n. ae=-.. · increasing and today they may serve as permanent retaining walls or as navigation or waterfront structures. Conventional design methods for cellular cofferdams are based

FINITE ELEMENT ANALYSES OF CELLULAR COFFERDAMS

by

Yash Pal Singh

Dissertation submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

T. Kuppusamy

T. L. Brandon

in

Civil Engineering

APPROVED:

G. W. cl>ugh, Chairman

October, 1987

Blacksburg, Virginia

. . "'n. Duncan

R. A. Heller

ae=- ..

FINITE ELEMENT ANALYSES OF CELLULAR COFFERDAMS

by

Yash Pal Singh

G. W. Clough, Chairman

Civil Engineering

(ABSTRACT)

Cellular cofferdams have primarily been used as temporary systems which serve to allow

construction of facilities in open bodies of water. Applications for these structures have been

increasing and today they may serve as permanent retaining walls or as navigation or

waterfront structures. Conventional design methods for cellular cofferdams are based on

semi-empirical approaches largely developed in the 1940s and 1950s. None of the available

traditional procedures are capable of predicting cofferdam deformations, a parameter of key

importance to the cofferdam performance, and which is often observed during construction for

purposes of safety monitoring. Also, there is evidence that much of the conventional design

technology is conservative, in some cases predicting loading by more than twice that which

actually occurs. Recently, the finite element method has shown promise as a tool which can

be used to help resolve some of the outstanding problems with cofferdam design.

There are three primary objectives of this work: (1) enhance existing finite element pro-

gram to allow for more accurate and refined analysis of cellular cofferdams, (2) use the en-

hanced finite element programs to assess the degree of conservatism in conventional design

methods for cofferdams founded on sandy soils, and (3) use the results of parametric studies

of cofferdams founded on sandy soils to develop a simplified procedure to predict cofferdam

movements and determine potential for internal failure. The first of the objectives involves

adding better bending elements to the program SOILSTRUCT to represent the sheet pile sys-

tem In axisymmetric and plane strain analyses. Also, in the case of the plane strain program,

a new method is developed to allow shear transfer through the sheet pile system. Through

case history and theoretical analyses, the enhanced programs are demonstrated to yield ac-

curate and realistic results.

Parametric studies using the axisymmetric program show that conventional design meth-

ods overpredict, in some areas strongly, the interlock forces which develop during filling of the

cofferdam. Parametric studies using the plane strain program suggest that there is also

considerable conservatism in design methods to predict internal stability of the cofferdam. A

new, simplified method is proposed for this type of analysis. In addition, it is shown that the

deformations of cofferdams on sand follow consistent trends and can be set into a non-

dimensionalized context which can be used to predict future cofferdam movements.

Acknowledgements

The author wishes to express his deep gratitude to his advisor, Dr. G. W. Clough, for his

guidance during the course of this research. I am extremely grateful to Dr. Clough for his

constant encouragement, tremendous patience, and very sincere personal considerations

without which the completion of this work could not have been possible. Special thanks are

due to Dr. T. Kuppusamy for his encouragement and reviewing of the research work from time

to time and soliciting advice. Much appreciation is extended to my other committee members,

Dr. J. M. Duncan, Dr. T. L. Brandon and Dr. R. A. Heller, for their interest in my studies and

research. Thanks are due to Dr. J. N. Reddy for his advice on some part of the research and

for his time.

I express gratitude to U.S.Army Corps of Engineers, Waterways Experiment Station for

funding this research project under contract No. DACW 39-86-K-0007. Support from personnel

of the St.Louis District of Corps of Engineers was provided at various times during the course

of the work. In particular, valuable instrumentation data for the Lock and Dam 26(R) cofferdam

were made available for this research. Thanks are extended to Mr. Reed Mosher, Dr. N.

Radhakrishnan, Mr. Donald Dressler and Mr. Tom Mudd for their help during the course of the

work.

Acknowledgements iv

I am indebted to my wife, for her continuous encouragement, moral sup-

port, facing all the hardships with lot of courage and assuming complete responsibility of the

family during all these years. Without her support, I could not have accomplished this task.

I have a lot of appreciation for my two children, : md who have shown

unbelievable cooperation, great understanding, and a lot of patience. Thanks and appreci-

ation are due to Or. M.P. Singh and Mrs. Kusum Singh for their encouragement and moral

support during these years. Thanks to all the friends and relatives who helped me in this

endeavour. Last but not feast, I tha.nk Miss Cathy Barker for her expert and efficient typing

of the dissertation and meeting all the deadlines without exception.

Acknowledgements y

Table of Contents

INTRODUCTION • . • • . • • • . . . • . • • • . . . . • • • . . . • . . . • • • . . • . . . • • • • • • • • • . . • . . . • • • 1

BACKGROUND • • • • • • . . . . . . • • • . • . . • • • • • . • • . . • . • . . . . • • . . . . . . . • • . . • • • • . . • • 6

2.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Construction of Cellular Cofferdams .....................................• 7

2.3 Failure of Cellular Cofferdams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Existing Design Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4.1 Interlock Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.2 Shear in Cell Fill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5 Finite Element Analysis Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5.1 Early Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5.2 Lock and Dam 26 (R) Cofferdam Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.6 Summary and Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

AXISYMMETRIC VERSION OF FINITE ELEMENT PROGRAM (SOILSTRUCT) . • • . • • • • • • • 36

3.1 Modification in Axisymmetric Finite Element Program: Provision of Shell Element . . 37

3.2 Test Problems to Check Shell Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Table of Contents vi

3.2.1 Test Problem 1 ................................................. 44

3.2.2 Test Problem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.3 Problem of Interaction of Shell Element with Two-Dimensional Elements in Program

SOILSTRUCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.4 Case History Analysis Using One-Foot Thick Solid Element and New Shell Element for

Sheet Piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.4.1 Case History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.4.2 Previous Predictions and Observed Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.4.3 Predictions Using New Shell Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

PARAMETRIC ANALYSES WITH THE AXISYMMETRIC FINITE ELEMENT PROGRAM 60

4.1 Effect of Depth of Embedment on Sheet Pile Deflections and Interlock Forces 61

4.2 Effect of Free Cell Height on Sheet Pile Deflection and Interlock Forces . . . . . . . . . . 71

4.3 Effect of Foundation Soil And Cell Fill Parameters on Sheet Pile Deflection and Inter-

lock Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

PLANE STRAIN VERSION OF FINITE ELEMENT PROGRAM (SOILSTRUCT) • • • • • • . • • • • 81

5.1 Modifications in Plane Strain Finite Element Program. . . . . . . . . . . . . . . . . . . . . . . . 83

5.2 Provision of Beam Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.2.2 Test Problems to Check Beam Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.2.3 Problem of Interaction of Beam Element with Two-Dimensional Elements in Pro-

gram SOILSTRUCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.2.4 Comparison With Previous Results - Cell Filling Case . . . . . . . . . . . . . . . . . . . . 90

5.3 Provision of Shear Transfer Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.3.1 Method of Computing Modulus (E) of Shear Transfer Elements for Use in Analyses 95

Table of Contents vii

CASE HISTORY STUDIES USING MODIFIED PLANE STRAIN FINITE ELEMENT PROGRAM 104

6.1 Second Modulus Reduction Factor and General Analyses Procedures . . . . . . . . . . 105

6.2 Willow-Island Second Stage Cofferdam - Cell 27 . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.2.1 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.2.2 Site Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.2.3 Finite Element Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6.3 Willow Island Second-Stage Cofferdam Cloverleaf Cell 33 . . . . . . . . . . . . . . . . 119



6.4 Lock and Dam No. 26 (Replacement), First-Stage Cofferdam . . . . . . . . . . . . . . . . . 124



6.5 Summary of Case Histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.6 Stress Transfer Mechanism From Outboard to Inboard Sheet Pile . . . . . . . . . . . . . 130

PREDICTED RESPONSE OF LOCK AND DAM 26 (R) TO LATERAL LOADING ••••••••• 133

7.1 Analysis Procedures and Assumptions Therein . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.2 Cell Filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

7.3 Predicted Response for Flood-Type Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.3.1 Deflection of Sheet Piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.3.2 Lateral Earth Pressure Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

7.3.3 Base Pressure Distribution 146

7.3.4 Change of Vertical Stress in Cell Fill and Foundation . . . . . . . . . . . . . . . . . . . . 150

7.4 Predicted Response for High Lateral Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

7.4.1 Deflection of Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

7.4.2 Load-Deflection Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

7.4.3 Lateral Earth Pressure Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.4.4 Possible Failure Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Table of Contents viii

7.4.5 Vertical Displacement of Cell Fill and Slippage of Sheet Piles During Lateral

Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

7.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

PARAMETRIC STUDIES AND METHODS TO PREDICT CELL DEFORMATIONS AND FAIL·

URE UNDER LATERAL LOADINGS ..••...•..••••••.•.....•••....•••... , ... 176

8.1 Parametric Studies 178

8.1.1 Deflected Shapes of Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

8.1.2 Effect of Depth of Embedment on Sheet Pile Deflections Due to Lateral Loading 184

8.1.3 Load Deflection Response of Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

8.1.4 Vertical Displacement of Cell Fill and Slippage of Sheet Piles . . . . . . . . . . . . . 190

8.1.5 Failure Mechanisms Under Extreme Lateral Loadings . . . . . . . . . . . . . . . . . . . 190

8.2 Proposed New Method For Determination of Lateral Capacity of Cellular Cofferdams 192

8.2.1 An Example Problem to Compute Failure Load . . . . . . . . . . . . . . . . . . . . . . . . 202

8.3 Comparison of Shear Failure Analyses Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 206

SUMMARY AND CONCLUSIONS • . • • . . . • • • • . . • . • . • • . • • • • • • • • • . • • • . • . . • • . . • 210

9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

9.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

9.2.1 Modifications in SOILSTRUCT Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

9.2.2 Cell Filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

9.2.3 Differential Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

APPENDIX A • • • • . • . . • • • . • • • • • . . . • • . • • • • . • . • . . • . . . • . . • • . • • • . • • • • • • . . • • 216

APPENDIX B • • • . • • • • • • • • • • • • . . • • . . • • • . • . . • • • . . • . • • . . • • • • • . • • • • • • • . . • . 227

REFERENCES ...... I ••• I I •• I •••• I ••••••• I • I ••••••••• I I I • I • I ••••••• I • • • 238

Table of Contents Ix

VITA ............................................................... 242

Table of Contents x

LIST OF ILLUSTRATIONS

page

Figure 2.1. Common cell configurations (Lacroix, et al. 1970). 8

Figure 2.2. Conventional analyses methods for interlock force (from Shannon and Wilson, 1982). • . • • • • • . • 14

Figure 2.3. Interlock force, comparison of different conventional methods. . . . . . . . . . . . . . . . . . . . . 16

Figure 2.4. Terzaghi's vertical shear method •••• 18

Figure 2.5. Failure surfaces suggested by different authors. . • • 21

Figure 2.6. Finite element models (from Shannon and Wilson, 1982). 24

Figure 2.7. Non-linear stress strain behavior of soils •••

Figure 2.8. Comparison of results from axisymmetric and vertical slice analyses for cell filling (from Shannon and

28

Wilson, 1982). . • • . • • • • • • • • • • • . • • • • 30

Figure 2.9. Comparison of interlock forces predicted by various methods at the end of cell filling (from Clough and Kuppusamy, 1985) •.••••••.•

Figure 2.10. Vertical slice analysis, sheet pile deflections for different construction stages (from Shannon and

31

Wilson, 1982). • . • • . • • • . • • • • • • • . • • . 33

Figure 3.1. A thin cylindrical shell ••• 38

Figure 3.2. Test Problem 1, long cylinder subjected to internal pressure. . . . . . . . . . . . . . . . . . . . . 45

Figure 3.3. Test Problem 2, cylindrical tank with hydrostatic pressure. • • • 47

Figure 3.4. Lock and Dam 26 (R) cofferdam, basic conditions. • • • 51

Figure 3.5. Axisymmetric analysis, using one-foot thick element, sheet pile deflections and interlock forces at the end of cell filling. • • • • • • • • • • • • • • • • • • • 54

Figure 3.6. Finite element mesh for axisymmetric analyses of Lock and Dam 26 (R) cofferdam.. • • • • • • • • • • • • • • 56

List of Illustrations xi

Figure 3.7. Lock and Dam 26 (R)' sheet pile deflections at the end of cell filling. . . . . . . . . . . . . . . . . 57

Figure 3.8. Lock and Dam 26 (R)' interlock forces at the end of cell filling. . . . . . . . . . . 58

Figure 4.1. Deflected shapes of cofferdam cell at the end of cell filling. . . . . . . . . . . . . . . . . 62

Figure 4.2. Maximum sheet pile deflections at the end of cell filling. . . . . . . . . . . . . . . . . . . 64

Figure 4.3. Lateral earth pressures against sheet pile at the end of cell filling. . • • • • • . • . • • . • • • • • 65

Figure 4.4. Maximum interlock forces at the end of cell filling. • 66

Figure 4.5. Cell deflections below dredge line at the end of cell filling. . . . . . . . . . . . . . . . . . . . . . . . 68

Figure 4.6. Effect of depth of embedment on location of maximum cell deflection and interlock force at the end of cell filling. . . . . . . . . . . . . . . . . . . . . . 69

Figure 4.7. Lock and Dam 26 (R), interlock forces at the end of cell filling. Comparison of FE analysis and conventional design methods. • • • • • • . • . • • • 70

Figure 4.8. Effect of cell fill material on maximum sheet pile deflections at the end of cell filling. 72

Figure 4.9. Effect of cell fill material on maximum interlock forces at the end of cell filling. • • • • • • • • • • • 73

Figure 4.10. Effect of free cell material on maximum interlock force (FEM and Schroeder and Maitland method) at the end of cell filling. . . . . . . . . . . . . . . . . . . . . . 75

Figure 4.11. Effect of free cell height on location of maximum cell deflection and interlock force at the end of cell filling. . . . . . . . . . . . . . . . . 76

Figure 4.12. Effect of foundation material on maximum sheet pile deflections at the end of cell filling. • • • • • • • 77

Figure 4.13. Effect of foundation material on maximum interlock forces at the end of cell filling. • • 78

Figure 5.1. Planar representation of cofferdam cell for FEM analysis (from Hansen and Clough, 1982). • • • • • ••• 82

List of Illustrations xi\

Figure S.2. A beam element. . . . . . . . . . . . . . . . . . . . . 8S

Figure S.3. Test problem l, beam with transverse load. . . . . . . 87

Figure S.4. Test Problem 2, beam on elastic foundation. . . . . . . 89

Figure S.S. Test Problem 2, deflection of beam on elastic foundation. . . . . . . 91

Figure S.6. Finite element mesh for Lock and Dam 26 (R) first stage cofferdam. . . . . . . . . . . . . . . . . . . 93

Figure S.7. Deflection of sheet pile at the end of cell filling, Lock and Dam 26 cofferdam. • • • • • • • • • • • • . • 94

Figure S.8. Isometric view of cell fill elements and overlapping shear transfer elements. • • . • . • • • • • • • . • • 96

Figure S.9. Schematic details of thin cylinder and finite element mesh. . . . . . . . . . . . . . . . . . . . . 98

Figure S.10. Deflection ratio versus modulus ratio for Lock and Dam 26 (R). . • • . • • . • • • • • . 101

Figure S.11. H/B versus modulus ratio. 103

Figure 6.1. Deflection of sheet piles due to lateral load. 106

Figure 6.2. Willow Island second-stage cofferdam location plan ••• 109

Figure 6.3. Finite element mesh for Willow Island cofferdam, cell no. 27. . . . . . . . . . . . . . . . . . 112

Figure 6.4. Willow Island Cofferdam, Cell 27, construction sequence modeled. • • • • • • • • 114

Figure 6.S. Willow Island Cofferdam, Cell 27, inboard sheet pile deflections due to initial dewatering. • • • • • • • • 116

Figure 6.6. Willow Island Cofferdam, Cell 27, inboard sheet pile deflections due to initial dewatering and equipment surcharge load. . • • • . . • • . • • • 11 7

Figure 6.7. Willow Island Cofferdam, Cell 27, inboard sheet pile deflections due to initial dewatering, using springs and shear transfer elements. • • • • • • • • . • 118

Figure 6.8. Finite element mesh for Willow Island cofferdam, cloverleaf cell no. 33 ••••••••••••••••• 120

Figure 6.9. Willow Island Cofferdam, cloverleaf cell 33, deflections

List of Illustrations xiii

of inboard sheet pile due to initial dewatering. . • • 122

Figure 6.10. Finite element mesh for Lock and Dam 26 (R) first stage cofferdam. . • . • • . . . • • . • • • • . • . 123

Figure 6.11. Lock and Dam (R) cofferdam, construction sequence modeled. . . . . . . . . . . . . . . 126

Figure 6.12. Lock and Dam 26 (R) cofferdam, deflection of sheet piles due to berm placement. . . • • • . • • 127

Figure 6.13. Lock and Dam 26 (R) cofferdam, deflection of inboard sheet pile due to initial dewatering. • • . • 129

Figure 6.14. Lock and Dam 26 (R) cofferdam load transfer from outboard to inboard sheet pile at El. 105 for hydros ta tic load 1 lwh. • . • • • • • • • • • 131

Figure 7.1. Schematic representation of a cofferdam cell subjected to lateral load. • • • • • • • • • 135

Figure 7.2. Lateral earth pressure coefficient (K) for cell filling. . . . . . . . . . . . 138

Figure 7.3. Deflected shape of a cofferdam cell due to lateral load. . . . . . . . . . . . . . . . . 140

Figure 7.4. Deflection of sheet piles due to lateral load. • • • • 141

Figure 7.5. Lock and Dam 26 (R), observed cell deflection for flood load (from Martin, 1987). • • • • . • 143

Figure 7.6. Lock and Dam 26 (R), average response of 11 typical cells to lateral loading (from Martin, 1987). • • • 144

Figure 7.7. Lateral earth pressure coefficients (K) for hydrostatic load 3 lwh. • • • • • • • • • • • • • • • 145

Figure 7.8. Base pressure at end of cell filling, Lock and Dam 26 (R) cofferdam. • • • • • • • • . • • . . • • 147

Figure 7.9. Base pressures at dredge line due to lateral load, Lock and Dam 26 (R) cofferdam. . . • • • • • • • • • 148

Figure 7.10. Change of vertical stress in cell fill due to lateral load, Lock and Dam 26 (R) cofferdam. • • • • • 151

Figure 7.11. Change of vertical stress in foundation due to lateral load, Lock and Dam 26 (R) cofferdam. • • • • • • 152

Figure 7.12. Lock and Dam 26, deflected shape of cell for lateral

List of Illustrations xiv

loads. • . • 155

Figure 7.13. Lock and Dam 26, deflected shape of cell for collapse lateral load 7lwh. • • • . 156

Figure 7.14. Lock and Dam 26, lateral load versus deflection of sheet pile top. . • • • . • • . . • • • • • • • 157

Figure 7.15. Lateral earth pressure coefficient (K) for hydrostatic lateral load 3lwh. • • . . . • . • • . • . 160

Figure 7.16. Lateral earth pressure coefficient (K) for hydrostatic lateral load 5lwh. • • . . • . . • • . 161

Figure 7.17. Determination of direction of failure planes. • . 163

Figure 7.18. Lock and Dam 26, failed soil elements and failure loads. • . • • . . • • • . • • • • • • • • 164

Figure 7.19. Lock and Dam 26, failure plane directions and failure surfaces due to lateral loads. . • • • • • • . • . 165

Figure 7.20. Lock and Dam 26, vertical displacements at top of cell fill without and with soil interfaces. • • • • • . 167

Figure 7.21. Lock and Dam 26, effect of soil interfaces on sheet pile deflections during lateral loading. • • • • • • • 169

Figure 7.22. Schematic representation of slippage of sheet piles due to lateral loads. • • • • • • • • • • • • • • 171

Figure 7.23. Lock and Dam 26, axial pull and interlock resistance in inboard sheet pile due to lateral load. • 172

Figure 8.1. Deflected shapes of 63 feet and 40 feet wide cells for load llwh. • • • • • • • • • 181

Figure 8.2. Deflected shapes of cofferdam cell for collapse lateral load. . . . . . . . . . . . . . . . . . . . . . . . 182

Figure 8.3. Deflected shapes of cofferdam cell with and without scour. 183

Figure 8.4. Effect of depth of embedment on sheet pile deflection during lateral loading. • • • • • ••••••••• 185

Figure 8.5. Sheet pile deflection as percentage of cell height for different depths of embedment and cell width. • • • . • 187

Figure 8.6. Lateral load versus deflection of sheet pile top for cell width of 63 feet. • • • • • • . • • • • • • • • • • • • 188

Figure 8.7. Lateral load versus deflection of sheet pile top for cell

List of Illustrations xv

width of 40 feet .•.• . • 1a9

Figure a.a. Radius versus center of rotation of curved failure surface . ...... . 191

Figure a.9. Shear failure analysis with curved failure surface •.. 195

Figure 8.10. Shear failure analysis with vertical failure surface .• 197

Figure a.11. Cofferdam circular cell, location of vertical shear failure surface •. 200

Figure a.12. Schematic representation of failure surfaces and free body diagram showing forces. • • • • • . • . 205

Figure a.13. Comparison of shear failure analyses methods, load-deflection curves for cell width 63 feet • • • . . • • 207

Figure a.14. Comparison of shear failure analyses methods, load-deformation curves for cell width 63 feet • • • . • • 2oa

List of Illustrations xvi

LIST OF TABLES

page Table 3.1. Predicted deflections and hoop stresses in a hollow

cylinder. . • • • • • • • . • • 48

Table 3.2 Soil parameters for finite element analysis of Lock

Table 5.1

Table 6.1

Table 8.1.

and Dam 26 (R). • • . . . . . • • • • • . • 52

Dimensions of cylinders used in parametric studies to evaluate response of shear transfer elements ••••.• 100

Soil or rock properties for Willow Island cofferdam ••• 113

Circular Failure Surfaces ••••• . .193

List of Tables xvii

Chapter I

INTRODUCTION

Cellular cofferdams are used to retain soil or water or both. Initially, they were generally

built only as temporary structures to exclude water from an excavation to ensure construction

in dry conditions, but today they are also used as permanent structures such as piers,

wharves and jetties. They are constructed of interlocking sheet piles forming adjacent cells

and are usually filled with free draining cohesionless material. Shapes of cofferdam cells are

circular, diaphragm, and cloverleaf. However, circular cells are most commonly used.

Conventional design methods for cellular cofferdams consider sliding, overturning, inter-

lock tension and vertical shear failure of cell fill. The most frequent cause of cell failure has

been related to the interlock tension issue. Even though these problems were largely attri-

buted to structural failure of fabricated tees and wyes due to inadequately designed con-

nections or faulty fabrication, the nature and magnitude of interlock tension per se, and the

use of proper factor of safety remains a matter of concern. There are a number of different

design methods for determining interlock tensions, and each assumes different lateral earth

pressure magnitudes and distributions in the calculation technique. As a result, significantly

INTRODUCTION 1

different predictions can be made for interlock tension. Comparison with observed data sug-

gests that predictions of most of the conventional methods are conservative. Similar prob-

lems exist concerning the possibility of shear failure of cell fill during lateral loading. The

conventional theories for analyzing this failure differ in both the assumption of failure surface

as well as lateral earth pressure coefficient, and these as well have been shown to largely

yield overly conservative results.

Although some modifications have been proposed in the last decade for cofferdam design,

most of the design methods were developed more than 30 years ago, and the alternatives lead

to considerable differences in predicted behavior. These methods are also lacking in that:

• There is no means to predict cell wall movements and deflections.

• Explicit procedures to consider soil-structure interaction effects are not provided.

• The effect of alternative construction sequences cannot be predicted.

The first deficiency is particularly important because safety instrumentation for cofferdams is

mainly directed at measurement of cell movement.

In the past decade, a number of investigators have begun to apply the finite element

method to the cofferdam problem. This method offers the possibility to predict cofferdam be-

havior while analyzing the cofferdam as a unit, and accounting for many of the aspects of the

system that elude conventional procedures. Both two and three dimensional models have

been proposed for analysis of cofferdams. The three-dimensional model provides the means

for accurately accounting for the complex geometry of the cellular cofferdam, but it is expen-

sive to use, and remains beyond the reach of most applications. Two-dimensional models

offer utility in the study of cofferdams through parametric studies; however, the models used

to date have mainly been designed for specific applications.

INTRODUCTION 2

In one of the most extensive studies of a specific project, Clough and Kuppusamy (1985)

undertook analyses for the Lock and Dam 26 Replacement (R) cofferdam. This cofferdam was

one of the largest projects of its type in the world, and its first stage was well instrumented.

In the course of this study, the program SOILSTRUCT was modified to be used in three ver-

sions, with each version designed to address some important aspect of the cofferdam re-

sponse. To model orthotropic behavior of sheet piles, an E-ratio concept was introduced.

