Embed Size (px)
Citation preview
EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF
THE IMPACT OF EROSION VOIDS ON RIGID PIPES
By
Sherif Kamal Fouad Kamel
Department of Civil Engineering and Applied Mechanics
McGill University
Montréal, Québec, Canada
May 2012
A thesis submitted to McGill University in partial fulfillment of
the requirements of the degree of Doctor of Philosophy
© Sherif Kamel, 2012
i
ABSTRACT
The design of buried pipes requires the consideration of full contact between the
pipe and the surrounding soil. After installation, loosening of surrounding soil may
occur with time leading to the development of erosion voids next to the pipe wall.
This phenomenon is known as ground support loss and has been known to
cause pipe damage and in some cases has lead to complete failure. Previous
studies were limited to numerical modeling using two-dimensional analyses. The
main objectives of the present research program are: (1) to experimentally study
the impact of erosion void located next to the pipe wall on the changes in earth
pressure acting on the pipe and (2) to develop a three-dimensional numerical
model to investigate the effect of void size on the changes in earth pressure and
stresses in the pipe wall due to the introduction of a finite void around the pipe.
An experimental setup that allows for the introduction of a physical gap between
the backfill material and the pipe is designed and used throughout the
experimental work. Validated using the experimental results, two-dimensional
finite element model is used to examine the adequacy of the mechanically
retractable strip technique used in the experiments to simulate the void next to
the pipe wall.
A series of three-dimensional nonlinear finite element analyses is then performed
to investigate the impact of void length, depth and location on the earth pressure
ii
distribution on a rigid pipe as well as the pipe wall stresses. A summary table is
provided comparing the changes in pipe responses with respect to initial
conditions under different void configurations. This study emphasized the
importance of detecting and repairing erosion voids around existing rigid pipes to
avoid costly failures.
iii
RÉSUMÉ
La conception des tuyaux enterrés nécessite l'examen du full-contact entre le
tuyau et le sol entourant. Après l'installation, le relâchement du sol entourant
peut se produire avec le temps menant au développement des vides d'érosion à
côté de la paroi du tuyau. Ce phénomène est connu comme la perte de soutien
du sol et a été connu pour causer des dommages sur le tuyau et dans certains
cas a mené à une rupture complète. Les études antérieures ont été limitées à la
modélisation numérique à des analyses de deux-dimensions. Les principaux
objectifs de la présente programme de recherche sont les suivants: (1) d'étudier
expérimentalement l'impact de vide d'érosion situé à côté de la paroi du tube sur
les changements de charge du sol agissant sur le tuyau (2) de développer un
modèle numérique à trois-dimensions afin d'étudier l'effet de la taille des vides
sur les changements de charge du sol et des contraintes dans la paroi du tuyau
causé par l'introduction d'un vide finie autour du tuyau.
Un dispositif expérimental qui permet l'introduction d'un écart physique entre le
matériau de remblai et le tuyau est conçu et utilisé tout au long du travail
expérimental. Validé en utilisant les résultats expérimentaux, une modèle
d'éléments finis à deux-dimensions est utilisée pour examiner l'adéquation de la
technique mécanique rétractable d'une bande utilisée dans les tests afin de
simuler le vide à côté de la paroi du tuyau.
iv
Une série d'analyses par éléments finis non linéaires à trois-dimensions est
ensuite réalisée pour étudier l'impact de la longueur du vide, la profondeur et
l'emplacement sur la distribution de la charge du sol sur un tuyau rigide ainsi que
les contraintes dans la paroi du tuyau. Un tableau sommaire est fourni en
comparant les changements des réactions tuyau par rapport aux conditions
initiales dans le cadre des configurations différentes vides. Cette étude a
souligné l'importance de la détection et la réparation des vides d'érosion autour
des tuyaux rigides existants pour éviter les ruptures coûteuses.
v
ACKNOWLEDGMENTS
I would like to express my profound gratitude to Prof. Mohamed Meguid for his
invaluable contribution through supervision of this PhD research. He had a
paramount input into this research through his guidance from initial proposition to
its completion and brought out the best of me.
I would like to thank the technicians: Damon Kipperchuk, Ron Sheppard, Marek
Przykorski and especially John Bartzak for their help in building the experimental
set up. I would also like to thank Dr. William Cook and Jorge Sayat for their help
in setting up the MTS and the data acquisition system.
Thanks go to all my graduate colleagues; namely, Mahmoud Ahmed, Cheehan
Leung and Mahmoud Gad who helped during the experimental tests as well as
the numerical runs.
I would like to thank the FQRNT (Le Fonds Quebecois de La Recherche sur la
Nature et les Technologies) and the Faculty of Engineering and the Department
of Civil Engineering at McGill for financially supporting my research.
Special thanks go to my father Kamal, my mother Lorna and my brother Karim
who encouraged me during my PhD study and were of great support.
Last, but definitely not least, special thanks go to my lovely wife Nermine and my
daughter Carolina for being so patient, thoughtful and caring.
vi
TABLE OF CONTENTS
ABSTRACT ............................................................................................................ I
RÉSUMÉ ............................................................................................................. III
ACKNOWLEDGMENTS ...................................................................................... V
TABLE OF CONTENTS ...................................................................................... VI
LIST OF FIGURES ............................................................................................. IX
LIST OF TABLES ............................................................................................... XII
LIST OF SYMBOLS ................................. ERROR! BOOKMARK NOT DEFINED.
1. INTRODUCTION .............................................................................................. 1
1.1. Introduction ........................................................................................... 1 1.2. Research Motivation ............................................................................. 2 1.3. Objectives and Methodology ................................................................ 5
1.3.1. Experimental Program ....................................................................... 5 1.3.2. Numerical Program ........................................................................... 6
1.4. Statement of Originality ........................................................................ 7 1.5. Thesis Organization .............................................................................. 7
2. LITERATURE REVIEW .................................................................................... 9
2.1. Chapter Overview ................................................................................. 9 2.2. Soil Arching Theory ............................................................................ 10 2.3. Design of Buried Pipes ....................................................................... 14
2.3.1. Empirical Method ............................................................................ 14 2.3.2. Analytical Methods .......................................................................... 21 2.3.3. Numerical Methods ......................................................................... 27
2.4. Deterioration of the Soil-Pipe System ................................................. 30 2.4.1. Pipe Deterioration............................................................................ 30 2.4.2. Soil Deterioration ............................................................................. 33
2.5. Case Studies of Ground Support Loss around Buried Pipes .............. 34 2.6. Previous Work related to Erosion Voids and Underground Structures35 2.7. Gaps in Knowledge and Research Needs .......................................... 39
3. EXPERIMENTAL ANALYSIS .......................................................................... 41
3.1. Chapter Overview ............................................................................... 41 3.2. Objective of The Experimental Study ................................................. 41 3.3. Experimental Setup ............................................................................ 43
3.3.1. Steel tank ........................................................................................ 43 3.3.2. Rigid Pipe ........................................................................................ 44
vii
3.3.3. Instrumentation ............................................................................... 48 3.3.4. Fine sand ........................................................................................ 50
3.4. Testing Plan........................................................................................ 51 3.4.1. Load cell calibration......................................................................... 51 3.4.2. Procedure ........................................................................................ 51 3.4.3. Tests performed .............................................................................. 54
3.5. Experimental Results .......................................................................... 54 3.5.1. Contact loss at the springline .......................................................... 56 3.5.2. Contact loss at the haunch .............................................................. 57 3.5.3. Contact loss at the invert ................................................................. 58
3.6. Summary of Results ........................................................................... 59
4. VALIDATION OF THE NUMERICAL MODEL ................................................. 61
4.1. Numerical Details ............................................................................... 61 4.1.1. Constitutive Models ......................................................................... 61 4.1.2. Boundary Conditions and Finite Element Mesh .............................. 63 4.1.3. Element Type .................................................................................. 64 4.1.4. Soil -Pipe Interface .......................................................................... 65 4.1.5. Stages of Analysis ........................................................................... 66 4.1.6. Modeling the Section Retraction ..................................................... 67
4.2. Model Validation ................................................................................. 67 4.3. Evaluation of the Segment Retraction Technique used in The Experiments ................................................................................................. 68 4.4. Numerical Results .............................................................................. 71
5. THREE-DIMENSIONAL NUMERICAL ANALYSIS ......................................... 76
5.1. Chapter Overview ............................................................................... 76 5.2. Problem Statement ............................................................................. 76 5.3. Numerical Details ............................................................................... 78
5.3.1. Constitutive Models ......................................................................... 78 5.3.2. Boundary Conditions and Finite Element Mesh .............................. 79 5.3.3. Element Type .................................................................................. 82 5.3.4. Soil- Pipe Interaction ....................................................................... 83 5.3.5. Modeling Erosion Voids ................................................................... 85 5.3.6. Stages of Analysis ........................................................................... 87
5.4. Model Validation ................................................................................. 88 5.4.1. Validation of Initial Earth Pressure .................................................. 88 5.4.2. Validation of Ring Moments ............................................................ 89
5.5. Changes in Earth Pressure ................................................................ 91 5.5.1. Transverse section of the pipe ........................................................ 91 5.5.2. Longitudinal Sections along the Pipe .............................................. 95
viii
5.5.2.1. Effect of void length .................................................................. 95 5.5.2.2. Effect of void depth ................................................................... 99 5.5.2.3. Effect of void Angle ................................................................ 103
5.6. Changes in Pipe Stresses ................................................................ 104 5.6.1. Changes in circumferential stresses along the pipe ...................... 104 5.6.2. Changes in bending moments along the pipe ............................... 111 5.6.3. Changes in tensile and compressive stresses at the pipe extreme fibres ...................................................................................................... 116 5.6.4. Changes in longitudinal stresses at the pipe outer fibre ................ 120
6. CONCLUSIONS AND RECOMMENDATIONS ............................................. 123
6.1. Conclusions ...................................................................................... 123 6.1.1. Experimental Program ................................................................... 123 6.1.2. Two-Dimensional Analyses ........................................................... 124 6.1.3. Three-Dimensional Analyses ........................................................ 125
6.1.3.1. The changes in earth pressure ............................................. 125 6.1.3.2. The changes in pipe stresses ................................................. 126
6.2. Practical Significance ....................................................................... 127 6.3. Limitations and Recommendations for Future Work ......................... 129
A. VOID DETECTION METHODS .................................................................... 131
B. EFFECT OF VOID LENGTH ON EARTH PRESSURE ................................ 140
C. EFFECT OF VOID DEPTH ON EARTH PRESSURE .................................. 145
D. CHANGES IN CIRCUMFERENTIAL PIPE STRESSES ............................... 150
F. CHANGES IN LONGITUDINAL PIPE STRESSES ....................................... 155
REFERENCES ................................................................................................. 165
ix
LIST OF FIGURES
Figure 1.1 : Load transfer mechanism (a) rigid pipe and (b) flexible pipe ....................................... 2 Figure 1.2 : History of buried pipe design methods ......................................................................... 3 Figure 1.3 : Erosion void development behind a buried pipe wall ................................................... 4 Figure 1.4 : Void representation (a) previous work and (b) present research ................................. 5 Figure 2.1: A yielding soil strip between vertical soil surfaces (a) classical rectangular representation; (b) catenary representation (McKelveyIII, 1994) .................................................. 10 Figure 2.2 : Soil arching effect (a) positive arching; (b) negative arching ..................................... 13 Figure 2.3 : Settlements which influence loads on embankment pipe installation ........................ 16 Figure 2.4: Three-edge bearing test set up (Adapted from ACPA, 2007) ..................................... 18 Figure 2.5 : Class of bedding and ranges of bedding factors ........................................................ 20 Figure 2.6 : Notation ..................................................................................................................... 22 Figure 2.7 : Attenuation of conduit loads, stresses and displacements ........................................ 24 Figure 2.8 : Heger earth pressure distribution (ACPA, 2007) ....................................................... 29 Figure 2.9 : Typical defects encountered in a buried pipeline (a) circumferential crack, (b) longitudinal crack, (c) hole in pipe wall, and (d) infiltration ............................................................ 31 Figure 2.10 : The three stages of sewer failures (Davies et al., 2001) .......................................... 33 Figure 2.11 : Mechanism of erosion voids development around a pipe ........................................ 34 Figure 2.12 : Gap reported at pipe invert ...................................................................................... 35 Figure 2.13 : Changes in circumferential stresses at crown induced by erosion voids (Tan and Moore, 2007) ................................................................................................................................. 36 Figure 2.14 : Location of voids and sizes studied (Meguid and Dang, 2009) ............................... 37 Figure 2.15 : Bending moments as a function of the void size at (a) springline and (b) invert (Meguid and Dang, 2009) .............................................................................................................. 38 Figure 3.1: Rigid pipe subjected to local contact loss ................................................................... 42 Figure 3.2: The three test sets investigated experimentally .......................................................... 42 Figure 3.3 : Experimental setup ..................................................................................................... 43 Figure 3.4 : Different parts used in assembling the segmented pipe ............................................ 45 Figure 3.5 : Top view of the assembled pipe spanning the steel tank .......................................... 46 Figure 3.6 : The retractable strip (a) inner mechanism and (b) outer side .................................... 48 Figure 3.7 : A schematic showing half the pipe and all sensor locations ...................................... 49 Figure 3.8 : Stages of sand placement in the experiments ........................................................... 53 Figure 3.9 : Measured changes in earth pressure away from the retracted strip - at the springline ....................................................................................................................................................... 55 Figure 3.10 : Measured changes in earth pressure around the retracted strip - at the springline 57 Figure 3.11 : Measured changes in earth pressure around the retracted strip - at the haunch .... 58
x
Figure 3.12 : Measured changes in earth pressure around the retracted strip - at the invert ....... 59 Figure 3.13 : Average changes in pressure as recorded by sensors 11 and 13 ........................... 60 Figure 3.14 : Average changes in pressure as recorded by sensors 12 and 14 ........................... 60 Figure 4.1 : Mohr-Coulomb failure criterion in 2D space ............................................................... 62 Figure 4.2 : Typical finite element mesh ........................................................................................ 64 Figure 4.3 : Node numbering and integration points of a typical CPE8 element (Adapted from ABAQUS, 2009)............................................................................................................................. 65 Figure 4.4 : Steps used in the finite element analysis ................................................................... 66 Figure 4.5 : Measured and calculated initial earth pressure (in kPa) before void introduction ..... 68 Figure 4.6 : Changes in earth pressure due to contact loss introduced at invert .......................... 70 Figure 4.7 : Comparison between the calculated and measured earth pressures at the springline ....................................................................................................................................................... 71 Figure 4.8: Comparison between the calculated and measured earth pressures at the haunch .. 72 Figure 4.9 : Comparison between the calculated and measured earth pressures at the invert .... 73 Figure 4.10 : Soil yield regions around the pipe for a gap at the springline .................................. 74 Figure 4.11 : Soil yield regions around the pipe for a gap at the haunch ...................................... 75 Figure 4.12: Soil yield regions around the pipe for a gap at the invert .......................................... 75 Figure 5.1 : Typical pipe segment ................................................................................................ 77 Figure 5.2 : Model geometry .......................................................................................................... 78 Figure 5.3 : Vertical displacement field in the x-z plane ................................................................ 80 Figure 5.4 : Radial earth pressure calculated versus different ratios of model length to pipe diameter ......................................................................................................................................... 81 Figure 5.5 : Typical 3D finite element mesh .................................................................................. 82 Figure 5.6 : Node numbering and integration points of a typical C3D20 element (Adapted from ABAQUS, 2009)............................................................................................................................. 83 Figure 5.7 : Master and slave surface representing the soil - pipe interaction .............................. 84 Figure 5.8 : A 3D schematic of the pipe with deteriorated soil (a) void parameters and (b) pipe segment with a void at the springline ............................................................................................ 86 Figure 5.9 : Measured and calculated earth pressure distribution using different method ........... 89 Figure 5.10 : Calculated ring moment distribution using different methods .................................. 91 Figure 5.11 : Changes in earth pressure at section A-A for voids at springline ............................ 93 Figure 5.12 : Changes in earth pressure at section A-A for voids at invert ................................... 94 Figure 5.13: Effect of void length on the changes in earth pressure along the pipe for voids at the springline ....................................................................................................................................... 97 Figure 5.14 : Effect of void length on the changes in earth pressure along the pipe for voids at the invert .............................................................................................................................................. 98 Figure 5.15 : Effect of void length on the changes in earth pressure ............................................ 99
xi
Figure 5.16 : Effect of void depth on the changes in earth pressure along the pipe for voids at the springline ..................................................................................................................................... 101 Figure 5.17 : Effect of void depth on the changes in earth pressure along the pipe for voids at the invert ............................................................................................................................................ 102 Figure 5.18 : Effect of void depth on the changes in earth pressure ........................................... 103 Figure 5.19 : Effect of void angle on the changes in earth pressure ........................................... 104 Figure 5.20 : Sketch illustrating circumferential pipe stresses .................................................... 105 Figure 5.21 : Effect of void length on the changes in pipe circumferential stresses for voids with VA/2π = 9% at the springline ....................................................................................................... 107 Figure 5.22 : Effect of void length on the changes in pipe circumferential stresses for voids with VA/2π = 17.5% at the springline .................................................................................................. 108 Figure 5.23 : Effect of void length on the changes in pipe circumferential stresses for voids with VA/2π = 9% at the invert .............................................................................................................. 109 Figure 5.24 : Effect of void length on the changes in pipe circumferential stresses for voids with VA/2π = 17.5% at the invert ......................................................................................................... 110 Figure 5.25 : Calculated ring moments when voids are introduced at (a) the springline and (b) the invert ............................................................................................................................................ 113 Figure 5.26 : Percentage change in ring moment along the pipe calculated at (a) ..................... 114 Figure 5.27 : Percentage change in ring moment along the pipe calculated at (a) crown , (b) springline and (c) invert for voids at the invert ............................................................................. 115 Figure 5.28 : Sketch illustrating the tensile and compressive pipe stresses ............................... 116 Figure 5.29: Percentage change in maximum tensile stresses calculated at crown, springline and invert for voids introduced at (a) springline and (b) invert ........................................................... 118 Figure 5.30 : Percentage change in maximum compressive stresses calculated at crown, springline and invert for voids introduced at (a) springline and (b) invert ................................... 119 Figure 5.31 : Sketch illustrating longitudinal pipe stresses ......................................................... 120 Figure 5.32 : Changes in longitudinal stresses at extreme outer fibre for voids at springline ..... 121 Figure 5.33 : Changes in longitudinal stresses at extreme outer fibre for voids at invert ........... 122
xii
LIST OF TABLES
Table 3.1: Soil properties .................................................................................... 50
Table 4.1 : Material parameters assigned in the numerical model ...................... 63
Table 5.1 : Material parameters assigned in the numerical model ...................... 79
Table 5.2 : Void Parameters investigated ........................................................... 87
Table 6.1 : Summary of the pipe response showing the critical void sizes and locations ............................................................................................................ 128
xiii
LIST OF SYMBOLS
All variables in this thesis are expressed in SI units. Unless otherwise stated, default
units are kg, N, m, s.
