundation materials supporting the roof of a pipe in the foundation using Table 11.1.

In most cases, the core of the embankment is capable of providing a roof to a developing pipe in the foundation. However, if there are upstream or downstream zones of non plastic granular material in the embankment that are not capable of supporting a roof of a pipe (e.g., rockfill or gravel shells), then a pipe through the foundation may not be able to fully develop. Figure 11.1(b) shows an example of this.


11-2

(a) Homogeneous earthfill dam

(b) Dam with gravel or rockfill shells

Figure 11.1 – Scenarios for holding a roof of a pipe for internal erosion through the foundation

SAND

1

SAND

1 3

2 2

3

ROCKFILL OR GRAVEL SHELLS

PIPE COLLAPSE LEADING TO SINKHOLE


11-3

Table 11.1 – Probability of a soil being able to support a roof to an erosion pipe (PPR)

Soil Classification Percentage Fines

Plasticity of the Fines Moisture Condition Likelihood of

Supporting a Roof

Clays, sandy clays (CL, CH, CL-CH)

> 50% Plastic Moist or saturated 1.0

ML or MH >50% Plastic or non-plastic

Moist or saturated 1.0

Sandy clays, Gravely clays, (SC, GC)

15% - 50% Plastic Moist or Saturated 1.0

Silty sands, Silty gravels,

Silty sandy gravel (SM, GM)

> 15% Non-plastic Moist Saturated

0.7 to 1.0 0.5 to 1.0

Granular soils with some cohesive fines (SC-SP, SC-SW, GC-GP, GC-GW)

5% to 15% Plastic Moist Saturated

0.5 to 1.0 0.2 to 0.5

Granular soils with some non plastic fines (SM-SP, SM-SW, GM-GP, GM-GW)

5% to 15% Non-plastic Moist Saturated

0.05 to 0.1 0.02 to 0.05

Granular soils, (SP, SW, GP, GW)

< 5% Non-plastic

Plastic

Moist and saturated

Moist and saturated

0.0001

0.001 to 0.01

Notes: (1) Lower range of probabilities is for poorly compacted materials (i.e., not rolled), and upper bound for well compacted materials.

(2) Cemented materials give higher probabilities than indicated in the table. If soils are cemented, use the category that best describes the particular situation.


11-4

11.3 Probability of Crack Filling Action Being Ineffective

11.3.1 Internal erosion through the embankment

Estimate the probability of crack filling action not stopping pipe enlargement using Table 11.2.

For piping through the dam or piping from the dam into a rock foundation, crack filling from an upstream zone can limit the extent of erosion in the core if the materials washed into the crack or pipe are capable of filtering against the downstream filter or transition zone. The washed in materials aid in the filtering action against the downstream zone. This will be of greatest benefit in cases where there is poor filter compatibility between the core and downstream filter due to a lack of sand size particles in the core. In these cases, the probability of continuation may be high, but the washed in materials may be capable of filtering against the downstream filter zone and this reduces the potential for the pipe enlarging. There is less benefit where the materials that are washed in are of similar sizes to those already in the core. Hence the probabilities for crack filling in Table 11.2 are higher for a well graded core material compared to those for a core which is deficient in sand sizes. There is very little benefit where there is no downstream filter/transition zone.

11.3.2 Internal erosion through the foundation

The potential for crack filling action for internal erosion in the foundation applies only if a filtered exit exists. In most cases, PPC will be 1.0.

11.3.3 Internal erosion of the embankment into or at the foundation

The potential for crack filling action for internal erosion of the embankment into or at the foundation applies only if a filtered exit exists. In most cases, PPC will be 1.0.


11-5

Table 11.2 – Probability for crack filling action not stopping pipe enlargement for internal erosion through the embankment (PPC)

Embankment Zoning Upstream Granular Zone

Downstream Filter or Transition or other granular

material

Likelihood of Piping Progressing – Crack Filling

Action Not Effective

Homogeneous, earthfill with toe drain, earthfill with horizontal drain, concrete face earthfill, puddle core earthfill, earthfill with corewall, hydraulic fill

None except for rip rap and filters under these

None or none effective

1.0

Earthfill with vertical and horizontal drain, zoned earthfill

None Present 1.0

Central and sloping core earth and rockfill (or gravel shoulders)

Present Present 0.1 to 0.9 If the core is well-graded and has fine to coarse sand sizes

(0.075 – 4.75 mm) already present (1)

0.01 to 0.1

If the core is deficient in sand sized particles, and washed in sand material aids in sealing

the downstream zone (2).

Notes: (1) Crack filling is more likely to stop pipe enlargement when the core zone is deficient in sand size particles and these particles can be provided by washing in from the upstream zone. This aids in sealing of the downstream filter zone. If the core is well-graded and has sand sizes present, then the potential benefits of crack filling are less as the sand size particles are already present.

(2) Probability dependent on compatibility of particle sizes of granular soils upstream of the core and in the downstream filter transition.


11-6

11.4 Probability for Limitation of Flows

11.4.1 Flow limitation by upstream zone

Estimate the probability that flow in the developing pipe will not be restricted by an upstream zone using Table 11.3. This considers the potential for flow limitation due to zoning within the dam or cutoff walls or other structural elements within the dam or foundation.

11.4.2 Flow into/out of open joint in conduits

Limitation of flows for flow into a non-pressurized conduit is shown in Table 11.3. Erosion into open defects in a conduit may lead to the development of a sinkhole on the embankment, and this is considered under the breach node of the event tree (refer to Section 13.5).

Leakage out of a pressurized conduit is likely to be limited by the defect in the pipe. Estimate the potential flows out of the defects in the conduit pipe, and this is used in Section 13.3 to estimate the likelihood for it to cause slope instability.

11.4.3 Flow into jointed bedrock

The possible scenarios are:

• Erosion initiating at the core-foundation contact where there is no or a shallow cut-off trench. This is likely to lead to the pipe forming through the embankment. For this case, estimate the probability that flow in the developing pipe will not be restricted by an upstream zone use Table 11.3.

• Erosion initiating within a deep cutoff trench into open joints in a rock foundation. The extent of erosion may become limited by the opening width of the rock defects. This is embedded in the system for estimating the likelihood of breach due to the flow through the open joints in the rock foundation (Section 13). The limitation of flows is therefore not applicable to this scenario and a probability of no flow limitation of 1.0 should be used.

Table 11.3 – Probability that flow in the developing pipe will not be restricted by an upstream zone, cut-off wall or a concrete element in the erosion path (PPL)

Characteristics of Upstream Zone, Concrete Element, or Cut-off

Likelihood for No Flow Restriction

Flow limitation by an upstream zone: No zone upstream of core (e.g., homogeneous, earthfill with toe drain, earthfill with filter drains) 1.0


11-7



High permeability zone (e.g., clean rockfill) 1.0

Fill with > 15% cohesive fines, highly likely to support a roof, Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g., common cause cracking)

0.8 to 1.0

Fill with > 15% cohesive fines, highly likely to support a roof, features causing cracking or flaw in the core are not present below the upstream shell

0.01 to 0.1 depending on the confidence that there is not a common

cause defect

Fill with 5% to 15% cohesive fines, likely to support a roof. (1) Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g., common cause cracking)

0.5 to 0.7

Fill with 5% to 15% cohesive fines, likely to support a roof (1), features causing cracking or flaw in the core are not present below the upstream zone


cause defect and fines content

Fill with <15% cohesionless fines, unlikely to support a roof (1) Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g., common cause cracking)

0.4 to 0.9 if gradient across upstream zone is > 1

0.1 to 0.4 if gradient across upstream zone is < 1

Fill with <15% cohesionless fines, unlikely to support a roof (1), features causing cracking or flaw in the core are not present below the upstream zone

0.01 to 0.1 if gradient across upstream zone is <1 (assign a probability

depending on the confidence that there is not a common cause defect)

0.05 to 0.2 if gradient across upstream zone is > 1

Fill with 15% to 30% cohesionless fines, may support a roof, Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g., common cause cracking)

0.2 to 0.8

Fill with 15% to 30% cohesionless fines, may support a roof, features causing cracking or flaw in the core are not present below the upstream shell


cause defect

Fill with > 30% cohesionless fines, may support a roof, Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g., common cause cracking)

0.8 to 1.0

Fill with > 30% cohesionless fines, may support a roof, features causing cracking or flaw in the core are not present below the upstream shell


cause defect

Upstream low permeability blanket (for internal erosion in the foundation)

0.01 to 0.1 depending on the extent of coverage of the piping soil layer

Flow limitation by a concrete element in the embankment: Concrete slab on upstream slope 0.1 to 0.5


11-8



Soil cement wave protection 0.05 to 0.2

Partially penetrating concrete core wall in dam (for internal erosion and piping along foundation contact)

0.01 to 0.001 for piping along the core-foundation contact (depending on

height of the wall)

Flow limitation by cut-off walls in the foundation (for internal erosion and piping in the foundation): Sheet pile walls Extruded: 0.01 to 0.5

Cold-rolled: 0.1 to 0.9 (may use lower bound or possibly even lower if good piezometer data shows wall is integral)

Concrete core wall within embankment (1920’s-1930’s) 0.01 to 0.001(2)

Modern diaphragm walls: Cementitious walls (e.g., conventional concrete, plastic concrete, cement bentonite)

Well-constructed: 0.0001

Serious defects suspected: 0.001

Non-cementitious walls (e.g., soil-bentonite) 0.001 to 0.01

Soil-cement-bentonite wall 0.01 to 0.1

Column walls (e.g., jet grouting, soil mixing) 0.01 to 0.1

Open joint, water stop, crack or other defect in the conduit 0.05 to 0.2

Notes: (1) Need to check whether the upstream zone materials are susceptible to suffusion and backward erosion. If so, fines can wash out and lead to higher permeability, and/or a pipe may develop. At gradients > 1.0, backward erosion is likely.

(2) Need to consider potential size of pipe and ability of downstream shoulder to handle flows. (3) For these walls the soil is excavated by excavator or dragline, and the bentonite mixed with the excavated soil using

earth-moving equipment.

Probability of Unsuccessful Intervention Section 12

12-1

12 Probability of Unsuccessful Intervention

12.1 General Principles

The likelihood that a particular failure path can be detected, and if so, whether it is possible to intervene (e.g., by lowering the reservoir level) or carry out repairs to prevent the dam breaching, is usually best considered as two questions:

1. Will this failure path be detected?

2. Will intervention and repair be possible?

A probability is assigned to each of these questions. The overall probability of detection, intervention and repair is the product of these two probabilities.

The likelihood of detection and successful intervention and repair is dependent on a number of factors including:

a) The category of internal erosion and piping (i.e., internal erosion in the embankment, in the foundation or from the embankment into or at the foundation).

b) The mechanism of initiation of internal erosion (i.e., erosion in a crack, suffusion or backward erosion).

c) The breach mode (i.e., gross enlargement of a pipe, instability of the downstream slope, unraveling or sloughing of the downstream slope, settlement of the foundation, sinkhole development).

d) The nature of and the geometry of the materials in the foundation.

e) The zoning of the embankment, and the materials in the embankment.

f) The reservoir level at the time of the piping incident, and how rapidly it can be drawn down.

g) The type and frequency of monitoring and surveillance at the dam and the training of the staff to recognize a developing internal erosion and piping incident.

h) The ability to get trained personnel out to the site in the event of a piping incident.

i) The ability of those responsible to be able to direct emergency release of the reservoir.

j) The availability of materials and equipment to intervene and carry out repair works.