Reasonable predictions of the behavior of the cofferdam were made, and verified through the

instrumentation results from the first stage of the cofferdam. However, it was apparent that

improvements in the modeling techniques could be made, and that this was advisable before

any general parametric studies were conducted with the programs.

This particular investigation was undertaken with the general objective of adding needed

enhancements to the SOILSTRUCT cofferdam programs, as discussed in following para-

graphs, and conducting parametric studies to aid in developing improvements to the existing

design technology for cofferdams. At about the same time as this work began, a comple-

mentary effort was undertaken at the U.S. Army Corps of Engineers Waterways Experiment

Station by R. Mosher to develop a three-dimensional finite element program for analysis of

cofferdams. It was decided that where possible, the programs for the three-dimensional

analysis and two-dimensional analysis would be made compatible. Thus, the objective of the

present effort was expanded with this goal in mind.

In Chapter 2, a review of the literature on cofferdams is presented. This includes historical

background, techniques for construction, examples of failures of cofferdams, existing design

approaches, and available finite element techniques. Areas where improvements are needed

in finite element analysis procedures are noted.

Chapter 3 presents the documentation for inclusion of a shell element in the axisymmetric

version of SOILSTRUCT finite element program. The shell element is provided to make it

INTRODUCTION 3

possible to model sheet pile thickness exactly, to account for their bending characteristics,

and to make this program compatible with three-dimensional version being developed at

Waterways Experiment Station. Predicted results using the new program are verified against

closed form solutions and compared to predictions for the Lock and Dam 26 (R) cofferdam,

made previously using two and three dimensional finite element models.

Parametric studies of the cell filling case using the modified axisymmetric program are

outlined in Chapter 4. Effects of depth of cell embedment, free cell height, and the strength

of soil in the cell fill and foundation on the maximum sheet pile deflections and maximum

interlock forces are investigated.

In Chapter 5, modifications to the plane strain version of SOILSTRUCT are described. The

plane strain model is used to examine the response of a vertical slice cut through the

cofferdam. This model allows one to study the response of the cofferdam to differential load-

ing as a result of berm placement, dewatering, and river flooding. The first of the modifica-

tions involves the addition of a beam element to the program to allow for improved modeling

of the structural system used for the cells, as actual thickness and bending behavior of sheet

piles could be modeled. The beam element serves to represent the "front and back walls" of

the cell in the vertical slice analysis. The second modification is the formulation of a new

method for the system used to connect the front and back walls of the cell. The connection

system in essence serves as the means to realize the effects of the "missing" part of the cells

that exists between the front and back walls. In the new approach, a set of special shear

transfer elements are used which overlay the soil elements representing the cell fill. Also

included in Chapter 5 are theoretical analyses designed to determine one of the two modulus

reduction factors for the shear transfer elements.

Chapter 6 is devoted to a series of case history studies using the modified plane strain

program. These studies are designed to test the ability of the new program to predict actual

INTRODUCTION 4

behavior of cofferdams where instrumentation results are available to check the response.

A secondary purpose of the case history analyses is to compute the second modulus re-

duction factor to arrive at stiffness that is needed for the shear transfer elements.

Chapters 7 and 8 are devoted to use of the modified plane strain program for studying the

behavior of Lock and Dam 26 (R) cofferdam during differential loading and conducting

parametric studies. The results are applied to evaluation of conventional analyses of internal

failure of cofferdam cells. Particular attention is given to deformations of the cells to provide

the designer with useful information that can guide decisions about how much deformation

will occur in future cofferdams. Finally, a new method for the analysis of internal failure of

cofferdams is proposed. This method is less conservative than those now existing.

The last chapter presents a summary of the information in this document. Also, conclu-

sions that can be drawn from the results of the study are made.

INTRODUCTION 5

Chapter II

BACKGROUND

2.1 Historical Background

The cellular cofferdam was first used as a temporary structure to exclude water from an

excavation so that construction could proceed in the dry condition. Today, cofferdams are

used to retain both soil and water and may be permanent structures, such as piers, wharves

and jetties. Cellular cofferdams are used in lieu of earth or rockfill dams when the width of

the structure must be small, when a vertical face is required, or when stability against scour

is required. The first cellular cofferdam was built in 1908 at Black Rock Harbor, Buffalo, N.Y.

with a height of 30 feet and using square cells. Top of cell movements were as large as 3.5

feet between crosswalls (Stevens, 1980). Circular cells were used two years later in a

cofferdam built to raise the battleship Maine in Havana Harbor. An internal earth berm was

used to stabilize the cofferdam because of excessive movements during dewatering.

Diaphragm cells, consisting of curved cell faces and straight crosswalls, were used by the U.S.

Army Corps of Engineers in 1915 at Troy, N.Y.

BACKGROUND 6

2.2 Construction of Cellular Cofferdams

Cellular cofferdams are constructed using interlocking steel sheet piles forming adjacent

cells which are usually filled with free-draining cohesionless material. The combination of

steel cells and fill, which individually are unstable, make cofferdams a unique type of structure

which is capable of withstanding lateral loads. They are usually temporary, may have a low

factor of safety, can resist large lateral loads that may cause noticeable cell movements

without hindering their performance, and are often constructed where difficult site conditions

exist.

Cells are commonly of circular, cloverleaf and diaphragm configurations, as shown in Fig-

ure 2.1. Circular cells are constructed using a template, or frame, having the same plan area

as the cell. Connection sheet piles are set first against the outer perimeter of the template,

and are held in place by spot welding and guy lines. Closure is made by sticking the re-

maining sheet piles, usually in groups of three or four to minimize interlock tension. For cells

on a rock foundation, sheet piles are driven individually into or to refusal on rock to increase

the resistance to sliding, decrease the interlock tension at the toe of the cell, and minimize the

possibility of cell fill loss. Penetration is usually limited to about five feet in hard clay and ten

feet in dense sand so pre-excavation may be required. Higher penetrations are sometimes

used depending upon project requirements. Hard driving is avoided to decrease the chance

of driving out of interlock. Splices are staggered to limit deformation, and the piling should

be long enough to extend above the water level.

Circular cells are often filled hydraulically with sand and gravel dredged near the site. This

eliminates the need for compaction and actually pretests the interlocks because the maximum

interlock stresses may occur during filling if the water inside the cell is high and the water

elevation outside is low. The template is removed after partial filling has given the cell

BACKGROUND 7

8 "

B b

a. Circvl<Y CoFkrrlom

J. -

' ' c,.,, . ..,.~,""

b 8 .

- -b. Dlophrom Col/~rtlom

c. Clovtrleal C"llerr:bm l~9~nd

IJ 'V"'°"'k"I wid'lh or c1Bu/o,. col'l'1rdom; wio'flJ of /'.c/i,,ew• sl'fll~l-wr1// ""°/"""'°"7 IY ~ "'"" au11 o,. s~clio,, A'loo'u/11, 9~"~r411}' o•a8/J lo a9/J

b lolol """" o' i:'I/,.. ~""°" (. o.-~ra91 di.s/oM>~ '4/,tt11 uon woQ r r"o'i'vs ~ circubr all lfOll. d.O~ "1011, or clowr/MI" w"ll

tn U>Own

Figure 2.1. Common cell configurations (Lacroix, et al. 1970).

BACKGROUND 8

enough stability to prevent racking. Circular cells are filled before the connecting arcs. An

alternative to the use of dredging the fill is placement by clamshell process. This leads to

lower interlock stresses during cell filling. Diaphragm cells are filled progressively, so that the

difference in elevation of the fill does not exceed three to five feet on opposite sides of each

crosswall.

In response to cell filling, the cell walls barrel out as the piling is laterally loaded and the

slack in the interlocks is taken up. The maximum bulging, and the maximum interlock tension,

occurs at a point usually located one-third to one-quarter of the cell height above the dredge

line (Stevens, 1980).

The cell fill settles as the cofferdam is dewatered. During subsequent fluctuations of the

phreatic surface, additional settlement occurs, particularly on the unloaded side of the

cofferdam. Extensive movement of heavy construction equipment over the top of the cells also

contributes to the compaction of the fill. Lacroix et al. (1970) report total cell fill settlement

may be as much as six inches for high cofferdams with heights greater than 50 feet. Cells

founded on sandy or silty soils may experience total settlements as large as fifteen inches

(Stevens, 1980).

In response to dewatering, top of cell movements in the horizontal direction of three to six

inches are normally experienced for high cofferdams with good foundation conditions. One

exception was the New Cumberland cofferdam which consisted of fifty-four foot diameter cells

sixty feet high founded on rock. This is the smallest width to height ratio attempted in the

series of Ohio River cofferdams. Swatek (1966) reported that the cofferdam "performed ad-

mirably" despite eighteen inches of horizontal movement at the top of the cell. Schroeder,

Marker and Khyujerernpanishk (1977) also reported nine inches of movement at the top of a

56-foot high cellular bulkhead founded on sand without impairment of performance. Lacroix

BACKGROUND 9

et al. (1970) have concluded that top of cell movements would have to be several feet before

interlock rupture would occur.

2.3 Failure of Cellular Cofferdams

Lacroix et al. (1970) reported that the most frequent cause of cell failure in the cases they

reviewed was excessive interlock tension, which may have resulted from inadequately de-

signed connection of sheet piles or excessive cell deformation. In a later report by the U.S.

Army Corps of Engineers (1974), it was concluded that structural failure of fabricated tees and

wyes has been a common cause of cell rupture. The Corps (1974) reported ten failures of 90°

welded tees and four failures of 78° welded wyes. Failure of welded connectors usually oc-

curred in the web of the main sheet pile, or through web rupture on both sides of the stem,

separating the connector into three pieces. The inherent weakness of welded fabrications

prompted the Corps to require riveted connectors in 1965 (Stevens, 1980).

Failures of connectors were noted to usually occur during cell filling, although one failure

took place during dewatering and another as overburden inside the cofferdam was removed.

It is recommended that to decrease the pull exerted by the stem of a connector, the radius

of the connecting arc should be as small as possible, never exceeding one-half the cell radius.

Because the component of the stem force normal to the sheet pile for a 30° wye is one-half

that for a tee, Lacroix et al. (1970) recommended that riveted tees only be used for cell heights

of less than 40 feet.

During easy driving, piling may not seat in rock when uneven pile lengths are driven in

pairs or the rock surface is very irregular. During hard driving, piling can be driven out of

interlock. High velocity flow will scour the overburden and weathered rock, exposing windows

BACKGROUND 10

at the base of the cell. The current pulls the cell fill out, forming a pipe to the top of the cell

along the sheet pile wall. Cell collapse may be prevented by dumping in coarse rock or baled

hay, but must not be delayed because a cell can empty and collapse in a few hours. The

windows can also be sealed from outside the cell. The Corps (1974) reported the collapse of

three cells at Webbers Falls Locks and Dam and one at Holt Lock and Dam by removal of fill

by scour. At Keystone Dam, 2.5 feet of the shale foundation was eroded during a long period

of high spillway discharge, but cell rupture was averted.

The catastrophic failure of the second stage cofferdam at Cannelton was attributed to pip-

ing. The failure occurred during high water at a tie-in arc connecting the downstream arm of

the cofferdam to the sloping face of the river lock wall. The seals provided were not adequate

to limit seepage along the fill-concrete interface. As the cell unloaded, the piling moved away

from the lock wall, and water rushed in, flooding the cofferdam.

Driving piling out of interlock is a common occurrence. Although split interlocks usually

do not lead to cell rupture, loss of cell fill due to piping may occur when overburden is re-

moved by scour or excavation. Only three cases of total interlock failure were reported by the

Corps of Engineers (1974), all occurring during cell filling. Splits discovered after dewatering

are repaired by welding steel plates across the gap. To avoid split interlocks, piling should

not be driven through overburden containing boulders or other obstructions. To ensure that

used sheet piles interlock properly, the amount of spread between thumb and finger as well

as the overall distortion needs careful inspection. Sheets at splices must be dimensionally

compatible to prevent high localized stresses in the interlocks and webs.

When divers inspected the 12 cells forming the river arm of the first stage cofferdam at

Cannelton, of the 14 splits discovered, 12 occurred in connecting areas. A preponderance of

splits occurs in connecting arcs when the arcs are driven after the adjacent main cells have

been filled. The sheet piles of the arc must conform to the curvature of the connectors. Some

BACKGROUND 11

adjustment is possible within the interlocks, but the main cell barrels out so much that driving

out of interlock occurs frequently. This is prevented by driving at least the first two sheets of

the connecting arc prior to filling the main cell.

The first stage cofferdam at Uniontown Locks and Dams failed by deep-seated sliding

during a rising river ten days after dewatering was completed. Seven downstream arm cells

slid with the shale and limestone foundation on an underlying coal and clay seam. Four cells

remained essentially intact, sliding 37 to 72 feet into the cofferdam interior. The two adjacent

cells ruptured, and the cofferdam was flooded in less than ten minutes after movement was

first noticed. The failure plane was located at a maximum depth of 16 feet below the top of

rock, but daylighted at a normal fault near the center of the cofferdam (Stevens, 1980).

The sub-cofferdam located inside the first stage cofferdam at Cannelton Locks and Dam

failed when seven cells slid eleven feet toward the nearly completed pier excavations, with

one cell rupturing at 90° riveted tee (Stevens, 1980). Failure resulted because the cells were

too near the excavation and the rock surface was of poor quality.

2.4 Existing Design Theories

The present basis for design of cellular cofferdams is essentially semi-empirical. Design

methods were originally suggested by Pennoyer (1934) and were later modified and extended

by Terzaghi (1945). Alternative design concepts and modifications have been proposed by

Cummings (1957), Krynine (1945), Hansen (1953, 1957), Department of Navy (1977), and

Schroeder and Maitland (1979).

BACKGROUND 12

The usual design approach for cellular structures involves consideration of both internal

and external stability. External stability requires adequate factor of safety against (i) sliding

and (ii) overturning. The internal stability considers safety against (i) bursting of interlocks

and (ii) shear distortion of cell fill. The methods for design have been discussed by Terzaghi

(1945), Lacroix et al. (1970), Dismuke (1975), Schroeder and Maitland (1979) and U.S. Army

Engineer Waterways Experiment Station (1986).

Based on experimental evidence, Schroeder and Maitland (1979) have indicated that nei-

ther sliding nor overturning can occur before a typical cell embedded in deep sand will fail

because of loss of internal stability. Therefore, in designing such cellular structures, it be-

comes important to provide an adequate design for internal stability.

2.4.1 Interlock Tension

Design for interlock tension has been discussed by Terzaghi (1945), Lacroix et al. (1970)

and Schroeder and Maitland (1979). Four recommended design pressure diagrams for cal-

culating interlock forces are presented in Figure 2.2. These differ in the distribution and

magnitude of lateral earth pressure applied to cell walls. The computed maximum lateral

earth pressure is converted to an interlock force using following formulae:

Main cell piles:

T = Px R

where:

T = Interlock force

P = Lateral earth pressure

R = Radius of cell

BACKGROUND 13

TERZAGHI METHOD ---------------I

·' , I

I I

I I - I -

I I

I I p I

K = 0.4

TVA METHOD ----------I

I I

I I , - I

I

' ' '

P =Ka ' at 0.75H av K • tan2 (45-! )

a 2

·iP H

U.S. ARMY CORPS OF ENGRS METHOD SCHROEDER '& MAITLAND METHOD -----------------------~----- ---------------------------

-

p

K

/ /

I I

I I

I p I

Kcr ' at H v 0.5

/ /

/

H I I I

/ ,'

/ /

/

I p

' ' ' ~:r ', d' '

P = Kcr ' at 2 H' v -3-

H' = H+d' d'= 5 ft.

T

K=l.2 to 1.6 tan2 (45-! ) 2

NOTE: crv' is vertical effective stress

Figure 2.2. Conventional analyses methods for Interlock force (from Shannon and Wilson, 1982).

BACKGROUND

H'

14

Common wall piles:

T = P x L x Seca

where:

L = center line distance between main and arc cells

a = angle between center line of main cell and Y-connection point

In computing maximum interlock force, the Terzaghi and Corps of Engineers methods

consider lateral earth pressure increasing up to dredge line, assuming a lateral earth pres-

sure coefficient as 0.4 and 0.5, respectively. The lateral earth pressure in the TVA method

increases up to one-fourth of free cell height from dredge line, and then decreases to zero at

dredge line, with the lateral earth pressure coefficient being taken as active earth pressure

coefficient. Schroeder and Maitland method considers the plane of fixity below dredge line

and assumes maximum lateral earth pressure at a distance of one-third of the height from

point of fixity to top of cell measured from point of fixity.

For a direct comparison of these methods, consider a cofferdam cell with cell diameter of

63 feet, free cell height of 60 feet, depth of embedment 20 feet, a cell fill total unit weight and

friction angle of 123 pcf and 30 degrees, respectively, and water level at 30 feet from top of the

cell. The predictions of interlock forces using these design methods are shown in Figure 2.3.

The TVA method predicts the smallest interlock force, and the Schroeder and Maitland

method, Terzaghi method and Corps of Engineers method yield maximum interlock force val-

ues which are higher by 36%, 47% and 83%, respectively, as compared with TVA values.

BACKGROUND 15

-., QJ QJ ~ '-'

i::: 0 ~ ., cu > QJ

..-t f%l

70

60

50

40

30

20

10

.,,.

Engineers & Maitland

Terzaghi

Interlock Force (Kip/inch)

Figure 2.3. Interlock force, comparison of different conventional methods.

BACKGROUND 16

2.4.2 Shear in Cell Fill

Terzaghi (1945) suggested that before failure due to overturning occurs, the cofferdam is

likely to fail due to shearing of soil along vertical line gh (Figure 2.4) at center of cell during

application of lateral loads. He developed the design approach for vertical shear for

cofferdams founded on rock. However, he indicated that results of such an analysis were not

greatly different for structures on rock or on sands and proposed that the rules developed for

analysis of cofferdams on rock would apply to all cases.

In his vertical shear analysis, Terzaghi (1945) assumed a straight line distribution of pres-

sure on the base of cofferdam (Figure 2.4).

Q = Total force represented by each triangle of base pressure diagram

M = Overturning moment

M = 2bQ 3

or Q = 3M 2 b

(2.1)

The shearing resistance S' on vertical plane gh = PcTan<p .

where: Pc = Earth pressure on gh per unit length of cofferdam

q> = Coefficient of internal friction of cell fill

Pc = 1/2yKH2 •

where: y = unit weight of cell fill

H = height of cell

K = coefficient of lateral earth pressure at center line of cell

BACKGROUND 17

BACKGROUND

J• b

~rrM g

I oJllo

I

m Rock

.. ,

I H

~ Pressure diagram at base n

! +Q I-- 2b/3--f

Figure 2.4. Terzaghi's vertical shear method.

18

Therefore, S' = 1/2 y K H2 tan q>. Total tension in a interlock with length H is:

T = 1/2 KyH 2r

where: r = radius of cell

Total resistance against slippage in interlock is:

T f = 1/2 yKH 2r f

where: f = coefficient of interlock friction.

Circular cells contain two cross walls per cell and length of each cell is 2L.; those of the

diaphragm type contain one cross wall per cell and the length of each cell is L. Hence, the

resistance to shearing along gh contributed by interlock per unit length.

S" = rL = .1.yKH2L.r L 2 L

[2.2]

Total average shearing resistance S is given by:

S = S' + S" = .1.yKH2( tan q> + L.r, 2 L

[2.3]

the ratio r/L is close to or equal to unity. Hence, approximately:

S = 1/2 y K H2 (tanq> + f).

The corresponding factor of safety:

2 Gs= ~ = y~~ K(tanq> + f) [2.4]

Terzaghi proposed that the lateral earth pressure coefficient K within the cell should re-

main at its initial value of something less than 0.5. The factor of safety G, is taken as equal

to or greater than 1.25 and 1.5 for temporary and permanent structures, respectively.

BACKGROUND 19

Since its proposal by Terzaghi, the vertical shear concept has been the subject of consid-

erable criticism, in part directed towards the assumption of the vertical shear mechanism, and

in part towards the use of 0.5 for the lateral earth pressure coefficient. Concern about the use

of the vertical shear surface was first voiced by Pennoyer (1945), who analyzed a number of

cofferdams that had performed well, and found that only 60% of them were predicted to be

stable using the Terzaghi mechanism. Notably, all of the cofferdams had a large width relative

to their height, and Pennoyer felt that the shear surface should be a function of cell width.

Subsequently, three authors suggested alternative methods of analysis based on different

assumptions for the internal failure surface as shown in Figure 2.5. Krynine (1945) proposed

that the failure surface should be curved, and follow a path from the bottom of the outboard

sheet up to the top of the inboard sheet. This mechanism then allows for increased resistance

as the cell width gets larger. Hansen (1953, 1957) followed a different track, and suggested

that the failure surface would be located near the bottom of the cell and have a shape of log-

arithmic spiral passing from outboard to inboard sheet piles. In a simplified version of this

approach, Cummings (1957) proposed a method of analysis based on horizontal shear con-

cept. He suggested that the failure surfaces could be taken as a straight horizontal shear

planes through the cell fill. Schroeder and Maitland (1979) reported that Cummings' approach

overestimates moment resisting capacity of cofferdam cells.

In an effort to sort out the controversy about the type of failure surface which should be

used to analyze for failure under lateral loading, Schroeder and Maitland (1979) performed a

series of large scale model tests of cellular cofferdams. In the tests, the cells were loaded to

complete failure, and it was found that sharply defined terraces formed at the surface of the

cell fill. In addition, slippage was observed along the sheet pile interlocks in the middle and

inboard portions of the cell. The observed slippages in the fill and the sheet pile interlocks

were considered to support the original Terzaghi vertical shear mechanism. Notably, at the

stage of the tests where the failure mechanism was clearly visible, the deformations of the

cells were very large, with lateral movements of the tops of the sheet piles reaching up to 50%

BACKGROUND 20

Load Failure I Surface / >·/·

KRYNINE (1945)

Load

Load

- - - -- - - - - ---t'11n'l~

(~~~!._ ~~~:~e . '·

HANSEN (1953 ,1957)

CUMMINGS ( 195 7)

Figure 2.5. Failure surlaces suggested by different authors.

BACKGROUND 21

of the cell height. This suggests the need for the application of a significant factor of safety

against this failure mode if deformations are to be kept to reasonable levels.

While Schroeder and Maitland (1979) generally supported the failure mode of Terzaghi,

they disagreed with his proposed lateral earth pressure coefficient to be used in the vertical

shear calculation. Earlier, Krynine (1945) had noted that there was reason to believe that the

coefficient of lateral earth pressure during lateral loading should be higher than 0.5, and could

be slightly higher than the at-rest coefficient. Schroeder and Maitland (1979) found that if the

Terzaghi vertical shear mechanism is used, then a coefficient of earth pressure of one should

be used in the calculations. This leads to an automatic doubling of the predicted lateral load

capacity relative to that originally proposed by Terzaghi.

Considering all of the proposed methods, one point is clear. The end result is not simply

a product of using one of the assumptions about failure surface or coefficient of lateral earth

pressure. The final result reflects a combination of the type of failure surface, the lateral earth

pressure coefficient, and the factor of safety applied. Debate about one or the other of the

factors on an independent basis is somewhat artificial since all of them are linked.

2.5 Finite Element Analysis Capabilities

Conventional design methods for cellular cofferdams typically consider analyses for inter-

lock tension, vertical shear and overall stability independently, and none of the existing pro-

cedures predict cell movements and deflections. Although Schroeder and Maitland (1979)

modified design procedures few years ago, most of the design techniques were developed

more than 30 years ago, and the different methods often lead to considerable differences in

results.

BACKGROUND 22

2.5.1 Early Investigations

In the late 1960s, the finite element method was finding application to problems involving

soil-structure interaction because it could be used to consider the soil and the structure as a

single unit, and predict deformations as well as structural loads and behavior. It was not until

the mid 1970s that investigators began to experiment with the finite element method for

cofferdams. Kittisatra (1976) proposed to analyze the problem of cell filling using an

axisymmetric model {Figure 2.6). His results were interesting, but did not appear to be real-

istic, a finding which probably results from the fact that his model was limited. Kittisatra as-

sumed that the cell was a perfect pressure vessel, the soil was a linear elastic medium, and

that no deformations occurred between the fill and the cell walls as the backfill was placed.

Clough and Hansen (1977) and Hansen and Clough (1982) proposed the use of "vertical

slice" plane strain type of analysis to approximately model the effects of cell filling, dewatering

and interior excavation at the Willow Island cofferdam located on the Ohio River. Circular and

cloverleaf cells were considered in the analyses. Internal springs were used to connect the

front and back wall of cofferdam {Figure 2.6). Spring stiffnesses were designed to represent

the connecting effect exerted by circular cell shape. The soil in the cell fill and foundation was

assumed to behave as a nonlinear medium and slippage between the cell walls and the soil

was allowed by the use of special interface elements. Stevens (1980) extended the vertical

slice model idea of spring elements by his proposal to reduce the internal spring stiffnesses

from those of the of the perfect pressure vessel to allow for interlock yielding and slack.

