EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE EVOLUTION OF PIPING AND RESULTING BREACH IN EARTH- FILL DAMS

Abstract

Earth-fill dams have been constructed for decades by compacting natural soil materials near the dam site. Piping is of the most important causes of their failure.
In the scope of this thesis, 2 m in length homogenous earth-fill dams were constructed in a rectangular flume in the laboratory of the Izmir University of Economics. The experimental and numerical investigations on a breach by generating piping were realized with different weak zone scenarios. Three experiments were performed by placing a weak layer cross-section 5x5 cm2 at the dam bottom center. One scenario was performed by locating a weak layer of 2x2 cm2, 28 cm above the bottom.
Temporal breach areas and the breach-wetted areas are evaluated on scaled screenshots by using Gauss’s area formulation. The Temporal breach discharges were calculated from the continuity equation.
Furthermore, finite element analyses on the breaching of homogenous earth-fill dams in different scenarios were performed by comparing the hydraulic gradient with the critical value. In addition to the bottom and middle scenarios, two upper scenarios were also modeled. The water depths were used for each scenario to represent the experimental conditions, and some approaches were made for the weak zones. To simulate the breach mechanism with different loops, a python algorithm was integrated with the Jupyter console. As a result of the simulations, it has been observed that the findings obtained by simulations were in accord with the experimental studies, and the dams were exposed to backward piping starting from downstream towards upstream.

Full text

EXPERIMENTAL AND NUMERICAL
INVESTIGATION OF THE EVOLUTION OF
PIPING AND RESULTING BREACH IN EARTH-
FILL DAMS
A Thesis Submitted to
the Graduate School of Engineering and Sciences of
İzmir Institute of Technology
in Partial Fulfillment of the Requirements for Degree of
MASTER OF SCIENCE
In Civil Engineering
by
Emre DUMLU
December 2022
İZMİR

ACKNOWLEDGEMENTS
To begin with, I would like to thank The Scientific and Technological Research
Council of Turkey (TUBITAK) for their financial support in the scope of project
119M609, since this support allowed the realization of the elaborate experimental and
numerical studies.
I owe my special thanks to my advisor Prof. Dr. Gökmen TAYFUR, who gave
me a chance to build my career and supported me throughout my master’s. This thesis
wouldn’t be completed without his kind, supportive, patient guidance without giving up
on me and his teaching skills. I would also like to thank him for allowing me to meet Prof.
Dr. Şükrü GÜNEY.
I would like to state that I am pleased to have had the opportunity to work with
Prof. Dr. GÜNEY, the coordinator of the TÜBİTAK 119M609 project, from the
beginning to the end, as he trusted me in every part of the project and allowed me to
express my creativity. I appreciate for allowing me to represent our project at national
and international conferences many times. I learned from him how to find solutions when
faced with a problem. He was the one who brought my guidance and engineering
knowledge to the next level throughout the project, not only completing works but also
including the concept of time in these works and educating me on time management.
Another Professor that Prof. GÜNEY allowed us to meet throughout the project
is Prof. Gürkan ÖZDEN. I am proud to know that I am the only hydraulics student he has
studied. I learned to study rationally and calmly, and steadily from him. I would like to
thank him very much for being able to receive geotechnical and numerical analysis
support and, for sharing his experiences even during his busy times.
I would also like to thank Merve OKAN, who was involved in the project, for her help
and for having a chance to present and discuss a different perspective.
Also, I would like to thank İsmail KESKİN, who is a technician at the laboratory
of the Izmir University of Economics, for getting support from him in the construction of
the dams and for helping us under all circumstances.
Also, I like to be grateful to the management and dedicated teams of the Izmir
University of Economics for their support during the project.

I would also show all my special respect to Prof. Dr. Şebnem ELÇİ for her support
during my master's degree. We worked together on many studies apart from this thesis.
She gave me a different and comprehensive perspective, improved my practical work,
and broadened my horizons.
I would also like to thank Bahadır ÖZTÜRK, whom I met in the last period of my
master's degree and received his ideas, helps, and offering good friendship during my
thesis writing process.
I show my gratitude to my family, that we are a team within a team, Cevriye
DUMLU, Emin DUMLU, Ecenur KURT, and Gökhan KURT who gave me all their
unconditional support, endless love, and motivation throughout my life. Glad you are my
family.

iii
ABSTRACT
EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE
EVOLUTION OF PIPING AND RESULTING BREACH IN EARTH-
FILL DAMS
Earth-fill dams have been constructed for decades by compacting natural soil
materials near the dam site. Piping is of the most important causes of their failure.
In the scope of this thesis, 2 m in length homogenous earth-fill dams were
constructed in a rectangular flume in the laboratory of the Izmir University of Economics.
The experimental and numerical investigations on a breach by generating piping were
realized with different weak zone scenarios. Three experiments were performed by
placing a weak layer cross-section 5x5 cm2 at the dam bottom center. One scenario was
performed by locating a weak layer of 2x2 cm2, 28 cm above the bottom.
Temporal breach areas and the breach-wetted areas are evaluated on scaled
screenshots by using Gauss’s area formulation. The Temporal breach discharges were
calculated from the continuity equation.
Furthermore, finite element analyses on the breaching of homogenous earth-fill
dams in different scenarios were performed by comparing the hydraulic gradient with the
critical value. In addition to the bottom and middle scenarios, two upper scenarios were
also modeled. The water depths were used for each scenario to represent the experimental
conditions, and some approaches were made for the weak zones. To simulate the breach
mechanism with different loops, a python algorithm was integrated with the Jupyter
console. As a result of the simulations, it has been observed that the findings obtained by
simulations were in accord with the experimental studies, and the dams were exposed to
backward piping starting from downstream towards upstream.

iv
ÖZET
TOPRAK DOLGU BARAJLARDA BORULANMA VE BORULANMA
NEDENLİ GEDİK OLUŞUMUNUN DENEYSEL VE SAYISAL
ARAŞTIRILMASI
Toprak dolgu barajlar, onlarca yıldır baraj sahasının yakınında doğal toprak
malzemelerinin sıkıştırılmasıyla inşa edilmiştir. Borulama, baraj yıkılmalarının en önemli
nedenlerinden biridir.
Bu tez kapsamında, İzmir Ekonomi Üniversitesi laboratuvarında dikdörtgen bir
kanal içine 2 m uzunluğunda homojen toprak dolgu barajları inşa edilmiştir. Farklı zayıf
bölge senaryoları ile borulama oluşturularak bir gediklenmenin deneysel ve sayısal
incelemeleri gerçekleştirilmiştir. Baraj tabanı ve ortasında 5x5 cm2 en kesitinde bir zayıf
bölge yerleştirilerek üç deney, tabandan 28 cm yukarıya 2x2 cm2'lik bir zayıf bir bölge
yerleştirilerek bir deney gerçekleştirildi.
Zamansal gedik alanları ve gedik-ıslak alanları Gauss alan formulasyonu
kullanılarak ölçekli ekran görüntüleri üzerinde değerlendirildi. Zamansal gedik debileri
ise süreklilik denkleminden hesaplandı.
Deneysel çalışmalara ilaveten, hidrolik eğim ile kritik eğim karşılaştırılarak farklı
senaryolarda homojen toprak dolgu barajlarda borulanma üzerine sonlu elemanlar
analizleri yapılmıştır. Alt ve orta senaryolara ilaveten, iki adet üst senaryo da
modellenmiştir. Deneysel koşulları gerçekleştirmek etmek için her senaryoda zamana
bağlı su derinlikleri kullanılmış ve zayıf bölgeler için bazı yaklaşımlar yapılmıştır. Gedik
mekanizmasını farklı döngülerle simüle etmek için Jupyter konsoluna bir python
algoritması geliştirildi. Simülasyonlar sonucunda simülasyonlarla elde edilen bulguların
deneysel çalışmalarla uyumlu olduğu ve barajların mansaptan başlayarak membaya doğru
geriye doğru borulamaya maruz kaldığı görülmüştür.

v
TABLE OF CONTENTS
LIST OF FIGURES ....................................................................................................... vii
LIST OF TABLES ........................................................................................................ xiv
CHAPTER 1. INTRODUCTION .................................................................................... 1
1.1. Background ............................................................................................. 1
1.2. Problem Statement .................................................................................. 3
1.3. Research Objectives ................................................................................ 3
1.4. Dissertation Outline ................................................................................ 4
CHAPTER 2. LITERATURE REVIEW ......................................................................... 5
2.1. Experimental Studies .............................................................................. 5
2.2. Theoretical and Numerical Studies ......................................................... 7
CHAPTER 3. SOIL MECHANICS TESTS AND EXPERIMENTAL SETUP ........... 10
3.1. Soil Mechanics Tests ............................................................................ 10
3.2. Experimental Setup ............................................................................... 13
CHAPTER 4. EXPERIMENTAL PROCEDURE……………………………………..15
4.1. Construction Procedure ......................................................................... 15
4.2. Evaluation of the Experiments .............................................................. 17
CHAPTER 5. EXPERIMENTAL FINDINGS .............................................................. 20
5.1. First Experiment ................................................................................... 20
5.2. Second Experiment ............................................................................... 30
5.3. Third Experiment .................................................................................. 38

vi
5.4. Fourth Experiment ................................................................................ 46
5.5. The compaction density effects ............................................................ 58
5.6. Results and Discussions ........................................................................ 61
CHAPTER 6. 3D FINITE ELEMENT ANALYSIS OF BREACHING OF
HOMOGENOUS EARTH-FILL DAMS .................................................... 65
6.1. Finite Element Method ......................................................................... 65
6.1.1. Methodology .................................................................................... 65
6.1.2. The Soil Properties .......................................................................... 67
6.1.3. Modelling of Piping Evolution ........................................................ 68
6.2. Numerical Simulation of the Experimented Dams ............................... 71
6.2.1. Numerical analysis corresponding to the first experiment .............. 71
6.2.2. Numerical analysis corresponding to the fourth experiment ........... 82
6.2.3. Case 1: Seepage Starting at the Upper-Middle ................................ 92
6.2.4. Case 2: Seepage Starting at the Upper-Corner .............................. 103
6.3. Results and Discussions ...................................................................... 116
CHAPTER 7. CONCLUSION AND RECOMMENDATIONS ................................. 118
REFERENCES ............................................................................................................ 120

xiv
LIST OF FIGURES
Figure Page
Figure 2.1. Piping failure processes resulted in a breach, (a) initiation,
(b) continuation, c) progression, d) the collapsing of the dam roof,
e) final breach formation ................................................................................ 6
Figure 3.1. The distributions of grain size of the mixtures ............................................. 10
Figure 3.2. 13 blows proctor test curve for mixture 1 .................................................... 11
Figure 3.3. 13 blows proctor test curve for mixture 2 .................................................... 12
Figure 3.4. The experimental setup (a) schematic longitudinal view,
(b) Upper channel (c) Transmission line ..................................................... 14
Figure 4.1. The construction process (a) dry mixing, (b) preparation of soil mixture,
(c) creating the weak zone, (d) construction of the first 10 cm layer, (e)
scraping the second layer, (f) the constructed third layer, (g)
construction in the fourth layer, (h) pouring and grinding at the fifth
layer, (i) compaction at the sixth layer, (j) before the trimming .................. 16
Figure 4.2. n-sided polygons on Get-data Graph Digitizer 2.26 ..................................... 19
Figure 5.1. View of the dam from (a) upstream, (b) downstream, (c) side, (d) top ....... 21
Figure 5.2. The downstream temporal breach developments (a) t=0 h, (b) t=24 h,
(c) t= 48 h, (d) t= 192 h ................................................................................ 21
Figure 5.3. Downstream breach surfaces at (a) t=193 h, (b) t=194 h ............................. 22
Figure 5.4. Downstream breach surfaces at t=196 h (a) downstream view,
(b) close-up view of the breach .................................................................... 22
Figure 5.5. Downstream breach surfaces at t=208 h (a) downstream view,
(b) close-up view of the breach .................................................................... 23
Figure 5.6. Downstream breach surfaces at t= 216 h (a) downstream view,
(b) close-up view of the breach, (c) eroded and transported soil materials
due to the seepage ........................................................................................ 23
Figure 5.7. The breach developments at t= 230 h (a) downstream, (b) upstream ......... 24
Figure 5.8. The seepage discharges before the breach did not reach the upstream face. 24
Figure 5.9. The breach views from downstream (a) t=0 s, (b) t=5 s, (c) t=10 s,
(d) t=20 s, (e) t=50 s, (f) t=315 s ................................................................. 25
Figure 5.10. The breach views from upstream (a) t=0 s, (b) t=5 s, (c) t=10 s,
(d) t=20 s, (e) t=50 s, (f) t=315 s ............................................................... 26

xv
Figure Page
Figure 5.11. The breach views from top (a) t=0 s, (b) t=5 s, (c) t=10 s, (d) t=20 s,
(e) t=50 s, (f) t=315 s ................................................................................. 27
Figure 5.12. Temporal changes in water depths in the channel ...................................... 28
Figure 5.13. The upstream and downstream temporal breach developments ................. 28
Figure 5.14. The upstream and downstream temporal variations of the
breach-wetted areas ................................................................................... 29
Figure 5.15. Temporal breach discharges ....................................................................... 29
Figure 5.16. The time-varied upstream and downstream breach velocities ................... 30
Figure 5.17. The final views of the second experiment, (a) upstream, (b) downstream,
(c) left side, (d) top side ............................................................................. 30
Figure 5.18. The breach views from downstream (a) t=0 h, (b) t=1.1 h, (c) t=2 h,
(d) t=3 h, (e) t=4 h, (f) t=4.8 h ................................................................... 31
Figure 5.19. The breach views from the top (a) t=0 h, (b) t=1.1 h, (c) t=2 h, (d) t=3 h,
(e) t=4 h, (f) t=4.8 h ................................................................................... 32
Figure 5.20. The breach views from downstream (a) t=0 s, (b) t=20 s, (c) t=60 s,
(d) t=80 s, (e) t=120 s, (f) t=150 s ............................................................. 33
Figure 5.21. The breach views from upstream (a) t=0 s, (b) t=20 s, (c) t=60 s,
(d) t=80 s, (e) t=120 s, (f) t=150 s ............................................................. 34
Figure 5.22. The breach views from top (a) t=0 s, (b) t=20 s, (c) t=60 s, (d) t=80 s,
(e) t=120 s, (f) t=150 s ............................................................................... 35
Figure 5.23. Temporal changes in water depths in the channel ...................................... 36
Figure 5.24. The upstream and downstream temporal breach developments ................. 36
Figure 5.25. The upstream and downstream temporal variations of the breach-wetted
areas ........................................................................................................... 37
Figure 5.26. Temporal breach discharges ....................................................................... 37
Figure 5.27. The time-varied upstream and downstream breach velocities ................... 38
Figure 5.28. The final view of the dam ........................................................................... 38
Figure 5.29. The breach views from downstream (a) t=0 s, (b) t=50 s, (c) t=1710 s,
(d) t=2230 s, (e) t=2410 s, (f) t=2485 s ..................................................... 39
Figure 5.30. The breach views from top (a) t=0 s, (b) t=50 s, (c) t=1710 s,
(d) t=2230 s, (e) t=2410 s, f) t=2485 s ....................................................... 40