It is necessary to use judgment to assess these probabilities.


12-2

12.2 Some Information on the Rate of Internal Erosion and Piping

The likelihood of detection and successful intervention or repair depends on the time from when the internal erosion process may be detected to when breach begins.

Fell et al. (2001, 2003) studied case histories of failures and accidents for piping in the embankment, foundation, and embankment to foundation. Based on the case histories and an understanding of the physical processes they provided guidance on the time for progression beyond when a concentrated leak is first observed, and development of a breach. Table 12.1 to Table 12.3 are based on that study.

Table 12.1 should be used to estimate the approximate likely time to dam failure after a concentrated leak is first observed. Table 11.1, Table 12.2, Table 11.3, and Table 12.3 are used in Table 12.1 working from left top right.

Table 12.3 replaces an original table to assess the likely rate of erosion of the core of the embankment or the soil in the foundation. Table 11.1 and Table 11.3 should be used to assess the ability to support a roof and upstream flow limitation respectively.

In these tables the terms for rates are defined as shown in Table 12.4. Dual descriptors are used to describe intermediate terms (e.g., very rapid – rapid for 6 hours). The terms are applied to part (e.g., progression) or the whole process.

Most of the cases studied were for breach by gross enlargement, so the method is applicable to cases where the mechanism is gross enlargement. It is considered to be reasonably applicable to cases where the final breach is by slope instability, following development of a pipe. It will probably underestimate the time for breach by sloughing. Sloughing is a slowly developing breach mode which should take days or weeks to lead to breach.

Breach by sinkhole development is potentially a rapid process in the final stages when the sinkhole emerges into the reservoir. We would expect breach to occur in a small number of hours but do not have case data to support a more refined estimate.

Table 12.1 is used by assigning the values to the first four columns, and selecting the likely time for progression and breach which best fits the data.


12-3

Table 12.1 – A method for the approximation estimation of the time for progression of piping and development of a breach, for breach by gross enlargement, and slope instability linked

to development of a pipe (Fell et al 2001, 2003)

Factors Influencing the Time for Progression and Breach

Ability to Support a Roof

from Table 11.1

Rate of Erosion

from Table 12.2

Upstream Flow Limiter

from Table 11.3

Breach Time

From Table 12.3

Approximate Likely Time (Qualitative)

Approximate Likely Time

Yes R or VR No VR or R-VR Very Rapid < 3 hours

Yes R No R Very Rapid to Rapid 3 to 12 hours

Yes R-M No VR

Yes R No R-M Rapid 12 to 24 hours

Yes R No M or S

Yes R or R-M No M or M-S

Yes M or R-M Yes R or R-M

Rapid to Medium 1 to 2 days

Yes M or R-M No S

Yes R-M or M Yes S Medium 2 to 7 days

Yes M Yes or No S Slow Weeks, even months or years

Note: VR = Very Rapid; R = Rapid; M = Medium; and S = Slow.


12-4

Table 12.2 – Rate of erosion of the core or soil in the foundation

Time for erosion in the core of the embankment or in the foundation Soil Classification

Best Estimate Erosion Rate Index

(IHET) Gradient along pipe 0.2 Gradient along pipe 0.5

SM with <30% fines <2 Very Rapid Very Rapid

SM with > 30% fines 2 to 3 Very Rapid Very Rapid

SC with < 30% fines 2 to 3 Very Rapid Very Rapid

SC with >40% fines 3 Rapid Very Rapid

ML 2 to 3 Very Rapid to Rapid Very Rapid

CL-ML 3 Rapid Very Rapid

CL 3 to 4 Rapid Very Rapid to Rapid

CL-CH 4 Rapid Rapid

MH 3 to 4 Rapid Very Rapid to Rapid

CH with LL < 65 4 Rapid to Medium Rapid

CH with LL > 65 5 Medium to Slow Medium

Table 12.3 – Influence of the material in the downstream zone of the embankment on the likely time for development of a breach

Material Description Likely Breach Time

Coarse grained rockfill Slow – medium

Soil of high plasticity (PI > 50) and high clay size content including clayey gravels

Medium – rapid

Soil of low plasticity (PI < 35) and low clay size content, all poorly compacted soils, silty sandy gravels

Rapid – very rapid

Sand, silty sand, silt Very rapid

Table 12.4 – Qualitative terms for times of development of internal erosion, piping and breach (Fell et al 2001, 2003)

Qualitative Term Equivalent Time

Slow (S) Medium (M)

Rapid (R) Very Rapid (VR)

Weeks or months, even years Days or weeks

Hours (>12 hours) or days <3 hours


12-5

Note that the dispersivity of the soil does not significantly affect the rate of erosion so is not listed as a factor in Table 12.2. For a homogeneous dam, the whole of the embankment is the same soil, so in Table 12.2 the soil is considered as the core, and in Table 12.3 as the downstream zone.

Fell et al (2001, 2003) show that the method gives a reasonable estimate of the time for progression beyond where a concentrated leak is observed and breach and the times are acceptably accurate for the purpose here which is to assess the likelihood of detection, intervention and repair. Fell et al (2001, 2003) caution however, against over-reliance of these figures for life loss estimates where the estimates are sensitive to the assumed warning times. The times estimated in Table 12.1 are only approximate, and hidden or unknown details within a dam or its foundation may give shorter or longer times.

12.3 Detection

12.3.1 Some general principles

Detection may be possible in the continuation or early progression phase, or more likely, in the advanced stages of progression and breach formation. Detection is likely to be by:

1. Observation of increased seepage out of the downstream face of the embankment or in the foundation. This may be by visual observation, or by seepage measurement, or more sophisticated methods such as thermal monitoring of the foundation or the downstream slope.

2. Measured higher pore pressures in the foundation and/or embankment.

3. Settlements, deformation and cracking in the embankment or area downstream of the dam.

Whether detection is likely depends on:

1. The rate at which the internal erosion and piping, and associated processes, such as instability of the downstream face, occurs.

2. The frequency of inspections, and measurement of monitoring equipment.

3. The dam zoning and the location of the concentrated leak and whether the leak will be visible to those doing the inspection.

For example if a process may go from initiation or first presence of a concentrated leak to breach in say 6 hours, and the dam is only inspected or monitored weekly, it is very unlikely that a piping incident will be detected before breach occurs. However, if the dam is visible by the general population, there is some chance the leak may be noticed none-the-less.


12-6

Detection early in the internal erosion process is usually difficult, particularly for erosion initiating along a crack, or by backwards erosion because the amount of leakage is very small at the start. Fell et al (2001, 2003) record that most piping incidents are first identified as a concentrated leak in the progression phase. Suffusion is more likely to be detected by piezometers because the process is slower to develop. The presence of conditions potentially leading to heave and backward erosion in the foundation may also be detected by piezometers provided they are correctly positioned and read as reservoir levels rise.

Visual inspection is a vital tool in detecting internal erosion and piping, whether it is successful is dependent on the factors discussed above, but also on such practical issues as:

• Inspections are seldom practical at night, so there is 30% to 50% of the time (varying throughout the year) when detection will not be effective, particularly for rapidly developing piping mechanism. Many dams are not inspected on weekends, further reducing the likelihood of detection.

• Dense vegetation, runoff from rainfall, snow cover can all hide the presence of a concentrated leak. However it can be the case that melted snow is a good indicator of areas affected by seepage.

• For very long embankments, it is not practical to walk to inspect, so it is less likely small leaks are detected.

It is known that most internal erosion and piping failures occur at reservoir levels close to or above historic high, and the physical processes are driven by the reservoir water. Hence a good monitoring and surveillance program will have a greatly increased frequency of inspections and reading of critical instruments under such reservoir conditions.

12.3.2 Probability of not detecting internal erosion (Pndi)

The probability of not detecting internal erosion is determined by

• Assess the probability of not observing the concentrated leak (Pnol) allowing for the location of the leak for the failure mode under consideration and factors which may mean the leak cannot be observed. This is done using Table 12.5 and Table 12.6.

Assess the probability that given the leak is observable (1 – Pnol), it is not detected (Pnd) allowing for the time between the first appearance of the concentrated leak, and the frequency of inspections and/or reading of monitoring instruments. This is done using:

• Table 12.7.

• The probability of not detecting the concentrated leak given it is observable, Pndi = Pnol + [(1 – Pnol) Pnd].

When using these tables, take account of:


12-7

• The location of the potential leak when assessing the probabilities. For example, there might be a dam where leaks in the abutment area may be readily observed because the foundations are low permeability, and the vegetation is clear, while they may be difficult to observe in the river section because the foundation is high permeability alluvium and the toe overgrown with vegetation.

• The toe of the embankment being drowned out by another reservoir or is in the river, which may make it virtually impossible to detect leaks in this part of the dam.

• The internal erosion mechanism. It may be easier to detect some such mechanisms than others (e.g., backward erosion piping in the foundation because sand boils will form).


12-8

Table 12.5 – Factors influencing the likelihood of not observing a concentrated leak

Influence on Likelihood of Not Observing

Factor Relative

Importance of Factor

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Can a concentrated leak be observed at toe?

(3) Foundation low permeability soil or rock, so leaks will emerge at the toe and No vegetation or only mown grass at toe, observation of leakage is easy

Foundation low permeability soil or rock so leaks will emerge at the toe and/or Vegetation at toe may preclude observation of seepage

Foundation medium permeability soil or rock so leaks may remain in the foundation and not emerge at the toe and/or

Dense vegetation at toe makes observation of seepage difficult

Tailwater drowns part or all of toe, or foundation permeable alluvium so leaks may not emerge at the toe and

Dense vegetation at toe makes observation of seepage difficult

Dam zoning which affects whether leaks emerge on the downstream face of the embankment

(2) Homogeneous, earthfill with core wall, concrete face earthfill

Earthfill with toe drain, zoned earthfill dam, Puddle core,

Earthfill with horizontal and chimney drains, zoned earth and rockfill

Central core earth and rockfill dams, concrete face rockfill, rockfill with core wall

Seepage instrument-tation weirs, etc.

(1) Seepage collected to flow to readily observed measuring weir or real time monitored

Seepage partly collected to flow to measuring weir

Seepage partly collected to flow to measuring weir but masked by rainfall effects

No seepage collection system


12-9

Table 12.6 – Probability of not observing a concentrated leak (Pnol) versus ∑(RFxLF) for internal erosion in an embankment

0.05 0.1 0.2 0.3 0.5 0.9

6 9 12 15 18 24 RFxLF

Table 12.7 – Probability that given the leak is observable it is not detected given the time between the first appearance of the concentrated leak, and the frequency of inspections

and/or reading of monitoring instruments (Pnd)

Probability of Not Detecting the Internal Erosion (Pnd) Given the Time for Development of Concentrated Leak to Initial Breach From Table 12.1

Frequency of Inspection

and /or Monitoring <3 hr 3 to 12 hr 12 to 24 hr 1 to 2 days 2 to 7 days Weeks or

months

Monthly, no public nearby

0.999 0.99 0.95 0.9 0.6 0.1

Monthly, public nearby

0.999 0.8 0.5 0.25 0.1 0.05

Weekly, no public nearby

0.99 0.95 0.9 0.7 0.2 0.1

Weekly, public nearby

0.99 0.75 0.5 0.2 0.1 0.05

Daily, no public nearby

0.9 0.6 0.5 0.1 0.05 0.01

Daily, public nearby

0.8 0.5 0.4 0.1 0.05 0.01

Daily with real-time monitoring of leakage

0.2 0.15 0.1 0.1 0.05 0.01


12-10

12.4 Intervention and Repair

Intervention and repair to prevent the progression of internal erosion and piping and breach can take several forms including:

(i) Drawing down the reservoir level using spillway gates or outlet valves.