Roman Symbols
∗,∗ , ∗ Burns and Richard's equation constants
, , Hoeg's equation constants
B Width of the excavation
Bc Outside width of the conduit
Bd Horizontal width of the ditch
Bf Bedding factor
B*,C* Constants related to the lateral stress ratio
C Compressibility ratio
c Cohesive strength of the soil
Cc Coefficient of curvature
Cd Load coefficient
Cu Coefficient of uniformity
dc Shortening of the vertical height of the conduit
E Modulus of elasticity
EA Circumferential extensional stiffness per unit length
Ec Conduit Young's modulus
EI Circumferential bending stiffness per unit length
Ep Pipe modulus
xiv
F Flexibility ratio
H Overburden height
Ip Second moment of area of the pipe cross section
K Rankine's lateral earth pressure coefficient
K0 Lateral earth pressure coefficient at rest
Ka Rankine's active earth pressure coefficient
Kw Handy's earth pressure coefficient
Lateral pressure factor
Lp Pipe segment length
Lv Void arc length
M Bending moment
M* Constrained modulus
Mθ Ring bending moment
P Free field vertical stress
P/P0 Normalized earth pressure
Pr Radial load applied on the buried structure
q Surface surcharge
R Mean radius of the conduit
r Distance from the pipe center to soil element
rsd Settlement ratio
sf Settlement of the conduit into its foundation
sg Settlement of the natural ground surface adjacent to the conduit
xv
sm Compression strain of the side columns of soil of height
t Pipe wall thickness
T.E.B Three-edge bearing strength
U,V,W Displacements in the x, y, and z directions
UF Extensional flexibility
Ux,Uy,Uz Constraints in the x, y and z directions
VA Void angle
VD Void depth
VL Void length
VL/Lp Normalized void length
VF Bending flexibility
Wc Vertical weight applied on the pipe
WL Weight of live load
Y/L Normalized position along the pipe
z Thickness of the soil overlying the element
Greek Symbols
α 45 + ϕ/2
β Material constant of Drucker-Prager model
γ Unit weight of the soil
γd Dry unit weight
γmax Maximum dry unit weight
γmin Minimum dry unit weight
xvi
γw Unit weight of water
Retraction of the strip
ε1,ε2 Inner and outer circumferential strains
θ Angle along the pipe circumference
μ Coefficient of friction of fill material
μ' Coefficient of friction between the backfill and the prism sides
ρ Density
1/ρ Change in pipe curvature
σh Horizontal earth pressure
σL Longitudinal pipe stress
σL/σL0 Normalized longitudinal pipe stress
σr Radial earth pressure
σv Vertical earth pressure
σθ Circumferential stress
σθ/σθ0 Normalized circumferential pipe stress
σ1 Maximum principal stress
σ3 Minor principal stress
τ Shear strength of the soil
ν Medium Poisson's ratio
νc Conduit Poisson's ratio
ϕ Friction angle of the soil
ψ Dilation angle
1
Chapter 1
Introduction
1. Dummy Chapter Numbering 1.1. Introduction
Buried pipes are important infrastructure to modern society. They are universally
used in transporting essential bulk fluids such as water, wastewater and energy
resources (i.e, oil and gas) and play an important role on the economic growth
and quality of life in urban areas.
In general, buried pipes fall into two main categories either rigid or flexible pipes.
Examples of rigid pipes are those made from concrete and clay. This category of
pipes experiences very small deformation under applied loads in such way that
no horizontal passive resistance from the surrounding soil is produced. The
carrying capacity of rigid pipes is gained from longitudinal and circumferential
bending resistance. On the other hand, plastic and steel pipes are considered to
be flexible as they are able to deflect up to 2% of their diameter without
experiencing any sign of structural failure (Najafi, 2010). Such deformation is
sufficient to mobilize the passive resistance of the surrounding soil which
enhances its supporting capacity. Figure 1.1 illustrates the load transfer
2
mechanism under vertical earth pressure for (a) rigid pipe and (b) flexible pipe,
respectively.
(a) Rigid pipe (b) Flexible pipe
Figure 1.1 : Load transfer mechanism (a) rigid pipe and (b) flexible pipe
1.2. Research Motivation
Contrary to above ground structures, design of buried pipes requires the
consideration of the contact between the surrounding soil and the pipe. Since
early 1900's, researchers have been focusing on the development of design
methods for buried pipe. Improvements to existing methods continued and new
methods evolved over the years in order to cope with the changes in pipe
materials, sizes, and loading conditions. The evolution of the different design
methods is depicted in Figure 1.2.
Soil Load
Original undeformed pipe shape
Soil Load
3
Figure 1.2 : History of buried pipe design methods
Existing design methods generally consider defect free pipe and ideal ground
conditions. With time, buried pipes experience different signs of deteriorations
including cracks, loss of material and open joints. Deterioration of buried
infrastructure is a well documented problem. In Montreal, 33% of water
distribution pipes and 3% of the sewage pipes reached their end of service life in
2002, and another 34% of the water-pipe stock will follow by 2020 (Mirza, 2007).
Similarly, Ontario’s water mains experience 25 breaks per 100 km per year;
therefore, 25% of the water pipe system must be replaced and 50% must be
restored over the next 60 years (water infrastructure, 2004). These defects in the
system cause infiltration and exfiltration processes to take place, which may lead
to loosening the surrounding soil and the development of erosion voids behind
the pipe wall (see Figure 1.3).
Empirical Method
Marston and Anderson (1913)
Analytical Solutions
Burns and Richard (1964)
Hoeg (1968)
Numerical Methods
Katona and Smith(1976)
Heger et al. (1985)
4
Figure 1.3 : Erosion void development behind a buried pipe wall (Adapted from Moore, 2008)
Ground support loss around a buried pipe has been reported in the literature and,
in some cases, has lead to a complete failure of the pipe. Different studies
examined the effect of erosion void formation on the structural integrity of a
buried pipe; however, these studies were limited to two-dimensional (2D)
analyses where the void is assumed to extend along the entire pipe length.
Since erosion void development is a three-dimensional (3D) phenomenon, a 3D
study examining the effect of erosion voids behind a pipe wall on the earth
Void at pipe springline
5
pressure acting on the pipe and the changes in pipe wall stresses is therefore
needed. Figure 1.4 compares the current research program to previous work
reported in the literature.
(a) Previous work (b) Present research
Figure 1.4 : Void representation (a) previous work and (b) present research
1.3. Objectives and Methodology
The main objective of this research program is to study experimentally and
numerically the effects of erosion void located behind the wall of a rigid pipe on
the earth pressure distribution and the changes in stresses in the pipe wall.
1.3.1. Experimental Program
The experimental program involves the design of a small scale apparatus that
allows for the measurement of the changes in soil pressure around an existing
pipe due to the introduction of a physical gap between the pipe wall and the
Long void under the entire pipe Void of finite length
Soil Pipe Pipe Soil
6
surrounding backfill. The objectives of the experiments are to investigate the
following aspects:
(i) To examine the impact of void location with respect to the pipe
circumference on the earth pressure distribution.
(ii) To evaluate the effect of the gradual increase in void depth on the
measured earth pressure around the void.
1.3.2. Numerical Program
The nonlinear finite element package ABAQUS is used throughout this study to
perform both the 2D and 3D numerical simulations. The purpose of the 2D
analysis is to validate the numerical model using the laboratory data and assess
the effect of the gap simulation procedure used in the experiments on the
measured results. In the 2D analyses, the following aspects are considered:
(i) The gap location around the pipe is changed in consistency with the
examined locations in the experimental program.
(ii) Two different interface conditions are evaluated: Free Slippage and No
Slippage interface.
(iii) The depth of the gap between the pipe wall and the backfill is gradually
increased to simulate the actual experiments.
The 3D finite element analysis is then used to study the effect of void size in 3D
space on the changes in earth pressure and stresses in the pipe wall due to the
introduction of a finite void around the pipe. The following aspects are considered
in the 3D analysis:
(i) The voids are introduced at two critical positions: springline and invert.
7
(ii) The void sizes are varied spatially in the x, y and z directions to reflect
the effect of increasing the void depth, length, and angle, respectively,
on the pipe response.
1.4. Statement of Originality
The original contributions described in this research include:
(i) A laboratory set up is designed to facilitate the simulation of the local
pipe wall separation from the surrounding soil and measure the
changes in earth pressure at selected locations along the pipe
circumference. A laboratory procedure was also developed to ensure
consistent and repeatable initial conditions.
(ii) A 2D numerical model is developed and validated by comparing the
calculated results with those measured in the experiments. The
calibrated model is then used to examine the adequacy of the
mechanical adjustable strip used to simulate the physical gap around
the pipe.
(iii) A 3D numerical model is developed to simulate the relevant aspects of
the problem including: void location, void angle, void depth, and void
length. Relationships are established between the studied parameters
related to the void size and the changes in earth pressure and pipe
wall stresses.
1.5. Thesis Organization
The thesis is organized in six chapters. After this introductory chapter, there are
five chapters in this thesis and their content is as follow:
Chapter 2 begins with a review of the literature related to the soil arching theory
and existing design methods of buried pipes. This is followed by a discussion of
the progressive deterioration that a buried pipe may experience through its
8
service life including common signs encountered in pipe inspections. Then,
previous case studies and research work related to the effects of support loss
and erosion voids on buried structures are summarized. Appendix A
complements this section by presenting existing techniques used in detecting
erosion voids around buried structures.
Chapter 3 describes the experimental set up and the testing procedure used in
the laboratory experiments. This is followed by a discussion of the recorded
changes in earth pressure measured on the model pipe after introducing a
physical gap at selected locations with respect to the pipe circumference.
Chapter 4 presents the 2D finite element analyses used in validating the
numerical model and the adequacy of the retracted strip technique used to
simulate the contact loss around the pipe.
Chapter 5 details the 3D finite element analyses used to examine the size effect
of the erosion void on the changes in earth pressure and wall stresses of a
concrete pipe installed using the embankment construction method.
Chapter 6 presents the conclusions drawn from this research and highlights the
practical significance of the findings deduced from this study. Finally, the
limitations and recommendations for future work are presented.
9
Chapter 2
Literature Review
2. Dummy Chapter Numbering 2.1. Chapter Overview
Underground infrastructure has recently gained special attention due to its aging
and the advanced state of deterioration that has been reached. Formation of
erosion void behind the walls of subsurface structures is a well documented
problem that may threaten the structural integrity of these structures. To study
the effect of erosion void formation on buried pipes, an assessment of the
research available in the literature has to be performed by reviewing three main
areas. The first area deals with the theory behind the design of buried pipes and
the development through the past few decades. The second area is related to
the factors affecting pipe deterioration and failure. This allows one to identify the
different failure modes of pipes and relate the failure mechanism to the possible
soil erosion behind the pipe wall. Finally, recent studies dealing with erosion
voids around buried structures will be reviewed. Based on the reviewed studies,
research gaps will be indentified, thus setting the objective of the present
research program.
10
2.2. Soil Arching Theory
In soils, arching takes place when a soil prism yields while the remainder soil
mass stays stationary. The relative movement of the yielding mass is opposed by
friction forces (i.e. shear forces) acting on the sides between moving and
stationary parts as shown in Figure 2.1. The shear forces tend to stabilize the
yielding mass in place, which results in pressure reduction on the yielding mass
and pressure increase on the stationary mass. Terzaghi (1943) defined this
pressure transfer from a yielding soil mass to adjoining stationary parts as
arching effect. He emphasized also that arching is one of the most universal
phenomena encountered in soils both in the field and in the laboratory.
Figure 2.1: A yielding soil strip between vertical soil surfaces (a) classical rectangular representation; (b) catenary representation (McKelveyIII, 1994)
dw
σhσh
σ1
σ3 σ3
σ1
τ
Bd
τ
σV
(a) Classical representation
τ c σhtanϕ
σh Kaσv
Ka 1‐ sinϕ/1 sinϕ
dW γBd dh
(b) Catenary representation
σh Kwσv
Kw 1.06 cos2θ Kasin2θ
θ 45 ϕ/2
Ka tan2 45‐ ϕ/2
dh
dw
σh σh
ττ
dh
σVBd
σV dσV
Backfill
Bedding layer
Pipe
11
Soil arching theory plays a tremendously important role in calculation of earth
loads acting on underground structures. Therefore, understanding the mechanics
of soil arching theory has been the focus of many researchers. McKelveyIII
(1994) presented the arching phenomenon in a step-by-step procedure and
explained the difference between a classical rectangular arch representation and
a catenary arch representation. Figure 2.1(a) shows a rectangular soil element
having a thickness (dh) and weight (dw) with a vertical stress (σv) acting on its
top surface. The vertical movement of this soil element under the effects of its
own weight and the applied vertical stress is resisted by the soil mass underlying
this element (σv dσv) and the shear forces (τ) acting on both sides of the
element. Under equilibrium, the sum of the forces acting on the soil element in
the vertical direction should be equal to zero. The integration of the expression of
the sum of the vertical forces developed for the differential soil element from 0 to
a thickness z above the yielding soil strip reveals the following equation for the
stress applied on a buried structure located under a yielding soil mass
McKelveyIII (1994).
2c/B
2 tan 1 / / (2.1)
12
where:
Bd = The width of the excavation;
γ = Unit weight of the soil;
q = Surface surcharge
c = The cohesive strength of the soil;
Ka = Rankine's active earth pressure coefficient;
ϕ = The angle of internal friction of the soil; and
z = The thickness of the soil overlying the element.
For a catenary arch representation, the stress equation is derived in the same
way as the classical rectangular arch representation. The difference in a catenary
arch equation is that Rankine's active earth pressure coefficient (Ka) used to
relate horizontal earth pressure (σh) to vertical earth pressure (σv) in the classical
representation should be replaced by Handy (1985)'s earth pressure coefficient
(Kw) which states that the form of the inverted arch describes the path of the
minor principal stress (see Figure 2.1(b)).
Tien (1996) presented a thorough review of the arching effect and its important
role in various geotechnical applications; including buried conduits. A key factor
controlling the earth pressure acting on a buried structure is the direction of shear
forces along the sides of the yielding soil prism. It is the relative stiffness between
the soil medium and the buried structure that governs whether positive (i.e.
active) or negative (i.e. passive) arching condition develops. Positive arching
occurs when the structure is more compressible than the soil medium, as shown
13
in Figure 2.2(a). In positive arching, the yielding soil prism moves downward
while the shear resistance acts upward causing a reduction in the stress applied
on the structure. On the other hand, negative arching occurs when the soil
stiffness is relatively lower than the buried structure as illustrated in Figure 2.2(b).
In negative arching, the upward movement of the yielding soil prism renders the
shear resistance to move downward increasing the stress acting on the structure.
Therefore, buried rigid pipes are prone to higher earth loads compared to flexible
pipes.
Figure 2.2 : Soil arching effect (a) positive arching; (b) negative arching
Flexible pipe
Earth pressure
She
ar fo
rce
She
ar fo
rce
(a) Positive arching
Rigid pipe
Earth pressure
She
ar fo
rce
She
ar fo
rce
(b) Negative arching
14
2.3. Design of Buried Pipes
In the early 1900's, Iowa State invested extensively in large drainage projects.
During this period, many pipe failures were reported due to the absence of
design standards and practical installation guidelines. At that time, it was
recognized that there is a need for developing design methods that allow one to
select buried pipes precisely based on a rational basis (Spangler and Handy,
1973).
In contrast to above ground structures, design of underground conduits should
consider the interaction between the surrounding soil and the buried pipe. Since
the early 1900's, many researchers focused on estimating the earth loads acting
on buried pipes as well as stresses in the pipe wall. Different analysis and design
methods are available nowadays including empirical, analytical and numerical. In
the following sections, a review of commonly used design methods of buried
pipes is discussed.
2.3.1. Empirical Method
Marston and Anderson (1913) developed a theory to calculate the earth load
acting at the top of a buried conduit. They found that the load on a buried pipe is
not the total weight of the soil prism above the conduit, since a portion of this
load is transferred to the adjacent soil influenced by the soil arching effect. The
load equations were grouped according to the pipe installation procedures. The
15
two common installation methods are: a ditch pipe where the pipe is placed in a
trench excavated through existing natural ground, and an embankment pipe
where the pipe is laid on the natural ground level above which an embankment is
built. For a ditch conduit, the load acting on a rigid conduit can be calculated
using the following equation:
(2.2)
1
2 (2.3)
in which:
Wc = The vertical weight of soil applied on the pipe;
γ = Soil unit weight;
Cd = Load coefficient;
Bd = The horizontal width of the trench;
K = Rankine's lateral earth pressure coefficient;
μ' = Coefficient of friction between the backfill and the prism sides; and
H = Overburden height.
In an embankment installation, there are two common installation methods. The
first involves placing the pipe right on the natural ground above which the
embankment is constructed, which is known as a positive projection condition.
The second is to dig a trench where the pipe is laid under the natural ground
level on top of which the embankment is built; this is referred to as a negative
16
projection condition. The shearing forces generated on the planes extending
upward from the sides of the pipe as shown in Figure 2.3, play an important role
in the development of the soil arching effect and the resultant load reaching the
buried pipe. The relative movement between the inner soil prism and the
surrounding soil is the major factor controlling the direction of shearing forces,
which are affected by the settlement of the pipe and the surrounding soil as
shown in Figure 2.3.
(a) Rigid pipe/ Projection condition (b) Flexible pipe/ Ditch condition
Figure 2.3 : Settlements which influence loads on embankment pipe installation
Marston grouped the different settlement elements into an abstract ratio, referred
to as the settlement ratio, given by the following equation:
Sf
Sg
Sf dc Sm Sg
Criticalplane
Naturalground
Shearforces
ShearforcesH
B
Sf
Sg
Sf dc Sm Sg
Criticalplane
Naturalground
Shearforces
Shearforce s
H
Bc
17
(2.4)
where:
rsd = Settlement ratio;
sm = Compression strain of the side columns of soil of height;
sg = Settlement of the natural ground surface adjacent to the conduit;
sf = Settlement of the conduit into its foundation; and
dc = Shortening of the vertical height of the conduit.