xvi
Figure Page
Figure 5.31. The breach views from downstream (a) t=0 s, (b) t=10 s, (c) t=30 s,
(d) t=40 s, (e) t=60 s, (f) t=150 s ............................................................... 41
Figure 5.32. The breach views from upstream (a) t=0 s, (b) t=10 s, (c) t=30 s,
(d) t=40 s, (e) t=60 s, (f) t=150 s ............................................................... 42
Figure 5.33. The breach views from top (a) t=0 s, (b) t=10 s, (c) t=30 s, (d) t=40 s,
(e) t=60 s, (f) t=150 s ................................................................................. 43
Figure 5.34. Temporal changes in water depths in the channel ...................................... 44
Figure 5.35. The upstream temporal breach developments ............................................ 44
Figure 5.36. The upstream temporal variations of the breach-wetted areas ................... 45
Figure 5.37. Temporal breach discharges ....................................................................... 45
Figure 5.38. The time-varied upstream breach velocities ............................................... 46
Figure 5.39. The final view of the dam from (a) top (b) downstream ............................ 46
Figure 5.40. The breach views at t=0 s (a) upstream of the first dam, (b) upstream of
the second dam, (c) downstream of the first dam, (d) downstream of the
second dam ................................................................................................ 47
Figure 5.41. The breach views at t=15 s (a) upstream of the first dam, (b) upstream
of the second dam, (c) downstream of the first dam, (d) downstream of the
second dam ................................................................................................ 48
Figure 5.42. The breach views at t=25 s (a) upstream of the first dam, (b) upstream
of the second dam, (c) downstream of the first dam, (d) downstream of the
second dam ................................................................................................ 49
Figure 5.43. The breach views at t=40 s (a) upstream of the first dam, (b) upstream
of the second dam, (c) downstream of the first dam, (d) downstream of the
second dam ................................................................................................ 50
Figure 5.44. The breach views at t=60 s (a) upstream of the first dam, (b) upstream
of the second dam, (c) downstream of the first dam, (d) downstream of the
second dam ................................................................................................ 51
Figure 5.45. The breach views at t=90 s (a) upstream of the first dam, (b) upstream
of the second dam, (c) downstream of the first dam, (d) downstream of the
second dam ................................................................................................ 52

xvii
Figure Page
Figure 5.46. The breach views at t=134 s (a) upstream of the first dam, (b) upstream
of the second dam, (c) downstream of the first dam, (d) downstream of the
second dam ................................................................................................ 53
Figure 5.47. Temporal changes in water depths in the channel ...................................... 54
Figure 5.48. The downstream temporal breach developments ....................................... 54
Figure 5.49. The upstream temporal breach developments ............................................ 55
Figure 5.50. The temporal variations of the breach-wetted areas at downstream .......... 55
Figure 5.51. The temporal variations of the breach-wetted areas at upstream ............... 56
Figure 5.52. Temporal breach discharges ....................................................................... 56
Figure 5.53. The time-varied downstream breach velocities .......................................... 57
Figure 5.54. The time-varied upstream breach velocities ............................................... 57
Figure 5.55. Temporal changes in water depths in the channel together with lower
and higher density dams ............................................................................ 58
Figure 5.56. The temporal breach developments at upstream together with the lower
density and higher density dams ................................................................ 59
Figure 5.57. The temporal variations of the breach-wetted areas at upstream together
with the lower density and higher density dams........................................ 59
Figure 5.58. The temporal breach discharges together with the lower density and
higher density dams ................................................................................... 60
Figure 5.59. The time-varied upstream breach velocities together with the lower
density and higher density dams ................................................................ 60
Figure 6.1. The representation of wetted area together with phreatic surface ................ 66
Figure 6.2. Not scaled representation of the creation of breach surfaces ....................... 69
Figure 6.3. Flow chart of the applied 3D python algorithm ........................................... 70
Figure 6.4. The final geometry of the first experiment ................................................... 71
Figure 6.5. Experimental and numerical seepage discharges before the breach
reached upstream face .................................................................................. 71
Figure 6.6. Hydraulic gradient distribution along the dam before the breach did not
reach the upstream face for (a) 0 days, (b) 4 days ....................................... 72
Figure 6.7. Hydraulic gradient distribution along the dam after the breach reached
the upstream face for (a) 10 s, (b) 20, (c) 30 s, (d) 120 s ............................. 74
Figure 6.8. Flow distributions along the dam for (a) 10 s, (b) 20 s, (c) 30 s, (d) 120 s .. 76

xviii
Figure Page
Figure 6.9. The downstream temporal breach developments (a) t=0 s, (b) t=10 s,
(c) t=120 s .................................................................................................... 77
Figure 6.10. The upstream temporal breach developments (a) t=0 s, (b) t=10,
(c) t=30 s, (d) t=120 s ................................................................................ 78
Figure 6.11. The downstream temporal breach developments together with
experimental and numerical ...................................................................... 79
Figure 6.12. The upstream temporal breach developments together with experimental
and numerical ............................................................................................ 79
Figure 6.13. The time-varied downstream breach velocities together with
experimental and numerical ...................................................................... 79
Figure 6.14. The time-varied upstream breach velocities together with experimental
and numerical ............................................................................................ 80
Figure 6.15. The temporal changes in downstream breach-wetted areas together with
experimental and numerical ...................................................................... 80
Figure 6.16. The temporal changes in upstream breach-wetted areas together with
experimental and numerical ...................................................................... 80
Figure 6.17. The temporal discharge values together with experimental and
numerical ................................................................................................... 81
Figure 6.18. The final geometry of the middle-middle scenario .................................... 82
Figure 6.19. Hydraulic gradient distribution along the dam for (a) t=0 s, (b) t=10 s,
(c) t=40 s, (d) t=80 s .................................................................................. 83
Figure 6.20. Flow through the breach a) t=10 s, b) t=40 s, c) t=80 s ............................. 85
Figure 6.21. The downstream temporal breach developments a) 0 s, b) 40 s, c) 80 s .... 86
Figure 6.22. The upstream temporal breach developments a) 0 s, b) 40 s, c) 80 s ......... 87
Figure 6.23. The downstream temporal breach developments together with
experimental average and numerical ......................................................... 88
Figure 6.24. The upstream temporal breach developments together with experimental
average and numerical ............................................................................... 88
Figure 6.25. The time-varied downstream breach velocities together with
experimental average and numerical ......................................................... 89
Figure 6.26. The time-varied upstream breach velocities together with experimental
average and numerical ............................................................................... 89

xix
Figure Page
Figure 6.27. The temporal changes in downstream breach-wetted areas together
with experimental and numerical .............................................................. 90
Figure 6.28. The temporal changes in upstream breach-wetted areas together with
experimental and numerical ...................................................................... 90
Figure 6.29. The average temporal discharge values together with experimental and
numerical ................................................................................................... 91
Figure 6.30. The construction stages of the upper-middle scenario (a) Top view of
the third layer during construction, (b) Left view of the third layer during
construction, (c) final upstream view, (d) final downstream view ............ 92
Figure 6.31. The experiment process for the upper-middle scenario (a) downstream
beginning, (b) downstream ending, (c) upstream beginning, (d) upstream
ending ........................................................................................................ 93
Figure 6.32. The temporal water depths of the upper-middle scenario .......................... 93
Figure 6.33. The final geometry of the upper-middle scenario ...................................... 94
Figure 6.34. Hydraulic gradient distribution along the dam (a) 0 s, (b) 40 s, (c) 160 s,
(d) 240 s (e) 380 s ...................................................................................... 94
Figure 6.35. Flow through the breach a) 40 s, b) 160 s, c) 240 s.................................... 96
Figure 6.36. The downstream temporal breach developments (a) 0 s, (b) 40 s,
(c) 240 s, d) 380 ......................................................................................... 97
Figure 6.37. The upstream temporal breach developments (a) 0 s, (b) 40, (c) 240 s,
(d) 380 s ..................................................................................................... 98
Figure 6.38. The downstream temporal breach developments together with
experimental and numerical ...................................................................... 99
Figure 6.39. The upstream temporal breach developments together with
experimental and numerical .................................................................... 100
Figure 6.40. The time-varied downstream breach velocities together with
experimental and numerical .................................................................... 100
Figure 6.41. The time-varied upstream breach velocities together with experimental
and numerical .......................................................................................... 101
Figure 6.42. The temporal variations of downstream wetted areas together with
experimental and numerical .................................................................... 101

xx
Figure Page
Figure 6.43. The temporal variations of upstream wetted areas together with
experimental and numerical .................................................................... 102
Figure 6.44. The temporal discharges together with experimental and numerical ....... 102
Figure 6.45. The construction stages of the upper-corner scenario (a) construction
of the first layer on the top view, (b) construction of the first layer on
the left view, (c) final upstream view, (d) final downstream view .......... 104
Figure 6.46. The experiment process for the upper-corner scenario (a) downstream
beginning, (b) downstream ending (c), right side beginning (d), right
side ending, (e) upstream beginning, (f) upstream ending ...................... 104
Figure 6.47. The final geometry of the upper-corner scenario ..................................... 105
Figure 6.48. The changes in water level in time for the upper-corner scenario ........... 106
Figure 6.49. Hydraulic gradient distribution along the dam for (a) 0 s, (b) 40 s,
(c) 160 s, (d) 500 s, (e) 640 s ................................................................... 106
Figure 6.50. Flow through the breach a) 40 s a) 40 s, b) 160 s, c) 500 ........................ 109
Figure 6.51. The downstream temporal breach developments a) 0 s, b) 40 s,
c) 500 s, d) 640 s ...................................................................................... 110
Figure 6.52. The upstream temporal breach developments (a) 0 s, (b) 300,
(c) 500 s, (d) 640 s ................................................................................... 111
Figure 6.53. The downstream temporal breach developments together with
experimental and numerical .................................................................... 112
Figure 6.54. The upstream temporal breach developments together with
experimental and numerical .................................................................... 112
Figure 6.55. The time-varied downstream breach velocities together with
experimental and numerical .................................................................... 113
Figure 6.56. The time-varied upstream breach velocities together with experimental
and numerical .......................................................................................... 113
Figure 6.57. The temporal variations of the downstream wetted areas together with
experimental and numerical .................................................................... 114
Figure 6.58. The temporal variations of the upstream wetted areas together with
experimental and numerical .................................................................... 114
Figure 6.59. The temporal discharges together with experimental and numerical ....... 115

xxi
LIST OF TABLES
Table Page
Table 3.1. The soil parameters used in different experiments ........................................ 12
Table 3.2. Direct shear test results .................................................................................. 13
Table 3.3. Consolidation test results ............................................................................... 13
Table 5.1. The details of different experiments ............................................................. 20
Table 5.2. The so-obtained comparative results for at most 10 % .................................. 61
Table 5.3. The temporal discharges for different time intervals ..................................... 61
Table 5.4. The temporal breach developments at downstream for different time
intervals .......................................................................................................... 62
Table 5.5. The temporal breach developments at upstream for different time
intervals .......................................................................................................... 62
Table 5.6. The temporal variations of downstream breach-wetted areas for different
time intervals .................................................................................................. 62
Table 5.7. The temporal variations of upstream breach-wetted areas for different
time intervals ................................................................................................. 62
Table 5.8. The time-varied downstream breach velocities for different time intervals .. 63
Table 5.9. The time-varied upstream breach velocities for different time intervals ....... 63
Table 6.1. The soil properties used in the finite element analyses ................................. 68
Table 6.2. RMSE and MAE values for each finding at the bottom-middle scenario ..... 81
Table 6.3. RMSE and MAE values for each finding at the middle-middle part............. 91
Table 6.4. RMSE and MAE values for each finding at the upper-middle part............. 103
Table 6.5. RMSE and MAE values for each finding at the upper-corner part ............. 115

1
CHAPTER 1
INTRODUCTION
1.1. Background
Dams are hydraulic structures having a variety of beneficial purposes such as
flood control, irrigation, water supply, hydroelectric energy production, and reservoir
water management. An earth-fill dam is a type of artificial water barrier that can be
homogeneous or non-homogeneous (with a clay core or impervious layer) and is made
up of a compacted mixture of soil (sand, clay, and silt or rock). Earth-fill dams were used
for years, and they continue to be used nowadays. Some advantages of earth-fill dams are
as follows (Okan, 2022):
• They can be easily built using soil materials that are readily available nearby.
• Their design is relatively easy by allowing a range of materials to be employed in
their construction.
• They are economical to construct with locally available soil materials.
• Their compaction styles are suitable to be improved by technological
developments.
• The earth-fill dams are environmentally friendly dam types because of consisting
of natural and organic soil materials.
Although earth-fill dams have some advantages, there are some disadvantages, as
well:
• It is possible to occur miscalculations in the project or construction stages caused
by human factors, machines, or due to environmental factors such.
• Before the construction stages, laboratory tests needed to be performed that
means, compared to concrete gravity dams, it has additional labor costs.
• They may have unexpected behavior in the case of choosing improper soil
material.

2
• After the construction, they need to be maintained, controlled, and observed since
one of the most common problems is internal erosion caused by improper soil
material or lack of maintenance.
• The seismic activities may result in liquefaction within the dam body, creating
stability issues that could eventually lead to seepage and failure.
In the literature, there are many tragic examples. One of the most prominent is the
Teton dam. Teton earth-fill dam was constructed on Teton river, Idaho with a geometry
of 93 m in height, 940 m in length, and 520 m in bottom width. After the construction of
the dam in November 1975, the reservoir started to be filled 30 cm per day. One month
later, the filling process was increased up to 1.2 m per day, due to the groundwater flow
being greater than expected (Perrow, 1984). When the reservoir was nearly full-on June
3 and 4, 1976, three minor leaks were seen on the dam's downstream side. A wet spot was
observed at the downstream side of the dam on June 5, 1976. Then, the downstream soil
material started to erode, while seepage discharges were measured at less than 1 m3 per
second. On the same day, the breach developed toward the upstream sides and a sudden
failure occurred with an estimated discharge of about 57,000 m3/s that resulted in the
sediment being reached more than 10 km from the dam location (No Finger in the Dike
Could Have Stopped It!, 2018). The failure resulted in up to $2 billion in losses (Reisner,
1993).
New Orleans levee failure (Sills et al., 2008), the Horse Creek Dam (Hinderlider,
1914), Davis Reservoir Dam (Justin, 1932), Lyman Dam (Babb, 1968), Baldwin Hills
Dam (Sharma et al., 2013), Tunbridge Dam (Fisher et al., 2017) and Sparmos Dam
(Tournier et al., 2019) are some known and documented dam failures.
Internal erosion is one of the major causes of dam failures and incidents,
accounting for 28% of earthen embankment failures (Costa, 1985).
Foster et al. (2000a) concluded that homogenous earth-fill dams built before 1900
tend to fail roughly ten times higher than dams built after 1950.
According to Chen et al (2019), piping was the cause of more than 30% of dam
failures that occurred between 1954 and 2018.