(ii) Installing pressure relief wells in the foundation of the embankment.

(iii) Building reverse filters over “boils” or areas where eroding material is emerging from the foundation of the embankment.

(iv) Building a weighting berm to reduce the likelihood of heave, or slope instability, or unraveling.

(v) Dumping granular material (sand/gravel/rockfill) into the upstream side of sinkholes to try to block them.

More than one of these measures may be used together. Which is applicable or feasible will depend on the particular circumstances of the dam.

It should be recognized that there may be reluctance on the part of the reservoir owner or operator to release water given the lost revenue that may result, or if release of reservoir water is likely to result in property damage and loss of life, for example if levee banks downstream of the dam are likely to be overtopped by the flood resulting from release of the water.

Table 12.8 should be used to assess the probability that given the concentrated leak is detected, intervention and repair is not successful. This is done for each pool (reservoir) level partition. It is not practical to cover all the possible scenarios and those doing the risk analysis are required to make their assessment within the range of probabilities shown. In making this assessment consideration should be made for the failure mode and location of the developing pipe.


12-11

Table 12.8 – Assessment of the probability that given the concentrated leak is detected, intervention and repair is not successful (Pdui)

Time for Development of Concentrated Leak to Initial

Breach

What can be done Probability of

Not Intervening

<3 hrs There is too little time to successfully intervene regardless of the failure mode

0.99

3 to 12 hrs In most cases it will be impractical to intervene successfully in this amount of time. Only in cases where there is a straight forward method of intervention, and there are personnel, equipment and materials available will intervention be successful.

0.9

12 to 24 hrs In many cases it will be impractical to intervene successfully in this time. Only in cases where there is a straight forward method of intervention, and there are personnel, equipment and materials available will intervention be successful; or it is a small storage which can be drawn down to stop the failure mode.

0.7

1 to 2 days In many cases it will be impractical to intervene successfully in this time. Only in cases where there is a straight forward method of intervention, and there are personnel, equipment and materials available will intervention be successful; or it is a small storage or medium storage with large gate discharge capacity which can be drawn down to stop the failure mode.

0.5

2 to 7 days In some cases it will be practical to intervene successfully in this time. In cases where there is a straight forward method of intervention, and there are personnel, equipment and materials available; or it is a small storage or medium storage with large gate discharge capacity allowing the reservoir to be drawn down to stop the failure mode.

0.1

Weeks or months In some cases it will be practical to intervene successfully in this time. Where there is a straight forward method of intervention, and there are personnel, equipment and materials available and large resources intervention has a fair chance of being successful; or it is a small or medium storage with large gate discharge capacity allowing the reservoir to be drawn down to stop the failure mode

0.01


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12.5 Probability of Unsuccessful Intervention

The probability of unsuccessful intervention is calculated as follows:

Probability of unsuccessful intervention = [Probability of not observing the concentrated leak because it is not observable] + [Probability leak is observable but not detected] + [Probability leak is observable and detectable but intervention fails], where

[Probability of not observing the concentrated leak because it is not observable] = Pnol

[Probability leak is observable but not detected] = (1 – Pnol) Pnd

[Probability leak is observable and detected but intervention fails] = (1 – Pnol)(1 – Pnd) Pdui

or

Pui = Pnol+ [(1 – Pnol) Pnd] + [(1 – Pnol)(1 – Pnd) Pdui]

This calculation is represented by the sub-event tree structure shown in Figure 12.1.

1 - Pdui

1 - Pnd Intervention successful?

Pdui (1 - Pnol)(1 - Pnd)(Pdui)

1 - Pnol Concentrated leak detected?

Pnd (1 - Pnol)(Pnd)

Concentrated leak observable?

Pnol Pnol

Intervention

Yes

No

Yes

No

Yes

No

Probability of Unsuccessful Intervention,Pui = Summation of these 3 branches

Figure 12.1 – Sub-event tree for calculating the probability of unsuccessful intervention

Probability of Breach Section 13

13-1

13 Probability of Breach

13.1 Overall Approach and Screening


For each general failure mode including internal erosion through the embankment, through the soil foundation, and from the embankment into or at the foundation:

Step 1: Screen the breach mechanisms depending on the dam zoning type using Table 13.1.

Step 2: Estimate the probability of breach by gross enlargement of the pipe using Section 13.2.

Step 3: Estimate the probability of breach by instability of the downstream slope using Section 13.3, which estimates the probability of slope instability and the probability of loss of freeboard given instability.

Step 4: Estimate the probability of breach by sloughing or unraveling of the downstream slope of the embankment using Section 13.4.

Step 5: Estimate the probability of breach by sinkhole development using Section 13.5.

Step 6: Estimate the overall probability of breach by combining the probabilities for each of the four mechanisms, using the appropriate statistical summation Pbreach = 1 – [(1 – Pge) (1 – Psi) (1 – Psu) (1 – Psd)].

13.1.2 Screening of breach mechanisms

For most dam types and failure modes, the likelihood for breach development will be dominated by one or two of the potential breach mechanisms. Breach mechanisms will not necessarily be applicable to some dam zoning types or modes of piping and can be ignored.

Table 13.1 lists those breach mechanisms which should be considered in the assessment depending on the dam zoning type and mode of internal erosion for internal erosion in the embankment due to a crack or poorly compacted zone. Table 13.1 also applies to internal erosion in a soil foundation. Figure 1.1 in Section 1.2 shows the dam zoning types.


13-2

Table 13.1 – Screening of breach mechanisms for internal erosion through the embankment, internal erosion through soil foundations, and of the embankment into the foundation

Breach Mechanisms Dam Zoning Type Gross

Enlargement Slope Instability Sloughing or Unraveling

Sinkhole Development

Homogeneous earthfill * Exclude, except if downstream fill is

cohesionless

Earthfill with filters * Exclude, except if downstream fill is

cohesionless

Earthfill with rockfill toe * Exclude, except if downstream fill is

cohesionless

Zoned earthfill Exclude, except if downstream fill can

support a roof

Exclude, except if downstream fill is

cohesionless

Zoned earthfill and rockfill

Exclude, except if downstream fill can

support a roof

*

Central core earth and rockfill (or gravel shells)

Exclude, except if downstream fill can

support a roof

Exclude, except if existing dam has marginal stability

*

Concrete face earthfill * Exclude, except if downstream fill is

cohesionless

Concrete face rockfill (including gravel fill)

Exclude Exclude, except if dam is gravel or low

permeability

* Exclude

Puddle core earthfill * Exclude, except if downstream fill is

cohesionless

Earthfill with corewall Exclude * Exclude, except if downstream fill is

cohesionless

Rockfill with corewall Exclude Exclude, except if existing dam has marginal stability

*

Hydraulic fill Exclude, except if downstream fill can

support a roof

*

Key: Breach mechanism should be included in the probability estimate. * Breach mechanism should be included in probability estimate and is usually the more critical mechanism.


13-3

Internal erosion by the process of suffusion is very unlikely to lead to the formation of a pipe through the dam or its foundation, and hence the probability of breach by gross enlargement where the mode of erosion is suffusion can be excluded. Breach by slope instability or sloughing/unraveling are usually the more critical mechanisms for suffusion, although the probabilities for breach are usually relatively low for this mode internal erosion.

Erosion into open defects in a non-pressurized conduit is likely to lead to the development of a sinkhole on the embankment, and hence the other breach mechanisms can be excluded. Leakage out of a pressurized conduit is likely to cause slope instability, and hence the other breach mechanisms can be excluded.

13.2 Probability of Breach by Gross Enlargement (Pge)

13.2.1 Screening for internal erosion through the embankment, through the soil foundation, and from the embankment into or at the foundation

• Breach by gross enlargement of the pipe requires a continuing erosion condition.

• For internal erosion through the embankment, breach by gross enlargement can be considered negligible in cases where the downstream shell is unable to support a roof of a pipe. Use Table 13.2 to assess if this applicable.

• If applicable, estimate the probability of breach by gross enlargement using Table 13.3. This considers whether the reservoir will drop below the level of the pipe before the enlarging pipe develops into a breach.

Table 13.2 – Screening for probability of breach by gross enlargement of the pipe: ability to support a pipe

Downstream shell/zone Ability to Support a Roof

Probability of Breach by Gross Enlargement

Downstream shell comprises free draining rockfill, or coarse sandy gravel

Downstream shell comprises sand and gravel, <5% plastic fines or <15% non plastic fines

Very unlikely for piping through dam

Not a likely mode of breach for piping through the dam. Breach by slope instability or unraveling/sloughing are likely to be more critical. Assign probability of breach by gross enlargement Pge = 0.

All other cases Likely Assess using Table 13.3


13-4

13.2.2 Assessment for internal erosion through the embankment, through the soil foundation, and from the embankment into or at the foundation

For breach to occur by gross enlargement of a pipe; the pipe must stay open until it is so large that the settlement of the crest due to the pipe, or collapse of the embankment into the pipe lowers the crest to below the reservoir level. For rock foundations with open defects, gross enlargement can occur if the soil roof (core or foundation materials) is in contact with the defect.

If there is no intervention, the process can only stop if one or more of the following occurs:

a) The hydraulic shear stresses in the pipe reach an equilibrium condition with the erosion resistance of the soil. This will not happen unless the reservoir level drops giving a lower gradient, as the hydraulic shear stress increases with hole diameter for a constant gradient.

b) The reservoir empties or falls below the entrance of the pipe before a breach mechanism is able to develop. This is a common consideration where internal erosion may develop in the upper part of the dam under short duration flood loading conditions.

Table 13.3 provides guidance on the probability of breach by gross enlargement assuming there is no restriction on flows. Table 13.3 considers the duration that the reservoir level is above the pipe. This duration is based on ability of the project to pass the flood loading under normal operations (i.e., through overflow spillway) and not by intervention. Intervention is accounted for separately in Section 12 and thus for breach to occur intervention has failed. For normal reservoirs levels the pool will remain long enough to lead to gross enlargement for IHET < 6 unless normal operations lowers the pool very rapidly. For high reservoir levels leading to spillway flows, the spillway may drawdown the reservoir level below the pipe before gross enlargement leading to breach occurs. Most projects the reservoir levels will remain long enough (> 2 weeks) for gross enlargement for IHET < 6 for all pools under consideration. Use the maximum range given in column 4 unless you have a condition where the pool will only be above the pipe for a very short period. A defect that is above the invert of a dam with an uncontrolled spillway is case where the lower values may apply.