While the analyses using the vertical slice model gave reasonable predictions of general

cell deformation and overall behavior, they provided no rigorous accounting for any form of

three-dimensional interaction between the cell. Thus, the interactions at common walls be-

tween cells and at critical connection points could not be checked.

BACKGROUND 23

AXISYMMETRIC MODEL

VERTICAL SLICE MODEL

HORIZONTAL SLICE MODEL

[QuiPOl•ftti•I lines (typ;"''

Figure 2.6. Finite element models (from Shannon and Wilson, 1982).

BACKGROUND 24

2.5.2 Lock and Dam 26 (R) Cofferdam Studies

In the early 1980s, the U.S. Corps of Engineers proposed to apply the finite element method

to the analysis of the Lock and Dam 26 (Replacement) cofferdam. This cofferdam was signif-

icant because it was to be one of the largest in the world, and it was to be instrumented, al-

lowing for evaluation of the observed behavior against that predicted. The location for the

cofferdam is on the Mississippi River at a site about 20 miles upstream from St. Louis,

Missouri. The cofferdam is described in the publications by Shannon and Wilson (1982),

Moore and Kleber (1985), and Clough and Kuppusamy (1985). Details of the cofferdam will

be given later in this document as it is used in a number of test analyses herein. For purposes

of introduction, the cofferdam was conceived of as consisting of three stages. The first stage

was built in 1982, and work with it was completed in 1985. The second stage was built in 1986

and is presently in place. The third stage is to be built in 1989. In stage one, the cells were

approximately 63 ft. in diameter, and stood 60 ft. above the mudline of the river. Stage two

cells have the same diameter as the first stage, but on the average, the cells are 80 ft. above

the dredge line for stage two. The sheet piles for the cells consisted of U.S. Steel Designations

PS-32 for the main and arc cells, and PSX-32 for the common walls. In the stage one

cofferdam, the sheet pile penetrated some 35 ft. into the riverbed. Foundation soils consisted

of medium-dense to dense sands. The cell fill was obtained from the riverbed sands, and was

clamshelled into place in the cell.

The instrumentation effort was primarily focused on the stage one cofferdam. Many types

of measurements were made, and the monitoring was done frequently. Stage two behavior

was monitored mainly through the use of a survey net aimed at measuring top of cell move-

ments.

BACKGROUND 25

The initial finite element analyses of the cofferdam consisted of two-dimensional models,

and these were unique in that three different approaches were used in an attempt to gain an

insight to all of the important facets of the cofferdam behavior. Details are given by Shannon

and Wilson (1982), Clough and Kuppusamy (1985). and Kuppusamy et al. (1985). Of the three

approaches, two were the previously described axisymmetric and vertical slice analyses. The

third was a new analysis which is termed the horizontal slice, or the generalized plane strain

model. Schematically, this is shown in the right-hand portion of Figure 2.6 as consisting of a

horizontal slice cut through the cofferdam. It will be described subsequently. All of the

models, schematically shown in Figure 2.6, were handled using three different versions of the

program SOILSTRUCT, developed by Professor G. W. Clough and his co-workers to analyze

soil-structure interaction problems. In all three analysis types, allowances were made for

sequential staging of the loading, non-linear soil behavior, slip of the soil on the interface be-

tween the soil and the sheet piles, and yielding in the interlocks of the sheet piles.

The vertical slice model used for the initial studies of Lock and Dam 26 (R) was similar to

that first proposed by Clough and Hansen (1977), except that provisions were made for sheet

pile interlock yielding. Stevens (1980) first recognized that there was a need for extra flexi-

bility in sheet pile systems due to slack and yielding in interlocks and made reductions in

connector spring stiffness. To represent this behavior, Clough and his co-workers proposed

an E-ratio concept for Lock and Dam 26 (R) studies, where the E-ratio is the ratio of the re-

duced horizontal modulus to that of steel. In the axisymmetric analysis, the sheet pile system

was treated as an orthotropic shell with reduced modulus in radial direction. In the vertical

direction, the steel modulus was used. This will be discussed in more detail later. In the

vertical slice analyses, the stiffnesses of the connecting springs were reduced by amounts

based on the E-ratio concept for case of cell filling. Based on case history analyses, it was

concluded that the appropriate E-ratio for a typical cofferdam lies between 0.1 and 0.03 for cell

filling. It was also observed that predictions using an E-ratio of 0.03 reasonably modeled the

average observed behavior for the Lock and Dam 26 (R) stage one cofferdam. Subsequently,

BACKGROUND 26

interlock connection testing of PS32 and PSX32 sheet piles was performed by Barker et al.

(1985), substantiating that the average E-ratio was 0.03 during filling.

It was judged by Clough and Kuppusamy (1985) that after cell filling, much of the interlock

deformation and sheet pile re-alignment should have occurred. Thus, they proposed that an

E-ratio of one was appropriate for loading after filling for the vertical slice analysis.

The new horizontal slice model was proposed to provide a means of analyzing the inter-

action between main and arc cells. A horizontal slice is cut through the cofferdam system at

some level above dredge line {Figure 2.6). This approach assumes that a constant strain ex-

ists in the out of plane direction. generated by the vertical gravity loads above the plane.

Horizontal load effects are generated automatically as a part of the analysis. The analysis

provides results on interlock tensions and cell deformations for the main and arc cells, the

common wall, and the critical wye section where the two cells are joined. This model cannot

account for the lateral support of foundation soils, and thus is applicable only for the upper

two-thirds or so of the cells where the dredge line effects have little influence. In this ap-

proach, only the horizontal response of the cells is considered, and the modulus of the sheet

piles was reduced to accommodate the E-ratio effect.

In all the Lock and Dam 26 (R) analyses. the soil behavior was simulated by a nonlinear.

elastic stress-strain response (Figure 2.7). The model followed similar lines of response to

that described by Duncan et al. (1980). The modulus at any point on the nonlinear loading

portion of the stress-strain curve is defined as the tangent of a hyperbola which fits the curve.

The shear and bulk modulus values of the soil were varied to accommodate the changes in

shear and confining stresses, which occur during the step-by-step simulation of construction

loading process (Clough and Kuppusamy, 1985). The modulus of each element in the mesh

was modified after each step of loading, and the entire stiffness matrix reformulated.

BACKGROUND 27

f O"' C\J

L&J (.) z L&J a:: w u. u. 0 (/) (/) L&J a:: ..... (/)

...J

ci: (.) z a:: a.

BACKGROUND

PRIMARY LOADING

UNLOAD-RELOAD

STRAIN

Figure 2.7. Non-linear stress strain behavior of soils.

28

The predicted behavior for Lock and Dam 26 (R) cofferdam stage one allowed comparisons

of the different models and of the models to the observed behavior. In the model to model

comparison, the case of cell filling was used since all three were applied for this stage.

Comparison of the axisymmetric and vertical slice results for cell filling is given in Figure 2.8,

where interlock forces and cell denections are given for the final filling stage of the cofferdam.

It can be seen that the two different analyses produce very comparable results. The cell wall

denections show the cofferdam to exhibit a bulging profile with the maximum radial denection

occurring at a position above the mudline. The interlock forces follow this same general trend

as they should since the interlock forces are proportional to the cell deflections in the filling

stage. Similar comparisons between the horizontal slice model results and those of the other

two are given by Kuppusamy et al. (1985), where it is shown that for the main cell, the three

different models yield similar results. No comparisons are made for the predictions of hori-

zontal slice model for the arc cells and the common wall, since only the horizontal slice model

is capable of analyzing for these conditions.

The Shannon and Wilson (1982) report gives comparisons of the various finite element

model predictions for interlock forces for cell filling and those obtained from conventional

interlock force procedures (Figure 2.9). Of the conventional methods, those of Schroeder and

Maitland (1979) and TVA yield a distribution similar to that predicted by the finite element an-

alyses. In this case, the interlock forces first increase with depth below the cell top, and then

break and decrease in the area near the mudline. The other conventional analysis procedures

predict interlock forces increasing continuously to the mudline. In terms of magnitudes of the

interlock forces, the finite element predictions of the E-ratios of 0.03 and 0.1 fall between those

of Schroeder and Maitland (1979) and the TVA procedure.

Comparisons of the interlock forces from the finite element predictions to those observed

showed a reasonable agreement. There was considerable scatter in the observed data, and

BACKGROUND 29

QI )> n ,.. Ci') ::u 0 c z c

w 0

Interlock Force(Kip/in) Horiz.Deflections(ln.)

430° 2 4 6 430° 1 2 3 4

420 420

~ 410 ~ 410 (.!) (.!)

\ z W.T. ~ 400 I W.T.

- 400 + µ I µ C1I \

C1I C1I C1I

t. 390 I t. 390 c: \ c: 0 I 0

-r-l j •.-4

~ 380 µ

I Ill 380 :> /

:> C1I C1I

...... r-1

w 370 w 370

I Axisymmetric t

360 rr /•rt ical slice 360 11 r-Vertical slice1 350 ~ I 350 f

I I

340 11 J j 340 I

I I I I I I I J L I

Figure 2.8. Comparison of results from axlsymmetrlc and vertical slice analyses for cell filling (from Shannon and Wilson, 1982).

Interlock Force Kips/inch

420

410

~ 402 SJ.-cu 400 cu

......... ...... '

fa.

c: 390 E-Ratio= 0 • 03

~

c: 0 380 ~

~

co > cu 370 ..-4

fzl

360

350

340

Legend

--- Schroeder ----~Axisymrnetric FE Analysis --- Terzaghi ------TVA - --Corps of Engineers -·-·-DM-7

Figure 2.9. Comparison of Interlock forces predicted by various methods at the end of cell filling (from Clough and Kuppusamy, 1985).

BACKGROUND . 31

the finite element models tended to give interlock forces that agreed well with the average

results.

Of the two-dimensional models used in the initial studies of the Lock and Dam 26 (R)

cofferdam, only the vertical slice is able to predict behavior for loadings beyond filling. Figure

2.10 gives predicted wall displacements for a series of loading stages after cell filling. Com-

parisons to observed behavior showed that there was general agreement with the predictions

in qualitative response, but that magnitudes of movements were only approximately modeled.

Clough and Kuppusamy (1985) suggested that better predictions could be made if the shear

transfer mechanisms from one side of the vertical slice model to the other could be improved.

Following the initial finite element investigation for Lock and Dam 26 (R), additional studies

have been performed aimed at this project. One of these involved two-dimensional analyses

to determine the effect of depth of penetration of the sheet piles. This led eventually to the

use of lessened penetrations of the second stage cofferdam. In addition, an effort was

undertaken to develop a three-dimensional finite element model for the cofferdam by R.

Mosher at the Waterways Experiment Station. Results from this study are in the process of

being published and will be covered later in this document as a basis for comparison to the

new two-dimensional models used herein (Clough et al., 1987).

2.6 Summary and Recommendations

The conventional design methods for cellular cofferdams were largely developed over 30

years ago. Recently, Schroeder and his co-workers have proposed significant modifications

to the conventional methods that lead to less conservative results than those of the older

technology.

BACKGROUND 32

GI

~ ~ a ::0 0 c z g

w w

0 > (!) z • t;j

L&J ..... z z 0 ~ ~ ~ L&J

Lateral Deflection of Inboard SldeWall,ln. Lateral Deflectlon of Outboard Side Woll, in. 430 4 3 2 I . I I ' I

I I

4201- I ,, I

I I

410 I I

I I

I 400 I

I I \

390 \ \ \ I ~d Sldt \

\ \ 380 ,, \~ ....... .... ' 370

........ '

380~ Outboard Side

I

Inboard~

3!10

340

0 0 I 2 3 ~ 1430 ------'T"'----,1 WI R M I I

\

' ' 420

410

400

390

380

Drtde• Lint II / _,,,,, I 310

I If( I~~/ - Complttlon of cell flll

///J -· Completion of btrn fl II

I - Dtwoterln9 - Eacovotlon - Flood W.T. El 428

360

3!10

340

Figure 2.10. Vertical slice analysis, sheet pile deflections for different construction stages (from Shannon and Wilson, 1982).

The basic design procedures for cofferdams assume that the problem is to be divided in

two parts which are analyzed independently of each other. Thus, cell filling is treated as one

case, and differential lateral loading as another. In each situations, earth and water loadings

are assumed, and applied to the structure without a formal consideration for the effects of

soil-structure interaction. None of the existing methods have a technique for predicting def-

ormations and deflections of the cells. This latter deficiency is important in that safety

instrumentation for cofferdams is largely directed at measurement of movements.

Finite element procedures offer the possibility of dealing with the cofferdam system as a

soil-structure unit, and providing the means to predict cofferdam movements and cell de-

flections. To date, three two-dimensional finite element models have been proposed for

analysis of cofferdam structures - axisymmetric, vertical slice and horizontal slice. Also, a

new three-dimensional model is being developed at the U.S. Army Engineers Waterways Ex-

periment Station.

The two-dimensional models will remain the primary analysis tool, however, because of

their relative simplicity and ease of application. The two-dimensional finite element analysis

methods were developed primarily to meet certain job-specific needs. As such, they are in

need of improvement. This review of the previous work suggests that the following refine-

ments in the two-dimensional model are needed:

1. Provision of a shell element in the existing axisymmetric finite element program to model

the sheet pile thickness exactly and avoiding the need for reducing modulus value as is

presently done using one-foot thick two-dimensional elements.

2. Inclusion of a beam element in the existing vertical slice finite element program to model

the sheet pile thickness exactly and avoiding the need for reducing modulus value as is

presently done using two-dimensional bending elements.

BACKGROUND 34

3. Incorporation of a continuous load transfer element to represent the "missing" part of the

cell in the vertical slice analysis as opposed to the use of discrete springs.

The review of the literature also shows that there is a need for studies which can be used

to test proposed conventional methods of analysis of cofferdams, and to possibly provide in-

formation that can be used to predict deflections and movements of cofferdams. Areas which

appear to be useful to study through finite element parametric study include:

1. Effects of depth of sheet pile embedment, cell height, and properties of the cell fill and

foundation soils on movements and interlock forces.

2. Simplified methods to predict movements of cell walls during cell filling and differential

loadings.

3. Potential failure mechanisms in the cell fill during lateral loading.

4. Lateral earth pressure conditions in the cell fill during lateral loading.

BACKGROUND 35

Chapter Ill

AXISYMMETRIC VERSION OF FINITE ELEMENT

PROGRAM {SOILSTRUCT)

The program SOILSTRUCT was originally developed by Clough (1969) for plane strain

analysis of soil-structure interaction problems. In the early 1980's, it was modified by Clough

and his co-workers for axisymmetric analysis so that it could be used to study the effects of

filling of an isolated cofferdam cell (Clough and Kuppusamy, 1985). Radial, tangential and

vertical sheet pile deflections and stresses can be predicted along with profiles of sheet pile

deflections and stresses of the cell fill and foundation soils. In this version of the program, the

sheet piles are modelled by one-foot thick, four-node solid element having two degrees of

freedom at each node. A thickness of one foot was chosen from the aspect ratio point of view

to avoid numerical problems. The modulus value for the sheet pile is reduced in certain

proportion of the ratio of area of one-foot thick element and that of actual sheet pile. The

four-node solid element used for steel sheet piles, however, cannot take into account the true

bending characteristics of the sheet piles, and has thickness greater than that of the actual

sheet pile.

AXISYMMETRIC VERSION OF FINITE ELEMENT PROGRAM (SOILSTRUCT) 36

To circumvent these problems, the existing axisymmetric version of SOILSTRUCT was

modified in this work to incorporate a shell element for modelling the behavior of sheet piles.

This allows the thickness of shell element to be taken the same as that of sheet piles. Three

degrees of freedom (i.e., axial and radial displacements and rotation) are considered at each

shell element node to account for the bending characteristics of sheet piles. The modification

of the program to include a shell element also provides compatibility with a three dimensional

code developed by Mosher (1987).

3.1 Modification in Axisymmetric Finite Element Program:

Provision of Shell Element

The existing axisymmetric version of SOILSTRUCT finite element program was modified to

incorporate the two-node shell element described by Zienkiewicz (1977). Each node has three

degrees of freedom.

For a thin cylindrical shell (Figure 3.1), the three strain components are given the following

expression:


(a) Displacements and Stresses

( b) A Shell Element

Figure 3.1. A thin cylindrical shell.


where: E, = Axial strain

E9 = Hoop strain

x, = Rotation

v = Axial deformation

w = Radial deformation

r = Radius of cylinderical shell.

The corresponding stress resultants are:

{cr} -[ ~ ]- (D]{t}

where [DJ is elasticity matrix.

For isotropic shell:

1 v 0

[DJ= E.t v 1 0 1 - v2 t2

0 0 12

where: E = Modulus of elasticity

t = Thickness of shell

v = Poissons ratio .

For an orthotropic shell consider:

E1 = Value of modulus of elasticity in axial direction

E2 = Value of modulus of elasticity in circumferencial direction.

According to Goodman (1980):


V12 = Vz1 or, E1 Ez

where: v11 determines normal strain in symmetry direction j when stress is added in symmetry

direction i.

For an orthotropic shell, the matrix D becomes:

E1t V12E2t 0

1 - V12V21 1 - V12V21

[DJ= V21E1t E2t 0

1 - V12V21 1 - V12V21

0 0 E1t3

12(1 - V12V21)

and

E - Ration = Ez!E1

1 nv12 0

[DJ = E1t nv12 n 0

(1 - V12V21) t2 0 0

12

if V12 = V21 = v I


1 nv 0

[O] = E1t nv n 0

(1 - v2) t2 0 0

12

The shell element with two nodes, i j, possesses six degrees of freedom determined by the

element displacements:

where a,= [;]

The displacements within the element have to be uniquely determined by nodal displace-

ments a• and the position s, and maintain slope and displacement continuity.

In local coordinates, we have:

If v is taken as varying linearly with s and w as a cubic in s:

v = <11 + <1zS

r.t.=(dw). and r.t,=(dw). ,.,, ds ' ,., ds 1

AXISVMMETRIC VERSION OF FINITE ELEMENT PROGRAM (SOILSTRUCT) 41

w,

~j

Where, S' = SIL

or {u} = [NJ {q}.

The strain components are:

Where,

0 -1/L 0 0 1/L 0

[8] = 1 - 3S'2 + 2S,a J:..(S' - 2S'2 + S'3) (3S'2 - 2S'3) .!;-( -S'2 + S'3) r 0 r 0 r r (6 - 12S')

0 (4 - 6S') ( -6 + 12S')

0 (2 - 6S')

L2 L L2 L

The stiffness matrix K becomes:

dA = 2nrds = 2nrLds'


Where: S' = SIL

S' varies from 0 to 1

K = 2nrjJ(BTDBL) ds' n

or, K = 2nr I, H/(a) 1-1

For numerical integration of the above equations, the following formulae has been used to

change integration limits from a to b to -1 to 1:

b b - a n Z;(b - a) + b + a faf(x)dx = 2 _L W; f( 2 ) J, 1=0

In our case a=O and b=1.

The two-point integration has been used. For two-point integration:

f1f(x)dx = j_[1 x f{ (0.577350269189626 x 1) + 1} + 1 x f{ ( -0.577350269189626 x 1) + 1 }] JO 2 2 2

= ~ [f(0.788675124594813) + f(0.211324865405187)]

The above values are used in the finite element program to compute the shell element

stiffness matrix K.


3.2 Test Problems to Check Shell Element

Two test problems were solved using the modified finite element program to check the

accuracy of implementation techniques for the shell element in the program.

3.2.1 Test Problem 1

Consider long cylindrical shell subjected to uniform internal pressure (Figure 3.2). Ac-

cording to Timoshenko and Krieger (1970), the closed form solution for deflection and hoop

stress at center are:

w = pr2/Eh

O'r = pr/h

where: w = Radial deflection at center

O'r = Hoop stress at center

We assume for an example:

p = Internal pressure = 1000 psf

r = Radius of shell = 4.0 ft.

E = Modulus of elasticity for shell = 4.32 x 109 psf

h = Thickness of shell = 0.042 ft. (0.5 inch)

Based on closed form solution, the radial deflection and hoop stress at center are:

w = (1000 x 16)/(4.32 x 109 x 0.042) = 0.88 x 10-4 ft.

and O'r = (1000 x 4)/0.042 = 0.95 x 105 psf.


i I - 10 . I 9 -I

8 . -- 7

- 6 9 she 11 elements 1000 ~ 5 @ 4.0 ft each

- 4

- 3

- 2

-'"' 4.0 ft,,

Figure 3.2. Test Problem 1, long cylinder subjected to Internal pressure.


Using finite element program, the predicted radial deflection and hoop stress at center of

the cylindrical shell are 0.85 x 10-4 and 0.96 x 105 psf, respectively, which match the closed

form solution very well.

3.2.2 Test Problem 2

Consider a cylindrical tank with hydrostatic pressure inside (Figure 3.3). According to

Timoshenko and Krieger (1970), the closed form solution is:

w" = y(d - x)r2/Eh

<rt" = y(d - x)rlh

where: w" = Radial deflection at distance x from bottom

<rt = Hoop stress at distance x from bottom )(

We assume for an example that:

y = Unit weight of fluid = 100 psf

d = Height of tank = 36 ft.

r = Radius of tank = 4.0 ft.

E = Modulus of elasticity = 4.32 x 109 psf

h = Thickness of the wall of the tank = 0.042 ft. ( = 0.5 inch)

The deflections and hoop stresses using the closed form solution and predicted by the ti-

nite element program are given in Table 3.1. These results indicate that the finite element

predictions are consistent with the closed form solutions.


~ ,-' I I I I I I i i 4.0 ft -i I•

10

9

8

7

6

5

4

3

2

9 shell elements @ 4.0 ft each

Figure 3.3. Test Problem 2, cylindrical tank with hydrostatic pressure.


Table 3.1

Predicted Deflections and Hoop Stresses in a Hollow Cylinder

Distance from Radial Deflection Wx Hoop Stress at Bottom (x) (ft.) (ft.) (psf)

Closed Form FEM Closed Form FEM

6.0 0.2857 x 1011 0.259 x 1()6

8.0 0.2469 x 10-3 0.2541 x 10-s

10.0 0.247 x 1D6 0.244 x 1D6

22.0 0.1333 x 108 0.133 x 1()6

28.0 0.706 x 10-• 0.704 x 10-•

30.0 0.5714 x 1D6 0.576 x 1a5

32.0 0.3528 x 10-• 0.350 x 10-•


3.3 Problem of Interaction of Shell Element with

Two-Dimensional Elements in Program SOILSTRUCT

As shell element nodes have three degrees of freedom and two-dimensional soil element

nodes have two degrees of freedom, this results in incompatibility between two elements.

This incompatibility will have insignificant effect on deflections. However, the rotation and

bending moments obtained from the results of analyses are incorrect. To check the deflection

results using shell elements along with two-dimensional solid elements, a case history is an-

alyzed in the following section.

3.4 Case History Analysis Using One-Foot Thick Solid

Element and New Shell Element for Sheet Piles

3.4.1 Case History

Lock and Dam 26 (R) stage one cofferdam was considered for analysis because this re-

presents a typical size cofferdam and was well instrumented. Details describing this

cofferdam are given in Shannon and Wilson (1982) and Moore and Kleber (1985). Figure 3.4

depicts the basic conditions for Lock and Dam 26 (R) stage one cofferdam. The cofferdam

cells are approximately 63 feet in diameter and 60 feet high above dredge line. The

embedment depth of sheet piles is about 35 feet. The cells were filled by dumping riverbed

sands with a clamshell. The foundation soil is medium to dense sand. Same soil parameters

AXJSYMMETRIC VERSION OF FINITE ELEMENT PROGRAM (SOILSTRUCT) 49

as used in previous analyses and described in Shannon and Wilson (1982) were considered.

These are given in Table 3.2. The water level during cell filling was 32 feet above dredge line.

The sheet piles for main cell consisted of U.S. Steel designation PS-32.

As per previous analyses, the soil was modelled as nonlinear material following a

hyperbolic elastic model as described by Duncan et al. (1980). The modulus at any point of

nonlinear curve is defined as:

where: Er = stress dependent tangent modulus

E; = initial tangent modulus

R, = curve fitting parameter

SL = stress level or ratio of the present value of principal stress difference to that at failure

For most soils, R, is in the range of 0.8 to 0.9.

where: Km = modulus number

P. = atmospheric pressure

n = modulus exponent

crc = confining stress .