3
1.2. Problem Statement
As a result of being washed out of the soil by the effects of the groundwater,
voids are created in the dam body (Van Beek et al., 2015). Backward erosion causes the
soil particles to be transported out of the structure by forming a pipe or tunnel shape.
Backward erosion piping might occur because of cracks, soil properties, environmental
factors, and practical failures. Some studies show that initiation and progression may take
several days or weeks.
The parameters that cause piping are not yet fully understood due to the behavior
of the cohesive soil used in the dam body and many environmental factors. The
investigations are limited because the development of the piping mechanism is difficult
to visualize and its progress in the structure can not be accurately followed by
experimental and numerical studies.
Although there have been few studies, piping is one of the major reasons that
earthen dams fail. Since the initiation of piping cannot be parameterized individually, the
most dominant and complex factors are geotechnical and hydraulic parameters, such as
geometry and type of structure, erodibility of the soil, water level, compaction densities,
reservoir volume, particle size distribution, sample aspect ratio, friction coefficients,
hydraulic gradient, groundwater flow, permeability, void ratio, porosity, unit weights of
soil, cohesion, internal friction, specific gravity, and others.
The dominant factors governing the mechanism of erosion are influenced by
different geotechnical characteristics of the soil (Sharif, 2013). Cohesive soil mixtures
used in dam bodies consist of fine or very fine materials such as sand or clay and silt,
which play an important role in the behavior of piping and breach according to the
compaction rate and water content. Therefore, it is important to fully understand the
determination of geotechnical parameters to predict piping erosion mechanisms.
1.3. Research Objectives
Dam failures not only jeopardize public safety but also have the potential to cost
the economy millions of dollars. Dam failures not only affect the dam site but also have

4
the potential to degrade several other facilities, including roads, bridges, and water
systems.
The objective of this research is to conduct experiments at the Hydraulic Laboratory
of Izmir University of Economics (IEU) by generating piping via weak layers at two
different locations and dimensions of the homogenous earth-fill dams.
In addition, this research involves the realization of numerical analyses and the
comparison of the numerical results with experimental findings. The numerical analyses
were performed by using a commercial software, PLAXIS 3D by integrating a python
algorithm with the Jupyter console. The so-integrated python algorithm searches for the
hydraulic gradient within the dam body and compares it with the critical hydraulic
gradient (threshold). Once the hydraulic gradient reached the threshold, the breached soil
volumes were defined in that region by considering that the piping was initiated.
1.4. Dissertation Outline
In the scope of this thesis, The piping mechanism resulting in a breach in the
homogenous earth-fill dams is investigated by creating a weak zone at different locations.
This thesis is composed of 7 chapters in total.
In Chapter 1, the description of the earth-fill dams, their purposes, advantages, and
shortcomings are discussed. The problem definition was stated by giving historical cases
and statistical information about the dam failures due to piping.
The previous relevant studies are summarized in Chapter 2.
Chapter 3 contains the description of the experimental setup and the soil mechanics
tests performed before the piping experiments.
The different scenarios are presented in Chapter 4, together with construction and
experimental procedures.
Experimental findings are presented in Chapter 5.
Chapter 6 involves numerical investigations.
Conclusions and recommendations are given in Chapter 7.

5
CHAPTER 2
LITERATURE REVIEW
The literature reviews are composed of two sections. The first section focuses on
experimental studies on piping and its mechanism while the second focuses on numerical
studies on piping and breach mechanism initiation.
2.1. Experimental Studies
There has been a lot of research on dam failures, especially about overtopping.
However, because it is very challenging the monitoring the erosion and carry out
experiments, there have only been a few surveys on piping and breach mechanism:
(Khilar et al. 1985; Ojha et al. 2003; Okeke et al. 2012; Richards and Reddy 2012; Sharif
2013; Borragan 2014; Elkholy et al. 2015; Sharif et al. 2015b; Zhenzhen 2015; Chen et al.
2019; Shin et al. 2019; Al-Janabi et al. 2020; Ke and Takahashi, 2022).
Khilar et al. (1985) created a capillary model of plugging as a result of their
experimental observations to predict the piping in what conditions are likely to occur.
Ojha et al. (2003) developed an analytical model to estimate critical heads obtained
from their laboratory test. They found that the length of the structure, soil types, and fluid
properties affect the critical head.
Okeke et al. (2012) carried out twelve experiments on a homogenous dam by
triggering the piping by using a horizontal pipe with different lengths and positions. They
build a homogenous dam with a height ranging from 20 cm to 35 cm, a constant width of
45 cm, and various side slopes of 35⁰ to 45⁰ in a 5⁰ degree slope rectangular flume with
2 m long, 0.45 m high, and 0.45 m wide. They observed four failure processes in their
backward erosion piping experimental study, including forming a wet spot, continuation,
progression, and breach. Once erosion reached the downstream face, wet spot formation
was apparent to such an extent that pipe enlargement, progression, and breach occurred
consequently. They assumed that the erosion started when the wet spot appeared at the

6
downstream face of the dam (Figure 2.1 (a)). It took an early decrease in the water level
with the enlargement of the erosion due to piping (Figure 2.1 (b)). Water levels continue
to decrease during piping progress in terms of downstream slope angle, reservoir, and
dam volume (Figure 2.1 (c)). After the piping progression, the breach results in the
collapse of the roof of the dam. Consequently, the presence of the removal soil did not
allow enough water to flow through the dam, the water level increased (Figure 2.1 (d))
and the breach became its final form (Figure 2.1 (e)).
Figure 2.1. Piping failure processes resulted in a breach, a) initiation, b) continuation,
c) progression, d) the collapsing of the dam roof, e) final breach formation
(Okeke et al, 2012)
Richards and Reddy (2012) conducted experiments on field and laboratory mixed
soils in a new true-triaxial test apparatus to observe the factors influencing piping
initiation in non-cohesive and cohesive soils.
Sharif (2013) and Elkholy et al. (2015) used different compositions of mixture
which consists of sand, silt, and clay with various rates of compaction by constructing a
15 cm high dam in a laboratory flume to investigate the erosion process.
Borragan (2014) studied the failure mechanisms of an embankment dam to validate
the reliability of a risk analysis upon a dam breach.
In the research of Sharif et al. (2015b), the behavior of soil material changed during
internal erosion, and they stated that the characteristics of soil have a significant impact
on earth-fill dam failure, the proper compaction being the major component.

7
Zhenzhen (2015) defined backward erosion as the erosion induced by washing soil
particles out and she defined erosion as the erosion caused by a concentrated leak where a
pipe is formed due to a fracture, hollow, or void.
Chen et al. (2019) performed a sensitivity study on soil erodibility by different
initial pipe positions. They found that soil erodibility can have an impact on breach
evolution.
Shin et al. (2019) performed experiments by creating a weak zone in the middle of
the earthen dam model to characterize temporal changes in sub-surfaces via a sandbox.
Al-Janabi et al. (2020) investigated seepage through a homogenous earth-fill dam
with toe drains in different positions.
Ke and Takahashi (2022) performed a series of seepage tests on different soil
compositions, densities, and hydraulic gradients by executing the cone penetration test.
They found that the internal erosion affected the void ratio and the permeability resulting
in a decrease in soil strength.
2.2. Theoretical and Numerical Studies
Different numerical methods such as finite element methods (FEM), discrete
element methods (DEM), material point methods (MPM), finite difference methods
(FDM), and computational fluid dynamics (CFD) are used to investigate the piping
phenomenon:
Greco et al. (2008) simulated a 2D depth-averaged numerical model to investigate
breach evolution in an earthen dam.
Lachouette et al. (2008) performed a numerical analysis to show that the particle
concentration can be a significant factor at the beginning of the erosion process, resulting
in the enlargement of the hole at the exit.
Gattinoni and Francani (2009) considered the phenomenon of backward piping
evolution in the analysis of a slope, where for each simulation the corresponding
hydraulic gradient in the nearby area was increased.
Kermani and Barani (2012) used a five-point approximation technique and
compared it with the finite difference method.
Xu and Zhang (2013) used a physical-based numerical model for simulating piping
in earth dams due to concentrated leak erosion.

8
Vandenboer et al. (2014) demonstrated and discussed a numerical methodology
using the 3D finite element method for the groundwater flow that results in backward
erosion piping.
Athani et al. (2015) used finite element analysis to investigate the seepage and
stability with different withdrawal water level effects on the earth-fill dam to obtain the
water head levels within the dam body.
Sazzad et al. (2015); Aslan and Temel (2022) used both analytical and numerical
methods to analyze seepage discharge rates at different dam bodies.
Tao and Tao (2017) performed a numerical investigation to understand the factors
of the piping resistance by using both coupled computational fluid dynamics (CFD) and
the discrete element method (DEM). Additionally, they considered the equilibrium of a
soil column at various soil properties such as hydraulic critical states, soil specific gravity,
initial void ratio, particle size distribution, and friction coefficients, a concise model of
piping resistance.
Zhong et al. (2018) performed a numerical simulation to improve the prediction of
breach hydrograph and evaluate the breach morphology during the breaching
Chen et al. (2019) developed a numerical model by assuming the bottom, the top,
and the channel of the pipe are an arch, rectangular, and a semicircle.
Saliba et al. (2019) performed finite element analysis to observe the piping path in
steady conditions by using an iterative approach based on the simulated hydraulic
gradient exceeding or reaching the threshold value
Al-Janabi et al. (2020) performed a series of finite element analyses with different
types of toe drains to prevent seepage flow within both homogenous and clay-core earth-
fill dams.
Al-Mansori et al. (2020) performed a seepage analysis to determine the quantity of
seepage through the earth-fill dam by using the combination of the finite element method
and artificial neural network.
Li et al. (2021) performed a combination of discrete element method (DEM) and
computational fluid dynamics (CFD) analyses to investigate the longitudinal breach
process of landslide dams.
Ghonim et al. (2022) performed computational fluid dynamics analyses (CFD) to
investigate and compare the effects of initial artificial breach dimensions and locations
on the peak outflow through the earth-fill dam.

9
Foster and Fell (1999) described how soil erosion might happen through an
embankment, a foundation, or from an embankment to a foundation in earth structures,
notably in earth dams and levees. He defined the processes as initiation, continuation,
progression, and breach formation.
Bonelli (2013) described the four key mechanisms which initiate the backward
erosion piping in earth-fill dams: concentrated leak erosion, backward erosion, contact
erosion, and suffusion.
According to ICOLD (2017), suffusion can happen when seepage flow causes fine soil
particle movements through the pores of coarse soil particles, whereas contact erosion
happens when soil gradations come into contact and fine soils are washed away by the action
of the water to the coarse particles.
Insufficient compaction of soil, different settings in the dam body, seismic hazards,
and cracks caused by trees and animals also cause the piping (Hanson et al. 2010).

10
CHAPTER 3
SOIL MECHANICS TESTS AND EXPERIMENTAL SETUP
Before constructing the dam, soil mechanics tests were conducted. The ASTM
requirements were followed during the realization of the soil mechanics tests. The
required soil parameters were determined from specific weight tests, hydrometer
analyses, wet sieve analyses, permeability tests, direct shear tests, consolidation tests as
well as the standard proctor tests.
3.1. Soil Mechanics Tests
Mixture 1 consisted of 85 % (0-1 mm) sand-15 % clay while mixture 2 consisted
of 85 % (0-0.4 mm) sand-15 % clay. Figure 3.1 shows distributions of grain sizes for two
mixtures as determined by the wet sieve and hydrometer analyses.
Figure 3.1. The distributions of grain size of the mixtures
From Figure 3.1, for mixture 1, D10= 0.006 mm, D30= 0.075 mm, D50= 0.3 mm,
and D60= 0.4 mm. The coefficient of uniformity, Cu, and the coefficient of curvature, Cc,
are found to be 66.7 and 2.34, respectively.
0
20
40
60
80
100
0.00010.0010.010.11
Percent Passing (%)
Diameter (mm)
Mixture 1
Mixture 2

11
According to Figure 3.1, for mixture 2, D10= 0.078 mm, D30= 0.13 mm, D50= 0.17
mm, and D60= 0.21 mm. The coefficient of uniformity, Cu, and the coefficient of
curvature, Cc, are found to be 2.69 and 1.03, respectively.
From Figure 3.1, for mixture 1, D10= 0.006 mm, D30= 0.075 mm, D50= 0.3 mm,
and D60= 0.4 mm. The coefficient of uniformity, Cu, and the coefficient of curvature, Cc,
are found to be 66.7 and 2.34, respectively.
According to Figure 3.1, for mixture 2, D10= 0.078 mm, D30= 0.13 mm, D50= 0.17
mm, and D60= 0.21 mm. The coefficient of uniformity, Cu, and the coefficient of
curvature, Cc, are found to be 2.69 and 1.03, respectively.
The ASTM D854-14 test was applied to obtain the specific weights of the
mixtures, as Gs1= 2.63 and Gs2= 2.67.
In order to facilitate the piping process, the standard proctor test (ASTM-698) was
used, by reducing the applied energy by 50 % (13 blows instead of 25). The obtained
curves mixture 1 and mixture 2 are given in Figure 3.2 and Figure 3.3, respectively.
From Figure 3.2, the maximum dry density was found to be 1.79 g/cm3 at
wopt=12.5% for mixture 1.
From Figure 3.3, the maximum dry density was found to be 1.65 g/cm3 at
wopt=15.4% for mixture 2.
Figure 3.2. 13 blows proctor test curve for mixture 1
1.74
1.77
1.8
10.00 11.00 12.00 13.00 14.00 15.00
Dry Density (g/cm3)
Water Content (%)

12
Figure 3.3. 13 blows proctor test curve for mixture 2
The permeability was obtained from the falling head permeability test. The soil
parameters used in different experiments are given Table 3.1.
Table 3.1. The soil parameters used in different experiments
Experiment
Dry Density
(dry)
(g/cm3)
Water
Content
w(%)
Bulk density
󰇛 
󰇜
(g/cm3)
Void ratio
󰇛
󰇜
Permeability
(k)
(m/s)
First and Second
Experiments
1.79
12.5
2.0
0.47
4.66·10-7
Third Experiment
1.50
12.5
1.7
0.75
6.24·10-6
Fourth Experiment
1.79
12.5
2.0
0.49
1.18·10-6
Although the first two experiments were conducted by using mixture 1, the dam
heights differed from each other.
The third experiment was conducted with lower density, while the fourth
experiment was carried out by mixture 2.
The direct shear test was applied by satisfying the requirements of ASTM D3080,
and the so obtained internal friction angle (o) and cohesion (c’) parameters for different
conducted experiments are given in Table 3.2.
1.58
1.61
1.64
1.67
10% 12% 14% 16% 18% 20%
Dry Density (g/cm³)
Water Content (%)

13
Table 3.2. Direct shear test results
Experiment
Internal Friction Angle (o)
Cohesion (c’) kN/m2
First and Second Experiments
33.9
15.3
Third Experiment
28.4
12.8
Fourth Experiment
39.8
11.7
The consolidation test results by following ASTM D2435 standards are given in
Table 3.3.
Table 3.3. Consolidation test results
Experiment
Eodemetric
Modulus
(Eoed) kN/m2
Swelling
Index
(Cs)
Recompression
Index
(Cr)
Compression
Index
(Cc)
First and Second
Experiments
35,700
0.01
0.01
0.1
Third Experiment
26,700
0.02
0.03
0.18
Fourth Experiment
13,800
0.02
0.02
0.13
3.2. Experimental Setup
Experiments were conducted in the rectangular flume 1 m wide and consisting of
two channels. The dams are built in the upper channel, and the lower channel contains
the required water pumped by means of a centrifugal pump.
The upper channel is 5.44 m long, and 0.81 m high. A double honeycomb and a
mini tank were set to tranquil the water.
An electromagnetic sensor was placed to provide a constant water level.
Tempered glass of 2 cm thickness was used on the side walls.
The sinking pool and water tank are divided with a 0.6 m high obstacle to avoid
mixing the fresh water and collected sediment as much as possible.
The transmission line involves a pump, a check valve, a regulating valve, and a
magnetic flowmeter. The experimental setup is given in Figure 3.4.