The horizontal plane passing through the pipe crown is defined as the critical
plane. This plane settles more than the top of the pipe as shown in Figure 2.3a,
rsd is positive and the shear forces acting on the sides of the inner prism are
directed downward and the resultant load on the buried conduit is greater than
the weight of the soil prism. This condition is known as a projection conduit. On
the other hand, if the critical plane settles less than the top of the pipe as
illustrated in Figure 2.3b, rsd is negative and the shear forces acting on the sides
of the inner prism are directed upward and the resultant load acting on the buried
conduit is less than the soil prism weight. This condition is referred to as a ditch
conduit. Marston grouped the above parameters and derived the following
equation to calculate the load on a buried conduit in an embankment installation:
(2.5)
18
1
2
(2.6)
in which:
Wc = Load on conduit;
γ = Unit weight of embankment soil;
Bc = Outside width of conduit;
H = Height of fill above conduit;
K = Rankine's lateral earth pressure ratio; and
μ = Coefficient of friction of fill material.
The pipe strength is determined using the three-edge bearing test. Figure 2.4
illustrates the typical set up of three-edge bearing test, where the in-situ loading
condition is presented by three point loads.
Figure 2.4: Three-edge bearing test set up (Adapted from ACPA, 2007)
Rigid Steel
Member
Concrete Pipe Sample
Bearing
Strips
19
The design load acting on the pipe crown is converted into an equivalent three-
edge bearing load through a factor of safety (F.S.) and a bedding factor Bf
calculated using the following equation:
. . . . (2.7)
in which:
T.E.B = Three-Edge Bearing strength;
Bf = Bedding factor;
F.S. = Factor of safety;
Wc = Weight of soil column; and
WL = Weight of live load.
The bedding factor is defined as the ratio of the supporting strength of the buried
pipe to the strength of the pipe derived from the three-edge bearing test. The
different bedding factors are presented in Figure 2.5.
The pipes are designed to sustain the equivalent three-edge bearing load test
(ASTM C497M), where the pipe size can be selected from standards (ASTM
C14M, ASTM C76M) providing details on unreinforced and reinforced concrete
pipes.
20
Figure 2.5 : Class of bedding and ranges of bedding factors (Adapted from Moser, 2001)
Class A
Concrete cradle Concrete arch
Compacted granular bedding
Class B
Granular bedding
Class C
Flat bottom
Class D
Bedding Class Bedding Factor (Bf)
A 2.8‐3.4
B 1.9
C 1.5
D 1.1
21
2.3.2. Analytical Methods
Burns and Richard (1964) studied the interaction of a circular cylinder buried in
soil medium and derived equations for the thrusts, moments and displacements
in the buried structure; as well as for the stresses and displacements in the
surrounding soil. In Burns and Richard's analysis, the soil and the buried
structure were assumed to behave elastically. In addition, the influence of
different parameters such as the extensional flexibility, the bending flexibility and
the interface between the buried structure and the adjacent soil on the different
quantities was accounted for in the derived formulae.
The two constants related to the lateral stress ratio are defined by:
∗ 1
21
12
11
(2.8)
∗ 1
21
121 21
(2.9)
where :
K = The lateral earth pressure ratio [ν/ 1‐ν)]
= The medium Poisson's ratio
The extensional flexibility (UF) and the bending flexibility (VF) are given by:
2 ∗∗
1∗
(2.10)
22
2 ∗∗
61
∗
6 (2.11)
where:
M* = The constrained modulus;
R = The mean radius of the conduit;
EA = The circumferential extensional stiffness per unit length; and
EI = The circumferential bending stiffness per unit length.
Figure 2.6 : Notation
The different parameters used in Burns and Richard's analysis are illustrated in
Figure 2.6. For a fully bonded interface, the radial load applied on the buried
structure is calculated by:
τrθ
U V σr
σθ
σθ
σz τθr
Pr
Q
N
M
Trθ V W
X
Y
Z θ
23
∗ 1 ∗ ∗ 1 3 ∗ 4 ∗ cos 2 (2.12)
and the moment equation is given by:
∗
61 ∗
∗
21 ∗ 2 ∗ cos 2 (2.13)
where:
∗ 1
∗/ ∗ (2.14)
∗
∗ 1∗
∗ 2 ∗
1 ∗ ∗ 1∗ 2 1 ∗
(2.15)
∗
∗ ∗ 2 ∗
1 ∗ ∗ 1∗ 2 1 ∗
(2.16)
P = Free field vertical stress
The analytical solutions were used to examine: conduit loads, attenuation of
stresses in medium, conduit displacements and attenuation of displacements in
medium considering two interface conditions (i.e. no slippage and free slippage)
and varying the flexibility parameters of the conduit (i.e. the extensional and
bending flexibility). Charts summarizing the changes in loads, stresses and
displacements at the conduit interface and at different locations in the medium
were developed. Figure 2.7 shows sample of Burns and Richard (1964)'s charts.
24
Figure 2.7 : Attenuation of conduit loads, stresses and displacements ( Burns and Richard (1964) )
K = 0.5, UF = 0.1, VF = 3
K = 0.5, UF = 0.1, VF = 3
Conduit displacements and attenuation of displacements in medium No Slippage interface
Conduit loads and attenuation of stresses in medium No Slippage interface
25
Hoeg (1968) conducted experiments to measure the contact pressure acting on a
cylinder buried in a homogenous medium. Different test series were performed
where the effects of burial depth, pipe rigidity and surface pressure on the
applied earth pressure were examined. The experimental results were used to
derive an analytical closed form solution to calculate the earth loads acting on a
buried conduit considering free slippage and no slippage interface between the
surrounding soil medium and the buried structure. In the mathematical
formulation, the relative stiffness between the buried conduit and the surrounding
soil was expressed by the following stiffness ratios:
12
11
∗
1
(2.17)
141 21
∗
1
(2.18)
in which:
= The medium Poisson's ratio;
M* = The constrained modulus;
Ec = The conduit Young's Modulus;
D = Pipe diameter;
t = Pipe wall thickness; and
= The conduit Poisson's ratio.
26
The earth pressure is given by:
12
1 1 1
1 3 4 cos 2
(2.19)
For a fully bonded interface the following constants are defined
1 2 11 2 1
(2.20)
1 2 1 12 1 2 2
3 2 1 2 52 8 6 6 8
(2.21)
1 1 2 12 1 2 2
3 2 1 2 52 8 6 6 8
(2.22)
in which:
= The medium Poisson's ratio;
= The lateral pressure factor;
R = The pipe radius;
r = The distance from the pipe center to the medium soil element;
C = The Compressibility ratio; and
F = The Flexibility ratio.
The contact pressure measured in the experiments was located between the
mathematical contact pressure calculated for no slippage and full slippage
27
interface between the buried structure and the adjacent soil. For a rigid pipe, the
results of contact pressure calculated were closer to a no slippage condition
rather than free slippage condition.
Various researchers focused on the modification and development of simplified
analytical solutions based on the above classical elastic solutions. Moore (2001)
presented a summary of the different methods used in the design of buried
conduits including rigid, semi-flexible, flexible and compressible pipes. Both the
compressibility and flexibility ratios defined by Hoeg (1968) were adapted and a
pipe stiffness table was presented where the ranges of the compressibility and
flexibility for different pipe categories were defined. A general analytical solution
considering both no-slippage and free-slippage interface between the soil-pipe
system was introduced.
2.3.3. Numerical Methods
Heger et al. (1985) presented a finite element program SPIDA: (Soil-Pipe
Interaction Design and Analysis) that analyzes a soil-pipe system. The program
allows for both trench and embankment installation methods to be simulated. It
also simulates the staged construction procedure and the variation in soil
stiffness with depth. Results are expressed in terms of the total field load acting
on the pipe and the earth pressure distribution at the soil-pipe interface, in
addition to the moments, thrusts and shear forces in the pipe. This finite element
28
program is limited to two-dimensional (2D) analysis for the soil-pipe system. This
design method is referred to as the direct design technique since pipes are
designed directly according to the resulting stresses in the pipe wall.
Kurdziel and McGrath (1991) presented a comparison between the classical
indirect design method (Spangler and Marston Method) and the direct design
method (SPIDA method) for concrete pipe. They found that SPIDA results
allowed developing a new and more realistic type of earth pressure distribution
acting on the pipe. This pressure distribution was named after its developer as
illustrated in Figure 2.8. A comparison of the reinforcement requirements for the
indirect design method with the direct design method showed that the latter
indicates substantial savings in the reinforcement requirements.
29
Figure 2.8 : Heger earth pressure distribution (ACPA, 2007)
Another commonly used software for the analysis of buried pipes is the Culvert
Analysis and Design (CANDE) software. Katona and Smith (1976) provided a
detailed description of the software including its different capabilities and
modules. Again, this program is limited to 2D analysis.
The American Society of Civil Engineers adopted the Standard Installation Direct
Design method (SIDD) in its standard for buried pre-cast concrete pipes in 1993
under the designation ASCE 15-93 (ASCE, 1993). Various municipalities and
states funded research projects to evaluate the SIDD method before its utilization
in practice. Full scale experiments were conducted by several researches (e.g.
Hill et al., 1999; Zhao and Daigle, 2001; Smeltzer and Daigle, 2005; Wong et al.,
30
2006; and Erdogmus et al., 2010). It has been agreed that the direct design
method is a modern practice for the design of reinforced concrete pipe (RCP)
considering the different factors that affect RCP behavior. The direct design
method uses modern concepts of reinforced concrete and limit state approach,
which provides economic and conservative design for a wide variety of
installation characteristics. The method has also been adapted in the Canadian
Highway Bridge Design Code for design of buried structures.
2.4. Deterioration of the Soil-Pipe System
The above section covers the different methods used in the design of pipe. With
time, both pipes and surrounding soils may deteriorate leading to changes in the
earth pressure distribution on the pipe. These changes may affect the long-term
performance of the soil-pipe system. A review of pipe and soil deterioration
mechanisms is discussed below.
2.4.1. Pipe Deterioration
Jewell (1945) discussed the different factors that can negatively impact the
service life of a buried pipe including disintegration, decomposition, corrosion,
chemical attack and erosion.
Intensive inspection programs have been conducted in the United Kingdom
(U.K.) early 1980s to evaluate the factors affecting the deterioration of sewer
pipes based on the analysis of various CCTV (Closed Circuit Television) survey
31
inspections. The reported defects (Lester and Farrar, 1979, O’Reilly et al., 1989
and Davies et al., 2001) include longitudinal and circumferential cracks, root
penetration, surface damage, encrustation, deformation and defective joints.
Some of the observed deterioration modes in buried pipelines are presented in
Figure 2.9.
Figure 2.9 : Typical defects encountered in a buried pipeline (a) circumferential
crack, (b) longitudinal crack, (c) hole in pipe wall, and (d) infiltration
Defective joints occupied considerable share among other reasons. Displaced
joints represented 57% of the defects observed and 34% of the connections were
(c) Hole in pipe wall
(a) Circumferential crack (b) Longitudinal crack
(d) Infiltration
32
defective in the 6 km of sewer analyzed by Lester and Farrar (1979). The
analysis conducted by O’Reilly et al. (1989) of 180 km of sewer revealed that
quarter of the connections investigated were found to be faulty. Despite the joint
type change from rigid to flexible, they still represent a considerable weakness.
Davies et al. (2001) discussed the different factors influencing the structural
integrity of a sewer pipe. It has been emphasized that there are three main
phases that a rigid pipe undergoes before reaching complete collapse. The first
phase involves minor unnoticed defects and cracks resulting from either
subsequent overloading or construction oversight. Such cracks usually take
place at the invert, crown and springlines. At this stage, defects do not have a
serious effect on the structural integrity of the pipe; however, they can lead to
further degradation of the sewer system.
The second phase of failure incorporates infiltration and exfiltration of water
through the existing defects in the pipeline. Soil particles are transported with
groundwater flowing into the pipe and similarly from the system, which results in
soil loosening and sometimes voids can develop behind the pipe wall. Ground
support loss may result in changes in soil reaction and progressive deformation
of the pipe. This can turn the existing cracks into larger fractures favouring more
infiltration and exfiltration at the interface. At this stage, noticeable deformation
33
(decreases in vertical diameter, and increases in horizontal diameter) can
develop following the pipe fractures (see Figure 2.10 ).
The third and last phase of failure is the collapse of the pipe. This happens
primary when the pipe deformations exceed 10% of its initial design. Such
deformation of the pipe is mainly resulting from the growth of voids in the close
vicinity of the pipe and loss of soil side support. At this point, the pipe is no longer
functional and immediate repair or replacement is required. Figure 2.10 shows
the three stages of sewer failure.
Phase 1 Minor defects
Phase 2 Fractures
Phase 3 Failure
Figure 2.10 : The three stages of sewer failures (Davies et al., 2001)
2.4.2. Soil Deterioration
Soil erosion around defective pipes is generally controlled by three main factors:
soil properties (grain size, plasticity and density), defect size and hydraulic
conditions. Jones (1984) discussed the soil loss phenomenon for both cohesive
and cohesionless soils. For cohesionless soils, a loose particle directly filtrates
throu
only
force
cohe
2.11
2
Helfr
vitrifi
inves
unde
geote
save
Tales
conc
ugh the pip
when the
es induced
esion and fr
illustrates
Figure 2.1
.5. Case St
rich (1997)
ed clay bu
stigation wa
er the pipe
echnical inv
ed 30 times
snick and
crete-lined
e anomalie
cohesive a
by the flow
riction, the
how erosio
11 : Mecha
tudies of Gr
reported t
uried at dep
as the main
invert by a
vestigation
the replace
Baker (19
steel sew
es. For cohe
attraction of
w into the
erosion pro
n voids dev
nism of ero
round Supp
the failure
pths that ra
n reason re
about 50 m
and the ad
ement costs
999) also p
er pipe bu
esive soils,
f soil partic
pipe. For s
ocess is a
velop aroun
osion voids
port Loss ar
of a 0.3 m
ange from 3
sulting in th
mm. The co
ddition of m
s.
presented t
uried in c
, the erosio
cles is over
soils inherit
mix of the
nd a defecti
developme
round Burie
m diameter
3 to 6 m. I
he settleme
osts assoc
more beddin
the failure
clayey soils
on process
rcome by t
ting their st
two proces
ive pipe wa
ent around
ed Pipes
r sewer pip
Inadequate
ent of the su
ciated with
ng material
of a 1.2
s. Field in
3
is mobilize
the seepag
trength from
sses. Figur
all.
a pipe
pe made o
e subsurfac
ubgrade so
the detaile
would hav
m diamete
nvestigation
34
ed
e
m
re
of
ce
oil
ed
ve
er
ns
Pipe wall
35
revealed the formation of a physical gap of approximately 20 mm between the
invert and the bedding layer supporting the pipe (see Figure 2.12 ). Severe
cracking developed at the crown and springline along a 300 m segment of the
pipeline. Although the loss of soil support in the above examples may not have
been due to erosion void formation, these case studies illustrate the possible
destructive consequences that could be induced by the ground support loss
around and under buried pipes.
Figure 2.12 : Gap reported at pipe invert (Adapted from Talesnick and Baker, 1999)
2.6. Previous Work related to Erosion Voids and Underground Structures
Tan and Moore (2007) investigated numerically the effect of void formation on
the performance of buried rigid pipes. The influence of both the void size and
location (e.g., springline and invert) on the stresses and bending moments in the
Gap at pipe invert
Sand
Pipe
36
pipe wall was investigated using 2D finite element analysis. Results of an elastic
model showed that the presence of a void at springline lead to an increase in the
extreme fibre stresses and bending moments at all critical locations: crown,
springlines and invert. The rate of increase is controlled by the growth of the void
in contact with the rigid pipe as shown in Figure 2.13. Extending the model to
include the soil shear failure resulted in stresses and moments higher than those
reported in the elastic analysis. Changing the location of the void from springline
to invert resulted in reduction in bending moment values followed by a reverse of
the moment sign.
Figure 2.13 : Changes in circumferential stresses at crown induced by erosion voids (Tan and Moore, 2007)
-200
-150
-100
-50
0
50
100
150
200
250
0 30 60 90
Per
cent
age
Cha
nge
in S
tres
s (%
)
Void Angle (degrees)
Tension Stress
Compression Stress
Soil
Voids
Pipe
30°60°90°
Megu
arou
differ
2.14)
inves
earth
the
signi
the s
void
rever
prese
F
uid and Da
nd an exis
rent sizes
). A series
stigate the
h pressure
lining. Wh
ficantly inc
same cond
at the lini
rsal in the
ents the ca
Figure 2.14
ang (2009) s
sting tunnel
were introd
s of elastic
effect of d
at rest and
en the vo
creased. Sim
ditions rega
ing invert w
sign of th
alculated be
: Location o
studied num
l on the cir
duced at th
c-plastic fin
different pa
d void size
oid was lo
milar result
ardless of t
was found
he momen
ending mom
of voids and
merically th
rcumferenti
he tunnel s
nite eleme
rameters (e
e) on thrust
cated at t
ts were rep
he flexibilit
to reduce
nt as the v
ments as a f
d sizes stud
he effect of
ial stresses
springline a
ent analyse
e.g., flexibi
t forces and
the springl
ported for t
ty ratio. Th
e the bend
void size in
function of
died (Megu
r = D/2
erosion vo
s in the lin
and invert
es was ca
ility ratio, c
d bending
ine, bendi
the thrust f
e presence
ding mome
ncreased.
the void siz
uid and Dan
Lv
3
oid formatio
ing. Void o
(see Figur
rried out t
coefficient o
moments i
ng momen
forces unde
e of erosio
ents causin
Figure 2.1
ze.
ng, 2009)
Simplified Voids
37
on
of
re
to
of
n
nt
er
on
g
5
Figgure 2.15 : Bending mand (
(a) At the
(b) At th
oments as b) invert (M
tunnel spri
he tunnel in
a function Meguid and
ingline
nvert
of the voidDang, 200
size at (a) 9)
3
springline
38
39
2.7. Gaps in Knowledge and Research Needs
From the review of the literature, the following can be concluded:
Cracks and open joints are among the common failure modes of
pipes. Through these defects, infiltration and exfiltration may take
place. This can result in soil loosening around the pipe and sometimes
voids could develop behind the pipe wall.
Design methods of earth load acting on buried pipes do not consider
the effect of local support loss between the pipe wall and the
surrounding backfill. A factor of safety ranging from 1 to 1.7 is
generally used in practice to account for construction related
imperfection.
Previous studies are limited to two-dimensional 2D analyses assuming
that the erosion void extends along the entire length of the pipe wall.