If unloading or reloading occurs, then the response is assumed to be linear and defined

AXJSYMMETRIC VERSION OF FINITE ELEMENT PROGRAM (SOILSTRUCT) 50

,.. 63 ftr--+f

' . 60ft. Cell fill

. . . . T T 28ft. 1

. . •' Alluvial Outwash ..l_ ~~-..P':r.l~:ir.'11:1- :..: :_: ~ -~ -~~-~ _· .. ·"""'*""'-'"'""-~,..,,.,,..,< .... s ....... an .... a...-· • .... r ..... >__,,.....,..-

12 ft. T -------1---------2a ft.

t 30 ft.

35ft. l_

Wisconsin Outwash (Sand II)

Illinoisan Ice Contact (Sand III) J_

... >::>:> >>.» >:?7~/,?.??77 4/,,..,,,-,,,,.;» ./,/,,,,.;r,..,.;?/ff /,//7.//////.,?.///,//////,/7//77.¢

ROCK

Figure 3.4. Lock and Dam 26 {R) cofferdam, basic conditions.


~ (I) -< 3: 3: m ~ n < m :u (It

0 z 0 "" ::!! z =i m m r m 3: m z -I "V :u 0 C') :u ,,. 3: (ii Q r (It -I :u c (') .:j

"' N

Table 3.2

Soil Parameters for Finite Element Analyses of Lock and Dam 26 (R)

SOIL PROPERTIES

Total Unit Friction

Weight Poisson Angle y Ratio cp Cohesion

Material (pcf) v (degrees) c

Cell Fill 123 0.45 35.0 0.0

Foundation 133 0.45 41.0 0.0 (alluvial outwash)

Foundation 133 0.45 41.0 0.0 (Wisconsin outwash)

Foundation 133 0.45 41.0 0.0 (lllinoisian ice contact)

NOTE: For foundation soil profile, see Figure 3.4.

•km = coefficient in the initial tangent modulus expression E; = P.Km<.!!!.r P.

•Kur = coefficient in unload-reload modulus expression Eu, = P.Ku,( ~3 )n •

·n = exponent in modulus expression

Earth Pressure

Coefficient Ko

0.4

0.6

0.5

0.5

•Rf = strength factor: ratio of measured strength at failure to ultimate hyperbolic stength.

HYBERBOLIC PARAMETERS

Km•

800

1600

1700

1700

Kur•

800

1600

1700

1700

n·

0.65

0.5

0.5

0.5

Rf*

0.82

0.85

0.85

0.85

by the modulus value Eur , which is calculated as:

where: Kur = unload-reload modulus number .

3.4.2 Previous Predictions and Observed Behavior

The previous axisymmetric analyses for cell filling for Lock and Dam 26 (R) cofferdam

performed by Clough and Kuppusamy (1985) used one-foot thick solid element to model sheet

piles. To take into account the slack and yielding of interlocks, the sheet pile system was

modeled as orthotropic shell with reduced modulus in radial direction using E-ratio concept.

E-ratio is defined as ratio of modulus in radial direction to steel modulus, and values of 1, 0.1

and 0.03 were used in analyses. The predicted radial denections and interlock forces at the

end of main cell filling using E-ratio of 0.03 are shown in Figure 3.5. The results show that the

denection and interlock force increase to a depth of about one fourth the height of the cell

above dredge line, whereupon they decrease. The maximum denection and maximum inter-

lock force for E-ratio of 0.03 are approximately 3 inches, and 3.5 kip/inch, respectively.

3.4.3 Predictions Using New Shell Element

The finite element mesh used for axisymmetric analyses using the new shell element is

shown in Figure 3.6. As an E-ratio of 0.03 predicted results more consistent with observed

data during previous analyses, this was also used for analyses using shell element. As sheet

piles are modeled using shell elements, the E-ratio in this case is defined as ratio of

circumferential modulus to steel modulus. The predicted radial denections at the end of main


~ (I) -< ii: s: m n < m :u (I)

0 z 0 "'II

::!! z =t m m r m ii: m z ~ .,, :u 0 () :u )> ii: (ii 0 ;::: (/) ~ :u c (') .d

UI •

Interlock Force(Kip/in) Radial Deflection(inches)

4309 2 4 6 430° 1 2 3 4 I I I I I I I

420 L \ J 420

410 0 410

~ ::> W.T. W.T. (.!)

:z:. 400 + ~ 400 I \ + -4-1 QI QI ~ ......,,

i:: 0 ..... 4-1 co > QI ~ f..t.l

-4-1 QI

390 QI 390 ~ ......,,

i:: 0 380 ..... 380 4-1 co :> QI rl 370 f..t.l 370 . . '

360 u J 360

350 ~ -/ 350

340 ... -l 340

Figure 3.5. Axlsymmetrlc analysis using one-foot thick element, sheet pile deflections and Interlock forces at the end of cell filling.

cell filling with the shell element and those obtained in three-dimensional analyses by Mosher

(1987) for an E-ratio of0.03 are given in Figure 3.7, along with the range ofthe observed values

for the two instrumented cells of Lock and Dam 26 (R) cofferdam - Stage I. The results of the

original analysis using the one-foot thick, solid element and E-ratio of 0.03 are also presented

in Figure 3.7 for comparison. All the analyses give qualitatively similar predictions. The new

analyses with shell elements match well with those obtained during previous axisymmetric

analyses using one-foot thick, solid element, and the observed radial deflections bound the

predicted values. The results of three-dimensional analysis show similar trend but yield lower

values as compared to those obtained from axisymmetric analyses. This discrepency is be-

cause three-dimensional analysis uses modified hyperbolic model for non-linear soil behavior,

taking into consideration the effect of intermediate principal stress. Also, the three-

dimensional finite element mesh includes the sheet pile system for arc cell also which will

have restraining effect on deflections of main cell during main cell filling.

The interlock forces for case of cell filling obtained from axisymmetric analyses (using

one-foot thick element and shell element). and three-dimensional analyses and those obtained

from instrumentation data (Moore et al., 1985) are shown in Figure 3.8. The results show that

the predictions of both axisymmetric analyses and three-dimensional analyses have similar

trends, and that they fall within the bands of observed data at almost all elevations. However,

three-dimensional analysis predicts lower interlock forces as compared to axisymmetric ana-

lyses for the same reason as explained above in case of radial deflections.

3.5 Summary

A shell element is incorporated in the program SOILSTRUCT to model sheet pile thickness

exactly for analyzing behavior of cofferdam cell during filling. Comparison of predicted results


~ en ~ s:: ~ n :ii ::u en 0 z 0 "Tl

:!! z ~ m J;; s:: m z -f -a ::u g ::u )> s:: c;; 0 ;::

~ c 2

C.11 Ol

<t, CIRCULAR CELL 160 ft

i--31.5 ft ---t - El 430 ~ 7'.: ~ 1---shell Element 7" -I"." 7-r

7-

r- lnterf oce Elements on either side - of Shell Elements ., -;--::-~ ,... ;-, r-

·~ ~ -;-

hi ) ~ ) • h.t .. ,.~~ht h: )-,> h: ),;t hJ

l l

-=---~

-,..

--

). >

-El. 370 ( Ored~e I ine)

El. 300

Figure 3.6. Finite element mesh for axlsymmetric analyses of Lock and Dam 26 (R) cofferdam.

-t-w w lL.

z 0 t-~ w _J w

410.0

400.0

390.0

380.0

370.0

360.0

0 Axisymmetric Analysis With I ft thick element (£-ratio =0.03}

• Axisymmetric Analysis With Shell Element (£-Ratio= 0.03)

0 Three- Dimensional Analysis (E-Rotio=0.03}

Range of Observed Values

350.0 ... J----.L-----.......... --_ _._ ___ __.._ __ __. 0.0 2.0 4.0 6.0 8.0 I 0.0

RADIAL DEFLECTION (INCHES)

Figure 3.7. Lock and Dam 26 (R), sheet pile deflections at the end of cell filling.


430.0

0 Axisymmetric Analysis With One Foot thick element

420.0 (E-Ratio=0.03)

• Axisymmetric Analysis With Shell Element (E-Ratio =0.03)

410.0 a Three-Dimensional Analysis ( E-Ratio•0.03)

1---i Observed Values

400.0 -..... I.LI I.LI u..

z 390.0 0 t-<t > I.LI ....J I.LI 380.0

360.0

350.0-----+--.&--------'---------"-----------------" 0.0 2.0 4.0 6.0 8.0 I 0.0

INTERLOCK FORCE (KIPS/INCH}

Figure 3.8. Lock and Dam 26 (R), Interlock forces at the end of cell filling.


with closed form solution indicates that inclusion of shell element in the axisymmetric pro-

gram has been done properly. The predictions using new shell element to model sheet piles

generally match well with the results of previous axisymmetric analyses and three-

dimensional analyses.


Chapter IV

PARAMETRIC ANALYSES WITH THE

AXISYMMETRIC FINITE ELEMENT PROGRAM

The new version of the finite element program which incorporates the shell element to

represent the sheet piles is used in this chapter to conduct parametric studies of the case of

filling of the cofferdam cell. The results of the analyses are compared to the predictions of

conventional methods for analyzing cofferdam response. The parameters considered in this

chapter are depth of cell embedment, free cell height above the mudline, and strength of cell

fill and foundation soils.

Lock and Dam 26 (R) stage one cofferdam is used as the base case for the analyses in-

asmuch as it represents a typical cofferdam designed to handle significant loads. An E-ratio

of 0.03 is assumed for the cell. It may be remembered that the cell embedment of the stage

one cofferdam for Lock and Dam 26 (R) was 35 feet, a relatively large value. For the

parametric studies, embedments of 0, 10, 20, 25 and 45 feet are also considered. Where the

free cell height for Lock and Dam 26 (R) was 60 feet, in the parametric studies, problems with

PARAMETRIC ANALYSES WITH THE AXISVMMETRIC FINITE ELEMENT PROGRAM 60

free cell heights of 40, 50, 60, 70, and 80 feet are analyzed. Finally, the effects of cell fill and

foundation sand strengths are considered in the use of friction angles of 35 and 41 degrees

at various times for both materials. The 35 degree case is representative of a medium sand,

while the 41 degree case is consistent with a dense sand.

4.1 Effect of Depth of Embedment on Sheet Pile

Deflections and Interlock Forces

The deflected cell shapes at the completion of cell filling for the three depths of

embedment, 10, 20, and 35 feet, are presented in Figure 4.1. As expected, in all cases there

is a bulging shape imparted to the cell, with the maximum lateral deflection of 3.03, 2.93, and

3.16 inches for depths of embedment of 10, 20 and 35 feet, respectively. Because of different

scales for cell geometry and cell deflection, it appears from Figure 4.1 that maximum lateral

deflections are occurring below dredge line, but it is not true. For depths of embedment of

10 and 20 feet, the maximum deflections occur at a point about one-fourth the height of the

cell from the mudline, and for the 35 feet embedment, at a point about one-sixth the height of

the cell above the mudline. Although there are similarities in the cell deflection patterns, it

can be seen in Figure 4.1 that there are differences. The lowest embedment case shows the

largest stretching of the cell bottom, a situation not unexpected in view of the fact that this

case should have the highest lateral stress imparted to the bottom of the cell. The highest

embedment case shows the sharpest reversal in cell curvature as the deflections penetrate

into the ground. This reflects the stiffening effect of the embedment, and the fact that little

movement penetrates to the bottom of the cell in this case.


.35 ft.

•

Hd is Depth of embedment.

-- lid

Hd _._,._ Hd

10 feet 20 feet

35 feet

Original sha?e of cell

11-.111-,,.-11-ir-11-k-x-x-x-JC. ·~·--·--·--·~·~·~·~-~·

Cofferddm Cell

l I

20.0ft. Scale :or cell geometry

2.0 inch Scale for cell de:lections

Figure 4.1. Deflected shapes of cofferdam cell at the end of cell filling.


The relative influences of cell embedment, and the presence of the open end of the cell

at full embedment lead to the maximum lateral cell deflections of the 20 foot embedment case

to fall in between those of the shallower and deeper embedment cases. In Figure 4.2, the

maximum radial deflection is plotted against depth of embedment, and it can be seen that the

smallest value occurs at 20 feet of embedment, although there are no great differences in any

case.

Due to the lateral cell deflection and the weight of the cell fill, the cell walls also undergo

a vertical movement. The vertical movement of the sheet piles are 1.1, 0. 7, and 0.4 inch for

the embedments of 10, 20 and 35 feet, respectively, as shown in Figure 4.1. Vertical movement

is higher for lesser embedments depth because of lower frictional resistance.

The lateral pressures acting on the interior of the cell walls for embedments of 10, 20 and

35 feet are shown in Figure 4.3. The pressures are very similar for all cases, and this is not

unexpected in view of the similarity in cell deflections for the different embedments. The

magnitude of Rankine's active earth pressure are also plotted in Figure 4.3 for comparison.

The lateral earth pressures acting on cell wall at the end of cell filling are approximately the

same as active earth pressures up to a distance of about H/5 above dredge line and there-

after, lateral earth pressure values are lower than active earth pressure values because of

embedment effects. Below dredge line, lateral earth pressures become higher because of

resistance of foundation soil against cell movement.

The maximum interlock forces are plotted versus depth of cell embedment in Figure 4.4.

As expected, there is not a large difference in the interlock forces, given that, as noted previ-

ously, there is not a large difference in lateral deflections or the earth pressures acting on the

cell walls. The lack of influence of cell embedment on interlock forces reinforces the idea that

cell embedment is provided for reasons other than for reducing interlock forces.


-Cll QJ .c 3.0 CJ c H .._,, c 0 ...... .i.J CJ 2.0 CJ

..-1 ...... E-Ratio 0.03 CJ 0 ..-1

C1l 1.0 ...... 'O

C1l ~

e :I e ...... x C1l ~ 0.0 10.0 20.0 30.0 40.0 50.0

Depth of Embedment (Feet)

Figure 4.2. Maximum sheet pile deflections at the end of cell filling.


....... ~ cu cu

130

120

110

100

e 90 i:: 0

-M ~ co > ~ 80 t>:l

70

60

50

40

0.0

W.T. -+

1.0 Lateral Earth Pressure

2.0

H is Free cell

Hd is Depth of

Hd 10

Hd 20 Hd 35

H/4 H/6

',~~' '-·~·, ...............

") ,.."'> ).- ...... , . " I.

I J I I I I . I I I I \

,,

(Ksf)

3.0

height

Embedment

feet

feet

feet

line

Figure 4.3. Lateral earth pressures against sheet pile at the end of cell filling.

PARAMETRIC ANALYSES WITH THE AXISYMMETRIC FINITE ELEMENT PROGRAM

4.0

65

E-Ratio 0.03 5.0 -..c:

(.) c:

H -0. 4.0 "" ::iG -(I) (.) M 0 ~

~ 3.0 (.) 0

.-l M (I) ~

c: H

e 2.0 § "" ~ co ~

1.0

0.0 l-~~~~L-~~~----11:---~~~--L~~~~--'-~~~~--' o.o 10.0 20.0 30.0 40.0 50.0


Figure 4.4. Maximum interlock forces at the end of cell filling.


There is one interesting issue related to the effect of embedment. Namely, is there a point

of fixity for the cell walls. As can be seen in the deflected cell shapes, the greater the

embedment, the less the bottom of the cell is deflected. In Figure 4.5, the lateral cell move-

ments below the dredge line are plotted against depth of embedment. There is an obvious

difference in the curvature of the embedded portion of the cell, depending upon the amount

of cell embedment. However, even for the case of 45 feet embedment, the bottom of the cell

is being deflected. Thus, for these cases, there is no point of absolute fixity for the cell.

The location of the point of maximum deflection and that for the maximum interlock force

is identical. As noted, this typically occurs slightly above the level of the mudline. In Figure

4.6, the location of the maximum deflection and interlock force above the mudline is plotted

against depth of embedment for the analyses performed in this study. The position of the

maximum of either parameter occurs at one-sixth to one-fourth of the free cell height above

the mudline. This location is similar to that reported for instrumented cofferdams with similar

conditions to those included in these analyses (Martin, 1987).

The interlock forces predicted by the finite element analyses can be compared to those

that are calculated by conventional design methods. This is done in Figure 4.7, where the

interlock forces calculated using the Corps of Engineers and the Schroeder and Maitland

procedures are plotted for Lock and Dam 26 (R) dimensions along with those determined us-

ing the finite element program. As has been shown in previous work by Clough and

Kuppusamy (1985), the finite element method typically predicts lower interlock forces than the

two conventional methods shown in Figure 4. 7.


.,, ,.. ::a ,.. 3:: m if c; ,.. z ,.. r-~ m en ;; ;! ;! m

~ c;; -< 3:: 3::

m c; .,, z =i m m r-m 3:: m z .... .,, ::a 8 ::a ,.. 3::

°' OJ

,-... ~ QJ QJ

i:z.. ._, ~

~ QJ a

'O QJ

.0 a ~

~ 0

..c ~

0.. QJ

Q

Sheetpile Deflections (Inches) line o.o 0.2 0.4 0.6 0.8 1.0 1. 6

0 ~ ;;;J;: ' --~..i-•.d-:1:-=,_...:!!..::-~1--..:= 'l: ......._.;;:;:c;:ll=-_ - - :=J_ - - - __ , __ - --

10

20

30

40

45

Hd is Depth of Embedment.

~ Hd = 10 feet

-·-·- Hd = 20 feet

---- Hd 35 feet

--·-Hd = 45 feet

Figure 4.5. Cell deflections below dredge line at the end of cell filling.

c:: 0 ~ ~ (J ...... <U ::i::

.-1 -..... <U x 0

~

E CO =' E <U ~ (J x ,... ca o L.,,. ..... ...:.:: 0 (J

0 c:: .-1 0 ,... ~ <U ~ ~

ca !:: (J H 0

....i""'

0.2

0.1

0.0 o.o 10.0

Free cell height H 60 ft

20.0 30.0 40.0 50.0 Depth of Embedment (Feet)

figure 4.6. Effect of depth of embedment on location of maximum cell deflection and Interlock force at the end of cell filling.


1-L&J La.I L&..

420.0

410.0

400.0

z 390.0 0

~ > La.I _J La.I 380.0

370.0

360.0

• Axisymmetric Analysis With Shell Element (E-Rotio s0.03)

~ Observed Values -- Corps of Engineers Method -Schroeder and Maitland

Method

350.09-~-+-~.._~~~..L-~~~...L-~~~-l-~~~.....J

0.0 2.0 4.0 6.0 8.0 I 0.0

INTERLOCK FORCE (KIPS/INCH)

Figure 4.7. Lock and Dam 26 (R), Interlock forces at the end of cell filling. Comparison of FE analysis and conventional design methods.


4.2 Effect of Free Cell Height on Sheet Pile Deflection and

Interlock Forces

Parametric studies were also performed for main cell filling using a problem following the

Lock and Dam 26 (R) history and soil conditions, to investigate effect of free cell height on

maximum sheet pile deflection and interlock force. The free cell heights used were 20, 30, 40,

50, 60, 70 and 80 feet. An E-ratio of 0.03 was used. The water level was considered at mid-

height of the cell above mudline. Maximum predicted radial deflection and maximum interlock

force values from the finite element analyses are plotted against free cell height in Figures

4.8 and 4.9. Values are shown for cell fill conditions with a friction angle of 35° (the base Lock

and Dam 26 (R) condition), and a cell fill with a friction angle of 41°. The effects of the cell fill

friction angle are covered in subsequent section.

These results show that maximum radial cell deflections and interlock forces show an in-

crease as free cell height increases. The relationship is approximately linear. Interlock forces

computed using Schroeder and Maitland method are plotted in Figure 4.10 against free cell

height along with those from the finite element method. In all instances, the Schroeder and

Maitland method yields higher values than those from the finite element analyses. For ex-

ample, for a cell height of 60 feet, the maximum interlock force computed based on Schroeder

and Maitland method is about 34% higher than that predicted by finite element method. No-

tably, the difference between the Schroeder and Maitland predictions and those of the finite

element method grow larger as the free cell height increases. The reason for this is that the

Schroeder and Maitland method does not consider the true nature of the soil-structure inter-

action process, and also the assumed location of maximum interlock force based on the

Schroeder and Maitland method is different than predicted by finite element analyses. The


-en G> ~ u c -c 0 ·.;: u .!?

4.0

3.0

':; 2.0 0

0 :0 0 a:: E 1.0 ::s E ·;c 0 ~

20.0 30.0 40.0 50.0

0 Cell fill cf> = 350

0 Cell fill "' = 41° Foundation material cf> =41°

60.0 70.0 80.0 Free Cell Height (Feet)

Figure 4.8. Effect of cell fill material on maximum sheet pile deflections at the end of cell filling.


-..c u c ........ a. ~

Q) u '-& ~ u 0 1: Q) -c

E ~

E )( 0 ~

0 Cell fill cp = 350

6.0 0 Cell fill cp = 410

Foundation material c/J =41°

5.0

0.0 --~~--~~~--~~~--~~~...__~~___,,~~~~ 20.0 30.0 40.0 50.0 60.0 70.0 80.0

Free Cel I Height (Feet)

Figure 4.9. Effect of cell fill material on maximum Interlock forces at the end of cell filling.


effect of maximum interlock force location becomes more pronounced as the cell height in-

creases.

Location of maximum cell deflection and maximum interlock force, as predicted by finite

element analyses, is plotted for different free cell heights in Figure 4.11 for a cell embedment

of 35 feet. This location remains constant at about 0.15 H from mud line for all values of cell

heights for depth of embedment of 35 feet.

4.3 Effect of Foundation Soil And Cell Fill Parameters on

Sheet Pile Deflection and Interlock Force

Parametric studies were also performed using the axisymmetric program varying the

foundation and cell fill soil strengths. The soil characteristics used were those given in Table

3.2, using friction angle <p = 35 and 41 degrees for both cell fill and foundation for different

analyses. The free cell heights used were 20, 30, 40, 50, 60, 70 and 80 feet. The E-ratio and

cell diameter were fixed at 0.03 and 63.0 feet, respectively. The water level in the cell was

assumed to be at mid-height from dredge line. The embedment depth of cell was 35.0 feet.

Maximum radial deflection and maximum interlock force values are plotted against free

cell height in Figures 4.8, 4.9, 4.12 and 4.13. Maximum interlock forces computed based on

Schroeder and Maitland method are also plotted for cell fill friction angles of 35 and 41 de-

gre~s in Figure 4.10. The following observations are made from these results:

1. The friction angle of cell fill has a significant effect on predicted deflections and

interlock forces (Figures 4.8 and 4.9). Increasing the fill friction angle from 35 to 41


-..c u c ........ Q. ~

Q) u '-if ..¥ u 0 '-Q) -c

E :l E )( 0 ~

6.0

5.0

4.0

3.0

0 Cell fill 4' = 35o

0 Cell fill cp = 41°

- FEM Predictions

-·-Schroeder and Maitland method

O.OL-~~~.&.-~~--1r.......~~---'~~~---'-~~~-'-~~~~

20.0 30.0 40.0 50.0 60.0 70.0 80.0 Free Cell Height (Feet)

Figure 4.10. Effect of cell fill material on maximum interlock force (FEM and Schroeder and Maitland method) at the end of cell filling.

PARAMETRIC ANALYSES WITH THE AXISVMMETRIC FINITE ELEMENT PROGRAM 75

c .Q -0 Q) --Q) :I: O-E >< ::J -eo ·- Cl) )( 0 0 ... :?if

0.3

0.2

Depth of embedment Hd=35 ft

H is Free cell height

-..:.:: 0 0 0.1 c.2 .2 ~ --oc o-

.3 ~ 0·~0L.o--3-o.1...o---4-10.-o--5.....JoL-.o--s-o..1....-o-----1~0-=.o:----a~o.o Free Cel I Height (Feet l

Figure 4.11. Effect of free cell height on location of maximum cell deflection and Interlock force at the end of cell filling.


-.,, CD .s= u c -c .2 -u .!! -... CD 0

.2 "O 0 a: E :I E ·;c 0 :E

4.0

3.0

2.0

0 Foundation cp = 35°

1.0 0 Foundation cf:>= 41°

Cell fill cp = 350

20.0 30.0 40.0 50.0 60.0 70.0 80.0 Free Cell Height {Feet)

Figure 4.12. Effect of foundation material on maximum sheet pile deflections at the end of cell filling.


-.J:: (J c

' a. ~

G) (J ... & ~ (J 0 ... G) -c

E :J E )( c ~

0 Foundation <j> = 35°

6.0 0 Foundation </> = 41°

Cel I Fi 11 </> = 35°

5.0

1.0

o.o--~~--~~~---~~~--~~~---~~~.__~~----

20.0 30.0 40.0 50.0 60.0 70.0 80.0 Free Cell Height ( Feet)

Figure 4.13. Effect of foundation material on maximum interlock forces at the end of cell filling.


degrees results in reductions of about 30% in maximum radial deflection and 35%

in maximum interlock force for all free cell heights.