14
(a)
(b) (c)
Figure 3.4. The experimental setup (a) schematic longitudinal view (b) Upper channel (c)
Transmission line

15
CHAPTER 4
EXPERIMENTAL PROCEDURE
4.1. Construction Procedure
Before preparing the dry mixture of the earth-fill dams, the soil mixture amounts
for each 10 cm layer were determined for different bulk densities considering the dam
heights.
The dry mixtures were mixed by using the concrete machine for 10 minutes to be
sure the sand and clay particles are mixed uniformly (Figure 4.1 (a)). Then the dry mixture
was poured into a wheelbarrow.
After adding 12.5 % water to the dry mixture, the wetted soil mixture was prepared
by using shovels so that any dry part does not exist (Figure 4.1 (b)).
The dam body was constructed by layers of 10 cm. Since the compaction of the
10 cm layers may bring up homogeneity problems, each layer was built in four sub-layers
of 2.5 cm thick.
After the construction of the first two sub-layers was completed, the 5x5 cm2 area
on the dam bottom center axis was dug up and the rock salt was poured to create the weak
zone (Figure 4.1 (b) and Figure 4.2 (c)).
The surfaces of the compacted sub-layers were scraped by means of a brush
(Figure 4.1 (e)).
The constructed third layer is given in Figure 4.1 (f). The construction of the
fourth layer is given in Figure 4.1 (g). The pouring and grinding procedure at the fifth
layer is given in Figure 4.1 (h). The compaction of the sixth layer is given in Figure 4.1
(i). The constructed dam body before trimming is given in Figure 4.1 (j).
The same construction procedures were followed for the middle-middle scenario.
After the construction of the first three layers, a 2x2 cm2 area was dug up along the dam
center axis at 28 cm above the bottom. Then the area was filled with rock salt and the
construction was continued. The final dams are 2 m in length, 1 m in width, and 0.6 m
and 0.65 m in height, respectively.

16
(a) (b)
(c) (d)
(e) (f)
Figure 4.1. The construction process (a) dry mixing, (b) preparation of soil mixture, (c)
creating the weak zone, (d) construction of the first 10 cm layer, (e) scraping
the second layer, (f) the constructed third layer, (g) construction in the fourth
layer, (h) pouring and grinding at the fifth layer, (i) compaction at the sixth
layer, (j) before the trimming
(cont. on next page)

17
(g) (h)
(i) (j)
Figure 4.1. (cont.)
Green spray paint was used for both sides to prevent the reservoir from appearing
turbidity.
While filling the reservoir, a trowel was placed at the exit of the weak zone, once
the reservoir reached the desired level the trowel was withdrawn, and experiments started.
4.2. Evaluation of the Experiments
The experiments were conducted in the laboratory of Izmir University of
Economics by using the soil mixture of 85% sand and 15% clay with different weak zone
scenarios in the rectangular flume 81 cm high, 614 cm long, and 100 cm wide. The
downstream and upstream slopes are the same at 1: vertical to 1.5: horizontal (Figure 3.4).
Six cameras placed at various locations monitored the progression of the breach.

18
An electromagnetic sensor was located in the channel to make start the pump
when the initial water level decreases by 1.5 cm.
The temporal breach discharges, the time-dependent flow velocities, time-varied
wetted areas, and temporal breach developments were calculated.
The temporal discharges through the breach were calculated by using the
continuity equation which is given in Equation (4.1).
∆S=(Qpump-Qbreach)∙∆t
(4.1)
where Qpump is the pump flow rate, Qbreach is the temporal breach discharges, ∆S is the
storage in the channel during the time interval ∆t.
The velocity V at the entrance and exit of the breach were approximately
calculated by using Equation 4.2.
V= Qbreach
A
(4.2)
where A denotes the wetted area at the entrance or exit of the breach.
The experimental findings were recorded by means of high-resolution cameras. To
obtain flatted recordings, the software Hitfilm Express v.2021.2 was used by selecting
suitable preset options and rotation in the z-direction for each recording until the real
boundaries fit the scale. Then, the flatted recording was used to obtain the changes in
channel water level.
The Get-Data Graph Digitizer 2.26 software was used to evaluate the breach areas
and wetted areas. The software can scale each recording by defining the dam boundaries
at both the upstream and downstream sides.
Gauss’s area Formulation was used to obtain the coordinates of the breach and its
wetted areas.
The cartesian coordinates of all vertices are required to use the formula for cross
multiplication (Figure 4.2).

19
Figure 4.2. n-sided polygons on Get-data Graph Digitizer 2.26
Gauss’s area formula also known as the Shoelace formula (Dahlke, 2017),
calculates the area of a polygon whose vertices are specified by their cartesian
coordinates. The formulation was described by Albrecht Ludwig Friedrich Meister in
1769 (Meister,1769) as follows:
The expressions of n-sided polygons area (x1, y1), (x2, y2), (x3, y3), …. (xn, yn) in
Gauss’s area formula is given in Equation 4.3.
󰇛󰇜
(4.3)
The formula can be written briefly,


 󰇛󰇜
(4.4)
or


 󰇛󰇜
(4.5)
where  is the number of the coordinates,  and  are abscissa and ordinate.

20
CHAPTER 5
EXPERIMENTAL FINDINGS
The experiments were performed with different high dams and various bulk
densities. The details of different experiments are given in Table 5.1. All the weak zones
consisted of rock salt.
Table 5.1. The details of different experiments
Experiment
Weak Zone
Dimensions
(cm2)
Mixture
Types
The bulk
density
(g/cm3)
Dam
Heights
(cm)
Water
Level
(cm)
Input
Discharge
(m3/h)
1
5x5
Mixture
1
2.0
60
55.5
9.0
2
5x5
Mixture
1
2.0
65
61
29.6
3
5x5
Mixture
1
1.7
65
61
6.2
4
2x2
Mixture
2
2.0
65
61
2.5
5.1. First Experiment
The final views of the constructed 60 cm high dam, the bulk density of 2 g/cm3, and
the weak zone of 5x5 cm2 located at the bottom are given in Figure 5.1.
After the dam was constructed, the reservoir was filled with water via the pump
until the electromagnetic sensor was activated at 55.5 cm.
Figures 5.2 shows the downstream temporal breach developments before the breach
appeared at the upstream face (until the time t=192 hours).

21
(a) (b)
(c) (d)
Figure 5.1. View of the dam from (a) upstream, (b) downstream, (c) side, (d) top
(a) (b)
(c) (d)
Figure 5.2. The downstream temporal breach developments a) t=0 h, b) t=24 h, c) t= 48
h, d) t= 192 h

22
With the removal of the eroded soil material from the dam boundary, the surface
area of the breach did not change significantly, but it gained length backward.
When t=193 h, it was seen that the exit of the breach was filled again with the
eroded soil material coming from inside (Figure 5.3 (a)). The length of the breach was
measured at 26 cm.
When t=194 h, with the removal of the eroded soil material, it was observed that
the surface area of the breach was not changed, and the length of the pipe was measured
as 34 cm (Figure 5.3 (b)).
(a) (b)
Figure 5.3. Downstream breach surfaces at (a) t=193 h (b) t=194 h
When t=196 h, although there was not significant eroded soil material, the
material coming from the breach was piled on top of each other (Figure 5.4).
(a) (b)
Figure 5.4. Downstream breach surfaces at t=196 h (a) downstream view, (b) close-up
view of the breach

23
A slight increase in the length of the breach was observed as shown in Figure 5.4
(a), while the change in the surface area was limited. The close-up view of the breach is
given in Figure 5.4 (b). The length of the breach was measured as 39 cm.
When t =208 h, the eroded soil material accumulated in front of the dam continued
to be removed without disturbing the breach. The breach length was measured by a laser
meter, and it became 65 cm. The view of the breach at t=208 h is given in Figure 5.5.
(a) (b)
Figure 5.5. Downstream breach surfaces at t=208 h (a) downstream view, (b) close-up
view of the breach
At t=216 h, not a significant change in the breach area was observed. The breach
length was measured as 91 cm. Downstream views of the breach are given in Figure 5.6.
(a) (b) (c)
Figure 5.6. Downstream breach surfaces at t= 216 h (a) downstream view, (b) close-up
view of the breach (c) eroded and transported soil materials due to the seepage

24
At t=230 h (12 minutes before the breach reached the upstream face), although
there was not a significant difference in the breach surface area, the seepage discharge
was measured as 6.3 cm3/s. The length of the breach was measured as 119.9 cm.
12 minutes later, the breach reached the upstream side of the dam as shown in
Figure 5.7.
The time-dependent discharge values corresponding to the interval at which the
breach reached the upstream face are given in Figure 5.8.
(a) (b)
Figure 5.7. The breach developments at t= 230 h (a) downstream, (b) upstream
Figure 5.8. The seepage discharges before the breach did not reach the upstream face.
The breach views corresponding to different times are given from Figure 5.9 to
Figure 5.11. The time t=0 represents when the breach appeared upstream.
0
2
4
6
8
0 30 60 90 120 150 180 210 240
Seepage discharge
(cm3/s)
Time (h)

25
(a) (b)
(c) (d)
(e) (f)
Figure 5.9. The breach views from downstream (a) t=0 s, (b) t=5 s, (c) t=10 s, (d) t=20
s, (e) t=50 s, (f) t=315 s

26
(a) (b)
(c) (d)
(e) (f)
Figure 5.10. The breach views from upstream (a) t=0 s, (b) t=5 s, (c) t=10 s, (d) t=20 s,
(e) t=50 s, (f) t=315 s

27
(a) (b)
(c) (d)
(e) (f)
Figure 5.11. The breach views from top (a) t=0 s, (b) t=5 s, (c) t=10 s, (d) t=20 s, (e) t=50
s, (f) t=315 s

28
The temporal changes in water depth during the experiment are shown in Figure
5.12
Figure 5.12. Temporal changes in water depths in the channel
The temporal breach developments at both sides are given together in Figure 5.13.
Figure 5.13. The upstream and downstream temporal breach developments
The temporal variations of the breach-wetted areas at upstream and downstream are
shown in Figure 5.14.
0
15
30
45
60
0 50 100 150 200 250 300 350
Water Depth (cm)
Time (s)
0
700
1400
2100
2800
0 50 100 150 200 250 300 350
Breach Area (cm²)
Time (s)
Upstream Downstream

29
Figure 5.14. The upstream and downstream temporal variations of the breach-wetted
areas
The temporal breach discharges calculated from Equation (4.1) are presented in
Figure 5.15.
Figure 5.15. Temporal breach discharges
The time-varied upstream and downstream breach velocities, calculated by using
Equation 4.2, are shown in Figure 5.16.
0
150
300
450
600
0 50 100 150 200 250 300 350
Breach-wetted Area (cm2)
Time (s)
Upstream Downstream
0
10
20
30
40
0 50 100 150 200 250 300 350
Breach Discharge (L/s)
Time (s)

30
Figure 5.16. The time-varied upstream and downstream breach velocities
5.2. Second Experiment
The final views of the second experiment are given in Figure 5.17.
(a) (b)
(c) (d)
Figure 5.17. The final views of the second experiment, (a) upstream, (b) downstream, (c)
left side, (d) top side
0
40
80
120
160
0 50 100 150 200 250 300 350
Velocity (cm/s)
Time (s)
Upstream Downstream

31
The breach views from the downstream and top are given in Figure 5.18 and Figure
5.19 for the downstream and top sides, separately. The time t=0 s represents the seepage
initiation.
(a) (b)
(c) (d)
(e) (f)
Figure 5.18. The breach views from downstream (a) t=0 h, (b) t=1.1 h, (c) t=2 h, (d) t=3
h, (e) t=4 h, (f) t=4.8 h

32
(a) (b)
(c) (d)
(e) (f)
Figure 5.19. The breach views from the top (a) t=0 h, (b) t=1.1 h, (c) t=2 h, (d) t=3 h, (e)
t=4 h, (f) t=4.8 h
The breach views corresponding to different times are given from Figure 5.20 to
Figure 5.22. The time t=0 represents when the breach appeared upstream side.

33
(a) (b)
(c) (d)
(e) (f)
Figure 5.20. The breach views from downstream a) t=0 s, b) t=20 s, c) t=60 s, d) t=80 s,
e) t=120 s, f) t=150 s

34
(a) (b)
(c) (d)
(e) (f)
Figure 5.21. The breach views from upstream a) t=0 s, b) t=20 s, c) t=60 s, d) t=80 s, e)
t=120 s, f) t=150 s

35
(a) (b)
(c) (d)
(e) (f)
Figure 5.22. The breach views from top a) t=0 s, b) t=20 s, c) t=60 s, d) t=80 s, e) t=120
s, f) t=150 s

36
The temporal changes in water depth during the experiment are shown in Figure
5.23.
Figure 5.23. Temporal changes in water depths in the channel
The temporal breach developments at both sides are given together in Figure 5.24.
Figure 5.24. The upstream and downstream temporal breach developments
The temporal variations of the breach-wetted areas at upstream and downstream are
shown in Figure 5.25.
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120 140 160
Water Depth (cm)
Time (s)
0
1500
3000
4500
6000
020 40 60 80 100 120 140 160
Breach Area (cm2)
Time (s)
Upstream Downstream

37
Figure 5.25. The upstream and downstream temporal variations of the breach-wetted
areas
The temporal breach discharges calculated from Equation (4.1) are presented in
Figure 5.26.
Figure 5.26.Temporal breach discharges
The time-varied upstream and downstream breach velocities, calculated by using
Equation 4.2 are shown in Figure 5.27.
0
60
120
180
240
020 40 60 80 100 120 140 160
Breach-wetted Area (cm2)
Time (s)
Upstream Downstream
0
10
20
30
40
50
020 40 60 80 100 120 140 160
Discharge (L/s)
Time (s)

38
Figure 5.27. The time-varied upstream and downstream breach velocities
5.3. Third Experiment
In the third scenario, the dam height was 65 cm, and the water level was 61 cm. The
bulk density, bulk, is 1.7 g/cm3. The final view of the third experiment is given in Figure
5.28.
Figure 5.28. The final view of the dam
The breach views from downstream and top corresponding to different times are
given in Figure 5.29 and Figure 5.30, respectively. The time t=0 represents when the
breach appeared upstream.
0
60
120
180
240
0 20 40 60 80 100 120 140 160
Velocity (cm/s)
Time (s)
Upstream Downstream

39
(a) (b)
(c) (d)
(e) (f)
Figure 5.29. The breach views from downstream a) t=0 s, b) t=50 s, c) t=1710 s, d) t=2230
s, e) t=2410 s, f) t=2485 s

40
(a) (b)
(c) (d)
(e) (f)
Figure 5.30. The breach views from top a) t=0 s, b) t=50 s, c) t=1710 s, d) t=2230 s, e)
t=2410 s, f) t=2485 s
At the time t=0, the seepage started from the weak area and turned into a breach,
then reached the upstream side in less than 1 hour. For the evaluation of the experimental
findings, when the breach reached the upstream was taken t=0 s. The breach views

41
corresponding to different times are given from Figure 5.31 to Figure 5.33. The time t=0
represents when the breach appeared upstream.
(a) (b)
(c) (d)
(e) (f)
Figure 5.31. The breach views from downstream a) t=0 s, b) t=10 s, c) t=30 s, d) t=40 s,
e) t=60 s, f) t=150 s