13-5

Table 13.3 – Probability of breach by gross enlargement of the pipe (Pge)

Characteristics of Core or Foundation Materials

Soil Classification Hole Erosion Index (IHET) (1)

Duration Reservoir is above Pipe

Probability of Breach by Gross Enlargement(2)

SM, SC, ML, dispersive soils

≤3

2 to 3

1.0

CL, CL-CH, MH or CH with LL < 65

4 (avg)

3 to 5

>2 days(3)

1-2 days <1 day

0.8 to 0.95(3)

0.6 to 0.8(4) 0.3 to 0.6(4)

CH with LL > 65 5 (avg)

4 to 6

> 2 weeks(3)

1 – 2 weeks <1 week

0.8 to 0.95(3)

0.3 to 0.8(4)

0.1 to 0.3(4)

CH with HET carried out >6 Pipe will likely self limit and probability of gross enlargement is

low regardless of duration

.001

Notes: (1) IHET from Hole Erosion Tests. (2) The basis for the judgmental probabilities is given in the supporting information document. (3) For most projects, the reservoir level under consideration will remain long enough to lead to breach by gross

enlargement for these soils. (4) Only use these ranges when the duration the pool is short under normal operating conditions such as a defect that is

above the invert of an uncontrolled spillway.

13.3 Probability of Breach by Slope Instability (Psi)

13.3.1 Approach

• For internal erosion in embankments, soil foundations and from embankment to foundation, estimate the probability of slope instability occurring due to the increased seepage flows (Psi-i) using Table 13.4 and Table 13.5.

• For internal erosion in rock foundations, use Section 13.3.3 and Table 13.6 to Table 13.9.

• Estimate the probability of loss of freeboard due to instability (Psi-lf) using Table 13.10 and Table 13.11.

• The probability of breach by slope instability is equal to (Psi-i) x (Psi-lf).


13-6

13.3.2 Probability of slope instability initiates for internal erosion through the embankment, through the soil foundation, and from the embankment into or at the foundation (Psi-i)

The assessment considers whether internal drainage measures in the dam are able to prevent pore pressures rising in the dam and/or foundation and whether the factor of safety of the dam falls below 1.0 if pore pressures do increase.

Estimate the probability of a downstream slide initiating using Table 13.4 and Table 13.5. It is assumed that seepage in a soil foundation will exit under the embankment.


13-7

Table 13.4 – Factors influencing the likelihood of breach by instability of the downstream slope: slide initiates for internal erosion through the embankment, through the soil

foundations, and from the embankment into or at the foundation


Factor

Relative

Importance of Factor

(RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Internal drainage measures in dam

(3) Good

Filter drains with good discharge capacity Or free draining rockfill or clean sandy gravel in the downstream zones

Moderate

Single stage filter zones Or sandy gravel, or moderate fines rockfill in the downstream zones

Limited

Filter drain with excessive fines, poor discharge capacity, Or silty sandy gravel, or high fines content weathered rockfill in the downstream zones

None

No or limited zoning of materials and no filter drains

Downstream Slope For dams with an earthfill downstream zone (a)

(2)

3H:1V or flatter

2.5H:1V

2H:1V

Steeper than 1.8H:1V

OR

For dams with a free draining rockfill downstream zone (b)

Flatter than 1.75H: 1V

1.5H: 1V Steeper than 1.4H: 1V

Steeper than 1.3H: 1V

Downstream shell materials

(1) Sandy gravel <5% fines, Coarse grained, free draining rockfill

Sandy gravel 5-20% fines “Dirty” rockfill

Silty sand, silty sandy gravel, 20-50% fines

Cohesive soils,

Fine grained rockfill

Notes: (a) Applies to the following dam types; homogeneous earthfill, earthfill with filter, earthfill with rock toe, zoned earthfill, concrete face earthfill, puddle core earthfill, earthfill with core wall and hydraulic fill.

(b) Applies to the following dam types; zoned earth and rockfill, central core earth and rockfill, concrete face rockfill and rockfill with core wall.


13-8

Table 13.5 – Probability of breach by slope instability: slide initiates for internal erosion through the embankment, through soil foundations, and from the embankment into or at the

foundation (Psi-i) versus ∑(RFxLF)

0.001 0.003 0.005 0.02 0.1 0.9

6 9 11 13 18 24 RFxLF

13.3.3 Probability of slope instability of the embankment initiates for internal erosion in a rock foundation (Psi-i)

• Estimate the probability that leakage through the rock foundations exits into the downstream shell PS using Table 13.6.

• Estimate the probability of slope instability initiating due to the increased leakage flows (Psi-i) using Table 13.7, Table 13.8 and Table 13.9.

The assessment considers whether the internal drainage measures in the dam are able to prevent pore pressures rising in the dam and/or foundation and whether the factor of safety of the dam falls below 1.0 if pore pressures do increase.


13-9

Table 13.6 – Probability of seepage exits from defects or solution features in a rock foundation into the downstream shell (PS)

Scenarios Probability of the Seepage

Path Exiting into the Downstream Shell

The open defect in the rock foundation daylights downstream of the dam, and the defect is not in direct contact with the downstream shell, and there is very limited interconnectivity through other joint sets

Negligible. Adopt PS = 0

The open defect in the rock foundation daylights downstream of the dam, and the defect is not in direct contact with downstream shell, but there is a likely connection into the downstream shell via an interconnected open joint set

0.1 to 0.5

The open defect in the rock foundation daylights downstream of the dam, and the defect is likely to be in direct contact with downstream shell

0.5 to 1.0 (a)

The open defect in the rock foundation does not daylight downstream of the dam, and the defect is in direct contact with downstream shell

1.0 (a)

Note (a) The geometry of the leakage flow path affects the flow rate. If the leakage path daylights downstream of the dam it is likely there will be less flow into the downstream shell of the dam.

Evaluate the relative discharge capacity of the foundation drains and downstream zone compared to the size of the defect in the rock foundation using Table 13.7.

Estimate the probability of a downstream slide initiating using Table 13.8 and Table 13.9.


13-10

Table 13.7 – Assessment of size of leak in defect or solution feature in a rock foundation relative to discharge capacity of foundation drains and downstream shell

Discharge capacity of foundation drain and downstream zone

Width of Defect or solution feature exiting into the

Downstream Zone

Poor No or limited zoning of materials and no

foundation filter drains

Limited Foundation filter

drain with excessive fines, poor

discharge capacity, Or silty sandy

gravel, or high fines content weathered

rockfill in the downstream zones

Moderate Single stage

foundation filter zone

Or sandy gravel, or moderate fines rockfill in the

downstream zones

Good Foundation filter drains with good

discharge capacity Or free draining rockfill or clean

sandy gravel in the downstream zones

<5 mm N N LL Negligible

5-25 mm ML ML N LL

25-100 mm MML MML ML N

>100 mm MML MML MML ML

Note: LL = Less Likely; N = Neutral; ML = More Likely; MML = Much More Likely


13-11

Table 13.8 – Factors influencing the likelihood of breach by instability of the downstream slope: slide initiates for internal erosion in rock foundation


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Size of leak relative to discharge capacity of the foundation drains and downstream shell (from Table 13.7)

(3) LL Refer to Table 13.7

N Refer to Table 13.7

ML Refer to Table 13.7

MML Refer to Table 13.7

Downstream Slope

For dams with an earthfill downstream zone (a)

(2)

3H:1V or flatter

2.5H:1V

2H:1V

Steeper than 1.8H:1V

OR

For dams with a free draining rockfill downstream zone (b)

Flatter than 1.75H: 1V



Downstream shell materials

(1) Sandy gravel <5% fines, Coarse grained, free draining rockfill

Sandy gravel 5-20% fines ‘Dirty’ rockfill

Silty sand, silty sandy gravel, 20-50% fines

Cohesive soils,


Notes: (a) Applies to the following dam types; homogeneous earthfill, earthfill with filter, earthfill with rock toe, zoned earthfill, concrete face earthfill, puddle core earthfill, earthfill with core wall and hydraulic fill.

(b) Applies to the following dam types; zoned earth and rockfill, central core earth and rockfill, concrete face rockfill and rockfill with core wall.


13-12

Table 13.9 – Estimation of the probability of breach by slope instability: slide initiates for internal erosion in rock foundations (Psi-i) versus ∑(RFxLF)

0.001 0.003 0.006 0.02 0.1 0.9

6 9 11 13 18 24 RFxLF

13.3.4 Loss of freeboard due to slope instability (Psi-lf)

The assessment considers whether the resulting sliding deformations are sufficient to result in loss of freeboard so the reservoir overtops the dam crest. Estimate the probability of loss of freeboard using Table 13.10 and Table 13.11.

Table 13.10 – Factors influencing the likelihood of breaching by instability of the

downstream slope: loss of freeboard


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Freeboard compared to dam height at the time of incident

(3) > 7% ≈ 5% < 3% < 1%

Presence of strain weakening soils in the embankment and foundation

(2) Sandy clays, low to medium plasticity, clay size content <20%, or medium dense to dense dilative non cohesive soils or rockfill.

Clays, sandy clays, clay size content 20% to 40%, or medium dense non cohesive soils.

Clays, sandy clays, high plasticity; clay size content (% passing 0.002 mm) > 40% or/and saturated, very loose sand, or loose silty sand contractive on shearing

As for more likely, but with very high clay size content or very loose contractive granular soil

Crest width (1) > 30 ft (9m) ≈ 20 ft (6m) < 13 ft (4m) ≤ 10 ft (3m)


13-13

Table 13.11 – Probability of breach by loss of freeboard (Psi-lf) versus ∑(RFxLF)

0.001 0.005 0.02 0.1 0.5 1.0

6 9 11 13 18 24

13.4 Estimation of the Probability of Breach by Sloughing or Unraveling (Psu)

For sloughing to occur, the downstream face would have to be relatively steep, and the shoulder material a cohesionless soil, probably sandy gravel, or gravely sand, possibly with some silty fines. The process would have to be allowed to continue until it gradually eroded away the crest and allowed the reservoir to overtop the embankment.

Unraveling usually relates to the progressive removal of individual rocks by fairly large seepage flows flowing through the downstream rockfill.

The approach is:

• For internal erosion in rock foundations, Estimate the probability that seepage through the rock foundations exits into the downstream shell PS using Table 13.6.

• For internal erosion in the embankment, soil foundation and embankment into foundation, assume that the seepage will emerge into the downstream shell of the embankment, so PS = 1.0.

• For dams with a downstream zone of earthfill (i.e., clay, silt, sand or gravel) use Table 13.12 and Table 13.13 to estimate the probability of breach by sloughing Psl.

• For dams with a downstream zone of rockfill, use Table 13.14 and Table 13.15 to estimate the probability of breach by unraveling Pun.

• The probability of breach by sloughing or unraveling is equal to (PS) x (Psl) for dams with a downstream zone of earthfill or (PS) x (Pun) for dams with a rockfill shell.


13-14

Table 13.12 – Factors influencing the likelihood of breaching by sloughing: dams with an earthfill downstream zone


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Material in downstream zone

(3) Cohesive soils


Sandy gravel <20% fines,

Silty sand, silty sandy gravel, 20%-50% non plastic fines.