2. The values of maximum interlock force from Schroeder and Maitland method are

higher than those predicted by finite element method for cell fill friction angles of

both 35 and 41 degress. The reduction in values from Schroeder and Maitland

method, using a cell fill friction angle of 41 degrees instead of 35 degrees is about

25% for all values of free cell height.

3. Changing the friction angle of the foundation soil type from 35 to 41 degrees has an

insignificant effect on maximum radial cell deflections and maximum interlock

forces (Figures 4.12 and 4.13.).

4.4 Discussion

The parametric studies presented in this chapter concern foundation and cell fill conditions

that are favorable for cofferdam performance. The soils are taken to be sands with high

strengths, and the cofferdam dimensions are within usual limits. For these circumstances, tile

analyses show that the most important parameters are free cell height and cell fill strength.

Within the limits of the parameters assumed, no unusual behavior trends are determined.

As has been observed in previous finite element studies, the depth of cell embedment is

not important to the maximum cell deflection or interlock force for the case of cell filling. Cell

embedment is governed by other considerations for cofferdam design. Also expected in the

analysis results is the finding that the finite element analyses predict lower interlock forces

than those obtained by conventional design methods. A new observation is that the conven-

tional design methods become more conservative relative to the finite element predictions as


the free cell height becomes larger. This could be significant in the design of future

cofferdams, and should be studied further.


Chapter V

PLANE STRAIN VERSION OF FINITE ELEMENT

PROGRAM {SOILSTRUCT)

The program SOILSTRUCT has been used to model response of a cofferdam due to cell

filling, berm placement, dewatering, excavation within the cofferdam, and flooding (Shannon

and Wilson, September 1982), in terms of a vertical slice analysis. In this case, the cofferdam

is visualized as a planar system. The cofferdam cells are depicted as if they consisted of two

walls separated by the main cell diameter with soil between the walls. To represent the effect

of the HmissingH part of the cells, Hansen and Clough (1982) proposed that the walls be con-

nected with one-dimensional spring elements (Figure 5.1). The springs can transmit only

tensile forces from the front to the back wall, thus they exert no restraint on the vertical

movement of the cell fill.

Stiffnesses of the spring elements were proposed to be determined from the response of

a cylindrical vessel subjected to an internal pressure (Hansen and Clough, 1982). In this ap-

proach, the sheet piles are modelled by one-foot thick, four-node solid element having two

PLANE STRAIN VERSION OF FINITE ELEMENT PROGRAM (SOILSTRUCT) 81

Connection spring

Cell wall Cell wall

Cell fill

Foundation

Figure 5.1. Planar representation of cofferdam cell for FEM analysis (from Hansen and Clough, 1982).


degrees of freedom at each node. A thickness of one-foot was chosen from an aspect ratio

point of view to avoid numerical problems. The modulus value for the sheet pile is reduced

in certain proportion of the ratio of moment of inertia of one-foot thick element and that of

actual sheet pile. To model the effects of an orthotropic cell, the stiffness of the spring ele-

ments are varied in proportion to the ratio of radial modulus due to presence of interlocks to

the modulus of sheet piles.

5.1 Modifications in Plane Strain Finite Element Program.

The existing finite element program has been shown to reasonably predict many aspects

of cofferdam behavior. However, there are several factors which can be improved. These

relate to the representations for the cell walls and the structural connections for the front and

back walls. In the case of the quadrilateral, one-foot thick solid element used for the sheet

piles, there are questions about the equivalent modulus for sheet piles. The spring elements

which serve as the front and back wall connections also suffer from the following drawbacks:

• The spring stiffnesses are computed based on assumption of pressure vessel sub-

jected to uniform internal pressure, a situation not applicable during differential

loading.

• The springs take only longitudinal force and no transverse force. During differential

loading, however, both longitudinal and transverse forces are generated.

• With springs, the connection is only from outboard to inboard sheet pile. However,

in actual case, the stresses in the cell sheet piles would vary from outboard to in-

board side under differential loading.


To obviate these problems, the existing plane strain version of SOILSTRUCT was modified

to incorporate a new beam element and shear transfer element. The beam element is used

for modelling the behavior of sheet piles, and it allows the thickness of beam element to be

taken the same as that of sheet piles. Three degrees of freedom (i.e., longitudinal and trans-

verse displacements and rotation) are considered at each beam element node to account for

bending characteristics of sheet piles.

The shear transfer element used is a plane stress element to model load transfer during

differential loading. These elements are placed overlapping all the soil elements within the

cell for outboard to inboard side, and provide continuous connection from outboard to inboard

sheet piles independent of the soil elements and their nodes. The beam and shear elements

are described in more detail in following sections.

5.2 Provision of Beam Element

5.2.1 Description

The beam element used is a two-node element as described by Desai (1979). Each node

has three degrees of freedom. A beam element and nodal degrees of freedom are shown in

Figure 5.2.


Figure 5.2. A beam element.


5.2.2 Test Problems to Check Beam Element

Two test problems were solved using the modified finite element program to check the

accuracy of implementation techniques for the beam element in the program.

Test Problem 1

Consider a beam with three nodes, fixed at both exterior nodes and subjected to concen-

trated transverse load at central node (Figure 5.3).

The closed form solution for maximum deflection and maximum moment are:

w/3 8 max= 192E/

Mmax = ~ 8

where:

W = transverse concentrated load ( = 1000 lb)

I = length of beam ( = 8.0 feet)

E = modulus of elasticity for beam ( = 4.32 x 109 psf)

I = moment of inertia of beam ( = 0.667 ft~)

Using the above values, 8 max and Mmax are computed as 0.139 x 10-3 feet and 1000 lb.

ft, respectively. The predicted values of 8 max and Mmax using modified finite element pro-

gram are 0.09255 x 10- 3 and 1000 lb. ft., respectively, which match the closed form solution


4.0 ft.

1000 lb.

4.0 ft.

Width of beam = 2.0 ft.

Height of beam = 1.0 ft.

Figure 5.3. Test problem 1, beam with transverse load.

PLANE STRAIN VERSION OF FINITE ELEMENT PROGRAM (SOILSTRUCl) 87

very well.

Test Problem 2

A problem of beam on elastic foundation was considered. Length, width and thickness of

the beam was 60 feet, 1 foot and 6 inches, respectively, and a uniformly distributed load was

applied in central 8.0 feet length of the beam. A Winkler type foundation having support

springs with spring constant K as 10,000 lb/ft was assumed. The model used for finite element

analysis is shown in Figure 5.4.

The closed form solutions (Boresi et al., 1978) for deflections at distance 'x' from center

of load are:

(i) for 'x' lying within loaded portion

(ii) for 'x' on right hand side of loaded portion

where:

Yx = deflection of beam at x

q = uniformly distributed load (1000 lb/ft)

k = spring constant (10,000 lb/ft)

a = distance of point of deflection from left end of the load


"V

~ z m

~ > z ;!ii ::a en 0 z 0 "" ::!! z ~ m r m 3: m z .... "V ::a 8 ::a > 3: (ii 0

~ c ~

Oii co

!4:of I I I

Beam

4.0 ft . ...j I•

Load q~lOOO lb/ft.

Sprngs, K=lOOOO lb/ft

30.0 ft.

Figure 5.4. Test Problem 2, beam on elastic foundation.

b = distance of point of deflection from right end of the load

E = Young's modulus of elasticity of beam (0.432 x 109 psf)

I = moment of inertia of beam

The results (Figure 5.5) show that the predicted deflections match well with those obtained

from closed form solution.

5.2.3 Problem of Interaction of Beam Element with Two-Dimensional

Elements in Program SOILSTRUCT

As in case of shell element discussed in Chapter 3, the inclusion of beam element in

SOILSTRUCT program results in incompatibility between beam element nodes having three

degress of freedom and adjoining two-dimensional element nodes with two degrees of free-

dom. This incompatibility means that the resulting rotations and bending moments from the

analyses would be incorrect, but it will have insignificant effect on deflections. To check de-

flections using beam elements along with two-dimensional solid elements, results of analyses

are compared with previous analyses using one-foot thick solid element for Lock and Dam 26

(R) in the following section.

5.2.4 Comparison With Previous Results - Cell Filling Case

To test the accuracy of the beam element for a cofferdam problem, an analysis was per-

formed for main cell filling of Lock and Dam 26 (R) cofferdam. The results were compared

with those obtained from earlier analyses.


-0

~ z m

~ )lo z < m :u en 0 z 0 "'II

::!! z ~ m r m 3: m z -t -0 :u 0 C'> :u ,,. 3: en 0 ;:: ~ :u c (') d

co ....

-Ill Q) .c u i::

1-t ._..

13 <ll Q) al

~ 0

i:: 0

•r-1 ~

u Q)

...... ~ Q)

Cl

-0.1

o.o

0.1

0.2

0.3

0.4

0.5

0.8 I

Closed form solution

FEM Predictions

Original position of beam

I _____ L__ _ __ l__ _____J o.o 5.0 10.0 15.0 20.0 25.0 30.0

Distance From Center of Beam (Feet)

Figure 5.5. Test Problem 2, deflection of beam on elastic foundation.

The original plane strain analyses performed for main cell filling of Lock and Dam 26 used

a one-foot thick solid element to model sheet piles (Shannon and Wilson, 1982). The equiv-

alent modulus value used for PSX32 sheet piles was 7.0Sx1a6 psf for steel. The reduction

factor used was about 613 computed on the basis of El values of one-foot thick element and

actual sheet pile, where E and I are modulus and moment of inertia, respectively.

The finite element mesh using beam elements to model sheet piles is shown in Figure 5.6.

The mesh, as shown, is not symmetrical because the same mesh was used for analyses of

cofferdam behavior due to different types of lateral loading. The soil parameters used in both

cases are given in Table 3.2. The dimensions and details of cofferdam are as described under

Section 3.4.

The predicted sheet pile displacements from the previous analyses and those using beam

element to model sheet pile behavior for an E-ratio of 0.03 are shown in Figure 5.7 for com-

pletion of cell filling. The results of the two different approaches agree very well. It is im-

portant to note that Clough and Kuppusamy (1985) indicated that the sheet pile deflections for

cell filling using one-foot thick solid elements for sheet pile and E-ratio of 0.03 were in general

agreement with the observed behavior. This indicates, therefore, that the beam element op-

tion included in the finite element program yields results which are in conformity with the re-

sults of observed behavior for Lock and Dam 26 (R).

5.3 Provision of Shear Transfer Element

In this investigation, provisions are made to provide a connection of front and back

cofferdam wall in the vertical slice analysis, using a plane stress shear transfer element. A

four-node plane stress element as described by Zienkiewicz (1977) is used. This element has


I

I J

I

(l(I • OS I 00·001

0 0 0 U'I

"' 0 0 0 0 "' 0 0 0 Ill ::I'

0 0 0 0 ::I'

0 0 0 U'I

.... 0 0 0 0 .., 0 0 0 U'I

"' 0 0 0 C'

"' c r c~

• 0 Cl

c CJ

I ·' C.·

c' V

'

.... c.:

PLA

NE

STR

AIN

VERSIO

N O

F FINITE

ELE

ME

NT P

RO

GR

AM

(SO

ILSTR

UC

T)

-- c CP E

CP u IV a. CP ~

co N

E

IV 0 i::J c IV

.lJlf. u 0

..J .. 0 -.c Ill CP E

- c CP E

.

CP E -

IV CP i::J .! ; c=

_

o

u.. u

93

130

120

110

100

90 t-w w LL

z 80 0 t-

~ w _, w 70

60

50

40

E- Ratio= 0.03

o One fod thick solid e~me

a Beam element ( 1/i'thick)

Dredge line ......... aazxaw•W

1.0 2.0 3.0 4.0 5.0 DEFLECTION (INCHES )

6.0

Figure 5.7. Deflection of sheet pile at the end of cell filling, Lock and Dam 26 cofferdam.

PLANE STRAIN VERSION OF FINITE ELEMENT PROGRAM (SOILSTRUCl) 94

a thickness of unity in the plane strain analyses. The shear transfer elements are provided

as superimposed on to the cell fill elements and connecting outboard and inboard sheet piles

over the entire height of cell as shown in Figure 5.8.

5.3.1 Method of Computing Modulus (E) of Shear Transfer Elements for

Use in Analyses

For the plane stress shear transfer element introduced in plane strain analyses to repre-

sent the cofferdam behavior under lateral loading, it is necessary to determine the appropriate

modulus (E) value of this element based on some factor applied to the modulus value of steel.

Two modulus reduction factors were considered for this purpose:

1. First modulus reduction factor computed based on comparison of theoretical solutions

and results of linear elastic finite element analyses using different set of parameters.

2. Second modulus reduction factor derived from testing the program against case history

data, taking into account the non-linear behavior of cell fill and foundation soils and the

soil-structure interaction effects. This reduction factor would include the effects of inter-

lock slack and yielding and the three-dimensional effects during lateral loading.

In this chapter, the technique for determining first modulus reduction factor is discussed. In

Chapter 6, the case history studies are done to compute the second modulus reduction factor.

A case of thin, hollow cylinder having height as equal to free cell height of cofferdam and

diameter as equal to width of cofferdam cell in plane strain analysis was considered appro-

priate for comparing results of finite element analyses with closed form solutions. The bottom

of the cylinder is fixed, and a uniform lateral load is applied on full height of cylinder. To ob-

tain closed form solution, cantilever beam theory is used for cylinder. In finite element ana-


F"ront wa// of Cofferdam

Shear ,,., · Ot7 ansfer elem

lo Ctlf/ fit/ , en1s su/Je, . e1emen1s r'"'Posea ,,----

'( )'\. I ff 5ection

Figure 5.8. Isometric view of cell fill elements and overlapping shear transfer elements.


lyses, beam elements were used to model front and back sheet piles of hollow cofferdam, and

shear transfer elements used connecting outboard and inboard sheet piles. No soil or inter-

face elements were used in these analyses, and only linear elastic analyses were done. The

sheet piles were fixed at dredge line, and uniform lateral loading was applied in entire height

of cofferdam. The schematic representation of the cylinder and the cofferdam is shown in

Figure 5.9.

The horizontal deflections of the sheet piles at top, mid-height and one-fourth height (near

dredge line) from bottom were compared with closed form solutions using cantilever beam

theory for the cylinder. The deflections for the cylinder are computed as:

8 max= wh" BE/

and

Sx = ~(x" - 4h 3x + 3h4) 24EI

where:

8 max = maximum deflection at top

w = uniform distributed load over height h

I = moment of inertia of thin cylinder

E = modulus of elasticity

ox = deflection at distance x from top

r = outside radius of cylinder

r0 = inside radius of cylinder


"'D s;: _z m

~ ~ z ~ ::u (/I

0 z 0 'Tl 'Tl z ~ m r-m

== m z -t "'D ::u 8 ::u ,.. :!: en 0 ~ ;i c n

..::I

co 00

Loadw

B

Thin Cylinder H

(a) Thin Cylindrical Shell ( Closed form solution )

B ,. .,

Loadw

Sheet pile (Beam elements)

Load Transfer Shear clements

(b) Schematic Mesh for Finite Element Analysis

Figure 5.9. Schematic details of thin cylinder and finite element mesh.

The ratios of deflections from finite element analyses o,em and deflections obtained from

closed form theory Ot1reoty were computed at top, mid-height and near dredge line for particular

value of height (H) and width (B) of cofferdam cell and for different ratio of modulus of steel

(Es) and modulus of shear elements (Eshear) used in analyses. The values of H and B used

for this parametric study are given in Table 5.1.

The results of the finite element analyses are compared to those of the closed form theory

in terms of the deflections predicted for the top, mid-height and near dredge line portion of the

cylinder on the side opposite of the loading. The deflection ratio is termed as o,,,,,,Jot1reoty . In

Figure 5.10, this ratio is plotted versus the ratio of modulus of steel (Es) to modulus of shear

transfer elements (Eshear) for a cylinder with dimensions like those of Lock and Dam 26 (R)

cells, free cell height (H) of 60 feet and cell width (B) of 63 feet. For other values of H/B ratio,

similar plots are presented in Appendix A. The factor by which the modulus of steel should

be reduced to compute the modulus for shear transfer element so that the predicted cell dis-

placements from finite element analyses equal the closed form solution, is obtained from

intersection of the curve at o,,,,,,Jot1r•oty equal to unity. In case of Lock and Dam 26 (R), these

values are 268, 235 and 100 for top, mid-height and lower part of cell, respectively (Figure 5.9).

Results of all of the analyses show that:

1. The value of the first modulus reduction factor Es/Eshear corresponding to o,,,m!Ot11eoty

equal to unity increases as cell height to cell width ratio H/B increases.

2. Reduction factor Es/Eshear for o,.,,,/ot1r•oty equal to unity is more for top of cell than for

mid-height of cell, indicating that higher reduction factor should be applied to steel

modulus for computing modulus for shear transfer elements for top portion of cell than for

middle portion.

3. The modulus of shear transfer elements has to become very much smaller than that of

steel to yield a deflection ratio o,.,,,/ot1r.oty of one.


Table 5.1.

Dimensions of Cylinders Used in Parametric Studies to Evaluate Response of Shear Transfer Elements

H B H/B (feet) (feet)

84.0 63.0 1.33 60.0 63.0 0.952 48.8 63.0 0.775 37.6 63.0 0.597 25.0 63.0 0.397 12.5 63.0 0.198 50.0 40.0 1.25 40.0 40.0 1.0 30.0 40.0 0.75 20.0 40.0 0.5 10.0 40.0 0.25


>-'-0 Q) .c -"° ........ ~ w LL

"° II

0.1

l

0.01

E5 /Eshr=235

H = 60 ft 8 = 63 ft H/8=0.952

.OOl'-----4~0-----8~0----~1720=----716~0:----:2~0~0:-----;2~4~0~-;:;;:280

Figure 5.10. Deflection ratio v/s modulus ratio for Lock and Dam 26 (R).


The first modulus reduction factors are computed for different values of H/B ratio and

presented in Figure 5.11. For the case of Lock and Dam 26 (R), the first modulus reduction

factors based on these curves are approximately 270 and 235 for top and mid-height of cell,

respectively. Values are plotted for cell width (B) of 63 and 40 feet for top and mid-height of

cell. As most of the cofferdams fall within B = 40 to 60 feet, it would be reasonable to use

these curves for computing first modulus reduction factor for shear transfer elements.

The curves discussed above, thus, yield the first modulus reduction factor for shear trans-

fer elements computed based on the comparison of theoretical solution and finite element

analyses. The second modulus reduction factor, based on case history evaluation, is dis-

cussed in Chapter 6.


.... 0 41 .s::. Ill

IJJ --Ill IJJ

100

10.0

Top of cell

For.lock & Dam 26 -- - - - - - - - - - - - - - - - - - -- -

Es= Young's modulus of steel

Eshear =Young's rrodulus of shear element

H = Free height of cell

B = Width of cell

--8 = 63.0Ft

-- --- B = 40.0 Ft

1.0--~~--i~~~--L~~~-L~~~-'-~~...._,,__~~--i~~~.....1 o.o 0.2 0.4 0.6 0.8 1.0 1. 2 1.4

H/B

Figure 5.11. H/B versus modulus ratio.


Chapter VI

CASE HISTORY STUDIES USING MODIFIED PLANE

STRAIN FINITE ELEMENT PROGRAM

To verify the predictions of the modified plane strain finite element program and to help

determine the second modulus reduction factor (RF2), it was considered necessary to analyze

case histories documented through instrumentation. The second modulus reduction factor

(RF2) is applied along with the first modulus reduction factor (RF1) to arrive at appropriate

stiffnesses for the shear transfer elements during lateral loading.

In Chapter 5, it was shown that the modulus of load transfer shear elements should be

reduced by first modulus reduction factor (RF1), depending on the ratio of the free height (H)

to width (B) for the cofferdam. However, the basis for the first modulus reduction is theore-

tical, and the case history analyses allow practical factors to be considered.

Three case histories are studied: (i) Willow Island second-stage cofferdam - cell 27, (ii)

Willow Island second-stage cofferdam - cloverleaf cell 33, and (iii) Lock and Dam 26 (replace-


ment) first-stage cofferdam. These case histories were selected firstly because they were well

instrumented and secondly because the cofferdam in these cases were founded on sandstone,

clay and deep sands, respectively, representing three different types of foundations.

6.1 Second Modulus Reduction Factor and General

Analyses Procedures

Before lateral loads are applied to cofferdam due to berm placement, dewatering or

flooding, the spring elements are removed and shear elements are installed instead. Al-

though during cell filling most of the interlock slacks and slippages must have been com-

pleted, there would still be some slack and slippage left. Also, there would be some rotation

or local yielding and imperfect alignment of interlocks which would result in further reductions

in modulus value of shear transfer elements during lateral loading after cell filling. Therefore,

analyses for lateral loading have to incorporate a second modulus reduction factor (RF2) to

be applied to steel modulus in addition to first modulus reduction factor (RF1) to compute

modulus of shear transfer elements. Moreover, it was observed for the case of Lock and Dam

26 (R) that both outboard and inboard sheet piles behave more or less like a cantilever beam

during lateral loading (Figure 6.1). During lateral loading, the horizontal distance between

outboard and inboard sheet piles decreases indicating general compression in the cell in

horizontal direction. Therefore, there should be a bulging force in other horizontal direction

towards the cross wall represented by shear elements. Thus, the modulus in circumferential

direction for shear transfer elements would become predominant and important during lateral

loading. The second modulus reduction factor determined based on case history analyses

would, therefore, also include the impact of reduced circumferential modulus of shear transfer

elements along with the three-dimensional behavior effects.


130.0

I

120.0 I Inboard I I ------ Out board I

110.0 I I I I

100.0 I - I I- I UJ I UJ lL. 90.0 I

I

z I 0 I

I I- 80.0 I <{ > I UJ I _, I UJ I Dredge line I 10.0 ~ '/ 1U\" <.;4,;

1.0.0

o.o o.s 1.0 1.5 2.0 2.s 3.0 3.5 DEFLECTION ( INCHES)

Figure 6.1. Deflection of sheet piles due to lateral load.

CASE HISTORIES USING MODIFIED PLANE STRAIN FINITE ELEMENT PROGRAM 106

Case history analyses were conducted in two stages. First stage of analysis was limited

to the cell filling operation which was done in a number of steps. Connecting springs with an

E-ratio of 0.03 were used between outboard and inboard sheet piles during cell filling. The

second stage of analysis considered berm placement, dewatering and application of equip-

ment load on top of cell fill as the case may be. Spring elements were replaced by shear

transfer elements between outboard and inboard sheet piles during second stage of analyses.

Results of first stage analysis were used as initial state of deflections and stresses for second

stage analyses. Results of these analyses are compared with the observed data to arrive at

an appropriate value of second modulus reduction factor (RF2) for shear transfer elements.

6.2 Willow-Island Second Stage Cofferdam - Cell 27

6.2.1 Project Description

The Willow Island Locks and Dam are located on the Ohio River 162 miles downstream of

Pittsburgh, Pennsylvania, at Willow Island, West Virginia. The project includes two parallel

locks, a high-lift gated dam, and a fixed overflow weir. The locks are located on the Ohio side

of the river and consist of a main lock 1200 feet long by 110 feet wide and an auxiliary lock 600

feet long by 110 feet wide. The dam has an overall length of 1,017 feet and consists of eight

tainter gates each 110 feet long by 34 feet high supported between nine reinforced concrete

piers. The weir is located on the West Virginia side and is 110 feet long. Normal upper and

lower pool elevations are 602.0 feet and 582.0 feet, respectively.

In order to construct the dam, a two-stage cofferdam was designed and built in the early

1970s. The first-stage cofferdam tied into the West Virginia bank and was used for the con-


struction of Piers 5 through 9. The second-stage cofferdam tied into Pier 5 and the river lock

wall and was used for the construction of Piers 1 through 4. Both cofferdams were instru-

mented to monitor movement, pore pressure and phreatic surface, but the second stage

instrumentation was more closely monitored than the first.

The second-stage cofferdam consisted of fourteen circular cells and five cloverleaf cells

interconnected by arcs as shown in Figure 6.2. Cells 14, 15 and 35 were part of the first-stage

cofferdam. Cloverleaf cells 31, 32 and 33 were constructed in the dry inside the dewatered

first-stage cofferdam and filled by clam shell. The remaining circular cells were filled hy-

draulically with well-graded, free-draining sand and gravel dredged from the river channel.

The water level was about 18 to 20 feet below top of cells.

The cells and connectors were constructed of type MP-102 steel sheet piling. The arcs

were joined to the cell by 30° wyes, and 120 ° wyes and cross-pieces were used to construct

the cross walls of the cloverleaf cells. These riveted connector piles were fabricated from type

MP-102 piling. The piling was driven to top of sandstone or six to eighteen inches into the

indurated clay layer where it was present. Weep holes were cut in the piling on the dry side

of all cells and connectors.