42
(a) (b)
(c) (d)
(e) (f)
Figure 5.32. The breach views from upstream a) t=0 s, b) t=10 s, c) t=30 s, d) t=40 s, e)
t=60 s, f) t=150 s

43
(a) (b)
(c) (d)
(e) (f)
Figure 5.33. The breach views from top a) t=0 s, b) t=10 s, c) t=30 s, d) t=40 s, e) t=60 s,
f) t=150 s

44
The temporal changes in water depth during the experiment are shown in Figure
5.34.
Figure 5.34. Temporal changes in water depths in the channel
The upstream temporal breach developments are given in Figure 5.35.
Figure 5.35. The upstream temporal breach developments
The upstream temporal variations of the breach-wetted areas are presented in Figure
5.36
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120 140 160
Water Level (cm)
Time (s)
0
1200
2400
3600
4800
0 20 40 60 80 100 120 140 160
Breach Area (cm2)
Time (s)

45
Figure 5.36. The upstream temporal variations of the breach-wetted areas
The temporal breach discharges calculated from Equation (4.1) are presented in
Figure 5.37.
Figure 5.37. Temporal breach discharges
The time-varied upstream and downstream breach velocities, calculated by using
Equation 4.2, are shown in Figure 5.38.
0
60
120
180
240
0 20 40 60 80 100 120 140 160
Breach-wetted Area (cm2)
Time (s)
0
8
16
24
32
0 20 40 60 80 100 120 140 160
Discharge (L/s)
Time (s)

46
Figure 5.38. The time-varied upstream breach velocities
5.4. Fourth Experiment
In the fourth experiment, the dam high was 65 cm, and the water level was 61 cm.
The bulk density, bulk, is 2 g/cm3. The dam was constructed by mixture 2 and created
2x2 cm2 weak layer at 28 cm above the bottom. The final views are given in Figure 5.39.
(a) (b)
Figure 5.39. The final view of the dam from (a) top (b) downstream
The breach views corresponding to different times are given from Figure 5.40 to
Figure 5.46. The time t=0 represents when the breach appeared upstream.
0
35
70
105
140
0 20 40 60 80 100 120 140 160
Velocity (cm/s)
Time (s)

47
(a) (b)
(c) (d)
Figure 5.40. The breach views at t=0 s a) upstream of the first dam, b) upstream of the
second dam, c) downstream of the first dam, d) downstream of the second
dam

48
(a) (b)
(c) (d)
Figure 5.41. The breach views at t=15 s a) upstream of the first dam, b) upstream of the
second dam, c) downstream of the first dam, d) downstream of the second
dam

49
(a) (b)
(c) (d)
Figure 5.42. The breach views at t=25 s a) upstream of the first dam, b) upstream of the
second dam, c) downstream of the first dam, d) downstream of the second
dam

50
(a) (b)
(c) (d)
Figure 5.43. The breach views at t=40 s a) upstream of the first dam, b) upstream of the
second dam, c) downstream of the first dam, d) downstream of the second
dam

51
(a) (b)
(c) (d)
Figure 5.44. The breach views at t=60 s a) upstream of the first dam, b) upstream of the
second dam, c) downstream of the first dam, d) downstream of the second
dam

52
(a) (b)
(c) (d)
Figure 5.45. The breach views at t=90 s a) upstream of the first dam, b) upstream of the
second dam, c) downstream of the first dam, d) downstream of the second
dam

53
(a) (b)
(c) (d)
Figure 5.46. The breach views at t=134 s a) upstream of the first dam, b) upstream of the
second dam, c) downstream of the first dam, d) downstream of the second
dam

54
The temporal changes in water depth during the experiment are shown in Figure
5.47.
Figure 5.47. Temporal changes in water depths in the channel
The temporal breach developments at downstream and upstream sides together with
the first and second experiment are given in Figure 5.48 and Figure 5.49, respectively.
The temporal variations of the breach-wetted areas at downstream and upstream
are shown in Figure 5.50 and Figure 5.51, respectively.
Figure 5.48. The downstream temporal breach developments
0
10
20
30
40
50
60
70
0 30 60 90 120 150
Water Depths (cm)
Time (s)
First Experiment Second Experiment
0
600
1200
1800
2400
0 20 40 60 80 100 120 140 160
Breach Area (cm2)
Time (s)
First Experiment Second Experiment

55
Figure 5.49. The upstream temporal breach developments
Figure 5.50. The temporal variations of the breach-wetted areas at downstream
0
400
800
1200
1600
0 20 40 60 80 100 120 140 160
Breach Area (cm2)
Time (s)
First Experiment Second Experiment
0
50
100
150
200
0 20 40 60 80 100 120 140 160
Breach-wetted Area (cm2)
Time (s)
First Experiment Second Experiment

56
Figure 5.51. The temporal variations of the breach-wetted areas at upstream
The temporal breach discharges calculated from Equation (4.1) are presented in
Figure 5.52.
Figure 5.52. Temporal breach discharges
0
50
100
150
200
250
0 20 40 60 80 100 120 140 160
Breach-wetted area (cm²)
Time (s)
First Experiment Second Experiment
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120 140 160
Discharge (L/s)
Time (s)
First Experiment Second Experiment

57
The time-varied downstream and upstream breach velocities, calculated by using
Equation 4.2, are shown in Figure 5.53 and Figure 5.54, respectively.
Figure 5.53. The time-varied downstream breach velocities
Figure 5.54. The time-varied upstream breach velocities
0
50
100
150
200
0 20 40 60 80 100 120 140 160
Velocity (cm/s)
Time (s)
First Experiment Second Experiment
0
80
160
240
320
0 20 40 60 80 100 120 140 160
Velocity (cm/s)
Time (s)
First Experiment Second Experiment

58
5.5. The compaction density effects
The experiments were conducted in the Izmir University of Economics laboratory
by using mixture 1. For investigating the compaction density effect on the piping
mechanism, the second and the third scenarios were compared to each other for the first
t=37 s. Both dams have the same geometry, 65 cm height, and the same reservoir level,
61 cm. The second experiment (Chapter 6.2) was constructed with 26 proctor hammer
blows to obtain a 2.5 cm sub-layer by providing the bulk density, bulk, 2.0 g/cm3 (higher
density) while the third experiment (Chapter 6.3) was conducted with 9 proctor hammer
blows to obtain a 2.5 cm sub-layer by, bulk, 1.7 g/cm3 (lower density) after pouring the
soil material in the same volume.
Each dam has a 5x5 cm2 weak zone which consists of rock salt along the dam axis.
The slopes of the downstream and upstream of the scenarios are 1 vertical to 1.5
horizontal. Once the water reached the desired levels, the experiments were started.
The experiments were conducted by arranging the input discharges of 29.6 m3/h for
the higher-density dam body, and 6.2 m3/h for the lower-density dam body.
The temporal changes in water depths in the channel together with lower and higher
density dams during the experiments are shown in Figure 5.55.
Figure 5.55. Temporal changes in water depths in the channel together with lower and
higher density dams
0
10
20
30
40
50
60
70
0 5 10 15 20 25 30 35 40
Water Depths (cm)
Time (s)
Lower density Higher density

59
The temporal breach developments at upstream together with the lower density and
higher density dams are given in Figure 5.56.
Figure 5.56. The temporal breach developments at upstream together with the lower
density and higher density dams
The temporal variations of the breach-wetted areas at upstream together with the
lower density and higher density dams are given in Figure 5.57.
Figure 5.57. The temporal variations of the breach-wetted areas at upstream together
with the lower density and higher density dams
0
1000
2000
3000
4000
5000
0 5 10 15 20 25 30 35 40
Breach Area (cm2)
Time (s)
Lower density Higher density
0
50
100
150
200
250
0 5 10 15 20 25 30 35 40
Breach- wetted Area (cm2)
Time (s)
Lower density Higher density

60
The temporal breach discharges calculated from Equation (4.1) together with the
lower density and higher density dams are presented in Figure 5.58.
Figure 5.58. The temporal breach discharges together with the lower density and higher
density dams
The time-varied upstream breach velocities, calculated by using Equation 4.2,
together with the lower density and higher density dams are presented in Figure 5.59.
Figure 5.59. The time-varied upstream breach velocities together with the lower
density and higher density dams
0
10
20
30
40
0 5 10 15 20 25 30 35 40
Discharge (L/s)
Time (s)
Lower density Higher density
0
60
120
180
240
0 5 10 15 20 25 30 35 40
Velocity (cm/s)
Time (s)
Lower density Higher density

61
5.6. Results and Discussions
The experimental findings are commented on by taking into consideration the
values corresponding to the interval where the initial water level decreased at most 10 %
(t10%). The so-obtained comparative results are given in Table 5.2. In this table,
Areadown10% and Areaup10% are the areas at downstream and upstream sides, respectively.
Wetdown10% and Wetup10% denote the wetted areas at downstream and upstream sides,
respectively. Q10% represents the flow rate through the breach. The velocities at
downstream and upstream are denoted by Velocitydown10% and Velocityup10%, respectively.
Table 5.2. The so-obtained comparative results for at most 10 %
Findings
Experiment
1
2
3
4
t10% (s)
19
37
37
33
Areadown10% (cm2)
721
2711
-
1890
Areaup10% (cm2)
365
452
1370
88.9
Wetdown10% (cm2)
398
165
-
174
Wetup10% (cm2)
365
183
233
88.9
Discharge10% (L/s)
28.6
28.3
28.8
24.2
Velocitydown10% (cm/s)
72
170
-
127
Velocityup10% (cm/s)
78
155
124
248
The flow rates values corresponding to the times t=10 s, t=20 s, and t=30 s are given
in Table 5.3
Table 5.3. The temporal discharges for different time intervals
Discharge (L/s)
Experiment
1
2
3
4
Q10
12.5
1.7
1.7
2
Q20
25.2
8.8
6.24
7.2
Q30
30.5
21.8
22.6
19

62
The downstream and upstream breach areas corresponding to the times, t=10 s,
t=20 s, and t=30 s are given in Table 5.4 and Table 5.5, respectively.
Table 5.4. The temporal breach developments at downstream for different time intervals
Downstream Breach Area
(cm2)
Experiment
1
2
3
4
Adown-10
551
1453
-
322
Adown-20
721
2145
-
1120
Adown-30
871
2406
-
1744
Table 5.5. The temporal breach developments at upstream for different time intervals
Upstream Breach Area
(cm2)
Experiment
1
2
3
4
Aup-10
144
58
118
27
Aup-20
365
148
553
54
Aup-30
753
290
703
81
The temporal variations of downstream and upstream breach-wetted areas
corresponding to the times, t=10 s, t=20 s, and t=30 s are presented in Table 5.6 and Table
5.7, respectively.
Table 5.6. The temporal variations of downstream breach-wetted areas for different time
intervals
Downstream Breach-wetted Area
(cm2)
Experiment
1
2
3
4
Wetteddownstream-10
242
124
-
60
Wetteddownstream-20
462
135
-
125
Wetteddownstream-30
441
152
-
152

63
Table 5.7. The temporal variations of upstream breach-wetted areas for different time
intervals
Upstream Breach-wetted Area
(cm2)
Experiment
1
2
3
4
Wettedıupstream-10
144
32
29
27
Wettedıupstream-20
365
99
82
54
Wettedıupstream-30
451
146
207
81
The time-varied of downstream and upstream breach velocities corresponding to
the times, t=10 s, t=20 s, and t=30 s are given in Table 5.6 and Table 5.7.
Table 5.8. The time-varied downstream breach velocities for different time intervals
Downstream
Velocity (cm/s)
Experiment
1
2
3
4
Vdown-10
52
14
-
34
Vdown-20
58
64
-
57
Vdown-30
64
143
-
152
Table 5.9. The time-varied upstream breach velocities for different time intervals
Upstream Velocity
(cm/s)
Experiment
1
2
3
4
Vup-10
87
54
58
75
Vup-20
69
86
76
151
Vup30
68
149
108
226
The time interval corresponding to the decrease of the initial water by 10% was
found to be nearly the same for the last three experiments, this time being nearly twice
that of the first experiment.
The flow rates are found to be nearly equal.
In all experiments, the downstream areas were found to be greater than the
upstream ones.

64
The orders of magnitude of the wetted areas were found to be similar for the dams
of heigh 60 cm and 65 cm.
The temporal changes of downstream breach areas are likely linear.
The breach areas at upstream were influenced significantly by the compaction
density, the compaction decreasing the breach areas.
It was revealed, the increase of the dam height and consequently the water head
resulted in increase of the breach areas at downstream and upstream sides.
The wetted areas were found to be larger in the dam 60 cm high compared to those
corresponding to the dam 65 cm high.
,

65
CHAPTER 6
3D FINITE ELEMENT ANALYSIS OF BREACHING OF
HOMOGENOUS EARTH-FILL DAMS
Numerical simulations were performed using PLAXIS 3D to compare with the
experimental findings.
The seepage forces can cause transportation according to the value of the hydraulic
gradient, , defined in Darcy’s equation (V=k·).
The critical hydraulic gradient, ,
which causes the erosion is given in Equation 6.1.
󰇛󰇜󰇛󰇜

(6.1)
where  is the saturated unit weight,  is the unit weight of water, and  denotes the
porosity.
6.1. Finite Element Method
6.1.1. Methodology
During the numerical analyses, after completing the dam geometry, mesh
generation was accomplished by selecting as 0.4 for the relative element size and 0.4635
m for element dimension. Enhanced mesh options were utilized by arranging the global
scale factor to 0.5 and the minimum element size factor to 5·10-6 m.
The surface groundwater flow boundary condition (Surface GWFlowBC) was
defined. The behavior was set as head option then the reference level was described as
initial water level.

66
The general subtree in the staged construction tab was arranged to represent the
experiment conditions. The water levels were arranged in steady-state calculation types
when the levels remain unchanged. The fully coupled flow deformations option was used
when the change in the water level occurred. For the simulations in time-dependent flow
conditions, the temporal changes in water level in each scenario were transferred to the
PLAXIS 3D as a table by assigning flow functions.
The flows within the dam body were obtained as a result of the simulations. To
obtain the average velocity values, the relevant soil numbers at the upstream and
downstream sides of the breach were considered. The values and corresponding soil
numbers were reached as a table sheet in the output file.
The wetted areas were considered as flow distributions at the breach upstream and
downstream sides and calculated by using Gauss’s area method. The surface areas are
calculated when hydraulic gradient values reach or exceed the threshold value at the dam.
Discharges at different time intervals are calculated by considering the wetted
areas and the average velocity at the downstream and upstream sides of the breach. They
calculated from Equation 4.2. The discharges are calculated for both downstream and
upstream sides and the average values were determined. Since the bottom and the lateral
sides of the dams were impermeable, the boundary conditions were selected as closed.
Consequently, the boundary conditions were Zmin=Closed, Zmax=Open, Ymin=Ymax=
Closed, and Xmin=Xmax= Open. The representation of wetted areas together with the
phreatic level is given in Figure 6.1.
Figure 6.1. The representation of wetted area together with phreatic surface

67
The Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), given in
following equations, were used to evaluate the compatibility between experimental and
numerical studies.