As for more likely, but uncompacted materials

Freeboard at the time of incident

(2) > 13 ft (4 m) ≈ 10 ft (3 m) < 6 ft (2 m) < 3 ft (1 m)

Downstream slope of the embankment

(1) 3H:1V or flatter 2.5H: 1V 2H: 1V Steeper than 1.8H: 1V

Note: Table 13.12 applies to the following dam types; homogeneous earthfill, earthfill with filter, earthfill with rock toe, zoned earthfill, concrete face earthfill, puddle core earthfill, earthfill with core wall and hydraulic fill.

Table 13.13 – Probability of breach by sloughing (earthfill) for internal erosion through the embankment, through soil foundations, and from the embankment into the foundation (Psl)

versus ∑(RFxLF)

negligible negligible 0.05 0.1 0.5 0.9 1.0

6 8 9 11 13 18 24 RFxLF

Note: For open rock defects, the defect must discharge into the downstream shell.


13-15

Table 13.14 – Factors influencing the likelihood of breaching by unraveling: dams with a rockfill downstream zone


Factor Relative

Importance of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Material in downstream zone

(3) Coarse grained free draining rockfill.

Medium grained “dirty” rockfill


As for more likely, but uncompacted materials

Downstream slope of the embankment

(2) Flatter than 1.75H: 1V



Freeboard at the time of incident

(1) > 13 ft (4 m) ≈ 10 ft (3 m) < 6 ft (2 m) < 3 ft (1 m)

Note: Table 13.14 applies to the following dam types; zoned earth and rockfill, central core earth and rockfill, concrete face rockfill and rockfill with core wall.

Table 13.15 – Probability of breach by unraveling (rockfill) for internal erosion through the embankment, through soil foundations, and from the embankment into the foundation (Pun)

versus ∑(RFxLF)

0.5 0.6 0.7 0.8 0.9 1.0

6 9 11 13 18 24 RFxLF

Note: For open rock defects, the defect must discharge into the downstream shell.


13-16

13.5 Probability of Breach by Sinkhole Development (Psd)

13.5.1 Approach

• Estimate the probability of a sinkhole developing as a result of the internal erosion (Ps-f).

• Estimate the probability that the sinkhole causes loss of freeboard (Ps-lf). Assume the sinkhole develops on the crest unless there is a specific reason to expect it to develop elsewhere on the embankment.

• The probability of breach by sinkhole development, Psd = (Ps-f) (Ps-lf).

13.5.2 Probability of sinkhole formation (Ps-f)

Estimate the probability of a sinkhole developing as a result of the internal erosion (Ps-f) using Table 13.16.

Table 13.16 – Probability of a sinkhole or crest settlement developing (Ps-f)

Mode of internal erosion Probability of sinkhole or crest

settlement developing given internal erosion has initiated

Internal erosion in the embankment and into the foundation

0.6

Internal erosion in the foundation 0.3

13.5.3 Probability of loss of freeboard due to sinkhole formation (Ps-lf)

For breach to occur by sinkhole development into an erosion pipe in the embankment, the sinkhole or crest settlement would need to be sufficiently large to settle the crest to below reservoir level. For internal erosion in the foundation, loss of freeboard can also occur by excessive settlement of the embankment induced by the loss of foundation materials.

Estimate the probability of loss of freeboard due to sinkhole formation using Table 13.17 and Table 13.18.


13-17

Table 13.17 – Factors influencing the likelihood of breaching by sinkhole development: loss of freeboard given sinkhole develops


Factor

Relative Importance

of Factor (RF)

Less Likely (1)

Neutral (2)

More Likely (3)

Much More Likely

(4)

Freeboard at the time of the incident

(3) > 13 ft (4 m) ≈ 10 ft (3 m) < 6 ft (2 m) < 3 ft (1 m)

Width of crest (2) > 30 ft (9 m) ≈ 20 ft (6 m) < 13 ft (4 m) ≤ 10 ft (3 m)

Material in the core of the embankment

(1) High plasticity clay, well compacted

Low to medium plasticity clays, and sandy clays

Non-cohesive, silty sand or silty sandy gravel

As for more likely, poorly compacted, loose

Table 13.18 – Probability of breach by sinkhole development: loss of freeboard given sinkhole develops (Ps-lf) versus ∑(RFxLF)

0.0002 0.0005 0.001 0.005 0.02 0.2

6 9 11 13 18 24 RFxLF

References Section 14

14-1

14 References

Barneich, J., Majors, D., Moriwaki, Y., Kulkarni, R. and Davidson, R., Application of reliability analysis in the Environmental Impact Report (EIR) and design of a major dam project. Proceedings of Uncertainty 1996. Geotechnical Engineering Division, ASCE.

Fell, R., Wan, C.F., Cyganiewicz, J. and Foster, M. (2001). The time for development and detectability of internal erosion and piping on embankment dams and their foundations. UNICIV Report No. R-399, ISBN: 84841 366 3. School of Civil and Environmental Engineering, The University of New South Wales.

Fell, R., Wan, C.F., Cyganiewicz, J. and Foster, M. (2003). Time for development of internal erosion and piping in embankment dams. ASCE Journal of Geotechnical and GeoEnvironmental Engineering, Vol. 129, No.4, 307-314.

Fell, R., Wan, C.F. and Foster, M. (2004). Methods for estimating the probability of failure of embankment dams by internal erosion and piping – piping through the embankment. UNICIV Report No. R-428, The University of New South Wales, Sydney, Australia. ISBN 85841 395 7.

Fell, R. and Wan, C.F. (2005) Methods for estimating the probability of failure of embankment dams by internal erosion and piping in the foundation and from embankment to foundation. UNICIV Report No R-436, The University of New South Wales, Sydney, Australia 2052.ISBN: 85841 403 1.

FEMA (2005) Conduits through Embankment Dams, Best practices for design, construction, problem identification and evaluation, inspection, maintenance, renovation and repair, L-266, Federal Emergency Management Agency.

Foster, M.A. (1999). The probability of failure of embankment dams by internal erosion and piping. PhD thesis, School of Civil and Environmental Engineering, The University of New South Wales.

Foster, M.A. and Fell, R. (1999a). A Framework for Estimating the Probability of Failure of Embankment Dams by Piping Using Event Tree Methods. UNICIV Report No. R-377. School of Civil and Environmental Engineering, The University of New South Wales. ISBN: 85841 343 4.

Foster, M.A. and Fell, R. (1999b). Assessing Embankment Dam Filters Which Do Not Satisfy Design Criteria. UNICIV Report No. R-376, School of Civil and Environmental Engineering, University of New South Wales. ISBN: 85841 343 4, ISSN 0077-880X.

Foster, M. and Fell, R. (2000). Use of Event Trees to Estimate the Probability of Failure of Embankment Dams by Internal Erosion and Piping. 20th Congress on Large Dams, Beijing. Vol. 1, 237-260. ICOLD, Paris.

Foster, M. and Fell, R. (2001). Assessing embankment dams, filters which do not satisfy design criteria, J. Geotechnical and Geoenvironmental Engineering, ASCE, Vol.127, No.4, May 2001, 398-407.

References Section 14

14-2

Maniam, M. (2004). Critical seepage gradients beneath embankment dams. Bachelor of Civil Engineering thesis, School of Civil and Environmental Engineering, The University of New South Wales, Sydney.

Pells, S. and Fell, R. (2002). Damage and Cracking of Embankment Dams by Earthquakes, and the Implications for Internal Erosion and Piping. UNICIV Report No. R-406, School of Civil and Environmental Engineering, The University of New South Wales, ISBN: 85841 375 2.

Pells, S. and Fell, R. (2003). Damage and Cracking of Embankment Dams by Earthquake and the Implications for Internal Erosion and Piping. Proceedings 21st Internal Congress on Large Dams, Montreal. ICOLD, Paris Q83-R17, International Commission on Large Dams, Paris.

Schmertmann, J.H. (2000). The non-filter factor of safety against piping through sands. ASCE Geotechnical Special Publication No. 111, Judgment and Innovation. Edited by F. Silva and E. Kavazanjian, ASCE, Reston.

Sherard, J.L. and Dunnigan, L.P. (1989). Critical filters for impervious soils. J. Geotech. Eng. ASCE, Vol.115, No.7, 927-947.

Skempton A.W. and Brogan, J.M. (1994). Experiments on piping in sandy gravels. Geotechnique 44, No.3, 449-460.

Sowers, G.B. and Sowers, G.F. (1970). Introductory Soil Mechanics and Foundations. MacMillan Publishing Co., New York.

Wan, C.F. and Fell, R. (2004). Experimental investigation of internal instability of soils in embankment dams and their foundations. UNICIV Report No.429, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, ISBN 85841 396 5.

Wan, C.F. and Fell, R. (2002). Investigation of internal erosion and piping of soils in embankment dams by the slot erosion test and the hole erosion test. UNICIV Report No. R-412, ISBN: 85841 379 5, School of Civil and Environmental Engineering, The University of New South Wales.

Wan, C.F. and Fell, R. (2004). Experimental investigation of internal instability of soils in embankment dams and their foundations. UNICIV Report No.429, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, ISBN 85841 396 5.

Wan, C.F. and Fell, R. (2004a). Investigation of rate of erosion of soils in embankment dams. ASCE Journal of Geotechnical and GeoEnvironmental Engineering, Vol. 130, No. 4, 373-380.

Wan, C.F. and Fell, R. (2004b). Laboratory tests on the rate of piping erosion of soils in embankment dams. Geotechnical Testing Journal, vol.27, No.3, 295-303.

Weijers, J.B.A and Sellmeijer, J.B. (1993). A new model to deal with the piping mechanism on “Filters in Geotechnical and Hydraulic Engineering. Brauns, Herbaum and Schuler (editors), Balkema, Rotterdam.

Appendix A Navigation Tables for Internal Erosion

through the Embankment

A-1

Table A1 – Probability of Failure by Internal Erosion through the Embankment (Sheet 1)

Initiating Mechanism Sketch

(1) Evaluate Probability of a

Flaw

Pflaw

(2) Evaluate the Probability of

Initiation of Erosion PI

(3) Probabilities for Continuing Erosion

PCE

(4) Probability of Progression

PP

(5) Probability of Breach

Pbreach

(6) Calculate the Probability of Failure

Pfail

(7) Probability of Unsuccessful Intervention

Pui

Initiation of Erosion in Transverse Cracks in the Embankment

IM1-IM8

Determine the probability of a crack using Section 5. This is also described in Table A2.

Pflaw(IMx)

Determine Probability of initiation for each crack initiating mechanism using Section 5. This is also described in Table A2.

PI

Evaluate the probabilities for Continuing Erosion for the failure path under consideration using Section 10

PCE

Estimate the probabilities for Progression for the failure path under consideration using Section 11

PP

Estimate the probabilities of breach using Section 13

Pbreach

Calculate the probability of failure for each IM using the event tree

Pfail =Pflaw(IMx) x PI x PCE x PP x Pbreach

Estimate the probability for unsuccessful intervention using Section 12

Breach

Progression Use Chapter 13

Use Chapter 11Continuation

Initiation Use Chapter 10

Use Section 5

Use Section 5

Traverse Crack in Embankment

Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach

* Evaluate the probabilty of unsuccessful intervention using Chapter 12. This will be input into the risk engine. Do not include it in the system response estimate.