The cells in the upstream arm of the cofferdam were 58 to 61 feet high. The cells in the

downstream arm were approximately four feet lower, ranging from 54 to 57 feet high. The

circular cells were 64 feet in diameter. The cloverleaf cells had a maximum diameter of 90

feet, and were capped with an eighteen inch layer of stone to prevent scour in the event of

overtopping. Timber seals were installed between the four tie-in cells and the existing river

lock wall or Pier 5. Cell 27 was 54 feet high and 64 feet in diameter and was founded on

sandstone caprock.


PIER 2 PIER I , ... , I I

I I I

r·· • ' • '

0 SO 100 ISO ZOO kxd I I

5CAU I• IHI

RIVER LOCK WALL

Figure 6.2. Willow Island second-stage cofferdam location plan.


6.2.2 Site Conditions

The bedrock at the Willow Island site consists of thick, marine, shallow water deposits

which consolidated to indurated clays, claystones, shales, siltstones and sandstones. These

deposits were uplifted and folded by the same intense tectonic forces acting from the south-

east which formed the Appalachian Mountains.

Erosion has exposed members of the Conemaugh Series of the Pennsylvanian Age. These

beds are variable in composition and thickness with frequent facies changes and limited lat-

eral extent. The top of rock within the second-stage cofferdam has an average elevation of

557 feet and consists of a moderately hard, fine to medium grained, gray, micaeous sandstone

which is ten feet thick under Cell 24 but pinches out in the area of Cell 33 (Figure 6.2). The

sandstone caprock is underlain by a massive fifteen foot formation of soft, red and gray, highly

slickensided indurated clay with siltstone phases. The top two to twelve inches of this mem-

ber had decomposed to a soft clay. Beneath the indurated clay is a second strata of moder-

ately hard, fine grained, gray silty sandstone interbedded with moderately hard, red and gray

siltstone. This fifteen foot bed is interrupted by a three foot finger of indurated clay, and Piers

1 through 4 are founded below this clay zone. The sandstone-siltstone member is underlain

by a ten-foot zone of soft, red and gray, highly slickensided indurated clay with silty zones and

twelve feet of moderately hard, red and gray, silty shale with sandy zones.

The instrumentation for the second-stage cofferdam consisted of five inclinometer wells,

five in-place deflectometer wells with four sensors per well, twelve pneumatic piezometers,

twenty phreatic piezometers and a survey control net.


The instrumentation was installed after cell filling, but before dewatering. It generally

performed well, but on Cell 27, the inclinometer casing was hit by a crane and top of cell

movement had to be estimated thereafter.

6.2.3 Finite Element Analyses

The finite element mesh used for plane strain analysis is shown in Figure 6.3. The soil and

rock properties used were derived from the work by Clough and Hansen (1977), and are given

in Table 6.1. The water level was 18 feet below top of cell.

The analysis procedures allowed for a step-by-step simulation of construction sequence

as shown in Figure 6.4. Initial stage consisted of installation of cofferdam cell sheet piles in

place with river water level at about 18 feet below top of cell. This was followed by cell filling

which was completed in nine steps. After cell filling, the initial dewatering was modeled as

the third stage of construction.

An E-ratio of 0.03 was used for cell filling. After cell filling, analyses were conducted for

initial dewatering using the second modulus reduction factors (RF2) of 33, 25, and 20 for shear

transfer elements. The H/B ratio for Cell 27 was 0.843 and for this value of H/B the first

modulus reduction factor (RF1) for shear transfer element was computed from Figure 5.11 as

250 for top half and 190 for bottom half of the cell height. Both modulus reduction factors, RF1

and RF2, were applied to steel modulus to determine the modulus of shear transfer elements

used in the analyses.

The sheet pile deflection for initial dewatering from these analyses and those observed in

field using inclinometers are shown in Figure 6.5. The finite element predictions for all the

values of RF2 show similar trends. Maximum deflections occur at about one-third of cell


0 •:J

·.:.> ._., '" 0 0

CJ 0

t") «' _____ ....... C\.I

CJ ------0 0 ':r'

1--t-+-+-+-+--i C\.I

0 t-+++-t-+-+-1-+-+-+--+-+-+-+-~ 0

IJ ................. ~ ............. -+-+--+-+-+-+--'"~

0 C."l

Ht-+-+-+-+~ 0 C\.I

-------=> co

u 0

H~-+--+--+-_.,.o ~

0 0

.-~~~--~~~~-.-~~~"-i.,...a...&....&....L--L

oo·cf GC 0 091 00·021 oo·oe OO"Oh

CASE HISTORIES USING MODIFIED PLANE STRAIN FINITE ELEMENT PROGRAM

....: N

ci c "i u e ftl -e ~ u ,, c ftl iii

.. .2 .c en

CD E -c CD E CD "i .! c Li: cw; cO 2! :I Q

Li:

112

n )lo> en m ::i:: iii a ::u < en 2 2 m en c en z C') ;: 0 2 'Tl iii c .,, ~ z m en -4 ::u )lo> z :!! z ~ m r-m s: m z -4 .,, ::u 0 C') ::u )lo> :s:

.... .... w

Cell Soil No. or

Rock Type

SS-1

Circular SS-2 Cell SS-3 27 SS-4

SS-5 rial

SS-6

Clover- SS-7 leaf SS-8 33 SS-9

SS-10 rial

Table 6.1 Soil or Rock Properties for Willow Island Cofferdam

Soil or Rock Properties Hyperbolic Parameters

Unit Modulus Friction Cohe- Pois- Earth weight E angle sion son pressure Remarks 'Y q> c ratio coefficient (pcf) {psf) {degrees) v Ko Km Kur n Rf

97.6 2.5x101 0.0 0.0 0.2 1.0 - - 0.0 - Up to 7.6 ft. depth in foundation

97.6 - 0.0 5760.0 0.2 1.0 2000.0 2000.0 0.3 0.9 7.6 to 21.3 ft. 97.6 6.51x107 0.0 0.0 0.2 1.0 - - 0.0 - 21.3 to 39.7 ft. 97.6 3.9x107 0.0 0.0 0.2 1.0 - - 0.0 - 39.7 to 50.0 ft. 110.0 - 30.0 144.0 0.2 0.7 500.0 1000.0 0.5 0.9 cell fill mate-

97.6 - 0.0 5760.0 0.2 1.0 2000.0 2000.0 0.3 0.9 Upto11.8ft. depth in foundation

97.6 2.5x101 0.0 0.0 0.2 1.0 - - 0.0 -- 11.8 to 28.8 ft. 97.6 -- 0.0 5760.0 0.2 1.0 2000.0 2000.0 0.3 0.9 28.8 to 34 ft. 97.6 3.9x107 0.0 0.0 0.2 1.0 - - 0.0 -- 34 to 54 ft. 110.0 -- 30.0 144.0 0.2 0.7 500.0 1000.0 0.5 0.9 cell fill mate-

n l:; m :J: iii d ::u iii fn c fn z a s:: 0 0 :!! m 0 "Q

~ z m en ~ > z :!! z ~ m r m s:: m ~ "Q ::u g ::u > s::

... ... ..

T 18ft

1--64£ t ,____

,,... T 60 ft.

~~'0-~~~~~~"~~~"' 1

(A) Cell In Place

· .. -: ~":..: .. ..: .... I • •

:"·' .'• ~ .. ·. . . . " ~ . . · ... '.

, ...... ·. , ·.... . ..

(B) Cell Filling (C) Initial Dewatering

Figure 6.4. Willow Island Cofferdam, Cell 27, construction sequence modeled.

height from dredge line. The results show that maximum deflection is more closely matched

with observed value if second modulus factor (RF2) of 25 is used for shear transfer elements.

The maximum deflections were of the order of 0.6 inch. However, observed deflections of

sheet pile top are higher by 0.15 inches than those predicted. This probably could be because

the inclinometer casing was hit by a crane. Also, movement of heavy equipment on top of cell

fill could also cause this. The load of the construction equipment was estimated to range from

500 to 1500 psf. To examine the effect of heavy machinery movement on top of cell fill, a load

of 500 psf was applied in this case as surcharge on top of cell fill over one-half of cell width

from center line of cell to cell wall. With this loading, the predicted sheet pile deflections

match well with those observed (Figure 6.6). Thus, a second modulus reduction factor of 25

is considered appropriate for shear transfer elements during lateral loading for this case.

It was considered useful to compare the response of Willow Island cofferdam cells using

connector springs with that using shear transfer elements between outboard and inboard

sheet piles during lateral loading. The sheet pile deflection results obtained using springs

with E-ratio of 1.0 and as reported by Hansen and Clough (1982) are plotted in Figure 6.7 along

with the predictions of present analyses using shear transfer element (with RF2 = 25) without

any surcharge equipment load. The observed data is also presented on this figure. These

results show that models using spring elements with E-ratio of 1.0 and shear transfer elements

with second modulus reduction factor (RF2) of 25 yield similar predictions.


110

9~ I •

100 9~ I •

¢~ I •

90 9 ~ • • RF2 is Second - ~~ Modulus Reduction ..... Factor for Shear L&J ' . Transfer Elements. L&J 80 ~\ IL.

z 0 ..... ~ 70 > UJ . ..J L&J

60

Dredge tine

• Observed (Inclinometer)

~ RF2=33 40

-·<>-· RF2 = 25 ---0--- RF2 = 20

0.2 0.4 0.6 0.8 1.0

DEFLECTION (INCHES)

Figure 6.5. Willow Island Cofferdam, cell 27, Inboard sheet pile deflections due to Initial dewatering.


100 • Observed

RF2=25

90 ---- With load on to

500 PSF ...... RF2 =25 LLJ LLJ u..

z 0 ...... < > RF2 is Second LLJ 70 Modulus Reduction ...J LLJ Foctor for Shear

Transfer Elements.

60

50

40 ........ ~~---''--~~-L.~~~-'-~~~--~~---' 0,0 o.s 1.0 1.5 2 .o 2 .5

DEFLEC110N (INCHES)

Figure 6.6. Willow Island Cofferdam, cell 27, inboard sheet pile deflections due to initial dewaterlng, and equipment surcharge load.


110

I 100 I

I I

90 -t-w w LL

80 z 0 t-< > l.JJ 70 ...J l.JJ

so

• Observed

With shear transfer elements (RF2=25)

----- With spring elements (E-ratio=LO)

RF2 is Second Modulus Reduction Factor for Shear Transfer Elements.

DEFLEC110N (INCHES)

Figure 6.7. Willow Island Cofferdam, cell 27, inboard sheet pile deflections due to initial dewatering, using springs and shear transfer elements.


6.3 Willow Island Second-Stage Cofferdam Cloverleaf

Cell 33


The general project description and site conditions at Willow Island cofferdam are given

in Section 6.2.1. The cloverleaf Cell 33 was founded directly in indurated clay (Figure 6.2).

Sheet pile penetration varied from 6 to 18 inches. The diameter of cell was about 90 feet and

the height 62 feet. The water level during cell filling was about 20 feet below top of cell.


The finite element mesh used for the analyses of Cell 33 is shown in Figure 6.8. One row

of sheet pile elements was used in the center of the cell to model crosswall in cloverleaf cell.

The soil properties used are given in Table 6.1. The sequence of construction followed in the

analyses was same as mentioned for Cell 27 in Section 6.2.3.

An E-ratio of 0.03 was assumed for cell filling, which was completed in nine steps. After

cell filling, analyses were done for initial dewatering using second modulus reduction factor

(RF2) of 25 for shear transfer elements. The H/B ratio for Cell 33 was approximately 0.62 and

the corresponding first modulus reduction factors (RF1) for shear transfer elements computed

from Figure 5.11 were 120 and 95 for top half and bottom half of the cell height, respectively.

Both modulus reduction factors RF1 and RF2 were applied to steel modulus to compute

modulus of shear transfer elements used in the analyses.


Cll 4-' i:: Q

) s Q

) r-4 tzl

r-4 r-4 cu !:l Cl) Cll 0 ,... u oo·oz1

oo·oe

. ' OO

"Oh

... 0 0 0 '° ...... 0 0 0 C\J (T

l

0 0 0 CD C

\I

0 0 . 0 =r C\J

0 a 0 0 C\J

0 0 . 0 •.J:)

0 0 0 C\J

0 0 0 (0

0 0 0 ::r

0 0 . oo·(f

CA

SE

HIS

TOR

IES

US

ING

MO

DIFIE

D P

LAN

E S

TRA

IN FIN

ITE ELE

ME

NT P

RO

GR

AM

C"> C">

0 c -8 'ti G> 'C

: 0 u .. .2 .c

= E

120

The predicted and observed sheet pile deflections due to initial dewatering are shown in

Figure 6.9. As the inclinometer casing was placed in cell fill at some distance from inboard

sheet pile, the predicted deflections are also ploted in Figure 6.10 for soil elements in cell fill

at about 12 feet distance from inboard sheet pile. The predicted soil deflections match well

with those observed up to about 15 feet from dredge line. Thereafter, the observed deflections

are greater than predicted, reaching a difference of about 0. 75 inches at top of the cell. As

indicated earlier in Section 6.2.3 for Cell 27, this discrepancy in deflections could probably be

due to movement of heavy machinery such as crane and loaders. As indicated earlier, the

load of this equipment was approximated to be about 500 to 1500 psf. In this analysis appli-

cation of a load of 1500 psf as surcharge on the cell fill over half of cell width resulted in rea-

sonable match of finite element predictions with the observed deflections.

As can be observed from the predicted pattern of deflections, use of RF2 of 25 for shear

transfer elements appears appropriate to match with observed values in the vicinity of dredge

line where deflections are not much affected due to equipment loading and other disturbances

on top of the cell. In case of Cell 27 also, discussed in Section 6.2, it was observed that a

second modulus reduction factor of 25 for shear transfer elements yields results which rea-

sonably represent the observed behavior.


120.0

110.0

100.0

-~

~ 90.0 LL

z 0 80.0 ~ < > LLJ 70.0 ...J LLJ

60.0

40.00.0 0.5

I I I I I

I I

• Observed RF2=25

----- RF2 = 25 for soil at 12Ft away

--- With load on top 1500psf

1 oredge line


1.0 1.5 2.0. 2 .s 3.0 DEFLECTION (INCHES)

3.5

Figure 6.9. Willow Island cofferdam, cloverleaf 33, deflections of inboard sheet pile due to Initial dewatering.


I

J

' I

oo·os1 0

0'0

01

oo·os

0 0 0 "' "' 0 0 0 0 .... ~ "' 0 0 0 Ill ':3'

0 0 0 0 ':3'

0 0 0 "' M 0 0 0 0 M

... 0 0 0 "' "' 0 0 0 0 "' 0 0 C)

, .... -0 0 0 0 -[l

c.• 0 II'

0 0

oo·cf

CASE H

ISTO

RIE

S U

SIN

G M

OD

IFIED

PLA

NE

STR

AIN

FINITE E

LEM

EN

T PR

OG

RA

M

;:-c CD E

3 ftl Ci. CD a: -

123

6.4 Lock and Dam No. 26 (Replacement), First-Stage

Cofferdam


General description of Lock and Dam 26 (R), stage one cofferdam is given in Chapters 2

and 3. The cofferdam cells are approximately 63 feet in diameter and 60 feet high above the

dredge line. The sheet piles penetrated into the riverbed soils a distance of 35 feet. The cells

under study were filled by dumping riverbed sands with a clamshell. The water level was at

28 feet below top of cell.

Foundation materials at the replacement site consist of about 70 feet of granular alluvium

overlying bedrock (Figure 3.4). The alluvium increases in grain size with depth. At the river

bottom, it is a medium sand and at greater depths, the alluvium contains lenses of cobbles

and boulders.

Two circular cells and one arc cell of the downstream leg of the cofferdam were instru-

mented through a cooperative effort between the Corps of Engineers, St. Louis District and

Shannon & Wilson, Inc. The instrumentation program and results obtained through the cell

filling operations and early dewatering efforts are described in Shannon & Wilson (1983).

Instrumentation included eight inclinometers, 410 strain gage bridges, and 24 earth pressure

cells. In addition, pneumatic and open piezometers were installed on the piles, trilateration

monuments were placed along the perimeter of the cell walls, and settlement points were

placed in the top of the cell fill.



The finite element mesh used for plane strain analyses of Lock and Dam 26 (R) first-stage

cofferdam is shown in Figure 6.10. The water level during cell filling was 28 feet below top of

cell. The soil parameters used are given in Table 3.2.

The construction sequence (Figure 6.11) modeled in the analyses considered cofferdam

cell placement with river water level at 28 feet below top of cell, followed by cell filling in ten

steps. Thereafter, berm placement on inboard side and initial dewatering were simulated as

separate construction stages representing application of lateral loads to cofferdam cell.

The cell filling was simulated in ten steps and E-ratio of 0.03 was used for the spring ele-

ments. After cell filling, analyses were performed for berm placement and dewatering using

second modulus reduction factor (RF2) of 25 for shear transfer elements. The H/B ratio was

0.95 and corresponding first modulus reduction factors (RF1), computed using Figure 5.11, are

270 and 230 for top half and bottom half of cell, respectively. Both modulus reduction factors,

RF1 and RF2, were applied to the modulus of steel to computed modulus of shear transfer

elements.

The predicted and observed sheet pile deflections due to berm placement are shown in

Figure 6.12. The results show general consistency with the observed behavior.

For dewatering, predicted and observed behavior of inboard sheet pile are shown in Figure

6.13. With the application of 1500 psf surcharge load due to construction equipment on top of

cell fill over half of cell width, the predicted sheet pile deflections match well with those ob-

served. These results confirm the observations from Willow Island cofferdam Cell 27 and Cell

33 analyses, discussed in Sections 6.2 and 6.3, that using the second modulus reduction factor


~63ft.--t Cell fill

T . ., . . . T 28 ft. . . . . . ..

. , .. ·." ... . -~ ·... . . : 60 ft.

Foundation

(A) Cell in Place (B) Cell Filling

, ....... _ ... · ....... .. . .. . ·· ... :-: ':: ,' ..... : .. _ .. : -: · ....

·. . .. ~ :' ~ ........ , .· . . ·. .. .. · .. ·. ' .. :. '..:. , : .. : : -===-,. .I~. .. • •• :· • •

. . . . • :· . • . . ·. . . . . . . . r-:----,'"'

.. ·. · .... <.": .= ..... · ... :;.·:: . ... : .. · .. ·. : : · ... · .. _ .· ........ . . : ....... ·. · .. · ...... : .. ~:

-~--I.. ....•

(C) Berm Placement (D) Initial Dewatering

Figure 6.11. Lock and Dam 26 (R) cofferdam, construction sequence modeled.


120 --+- Observed ( Inboard)

~ Observed (Out board)

110 --<>-- Predicted (In board) RF2.=25

-100 ---er.-- Predicted (out board) t- RF2=25 w w I LL ' 90 t> RF2 is Second z ' Modulus Reduction 0 Foctor for Shear t- Transfer Elements. < > w _, w

70

60

so

40

o.o 1.0 2.0 3.0 4.0 s.o 6.0 DEFLECTION ( INCHES )

Figure 6.12. Lock and Dam 26 (R) cofferdam, deflection of sheet piles due to berm placement.


of 25 for shear transfer elements yields results which reasonably match the observed behav-

ior.

6.5 Summary of Case Histories

As indicated in the earlier chapter, the appropriate modulus value of shear transfer ele-

ment should be determined on the basis of (i) comparison of finite element results with the-

oretical solutions and (ii) analyses of case histories. The first modulus reduction factor (RF1)

based on (i), discussed in Chapter 5, is obtained using the curve (Figure 5.11) for a particular

cell height and cell width ratio H/B. The second modulus reduction factor (RF2), based on

case histories discussed in this chapter, considers three-dimensional effects, and interlock

slack and yielding. during lateral loading.

Although the three case histories indicate that during lateral loading, the second modulus

reduction factor (RF2) of 25 for shear transfer elements yields results which agree most with

the general observed behavior, it is difficult to arrive at this conclusion for definite. The rea-

sons for this are 1) small amount of sheet pile deflections, 2) reliability of the instrumentation

data, and 3) expected disturbances due to construction equipment over the cell fill.

Nevertheless, RF2 of 25 could be used for shear transfer elements during lateral loading

to obtain reasonable results.

Both the above modulus reduction factors, RF1 and RF2, should be applied to the modulus

value of steel to compute the modulus of shear transfer elements for use in analyses.


120

100

-~

ttl 90 LL

z 80 0

t:= ~ w ...J 70 w

60

50

40

0.0

---o--- Observed

- - - --- Predicted (RF2

-....._..

=~5) with differential load

Predicted (RF2 = 25) with load on top =1500psf

Dredge line


1.0 2.0 3.0 4.0 5.0

DEFLECTION { INCHES }

6.0

figure 6.13. Lock and Dam 26 (R) cofferdam, deflection of inboard sheet pile due to initial dewatering.


6.6 Stress Transfer Mechanism From Outboard to Inboard

Sheet Pile

Analyses were done to study the effects of alternative methods for providing shear transfer

through cell fill during application of lateral loads. Lock and Dam 26 (R) dimension and soil

conditions were considered and hydrostatic loading was applied on full free cell height, as

discussed in detail in Chapter 7. Cases using shear transfer elements with second modulus

reduction factor RF2 of 25, springs with E-ratio of 1.0 and using no connectors between out-

board and inboard sheet piles were analyzed. Model using no connectors was considered to

compare and study the effect of presence of shear transfer mechanism.

The results of incremental horizontal stress (~ crx) over the cell width at El. 105 (25 feet

from top and 35 feet from dredge line) for hydrostatic load of 1ywh are shown in Figure 6.14

for cases with load transfer shear elements; with spring elements, and with no connectors

between outboard and inboard sheet piles.

The results with load transfer shear elements show a smoother transfer of lateral load

through cell fill as well as through shear elements. The maximum incremental horizontal

stress is near outboard sheet pile, and it is reduced to almost zero near inboard sheet pile.

In case of spring elements, the ~ crx near outboard sheet pile is very high and suddenly

drops near the center of cell fill. Similarly, with no connectors, there is very high ~ crx near

outboard sheet pile and drops to zero at 8/6 from center towards inboard sheet pile (Figure

6.14). The soil near inboard sheet pile beyond 8/6 from center experiences tensile stresses.


1.5 In cell fill with 1.4 ' shear elements

' With springs u. ' -·-Vl ' ~ 1.2 ' No connectors ' -----

~ \ In shear elements <J ' --·-9\ \ Vl 1.0 \ Dredge line El.= 70.0 Vl

L&J \ a:: \ ~ \ Vl \

...J 0.8 \ ~ \ ~ z \ 0 \ N 0.6 \ a:: \ . 0 \I :c z

0.4 \° w c.!) z ~ 0.2 :c u

0.0

l cell1 .... ____ -0.2 -0.3

0.0 10.0 20.0 30.0 40.0 50.0 60.0 Outboard DISTANCE {FEET) Inboard

side side

Figure 6.14. Lock and Dam 26 (R) cofferdam load transfer from outboard to inboard sheet pile at El. 105 for hydrostatic load 1ywh.


As the spring elements connect outboard and inboard sheet piles at some distance inter-

vals, while the shear transfer elements connect the sheet piles in full height. the shear ele-

ments are, therefore, expected to result in the load transfer mechanism which could be

somewhat closer to the realistic behavior.


Chapter VII

PREDICTED RESPONSE OF LOCK AND DAM 26 {R)

TO LATERAL LOADING

An important aspect considered in the design of cofferdams, other than interlock tension

issue discussed in Chapter 4, is the failure of cell fill during lateral loading. As noted before,

such failures have been rare, and it is believed that the conventional design methods for

vertical shear failure in cell fill are conservative. As an example, for Lock and Dam 26 (R)

stage one cofferdam, the factors of safety against vertical shear for the case of normal pool

are computed as 6 and 12 based on Terzaghi and Schroeder and Maitland method, respec-

tively. These values are 1.5 and 3.0 for normal flood case. At normal pool and flood loadings,

this cofferdam has been functioning as a safe structure, as borne out by its behavior observed

in the field. Considering the observed maximum sheet pile deflections of only 1to1.4 inch for

flood loading on Lock and Dam 26 (R), it could be deduced that both Terzaghi and Schroeder

and Maitland method yield conservative predictions as the cofferdam cell would need to un-

dergo substantial deformation before vertical shear failure could occur.