This does not allow for the effect of the void length to be considered in
the analysis.
There is a need to investigate the 3D effect of the erosion voids on the
pipe response in both the circumferential and longitudinal directions.
Physical models evaluating the impact of erosion voids located next to
pipe wall are scarce. Controlled laboratory tests that capture the local
support loss between the pipe wall and the surrounding medium will
40
allow for numerical models to be validated and help researchers
understand the progressive changes in earth pressure acting on an
existing pipe.
From the aforementioned remarks, it can be concluded that an experimental and
numerical study investigating the impact of erosion voids on the earth pressure
distribution acting on an existing pipe and the response of the pipe structure to
these changes is needed. The study should include the following aspects:
Experiments should be conducted to evaluate the impact of local
support loss between the pipe wall and the surrounding medium on
the initial earth pressure distribution on the pipe.
3D effects of void size (e.g., contact angle with pipe wall, length and
depth) and void location should be investigated to examine the
changes in earth pressure associated with the void formation in both
circumferential and longitudinal directions.
Finally, the study should be extended to investigate the corresponding
pipe response associated with such changes in earth pressure.
41
Chapter 3
Experimental Analysis
3. Dummy Chapter Numbering
3.1. Chapter Overview
In this chapter, the test setup and the procedure of the experimental program are
described. This is followed by a discussion of the changes in earth pressure
measured after introducing the gap between the pipe wall at the different
locations examined.
3.2. Objective of The Experimental Study
The objective of this study is to measure the changes in earth pressure resulting
from a local contact loss induced at different locations between the backfill
material and the wall of an existing pipe. A schematic showing a local support
loss at the invert of a rigid pipe is shown in Figure 3.1 along with a simplified
physical model.
42
Figure 3.1: Rigid pipe subjected to local contact loss
A series of laboratory experiments is conducted to evaluate the effect of local
separation between the pipe wall and the surrounding soil on the earth pressure
distribution acting on the pipe and the measured results are compared with the
initial earth pressure values. Three different locations of contact loss are
examined, namely; springline, haunch, and invert (see Figure 3.2).
Figure 3.2: The three test sets investigated experimentally
Granular backfill
Set A: Springline Set B: Haunch Set C: Invert
Physical model
Granular
Contact loss
Granular
43
3.3. Experimental Setup
A description of the different components and the procedure of the experiment is
given below.
3.3.1. Steel tank
The testing facility has been designed such that the entire pipe model was
contained in a rigid steel tank. As illustrated in Figure 3.3, the tank is
approximately 1410 mm long, 1270 mm high and 300 mm wide with a 12 mm
plexiglass face.
Figure 3.3 : Experimental setup
Length = 1410 mm Width = 300 mm
HSS reinforcement
LVDT
Pipe position
Hei
ght
= 12
10 m
m
Sliding plexiglass connection
44
Both the front and rear sides were reinforced using three 100 mm HSS sections.
The internal steel sides of the tank were painted and lined with plastic sheets to
reduce friction between the sand and the sides of the tank. On the front and rear
sides, a hole of 152 mm in diameter was drilled. The hole size was selected to be
larger than the outer diameter of the pipe to ensure that the pipe rests directly on
the sand. The location of the opening was chosen to minimize the influence of
the rigid boundaries on the measured earth pressure and to ensure sufficient
overburden pressure over the pipe (C/D = 2). This was achieved by placing the
lateral boundaries at a distance approximately four times the pipe diameter (4.2
D) measured from its circumference. The rigid base of the tank was located at a
distance of 2.2 D below the pipe invert.
3.3.2. Rigid Pipe
One of the challenges of the experimental setup was to develop a suitable
mechanism to simulate the local contact loss between the pipe wall and the
surrounding medium while recording the earth pressure changes around the
pipe. Researchers came up with different ideas to model voids in the ground.
These methods include: (a) pressurized air bags where a tube is pushed through
the soil or buried during the soil placement and a rubber membrane is then
inserted into the tube and pressurized. The void is created by deflating the
membrane leaving a vacant space within the soil. (b) polystyrene foam and
45
organic solvent, in this method a stiff tube of polystyrene foam is buried in the
soil. Once exposed to an organic solvent the foam dissolves leaving a void
behind. (c) mechanically adjustable devices that can be adjusted to provide the
desired volume loss. Additional details about these methods can be found in the
state-of-art review article by Meguid et al. (2008). In this study, a mechanically
adjustable physical model has been adopted that allows for controlling the
location of the support loss and minimizes the need for introducing new material
around the pipe. This was achieved by designing and machining a segmented
pipe composed of six curved segments sliced from a cold drawn steel pipe of 25
mm wall thickness (114 mm in diameter, and 610 mm in length) and six
aluminum strips. To hold the different circular sectors of the pipe, six stainless
steel U-shape grooved pieces were used and reinforcing stiffeners were used to
ensure the pipe rigidity (see Figure 3.4).
Figure 3.4 : Different parts used in assembling the segmented pipe
U-shaped holding pieces
Curved pipe segments Nut
Hinges Coupling nut
Threaded rod
Segment guide
46
The different pipe sectors were assembled such that the segments tightly fit
between the lips of the holding pieces. The U-shaped pieces were hinged to a 25
mm hexagonal nut screwed to a threaded rod passing along the pipe length. The
movement of the nuts allows for a total reduction of 3 mm in the outer diameter of
the pipe. The aluminum shims were placed such that one end is bolted to one of
the pipe segments while the other end is left to slide freely over the adjacent
segment. The small gaps between the shim and the pipe were sealed with clear
silicon caulking so that sand particles do not enter between the segments and
damage the sensors. The different parts used in assembling the segmented pipe
are shown in Figure 3.4, whereas a view of the fully installed pipe is shown in
Figure 3.5. Under full expansion condition, the pipe outer diameter is 150 mm.
Figure 3.5 : Top view of the assembled pipe spanning the steel tank
D = 150 mm
Futek sensors
Aluminum shims
Pipe segment
Scaime sensors
47
To simulate the local contact loss between the pipe wall and the backfill material,
a slot of 10 mm wide and 260 mm long was opened along the length of one of
the pipe segments. This opening served to host a steel strip, of similar dimension
and geometry, machined from another tube of the same curvature. The
movement of the steel strip was controlled using hinges and two threaded rods
connected at the centre of the pipe segment by a custom made coupling nut. To
move the steel strip, a threaded rod was turned, causing the hinges to move
towards the coupling nut and therefore the steel strip moves inward. The strip
movement was calibrated to retract exactly 1.5 mm per full 360° rotation with a
maximum retraction of 3.5 mm. The pipe was designed so that the retractable
strip could be placed at the springline, haunch and invert. The dimensions of the
retractable steel strip would correspond to approximately 1.5% of the pipe
circumference or a void angle of 5.1° as compared to Meguid and Dang (2009)
and Tan and Moore (2007), respectively. Figure 3.6a and Figure 3.6b show the
inside and outside views of the retractable strip, respectively.
48
(a) Inside view of the retractable strip
(b) Outside view of the retractable strip
Figure 3.6 : The retractable strip (a) inner mechanism and (b) outer side
3.3.3. Instrumentation
To measure the earth pressure distribution, the pipe was instrumented with eight
load cells connected to a data acquisition system. Four of them (Scaime AR)
have maximum capacity of 1200 g with accuracy of ±0.02% while the remaining
ones (Futek LBB) have maximum capacity of 250 g with accuracy of ±0.05%. All
load cells were mounted inside the pipe with only the sensing area installed flush
with the pipe circumference and exposed to the soil. The diameter of the sensing
area was 25 mm and 12 mm for the Scaime and Futek sensors, respectively.
Scaime sensors were installed along a circular cross section at the middle of the
Instrumented pipe segment with opening
Retractable steel strip
Guide Threaded rod Coupling nut
Hinge and nut
49
pipe. Futek sensors were placed on both sides of the retractable strip and ±19
mm from the middle of the pipe (see Figure 3.5). Such arrangement of the
sensors allowed the changes in earth pressure to be monitored in the close
vicinity of the strip and at other critical locations along the pipe circumference. It
should be emphasized that the sizes of the different load cells were selected
such that all sensors fit inside the pipe (particularly the four sensors around the
retractable strip) and at the same time provide the accuracy needed for the
expected changes in soil pressure. The locations of the load cells were chosen
based on the previously conducted numerical study (Meguid and Dang, 2009)
which concluded that changes in earth pressure develop mainly in the close
vicinity of the void. A schematic showing the position and numbering of the
sensors is shown in Figure 3.7.
Figure 3.7 : A schematic showing half the pipe and all sensor locations
Scaime sensors
Sensor 15 Sensor 16
Sensor 18 Sensor 17
Futek sensors 11 & 13
Futek sensors 12 & 14
Retractable steel strip
50
3.3.4. Fine sand
Quartz sand was used as the backfill material. Sieve analysis, direct shear and
other soil property tests were performed on several randomly selected samples.
The density of the sand in the tank was also measured during the tests by
placing small containers of known volume at different depths inside the tank. The
coefficients of uniformity (Cu) and curvature (Cc) of the sand were found to be
1.90 and 0.89, respectively. A summary of the sand properties is provided in
Table 3.1.
Table 3.1: Soil properties
Property Value
Specific gravity 2.66
Coefficient of uniformity (Cu) 1.9
Coefficient of curvature (Cc) 0.89
Maximum dry unit weight (max) 15.7 kN/m3
Minimum dry unit weight (min) 14.1 kN/m3
Experimental dry unit weight (d) 15.0 kN/m3
Unified soil classification system SP
Internal friction angle () 38.5°
Cohesion (c) 0.2 kPa
Coefficient of earth pressure at rest (Ko) 0.38
51
3.4. Testing Plan
3.4.1. Load cell calibration
To ensure that the load cells measure the correct pressure, the entire pipe model
was subjected to a hydrostatic pressure and the readings were recorded and
compared to the expected pressure values. At a depth of 0.9 m below water
surface, the maximum hydrostatic pressure was measured to be 8.6 kPa which is
in agreement with the theoretical value expected of whw = 9.81 0.9 = 8.8 kPa.
The load cells were also mounted on the side of a rigid vertical wall (0.5 m in
height and 1 m in length) and subjected to lateral soil pressure induced by sand
backfill. Results indicated a linearly increasing pressure with depth. The load cell
readings were consistent with the expected at-rest earth pressure under two-
dimensional condition (hK0). The coefficient of lateral earth pressure at rest, Ko,
was calculated using (1 - sin = 0.38). The angle of internal friction, , was
obtained from direct shear tests performed on the sand used throughout the
entire experimental program.
3.4.2. Procedure
The test procedure consisted of installing the pipe under contracted condition
(144 mm OD) in the tank. As the pipe crosses the tank face, two rubber
membranes having 150 mm diameter hole were slipped from inside the tank
along the pipe. The pipe was expanded to its maximum diameter (150 mm) and
52
its horizontal position was checked. While monitoring the horizontal position of
the pipe, two machined plexiglass connections were installed at the extremities of
the pipe to facilitate free sliding in the vertical direction as shown in Figure 3.3.
The external plexiglass connections attached to the pipe were lifted and clamped
to prevent the pipe from resting directly on the rigid boundaries of the tank and
allowing for the placement of the soil under the pipe invert while the pipe is at a
temporary elevated position. The role of the rubber membranes was to prevent
the sand leakage that may occur from the existing gap between the pipe and the
tank. To monitor the horizontal position of the pipe while the test is running, two
vertical LVDTs were attached to the plexiglass connections and the displacement
readings were recorded using, the data acquisition system.
After securing the pipe in its temporary position, a testing procedure was
developed in order to ensure consistent initial conditions (i.e. sand density)
throughout the conducted experiments. The sand was rained from a constant
height into the tank in layers. From the tank base up to the pipe invert, the soil
was placed in three layers 100 mm in height. Each layer was first graded to level
the surface then tamped using a steel plate attached to a wooden handle. The
sand placement continued up to the pipe invert. Above the invert, the rained sand
was placed up to the crown and gently pushed around the pipe to ensure full
contact between the sand and the pipe. At this stage, the sensors were switched
53
on to record the earth pressure. Then, another layer of sand was added to cover
completely the pipe. The remaining sand required to reach the height of two
times the pipe diameter above the crown was placed with no tamping to minimize
damage to the load cells. Figure 3.8 illustrates the sand placement sequence
followed in the experiments.
Figure 3.8 : Stages of sand placement in the experiments
The clamps holding the pipe were then removed simultaneously allowing the pipe
to slide vertically and rest on the bedding sand layer. The horizontal position of
the pipe was checked through the recorded readings of the vertical LVDTs
attached to the plexiglass connections.
Once the initial conditions were established, the next step was to retract the steel
strip to simulate a local support loss between the pipe and the backfill soil. Since
the strip could retract up to 3 mm, the retraction was split into two steps each
representing a movement of 1.5 mm away from the sand. After each step, the
sensor readings were recorded and the test completed. Finally, after the test,
Sand layers
Tamping Tamping Pipe
Add sand to the desired height Tamping
Sand pushed
Stage 1 Stage 2 Stage 3
54
while the tank was being emptied, the sand sampling cups were recovered and
the sand density was measured.
3.4.3. Tests performed
Three sets of tests were conducted following the described procedure above to
examine the effect of the retracted strip location (springline, haunch and invert)
on the changes in earth pressure acting on the pipe. The sequence of the
sensors varied for each set of tests according to the position of the retracted
section. Three tests were performed for each position with a total of nine tests
conducted in this study.
3.5. Experimental Results
The earth pressure results presented in this section are based on the load cell
readings taken at the sensor locations along the pipe circumference. The results
of the nine tests conducted (three tests for each position) revealed consistent
changes in earth pressure readings recorded by the load cells located in the
close vicinity of the retractable strip. In all tests, the readings of the sensors
located away from the retractable section did not register significant changes in
pressure after introducing the local contact loss.
Figure 3.9 shows the changes in contact pressure recorded by sensors 15
through 18, when the retracted section was positioned at the springline. The
measured earth pressure, p, is normalized with respect to the initial pressure, p0,
55
and plotted on the vertical axis whereas the retractable section movement,
(mm), is plotted on the horizontal axis. Insignificant changes in earth pressure
were measured at the above locations with a maximum pressure increase of 4%
as recorded by sensor 16 for a retraction of 3 mm. This behavior is consistent
with the findings of Meguid and Dang (2009), who concluded that changes in
lining response occur mostly in the close vicinity of the introduced void.
Figure 3.9 : Measured changes in earth pressure away from the retracted strip - at the springline
Pressure decrease
Pressure increase 12 & 14
11 & 13
15 16
1718
(mm)
Sensor position
56
Earth pressure changes in the vicinity of the retracted section are presented in
Figures 3.10 through 3.12. The pressure readings when the gap was introduced
at the springline, haunch, and invert are discussed below.
3.5.1. Contact loss at the springline
Figure 3.10 presents the changes in contact pressure measured by the load cells
located in the vicinity of the retractable section, for a local contact loss at the
springline. Different pressure readings were registered by the sensors located
above and below the retractable section. Sensors 11 and 13 located above the
retractable section recorded gradual reduction in pressure, while sensors 12 and
14 located below the section registered gradual increase in pressure. For a
retraction of 1.5 mm, the upper sensors recorded a maximum pressure reduction
of 20%. This pressure reduction was accompanied by a pressure increase of
18% as recorded by the lower sensors. This behavior can be explained by the
observed soil movement behind the strip under gravity, filling the created void
and causing additional pressure around the lower sensors. Further retraction of
the section to 3 mm, the pressure registered by the upper sensors dropped to
50% of the initial pressure, whereas, the lower sensors recorded 30% increase in
pressure.
57
Figure 3.10 : Measured changes in earth pressure around the retracted strip - at the springline
3.5.2. Contact loss at the haunch
Figure 3.11 shows the changes in contact pressure measured by the sensors
located in the vicinity of the retractable section when located at the haunch.
Sensors on both sides registered an increase in contact pressure induced by the
progressive retraction of 1.5 mm and 3 mm. For a retraction of 1.5 mm, the
pressure increased by 7% of the initial value and continued to increase to about
21% of the initial pressure when the retraction reached 3 mm.
Pressure decrease
Pressure increase
12 & 14
11 & 13
15 16
1718
(mm)
Sensor position
58
Figure 3.11 : Measured changes in earth pressure around the retracted strip - at
the haunch
3.5.3. Contact loss at the invert
Moving the position of the retractable section to the invert resulted in similar
behavior to that reported at the haunch where sensors on both sides registered
pressure increase (see Figure 3.12). For a 1.5 mm retraction, the pressure
increased by 12% of the initial value and further increased to 22 % when the
movement reached 3 mm.
Pressure increase
12 & 14
11 & 13
15
16
17
18
(mm)
Sensor position
59
Figure 3.12 : Measured changes in earth pressure around the retracted strip - at the invert
3.6. Summary of Results
To visualize the relative changes in contact pressure, the average of the
measured pressure changes registered by the sensors (11/13 and 12/14) located
at the boundaries of the retractable section are presented in Figure 3.13 and
Figure 3.14; respectively, based on the nine conducted tests. For a retraction of 3
mm, the changes in pressure were generally greater compared to those recorded
for 1.5 mm retraction. This behavior confirms that, for the investigated length of
the wall separation, the earth pressure significantly changes in the vicinity of the
area that has experienced contact loss.
12 & 14
15
16 17
18
(mm)
11 & 13
Sensor position
Pressure increase
60
Figure 3.13 : Average changes in pressure as recorded by sensors 11 and 13
Figure 3.14 : Average changes in pressure as recorded by sensors 12 and 14
Set A: springline
Set B: haunch Set C: invert
Set A: springline Set B: haunch Set C: invert
61
Chapter 4
Validation of the Numerical Model
4. Dummy Chapter Numbering 4.1. Numerical Details
In this chapter, a two-dimensional (2D) finite element model that is suitable for
the analysis of soil-pipe interaction is presented.
The numerical model is first validated by simulating the actual experiment and
comparing the calculated pressures with those measured in the laboratory. The
model is then used to examine the adequacy of the experimental technique used
to simulate the soil void around the pipe.
4.1.1. Constitutive Models
The elastic perfectly-plastic nonlinear behavior of the soil is modeled using the
Mohr-Coulomb failure criterion, which assumes that failure occurs when the
shear stress on any point in a material reaches a value that depends linearly on
the normal stress in the same plane (ABAQUS, 2009). In 2D space, the Mohr-
Coulomb model is based on plotting Mohr's circle for states of stress at failure in
the plane of the maximum and minimum principal stresses. The failure line is the
62
best straight line that touches these Mohr's circles as shown in Figure 4.1
(ABAQUS, 2009).