PCE

+

Pfail

Crack Cross Section

A-2

Table A1 – Probability of Failure by Internal Erosion through the Embankment (Sheet 2)



Flaw

Pflaw




PCE


PP


Pbreach


Pfail


Pui

Initiation of Erosion in Hydraulic Fractures in the Embankment

IM9-IM12

Determine the probability of a hydraulic fracture crack using Section 5. This is also described in Table A3.

Pflaw(IMx)


PI


PCE


PP


Pbreach




Breach




Use Section 5

Use Section 5

Hydraulic Fracture in Embankment

Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach


PCE

+

Probabilty of Failure

Pfail

Hydraulic Fracture

Cross Section

A-3

Table A1 – Probability of Failure by Internal Erosion Through the Embankment (Sheet 3)



Flaw

Pflaw




PCE


PP


Pbreach


Pfail


Pui

Initiation of Erosion in Poorly Compacted or High Permeability Zones in the Embankment

IM13-IM16

Cross SectionPoorly Compacted or High Permeability Zone



Determine the probability of a poorly compacted or high permeability zone using Section 6. This is also described in Table A4.

Pflaw(IMx)


PI


PCE


PP


Pbreach




Breach




Use Section 6

Use Section 6

Poorly Compacted or High Perm. Zone

Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach


PCE

+


Pfail

A-4




Flaw

Pflaw




PCE


PP


Pbreach


Pfail


Pui

Initiation of Erosion in Poorly Compacted or High Permeability Zones adjacent to a Conduit

IM17

Cross Section

Conduit

Cross Section

Conduit


Pflaw(IMx)


PI


PCE


PP


Pbreach




Breach




Use Section 6

Use Section 6


Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach


PCE

+


Pfail

A-5




Flaw

Pflaw




PCE


PP


Pbreach


Pfail


Pui

Initiation of Erosion into an Open Joint or Crack in a Conduit

IM18

Determine the probability of an open joint or crack in the conduit using Section 6

Pflaw(IMx)

Determine Probability of initiation using Section 6

PI


PCE


PP


Pbreach




Breach




Use Section 6

Use Section 6

Flaw in Conduit

Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach


PCE

+


Pfail

A-6




Flaw

Pflaw




PCE


PP


Pbreach


Pfail


Pui

Initiation of Erosion in Poorly Compacted or High Permeability Zones adjacent to a Spillway or Abutment Wall

IM19


Pflaw(IMx)

Determine Probability of initiation using Section 6. This is also described in Table A4.

PI


PCE


PP


Pbreach




Breach




Use Section 6

Use Section 6


Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach


PCE

+


Pfail

A-7


Initiating Mechanism Sketch (1) Evaluate Probability of a

Flaw

Pflaw




PCE


PP


Pbreach


Pfail


Pui

Initiation of Erosion in Traverse Cracks adjacent to a Spillway or Abutment Wall

IM20-IM21


Pflaw(IMx)

Determine Probability of initiation using Section 5. This is also described in Table A5.

PI


PCE


PP


Pbreach




Breach




Use Section 5

Use Section 5

Traverse Crack Adjacent to Wall

Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach


PCE

+

Pfail

A-8

Table A2 – Probability of a Crack in the Embankment and Initiation of Erosion

Probability of Cracking in the Embankment (Pflaw)

Probability of Initiation of Erosion (PI)

Initiating Mechanism for Transverse Cracking (1) Assess ∑(RFxLF)

and estimate probability of a crack

(PC.xx)

(2) Assess factors for measured settlement

and observed cracking (MOU) and

calculate Pflaw

(1) Estimate maximum likely crack width at the top of the core

(Cmax)

(2) Estimate maximum likely crack depth (D)

(3) Estimate likely crack width at

reservoir stage under consideration (W)

(4) Estimate probability of erosion

(PI)

IM1 – Cross valley differential settlement

Crack

Long Section

Crack

Long Section

Assess ∑(RFxLF) from Table 5.1 and estimate probability from Table 5.2

PC.1

Assess multiplication factors from Table 5.21 and Table 5.22 and select the maximum factor (MOU.1)

Pflaw.1 = PC.1 x MOU.1

Estimate maximum likely crack width from Table 5.23 using ∑(RFxLF)

Estimate maximum likely crack depth from Table 5.24 using Cmax

Estimate crack width at reservoir level under consideration assuming a uniformly tapered crack and using Cmax and D

Estimate probability of erosion from Tables 5.30 to 5.36 based on the core soil type and using W and average hydraulic gradient (iave)

PI.1

IM2 – Differential settlement adjacent to a cliff

Crack/Gap

Long Section

Crack/Gap

Long Section


PC.2







PI.2

IM3 – Cross section settlement due to poorly compacted shoulders

CrackingCross Section

Settlement of shoulders

CrackingCross Section

Settlement of shoulders


PC.3







PI.3

IM4 – Differential settlement in the foundation soil beneath the core



PC.4







PI.4

A-9



Initiating Mechanism for Transverse Cracking (1) Assess ∑(RFxLF)


(PC.xx)



calculate Pflaw


(Cmax)





(PI)

IM5 –Differential settlement due to embankment staging

Crack

Stage 2

Long Section

Stage 1

Crack

Stage 2

Long Section

Stage 1

Assess ∑(RFxLF) from Table 5.1 and estimate probability from Table 5.2 (refer to Section 5.2.5 on how to apply)

PC.5







PI.5

IM6 – Cracking in the crest due to desiccation



PC.6

Assess multiplication factor from Table 5.22 (MOU.6)






PI.6

IM7 – Cracking on seasonal shutdown layers during construction and staged construction surfaces due to desiccation

Crack

Stage 2 Stage 1

Long Section

Crack

Stage 2 Stage 1

Long Section


PC.7

Multiplication factor not applicable (MOU.7 = 1.0)

Pflaw.7 = PC.7

Estimate maximum likely crack width (at surface of seasonal shutdown layer or staged construction surface) from Table 5.23 using ∑(RFxLF)

Estimate maximum likely crack depth (from surface of seasonal shutdown layer or staged construction surface) from Table 5.25 using Cmax



PI.7

IM8 – Cracking due to an earthquake

Crack

Long Section

Crack

Long Section

Assess the damage class from Figure 5.6 for earthfill dams or Figure 5.7 for earth and rockfill dams and estimate probability from Table 5.14 using ∑(RFxLF) from IM1, IM2, or IM 4

PC.8

Multiplication factor not applicable (MOU.8 = 1.0)

Pflaw.8 = PC.8





PI.8

A-10

Table A3 – Probability of a Hydraulic Fracture in the Embankment and Initiation of Erosion

Probability of Hydraulic Fracturing in the Embankment (Pflaw)


Initiating Mechanism for Hydraulic Fracturing (1) Assess ∑(RFxLF)

and estimate the probability of a crack

(PC.xx)


and observed cracking (MOU or MOL)

and calculate Pflaw

(1) Estimate maximum likely crack width

(Cmax)

(2) Estimate likely crack location


reservoir level under consideration (W)


(PI)

IM9 – Cross valley arching

Crack

Long Section

Crack

Long Section


PC.9




Estimate the location of the crack below the crest using Table 5.28

Use W = Cmax Estimate probability of erosion from Tables 5.30 to 5.36 based on the core soil type and using W and average hydraulic gradient (iave)

PI.9

IM10 – Differential settlement causing arching of the core onto the shoulders of the embankment.


PC.10

Assess multiplication factor from Table 5.21 (MOL.10)

Pflaw.10 = PC.10 x MOL.10


At the phreatic line Use W = Cmax Estimate probability of erosion from Tables 5.30 to 5.36 based on the core soil type and using W and average hydraulic gradient (iave)

PI.10

IM11 – Differential settlement in the foundation soil beneath the core

Assess ∑(RFxLF) from Table 5.7 and estimate probability from Table 5.8 (IM4)

PC.11

Assess multiplication factor from Table 5.21 (MOL.11)

Pflaw.11 = PC.11 x MOL.11


At the base of the embankment


PI.11

IM12 – Differential settlement over small scale irregularities in the foundation/abutment profile beneath the core



PC.12

Multiplication factor not applicable (MOL.12 = 1.0)

Pflaw.12 = PCw.12


At the core-foundation/ abutment contact


PI.12

A-11

Table A4 – Probability of a Poorly Compacted or High Permeability Zone in the Embankment and Initiation of Erosion

Probability of a Poorly Compacted or High Permeability Zone in the Embankment (Pflaw)

Probability of Initiation of Erosion (PI) (Cohesionless Soils) – If both mechanisms

apply, carry both probabilities forward

Probability of Initiation of Erosion (PI) (Cohesive Soils)

Initiating Mechanism

(1) Assess ∑(RFxLF) and estimate the

probability of a poorly compacted or high permeability zone

(PP.xx)

(2) Assess factor for observed seepage (MOS) and calculate

Pflaw

(1) Estimate probability of initiation

of erosion by backward erosion

piping (BEP)


of erosion by suffusion

(1) Estimate likely crack width (G or W)


(PI)

IM13 – Poorly compacted or high high permeability layer in the embankment

Cross Section

High Permeability Zone

Cross Section

High Permeability Zone

Assess ∑(RFxLF) from Table 6.1 for cohesive soils or Table 6.2 for cohesionless soils and estimate probability from Table 6.3

PP.13

Assess multiplication factor from Table 6.20 (MOS.14)

Pflaw.13 = PP.13 x MOS.13

Refer to Section 6.6.2

Step 1. Assess whether there is time for seepage gradient to develop using Table 6.26 for reservoir levels above the normal operating pool level. Exclude if the reservoir level rise is insufficient for seepage gradient to develop

Step 2. Estimate average seepage gradient required to initiate and progress backward erosion: a) for 1 ≤ cu ≤ 6, estimate (ipmt)corrected; b) estimate critical gradient (icr), for cu > 6, adopt this gradient if smaller than (ipmt)corrected

Step 3. Estimate probability of initiation (PI.13) from Table 6.23 for compacted layers and Table 6.24 for uncompacted layers based on the average seepage gradient across the embankment core (iave) and (ipmt)corrected or icr.


Step 1. Determine if the proportion of the finer fraction is less than 40% of the total mass of the soil. If the finer fraction is more than 40% then suffusion is not possible and continue to backward erosion piping.

Step 2. If the proportion of the finer fraction is less than 40%, estimate probability the soil is internally unstable (PIUS) using Figure 6.8 or Figure 6.9

Step 3. Estimate the probability of initiation of erosion by suffusion given the soil is internally unstable (PSI) from Table 6.25 based on the average seepage gradient across the embankment core and porosity (n)

Step 4. Calculate probability of initiation of erosion by suffusion, PI.13 = PIUS x PSI


Step 1. Estimate the thickness of the poorly compacted layer (TP)

Step 2. Estimate the amount by which the layer may collapse (CF) from Table 26

Step 3. Estimate the height of the gap, G = TP x CF

Estimate probability of erosion from Tables 5.30 to 5.36 based on the core soil type and using G and average hydraulic gradient (iave)

PI.13

A-12








(PP.xx)


Pflaw



piping (BEP)





(PI)

IM14 – Poorly compacted or high permeability layer on the core-foundation contact




PP.14

Assess multiplication factor from Table 6.20 (MOS.14.)