PREDICTED RESPONSE OF LOCK AND DAM 26 (R) TO LATERAL LOADING 133

Following sections discuss the response of Lock and Dam 26 (R) cofferdam for normal flood

and higher lateral loads. Lock and Dam 26 (R) is considered for analyses as this represents

a typical large cofferdam. Analyses for normal flood load after cell filling are intended to ap-

proximately model the actual flood condition and study the behavior in respect of cell de-

flection, lateral earth pressure coefficients and base pressure distributions. Although

application of higher lateral loads to failure represents a condition not achievable in the field,

it is considered important to investigate what the nature of response will be. Also, the results

of analyses for loads to failure will give better idea of real factor of safety against failure and

help assess the degree of conservatism in the design. Development of failure surfaces during

high lateral loads is also discussed. The failure mechanism investigated would be helpful in

development of new design method of shear failure in cell fill presented in Chapter 8.

7.1 Analysis Procedures and Assumptions Therein

Using plane strain SOILSTRUCT program, vertical slice analyses were done for Lock and

Dam 26 (R) in two stages. First stage simulated cell filling in ten steps, using an E-ratio of 0.03

for springs. Following cell filling, lateral loads in steps of one hydrostatic pressure (1y.jJ) were

applied on entire free height of outboard sheet pile. The schematic representation of

cofferdam cell subjected to lateral loading is shown in Figure 7.1. Shear transfer elements

with RF2 of 25 were used during lateral loading. The finite element mesh used for analyses

is shown in Figure 6.10. The hydrostatic loading was considered because of following:

• As a base case, it represents the normal flood condition.


side -i r Inboard side

T .or-----~ Outboard

h

Cofferdam Cell H

y h w

Dredge line

Foundation

figure 7.1. Schematic representation of a cofferdam cell subjected to lateral load.

PREDICTED RESPONSE OF LOCK AND DAM 26 (R) TO LATERAL LOADING . 135

• Moment being the most important factor, any particular loading would be translated into

the aplied moment on the cell. Hydrostatic loading offers a general case and could be

related to any kind of specific load in terms of moment.

• Offers a simplified tool to allow comparison between conventional and finite element

methods.

• Failure of "safe" cofferdam could be reached by application of load increased by unit

hydrostatic load in each step.

It may be noted that the verification of shear transfer elements in SOILSTRUCT program

and computation of modulus reduction factors is based on analyses for working conditions

only. It could be possible that at higher lateral loads, local dislocations and relative dis-

placements in cell fill or slippage between sheet piles may occur that could affect the behavior

and failure mechanism of the cofferdam. The basic model does not consider the effects of

these factors, but they are examined later in the chapter.

Vertical slice analyses were conducted considering Lock and Dam 26 (R) dimensions and

soils. Cell width, free cell height and depth of embedment were taken as 63, 60 and 35 feet,

respectively. The soil parameters used were as given in Table 3.2. The water level was 28

feet below top of cell.

7.2 Cell Filling

Behavior of cofferdams during cell filling was studied in detail in Chapter 4 using

axisymmetric SOILSTRUCT program. In this section, the development of lateral earth pres-

PREDICTED RESPONSE OF LOCK ANO DAM 26 (R) TO LATERAL LOADING 136

sure coefficient in cell fill is discussed to compare with the values used in conventional de-

signs for interlock force.

As discussed in Chapter 2, various conventional design theories assume different values

of lateral earth pressure coefficient (Figure 2.2) to compute maximum lateral earth pressures

and maximum interlock force on sheet pile walls. As lateral earth pressure coefficient value

would affect the maximum interlock force in direct proportion, it is important to use the lateral

earth pressure coefficient value as close to reality as possible. The lateral earth pressure

coefficients (K) for cell fill and foundation soil within and just outside the cell in foundation at

the end of cell filling are shown in Figure 7.2.

Consider cell fill material having friction angle <P = 35°, the earth pressure coefficient at

rest, Ko, is defined as 1 - sin <p, and it equals 0.42. The active earth pressure coefficient is:

Ka = tan2(45 - <p/2)

or, = 0.27 for <P = 35°

The passive earth pressure coefficient is:

Kp = tan2(45 + q>/2)

or, = 3.69 for <P = 35°

The results for cell filling (Figure 7.2) show that lateral earth pressure coefficient values in

cell fill are between active and at rest coefficients and closer to at rest value Ko. The average

values near sheet piles are approximately 0.42. The range of values in cell fill is 0.37 to 0.49.

Terzaghi (1945) specified lateral earth pressure coefficient values of 0.3 to 0.5 for cellular

cofferdams. Both field and laboratory studies (Maitland and Schroeder, 1979) indicate that the

lateral earth pressure coefficient within the cell fill for cell filling condition lies between the

active and at rest coefficients. Schroeder and Maitland (1979) suggested that the lateral earth

pressure coefficient value ranges from 1.2 to 1.6 times Rankine active earth pressure coeffi-


... 1·------63. 0 Ft

--0.4 0.4 0.4 0.4 0.4

0.39 0.49 0.47 0.49 0.39

0.4 0.38 0.4 0.38 0.4

0.43 0.36 0.36 0.37 0.42

0.45 0.42 0.42 0.43 0.45 60.0A

Lo 0.43 0.38 0.37 0.38 0.43

aded side~ 0.42 0.38 0.37 0.38 0.42

0.41 0.39 0.39 0.39 0.41

0.41 0.41 0.41 0.41 0.41

Dredge line~ 0.49 0.44 0.44 0.44 0.49 "{'" _ .....

2.58 0.4 0.34 0.32 0.33 0.4 ~~ 2.57

1.67 0.43 0.35 0.32 0.35 0.43 1.65

JS.Of 1.33 0.43 0.37 0.34 0.37 0.43 1.31

1.05 0.43 0.4 0.39 0.4 0.42 1.0 -

t 0.97 0.42 0.44 0.43 0.44 0.42 0.95

// '///////////// / /'/ '//// / // / / / / / //

Figure 7.2. Lateral earth pressure coefficient (K) for cell filling.


cient KA . This gives a range of .32 to 0.43 for cell fill friction angle of 35 degrees. Schroeder

and Maitland (1979) suggested an average value of lateral earth pressure coefficient as 1.38

times active earth pressure coefficient. The average value of lateral earth pressure coefficient

based on this and cell fill friction of 35 degrees is 0.37.

7.3 Predicted Response for Flood-Type Load

This section deals with the response of Lock and Dam 26 (R) cofferdam for flood type

loading conditions represented by hydrostatic load 1 y..,)1 . The discussion is related to cell

deflection, lateral earth pressure coefficient, base pressures and vertical stress in cell fill.

7.3.1 Deflection of Sheet Piles

For purposes of understanding the general effect of the lateral loading, it is useful to first

examine the effects of the application of the hydrostatic load of 1 y..,)1 . The deflected shape

of cell due to application of flood load is shown in Figure 7.3, and the horizontal deflections

of the inboard and outboard sheet pile are shown in Figure 7.4. The following observations

are made from the results:

• The deflections of both outboard and inboard sheet piles under lateral loading resemble

cantilever behavior. Maximum deflections occur at top of sheet piles. Similar type of

behavior was observed for Willow Island cofferdam cells 27 and 33 for dewatering (Fig-

ures 6.5, 6.6 and 6.9) and for Lock and Dam 26 (R) for berm placement and dewatering

(Figures 6.12 and 6.13) as discussed in Chapter 6.


Loaded Side Original shape of cell

,.--.:_ ____ ~Deflected shape of cell

I -------1 I I I I I I I I f I

60ft. : Cofferdam Cell / I I I

I I / I

I I I I

,' I I I

I

I I I I I I

35ft. ! / l _:__'_-~---~---~-~-=------=--~~~ f ..-~~~~~63 ft·~--~---~-~~-_J

20.0ft. i--~~~- Scale for cell geometry.

1.0 inch .,__~~~~Scale for deflections.

Figure 7.3. Deflected shape of a cofferdam cell due to lateral load.


130.0

I

120.0 I Inboard I I

Out board I ------110.0 I

I I I

100.0 I I .... I I.LI

I.LI I IJ.. 90.0 I

I

z I 0 I .... ao.o I ~ I > I I.LI I ~ I I.LI I Dredge line 10.0 I

~'I QS;t\ cow

60.0

50.0.

40.0

o.o o.s 1.0 1.5 2.0 2.5 3.0 3.5 DEFLECTION ( INCHES)

Figure 7.4. Deflection of sheet piles due to lateral load.


• Outboard sheet pile deflections are more than inboard sheet pile above dredge line and

less below dredge line. Thus, soil in cell fill experiences some compression and foun-

dation soil is under slight tension.

The maximum deflections due to hydrostatic load are predicted as about 1.3 inches. The

observed deflections of a particular cell for flood load are shown in Figure 7.5 (from Martin,

1987). The maximum sheet pile deflection observed is 0.7 inch and according to these results,

outboard sheet pile moves only 0.4 inch which is less than inboard sheet pile deflection. This

is contrary to logical behavior. This, therefore, suggests that there could be some problem

with instrumentation data. However, based on optical survey, the observed average maxi-

mum sheet pile deflections for 11 cells for flood loading from point "B" to "D", ignoring fluctu-

ations, is about 1.4 inches as shown in Figure 7.6 for December, 1982 flood (Martin, 1987),

which compares well with the finite element predictions.

7.3.2 Lateral Earth Pressure Coefficients

The values of lateral earth pressure coefficients for lateral loading of 1 y.)7 are shown in

Figure 7.7. These results show that K increases substantially in cell fill near outboard sheet

pile and center of cell fill. The increase of K in soil near inboard sheet pile is only limited to

about 20 feet from top of cell. The maximum values of K within cell fill are about 0. 7 near

outboard sheet pile, the range being 0.4 to 0.71. The sheet pile deflections (Figure 7.4) also

show maximum compression near center and lower portion of cell. The K values are, there-

fore, higher near outboard sheet pile as the cell fill soil near outboard sheet pile shares more

lateral load compared to soil near inboard sheet pile.

In foundation soil within the cell, the K values do not change significantly during flood

loading. In foundation outside outboard sheet pile, the K value decreases substantially from


"O ::u m c

~ c ::u m (I) "O 0 z (I) m 0 "l'I

g " ,.. z c c ,.. 3: N

°' ~ ~

§ ::u ,.. r

g S! z a

.... t

-1ouTBOARO)

Ored9eline ") . /,/4\\fl// ----- ----;- - \"\'WT~·,

..

LOCK ANO DAM NO. 26 ( R) C e 11 on Sand Foundot ion

~4~

Sand Cell Fi IL

. .

I in

..

.. ·.

I I Displacement Scale

30 fl 1-------l Structure Scale

(INBOARD)--.

. . . . . .. '''"'''''' ... . . .....

...

Figure 7.5. Lock and Dam 26 (R), observed cell deflection for flood load (from Martin, 1987) .

--c <t w :c ~ <t .... z w a: w "-"-c

LOCK AND DAM NO. 26 ( R)

Cell on Sand Foundation (STAGE I)

II Typical cells

t 4.8 Hioh Water

/ 3.6

2.4

1.2

I Normal Oewatered Pool

l ®

PT to PT ACTIVITY

A II DEWATERING II C NORMAL FLUCTUATIONS C D DEC 1982 FLOOD D E FLOOD INTERIOR E F DEWATER INTERIOR F G APRIL t98l FLOOD G H FLOOD INTERIOR

• AveraQe of tnboord and Outboard Deflections

0 t.O 2.0 30 4.0

TOP DEFLECTION TOWARD INTERIOR 50

( in)

Figure 7.6. Lock and Dam 26 (R), average response of 11 typical cells to lateral loading (from Martin, 1987).


I """·------63.o Ft

- -0.4 0.42 0.55 0.63 0.57

0.43 0.65 0.62 0.62 0.47 0.5 0.49 0.51 0.46 0.46

0.55 0.48 0.47 0.43 0.46 0.58 0.56 0.54 0.49 0.48 60.0Ft

Lo 0.59 0.51 0.46 0.42 0.43 aded side~ 0.64 0.52 0.43 0.37 0.44

0.63 0.57 0.44 0.39 0.43 0. 71 0.56 0.49 0.42 0.41

Dredge line"-\ 0.69 0.57 0.49 0.46 0.5 ' ~'"'" 0.7 0.43 0.38 0.36 0.38 0.42 2.78

o. 76. 0.36 0.34 0.35 0.41 0.47 1. 76

35.0ft 0.76 0.46 0.38 0.36 0.39 0.46 1.42

o. 77 0.53 0.42 0.39 0.4 0.42 1.11

0.81 0.54 0.46 0.42 0.43 0.4 1.01

//nVa///////////////////////////

Figure 7.7. Lateral earth pressure coefficients (K) for hydrostatic load 1ywh.


average 1.4 to 0.78, indicating decrease in horizontal stress (ox) during flood loading. Outside

inboard sheet pile there is slight increase in K value, indicating some increase in ox.

7.3.3 Base Pressure Distribution

As discussed in Chapter 2, Terzaghi's method (1945) for vertical shear analysis considers

the rotation of cofferdam cell about the center of base line (dredge line) and assumes linear

pressure distribution about the center line of the base (Figure 2.4) during application of lateral

loads. Vertical slice analyses were done to study the rotation of cell and base pressure dis-

tributions and compare results with Terzaghi's assumptions.

The analyses were done for flood loading cases of 1 y.)> acting on entire free height of

outboard sheet pile and load 1 y.)> acting on upper half of outboard sheet pile height. A

hydrostatic load of 2 y.)> was also applied to confirm the pattern of base pressure distribution.

These analyses were performed after cell filling. The incremental base pressures (change in

vertical stresses) for cell filling and for hydrostatic loads at dredge line are plotted over the

cell width in Figures 7.8 and 7.9, respectively.

For cell filling, the base pressures are nearly uniform over the cell width, the average value

being about 5.0 ksf. For hydrostatic load of 1 y.)> and 2 y.)> acting on full height of outboard

sheet pile, the incremented base pressures are zero at a distance of about 8/8 (8 = width

of cofferdam cell) from center of cell towards outboard sheet pile. For 1 y.)> load in upper half

of outboard sheet pile height, incremental base pressures are zero at approximately 8/5 from

center of cell towards outboard sheet pile.


63 ft. I

t of cclli

<ti' 2.0 ~ -"' "' e -r.n ; Ci! ! <.J'

"€ > I 6.0

Figure 7.8. Base pressures at end of cell filling, Lock and Dam 26 (R) cofferdam.


-~000

----~~h¥SI~ 5 Rei~R£ - 2xh¥d£~sfi. lo~~ on u eig -· -·-i xh~d ros tli. l~rd on pp er a

-1200 t of cell

I - , .. BI 5. !,.I .... -860 co 0.

I I ..._,

QJ I

1 .. B/ s .. j,. ""' -400 B/S ~I ::I (I) "''' I I (I) I QJ ....

""' "-~,I p... 0 •I

QJ (I) 200 ca

l:Q

i: ~

QJ 660

00 i: ca

..c:: u HIOO

1400

1800

0.0 10.0 20.0 30.0 40.0 50.0 60.0 Distance from Outboard Side

Figure 7.9. Base pressures at dredge line due to lateral load, Lock and Dam 26 (R) cofferdam.


This means that under lateral loading the cofferdam cell tends to rotate along some point

on the dredge line which may be at a distance of 8/5 to 8/8 from center of cell towards out-

board sheet pile.

This result is in contradiction with the theory developed by Terzaghi suggesting that the

cofferdam tends to rotate along the center line of the base under lateral loading. The pre-

dieted behavior is probably because of the interaction between sheet piles and soil and also

stress transfer mechanism in cell fill. Terzaghi theory does not consider this effect.

Figure 7.9 also shows that maximum incremental compressive stresses occur at a distance

of about 8/5 from cell center towards inboard sheet pile and maximum incremental tensile

stresses occur at about 8/10 from cell center towards outboard sheet pile. Near inboard and

outboard sheet piles, the incremental stresses are reduced to almost negligible because of

slippage between sheet pile and the soil.

Due to interaction between sheet piles and soil, the incremental base pressures are re-

duced compared to the linear pressure distribution assumed in conventional design sug-

gested by Terzaghi (1945). As an example for Lock and Dam 26 (R), for normal flood load the

maximum incremental base pressure is computed as 9340 psf as compared to 4665 psf, pre-

dieted by finite element analysis (Figure 7.9). Thus, the maximum incremental pressures

could be about 50% of those computed using conventional design theories using simple laws

of mechanics. Terzaghi's (1945) vertical shear concept used to evaluate the failure due to

shear distortion in cell fill soil (as discussed in Chapters 2 and 8) suggests the computation

of vertical shear using following equation:

Q =3M 2b


This relationship is obtained assuming linear variation of base pressure due to lateral load.

The reduction in base pressures and their distribution pattern would result in substantial re-

duction in vertical shear (Q) values and thus higher factor of safety against vertical shear

failure compared to Terzaghi values. For 50% reduction in base pressure, the factor of safety

will be twice of that obtained using linear variation of incremental pressure on base.

7.3.4 Change of Vertical Stress in Cell Fill and Foundation

In addition to the study of development of base pressures at dredge line during lateral

loading as discussed under Section 7.3.3, an investigation was made of the change of vertical

stress in cell fill as well as in foundation soil to have an idea about the vertical stress transfer

through the height of the cell.

The results of changes in vertical stress (~ cry) at different elevations in cell fill and in

foundation soil within the cell for flood load of 1 y.jl on full outboard height are shown in Fig-

ures 7.10 and 7.11, respectively.

In cell fill (Figure 7.10), the maximum incremental vertical stresses near dredge line and

10 feet above dredge line (El. 73 and El. 80) occur at about 8/5 from center of cell. For El. 90

(20 feet above dredge line) maximum incremental compressive stresses occur near both

sheet piles and maximum incremental negative stress occurs at center of cell. This probably

is due to more prominent effect of interfaces between sheet pile and soil at this level. For El.

116 (14 feet from top) and El. 122 (8 feet from top) the maximum incremental compressive and

tensile stresses occur near outboard and inboard sheet pile, respectively. The stresses are

comparatively quite low at these elevations probably because of less unrestricted movement

of soil elements.


-0.4 -·-- EL-122.0

EL-116.0 EL-92.0 EL- 80.0 EL- 73.0

- -0.3 u. Vl ~ -~-0.2

I_, Dredge line EL '70.0

,.1 ' <l ... Vl Vl w 0:: ..... Vl

...J <{ u ..... 0:: w > z w I,!) z <{ :I: u

-0.1

0.0

0.1

0.2

0.3

0.4

. ' ' ' ' ' ~--

.>·?

¢.. ceu--l I

\ \ \ \ \ \ \

O.SL----l....--L-----'-----11---~--:-:--':""'""" 0 0 10.0 20.0 30.0 40.0 50.0 60.0

ou;ii:r~rd DISTANCE (FEET) ln5~~rd

Figure 7.10. Change of vertical stress in cell fill due to lateral load, Lock and Dam 26 (R) cofferdam.


2.0

-·-- EL-67. 0

1. 6 -·- EL-61.0

----- EL-45.0

u. 1.2 EL-33.0 Vl Dredge I ine EL = 70.0 ~

~ 0.8 <J

<t cell1 9' Vl 0.4 Vl w

I ~ I-Vl _J 0.0 <{ u I-~ w 0.4 > z w 0.8 ~ z <{ :I: u 1.2

1.6

2.0L-~~~~--1-~~.l.-~--L~~--'-~~-'-~ 0 10.0

Cfotboard side

20.0 30.0 40.0 50.0 DISTANCE (FEET)

60.0 Inboard

side

Figure 7.11. Change of vertical stress In foundation due to lateral load, Lock and Dam 26 (R) cofferdam.


For foundation soil within the cell (Figure 7.11), the change in vertical stress follows more

or less similar trend at different elevations. Maximum incremental tensile stresses occur near

outboard sheet pile, while maximum incremental compressive stresses occur at about 8/5

from cell center towards inboard sheet pile, as was observed in case of development of base

pressures. In this case also, rotation of cell takes place about the axis passing through points

at about 8/8 from center of cell towards outboard sheet pile.

7.4 Predicted Response for High Lateral Loads

To study the response and failure mechanism of cofferdam cell during application of high

lateral loads, vertical slice analyses were conducted for Lock and Dam 26 (R). The behavior

of cofferdam was studied in relation to cell deflection, load-deformation response, lateral earth

pressure coefficients and possible failure mechanisms.

7.4.1 Deflection of Cell

The deflected shapes for cofferdam cell for loads 1 y.)J, 2 y.)J, and 4 y.)J are shown in Figure

7.12 and for collapse of load of 7 y.)J in Figure 7.13. The deflected shapes at collapse load are

unrealistic as they represent the configuration of cell just before complete collapse due to

overturning, which normally would not happen because cofferdam would fail due to other

causes prior to collapse. Nevertheless. the deflected shapes give some information about the

deflection pattern of the cell during lateral loading. Results presented in Figures 7.12 and 7.13

indicate that there is a general tendency of lifting up of outboard sheet piles during application

of lateral loads. For load 4 y.)J the outboard sheet pile moves up by 3 inches and for 7 y.)J it

moves up by 6 feet, the maximum lateral deflection for these loads being 11 inches and 9.4


feet, respectively. The maximum lateral deflections for loads 1 y.jl and 2 y.jl are 2 inches and

3.2 inches, respectively.

The point of rotation (Figure 7.12) during successive application of lateral loads moves from

outboard side to inboard side from center of cell as the load increases. The inboard sheet

pile deflects as cantilever with restraint due to foundation.

7.4.2 Load-Deflection Response

The deflections of inboard sheet pile for different values of lateral loads are plotted in

Figure 7.14. The deflection for a normal flood load which is equal to 1 y.jl is approximately 2

inches. For lateral load of 1 y.jl representing the flood condition, sheet pile deflection is about

1.5 inches. Those for load of 4 to 5 y.jl at which the cell starts to show substantial defor-

mations are 11 to 23 inches. At collapse load of 7 y.jl, the sheet pile deflection, as predicted,

is 112 inches (approximately 9.4 feet). Failure loads predicted based on Terzaghi (1945) and

Schroeder and Maitland (1979) method of vertical shear analysis are also presented in Figure

7.14. These loads are 1.1 y.jl and 2.2 y.jl, the failure load from Schroeder and Maitland

method being twice that from Terzaghi method. The sheet pile deflections at failure loads are

2 and 3.3 inches, as predicted by Terzaghi and Schroeder and Maitland methods, respectively.

The fact that these deflections are much less compared to those corresponding to near failure

loads confirms the idea that conventional design methods are conservative.

The effects of relative movements in cell fill on load-deformation response are discussed

later in the chapter.


.,, ::u m c

~ c ::u m (I)

i (I) m 0 "II

g " > z c c > 3::: N

"' ~ a ~ ~ r-g 2 z C')

... UI UI

130

IU

.... t:i 98 u.. -z Q 82 .... ~ 1£1 jj 66

50

JS

Deflected shape of cell

------------1rr---7 =t·\\ l I

I

:'I t, l

\ . ~\

Original shape of cell

Drtdgt lint

\ \ : \ . I ', I : )i ,/ 1/ ,

\ I I I ,

//---;/-{ /" 1/ I • . ll ~ .. -------;... ". °=·---.-:..- .::::;~-?.}

~ 63.0 Ft j t ln~rd Outboard sidt sidt

Sc alt: 8.0 ft Gt0mtlry

~ Dtfltclions

Figure 7.12. Lock and Dam 26, deflected shape of cell for lateral loads .

1 x Hydrost. load

2 x Hydrost. load

4 x Hydrost .load

130

111.

.... 98 I.LI I.LI lJ..

z 82 0 .... <{ > I.LI _, 66 I.LI

so

JS Inboard

I ·

Depth of Embedment H0 = 35.0 ft.


63-0Ft

Deflective shape of cell

Scale

SD Ft Geometry

20A Deflections

Figure 7.13. Lock and Dam 26, deflected shape of cell for collapse lateral load 7ywh.


.,, ::u m g

~ g ::u m (I) .,, 0 z (I) m 0 '"" r-~ " > z g g > ~ N

°' -~ -t 0

E m ::u > r-r-0 > S? z a

... en .....

"'O 111 0 -l

(J •.-i ~

111 ~

C/l 0 S..

"'O >-::c

~-----,~-.--.~.---r~-r--r~i-:~---i 7.0

6.0

s.o

4.0

3.0

2.0

1.0

o.o 0

Cell Width B = 63 ft. Hd = Depth of Embedment

_ .. _____ (.Schroeder, F.S.=l.O )

------ ( Terzaghi, F.S.=l.O)

10 20 30 40 50 60 70 80 90 100 Horizontal Deflections, Ux (Inches)

Figure 7.14. Lock and Dam 26, lateral load versus deflection of sheet plle top

110

7.4.3 Lateral Earth Pressure Coefficient

Investigation of lateral earth pressure coefficients (K) at high lateral loads is considered

important to estimate the failure loads against shear failure in cell fill during lateral loading.

As indicated in Chapter 2, there have been controversies about K value to be used in the

anlyses for vertical shear failure.