(6.2)




(6.3)
where  is the number of data.
6.1.2. The Soil Properties
For the simulations, it is essential to define soil properties in each soil volume.
The dam soil properties have been obtained from the soil mechanics tests (see Chapter
3.1). Since air parameters can not be defined, an estimation was performed to describe
the properties of the weak zones such as hole or rock salt.
The H.S. Model-Undrained A model was used for the dam soil properties while
the H.S. model-Undrained B model was chosen for the weak and breached zones model
types.
The initial void ratio of the breach volume was selected as 0.9. Since the hole was
considered as the filled by the air, the unsaturated (ϒunsat-weak) was taken as air density.
When the hole was filled with water, the saturated unit weight (ϒsat-weak) was taken
because of considering filled by the water. The undrained shear strength (Su-weak) value
was taken as 0.1 kN/m2 to avoid numerical errors.
The oedometric modulus of deformation (Eoed) was obtained according to the
consolidation test. As average values for various soil types, Eur = 3·E50 and Eoed = E50 are
suggested as default settings. (PLAXIS user manual, 2022).
The permeability coefficients in the breach were calibrated according to the first
velocity measurement at the breach downstream. The permeability of the rock salt was

68
calibrated according to the first seepage discharge. When the erosion existed, the second
calibration was performed to satisfy the next seepage discharge measurement. When the
breached soil reached the upstream face, the third calibration was made to adjust the
downstream velocity at the experiment.
The soil properties used in the numerical analyses are given in Table 6.1.
Table 6.1. The soil properties used in the finite element analyses
6.1.3. Modelling of Piping Evolution
The critical hydraulic gradients,  for mixture 1 and mixture 2 were calculated
from Equation 3.1 and found to be 0.76 and 0.74, respectively.
The locations where is> icr were determined by means of a 3D python algorithm
integrated with the Jupyter console after the manual calculation at time t=0. If the
simulated hydraulic gradient reaches or exceeds the critical hydraulic threshold (), then
localized piping is initiated and developed in these locations (Saliba et al., 2019).
The dam geometries were defined as 2 m in length, 0.6 m or 0.65 m in height, and
1 m in width. After setting the boundary and initial conditions, the first simulation is
started manually, then the python algorithm takes over the analysis. After the
determination of the coordinates of the region where is= icr, x coordinates are sorted by
number starting from the downstream side with different intervals, dx, ranging from 5 to
10 cm. They were denoted by Xa, Xb, Xc… (Xa>Xb). Afterward, the y and z coordinates
at each corresponding x coordinate are sorted to create surfaces.
Middle breach
Upper-middle Upper-corner Breach zone Breach zone Rocksalt
Material
Drainage type
ϒunsat (kN/m3)1
ϒsat (kN/m3)
einit 0.469 0.488
E50, ref (kN/m2) 35,714 13,810
Eoed, ref (kN/m2) 35,714 13,810
Eur, ref (kN/m2) 107,142 41,430
c' (kN/m2)15.33 11.68
 (⁰) 33.9 39.84
Su (kN/m2) - -
k (m/s)
4.70·10-7 1.18·10-6 0.47 0.32 1 0.054/1.1 0.022
UND-A
20
21.2
Input
Mixture 1
Mixture 2
1000
1000
0.9
10
0.012
Hardening Soil
UND-B
0.1
-
-
3000
Upper breach
Bottom breach

69
Surfaces are created from the starting point (Ymin, Zmax) to the endpoint (Ymax,
Zmax) in the counterclockwise direction to cover the higher hydraulic gradient values by
obtaining Ymax and Ymin values at Zmin and Zmax and vice versa, respectively.
The simple and not scaled representation of the creation of breach surfaces is
given in Figure 6.2.
.
Figure 6.2. Not scaled representation of the creation of breach surfaces
The so obtained surfaces were linked to each other by extruding them in the x
direction via the intersection and re-cluster command to create the breached soil volume.
Since the created breached soil volumes have complex geometry, sometimes small or
external distances appeared in the intersection zone. In such cases, “check the geometry”
command was used to detect their locations. To do so, the locations partitioned with a
closed box for isolating each partition to mesh generation (Error When Generating 3D
Mesh - GeoStudio | PLAXIS Wiki - GeoStudio | PLAXIS - Bentley Communities, 2019b,
accessed on December 4th, 2022). After the definition of the soil parameters into the
breached soil volumes, the mesh generation was accomplished for the next time steps and
the input files were saved.
The flow chart corresponding to the python algorithm is given in Figure 6.3. For
the continuation of the simulation at new time steps, the initial flow boundary conditions
were set. Therefore, the python algorithm completes the loops until the criteria was no
longer satisfied.

70
Figure 6.3. Flow chart of the applied 3D python algorithm

71
6.2. Numerical Simulation of the Experimented Dams
6.2.1. Numerical analysis corresponding to the first experiment
The details of the experiment are given in Chapter 5.1. The final geometry of the
dam corresponding to the first experiment is given in Figure 6.4. The red color represents
the weak zone.
Figure 6.4. The final geometry of the first experiment
6.2.1.1. When the breach was not reached the upstream face
The experimental and numerical seepage discharges are given in Figure 6.5.
Figure 6.5. Experimental and numerical seepage discharges before the breach reached
upstream face
0
2
4
6
8
0 35 70 105 140 175 210 245 280
Seepage discharge
(cm3/s)
Time (h)
Experimental Numerical

72
The longitudinal views of the hydraulic gradient distributions together with cross
sections when the breach did not reach the upstream are given in Figure 6.6.
(a)
(b)
Figure 6.6. Hydraulic gradient distribution along the dam before the breach did not reach
the upstream face for a) 0 days, b) 4 days
(cont. on next page)

73
(c)
(d)
Figure 6.6. (cont.)

74
The numerical simulation was performed by considering the temporal changes in
the water level in Figure 5.12 and defined as time-dependent flow conditions in fully
coupled flow deformations.
6.2.1.2. When the breach reached the upstream face
When the breach reached the upstream side, the longitudinal hydraulic gradient
distributions in color scale with maximum and minimum values are given in Figure 6.7.
(a)
(b)
Figure 6.7. Hydraulic gradient distribution along the dam after the breach reached the
upstream face for (a) 10 s (b) 20 (c) 30 s (d) 120
(cont. on next page)

75
(c)
(d)
Figure 6.7. (cont.)

76
The flow through the breach together with upstream and downstream average
values are given in Figure 6.8.
(a)
(b)
(c)
Figure 6.8. Flow distributions along the dam for a) 10 s (b) 20 s (c) 30 s (d) 120 s
(cont. on next page)

77
Figure 6.8. (cont.)
The downstream and upstream temporal breach developments in the experiment
together with those obtained from the numerical analysis are given in Figure 6.9 and
Figure 6.10, respectively. The time t=0 s indicates the initiation of seepage.
(a)
(b)
(c)
Figure 6.9. The downstream temporal breach developments a) 0 s, b) 10 s, c) 120 s

78
(a)
(b)
(c)
(d)
Figure 6.10. The upstream temporal breach developments a) 0 s, b) 10, c) 30 s, d) 120 s
The experimental and numerical temporal breach developments are presented in
Figure 6.11 and Figure 6.12 for downstream and upstream, respectively.
The experimental and numerical time-varied breach velocities are presented in
Figure 6.13 and Figure 6.14 for downstream and upstream, respectively.

79
Figure 6.11. The downstream temporal breach developments together with experimental
and numerical
Figure 6.12. The upstream temporal breach developments together with experimental and
numerical
Figure 6.13. The time-varied downstream breach velocities together with experimental
and numerical
0
200
400
600
800
1000
1200
020 40 60 80 100 120 140
Surface Area (cm2)
Time (s)
Experimental Numerical
0
500
1000
1500
2000
2500
3000
0 20 40 60 80 100 120 140
Surface Area (cm2)
Time (s)
Experimental Numerical
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Velocity (cm/s)
Time (s)
Experimental Numerical

80
Figure 6.14. The time-varied upstream breach velocities together with experimental and
numerical
The temporal variations of wetted areas for downstream and upstream together
with experimental and numerical are given in Figure 6.15 and Figure 6.16, respectively.
Figure 6.15. The temporal changes in downstream breach-wetted areas together with
experimental and numerical
Figure 6.16. The temporal changes in upstream breach-wetted areas together with
experimental and numerical
0
35
70
105
140
0 20 40 60 80 100 120 140
Velocity (cm/s)
Time (s)
Experimental Numerical
0
100
200
300
400
500
600
0 20 40 60 80 100 120 140
Wetted Area (cm2)
Time (s)
Experimental Numerical
0
100
200
300
400
500
600
0 20 40 60 80 100 120 140
Wetted Area (cm2)
Time (s)
Experimental Numerical

81
The calculated temporal discharge values together with experimental and numerical
are given in Figure 6.17.
Figure 6.17. The temporal discharge values together with experimental and numerical
The calculated RMSE and MAE values to evaluate each error for each station are
given in Table 6.2.
Table 6.2. RMSE and MAE values for each finding at the bottom-middle scenario
Findings
Unit
Root Mean Square Error
(RMSE)
Mean Absolute Error
(MAE)
Vdownstream
(cm/s)
6.3
4.3
9.8
84.3
107.1
236.3
330.1
Vupstream
(cm/s)
13.8
Wetteddownstream
(cm2)
101.8
Wettedupstream
(cm2)
127.3
238.9
398.9
Surfacedownstream
(cm2)
Surfaceupstream
(cm2)
Discharge
(L/s)
4.6
3.1
The RMSE and MAE values are calculated for each finding. For the middle-bottom
part, RMSE and MAE values of the average value are calculated as 18.3% and 12.7% for
Vdownstream, 32.8% and 23.3% for Vupstream, 37.1% and 30.1% for Wetteddownstream, 54.6%
and 45.9% for Wettedupstream, 27.5% and 27.2% for Surfacedownstream, 30.8% and 25.5% for
Surfaceupstream, 35.4% and 23.3% for discharge, respectively.
0
10
20
30
40
020 40 60 80 100 120 140
Discharge (L/s)
Time (s)
Experimental Numerical

82
6.2.2. Numerical analysis corresponding to the fourth experiment
In the scope of this thesis, the middle-middle scenario was performed by building
a dam 65 cm high, 200 cm long, and 5 cm crest by creating a 2x2 cm2 weak zone at the
middle center along the dam to investigate the temporal changes in breach and the breach
discharge caused by piping.
The dam was constructed by mixture 2. The soil mechanics tests of mixture 2 and
the experimental findings can be found in Chapter 3.1 and Chapter 5.4, respectively.
The final geometry of the middle-middle scenario is given in Figure 6.18.
Figure 6.18. The final geometry of the middle-middle scenario
The defined dam body soil properties for the middle-middle part are given in
Table 6.1. The numerical analysis was performed by defining the flow functions
according to the temporal water depths in the experiment which was given in Figure 5.47.
During the numerical analysis, the first 10 s were performed as steady-state flow
calculation types since the water level was continuous and it does not change on time.
The rest of the analysis was performed as a time-dependent flow function by tabulating
the water level table at each corresponding time.
After starting the simulation, the obtained longitudinal hydraulic gradient
distributions in one color scale (green) with their maximum and minimum values are
given in Figure 6.19.

83
(a)
(b)
Figure 6.19. Hydraulic gradient distribution along the dam for (a) 0 s (b) 10 s (c) 40 s (d)
80 s
(cont. on next page)

84
(c)
(d)
Figure 6.19. (cont.)

85
The flow through the breach together with upstream and downstream average
values are given in Figure 6.20.
(a)
(b)
(c)
Figure 6.20. Flow through the breach a) 10 s, b) 40 s, c) 80 s

86
The downstream and upstream temporal breach developments in the experiment
together with those obtained from the numerical analysis are given in Figure 6.21 and
Figure 6.22, respectively. The time t=0 s indicates the initiation of seepage.
(a)
(b)
(c)
Figure 6.21. The downstream temporal breach developments a) 0 s, b) 40 s, c) 80 s

87
(a)
(b)
(c)
Figure 6.22. The upstream temporal breach developments a) 0 s, b) 40 s, c) 80 s

88
The numerical temporal breach developments together with experimental
averaged values are presented in Figure 6.23 and Figure 6.24, respectively.
Figure 6.23. The downstream temporal breach developments together with experimental
average and numerical
Figure 6.24. The upstream temporal breach developments together with experimental
average and numerical
The experimental and numerical time-varied average velocities are presented
Figure 6.25 and Figure 6.26 for downstream and upstream, respectively.
0
600
1200
1800
2400
0 20 40 60 80 100 120 140
Surface Area (cm2)
Time (s)
Numerical Experimental Average
0
400
800
1200
1600
0 20 40 60 80 100 120 140 160
Surface Area (cm2)
Time (s)
Numerical Experimental Average

89
Figure 6.25. The time-varied downstream breach velocities together with experimental
average and numerical
Figure 6.26. The time-varied upstream breach velocities together with experimental
average and numerical
The temporal variations of the downstream and upstream wetted areas together
with experimental average values and numerical are given in Figure 6.27 and Figure 6.28,
respectively.
0
40
80
120
160
200
0 20 40 60 80 100 120 140
Velocity (cm/s)
Time (s)
Numerical Experimental Average
0
100
200
300
0 20 40 60 80 100 120 140
Velocity (cm/s)
Time (s)
Numerical Experimental Average

90
Figure 6.27. The temporal changes in downstream breach-wetted areas together with
experimental and numerical
Figure 6.28. The temporal changes in upstream breach-wetted areas together with
experimental and numerical
The average temporal discharge values for both the experimental and numerical are
given in Figure 6.29.
0
50
100
150
200
0 20 40 60 80 100 120 140
Wetted Aerea (cm2)
Time (s)
Numerical Experimental Average
0
50
100
150
200
250
0 20 40 60 80 100 120 140
Wetted area (cm²)
Time (s)
Numerical Experimental Average

91
Figure 6.29. The average temporal discharge values together with experimental and
numerical
The calculated and compared the RMSE and MAE values for each finding are given
in Table 6.3.
Table 6.3. RMSE and MAE values for each finding at the middle-middle part
Findings
Unit
Root Mean Square Error
(RMSE)
Mean Absolute Error
(MAE)
Vdownstream
(cm/s)
23.1
18.5
30.7
20.1
40.9
356.8
71.8
Vupstream
(cm/s)
43.9
Wetteddownstream
(cm2)
27.0
Wettedupstream
(cm2)
51.2
426.1
102.1
Surfacedownstream
(cm2)
Surfaceupstream
(cm2)
Discharge
(L/s)
3.5
2.8
The RMSE and MAE values are calculated for each finding. For the middle-
middle scenario, RMSE and MAE values of the average value are calculated as 30.0%
and 24.0% for Vdownstream, 58.4% and 40.8% for Vupstream, 23.2% and 17.2% for
Wetteddownstream, 39.1% and 31.3% for Wettedupstream, 22.5% and 18.8% for
Surfacedownstream, 14.1% and 9.9% for Surfaceupstream, 36.0% and 28.2% for discharge,
respectively.
0
10
20
30
40
0 20 40 60 80 100 120 140
Qbreach (L/s)
Time (s)
Numerical Experimental Average

92
6.2.3. Case 1: Seepage Starting at the Upper-Middle
In the scope of the project TUBITAK 119M609, (Guney et al., 2022a and Okan,
2022) performed an experiment by building a 60 cm in height, 200 cm in length, and 20
cm in crest width dam. A tunnel of 2 cm diameter located 6 cm below the crest to
investigate temporal breach developments and the discharge through the breach caused
by piping.
6.1.1.1. Construction procedures and Experiment
During the construction of the earth-fill dam, the bulk density was used as 2 g/cm3
and in 12.5% optimum water content by the standard proctor test from Figure 3.2. The
construction stages of the upper-middle scenario are given in Figure 6.30.
(a) (b)
(c) (d)
Figure 6.30. The construction stages of the upper-middle scenario (a) Top view of the
third layer during construction, (b) Left view of the third layer during
construction, (c) final upstream view, (d) final downstream view (Guney et
al., 2022a and Okan, 2022)

