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SPECIALTY WORKSHOP: SPECIALTY WORKSHOP: SITES TRAINING AND SITES TRAINING AND
INTRODUCTION TO WINDAM INTRODUCTION TO WINDAM
ASDSO Dam Safety 2008ASDSO Dam Safety 2008
PART 2 – SITES EARTH SPILLWAYPART 2 – SITES EARTH SPILLWAY EVALUATION EVALUATION
B.B. Earth Spillway Integrity AnalysisEarth Spillway Integrity Analysisiii. Phase 3 (Headcut Advance)iii. Phase 3 (Headcut Advance)
3 PHASE Spillway Erosion Model
1. SURFACE EROSION (Cover Destruction)
3. HEADCUT ADVANCE
2. CONCENTRATED FLOW EROSION
HEADCUT ADVANCE
OBJECTIVES
• Phase 3
– Inputs and equations
– Relation of downcutting to headward advance
– Concept of multiple materials and weakest line of attack
– Concept of unraveling (implications of threshold-rate governing relations)
OBJECTIVES
• Phase 3
– Inputs and equations
– Relation of downcutting to headward advance
– Concept of multiple materials and weakest line of attack
– Concept of unraveling (implications of threshold-rate governing relations)
DOWNCUTTING andHEADCUT ADVANCE
dX/dt
d/dt
Parameters Impacting Phase 3 ErosionParameters Impacting Phase 3 Erosion
Multiple materials may be exposed in a single headcut face.
Downcutting controlled by the material exposed at the base for the time step.
Headcut advance controlled by the materials exposed on the headcut face.
SITESSITESAUXILIARY SPILLWAY EROSION
PHASE 3 INPUT PARAMETERSPHASE 3 INPUT PARAMETERS
DOWNCUTTINGDOWNCUTTING
• PARTICLE DIAMETERPARTICLE DIAMETER• DRY BULK DENSITYDRY BULK DENSITY• PERCENT CLAY orPERCENT CLAY or• kkdd DETACHMENT COEFFICIENT DETACHMENT COEFFICIENT
HEADCUT ADVANCEHEADCUT ADVANCE
• KKhh HEADCUT ERODIBILITY INDEX HEADCUT ERODIBILITY INDEX
SITESSITESAUXILIARY SPILLWAY EROSION: PHASE 3
DOWNCUTTINGDOWNCUTTING
eeddcc0.011 (H/d0.011 (H/dcc))0.5820.582
dd//ddt = kt = kdd((ee--cc))
HEADCUT ADVANCEHEADCUT ADVANCE
ddX/X/ddt = C (A - At = C (A - Aoo))
A = (qH)A = (qH)1/31/3
(NEH Part 628 Dams Ch 51 Eq 51-9)(NEH Part 628 Dams Ch 51 Eq 51-9)
SITESSITESAUXILIARY SPILLWAY EROSION: PHASE 3
DOWNCUTTINGDOWNCUTTING
eeddcc0.011 (H/d0.011 (H/dcc))0.5820.582
dd//ddt = kt = kdd((ee--cc))
HEADCUT ADVANCEHEADCUT ADVANCE
ddX/X/ddt = C (A - At = C (A - Aoo))
A = (qH)A = (qH)1/31/3
(NEH Part 628 Dams Ch 51 Eq 51-9)(NEH Part 628 Dams Ch 51 Eq 51-9)
SURFACE DETACHMENTSURFACE DETACHMENT
.
rr = detachment rate = detachment rate
kkd d = coefficient of = coefficient of
detachmentdetachmentee = effective stress = effective stress
cc = critical tractive = critical tractive
stressstress
.
a = exponent (~ 1)a = exponent (~ 1)
rr = k = kdd ( (ee - - cc))aa
Effective Stress, e
c
00
Det
achm
ent R
ate,
r
kd
1
• EFFECTIVE STRESS AT THE HEADCUT BASEEFFECTIVE STRESS AT THE HEADCUT BASE
e= dc 0.011(H/dc)0.582
H
dc
e
PHASE 3PHASE 3Headcut DeepeningHeadcut Deepening
H
CRITICAL STRESS for
Detachment
Critical stress based on loose particle condition for all materials.
DETACHMENT RATE COEFFICIENTDETACHMENT RATE COEFFICIENT
The detachment rate coefficient may be externally determined and entered directly in SITES or estimated by SITES from soil properties.