Refer to IM13 Refer to IM13 Refer to Section 6.6.4





PI.14

IM15 – Cracking in the crest due to desiccation by freezing



PP.15

Assess multiplication factor from Table 6.20 (MOS.16).


Not applicable Not applicable Refer to Section 6.6.5

Step 1. Estimate width (W) of frost-induced flaw using Table 6.27

Step 2. Estimate depth of frost penetration using local building code or Figure 6.10


PI.15

IM16 – Seasonal shutdown layers during construction and staged construction surfaces due to freezing.

Stage 1

Long Section

Stage 2 Stage 1

Long Section

Stage 2


PP.16



Not applicable Not applicable Refer to Section 6.6.5

Step 1. Estimate width (W) of frost-induced flaw (at surface of seasonal shutdown layer or staged construction surface) using Table 6.27

Step 2. Estimate depth of frost penetration (from the surface of seasonal shutdown layer or staged construction surface) using on local building code or Figure 6.10


PI.16

A-13








(PP.xx)


Pflaw



piping (BEP)





(PI)

IM17 – Poorly compacted or high permeability layer around a conduit through the embankment




PP.17








PI.17

IM19 – Poorly compacted or high permeability zone associated with a spillway or abutment wall


PP.19




If the crack width is unknown from inspection, assume a 5 mm wide gap full-height of the wall


PI.19

A-14

Table A5 – Probability of a Crack or Gap in the Embankment adjacent to a Spillway or Abutment Wall and Probability of Initiation



Initiating Mechanism (1) Assess ∑(RFxLF)


(PC.xx)



calculate Pflaw


(Cmax)





(PI)

IM20 – Crack/gap adjacent to a spillway or abutment wall


PC.20




Estimate maximum likely crack depth using Figure 6.2 as a guide



PI.20

IM21 – Differential settlement adjacent to a spillway or abutment wall

Crack/Gap

Long Section

Crack/Gap

Long Section


PC.21







PI.21

Appendix B Navigation Tables for Internal Erosion

through Soil Foundations

B-1

Table B1 – Probability of Failure by Internal Erosion through a Soil Foundation (Sheet 1)


(1) Evaluate Probability of a Flaw

Pflaw

(2) Evaluate the Probability of Initiation of

Erosion

PI


PCE


PP


Pbreach


Pfail


Pui

Initiation of Backward Erosion in a Layer of Cohesionless Soil in the Foundation

IM22

Determine the probability of continuous cohesionless layer and a seepage exit using Section 7. This is also described in Table B2

Pflaw(IMx)

Determine Probability of initiation using Section 7. This is also described in Table B2

PI


PCE


PP


Pbreach




Breach


Backward Erosion Piping Use Chapter 11Continuation


Use Section 7

Use Section 7

Continuous Cohesionless layer with Seepage Exit

Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach


PCE


Pfailure

313

Backward erosion piping

313 313


B-2




Pflaw


Erosion

PI


PCE


PP


Pbreach


Pfail


Pui

Initiation of Suffusion in a Layer of Cohesionless Soil in the Foundation

IM23

Determine the probability of continuous cohesionless layer and a seepage exit using Section 7. This is also described in Table B3

Pflaw(IMx)


PI


PCE


PP


PBreach




Breach


Suffusion Use Chapter 11Continuation


Use Section 7

Use Section 7

Continuous Cohesionless layer with Seepage Exit

Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach


PCE


Pfailure

313

Internally unstable soil

313 313


B-3




Pflaw


Erosion

PI


PCE


PP


Pbreach


Pfail


Pui

Initiation of Erosion in a Crack in Cohesive Soil in the Foundation

IM24

Determine the probability of continuous cracking in the foundation using Section 7. This is also described in Table B4

Pflaw(IMx)


PI


PCE


PP


Pbreach

Calculate the probability of failure for each IM using the event tree.



Probability of Failure

Breach




Use Section 7

Use Section 7

Transverse Crack in Foundation

Yes

No

Yes

No

Yes

No

Yes

No

Pflaw

PI

PP

Pbreach


PCE

+

Pfail

313

Desiccation cracks in clay

313


B-4

Table B2 – Probability of Initiation by Backward Erosion Piping in a Cohesionless Layer in the Soil Foundation

Probability of a Continuous Layer of Cohesionless Soil with a Seepage Exit (Pflaw)

Probability of Initiation (PI)

Initiating Mechanism (1) Assess probability of a

continuous layer from upstream to downstream

(Pcl)

(2) Assess probability of a seepage exit (PSEC) and calculate

Pflaw

(1) Estimate probability of initiation and progression of backward erosion piping given a seepage exit is predicted (PI)

IM22 – Backward erosion piping in a cohesionless soil foundation


Estimate probability of a continuous layer of cohesionless soil from upstream to downstream across the core.

Pcl


Step 1. If the cohesionless layer daylights downstream, assume PSEC = 1.0

Step 2. Estimate the probability of a seepage exit occurring through heaving of the confining layer (PSEC) using Table 7.1 based on the factor of safety against heave (FUT).

Step 3. Assess ∑(RFxLF) from Table 7.2 for and estimate probability of seepage exit occurring due to defects in the confining layer (PSEC) from Table 7.3

Step 4. Select the maximum probability and calculate Pflaw.22

Pflaw.22 = Pcl x MAX(PSEC)

Refer to 7.2.4

Estimate the probability of backward erosion given heave has occurred as follows:

Step 1. If sand boils have been observed, PI = 1.0 for reservoir levels at or above the level at which sand boils have been observed.

Step 2. If sand boils have not been observed, estimate probability of initiation of backward erosion given a seepage exit exists as follows:

• Estimate the average seepage gradient (iavf) through the cohesionless soil layer in the foundation beneath the dam at the midpoint of the pipe path (not at the toe where there are likely to be locally higher gradients) for the level for the reservoir stage under consideration.

• From the particle size distribution of the foundation material, estimate a representative uniformity coefficient, cu = D60/D10.


• Correct this average gradient for the geometry, horizontal to vertical permeability ratio of the zone subject to backward erosion, and grain size as detailed in Section 6.6.2 to obtain (ipmt)corrected.

• Estimate the critical gradient (icr) from icr = (γsat – γw)/ γw for vertical exits or icr = [(γsat– γw)/ γw] tan(φ) for horizontal exits (e.g., cohesionless layer daylights into a toe ditch). If cu > 6, adopt this gradient if it is smaller than (ipmt)corrected.

• Estimate probability of initiation given a seepage exit occurs (PI.22) from Table 7.4 based on the average seepage gradient across the foundation (iavf) and ipmt or icr.

313


313 313


B-5

Table B3 – Probability of Initiation of Erosion by Suffusion in a Cohesionless Layer in the Soil Foundation

Probability of a Continuous Layer of Cohesionless Soil with a Seepage Exit (Pflaw)

Probability of Initiation (PI)


(1) Assess probability of a continuous layer from

upstream to downstream (Pcl)

(1) Estimate probability of initiation and progression of backward

erosion piping given a seepage exit is predicted (PI)

(1) Estimate probability of initiation of suffusion given the soil is internally unstable (PI)

IM23 – Suffusion in a cohesionless soil foundation


Estimate probability of a continuous layer of cohesionless soil from upstream to downstream across the core.

Pcl


Step 1. If the cohesionless layer daylights downstream, assume PSEC = 1.0

Step 2. Estimate the probability of a seepage exit occurring through heaving of the confining layer (PSEC) using Table 7.1 based on the factor of safety against heave (FUT).

Step 3. Assess ∑(RFxLF) from Table 7.2 for and estimate probability of seepage exit occurring due to defects in the confining layer (PSEC) from Table 7.3


Pflaw.23 = Pcl x MAX(PSEC)


Step 1. Determine if the proportion of the finer fraction is less than 40% of the total mass of the soil. If the finer fraction is more than 40% then suffusion is not possible and continue to backward erosion piping.

Step 2. If the proportion of the finer fraction is less than 40%, estimate probability the soil is internally unstable (PIUS) using Figure 6.8 or Figure 6.9

Step 3. Estimate the probability of initiation of erosion by suffusion given the soil is internally unstable (PSI) from Table 6.25 based on the average seepage gradient across the embankment core and porosity (n)

Step 4. Calculate probability of initiation of erosion by suffusion, PI.23 = PIUS x PSI

313


313 313


B-6

Table B4 – Probability of Initiation of Erosion in a Crack in a Cohesive Layer of in the Soil Foundation

Probability of Cracking in the Foundation due to Differential Settlement or Desiccation (Pflaw)

Probability of Initiation of Erosion (PI) Failure Path/Location

(1) Assess probability of a continuous layer from

upstream to downstream (Pcl)

(2) Assess ∑(RFxLF) and estimate probability of a

crack (PC,xx)

(3) Assess factor for measured settlement (MOL)

and calculate Pflaw

(1) Estimate likely crack width (W)

(2) Estimate probability of erosion (PI)

IM24 – Erosion in cracks in a cohesive soil foundation due to differential settlement or desiccation

Estimate probability of a layer of cohesive soil containing a continuous crack or interconnected pattern of cracks across the core

Pcl

Step 1. If IM4 Scenario (b) from Figure 5.4 is applicable, assess ∑(RFxLF) from Table 5.7 and estimate probability from Table 5.8 PC.4

Step 2. Assess ∑(RFxLF) from Table 5.11 and estimate probability from Table 5.12 using Below POR

PC.7

Step 1. For IM4, assess multiplication factor from Table 5.21 (MOL.4) Pflaw.4 = PC.4 x MOL.4

Step 2. For IM7, multiplication factor not applicable (MOL.7 = 1.0) Pflaw.7 = PC.7


Pflaw.24 = Pcl x MAX(Pflaw.4 or Pflaw.7)

If the crack width is unknown from inspection, assume a 5 mm wide crack


PI.24

313


313


Appendix C Navigation Tables for Presence of

Continuous Rock Defects

C-1

Table C1 – Probability of Continuous Defects Related to Stress Relief Effects in the Valley Sides in a Rock Foundation

Failure Path/Location Probability of Continuous Defects

Based on Geology and Topography

PGT

Probability of Continuous Defects

Based on Site Investigation and Construction Data

PSC

Combine the Two Probability Estimates

for Continuous Defects

Pw

Assess the Probability that

Grouting is Ineffective in

Cutting Off the Defects

PGI

Assess the Probability that Cut-off Wall is Ineffective in


PCI


Surface Treatment is Ineffective in Cutting Off the

Defects

PTI

Compute the Probability of a Continuous Rock Defect

PCR

Describe the Extent of the Defects

Identify potential failure paths for initiation of erosion in defects related to stress relief effects in the valley sides.

Stress Relief Defects

Long Section

Stress Relief Defects

Long Section

Use this process to evaluate each of the 4 defect sizes.

<5 mm

5 mm to 25 mm

25 mm to 100 mm

>100 mm

Estimate the probability of a continuous defect in the rock foundation from upstream of the core to downstream of the core.