Figure 4.1 : Mohr-Coulomb failure criterion in 2D space
In a plane strain analysis, the ABAQUS Mohr-Coulomb model uses a different
flow potential from the classical Mohr-Coulomb (ABAQUS, 2009). In order to
represent the classical Mohr-Coulomb behavior in Abaqus, one can match the
flow potential of the ABAQUS Mohr-Coulomb to that of the Drucker-Prager
model. This is achieved by relating the friction angle, ϕ, of the classical Mohr-
Coulomb to the material constant of Drucker-Prager model, then assigning a
dilation angle of the ABAQUS Mohr-Coulomb that matches the classical Mohr-
Coulomb and Drucker-Prager as shown in the following equations (ABAQUS,
2009):
σ1 σ1 σ3 σ3 ϕ
c
σ
τ
63
tan
3 sin6 cos
tan (4.1)
tan3√3 tan
9 12tan (4.2)
The rigid pipe was modeled as linear elastic material. Table 4.1 summarizes the
soil and pipe parameters used in the numerical analysis. It is worth mentioning
that the soil density used is consistent with that measured during the experiments
as discussed in chapter 3. The soil friction angle is obtained from direct shear
tests performed on selected sand samples. The deformation parameters, on the
other hand, were chosen in consistency with the values recommended by
McGrath et al. (1999) using the available soil properties (grain size, relative
density and stress level).
Table 4.1 : Material parameters assigned in the numerical model
Material Density
(t/m3)
Elastic Modulus
(kPa) Poisson Ratio
Friction Angle
(°)
Dilation Angle
(°)
Soil 1.5 10 x 103 0.3 38.5 27
Pipe 7.8 200 x 106 0.3
4.1.2. Boundary Conditions and Finite Element Mesh
The model dimensions were chosen in consistency with the experimental setup
presented in chapter 3, to ensure that the boundaries are located at sufficient
64
distances from the pipe; the finite element mesh was generated using model
dimensions that are (4.2D) in the x-direction from the pipe springline and (2D) in
the y-direction from the pipe invert. The boundary conditions were selected to
represent smooth rigid side boundaries and a rough rigid base boundary. The
finite element mesh used to study the condition of a contact loss at the springline
is shown in Figure 4.2.
Figure 4.2 : Typical finite element mesh
4.1.3. Element Type
Both the soil and the pipe were modeled using continuum elements (CPE8 8-
node biquadratic element) throughout the analysis. This second-order element
type was selected as it provides higher accuracy in Abaqus/Standard compared
1.4 m
D 0.75 m
4.2D
Ux = 0
Ux = 0
2D
Ux = Uy = 0
65
to first-order elements for problems that do not involve complex contact
conditions, impact, or severe element distortions. They capture stress
concentrations more effectively and can model geometric features (curved
surfaces) with fewer elements (ABAQUS, 2009). Figure 4.3 presents the node
numbering and the location of integration points in a typical CPE8 element.
Figure 4.3 : Node numbering and integration points of a typical CPE8 element (Adapted from ABAQUS, 2009)
4.1.4. Soil -Pipe Interface
The interaction between the soil and the buried pipe is modeled using the
surface-to-surface interaction technique. Both fully bonded and free slippage
interface conditions between the soil and the pipe were simulated. It is worth
noting that the free slippage condition was modeled by defining normal and
tangential contact properties with a friction coefficient of 0.01.
Nodes Integration Points
66
4.1.5. Stages of Analysis
The sand placement procedure used in the experiments was duplicated in the
numerical analysis (see Figure 4.4).The steps used in the analysis were as
follow:
(a) Generating the in-situ geostatic stresses in the base soil layer. The
coefficient of earth pressure was taken as Ko = 1 - sin ( = angle of
internal friction of the soil).
(b) The pipe and the first soil layer (around the pipe) are activated.
(c) The soil layer above the pipe springline is activated.
(d) The final soil layer is activated to reach the target soil level.
(e) The local gap between the pipe wall and soil is introduced at the
investigated location.
Figure 4.4 : Steps used in the finite element analysis
Step a
Step c
Step d
Step b
Step b
Step e
67
4.1.6. Modeling the Section Retraction
To simulate the local retraction of the steel strip, the mesh of the pipe wall was
discretized with element sizes that correspond to the displacements used in the
experiments. Using the element deactivation and activation procedure allowed
for the simulation of the sequential retraction.
4.2. Model Validation
Figure 4.5 shows the initial earth pressures calculated along with the
experimentally measured values before the gap introduction. Higher pressures
were generally calculated at the invert compared to the crown and springline. It
was found that, at the sensor locations, the numerical model was able to capture
the general trend of pressure distribution around the pipe. The interface condition
was found to affect the calculated pressures at the crown (90o) and invert (270o)
as illustrated by the solid and broken lines in Figure 4.5. However, since the
change in earth pressure due to local contact loss is of prime interest and the
initial conditions are generally used as a reference, the results of the numerical
analysis are considered acceptable.
68
Figure 4.5 : Measured and calculated initial earth pressure (in kPa) before void introduction
4.3. Evaluation of the Segment Retraction Technique used in The
Experiments
A numerical investigation was conducted to evaluate the effect of the section
retraction technique used in the experiments on the measured earth pressures.
The void was simulated numerically by incrementally removing the eroded soil
elements from the model leaving a gap between the pipe and the surrounding
soil. The results are then compared to the experimental data and presented in
the polar plot as illustrated in Figure 4.6. The difference between the measured
0
45
90
135
180
225
270
315
Experimental Numerical Fully Bonded Numerical Free Slippage
P = 10 kPa
P = 6 kPa
P = 14 kPa
P = 4 kPa
69
and calculated pressures at the sensor locations was found to be insignificant. In
addition, the measured pressures were found to be located between the two
investigated interface conditions. These results indicate that the retracted section
approach used in the experiments had little effect on the measured earth
pressure.
70
Figure 4.6 : Changes in earth pressure due to contact loss introduced at invert
0
45
90
135
180
225
270
315
Initial condition Numerical fully bonded Numerical free slippage Experimental
Simplified Experimental model
Granular
Numerical Model
Granular
P/P0 = 0.25
P/P0 = 0
P/P0 = 1.25
P/P0 = 1
Fully bonded
Free slippage
71
4.4. Numerical Results
The role of interface condition is further investigated using polar plots of the
measured and calculated changes in pressure using free slippage and fully
bonded interface between the pipe and the surrounding soil. It was found that the
numerically calculated changes in pressure are independent of the retracted
distance (1.5 mm and 3 mm). This is attributed to the continuum nature of the
model that does not allow particle movement and, therefore, the only final state
of stresses for 3 mm retraction is used in this section. The earth pressure, p, is
normalized with respect to the initial pressure, p0, and plotted on the radial
directions for different angles with the horizontal.
Figure 4.7 : Comparison between the calculated and measured earth pressures at the springline
0
45
90
135
180
225
270
315
Initial condition Numerical fully bonded Numerical free slippage Experimental
P/P0 = 0.25
P/P0 = 0
P/P0 = 1.25
P/P0 = 1.00
Fully
Free
= 3 mm
72
At the springline Figure 4.7, a mix of pressure increase and decrease was
calculated at the boundaries of the induced gap; the reduction in pressure is
found to be about 50% and the increase in pressure is about 25%.
At the haunch and invert (Figure 4.8 and Figure 4.9), a consistent pressure
increase of 20% at the gap boundaries is calculated. The results of the two
contact conditions (fully bonded and free slippage) represented the upper and
lower bounds of the contact pressure.
Figure 4.8: Comparison between the calculated and measured earth pressures at the haunch
0
45
90
135
180
225
270
315
Initial condition Numerical fully bonded Numerical free slippage Experimental
= 3 mm
P/P0 = 0.25
P/P0 = 0
P/P0 = 1.25 P/P0 = 1
Fully bonded
Free slippage
73
Figure 4.9 : Comparison between the calculated and measured earth pressures at the invert
Based on the results presented in Figures 4.7 through 4.9, it has been noted that
the measured pressures are bound by those numerically calculated under fully
bonded and free slippage interface conditions with more tendency towards the
fully bonded interface. This can be explained by the fact that the actual interface
between the pipe and the soil is not perfectly smooth particularly around the
retracted section due to the presence of the sensors.
Figures 4.10 through 4.12 present the regions of the soil yield (represented by
maximum difference in principal stresses) when the voids were introduced at the
springline, haunch and invert, respectively. It can be noticed that, for the
= 3 mm
0
45
90
135
180
225
270
315
Initial condition Numerical fully bonded Numerical free slippage Experimental
P/P0 = 0.25
P/P0 = 0
P/P0 = 1.25 P/P0 = 1
Fully bonded
Free slippage
inves
wher
F
stigated ga
re most of t
Figure 4.10
p size, soil
the stress c
0 : Soil yield
failure is g
concentratio
d regions ar
generally lo
on is measu
round the p
ocated arou
ured.
pipe for a ga
nd the gap
ap at the sp
7
p boundarie
pringline
74
es
Figure 4.1
Figure 4.
1 : Soil yiel
12: Soil yie
ld regions a
eld regions
around the
around the
pipe for a g
e pipe for a
gap at the h
gap at the
7
haunch
invert
75
76
Chapter 5
Three-Dimensional Numerical Analysis
5. Dummy Chapter Numbering 5.1. Chapter Overview
A 3D finite element model was developed to examine the 3D effects of erosion
voids located behind the wall of an existing sewer pipe on the changes in earth
pressure and pipe wall stresses.
The chapter starts by a description of the numerical model in which erosion voids
of different sizes are introduced at the springline and invert of the pipe. This is
followed by a validation of the finite element model where initial earth pressure
and ring moments are calculated and compared with field measurements and
closed form solutions. Finally, the effects of increasing the void length, depth and
angle on the earth pressure and pipe wall stresses in both the circumferential
and longitudinal directions are presented and discussed.
5.2. Problem Statement
The investigated problem involves a concrete pipe 600 mm in inner diameter and
70 mm in wall thickness installed using the embankment installation method with
3 m soil cover above the crown. The pipe is first placed in a large trapezoidal
shaped trench on a layer of bedding material and backfilled in layers and covered
77
by an embankment. The problem geometry and material properties used in this
investigation were based on the full scale experiments reported by Liedberg
(1991). This particular case study was chosen due to the availability of a
complete set of data, including, soil properties, measured earth pressure and
pipe moments, which is needed for the model validation. The details of a typical
pipe segment as reported by Liedberg (1991) are presented in Figure 5.1. The
problem geometry showing the pipe location is shown in Figure 5.2.
Figure 5.1 : Typical pipe segment
∅ = 600 mm
t = 70 mm
Lp = 2200 mm
740 mm
78
Figure 5.2 : Model geometry
5.3. Numerical Details
A total of eighteen (18) different numerical models were built in this study
including nine models for each void location (springline and invert). All models
were analyzed using the general nonlinear finite element code ABAQUS. Only
half of the geometry is modelled due to the symmetry of the problem.
5.3.1. Constitutive Models
To account for the shear failure of the soil around the pipe, the soil was modeled
using ABAQUS Mohr-Coulomb model. A detailed description of this constitutive
Native Soil
x y z
1.5 m
0.74 m
3.0 m
Backfill
Concrete pipe
5.5 m
5.0 m
79
model can be found in section 4.1.1. On the other hand, the concrete pipe was
modeled as linear elastic material.
The parameters used in modeling the pipe and the different soil layers are
summarized in Table 5.1. It should be mentioned that these parameters are
based on those reported by Liedberg (1991).
Table 5.1 : Material parameters assigned in the numerical model
(t/m3) E (kPa) (°) (°) c (kPa)
Native Soil 2.0 138 x 103 0.2 42.5 29.8 5
Backfill 1.7 2274 0.34 39 27.5 5
Concrete pipe 2.6 34 x 106 0.2 - - -
5.3.2. Boundary Conditions and Finite Element Mesh
The finite element mesh used in this study was generated using a model
dimensions that extend about 6 times the pipe diameter (6.4D) in the x-direction
from the pipe springline, about 7 times the diameter (6.8D) in the y-direction
along the pipe length and (2D) in the z-direction from the pipe invert.
The dimensions of the x-z plane were selected following the guidelines of McVay
(1982) who proposed a minimum side boundary location at a distance (3D) and
bottom boundary at a distance of (1D). In addition, to ensure that the boundaries
are at sufficient distance from the pipe; the vertical displacement of the soil-pipe
system was checked after completing all construction phases and before
introducing erosion void. A snapshot of the vertical displacement field in the x-z
80
plane is presented in Figure 5.3. As it can be noticed all arrows are attenuated
before reaching the side and bottom boundaries, which indicates that the
boundary locations have no effect on the pipe response to applied loading.
Figure 5.3 : Vertical displacement field in the x-z plane
The model extent in the y-direction was chosen based on the results of a
parametric study that has been conducted to evaluate the appropriate location of
the lateral boundary. Four different ratios of model length to pipe diameter (L/D=
3.4, 6.1, 8.8, and 11.5) were simulated and the earth pressure was calculated at
a middle section of the pipe for two distinct positions (crown and invert).
D 6.4D
2D
81
Figure 5.4 shows the earth pressure calculated in (kPa) on the vertical axis
versus the length to diameter ratio (L/D) on the horizontal axis. As it can be
noticed beyond L/D ratio of 6.1, the change in earth pressure becomes
insignificant. Thus, a model extent of (6.8D) in the y-direction assures that the
lateral boundary will not affect the numerical results calculated and keeps the
mesh size manageable to the model computational time.
Figure 5.4 : Radial earth pressure calculated versus different ratios of model length to pipe diameter
The model was restrained in the horizontal direction (i.e. smooth rigid) at the four
vertical boundaries whereas the lower boundary was restrained in all three
directions (i.e. rough rigid). A typical 3D finite element mesh is presented in
Figure 5.5.
60
65
70
75
80
85
90
95
100
105
0 1 2 3 4 5 6 7 8 9 10 11 12
Rad
ial e
arth
pre
ssur
e (k
Pa)
Ratio L/D
Invert
Crown
82
Figure 5.5 : Typical 3D finite element mesh
5.3.3. Element Type
Both the soil and the pipe were modeled using continuum elements (C3D20 20-
node quadratic brick element) throughout the analysis. This brick element has 20
nodes with 27 integration points. This second-order element type is known to
provide high accuracy in Abaqus/Standard compared to first-order elements. The
element is able to capture stress concentrations and is suitable for modeling
geometric features such as a curved surface with fewer elements (ABAQUS,
2009). Figure 5.6 presents the node numbering and integration points of a typical
C3D20 element.
1.5 m
0.74 m
3 m
5.5 m 5.0 m
UX = 0
UX = UY = UZ = 0
UY= 0
83
Nodes Integration points
Figure 5.6 : Node numbering and integration points of a typical C3D20 element (Adapted from ABAQUS, 2009)
5.3.4. Soil- Pipe Interaction
The ABAQUS surface-to-surface contact interface has been used to simulate the
interaction between the surrounding backfill and the buried pipe. Since the pipe is
stiffer compared to the surrounding backfill, the pipe was simulated as the
master-surface whereas the surrounding backfill represented the slave-surface
(see Figure 5.7).
84
Figure 5.7 : Master and slave surface representing the soil - pipe interaction
In all models, a fully bonded interface between the pipe wall and the backfill
material has been assumed. Such interface behavior was simulated using
surface tie constraint feature available in the ABAQUS interaction module.
In general, a surface tie constraint joins the two surfaces in contact together
such that each node on the slave surface will have the same degrees of freedom
as the point on the master surface to which it is closest (ABAQUS, 2009).
concrete pipe
Native Soil
Backfill
Slave surface Master surface
85
The surface tie constraint is formulated in ABAQUS by determining tie
coefficients. These tie coefficients are used to interpolate quantities from the
master nodes to the tie point. There are two approaches to generate these tie
coefficients: the surface-to-surface approach or the node-to-surface approach
(ABAQUS, 2009). The difference between the two approaches is that the
surface-to-surface approach enforces constraints in an average sense over a
finite region, rather at discrete points as in the traditional node-to-surface
approach. Thus, the surface-to-surface approach minimizes numerical noise for
tied interfaces involving mismatched meshes. The node-to-surface approach was
used in this study since it is more stable particularly when voids are introduced
around the pipe. In addition, it is known to reduce in computational time. This can
be explained by the fact that the node-to-surface approach sets the tie
coefficients equal to the interpolation functions at the point where the slave node
projects onto the master surface which makes such approach somewhat more
efficient and robust for complex surfaces (ABAQUS, 2009).
5.3.5. Modeling Erosion Voids
To simulate the presence of erosion voids around the existing pipe in 3D space,
semi-cylindrical zones were predefined at specific locations next to the pipe wall.
The void sizes have been varied spatially in the x, y and z directions to reflect the
effect of increasing the void depth, length, and angle, respectively (see Figure
86
5.8). The voids were introduced at two locations around the pipe circumference,
namely, springline and invert. The void depth (VD), length (VL), and angle (VA)
have been normalized with respect to the mean pipe radius (R), segment length
(Lp), and angle of 360° (2π), respectively, throughout the analysis. The above
controlling parameters have been varied incrementally as summarized in Table
5.2.
(a) Void parameters
(b) Pipe segment with a void at the springline
Figure 5.8 : A 3D schematic of the pipe with deteriorated soil (a) void parameters and (b) pipe segment with a void at the springline
VA = 31°VA = 47°
VA = 63°
Void length (VL)
Segment length
Average diameter
Pipe radius (R)
Void angle (VA) Void depth (VD)
Void length (VL)
Length (L)
87
Table 5.2 : Void Parameters investigated
Void Angle (VA)
(°)
Void Depth (VD)
(cm)
Void Length (VL)
(cm)
31
2.5
20, 40, 60
5
10
47
5
10
15
63
7.5
15
20
5.3.6. Stages of Analysis
Eleven steps were performed in each model to simulate the staged construction
process. The model was first subjected to geostatic stresses with lateral earth
pressure coefficient at rest ( 1 sin ) of 0.32. This was followed by the
placement of both the pipe and the bedding layer and the activation of the soil-
pipe interaction. Once the system equilibrium was reached, additional soil lifts
were placed in stages to reach the target height of the embankment. After
reaching the as-built condition, the erosion voids were introduced in three
consecutive steps to reflect the void growth in the close vicinity of the pipe. The
erosion void was simulated numerically using the element removal technique.
88
5.4. Model Validation
The validation of the 3D finite element model was performed considering two
different aspects for pipe behavior: (1) initial earth pressures are first calculated
and compared with field measurements and (2) initial ring moments before void
introduced were calculated and compared with those obtained from closed form
solutions as reported by Liedberg (1991).