93
The experimental processes of the upper-middle scenario are given in Figure 6.31.
(a) (b)
(c) (d)
Figure 6.31. The experiment process for the upper-middle scenario (a) downstream
beginning, (b) downstream ending, (c) upstream beginning, (d) upstream
ending (Guney et al., 2022a and Okan, 2022)
The temporal water depth is given in Figure 6.32.
Figure 6.32. The temporal water depths of the upper-middle scenario (Guney et al., 2022a
and Okan, 2022)
0
10
20
30
40
50
60
0 50 100 150 200 250 300 350 400
Water Depth (cm)
Time (s)

94
The numerical analysis was performed by defining the flow functions according
to the temporal water depths corresponding to the experiment in the laboratory. During
the numerical analysis, the first 200 s are performed as steady-state flow calculation type.
The rest of the 200 s parts were performed as a time-dependent flow function by
tabulating the water level table at each corresponding time. The geometry of the upper-
middle scenario in PLAXIS 3D is given in Figure 6.33.
Figure 6.33. The final geometry of the upper-middle scenario
The longitudinal one-color scale (green) hydraulic gradient distributions at y=0.5
m together with four cross-sectional views at different time steps are given in Figure 6.34.
(a)
Figure 6.34. Hydraulic gradient distribution along the dam (a) 0 s (b) 40 s (c) 160 s (d)
240 s (e) 380 s
(cont. on next page)

95
(b)
(c)
(d)
(cont. on next page)

96
(e)
Figure 6.34. (cont.)
The flow through the breach together with upstream and downstream average
values are given in Figure 6.35.
(a)
(b)
Figure 6.35. Flow through the breach a) 40 s, b) 160 s, c) 240 s
(cont. on next page)

97
(c)
Figure 6.35. (cont.)
The downstream and upstream temporal breach developments in the experiment
together with those obtained from the numerical analysis are given in Figure 6.36 and
Figure 6.37, respectively. The time t=0 s indicates the initiation of seepage.
(a)
(b)
Figure 6.36. The downstream temporal breach developments (a) 0 s, b) 40 s, c) 240 s, d)
380
(cont. on next page)

98
(c)
(d)
Figure 6.36. (cont.)
(a)
(b)
Figure 6.37. The upstream temporal breach developments (a) 0 s, (b) 40, (c) 240 s, (d)
380 s
(cont. on next page)

99
(c)
(d)
Figure 6.37. (cont.)
The numerical temporal breach developments together with experimental
averaged values are presented in Figure 6.38 and Figure 6.39 for the downstream and the
upstream sides, respectively.
Figure 6.38. The downstream temporal breach developments together with experimental
and numerical
0
500
1000
1500
2000
2500
050 100 150 200 250 300 350 400
Downstream Surfaces (cm2)
Time (s)
Upper middle-experimental Upper middle-numerical

100
Figure 6.39. The upstream temporal breach developments together with experimental and
numerical
The experimental and numerical time-varied average velocities are presented in
Figure 6.40 and Figure 6.41 for downstream and upstream, respectively.
Figure 6.40. The time-varied downstream breach velocities together with experimental
and numerical
0
450
900
1350
1800
0 50 100 150 200 250 300 350 400
Upstream Surfaces (cm2)
Time (s)
Upper middle-experimental Upper middle-numerical
0
15
30
45
60
0 50 100 150 200 250 300 350 400
Downstream Velocity (cm/s)
Time (s)
upper middle-experimental upper middle-numerical

101
Figure 6.41. The time-varied upstream breach velocities together with experimental and
numerical
The temporal variations of downstream and upstream wetted areas together with
experimental and numerical are given in Figure 6.42 and Figure 6.43 respectively.
Figure 6.42. The temporal variations of downstream wetted areas together with
experimental and numerical
0
15
30
45
60
050 100 150 200 250 300 350 400
Upstream Velocity (cm/s)
Time (s)
Upper middle-experimental Upper middle-numerical
0
60
120
180
240
0 50 100 150 200 250 300 350 400
Wetted Area (cm2)
Time (s)
Upper middle-experimental upper middle-numerical

102
Figure 6.43. The temporal variations of upstream wetted areas together with experimental
and numerical
The average temporal discharge values for both the experimental and numerical
are given in Figure 6.44.
Figure 6.44. The temporal discharges together with experimental and numerical
0
75
150
225
300
0 50 100 150 200 250 300 350 400
Wetted Area (cm2)
Time (s)
Upper middle-experimental upper middle-numerical
0
3
6
9
12
0 50 100 150 200 250 300 350 400
Discharges (L/s)
Time (s)
Upper middle-experimental Upper middle-numerical

103
The calculated RMSE and MAE values for each finding are given in Table 6.4.
Table 6.4. RMSE and MAE values for each finding at the upper-middle part
Findings
Unit
Root Mean Square Error
(RMSE)
Mean Absolute Error
(MAE)
Vdownstream
(cm/s)
5.6
4.7
6.0
19.1
32.5
224.8
100.6
Vupstream
(cm/s)
6.7
Wetteddownstream
(cm2)
24.9
Wettedupstream
(cm2)
41.8
316.8
143.6
Surfacedownstream
(cm2)
Surfaceupstream
(cm2)
Discharge
(L/s)
1.7
1.2
The RMSE and MAE values are calculated for each finding. For the upper-middle
part, RMSE and MAE values of the average value are calculated as 19.7% and 16.6% for
Vdownstream, 25.9% and 23.2% for Vupstream, 23.0% and 17.7% for Wetteddownstream, %36.0
and 28.1% for Wettedupstream, 27.4% and 19.4% for Surfacedownstream, 31.2% and 26.1% for
Surfaceupstream, 59.6% and 42.1% for discharge, respectively.
6.2.4. Case 2: Seepage Starting at the Upper-Corner
In the scope of the project TUBITAK 119M609, (Guney et al., 2022b and Okan,
2022) experimented by building a 60 cm in height, 200 cm in length, and 20 cm in crest
width dam which has a tunnel of 2 cm diameter located 6 cm below the crest corner to
investigate temporal breach developments and the discharge through the breach caused
by piping.
6.1.1.2. Construction procedures and Experiment
During the construction of the earth-fill dam, the bulk density was used as 2 g/cm3
and in 12.5% optimum water content by the standard proctor test from Figure 3.2.

104
The construction stages of the upper-corner section are given in Figure 6.45.
(a) (b)
(c) (d)
Figure 6.45. The constructions of the upper-corner scenario (a) the first layer from top
view (b) the first layer from left view (c) final upstream view (d) final
downstream view (Guney et al., 2022b and Okan, 2022)
The experimental processes of the upper-corner scenario for the downstream,
right side, and upstream are given in Figure 6.46, respectively.
(a) (b)
Figure 6.46. The experiment process for the upper-corner scenario (a) downstream
beginning (b) downstream ending (c) right side beginning (d) right side
ending (e) upstream beginning (f) upstream ending
(cont. on next page)

105
(c) (d)
(e) (f)
Figure 6.46. (cont.)
Once the dam geometry was defined, a 2 cm diameter hole was created by using
the poly curve at 6 cm below the dam crest corner. The final geometry of the upper-corner
scenario in PLAXIS 3D is given in Figure 6.47.
Figure 6.47. The final geometry of the upper-corner scenario
The numerical analysis was performed by defining the flow functions according to
the temporal water depths corresponding to the experiment in the laboratory which is

106
given in Figure 6.48. The first 230 seconds were simulated steady-state flow calculation
types while the rest of the analysis was simulated time-dependent.
Figure 6.48. The changes in water level in time for the upper-corner scenario (Guney et
al., 2022b and Okan, 2022)
The longitudinal one-color scale (green) hydraulic gradient distributions at y=0.98
m together with four cross-sectional views at different time steps are given in Figure 6.49.
(a)
Figure 6.49. Hydraulic gradient distribution along the dam for a) 0 s, b) 40 s, c) 160 s, d)
500 s, e) 640 s
(cont. on next page)
0
15
30
45
60
0 100 200 300 400 500 600 700 800
Water Level (cm)
Time (s)

107
(b)
(c)
(cont. on next page)

108
(d)
(e)
Figure 6.49. (cont.)

109
The flow through the breach is given in Figure 6.50.
(a)
(b)
(c)
Figure 6.50. Flow through the breach a) 40 s a) 40 s, b) 160 s, c) 500

110
The downstream and upstream temporal breach developments in the experiment
together with those obtained from the numerical analysis are given in Figure 6.51 and
Figure 6.52, respectively. The time t=0 s indicates the initiation of seepage.
(a)
(b)
(c)
(d)
Figure 6.51. The downstream temporal breach developments a) 0 s, b) 40 s, c) 500 s, d)
640 s

111
(a)
(b)
(c)
(d)
Figure 6.52. The upstream temporal breach developments (a) 0 s (b) 300 (c) 500 s (d)
640 s
The numerical temporal breach developments together with experimental are
presented Figure 6.53 and Figure 6.54 for the downstream and the upstream sides,
respectively.

112
Figure 6.53. The downstream temporal breach developments together with experimental
and numerical
Figure 6.54. The upstream temporal breach developments together with experimental and
numerical
The experimental and numerical time-varied average velocities are presented
Figure 6.55 and Figure 6.56 for downstream and upstream, respectively.
0
200
400
600
800
0 100 200 300 400 500 600 700 800
Downstream Surfaces (cm2)
Time (s)
Upper corner-experimental Upper corner-numerical
0
400
800
1200
1600
0 100 200 300 400 500 600 700 800
Upstream Surfaces (cm2)
Time (s)
Upper corner-experimental Upper corner-numerical

113
Figure 6.55. The time-varied downstream breach velocities together with experimental
and numerical
Figure 6.56. The time-varied upstream breach velocities together with experimental and
numerical
The temporal variations of the downstream and upstream wetted areas together with
experimental and numerical are given Figure 6.57 and Figure 6.58, respectively.
0
30
60
90
120
0 100 200 300 400 500 600 700 800
Downstream Velocity (cm/s)
Time (s)
upper corner-experimental upper corner-numerical
0
10
20
30
40
0 100 200 300 400 500 600 700 800
Upstream Velocity (cm/s)
Time (s)
Upper corner-experimental Upper corner-numerical

114
Figure 6.57. The temporal variations of the downstream wetted areas together with
experimental and numerical
Figure 6.58. The temporal variations of the upstream wetted areas together with
experimental and numerical
The average temporal discharge values for both the experimental and numerical
are given in Figure 6.59.
0
15
30
45
60
0 100 200 300 400 500 600 700 800
Wetted Area (cm2)
Time (s)
upper corner-experimental upper corner-numerical
0
40
80
120
160
0 100 200 300 400 500 600 700 800
Wetted Area (cm2)
Time (s)
Upper corner-experimental Upper corner-numerical

115
Figure 6.59. The temporal discharges together with experimental and numerical
The calculated RMSE and MAE values for each finding are given in Table 6.5.
Table 6.5. RMSE and MAE values for each finding at the upper-corner part
Findings
Root Mean Square Error
(RMSE)
Mean Absolute Error
(MAE)
Vdownstream (cm/s)
27.5
5.2
5.2
31.1
136.2
198.8
0.5
25.2
3.9
4.5
26.3
124.2
160.6
0.4
Vupstream (cm/s)
Wetteddownstream (cm2)
Wettedupstream (cm2)
Surfacedownstream (cm2)
Surfaceupstream (cm2)
Discharge (L/s)
For the upper corner scenario RMSE and MAE values of the average value are
calculated as 36.9% and 34.1% for Vdownstream, 29.2% and 21.5% for Vupstream, 24.5% and
21.2% for Wetteddownstream, %30.0 and 25.4% for Wettedupstream, 31.0% and 28.5% for
Surfacedownstream, 32.4% and 26.2% for Surfaceupstream, 27.5% and 21.9% for discharge.
0
1
2
3
4
0 100 200 300 400 500 600 700 800
Discharges (L/s)
Time (s)
Upper corner-experimental Upper corner-numerical

116
6.3. Results and Discussions
The numerical analyses were performed to realize the experimental conditions. In
the simulation of the first experiment, the piping process was started at the interaction
zone with the rock salt and the dam body, and it was continued to both sides, upstream
and downstream, respectively. The breached soil zone headed upstream side in t=4 days
and reached the upstream face after 11 days at 27 cm below the water surface. However,
the process took about 9 days and 16 cm below the water surfaces in the experiments.
The temporal discharge values were underestimated during the first 30 seconds
then, they decreased to the close parallel with the experiments. The time-dependent
upstream and downstream wetted areas were continued closely parallel to the
experiments, then it was overestimated during the numerical analysis. The time-related
velocities were underestimated for the first 50 seconds then they continued to closely
parallel the experiments. The downstream and upstream breach developments were
underestimated during the numerical analysis. The minimum error was found for the
downstream velocity while the maximum error was found for the wetted area upstream.
In the simulation of the fourth experiment, a similar breach formation was
observed. The piping was initiated at the interaction zone, and it continued and progressed
on both sides.
The temporal discharge values were calculated, and they were underestimated
until they reached their peak value of 24.35 cm3/s at t=50 s then the values were continued
closely in accord with the experiments. The changes in upstream breach-wetted areas
were underestimated during the analysis. However, the downstream sides continued
closely with the experimental findings. The downstream time-varied velocity values were
found close to the experiments while the upstream velocities were found to be
underestimated. The upstream temporal breach developments were found to be fairly in
accord with the experiment, however, the downstream sides were obtained as totally
underestimated.
The breach mechanism in the upper simulations were found to be similar for the
first t=160 s. In both simulations, the breach appeared on the upstream face at the same
interval. Then the peak discharges were occurred. In the upper-middle simulation, the
downstream temporal breach developments, downstream breach-wetted areas, and
downstream breach velocities are found the lowest errors, while the highest was found in

117
the temporal breach discharges. In the upper-corner simulation, The minimum error was
found in downstream wetted areas, while the maximum error was found to be downstream
velocities.