Assess ∑(RFxLF) from Tables 8.1 and 8.2 and estimate the probabilities for each defect size from Table 8.3.


Assess ∑(RFxLF) from Table 8.4 and estimate the probabilities for each defect size from Table 8.5.

Obtain the weighting factor (w) based on the quantity and quality of the investigation and construction data using Table 8.18.

Calculate the weighted estimate of the probability of continuous defects for each defect size.

Pw = w PGT + (1-w) PSC

Assess the likelihood of grouting not being effective using Tables 8.19 and 8.20.

Assess the likelihood of cut-off walls not being effective using Tables 8.21 and 8.22.

Assess the likelihood of surface treatment not being effective using Table 8.23.

PCR = (Pw) (PGI) (PCI) (PTI) Describe the defects in relation to the embankment details (refer to Section 8.11).

Describe the defects, their width, depth, spatial distribution in the foundation, and how these relate to the cut-off and general foundation of the embankment beneath the core. In particular, identify features which will be in contact with the core at the base of the cut-off and in the sides of the cut-off trench.

P CRP TI Probability of Continuous Rock Defect




Continuous Defect?Stress Relief in The Valley Sides

Yes

No

Yes

No

Yes

No

Yes

No

Evaluate:* Regional Geology and Topographic Data PGT

* Site Investigations, Construction, and Performance Data PSC

Repeat for each defect range size <5mm5mm to 25 mm25mm to100mm>100 mm

Sub-event tree structure to show computation of a continuous defect below the embankment

C-2

Table C2 – Probability of Continuous Defects Related to Stress Relief Effects in the Valley Floor – Valley Bulge and Rebound



PGT



PSC



Pw




PGI



PCI



Defects

PTI


PCR


Identify potential failure paths for initiation of erosion in defects related to valley bulge and rebound.

Valley Bulge Features

Long Section

Valley Bulge Features

Long Section


<5 mm

5mm to 25mm

25mm to 100mm

>100 mm


Assess ∑(RFxLF) from Tables 8.6 and 8.2 and estimate the probabilities for each defect size from Table 8.7.








Assess the likelihood of surface treatment not being effective using Tables 8.23.

PCR= (Pw) (PGI) (PCI) (PTI) Describe the defects in relation to the embankment details (refer to Section 8.11).






Continuous Defect?Valley Bulge and Rebound

Yes

No

Yes

No

Yes

No

Yes

No





C-3

Table C3 – Probability of Continuous Defects Related to Solution Features for Rock Subject to Solution



PGT



PSC



Pw


Grouting is ineffective in


PGI

Assess the Probability that Cut-off Wall is ineffective in


PCI


Surface Treatment is ineffective in Cutting Off the

Defects

PTI


PCR


Identify potential failure paths for initiation of erosion in defects related to solution features.

Solution Features

Long Section Limestone, dolomite

Solution Features

Long Section Limestone, dolomite


<5 mm

5 mm to 25 mm

25 mm to 100 mm

>100 mm











PCR= (Pw) (PGI) (PCI) (PTI) Describe the defects in relation to the embankment details (refer to Section 8.11).






Continuous Defect?Solution Features

Yes

No

Yes

No

Yes

No

Yes

No





C-4

Table C4 – Probability of Continuous Defects Associated with Other Geological Features such as Landslides, Faults and Shears



PGT



PSC



Pw




PGI



PCI



Defects

PTI


PCR


Identify potential failure paths for initiation of erosion in defects related to landslides, faults, and shears.

Fault or Shear ZoneLong Section

Defects associated with landslide

Fault or Shear ZoneLong Section

Defects associated with landslide


<5 mm

5 mm to 25 mm

25 mm to 100 mm

>100 mm











PCR= (PW) (PGI) (PCI) (PTI) Describe the defects in relation to the embankment details (refer to Section 8.11).






Continuous Defect?Landslide, Faults, and Shears

Yes

No

Yes

No

Yes

No

Yes

No





Appendix D Navigation Tables for

Internal Erosion of the Embankment into or at the Foundation

D-1

Table D1 – Probability of Failure by Internal Erosion of the Embankment due to Scour along Rock Defects < 25 mm

Failure Path/Location Sketch


Continuous Defect

PCR

(2) Evaluate the Probability of Initiation

of Erosion

PI

(3) Evaluate Probability of Continuing Erosion

PCE

(4) Probability of Progression PP


Pbreach


Pfail


Pui

IM25 – Scour along Rock Defects < 25 mm

Evaluate this mechanism for rock defect ranges:

<5 mm

5-25 mm

Erosion of core by water flowing in open rock defects

313

Erosion of core by water flowing in open rock defects

313 313

Estimate probability of a continuous rock

defect from Section 8.

Assess the probability of initiation of scour. See Section 9.4

Use a crack width of 2.5 mm for the defects < 5 mm and a width of 15 mm for the 5-25 mm defects.

Evaluate the probabilities for Continuing Erosion for the failure path under considering the exit conditions for the defects.

Unprotected exit: PCE = 1.0

Large capacity defect system: PCE = 1.0

Protected exit: Evaluate PCE using Scenario 3 (Section 10)

Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Section 11.

PP = PPR x PPC x PPL


Calculate the probability of failure using the event tree.

Pfail = PCR x PI x PCE x PP x Pbreach



Breach



Scour Initiation Evaluate Exit ConditionsUnprotected PCE = 1.0

Use Chapter 8 Large Capacity Defects PCE = 1.0Protected Use Scenario 3 in Chapter 10

Use Tables 5.30-5.36

<5mm or 5-25 mm Rock Defects

Yes

No

Yes

No

Yes

No

Yes

No

PCR

PI

PCE

PP

Pbreach


Pfail

D-2

Table D2 – Probability of Failure by Internal Erosion of the Embankment due to erosion into Rock Defects > 25 mm

Failure Path/Location

Sketch


Continuous Defect

PCR


Erosion

PIC

(3) Evaluate Probability of

Continuation into rock defects

PCED

(4) Evaluate Probability that the gradient through

the voids is sufficient for soil

transport

PSTD

(5) Evaluate Exit Conditions and

determine Probability of Continuing Erosion

PCE


PP


Pbreach

(8) Calculate the Probability of

Failure

Pfail


Pui

IM26 – Erosion into Rock Defects > 25 mm

Evaluate this mechanism for rock defect ranges:

25-100 mm

>100 mm

Estimate probability of a continuous rock

defect from Section 8.

Given there are continuous open defects in the foundation, the probability of initiation (PIC) should be assumed to be 1.0 for both cohesionless soils (backward erosion) and for cohesive soils (sinkhole stoping).

Assess the probability of continuation into the rock defect following the procedures for Scenario 4 in Chapter 10.

Use a crack width of 62.5 mm for 25-100 mm and a width of 300 mm for the >100 mm defects

Assess the probability that the average hydraulic gradient along the rock defect is sufficient to cause transport of soils through the voids (PSTD).

Use Table 9.2 in Section 9.5




Protected exit: Evaluate PCE using Scenario 3 (Section 10)




Calculate the probability of failure using the event tree. For each defect size.

Pfail = PCR x PI x PCEI x PSTV x PCE PP x Pbreach


Breach


Continuation Use Chapter 11

Soil Transport Through Defects Evaluate Exit ConditionsUnprotected PCE = 1.0

Large Capacity Defects PCE = 1.0Protected Use Scenario 3 in Chapter 10

Continuation into Defect Use Table 9.2 in Section 9.5

Initiation into DefectUse JOS with Scenario 4 in Chapter 10

Use Chapter 8

Assume PIC =1.0

25mm-100mm, >100mm Rock Defects

Yes

No

Yes

No

Yes

No

Yes

No

PCR

PIC

PCE

PP

Pbreach


Yes

No

PCED

Yes

No

PSTD


+

Pfail

3 13 3 13

D-3

Table D3 – Probability of Failure by Internal Erosion of the Embankment due to Scour along the Contact with Open-Work Granular Foundations

Failure Path/Location Sketch


Continuous Path

PCP

(2) Evaluate the Probability of Initiation

of Erosion

PI

(3) Evaluate Probability of Continuing Erosion

PCE


PP


Pbreach


Pfail


Pui

IM27 – Scour along the Contact with Open-Work Coarse-Grained Foundation Soil

Estimate probability of a continuous

pathway into open-work granular

foundation (PCP).

Use Section 9.3

Assess the probability of initiation of scour. See Section 9.4

Use a crack width equivalent to the D15/4 of the open granular foundation material




Protected exit: Evaluate PCE using Scenario 3 (Section10)




Calculate the probability of failure using the event tree.

Pfail = PCP x PI x PCE x PP x Pbreach



Breach



Scour Initiation Evaluate Exit ConditionsUnprotected PCE = 1.0

Use Section 9.3 Large Capacity Defects PCE = 1.0Protected Use Scenario 3 in Chapter 10

Assume Crack Width D15 /4Use Tables 5.30-5.36

Open Granular Foundations

Yes

No

Yes

No

Yes

No

Yes

No

PCP

PI

PCE

PP

Pbreach


Pfail

313 313

Erosion of core by water flowing (scour) in Open Granular Foundations

D-4

Table D4 – Probability of Failure by Internal Erosion of the Embankment due to erosion into Open-Work Granular Foundations

Failure Path/Location

Sketch


Continuous Path

PCP


Erosion

PIP

(3) Evaluate Probability of

Continuation into rock defects

PCED

(4) Evaluate Probability that the gradient through

the voids is sufficient for soil

transport

PSTD

(5) Evaluate Exit Conditions and

determine Probability of Continuing Erosion

PCE


PP


Pbreach

(8) Calculate the Probability of

Failure

Pfail


Pui

IM28 – Erosion into Open-Work Coarse-Grained Foundation Soil

Estimate probability of a

continuous pathway into open-work granular

foundation (PCP).

Use Section 9.3

Given there are continuous open defects in the foundation, the probability of initiation (PIP) should be assumed to be 1.0 for both cohesionless soils (backward erosion) and for cohesive soils (sinkhole stoping).

Assess the probability of continuation into the open granular foundation following the procedures for Scenario 3 in Chapter 10.

Assess the probability that the average hydraulic gradient along the rock defect is sufficient to cause transport of soils through the defects (PSTD).

Use Table 9.2 in Section 9.5




Protected exit: Evaluate PCE using Scenario 3 (Section10)




Calculate the probability of failure using the event tree. For each defect size.

Pfail = PCP x PI x PCEI x PSTD x PCE PP x Pbreach


Breach


Continuation Use Chapter 11

Soil Transport Through Defects Evaluate Exit ConditionsUnprotected PCE = 1.0

Large Capacity Defects PCE = 1.0Protected Use Scenario 3 in Chapter 10

Continuation into Defect Use Table 9.2 in Section 9.5

Initiation into DefectUse Scenario 3 in Chapter 10

Use Section 9.3

Assume PIP =1.0

Open Granular Foundation

Yes

No

Yes

No

Yes

No

Yes

No

PCP

PIP

PCE

PP

Pbreach


Yes

No

PCED

Yes

No

PSTD


+

Pfail

313 313

Erosion of core by water eroding into Open Granular Foundations

Documents

Internal_Erosion_Toolbox.pdf