5.4.1. Validation of Initial Earth Pressure
To validate the calculated earth pressure, the geometry and material properties
reported in the case study were adopted in the analysis and the earth pressure
acting on the pipe was calculated. The initial earth pressure results before voids
were introduced are presented in Figure 5.9 along with those reported by
Liedberg (1991). The calculated results at the crown (θ = 0°) and springline (θ =
90°) were in agreement with those measured and calculated using different
methods. It can be seen that the numerically calculated pressures at the pipe
invert ( = 180o) is in agreement with the other numerical solutions. The
difference between the measured and calculated results at the invert (using
different methods) is attributed to the sensitivity of the earth pressure to the
backfill quality located at the pipe haunch. Since the objective of this study is to
compare the earth pressures acting on the pipe before and after introducing
erosion voids, the initial pressures calculated numerically around the pipe using
89
the above described model are considered to be sufficient for the purpose of this
investigation.
Figure 5.9 : Measured and calculated earth pressure distribution using different method
5.4.2. Validation of Ring Moments
After comparing the earth pressure with field measurements and ensuring that
the model is predicting the soil-pipe response with acceptable tolerance. The
model validation was extended to evaluate the pipe ring moments.
Bending moments were calculated using the approach described by Munro et al.
(2009) as follow:
1 (5.1)
-300
-250
-200
-150
-100
-50
00 45 90 135 180
Rad
ial e
arth
pre
ssur
e (k
Pa)
Angle from crown θ (°)
Hoeg (Liedberg, 1991)
CANDE (Liedberg, 1991)
ABAQUS
Measured values (Liedberg, 1991)
θ
0°
90°
180°
CR
SL
IN
90
Where 1/ρ is the change in pipe curvature, ε1 and ε2 are the inner and outer
circumferential strains, respectively and t is the pipe wall thickness.
The moment can then be calculated as follows:
(5.2)
Where Ep is the pipe modulus and Ip = t3/12 is the second moment of area of the
pipe cross section.
The initial moment results (before voids introduction) are presented in Figure
5.10 along with those calculated using closed form solutions and the results
reported by Liedberg (1991). The calculated moments at the crown (θ = 0°) and
springline (θ = 90°) were in general agreement with those calculated by Liedberg
(1991) particularly at the pipe crown. It can be seen that the calculated moments
at the pipe invert ( = 180o) is in agreement with the analytical closed form
solutions. Similar to the earth pressure results, such discrepancy at the pipe
invert can be explained by the sensitivity of the results to the backfill quality
located at the pipe haunch. Since the main objective of this research program is
to examine the 3D effects of erosion voids on the pipe response, the response of
the pipe predicted using the finite element model is acceptable.
91
Figure 5.10 : Calculated ring moment distribution using different methods
5.5. Changes in Earth Pressure
To examine the 3D effects of erosion voids on the earth pressure distribution
around the investigated pipe, two different sets of graphs have been utilized. The
first set includes transverse section across the middle of the pipe and the second
includes longitudinal sections passing through the void boundary. The calculated
earth pressures (P) are normalized with respect to the initial earth pressure
values (P0) throughout this study.
5.5.1. Transverse section of the pipe
The changes in earth pressure, calculated at the transverse section (A-A) are
presented in Figure 5.11 and Figure 5.12 for voids introduced at the pipe
springline and invert, respectively. The earth pressure ratios (P/P0) are plotted on
the radial coordinates whereas the angles from the pipe crown in degrees are
0
20
40
60
80
100
120
140
160
180
-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00
Ang
le fr
om c
row
n, θ
Moment, Mθ (kNm/m)
Numerical calculation present study
Theoretical calculation (Burns and Richard's equation)
Numerical calculation using SPIDA (Liedberg, 1991)
Theoretical calculation using Marston and Spangler (Liedberg, 1991)
θ
0°
90°
180°
CR
SL
IN
92
plotted on the angular coordinates. The presented results are for void angles of
31° (VA/2π = 9%) and 63° (VA/2π = 17.5%). It is worth noting that the earth
pressures are evaluated at 2° angle from the void boundary. In general, earth
pressures increased sharply near the void boundaries and decreased to the
initial values (P/P0 = 1) at angles that range from 20° to 45° in the radial direction
from the boundary depending on the void location. At the springline, the pressure
ratio (P/P0) increased to about 2.5 and decreased sharply to the initial value at an
angle of approximately 20 degrees from the boundary (see Figure 5.11). Moving
the voids to the invert (Figure 5.12) caused a maximum increase in earth
pressure of about 1.25 times the initial values. Comparing Figure 5.11 and Figure
5.12, it can be noticed that the increase in earth pressure calculated for void at
springline was double the one reported at the pipe invert.
93
Voids at springline Section A-A
Void angle = 31° Void angle = 63°
Figure 5.11 : Changes in earth pressure at section A-A for voids at springline
0
45
90
135
180
0
45
90
135
180
P/P0 = 2.5
P/P0 = 2.0
P/P0 = 1.5
P/P0 = 1.0
P/P0 = 0.5
VA/2π = 9%
VD/R = 7% VD/R = 30%
P/P0 = 2.5
P/P0 = 2.0
P/P0 = 1.5
P/P0 = 1.0
P/P0 = 0.5
VA/2π = 17.5%
VD/R = 22%
VD/R =60%
θVD
R
A
A
VA
L
VL
94
Voids at invert Section A-A
Void angle = 31° Void angle = 63°
Figure 5.12 : Changes in earth pressure at section A-A for voids at invert
0
45
90
135
180
0
45
90
135
180
P/P0 = 0.75
P/P0 = 1.0
P/P0 =1.25
P/P0 = 0.75
P/P0 = 1.0
P/P0 =1.25
VA /2π = 17.5% VD/R = 7%
VD/R = 30%
VD/R = 22%
VD/R =60% VA/2π = 9%
VD
R
θ
L
A
VL
A
95
5.5.2. Longitudinal Sections along the Pipe
5.5.2.1. Effect of void length
The effects of void length on the changes in earth pressure along the pipe are
shown in Figure 5.13 and Figure 5.14 for voids introduced at the springline and
invert, respectively. The horizontal axis represents the normalized distance with
respect to the pipe length (Y/L). The presented changes in earth pressure are for
a void angle of 63°. Additional results are given in Appendix B for the other two
void angles 31° and 47° examined in this study. For a given void depth, the earth
pressure increased as the void length (VL/LP) increased. When the length of the
void reached 27% of the length of the pipe segment, the earth pressure reached
about 2.5 times the initial values. In all cases, the affected pipe length was found
to be approximately 1 meter or 20% of the pipe length. By comparing the three
plots in Figure 5.13, it can be seen that the changes in void depth from 22% to
60% of the pipe radius led to slight increase in the maximum earth pressure
calculated (about 0.6 times the initial values).
Similar trend was observed when the void was located at the pipe invert as
shown in Figure 5.14. For a void angle of 63o, the increase in void length led to
an increase in earth pressure at the boundary. The pressure increase was found
to be less significant compared to the springline with a maximum increase in
pressure ratio of about 1.3 times the initial values. It is worth mentioning that the
96
calculated pressure decreased with distance from the void centre and reached
P/Po values that are slightly higher than 1. This is attributed to the stress
redistribution around the created void under the pipe and the fact that the pipe is
rigid enough compared to the surrounding soil.
An interesting finding that can be deduced from Figure 5.13 and Figure 5.14 is
that the location of the erosion void can have a significant effect on the earth
pressure distribution around the pipe. When the voids develop at the springline,
earth pressure locally increases around the void boundaries to values that
depend mostly on the length of the void. At the pipe invert, in addition to the local
pressure increase at the void boundaries, the earth pressures slightly increase
along an extended length of the pipe due to gravity effects and the pipe
resistance to deformation under the applied loading.
97
Figure 5.13: Effect of void length on the changes in earth pressure along the pipe for voids at the springline
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
VD/R = 45%
VD/R = 60%
VD/R = 22%
P/P
0
Y/L
P/P
0
Y/L
P/P
0
Y/L
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
Initial earth pressure - No Void
Initial earth pressure - No Void
L/2
B
B VL/2
Section B-B
A
A
VA
L
VL
Y B
B
θ
VD
R
Section A-A
Voids at springline
98
\\
Figure 5.14 : Effect of void length on the changes in earth pressure along the pipe for voids at the invert
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
P/P
0
Y/L
P/P
0
Y/L
P/P
0
Y/L
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
VD/R = 45%
VD/R = 60%
VD/R = 22%
Initial earth pressure - No Void
Initial earth pressure - No Void
Initial earth pressure - No Void
VD
R
θ
L
B
B
A
A
VL
Y
Voids at invert & Section B‐B
Section A‐A
99
A summary of all results related to the effect of void length is shown in Figure
5.15. The presented results are calculated at about 6o angle away from the void
boundary to minimize the effect of pressure fluctuation near the void. An
increasing trend can be seen at both springline and invert. The increase in
pressure at the springline ranged from 25% (for void angle 31o) to approximately
45% (for void angle 63o) whereas the corresponding increase at the invert
ranged from 20% to 30%.
Figure 5.15 : Effect of void length on the changes in earth pressure
5.5.2.2. Effect of void depth
Figure 5.16 and Figure 5.17 show the effect of void depth (VD) on the changes in
earth pressure at the void boundary. The results are presented for a void angle of
1
1.1
1.2
1.3
1.4
1.5
8 10 12 14 16 18 20 22 24 26 28 30
P/P
0
VL/LP
Void angle 31o 47o 63o Springline Invert
100
63° and three different void lengths (VL/LP = 9%, 18%, and 27%). Additional
results are given in Appendix C for the other two void angles 31° and 47°
examined in this study. For a given void length, increasing the void depth (VD/R)
was found to slightly increase the contact pressure along the boundary. The
increase in pressure reached maximum values of about 40% of the initial
pressure and decreased rapidly with distance from the void. Similar behaviour
was found for voids located at the pipe invert as shown in Figure 5.17. The
maximum pressure increase was found to be about 15% of the initial values.
Figure 5.17 also shows that increasing the ratio of void depth from 45% to 60%
of the pipe radius did not cause additional increase in pressure.
101
Figure 5.16 : Effect of void depth on the changes in earth pressure along the pipe for voids at the springline
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
VL/LP = 18%
VL/LP = 27%
VL/LP = 9%
P/P
0
Y/L
P/P
0
Y/L
P/P
0
Y/L
VD/R = 22%
VD/R = 45%
VD/R = 60%
VD/R = 22%
VD/R = 45%
VD/R = 60%
VD/R = 22%
VD/R = 45%
VD/R = 60%
Initial earth pressure - No Void
Initial earth pressure - No Void
Initial earth pressure - No Void
L/2
B
B VL/2
Section B-B
A
A
VA
L
VL
Y B
B
θ
VD
R
Section A-A
Voids at springline
102
Figure 5.17 : Effect of void depth on the changes in earth pressure along the pipe
for voids at the invert
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
VL/LP = 18%
VL/LP = 27%
VL/LP = 9%
P/P
0
Y/L
P/P
0
Y/L
P/P
0
Y/L
VD/R = 22%
VD/R = 45%
VD/R = 60%
Initial earth pressure - No Void
VD/R = 22%
VD/R = 45%
VD/R = 60%
Initial earth pressure - No Void
VD/R = 22%
VD/R = 45%
VD/R = 60%
Initial earth pressure - No Void
VD
R
θ
L
B
B
A
A
VL
Y
Voids at invert & Section B‐B
Section A‐A
103
Figure 5.18 shows a summary of the calculated results at the springline and
invert (at 6o angle away from the boundary) emphasizing the effect of void depth
on the earth pressure represented by P/P0 ratio. It is evident from the figure that
for a given void angle increasing the void depth causes a consistent increase in
earth pressure with more increase at the springline compared to the invert.
Figure 5.18 : Effect of void depth on the changes in earth pressure
5.5.2.3. Effect of void Angle
Figure 5.19 presents the relationship between the normalized void angle (VA/2π)
and the earth pressure ratio (P/P0) for the investigated range of parameters (void
length of 60 cm and the corresponding void depths of each angle as defined in
(Table 5.2). The earth pressure was found to increase at both the springline and
invert with the increase in the normalized void angle. The maximum increase in
1
1.1
1.2
1.3
1.4
1.5
0 10 20 30 40 50 60 70
P/P
0
VD/R
Void angle 31o 47o 63o Springline Invert
104
earth pressure (at angle 6o away from the void) reached about 40% at the
springline and about 30% at the pipe invert.
Figure 5.19 : Effect of void angle on the changes in earth pressure
5.6. Changes in Pipe Stresses
To examine the 3D effects of erosion voids on the stresses and bending
moments in the pipe wall, two different sets of graphs have been used. The first
set includes longitudinal sections passing through the pipe crown, springline and
invert. Whereas the second set includes transverse sections across the middle of
the pipe.
5.6.1. Changes in circumferential stresses along the pipe
The effects of void length on the changes in circumferential stresses (see Figure
5.20) are presented in Figure 5.21 through Figure 5.24 for void angles of 31o
1
1.1
1.2
1.3
1.4
1.5
5 10 15 20
P/P
0
VA/2π
Void angle 31o 47o 63o
Springline Invert
105
(VA/2π = 9%) and 63o (VA/2π = 17.5%) at the springline and invert. Additional
results are given in Appendix D for the third void angle 47° examined in this
study. The circumferential stresses are normalized with respect to the initial value
and presented by the ratio (σθ/σθ0) on the vertical axis. The horizontal axis
represents the normalized distance with respect to the pipe length (Y/L).
Figure 5.20 : Sketch illustrating circumferential pipe stresses
For a given void depth, the circumferential stresses at both extremities of the
pipe wall increased as (VL/LP) increased due to the void introduction at the
springline. When the length of the void reached 27% of the length of the pipe
segment, the outer circumferential stresses slightly increased and reached about
1.15 and 1.35 times the initial values for void angles of 31o and 63o, respectively.
For the same void angles and void length, the increase in circumferential stress
ratios (σθ / σθ0) at the inner fibres was found to range from 1.10 to 1.20 times the
initial values as shown in Figure 5.21 and Figure 5.22.
Crown
Invert
Springline x x x
x x x σθ σθ
σθ σθ Outer fibre
Inner fibre
θ
106
Different trend was observed when the voids were located at the pipe invert as
shown in Figure 5.23 and Figure 5.24. Circumferential stresses at the inner and
outer fibres decreased as the void length (VL/LP) increased. It is worth mentioning
that the rate of decrease in stresses at the invert was found significant compared
to the rate of increase for voids at the springline. In addition, the maximum
change in circumferential stresses at the outer and inner fibres occurred when
the void angle increased to 63o and a void length of 27% of the pipe segment.
The maximum decrease in circumferential stresses at the outer fibres reached
45% of the initial value, while the decrease was about 55% of the initial value in
the inner fibres as shown in Figure 5.24. An interesting finding that can be
deduced from Figure 5.21 to Figure 5.24 is that the change in void depth has less
significant effect on circumferential stresses compared to the other parameters
such as void location, angle and length. By comparing the three plots in Figure
5.22, it can be noted that the changes in void depth from 22% to 60% of the pipe
radius led to an increase in the circumferential stress at the outer fibre by about
2%.
107
Figure 5.21 : Effect of void length on the changes in pipe circumferential stresses for voids with VA/2π = 9% at the springline
0
1.00
1.05
1.10
1.15
1.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.20
-1.15
-1.10
-1.05
-1.00
0
1.00
1.05
1.10
1.15
1.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.20
-1.15
-1.10
-1.05
-1.00
0
1.00
1.05
1.10
1.15
1.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.20
-1.15
-1.10
-1.05
-1.00
σ θ/σ
θ0
σ θ/σ
θ0
σ θ/σ
θ0
Y/L
Y/L
Y/L
Springline extreme outer fibre
Springline extreme inner fibre
VD/R = 7%
Springline extreme outer fibre
Springline extreme inner fibre
VD/R = 15%
VD/R = 30%
Springline extreme inner fibre
Springline extreme outer fibre
Voids at springline
A
A
VA
L
VL
Y
θ
VD
R
Section B-B
B B
Section A-A
VL/LP = 9% VL/LP = 27%
VL/LP = 18%No void
108
Figure 5.22 : Effect of void length on the changes in pipe circumferential stresses for voids with VA/2π = 17.5% at the springline
0
1.0
1.1
1.2
1.3
1.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.3
-1.2
-1.1
-1.0
0
1.0
1.1
1.2
1.3
1.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.3
-1.2
-1.1
-1.0
0
1.0
1.1
1.2
1.3
1.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.3
-1.2
-1.1
-1.0
Springline extreme outer fibre
Springline extreme outer fibre
Springline extreme outer fibre
Springline extreme inner fibre
Springline extreme inner fibre
Springline extreme inner fibre
VD/R = 22%
VD/R = 45%
VD/R = 60%
Y/L
Y/L
Y/L
σ θ/σ
θ0
σ θ/σ
θ0
σ θ/σ
θ0
Voids at springline
A
A
VA
L
VL
Y
θ
VD
R
Section B-B
B B
Section A-A
VL/LP = 9% VL/LP = 27%
VL/LP = 18% No void
109
Figure 5.23 : Effect of void length on the changes in pipe circumferential stresses for voids with VA/2π = 9% at the invert
00.50.60.70.80.91.01.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.1-1.0-0.9-0.8-0.7-0.6-0.5
00.50.60.70.80.91.01.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.1-1.0-0.9-0.8-0.7-0.6-0.5
00.50.60.70.80.91.01.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.1-1.0-0.9-0.8-0.7-0.6-0.5
Invert extreme outer fibre
Invert extreme inner fibre
VD/R = 30%
VD/R = 15%
VD/R = 7%
Y/L
Y/L
σ θ/σ
θ0
σ θ/σ
θ0
σ θ/σ
θ0
Invert extreme inner fibre
Invert extreme outer fibre
Invert extreme inner fibre Invert extreme outer fibre
Y/LVoids at invert & Section B-B
Section A-A
VD
R
θ
L
B
B
A
A
VL
VA
Y
VL/LP = 9% VL/LP = 27%
VL/LP = 18% No void
110
Figure 5.24 : Effect of void length on the changes in pipe circumferential stresses for voids with VA/2π = 17.5% at the invert
00.50.60.70.80.91.01.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4
00.50.60.70.80.91.01.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4
00.50.60.70.80.91.01.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4
Invert extreme outer fibreInvert extreme inner fibre
VD/R = 60%
VD/R = 45%
VD/R = 22%
Y/L
Y/L
σθ/σθ0
σθ/σθ0
σ θ
/σθ0
Invert extreme outer fibreInvert extreme inner fibre
Invert extreme inner fibreInvert extreme outer fibre
Y/L
Voids at invert & Section B-B
Section A-A
VD
R
θ
L
B
B
A
A
VL
VA
Y
VL/LP = 9% VL/LP = 27%
VL/LP = 18%No void
111
5.6.2. Changes in bending moments along the pipe
In order to investigate the effect of erosion voids on the ring moments developed
in the circumferential and longitudinal directions of the pipe, two different sets of
graphs have been utilized. The first includes the moments calculated at the
transverse section (A-A) across the middle of the pipe and are presented in
Figure 5.25. The second set includes the moments calculated at the longitudinal
sections (B-B) passing through the crown, springline and invert of the pipe as
presented in Figure 5.26 and Figure 5.27, respectively. The moments were
calculated using the change in circumferential strain across the thickness of the
pipe wall assuming a linear strain distribution and applying equations (5.1) and
(5.2). In Figure 5.25, the calculated moments Mθ are presented on the horizontal
axis and the angle from the pipe crown θ on the vertical axis. The results are
presented for a) the springline and b) the invert voids with length of 60 cm and
normalized void angle that ranged from 9% to 17.5%. It can be seen that voids at
the springline led to local increase in moment at the void location coupled with
small decrease in moment at the crown and invert (Figure 5.25a). The moment
increase was calculated to be about 40% (from about -1.4 to -1.7 kN.m/m). On
the other hand, at the pipe invert (Figure 5.25b), a local decrease in moment
from about 1.4 to 0.6 kN.m/m was calculated.