118
CHAPTER 7
CONCLUSION AND RECOMMENDATIONS
In the scope of this thesis, homogenous earth-fill dams 0.6 m high having a bottom
width of 2 m and side slopes 1 vertical to 1.5 horizontal were constructed in a rectangular
flume 1 m wide, 6.14 m long, and 0.81 m high, in the laboratory of the Izmir University
of Economics. Experimental and numerical investigation related to piping and resulting
breaches in the homogenous earth-fill dams were realized with different experiments. A
mixture consisting of 85 % sand and 15 % clay was used in the construction of the dams.
The piping was generated by locating weak layers at different locations of the dams. Three
experiments were performed by placing a weak layer of cross-section 5x5 cm2 at the
bottom of the dam along the centerline. One scenario was performed by locating a weak
layer of 2x2 cm2, 28 cm above the dam bottom. To facilitate the piping, each weak layer
consisted of rock salt.
The breaches started at the weak zone and progressed and continued backward, as
expected. The backward erosion within the first dam body was slower compared to other
experiments. The weak zones were located at the dam bottom during the first three
experiments while the fourth experiment was performed by placing the weak zone 28 cm
above the dam bottom.
The first two dams were constructed with a mixture of bulk density of 2 g/cm3.
The first dam height was 60 cm, and the water level in the channel was 55.5 cm.
The experiment took about 9 days for the breach to reach the upstream face,
approximately 16 cm below the water surface. In the first scenario, since the breach
appeared under the water, the upstream surface area increased equally with the wetted
area until the water level decreased. For these reasons, the obtained wetted areas in the
first experiment for the first t=20 s were found to be the greatest relative to the other
scenarios.
The second dam height was 65 cm, and the water level in the channel was 61 cm.
The experiment took about 8 hours for the breach to reach the upstream face. The

119
experiment took about 8 hours for the breach to reach the upstream face at water surface,
and the complete failure of the dam was observed.
The third dam was constructed with a mixture of bulk density of 1.7 g/cm3. The
dam height was 65 cm, and the water level in the channel was 61 cm. The soil erosion
was initiated at different locations of the downstream face. The experiment lasted
approximately 42 minutes and collapsed the dam crest, and the complete failure of the
dam was observed.
For the second and third scenarios, the first 37 seconds were compared. The
upstream breach area was eroded greater than in the second scenario. In conclusion, as
the compaction density decreases, the upstream breach erodes more rapidly.
The fourth dam height was 65 cm and the water level in the channel was 61 cm.
The experiment lasted approximately 2 minutes, being the experiment of the shorter
duration.
The simulations were performed by commercial software, PLAXIS 3D. The use of
the software by incorporating the python algorithm and the Jupyter console provided the
satisfactory compatibility between experimental findings and the numerical results. The
RMSE and MAE error parameters justified the accord between experimental findings and
numerical results.
The backward erosion piping was observed in numerical analysis as well as
experimental studies.
In the simulation of the first and fourth experiments, the piping initiated the
interaction between the weak zone and the dam body.
The numerical analyses were performed by using constant soil parameters such as
unit weights, void ratio, internal friction angle, oedometric modulus, permeability.
It is known that geotechnical parameters are affected by soil erosion resulting from
the piping. More realistic results can be obtained by performing numerical analyses with
time-dependent properties of geotechnical parameters.
.

120
REFERENCES
Shaikh, A., James, F. R., and Steven, R. 1988. “Erosion Rate of Compacted NA‐
Montmorillonite Soils.” Journal of Geotechnical Engineering, 114(3), 296–305.
https://doi.org/10.1061/(asce)0733-9410(1988)114:3(296).
Al-Janabi, A. M. S., Ghazali, A. H., Ghazaw, Y. M., Afan, H. A., Al-Ansari, N., and
Yaseen, Z. M. 2020. “Experimental and Numerical Analysis for Earth-Fill Dam
Seepage.” Sustainability, 12(6), 2490. https://doi.org/10.3390/su12062490.
Al-Mansori, N. J. H., Al-Fatlawi, T. A. F. J. M., Othman, N. Y., and Al-Zubaidi, L. S.
A. 2020. “Numerical Analysis of Seepage in Earth-Fill Dams.” Civil
Engineering Journal, 6(7), 1336–1348. https://doi.org/10.28991/cej-2020-
03091552.
Arulanandan, K., and Perry, E. B. 1983. “Erosion in Relation to Filter Design Criteria in
Earth Dams.” Journal of Geotechnical Engineering, 109(5), 682–698.
https://doi.org/10.1061/(asce)0733-9410(1983)109:5(682).
ASLAN, T. A., and TEMEL, B. 2022. “Finite element analysis of the seepage problem
in the dam body and foundation based on the Galerkin’s approach.” European
Mechanical Science, 6(2), 143–151. https://doi.org/10.26701/ems.1024266.
Athani, S. S., Shivamanth, Solanki, C., and Dodagoudar, G. 2015. “Seepage and
Stability Analyses of Earth Dam Using Finite Element Method.” Aquatic
Procedia, 4, 876–883. https://doi.org/10.1016/j.aqpro.2015.02.110.
Borragan, V. 2014. “Modelling Internal Erosion Within An Embankment Dam Prior To
Breaching”. [Master’s Dissertation].

121
Ojha, C. S. P., Singh, V. P., and Adrian, D. D. 2003. “Determination of Critical Head in
Soil Piping.” Journal of Hydraulic Engineering, 129(7), 511–518.
https://doi.org/10.1061/(asce)0733-9429(2003)129:7(511).
Chen, S. S., Zhong, Q. M., & Shen, G. Z. 2019. “Numerical modeling of earthen dam
breach due to piping failure.” Water Science and Engineering, 12(3), 169–178.
https://doi.org/10.1016/j.wse.2019.08.001.
Costa, J. 1985. “Floods from dam failures.” Open-File Report.
https://doi.org/10.3133/ofr85560.
Error when generating 3D mesh - GeoStudio | PLAXIS Wiki - GeoStudio | PLAXIS -
Bentley Communities. (2019, December 18).
https://communities.bentley.com/products/geotech-analysis/w/wiki/45545/error-
when-generating-3d-mesh.
Fisher, W. D., Camp, T. K., and Krzhizhanovskaya, V. V. 2017. “Anomaly detection in
earth dam and levee passive seismic data using support vector machines and
automatic feature selection.” Journal of Computational Science, 20, 143–153.
https://doi.org/10.1016/j.jocs.2016.11.016.
Foster, M. and Fell, R. 1999. “A framework for estimating the probability of failure of
embankment dams by internal erosion and piping using event tree methods.”
UNICIV Report No. R-377, University of New South Wales, Australia.
Foster, M., Fell, R., and Spannagle, M. 2000a. “The statistics of embankment dam
failures and accidents.” Canadian Geotechnical Journal, 37(5), 1000–1024.
https://doi.org/10.1139/t00-030.
Foster, M., Fell, R., & Spannagle, M. 2000b. A method for assessing the relative
likelihood of failure of embankment dams by piping. Canadian Geotechnical
Journal, 37(5), 1025–1061. https://doi.org/10.1139/t00-029.

122
Gattinoni, P., and Francani, V. 2009. “A Tool for Modeling Slope Instability Triggered
by Piping.” World Academy of Science, Engineering and Technology,
International Journal of Geological and Environmental Engineering, 3(8), 238–
244. https://publications.waset.org/3999/pdf.
Ghonim, M. T., Mowafy, M. H., Salem, M. N., and Jatwary, A. 2022. “Investigating the
peak outflow through a spatial embankment dam breach.” Ain Shams
Engineering Journal, 13(6), 101799. https://doi.org/10.1016/j.asej.2022.101799.
Guney, M. S., Dumlu, E., Okan, M., Bor, A., Aklık, P., and Tayfur, G. 2022a.
“Experimental Study of the Evolution of the Breach and the Temporal breach
discharges Resulting from Piping due to Seepage at the Earth-Fill Dam Bottom.”
Proceedings of the 7th International Conference on Civil, Structural and
Transportation Engineering (ICCSTE’22).
https://doi.org/10.11159/iccste22.215.
Guney, M. S., Dumlu, E., Okan, M., Bor, A., Aklık, P., and Tayfur, G. 2022b.
“Experimental Study of the Evolution of the Breach and the Temporal breach
discharges Resulting from Piping due to Seepage at the Earth-Fill Dam Top.”
Proceedings of the 39th IAHR World Congress (Granada, 2022).
https://doi.org/10.3850/IAHR-39WC2521711920221298.
Guney, M. S., Dumlu, E., Okan M., Tayfur, G. 2022c. “Experimental Study of Breach
Evolution and Discharge through Breach Resulting from Piping due to Seepage
at the Upper Corner of in an Earth-fill Dam.” Proceedings of 14th International
Conference on Hydroscience and Engineering.
Hanson, G., Ronald R. T., Sherry H., and Darrel T. 2010. “Internal Erosion and Impact
of Erosion Resistance.” In Proceedings of the 30th U.S. Society on Dams Annual
Meeting and Conference. April 12-16, 2010, 773–84. Sacramento, California.
Hinderlider, M. C. 1914. “Failure of Horse Creek Earth Dam.” Engineering News
Record, vol. 71, No. 16, April 16, 828-830.

123
ICOLD. 2017. “Internal Erosion of Existing Dams, Levees and Dikes, and Their
Foundations.”
Ke, L., and Takahashi, A. 2012. “Strength reduction of cohesionless soil due to internal
erosion induced by one-dimensional upward seepage flow.” Soils and
Foundations, 52(4), 698–711. https://doi.org/10.1016/j.sandf.2012.07.010.
Kermani, E., and Barani, G. 2012. “Seepage Analysis through Earth Dam Based on
Finite Difference Method.” J. Basic Appl. Sci. Res., 2, 11621–11625.
Khilar, K.C., Fogler, H.S., and Gray, D.H. 1985. “Model for Piping‐Plugging in Earthen
Structures.” Journal of Geotechnical Engineering, 111, 833-846.
Lachouette, D., Golay, F., and Bonelli, S. 2008. “One-dimensional modeling of piping
flow erosion.” Comptes Rendus - Mecanique, 336(9), 731–736.
https://doi.org/10.1016/j.crme.2008.06.007.
Li, D. Y., Zheng, D. F., Wu, H., Shen, Y. Q., and Nian, T. K. 2021. “Numerical
Simulation on the Longitudinal Breach Process of Landslide Dams Using an
Improved Coupled DEM-CFD Method.” Frontiers in Earth Science, 9.
https://doi.org/10.3389/feart.2021.673249.
Meister, A. L. F. 1769. "Generalia de genesi figurarum planarum et inde pendentibus
earum affectionibus.", Nov. Com. Gött. (in Latin), 1: 144.
Elkholy, M., Sharif, Y. A., Chaudhry, M. H., and Imran, J. 2015. “Effect of soil
composition on piping erosion of earthen levees.” Journal of Hydraulic
Research, 53(4), 478–487. https://doi.org/10.1080/00221686.2015.1026951.
Greco M., Pontillo M., Iervolino M., and Leopardi A. 2008. “2DH numerical simulation
of breach evolution in an earth dam.” River-flow2008, vol. 1, pp. 661–667.

124
Morris, M., Hassan, M., Kortenhaus, A., Geisenhainer, P., Visser, P., and Zhu, Y. 2008.
“Modelling breach initiation and growth.” Flood Risk Management: Research
and Practice, 581–591. https://doi.org/10.1201/9780203883020.ch67.
No Finger in the Dike Could Have Stopped It!. 2018. Newspapers.com.
https://www.newspapers.com/clip/23922672/no-finger-in-the-dike-could-have/
Okan, M. 2022. “Experimental and Numerical Investigation of Piping in Uniform
Embankment Dam with Weak Layer at the Upper Region [Master Thesis].”
Izmir Institute of Technology.
Okeke, A. C., Wang, F., Sonoyama, T., and Mitani, Y. 2012. “Laboratory Experiments
on Landslide Dam Failure Due to Piping: An Evaluation of 2011 Typhoon-
Induced Landslide and Landslide Dam in Western Japan.” Environmental
Science and Engineering, 525–545. https://doi.org/10.1007/978-3-642-29107-
4_30.
Perrow, C. 1984. “Normal Accidents.” New York: Basic Books. ISBN 0-465-05144-8,
pp.233–238.
PLAXIS. 2022. “PLAXIS material models manual 2022.” Tech. rep., Delft,
Netherlands, http://www.plaxis.nl/shop/135/info/manuals/.
Reisner, M. 1993. “Cadillac Desert.” pp. 407. ISBN 978-0-14-017824-1.
Richards, K., and Reddy, K. 2012. “Experimental investigation of initiation of
backward erosion piping in soils.” Géotechnique, 62(10), 933–942.
https://doi.org/10.1680/geot.11.p.058.
Saliba, F., Nassar, R. B., Khoury, N., and Maalouf, Y. 2019. “Internal Erosion and
Piping Evolution in Earth Dams Using an Iterative Approach.” Geo-Congress
2019. https://doi.org/10.1061/9780784482155.007.

125
Sazzad, M. M., Roy, and Rahman, M. M. 2015. “FEM based seepage analysis through
earth dam.” International Journal of Advances in Structural and Geotechnical
Engineering, 4(3), 158-164.
Sharif, Y. A. 2013. “Experimental Study On Piping Failure of Earthen Levee and
Dams.” [Doctoral dissertation]. The University of South Carolina. Retrieved
from https://scholarcommons.sc.edu/etd/2558.
Sharif, Y. A., Elkholy, M., Hanif Chaudhry, M., and Imran, J. 2015a. “Experimental
Study on the Piping Erosion Process in Earthen Embankments.” Journal of
Hydraulic Engineering, 141(7). https://doi.org/10.1061/(asce)hy.1943-
7900.0001019.
Sharif, Y. A., Elkholy, M., Hanif Chaudhry, M., and Imran, J. 2015b. “Experimental
Study on the Piping Erosion Process in Earthen Embankments.” Journal of
Hydraulic Engineering, 141(7). https://doi.org/10.1061/(asce)hy.1943-
7900.0001019.
Shin, S., Park, S., and Kim, J. H. 2019. “Time-lapse electrical resistivity tomography
characterization for piping detection in earthen dam model of a sandbox.”
Journal of Applied Geophysics, 170, 103834.
https://doi.org/10.1016/j.jappgeo.2019.103834.
Sills, G. L., Vroman, N. D., Wahl, R. E., and Schwanz, N. T. 2008. “Overview of New
Orleans levee failures: Lessons learned and their impact on national levee design
and assessment.” J. Geotech. Geoenviron. Eng., 134(5), 556–565.
Bonelli, S. 2013. “Erosion in geomechanics applied to dams and levees.” ISTE, Wiley
EBooks.
Tao, H., Tao, J. 2017. “Quantitative analysis of piping erosion micro-mechanisms with
coupled CFD and DEM method.” Acta Geotech. 12, 573–592.
https://doi.org/10.1007/s11440-016-0516-y

126
Temple, D.M., Hanson, G.J., Neilsen, M.L., and Cook, K.R. 2005. “Simplified Breach
Analysis Model for Homogeneous Embankments: Part I, Background and Model
Components.” In Proceedings of the 2005 U.S. Society on Dams Annual Meeting
and Conference, Salt Lake City, Utah, 151–61.
Van Beek, V. M., Van Essen, H. M., Vandenboer, K., & Bezuijen, A. 2015.
“Developments in modelling of backward erosion piping.” Géotechnique, 65(9),
740–754. https://doi.org/10.1680/geot.14.p.119.
Vandenboer, K., van Beek, V. M., and Bezuijen, A. 2014. “3D finite element method
(FEM) simulation of groundwater flow during backward erosion piping.”
Frontiers of Structural and Civil Engineering, 8(2), 160–166.
https://doi.org/10.1007/s11709-014-0257-7.
Xu, T., and Zhang, L. 2013. “Simulation of Piping in Earth Dams Due to Concentrated
Leak Erosion.” Geo-Congress 2013.
https://doi.org/10.1061/9780784412787.110.
Zhenzhen, L. 2015. “Hydro-Mechanical Analysis of Breach Processes Due to Levee
Failure.” [Master’s Dissertation]. Université D’aix-Marseille École.
Zhong, Q. M., Chen, S. S., Mei, S. A., and Cao, W. 2017. “Numerical simulation of
landslide dam breaching due to overtopping.” Landslides, 15(6), 1183–1192.
https://doi.org/10.1007/s10346-017-0935-3.