SITESSITESAUXILIARY SPILLWAY EROSION: PHASE 3
DOWNCUTTINGDOWNCUTTING
eeddcc0.011 (H/d0.011 (H/dcc))0.5820.582
dd//ddt = kt = kdd((ee--cc))
HEADCUT ADVANCEHEADCUT ADVANCE
ddX/X/ddt = C (A - At = C (A - Aoo))
A = (qH)A = (qH)1/31/3
(NEH Part 628 Dams Ch 51 Eq 51-9)(NEH Part 628 Dams Ch 51 Eq 51-9)
HEADCUT MIGRATION
dx/dt = C (A - Adx/dt = C (A - Aoo))dX/dt = rate of headcut
migration,
C = material dependent advance rate coefficient,
A = hydraulic attack, and
Ao = material-dependent threshold.
HYDRAULIC ATTACK
q
H
A = (qH)1/3
MATERIAL-DEPENDENTPARAMETERS
AAOO & C are a function of & C are a function of
KKhh = headcut erodibility = headcut erodibility
indexindex
AAOO = =
189 K189 Khh1/21/2exp(-3.23/ln(101Kexp(-3.23/ln(101Khh))))[[ ]]1/31/3
00 KKhh< 0.01< 0.01
KKhh> 0.01> 0.01__
ANDAND
C =C =
- 0.79 ln(K- 0.79 ln(Khh) + 3.04 K) + 3.04 Khh< 18.2< 18.2
0.75 K0.75 Kh h > 18.2> 18.2__
HEADCUT ERODIBILITYINDEX, Kh
KKhh= M= MSS x K x Kbb x K x Kdd x J x JSS
MMSS= material strength number= material strength number
of the earth material.of the earth material.KKbb= block or particle size.= block or particle size.
KKdd= discontinuity or inter-= discontinuity or inter-
particle bond shearparticle bond shear strength number.strength number.JJss= relative ground structure= relative ground structure
number.number.
Kb
Kd
Condition of the Joints• Rough or smooth• Open or closed• Gap size• material in joints
Js
Block size
Orientationto the flow
Kh = 0.01
DESCRIPTION: SM, very loose sand with little bonding
SITE: Buck and Doe Run 33, Missouri
COMMENT: Eroding material in spillway breach: deep deposit
Kh = 0.17
DESCRIPTION: CL , stiff
SITE: Rush Creek 12R, Oklahoma
COMMENT: Eroding material in headcut face.
Kh = 0.5
DESCRIPTION: Disintegrated shale
SITE: West Fork Point Remove 5, Arkansas
COMMENT: Eroding material in Gully Bank.
Kh = 20
DESCRIPTION: Jointed Sandstone
SITE: West Fork Pint Remove 5, Arkansas
COMMENT: Material remaining below surface erosion some minor detachment by flow.
Kh = 35000
DESCRIPTION: Massive rock (ryolite)
SITE: Painted Rock Dam, Arizona
COMMENT: Spillway outlet, negligible erosion.
OBJECTIVES
• Phase 3
– Inputs and equations
– Relation of downcutting to headward advance
– Concept of multiple materials and weakest line of attack
– Concept of unraveling (implications of threshold-rate governing relations)
SITES erosion material parameters include surface detachment coefficient kd and the headcut erodibility index Kh
kd
Kh = 20
DESCRIPTION: Jointed SandstoneSITE: West Fork Pint Remove 5, ArkansasCOMMENT: Material remaining below surface erosion some minor detachment by flow.
dX/dt
d/dt
H
OBJECTIVES
• Phase 3
– Inputs and equations
– Relation of downcutting to headward advance
– Concept of multiple materials and weakest line of attack
– Concept of unraveling (implications of threshold-rate governing relations)
KKhh for MULTIPLE MATERIALS for MULTIPLE MATERIALS
hi
h2
h3 Kh3
Kh2
Kh1
htotal
Kh = exp { }hi ln( Kh )i
h1
Auxiliary Spillway Profile ReachesAuxiliary Spillway Profile Reaches
1 2 3 4 5 6 7 8
INLET CREST EXIT
Auxiliary Spillway Profile ReachesAuxiliary Spillway Profile Reaches
1 2 3 4 5 6 7 8
INLET CREST EXIT
Reaches from the crest to valley floor are considered in integrity analysis.
SPILLWAY GEOLOGY
STATION
EL
EV
AT
ION
, ft
, ft
All materials in spillway to elevation of valley floor are described along a weakest path.
ERODED PROFILEE
LE
VA
TIO
N
STATION, ft
, ft
The eroded profile plotted in output is a composite of all headcuts considered while evaluating breach potential.
file: a:\claystr.bmp
OBJECTIVES
• Phase 3
– Inputs and equations
– Relation of downcutting to headward advance
– Concept of multiple materials and weakest line of attack
– Concept of unraveling (implications of threshold-rate governing relations)