112
For the same void sizes, the percentage change in ring moments calculated
along the pipe length at the crown, springline and invert locations are plotted
versus the normalized pipe length (Y/L) and presented in Figure 5.26 and Figure
5.27 for voids at the springline and invert, respectively. For voids at the springline
(see 3D view in Figure 5.26), an increase in moment of 24% was calculated at
the springline, while the increase at the crown and invert reached a maximum
value of about 10% (see Figure 5.26). For voids at the invert (Figure 5.27), a
maximum reduction in bending moments of -60%, -30% and -25% were
calculated at the invert, springline and crown, respectively. In all cases, the
affected pipe length is approximately 2.5 to 3 meters which corresponds to about
5 times the void length.
113
Figure 5.25 : Calculated ring moments when voids are introduced at (a) the
springline and (b) the invert
Section A-A
θ VD
R
A
A
VA
L
VL
Voids at springline
Ang
le fr
om c
row
n θ
180
135
90
45
0
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Initial condition no void
VA/2π = 13%
VA/2π = 9%
VA/2π = 17.5%
Moment Mθ (kN.m/m)
(a) Voids at springline
VD
R
θ Section A-A
L A
A
VL
Voids at invert
180
135
90
45
0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Initial condition no void
VA/2π = 13%
VA/2π = 17.5%
VA/2π = 9%
Moment Mθ (kN.m/m)
Ang
le fr
om c
row
n θ
(b) Voids at invert
114
Figure 5.26 : Percentage change in ring moment along the pipe calculated at (a) crown, (b) springline and (c) invert for voids at the springline
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-2%0%2%4%6%8%
10%12%14%16%18%20%22%24%
Y/L
Per
cent
age
chan
ge in
mom
ent
(a) Crown
(B1)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-2%0%2%4%6%8%
10%12%14%16%18%20%22%24%
Y/L
Per
cent
age
chan
ge in
mom
ent
(b) Springline
(B2)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-2%0%2%4%6%8%
10%12%14%16%18%20%22%24%
Y/L
Per
cent
age
chan
ge in
mom
ent (c) Invert
(B3)
Voids at springline
A
A
VA
L
VL
Y
Section B-B
B B
θ
VD
R
Section A-A
B1
B2
B3
VA/2π = 9% VA/2π = 13% VA/2π = 17.5%
115
Figure 5.27 : Percentage change in ring moment along the pipe calculated at (a) crown , (b) springline and (c) invert for voids at the invert
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-60%
-55%
-50%
-45%
-40%
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-60%
-55%
-50%
-45%
-40%
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-60%
-55%
-50%
-45%
-40%
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
Y/L
Y/L
Y/L
Per
cent
age
chan
ge in
mom
ent
Per
cent
age
chan
ge in
mom
ent
Per
cent
age
chan
ge in
mom
ent
(a) Crown
(b) Springline
(c) Invert
(B1)
(B2)
(B3)
L
B
B
A
A
VL
VA
Y
Voids at invert & Section B-B
Section A-A
VD
R
θ
B1
B2
B3
VA/2π = 9% VA/2π = 13% VA/2π = 17.5%
116
5.6.3. Changes in tensile and compressive stresses at the pipe extreme
fibres
The effect of increasing the void angles on the changes in maximum tensile and
compressive stresses (see Figure 5.28) are presented in Figure 5.29 and Figure
5.30, respectively.
Figure 5.28 : Sketch illustrating the tensile and compressive pipe stresses
In these figures, the percentage change in either tensile or compressive stress is
presented on the vertical axis at the crown, springline and invert, which are
presented on the horizontal axis. The results presented are calculated at section
A-A (shown in Figure 5.27) for three different void angles (VA/2π = 9%, 13%, and
17.5%) at (a) the springline and (b) the invert, when the voids reached their
maximum length of 60 cm (VL/LP = 27%) and void depths as defined in Table 5.2.
In general, there is a consistent increase in tensile stresses at all investigated
locations as the void angle increases. At the springline, a maximum increase in
tensile stress of about 36%; while the reduction in tensile stress is about 55% for
Crown
Invert
Springline x x x
x x x σt σt
σc σc Outer fibre
Inner fibre
117
voids at the invert (see Figure 5.29). Figure 5.30 shows that compressive stress
increased about 18% for voids at the springline with a maximum decrease of
65% for voids at the invert.
Figurcrow
Per
cent
age
chan
ge in
tens
ile s
tres
ses
Per
cent
age
chan
ge in
tens
ile s
tres
ses
re 5.29: Pewn, springlin
ercentage cne and inve
VA/2π = 9%VA/2π = 13VA/2π = 17
hange in mrt for voids
% 3% 7.5%
maximum teintroduced
nsile stressd at (a) sprin
VA/2π = 9%VA/2π = 13VA/2π =17.
ses calculatngline and
(a) Voids a
(b) Voids a
% % 5%
11
ted at (b) invert
t springline
at invert
18
Figuat cr
Per
cent
age
chan
ge in
tens
ile s
tres
ses
Per
cent
age
chan
ge in
tens
ile s
tres
ses
ure 5.30 : Prown, spring
Percentage gline and in
VA/2π = 9%
VA/2π = 13%
VA/2π = 17.
change in nvert for voi
%
%
.5%
maximum ids introduc
VA
VA
VA
compressivced at (a) s
A/2π = 9%
A/2π = 13%
A/2π = 17.5%
ve stressespringline an
(a) Voids
(b) Voids
11
s calculatednd (b) inver
s at springline
at invert
19
rt
e
120
5.6.4. Changes in longitudinal stresses at the pipe outer fibre
The effect of increasing the void length on the changes in longitudinal stresses
(see Figure 5.31) is presented in Figure 5.32 and Figure 5.33 for voids
introduced at springline and invert, respectively. The results presented are
calculated at section A-A (shown in Figure 5.27) at the extreme outer fibre for
three different void angles (VA/2π = 9%, 13%, and 17.5%), when the voids
reached their maximum depths as specified in Table 5.2. Additional results of the
changes in longitudinal pipe stresses along the pipe length calculated at different
positions of the pipe are presented in Appendix E.
Figure 5.31 : Sketch illustrating longitudinal pipe stresses
As it can be noticed the presence of the voids at the springline and invert
resulted in completely two opposite behavior. At the springline, there is
consistent increase in tensile stress as the void increases in size. The rate of
σL σL
σL σL
Crown
Invert
Inner fibre
Outer fibre
Outer fibre
A
A
121
increase in the longitudinal direction is much significant compared to the
circumferential direction since a maximum increase of 80% was calculated.
Contrary at the invert, the increase in void size resulted in reduction of
compressive stress even at certain critical void length and angle, the stress
switched towards becoming tensile. The presence of voids at the pipe invert is
more critical for non-reinforced concrete since a maximum tensile stress of 125%
was calculated.
Figure 5.32 : Changes in longitudinal stresses at extreme outer fibre for voids at springline
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
0 3 6 9 12 15 18 21 24 27 30
σL/σ
L0
VL/Lp
VA = 31
VA = 47
VA = 63
Tension
VA/2π = 9%
VA/2π = 13%VA/2π = 17.5%
122
Figure 5.33 : Changes in longitudinal stresses at extreme outer fibre for voids at invert
-1.20
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0 3 6 9 12 15 18 21 24 27 30
σL/σ
L0
VL/Lp
VA = 31
VA = 47
VA = 63
Tension
Compression
VA/2π = 9%
VA/2π = 13% VA/2π = 17.5%
123
Chapter 6
Conclusions and Recommendations
6. Dummy Chapter Numbering 6.1. Conclusions
The main objective of this research program was to study experimentally and
numerically the effects of erosion void located behind the wall of a rigid pipe on
the earth pressure distribution and the changes in stresses in the pipe wall. The
conclusions drawn from the experimental and numerical programs are
summarized below.
6.1.1. Experimental Program
Experimental investigations have been performed to examine the effect of
contact loss between a rigid pipe and the surrounding soil on the changes in
earth pressure distribution acting on the pipe. A mechanically retractable strip 10
mm in width and 260 mm in length positioned at three different locations
(springline, haunch and invert) has been used to simulate the contact loss. The
load cells installed at the boundaries of the retractable section measured the
changes in earth pressure. The progressive movement of the retractable section
from 1.5 mm to 3 mm caused additional changes in pressure around the area
124
experiencing the contact loss. Based on the nine tests conducted in this study,
the following conclusions were reached:
(1) In granular soils, a void may develop along the lower half of the pipe
circumference. The void size and location are considered to be the
main controlling parameters affecting the earth pressure distribution
around the pipe.
(2) The introduction of a local contact loss at the springline caused
pressure increase of about 30% of the initial value immediately below
the separation zone and a decrease of about 50% above.
(3) At the haunch and invert, the introduction of local contact loss caused
a consistent increase in earth pressure at the boundaries of the gap
with a maximum increase of 22% of the initial pressure.
6.1.2. Two-Dimensional Analyses
Two-dimensional elastic-plastic finite element analyses have been performed to
validate the numerical model and assess the effect of the gap simulation
procedure used in the experiments on the measured results. The earth pressure
calculated using the finite element method confirmed that most of the changes in
pressure take place in the close vicinity of the gap. The changes in pressure
measured in the experiments were located between those calculated numerically
for fully bonded soil-pipe interface and free slippage conditions.
125
6.1.3. Three-Dimensional Analyses
Series of 3D nonlinear finite element analyses have been performed to examine
the impact of varying the size of voids located behind the wall of a concrete pipe
in 3D space on the changes in earth pressure acting on the concrete pipe and
the corresponding changes in pipe wall stresses. In the numerical simulations,
voids were introduced at two main positions; namely, the springline and invert.
For each position, three different void angles, depths and lengths were studied.
The changes in earth pressure and pipe stresses were calculated at a transverse
section passing across the middle of the pipe as well as along the pipe length.
The conclusions arising from the 3D analysis are as follow:
6.1.3.1. The changes in earth pressure
(1) It has been found that the changes in earth pressure will mostly take
place at the void boundaries. For voids located at the springline, the
earth pressure increased to more than 100% of the initial values. Less
significant changes were found when the voids were located at the
invert with a maximum earth pressure of about 30%.
(2) The void location and length (along the pipe axis) are considered to be
the key factors affecting the changes in earth pressure. Less effect
was found when the void depth increased from about 20% to 60% of
the pipe radius, particularly for voids located at the invert. Similarly, the
126
void angle was found to slightly affect the earth pressure distribution at
the pipe invert.
6.1.3.2. The changes in pipe stresses
(1) It has been found that areas in the close vicinity of the voids are
experiencing the highest changes in pipe stresses.
(2) In general, the presence of the voids at the springline resulted in an
increase in the pipe stresses and bending moments. Different behavior
has been noted for voids introduced at the pipe invert where a
reduction in stresses and moments was calculated.
(3) The maximum increase in tensile stresses in the circumferential
direction was found to be about 36% for voids introduced at the
springline; when the voids were moved to the pipe invert, the
maximum reduction of -65% was found to be in compressive stresses.
(4) The changes in longitudinal stresses revealed significant change in
stresses at the outer fibre of the pipe at the location where the voids
were introduced. At the springline, an increase of 80% was calculated
for the initial tensile stress the pipe experienced. At the invert, the
initial compressive stress switched to tensile stresses leading to
about 225 % change in stresses.
127
6.2. Practical Significance
A factor of safety ranging from 1.0 to 1.7 is typically used in the design of
concrete pipes (ACPA, 2007). Most administrators of buried pipes are aware that
existing systems are suffering an advanced state of deterioration and agree on
rehabilitation measures should be taken. The findings of the present research
highlight that the development of voids under rigid pipes is the most critical
condition. A summary table has been produced based on the pipe geometry and
the soil properties investigated in this study. This should help decision makers to
evaluate the expected changes in earth pressure, ring moment and longitudinal
stresses induced by a given void size located next to the pipe wall as
summarized in Table 6.1. It has been shown that voids developing under the pipe
invert are more critical as tensile stresses may develop that could lead to pipe
cracking and failure. Pipe inspection using Pipe Penetrating Radar (PPR) will
allow the detection of existing voids behind the pipe wall. The location at which
the void was detected and its size will help making the appropriate remediation
measure. In this way, utility owners will be able to prioritize their repair and
maintenance plans, which usually play an important role on the improvement of
the quality of the services provided.
128
Table 6.1 : Summary of the pipe response showing the critical void sizes and locations
Void Location Springline Invert
Void Angle (VA/2π) 9% 13% 17.50% 9% 13% 17.50%
Void Length (VL/LP) 9% 18% 27% 9% 18% 27% 9% 18% 27% 9% 18% 27% 9% 18% 27% 9% 18% 27%
Earth Pressure (%) +13 +19 +22 +20 +30 +34 +26 +39 +45 +20 +26 +27 +19 +25 +27 +24 +30 +33
Ring Moment (%) +5 +9 +11 +7 +14 +18 +8 +17 +24 -19 -32 -41 -23 -40 -52 -26 -43 -57
Longitudinal Stress (%) +29 +35 +35 +42 +57 +62 +53 +78 +88 -92 -116* -126* -125* -164* -185* -146* -196* -225*
* critical length at which compressive stresses reversed to become tensile stresses
129
6.3. Limitations and Recommendations for Future Work
The conclusions drawn from the experimental program were based on laboratory
tests conducted under 1g conditions. The usefulness of 1g models is limited by
the fact that in situ stresses are not realistically simulated. However, 1g models
allow one to investigate complex systems in a controlled environment and are
considered to be more economical compared to centrifuge or field investigations.
Full scale measurements or centrifuge tests are needed to confirm the results
obtained using 1g models.
It is worth mentioning that the mechanically adjustable system used in the
experimental program was developed to allow for the simulation of the ground
support loss around a buried pipe and to measure the changes in the earth
pressure. Further tests are needed using different pipe size and stiffer ratios to
measure the changes in thrust forces and stresses in the pipe wall.
The conclusions arising from the 3D finite element models were based on
examining a concrete pipe of 600 mm in inner diameter. The finite element
models can be extended to investigate larger pipe sizes and pipes made from
other material such as plastic pipes.
The present numerical study examined the presence of a single void at the pipe
invert or springline, in some conditions multiple voids may develop at several
130
locations around the pipe leading to additional stresses and a different bending
moment distribution pattern. The finite element models can be extended to
investigate the effect of multiple voids located next to the pipe wall.
Finally, internal void grouting from inside the pipe is one of the common methods
used in practice to fill voids and reduce their negative effects. Further
investigation is needed to study how the presence of grouting can affect the earth
pressure distribution and the pipe stresses.
131
Appendix A
Void Detection Methods
132
Recently, innovative methods have been developed to detect voids formed
behind the wall of buried pipes. Feeny et al. (2009) reported the following
innovative techniques used in detection of voids next to the pipe wall:
Gamma-gamma logging, this method employs a gamma-gamma probe
composed of a source of gamma radiation such as cesium-137 and several
gamma detectors. The detectors are protected from direct radiation by a heavy
metal such as lead. The photons emitted by the gamma-gamma probe react to
surrounding material based on density. The photons are backscattered by the
surrounding material and data are recorded as a density log. Results of the
inspection reveals data on the average bulk density of the material encountered.
Properly constructed structures will have a consistent density. Although this
method is not yet used in pipeline inspection, recent research activities in
Germany confirmed the possibility of using a gamma-gamma probe in detecting
and measuring the size of voids existing in the bedding material surrounding a
buried pipe.
Ground penetrating radar (GPR), this technique involves a transmitting antenna
that discharges high-frequency radio waves into the ground. The waves
propagate through the medium until they encounter a material which has a
different conductivity and dielectric constant than the soil medium. The signal is
reflected and registered by a receiver. The amount of time it takes for the
133
electromagnetic radio waves to be reflected by subsurface materials can be
analyzed to determine the position and depth of features below the ground. GPR
are able to locate underground utility services as well as identify the presence of
voids in the pipe bedding.
Infrared thermography (IRT), this method employs the use of an infrared camera
to measure the temperature differential through the surface of an object. Software
can later be used to generate a colored contour image displaying the different
temperatures. In this way, the surface expression of thermal conditions beneath
the surface can be detected. This technique exists in two forms either passive
IRT which requires no external heat source or active IRT which requires the use
of a heat source such as infrared tube light. Recent research activities confirmed
the capability of IRT technique in detecting subsurface voids developed around a
buried pipe.
Crowder et al. (2011) reviewed the city of Hamilton's trial of using the Ground
Penetrating Radar (GPR) in the inspection of a 1524 mm diameter sewer pipe
buried at 28 m deep. In this inspection, two different antennas were used (500
MHz and 1000 MHz). The same clock positions and segment of the pipe were
scanned with both sensors separately for post inspection comparison and
analysis of the data recorded. As it was expected the antenna with 1000 MHz
revealed better resolution allowing to capture data with more details. While, the
134
sensor with 500 MHz had better penetration resulting in higher amplitude signals
which allows to detect features deeper behind the pipe wall. The inspection
carried by both sensors revealed the presence of inconsistency in the wall
thickness and voids within the pipe wall. To check the accuracy of the GPR
information, another man entry inspection was carried in order to drill holes
through the pipe walls at the locations scanned in the GPR data. The verification
inspection confirmed that the pipe wall depths are inconsistent which is in
agreement with the findings of the GPR inspection. After this successful trial, the
city of Hamilton undertook a pilot project to develop and design a full size Pipe
Penetrating Radar inspection tool that has the ability to scan the walls in the pipe
at positions varying from 9:00 o'clock to 3:00 o'clock. The PPR inspection
apparatus consists of 3 wheeled steel cart that carries adjustable arms that
support the sensor antennas directly against the inner side of the pipe as shown
in Figure A-1.
135
Figure A-1 : Pipe Penetrating Radar (PPR) inspection tool
(adapted from Crowder et al. (2011))
Ékes et al. (2011) described in details how the Pipe Penetrating Radar (PPR),
which is the underground in-pipe application of Ground Penetrating Radar (GPR),
works either robotically or by manned entry to inspect pipelines. It has also been
presented a historical review of the development of PPR and its successful
applications. This paper introduced both SewerVUE Surveyor and Pipe
Penetrating Radar Data Interpretation Application (PP-RADIAN). SewerVUE
Surveyor is the first commercial grade, robot mounted, multi sensor inspection
Antenna sensors
Box hosting electronics
136
tool. The SewerVUE Surveyor (Figure A-2) is composed of two independently
controllable high frequency antennas that can be adjusted to inspect pipes having
diameter ranging from 450 mm to 900 mm and can scan the pipe wall between 9
o'clock and 3 o'clock position with a maximum tether length of 183 m.
Figure A-2 : SewerVUE Surveyor
The main objective of a PPR inspection is to display an image of the pipe and its
bedding material with all anomalies encountered. The processed data of a PPR
inspection can be displayed in one of the following five types:
A one dimensional trace is the building block of all displays. This display
type allows to detect objects and determine their depth below a spot on
the pipe.
Antennas
Robot
137
A two dimensional cross section is a wiggle trace displaying grey-scale or
color scans. It is obtained by moving the antenna over the pipe wall and
recording traces at a fixed spacing.
A two dimensional depth slice is obtained by combining cross sections.
This display can be viewed as cross sections and as plan view maps
providing a quasi 3-D rendering of the surveyed pipe. Figure A-3 shows
sample of a depth slice scan. Objects with high conductivity contrast such
metallic targets are easier to identify compared to less conductive targets
such as air voids.
A three dimensional display is block views of PPR traces that are captured
at different locations on the pipe surface. This 3D block views are
constructed from several parallel, closely spaced lines.
An integrated pipe penetrating radar data display is a 3D representation of
key pipe attributes including pipe wall thickness, substrate voids and rebar
configuration in a reinforced concrete pipes.
PPRADIAN is the first commercial available integrated pipe penetrating radar
data processing display package released by SewerVUE technology Corp. This
application allows the display of the highest theoretical resolution of GPR data
possible to provide confident assessment of joint configuration, pipe wall
thickness and rebar cover (see Figure A-4).
Figgure A-3 : S
Sample of aa depth slicee scan
138
139
Figure A-4 : Sample of PPRADIAN views
140
Appendix B
Effect of Void Length on Earth Pressure
141
Figure B-1: Void angle 31° (VA/2π = 9%) at springline
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
VD/R = 7%
VD/R = 15%
VD/R = 30%
Y/L
Y/L
Y/L
P/P 0
P/
P 0
P/P 0
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
142
Figure B-2 : Void angle 47° (VA/2π = 13%) at springline
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
VD/R = 15%
VD/R = 30%
VD/R = 45%
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
Y/L
P/P 0
Y/L
Y/L
P/P 0
P/
P 0
143
Figure B-3 : Void angle 31° (VA/2π = 9%) at invert
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
VD/R = 7%
VD/R = 15%
VD/R = 30%
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
Y/L
Y/L
Y/L
P/P 0
P/
P 0
P/P 0
144
Figure B-4: Void angle 47° (VA/2π = 13%) at invert
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
VD/R = 15%
VD/R = 30%
VD/R = 45%
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
Y/L
Y/L
Y/L
P/P 0
P/
P 0
P/P 0
145
Appendix C
Effect of Void Depth on Earth Pressure
146
Figure C-1 : Void angle 31° (VA/2π = 9%) at springline
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
P/P 0
P/
P 0
P/P 0
Y/L
Y/L
Y/L
Initial earth pressure - No Void
VD/R = 7%
VD/R = 15%
VD/R = 30%
Initial earth pressure - No Void
VD/R = 7%
VD/R = 15%
VD/R = 30%
Initial earth pressure - No Void
VD/R = 7%
VD/R = 15%
VD/R = 30% VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
147
Figure C-2 : Void angle 47° (VA/2π = 13%) at springline
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
P/P 0
P/
P 0
P/P 0
Y/L
Y/L
Y/L
Initial earth pressure - No Void
VD/R = 15%
VD/R = 30%
VD/R = 45%
Initial earth pressure - No Void
VD/R = 15%
VD/R = 30%
VD/R = 45%
Initial earth pressure - No Void
VD/R = 15%
VD/R = 30%
VD/R = 45%
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
148
Figure C-3 : Void angle 31° (VA/2π = 9%) at invert
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
P/P 0
P/
P 0
P/P 0
Y/L
Y/L
Y/L
Initial earth pressure - No Void
VD/R = 7%
VD/R = 15%
VD/R = 30%
Initial earth pressure - No Void
VD/R = 7%
VD/R = 15%
VD/R = 30%
Initial earth pressure - No Void
VD/R = 7%
VD/R = 15%
VD/R = 30% VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
149
Figure C-4 : Void angle 47° (VA/2π = 13%) at invert
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
P/P 0
P/
P 0
P/P 0
Y/L
Y/L
Y/L
Initial earth pressure - No Void
VD/R = 15%
VD/R = 30%
VD/R = 45%
Initial earth pressure - No Void
VD/R = 15%
VD/R = 30%
VD/R = 45%
Initial earth pressure - No Void
VD/R = 15%
VD/R = 30%
VD/R = 45% VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
150
Appendix D
Changes in Circumferential Pipe Stresses
151
Figure D-1 : Springline extreme outer fibre changes in pipe circumferential stresses for voids with VA/2π = 13% at springline
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
VD/R = 15%
VD/R = 30%
VD/R = 45%
VL/LP = 9%
VL/LP = 18% VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18% VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18% VL/LP = 27%
Initial earth pressure - No Void
Y/L
Y/L
Y/L
σ θ/σ
θ0
σ θ/σ
θ0
σ θ/σ
θ0
152
Figure D-2 : Springline extreme inner fibre changes in pipe circumferential stresses for voids with VA/2π = 13% at springline
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.95
1.00
1.05
1.10
1.15
1.20
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18% VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18% VL/LP = 27%
Initial earth pressure - No Void
Y/L
Y/L
Y/L
σ θ/σ
θ0
σ θ/σ
θ0
σ θ/σ
θ0
VD/R = 15%
VD/R = 30%
VD/R = 45%
153
Figure D-3 : Invert extreme outer fibre changes in pipe circumferential stresses for voids with VA/2π = 13% at invert
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
Y/L
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
σ θ/σ
θ0
σ θ/σ
θ0
σ θ/σ
θ0
VD/R = 15%
VD/R = 30%
VD/R = 45%
154
Figure D-4 : Invert extreme inner fibre changes in pipe circumferential stresses for voids with VA/2π = 13% at invert
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
VL/LP = 9%
VL/LP = 18%
VL/LP = 27%
Initial earth pressure - No Void
Y/L
Y/L
Y/L
σ θ/σ
θ0
σ θ/σ
θ0
σ θ/σ
θ0
VD/R = 15%
VD/R = 30%
VD/R = 45%
155
Appendix E
Changes in Longitudinal Pipe Stresses
156
Figure E-1 : Crown extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 9% at springline
Figure E-2 : Crown extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 9% at invert
‐1.10
‐1.08
‐1.06
‐1.04
‐1.02
‐1.00
‐0.98
‐0.96
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
‐1.20
‐1.00
‐0.80
‐0.60
‐0.40
‐0.20
0.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
157
Figure E-3 : Springline extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 9% at springline
Figure E-4 : Springline extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 9% at invert
0.95
1.05
1.15
1.25
1.35
1.45
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
158
Figure E-5 : Invert extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 9% at springline
Figure E-6 : Invert extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 9% at invert
‐1.16
‐1.14
‐1.12
‐1.10
‐1.08
‐1.06
‐1.04
‐1.02
‐1.00
‐0.98
‐0.96
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
‐1.40
‐1.20
‐1.00
‐0.80
‐0.60
‐0.40
‐0.20
0.00
0.20
0.40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
159
Figure E-7 : Crown extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 13% at springline
Figure E-8 : Crown extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 13% at invert
‐1.40
‐1.20
‐1.00
‐0.80
‐0.60
‐0.40
‐0.20
0.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
‐1.4
‐1.2
‐1
‐0.8
‐0.6
‐0.4
‐0.2
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
160
Figure E-9 : Springline extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 13% at springline
Figure E-10 : Springline extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 13% at invert
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
‐0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
161
Figure E-11 : Invert extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 13% at springline
Figure E-12 : Invert extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 13% at invert
‐1.40
‐1.20
‐1.00
‐0.80
‐0.60
‐0.40
‐0.20
0.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
‐2.00
‐1.50
‐1.00
‐0.50
0.00
0.50
1.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
162
Figure E-13 : Crown extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 17.5% at springline
Figure E-14 : Crown extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 17.5% at invert
‐1.60
‐1.40
‐1.20
‐1.00
‐0.80
‐0.60
‐0.40
‐0.20
0.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
‐1.60
‐1.40
‐1.20
‐1.00
‐0.80
‐0.60
‐0.40
‐0.20
0.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
163
Figure E-15 : Springline extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 17.5% at springline
Figure E-16 : Springline extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 17.5% at invert
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
‐0.60
‐0.40
‐0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
164
Figure E-17 : Invert extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 17.5% at springline
Figure E-18 : Invert extreme outer fibre changes in pipe longitudinal stresses for voids with VA/2π = 17.5% at invert
‐1.60
‐1.40
‐1.20
‐1.00
‐0.80
‐0.60
‐0.40
‐0.20
0.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
‐2.00
‐1.50
‐1.00
‐0.50
0.00
0.50
1.00
1.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
σL/σ
L0
Y/L
No Void
VL/Lp = 9%
VL/Lp = 18%
VL/Lp = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
No Void VL/LP = 9% VL/LP = 18% VL/LP = 27%
165
References
ABAQUS. 2009. Documentation, version 6.9,Dessault Systèmes, Providence (RI).
ACPA (2007). "Concrete pipe design manual." American Concrete Pipe Association.
ASCE 15-93 (1994). "Standard practice for direct design of buried precast concrete pipe using standard installations (SIDD)." American Society of Civil Engineers, New York.
ASTM C14M "Standard specification for nonreinforced concrete sewer, storm drain, and culvert pipe (metric)." ASTM International.
ASTM C76M "Standard specification for reinforced concrete culvert, storm drain, and sewer pipe (metric)." ASTM International.
ASTM C497M "Standard test methods for concrete pipe, manhole sections, or tile (metric)." ASTM International.
Burns, J. Q., and Richard, R. M. (1964). "Attenuation of stresses for buried cylinders." Arizona. University -- Symposium of Soil-Structure Interaction -- Proceedings 378-392.
Crowder, D., Bauer, G., and Bainbridge, K. (2011). "Locating voids behind pipe walls in large diameter sewer using Pipe Penetrating Radar (PPR)." No-Dig Conference and Exhibition, North American Society for Trenchless Technology, Washington, D.C.
CSA (2006). Canadian highway bridge design code, Canadian Standards Association, Mississauga, Ontario.
Csaba, É., Boriszlav, N., and R., H. G. (2011). "GPR goes underground: pipe penetrating radar." No-Dig Conference and Exhibition, North American Society for Trenchless Technology, Washington, D.C.
Davies, J. P., Clarke, B. A., Whiter, J. T., and Cunningham, R. J. (2001). "Factors influencing the structural deterioration and collapse of rigid sewer pipes." Urban Water 3(1-2), 73-89.
Erdogmus, E., Skourup, B. N., and Tadros, M. (2010). "Recommendations for design of reinforced concrete pipe." Journal of Pipeline Systems Engineering and Practice, 1(1), 25-32.
Feeney, C. S., Thayer, S., Bonomo, M., and Martel, K. (2009). "White paper on condition assessment of wastewater collection systems." National Risk Management Research Laboratory, U.S. Environmental Protection Agency, Cincinnati, Ohio.
166
Handy, R. L. (1985). "Arch in soil arching." Journal of Geotechnical Engineering, 111(3), 302-318.
Heger, F. J., Liepins, A. A., and Selig, E. T. "SPIDA: an analysis and design system for buried concrete pipe." Proc., Advances in Underground Pipeline Engineering, Proceedings of the International Conference., ASCE, 143-154.
Helfrich, S. C. (1997). "Investigation of sewer-line failure." Journal of Performance of Constructed Facilities, 11(1), 42-44.
Hill, J. J., Kurdziel, J. M., Nelson, C. R., Nystrom, J. A., and Sondag, M. S. (1999). "Minnesota department of transportation overload field tests of standard and standard installation direct design reinforced concrete pipe installations." Transportation Research Record(1656), 64-72.
Hoeg, K. (1968). "Stresses against underground structural cylinders." American Society of Civil Engineers Proceedings, Journal of the Soil Mechanics and Foundations Division, 94(SM4), 833-858.
Jewell, H. W. (1945). "Factors affecting service life of underground pipe structures." Brick and Clay Record, 106(1), 39-42.
Jones, G. M. A. (1984). "The Structural deterioration of sewers." International Conference on the Planning, Construction, Maintenance and Operation of Sewerage Systems,September 12-14,Reading, U.K.
Katona, M. G., and Smith, J. M. (1976). "A modern approach for structural design of pipe culverts." EDN, IPC Sci and Technol Press, Ltd, Guildford, Surrey, Engl, London, Engl, 128-140.
Kurdziel, J. M., and McGrath, T. J. (1991). "SPIDA method for reinforced concrete pipe design." Journal of Transportation Engineering, 117(4), 371-381.
Lester, J., and Farrar, D. M. (1979). "Examination of the defects observed in six kilometres of sewers." TRRL Supplementary Report (Transport and Road Research Laboratory, Great Britain)(531).
Liedberg, S. (1991). "Earth pressure distribution against rigid pipes under various bedding conditions. Full-scale field tests in sand." Chalmers Tekniska Hogskola, Doktorsavhandlingar.
Marston, A., and Anderson, A. O. (1913). "The theory of loads on pipes in ditches and tests of cement and clay drain tile and sewer pipe." Iowa State College of Agriculture, 181.
McGrath, T. J., Selig, E. T., Webb, M. C., and Zoladz, G. V. (1999). "Pipe interaction with the backfill envelope." FHWA-RD-98-191, National Science Foundation, Washington, D.C.
167
McKelvey III, J. A. (1994). "Anatomy of soil arching." Geotextiles and Geomembranes, 13(5), 317-329.
McVay, M. C. (1982). "Evaluation of numerical modeling of buried conduits." Ph.D.'s thesis, University of Massachusetts Amherst, United States -- Massachusetts.
Meguid, M. A., and Dang, H. K. (2009). "The effect of erosion voids on existing tunnel linings." Tunnelling and Underground Space Technology, 24(3), 278-286.
Meguid, M. A., Saada, O., Nunes, M. A., and Mattar, J. (2008). "Physical modeling of tunnels in soft ground: A review." Tunnelling and Underground Space Technology, 23(2), 185-198.
Mirza, S., and Federation of Canadian, M. (2007). Danger ahead the coming collapse of Canada's municipal infrastructure, Federation of Canadian Municipalities, Ottawa, Ontario.
Moore, I. D. (2001). "Culverts and buried pipelines." Geotechnical and Geoenvironmental Handbook, K. R. Rowe, ed., Kluwer Academic Publishers, 541-568.
Moore, I. D. (2008). "Assessment of damage to rigid sewer pipes and erosion voids in the soil, and implications for design of liners." No-Dig Conference and Exhibition, North American Society for Trenchless Technology, Dallas, Texas.
Moser, A. P. (2001). Buried pipe design, McGraw-Hill, New York.
Munro, S. M., Moore, I. D., and Brachman, R. W. I. (2009). "Laboratory testing to examine deformations and moments in fiber-reinforced cement pipe." Journal of Geotechnical and Geoenvironmental Engineering, 135(11), 1722-1731.
Najafi, M. (2010). Trenchless technology piping : installation and inspection, McGraw-Hill Professional
O'Reilly, M. P., Rosbrook, R. B., Cox, G. C., and McCloskey, A. (1989). "Analysis of defects in 180km pipe sewers in Southern Water Authority ", Transport and Road Research Lab., Crowthorne (United Kingdom).
Smeltzer, P. D., and Daigle, L. (2005). "Field performance of a concrete pipe culvert installed using standard installations." 33rd CSCE Annual Conference, Canadian Society for Civil Engineering, Toronto, ON, Canada, GC-210-211-GC-210-210.
168
Spangler, M. G., and Handy, R. L. (1973). Soil engineering, Intext Educational Publishers, New York .
Talesnick, M., and Baker, R. (1999). "Investigation of the failure of a concrete-lined steel pipe." Geotechnical and Geological Engineering, 17(2), 99-121.
Tan, Z., and Moore, I. D. (2007). "Effect of backfill erosion on moments in buried rigid pipes." Transportation Research Board Annual Conference,Washington D.C.
Terzaghi, K. (1943). Theoretical soil mechanics, Chapman and Hall ; Wiley, London : New York.
Tien, H.-J. (1996). "A Literature study of the arching effect " Master of Science, Massachusetts Institute of Technology.
Water;Infrastructure (2004). "Research for policy & program development." Research and analysis infrastructure Canada.
Wong, L. S., Allouche, E. N., Baumert, M., Dhar, A. S., and Moore, I. D. (2006). "Long-term monitoring of SIDD Type IV installations." Canadian Geotechnical Journal, 43(4), 392-408.
Zhao, J. Q., and Daigle, L. (2001). "SIDD pipe bedding and Ontario provincial standards." Proceedings of the international conference on underground infrastructure research, Kitchener, Ontario, 143-152.