Terzaghi (1945) estimated lateral earth pressure coefficient (K) value for lateral loads as

0.4 to 0.6 for cellular cofferdams and recommended the use of 0.4 for analyses. Field obser-

vations (Schroeder et al., 1977) have shown that K may be as high as 0.7 during construction

of cofferdams.

Model studies (Schroeder and Maitland, 1979) on large and small cells indicated that back

filling increased the hoop stress, a function of K, at front sheet piles from 13% to 25% and

decreased hoop stress in back sheet piles by up to 50% over cell filling values. There was

no consistent correlation between depth of embedment and increase in hoop stresses. Con-

sidering an average value of K as 0.42 would mean a range of K as 0.47 to 0.53 for 13% to 25%

increase.

Maitland and Schroeder (1979) indicated the increase in earth pressure coefficient K is

most likely greater near center and lower portion of cell where compression of fill is larger

during application of lateral load.

For lateral loads up to failure due to vertical shear, Schroeder and Maitland (1979) indi-

cated that K values are above both at rest coefficient Ko and Krynine (1945) value. They

suggested that K during overturning and shear distortion can be approximated by unity.


Predicted K-values for hydrostatic load of 3 y.)7 (Figure 7.15) have a range of .44 to 2.2.

Maximum values occur near outboard sheet pile. The values at center of cell range from 0.58

to 0.93. For load 5 y.)7 , the predicted values of lateral earth pressure coefficient are shown

in Figure 7.16. The values near center of cell range from 0.5 to 1.8, the average value being

more than 1.0. Near inboard sheet pile, the values range from 0.26 to 1.7, the average being

approximately 0.75. It could be fairly concluded that near failure load, K values in center of

cell could reach approximately unity or even more than that, and near inboard sheet pile the

average K value could be considered as 0. 75.

Thus, the predicted results of lateral earth pressure coefficients during cell filling and

during lateral loads confirm the field and laboratory observations in general.

7.4.4 Possible Failure Mechanisms

To investigate the pattern of development of failure mechanism in cell fill, stress ratios

(ratio of shear stress to shear strength) for each soil element within cell fill and foundation

were studied at the end of each load step of 1 y.)7 . Elements having stress ratio equal to or

more than 1 (which represents the failure of the element) were marked for a particular loading

stage.

Possible Failure Surfaces

Based on angle e (the angle of major principal plane measured counterclockwise from the

positive Y-axis), obtained from finite element analyses results for soil elements failed in shear,

failure planes directions are determined using details given on Figure 7.17. The direction of

failure planes are then plotted for each failed element. Pattern and sequence of failure sur-


l ..... ..._ _____ 63.0 Ft

--0.41 0.66 0.93 0.94 0.75

0.6 0.94 0.89 0.81 0.56

0.73 o. 77 0.73 0.58 0.53

0.82 0.76 0.68 0.51 0.5

0.84 0.88 0.77 0.58 0.52 60.0Ft 0.9 0.86 0.63 0.47 0.56

L oaded side~ l.04 0.92 0.61 0.44 0.49

l. l l.09 0.58 0.48 0.46

1.5 0.96 0.62 0.47 0.44

Dredge line-, 2.2 0.92 0.64 0.52 0.5 ,. __ T

2.45 0.87 0.63 0.5 0.43 ~r

l.11 0.41 0.49 0.51 0.53 2.23

35 .. Oft 7.6 0.45 0.38 0.43 0.49 1.8

11. 5 0.41 0.37 0.38 0.39 l. 35

17.1 0.41 0.39 0.41 0.35 1.2

//////777////////777///// //77 /////

Figure 7.15. Lateral earth pressure coefficients (K) for hydrostatic load 3 y wh.


I .... ·------63-0 Ft - r-

0.25 0.9 1. 74 3.2 1. 7 I

0.41 1.14 1.64 1.97 0.92

0.61 1.02 1.53 1.68 0.82

0.91 1.14 1.69 1.17 0.95

1.08 1.42 1.84 1.09 0.79 60.0Ft

L 1.28 1. 71 1. 79 0.69 0.62

oaded side~ 1.6 2.34 1.11 0.58 0.76

1.82 2.59 1.83 0.41 0.31

1. 72 2.88 0.7 0.76 0.26

Dredge Ii ne """\ 4.56 1.6 0.48 0.42 0.34

'~-· 27.8 15.0 1.44 0.43 0.13 ,_,.._

3.94 High 1.6 0.56 0.46

35.0ft High High OL86 1.56 0.52

High High 0.66 0.27 0.42

High High 0.29 0.23 0.31 I

///////////////// // '//////////// //

Figure 7.16. Lateral earth pressure coefficients (K) for hydrostatic load 5 y wh.


faces in cell fill and foundation is then determined based on direction of failure planes of dif-

ferent failed soil elements and also the loading stage causing failure in particular soil element.

The multiple of hydrostatic load causing failure in soil elements is shown in Figure 7.18.

The direction of failure planes and resulting possible failure surfaces are presented in Figure

7.19.

The results show that active and passive failure conditions occur in foundation outside

outboard sheet pile and inboard sheet pile, respectively, for a load of 1 to 2 yjl acting on

outboard side before any failure surface develops in cell fill. The foundation soil within cell

is also subjected to failure near outboard sheet pile, initially.

On further application of lateral load, a curved (convex upward) failure surface develops

in cell fill near dredge line at a load of 4 to 5 yjl . The shape of failure surface could be

considered as nearly circular. This confirms the concept as suggested by Hansen (1953, 1957).

The soil in foundation within cell and in cell fill near dredge line in the vicinity of inboard sheet

pile also starts failing in shear at loads of 4 to 5 yjl , the failure planes being almost vertical.

However, till the failure load of 7 yjl causing tilt of the cell, the vertical shear develops only

up to approximately mid-cell height from dredge line. Thus, at any section, the soil in cell fill

does not fail in shear in full height until collapse. The tendency of vertical shear failure oc-

curring first at center of cell, as suggested by Terzaghi (1945) and confirmed by Schroeder and

Maitland (1979) was not observed as the failure takes place near inboard sheet pile first.


~

Major Principal Plane

.L. Failure Plane 11A11

/ ./

y =45°+:

Inclination of Failure Plane "A"

"' From X-Axis a= (90+9-y) =90+9-45-2

=(45+9-:)

Inclination of Failure Plane 11 8 11

From X-Axis {3 = -(90-9-y)

13: -(45-9- : )

Figure 7.17. Determination of direction of failure planes.


FAlLURE

lxy H w

3xy H w

7xywH.

Loaded side

LOAD

~ ~

- ji--•----63.Q Ft

~

60.0Ft

Figure 7.18. Lock and Dam 26, failed soil elements and failure loads


Outboard side

LOAD

Dredge line

I ... ·------63. 0 Ft EL 130.0

Inboard side

60.0Ft

otat ion t----"'-+----

ELO.O

Figure 7.19. Lock and Dam 26, failure plane directions and failure surfaces due to lateral loads.


7.4.5 Vertical Displacement of Cell Fill and Slippage of Sheet Piles

During Lateral Loading

As discussed in Section 7.4.4, vertical shear failure planes start developing in cell fill near

inboard sheet pile under high lateral loads, but the cell fill does not seem to fail in shear in

complete height before collapse. Some cases of vertical shear failure in cofferdams have,

however, been noticed. Model studies (Schroeder and Maitland, 1979) have also indicated

development of such failure at high loads. To explain the occurrence of such failures, the

other causes of failures such as vertical displacements of cell fill and possibilities of slippage

of sheet piles during application of lateral loads were studied.

Vertical Displacement of Cell Fiii

During large scale model tests (Schroeder and Maitland, 1979), some terraces were ob-

served at the surface of cell fill near inboard sheet pile and middle of cell during lateral

loading until failure. Vertical displacements of top of cell fill as predicted by finite element

analysis using no soil to soil interfaces in cell fill for lateral load of 3 y..)l are presented in

Figure 7.20. These results show general bodily tilt of cell fill without terrace formation, as

would be obviously expected from this model. To investigate the relative vertical displace-

ments of soil in cell fill, soil to soil interfaces having same angle of internal friction as cell fill

(i.e., 35 degrees) were provided throughout the cell height at a distance of 13 feet and 25 feet

from inboard sheet pile, and finite element analyses were done using different steps of lateral

loading. The intention to provide soil to soil interfaces was to model the vertical displace-

ments of soil more realistically. The results of vertical displacements of top of cell fill for lat-

eral load 3 y..)l from these analyses are also plotted in Figure 7.20. The results show that there

is a relative movement of the order of 0.6 to 0.7 inch in top of cell fill at the location of soil

interfaces and as a result, terraces are formed in cell fill.


~

c 0 .....

6.0

4.

2 .

Depth of embedment Hd=35 ft.

Load = 3y h w

Location of Soil Interfaces~, I I

Without soil y ~

I .u CJ QJ

.-4

...... Q)

Q

l--12 f~l3ft

I .-4 ~ O.q-"~~~~~~~~~_::::.....-~::::::~~:--~~~~~~-l

~ !' ...... : ......... . ,... '"(!) ...... ...... • QJ ' I > ...... ~

-2.0 With soil interfaces

-4.0

OUTBOARD SIDE Distance (Feet)

60 t INBOARD SIDE

Figure 7.20. Lock and Dam 26, vertical displacements at top of cell fill without and with soil interfaces.


To study the impact of providing soil interfaces on sheet pile deflections, the lateral de-

flections of inboard sheet pile top from analyses without and with soil interfaces are shown in

Figure 7.21 for different steps of lateral loadings until collapse. The results show that the trend

of deflection curve is similar in both cases and analyses with soil interfaces obviously yield a

more flexible response. At normal flood load equivalent to 1 y.)J , the deflections of sheet pile

top are within 2 to 3 inches range without and with soil interfaces. However, close to collapse

load, say 6 y.)1 , the deflections in case of model with soil interfaces are 106 inches (8.82 feet)

as compared to 48 inches (4.0 feet) without soil interfaces.

Thus, the finite element model without soil interfaces underestimates the sheet pile de-

flections substantially at high lateral loads. The use of load transfer shear elements as a

connection between outboard and inboard sheet piles may also contribute to some underes-

timation of sheet pile deflections. To represent cell fill soil more realistically, more soil

interfaces should be provided in cell fill to assess the sheet pile deflections at high loads.

However, at working loads of 1 to 3 y.)1, the effect of providing soil interfaces does not signif-

icantly affect the sheet pile deflections. Therefore, the finite element model could be consid-

ered to result in reasonably realistic predictions of sheet pile deflections during application

of normal working lateral loads on cofferdam. Based on deflection data shown in Figure 7.21,

it is recommended that a factor of 1.75 may, however, be used in estimating deflections due

to working lateral loads using the model to account for soil to soil interaction.

Slippage of Sheet Piles

Based on large scale model tests, Schroeder and Maitland (1979) indicated that the slip-

page of sheet pile interlocks occurred in front portion (unloaded side) along with shear dis-

tortion in cell fill under high lateral loads. The picture in the paper (Schroeder and Maitland,

1979) shows that at least 5-6 sheet piles had slipped together.


.,, ::0 m 0 n ;;l 0 ::0 m Cl> .,, 0 z Cl> m 0 "Tl

5 n " > z 0 0 > iii: N

°' ~ a ~ ::0 > r r 0 > 2 z a

.... °' co

"'Cl co 0

..J

u ..... ~

co ~ Ul 0

"' "'Cl >.

::i:

1.0~~--~~..--~-r-~-,~~-,-~-,~~-r~-,.~~,.-~-.~---,

6.0

s.o

4.0

3.0

2.0

1.0

0.0 0

. .,........- ------0------- -- ---.... ...- ...-c With soil interfaces .,..

Without soil interfaces Depth of ernbedrnent Hd = 35 ft

Cell Width B = 63 ft.

10 20 30 40 so 60 70 80 . 90 Horizontal Deflections, Ux (Inches)

Figure 7.21. Lock and Dam 26, effect of soil Interfaces on sheet pile deflections during lateral loading .

100 110

Analyses were therefore conducted to investigate the possibility of slippage of inboard

sheet piles due to lateral load, which could in turn result into failures of cell fill. The cofferdam

dimensions and soil properties used were same as that of Lock and Dam 26.

Axial pull in sheet pile was computed based on average axial forces in beam elements.

The results are multiplied by 1.33 to compute axial pull in one sheet pile which is 16 inches

(1.33 feet) wide. Axial pull for a number of sheet pile together is computed by multiplying this

number to the axial pull for one sheet pile.

Interlock resistance was calculated based on lateral stresses in cell fill near inboard sheet

pile. A friction factor of 0.3 was used between sheet pile interlocks. Total interlock resistance

against slippage was computed using entire height of sheet pile and considering two resisting

interlock surfaces as any slippage would involve at least two resisting surfaces. The sche-

matic representation of slippage of sheet piles on inboard side is shown in Figure 7.22.

Axial pull for different number of sheet piles and total interlock resistance considering two

slipping surfaces were plotted for different number of hydrostatic loads. The results are

shown in Figure 7.23.

When axial pull equals interlock resistance, slippage could occur. The results show that

for any stage of loading the interlock resistance is always much higher than axial pull for one

sheet pile. This suggests that if we consider individual sheet pile, the slippage shall not occur

unless there are interlock misalignment or other sheet pile installation defects. However, just

as an academic exercise, it was assumed that a group of sheet piles could act as one unit as

if there were no intermediate interlocks present. This would mean that although the total

interlock resistance (for two extreme interlocks) does not increase for a group of sheet piles,

the total axial pull is proportionately increased. Thus, based on this assumption, slippage of

the group of sheet piles could occur. The possible number of sheet piles that could be in-


Vl

ell

0..

- ell ell ..s:: V

l

{-----~-rr---------,---.

\ \ \ \ \ \ \

I I

I I

I

;----

c 0

0 c·-

·-- 0'1'-·-

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1.... 0

oc..

1.... ell

--(1.1

0 O

'l c

0 0

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c.. ·v; ·;;; 0 a..

"0

1....

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O-o

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r\_---_i (1.1

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tr

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I I

--:::;,

PR

ED

ICT

ED

RE

SP

ON

SE

OF

LO

CK

AN

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26 (R) T

O L

AT

ER

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LO

AD

ING

Vl

-c .X

u

ltJ

0 £

1.... «i

ell ...

-c Q

) ... ~ 0

-Q)

::I 'tJ Ill ~

a. ... Q

)

w

Q)

0 ~

Ill

Vl

- 0 0

Q)

Cl

0::: ltJ

~

a. 0

.e-CD

iii z

- 0 c 0 ; ltJ

- c Q)

Ill Q

) ... a. Q

) ... ()

; ltJ E

Q

) ~

()

Cl)

c:"i N

.....: Q

) ... ::I C

l u:

171

...J

...J ::::> a.. ...J < x <

700

600

500

" 1.00 w u z ;:! Vl Vl w a:: :x:: u 0 ...J a:: w .,_ z

300

Ho= 3 5.0 teet

• Interlock resistance

AXIAL PULL

One sheet pile Five sheet piles Eight sheet piles Ten sheet piles

3 " 5 HYDROSTATIC LOAD

6 7

Figure 7.23. Lock and Dam 26, axial pull and interlock resistance in inboard sheet pile due to lateral load.


volved in slip and the hydrostatic load that could cause slip are 10 and 1.7 y.ji . respectively.

For a load of 1 y.ji equivalent to nood load, the number of sheet pile required to act as a unit

for slippage is eleven.

The slippage of sheet piles could be possible during application of normal lateral load, only

if the group of sheet piles could act as one unit. However, this possibility appears to be un-

realistic because during loading, each interlock would start offering resistance to axial pull.

The number of sheet piles required for slippage increases with increase of depth of

embedment, which is quite logical. sheet piles will not slip due to the causes other than

misalignment and other structural defects.

7.5 Summary and Conclusions

Vertical slice analyses using spring elements with an E-ratio of 0.03 up to cell filling and

using shear transfer elements with second modulus reduction factor RF2 of 25 for lateral

loading suggest following:

Deflection pattern of sheet pile resembles cantilever behavior, outboard sheet pile de-

flections being slightly more than those of inboard sheet pile above dredge line and less

below dredge line.

Lateral earth pressure coefficient values in cell fill at the end of cell filling are between

active and at rest earth pressure coefficients and closer to at rest value. The average

value for cell fill soil having friction angle of 35 degrees is approximately 0.42, the range

being 0.37 to 0.49. The range of values suggested by Terzaghi (1945) and Schroeder and

Maitland (1979) are 0.3 to 0.5 and 0.32 to 0.43, respectively.


For lateral loads, Terzaghi (1945) estimated lateral earth pressure coefficient as 0.4 to 0.6.

Schroeder and Maitland (1979) indicated that for lateral loads up to failure due to vertical

shear, lateral earth pressure coefficient value at center of cell fill could be considered as unity.

The predicted lateral earth pressure coefficient values for lateral load 1 y.)1 and 3 y.)1 have a

range of 0.4 to 0.71, and 0.44 to 2.2. respectively. The values at center of cell for load 3 y.)1

range from 0.58 to 0.93. For load 5 y.)1 . the values of lateral earth pressure coefficient at

center of cell reaches more than unity and average value near the inboard sheet pile is ap-

proximately 0. 75.

Under lateral loading, cofferdam cell tends to rotate along some point on the dredge line

which may be at a distance of B/5 to B/8 from center of cell towards outboard sheet pile in-

stead of centerline as suggested by Terzaghi (1945). The pressure distribution at base

(dredge line) is curved instead of linear as assumed by Terzaghi. Interaction between sheet

piles and soil results is substantial reduction of base pressures as compared to those com-

puted based on Terzaghi theory.

Vertical stress distribution in cell fill due to lateral loading show no particular trend. In

foundation, however, the change in vertical stress follows more or less similar trend at dif-

ferent elevation, the zero stress change point being at about B/8 from center of cell towards

outboard sheet pile.

Study of deflected shapes of cofferdam cell, load-deflection curves, failure mechanism and

failure surfaces, and vertical displacements of cell fill without and with soil interfaces and

possibility of slippage of sheet piles due to high lateral loading suggest following.

Although, even at collapse load of 7 y.)1 , the vertical shear failure surface does not de-

velop in full height of the cell fill near inboard sheet pile, it does not necessarily mean that the

cell fill will not fail in vertical shear. The results obtained by inclusion of soil interfaces indi-


cate relative displacement of soil and formation of terraces. Some soil interfaces show shear

failure. Looking at the impact of both the results of vertical shear failure of soil elements and

the relative vertical slip of soil along soil interfaces, it may be fairly concluded that the cell fill

will fail in vertical shear also at a load of about 5 y..,/1 at which the curved failure surface de-

velops fully.

Slippage of sheet piles could only occur either due to some misalignment and other

structural defects or if a group of at least eleven sheet piles acts as a unit with no resistance

from intermediate interlock. The former problem cannot be accounted for in design. The later

cause seems to be a rare possibility.

Thus, assuming 5 y..,/1 as failure load for shear distortion in cell fill, the deflections of sheet

pile top at this load are 23 inches. Considering a factor of safety of 1.5, the allowable load

would become 3.3 y..,/1 and corresponding sheet pile deflections would be 7.5 inches for Lock

and Dam 26 (R).

Failure loads based on Terzaghi (1945) and Schroeder and Maitland (1979) method for Lock

and Dam 26 are 1.1 y..,/1 and 2.2 y..,/1 and the corresponding sheet pile deflections are 2 inches

and 3.3 inches for Terzaghi and Schroeder and Maitland method, respectively, as compared

to 23 inches from finite element analyses for failure load of 5 y..,/1 . Considering a factor of

safety of 1.5, the allowable loads are 0.75 y..,/1 and 1.5 y..,/1 and corresponding sheet pile de-

flections are 1.5 inches and 2.6 inches, for Terzaghi and Schroeder and Maitland method, re-

spectively; while they are 3.3 y..,/1 and 7.5 inches based on finite element analyses. The

conventional design methods, therefore, yield conservative predictions.


Chapter VIII

PARAMETRIC STUDIES AND METHODS TO

PREDICT CELL DEFORMATIONS AND FAILURE

UNDER LATERAL LOADINGS

One of the main design conditions for cofferdams occurs when they are subjected to the

lateral loads caused by dewatering and flooding. There is a tendency of shear distortion in

a cofferdam cell fill when lateral load is applied. Failure of cofferdams under these conditions,

however, is rare, and in most cases there is more concern about the magnitude of the defor-

mations that will occur than collapse. Deformation control for the cofferdam system is indi-

rectly insured in conventional design of cofferdams, as it is for many geotechnical problems,

by using what is perceived as an adequate factor of safety against failure. It would be of sig-

nificant importance to estimate the cell deflection at failure and arrive at allowable value

based on appropriate factor of safety. The performance of the cofferdam could then be mon-

itored in the field effectively as the instrumentation is generally done to measure cell de-

flections.

PARAMETRIC STUDIES AND METHODS TO PREDICT CELL DEFORMATIONS AND FAILURE UNDER LATERAL LOADINGS 176

The methods for calculating the factor of safety against collapse for a cofferdam under

lateral loading are described in Chapter 2. The most widely accepted technique for deter-

mining the factor of safety against collapse during lateral loading of a cofferdam was proposed

by Terzaghi (1945). There are two key aspects to the Terzaghi technique: (1) the cell fill is

assumed to fail along a vertical shear plane that passes through the center of the cell; and (2)

the lateral stresses acting on the vertical shear plane are assumed to be defined as the ver-

tical gravity stress in the cell fill multiplied by the lateral earth pressure coefficient of the cell

fill (usually taken to be 0.5). As noted in Chapter 2, a number of investigators have questioned

one or both of Terzaghi's assumptions, with most noting that they lead to overly conservative

answers for design.

Hansen (1953, 1957) suggested curved failure surfaces near dredge line and foundation

during application of lateral loads. Esrig (1970) had indicated that vertical shear concept is

invalid. Cummings (1957), working from observations on very small model cells with very rigid

sheet piles, proposed a method of analysis based on horizontal shear concept. Maitland and

Schroeder (1979) indicated that Cummings' method overestimates moment resisting capacity

of cells with embedded sheet piles.

Large scale model tests (Schroeder and Maitland, 1979) indicate that Terzaghi's vertical

shear concept is valid. There was no evidence in either the large or small scale model fail-

ures indicating a convex or concave circular or logarithmic spiral slip plane, as has been re-

ported in previous model studies. Therefore, to investigate further the response and failure

mechanism in cellular cofferdams due to high lateral loads, parametric analyses were done

using modified plane strain program SOILSTRUCT.


8.1 Parametric Studies

The study of response and failure mechanism under lateral load for Lock and Dam 26 (R),

discussed in Chapter 7, demonstrated the need for conducting some parametric studies to

investigate the effect of depths of embedment and cell width on sheet pile deflection and to

study the failure mechanism due to lateral loading for different size cofferdams and different

depths of embedment.

Including analyses done for Lock and Dam 26, presented in Chapter 7, finite element ana-

lyses were done using following set of parameters:

Cell Free Cell Depth of Hydrostatic Width Height Embedment Loads (8) Feet (H) Feet (Hd) Feet Applied

63 60 10 1 to 5 ywh 63 60 21 1 to 7 ywh 63 60 35 1 to 7 ywh 40 50 10 1 to 3 ywh 40 50 20 1 to 5 ywh 40 50 35 1 to 5 ywh

Separate analyses were also conducted for cell width of 60 feet and depths of embedment

of 21 and 35 feet providing soil to soil interfaces in cell fill. The soil types used were as given

in Table 3.2 for Lock and Dam 26 (R). The water level was 28 feet below top of cell for B = 63

feet and 25 feet below top of cell for B = 40 feet. Cell width B = 63 feet, free cell height H = 60

feet and depth of embedment Hd = 35 feet represents Lock and Dam 26 (R), stage one

cofferdam.


E-ratio of 0.03 was used up to cell filling. During application of lateral loads, second

modulus reduction factor (RF2) of 25 was used for shear transfer elements. The first modulus

reduction factor (RF1) was computed based on H/B ratio.

Lateral loads mentioned above were applied in full free height of outboard sheet pile in

steps of 1 y.jl . The stresses in soil of cell fill and foundation were studied for each step of

load.

The model tests conducted by Schroeder and Maitland (1979) had indicated that sheet piles

had undergone large amount of deflections under lateral loads before failure due to shear

distortion of cell fill occurred. The above mentioned hydrostatic loads were, therefore, applied

in finite element analyses to obtain maximum possible sheet pile deflections before tilting of

the cell.

8.1.1 Deflected Shapes of Cell

The deflected shapes of cells of cofferdam having cell widths of 63 feet and 40 feet and

depth of embedment of 35 feet are shown in Figure 8.1 for flood load of 1 y.jl. These results

show that trend of deflection in both cases is similar. Maximum lateral deflection for cell

widths 63 and 40 feet are 1.3 and 1.5 inches, respectively. Thus, for similar type of loading 40

feet cell deflects more than 63 feet cell. This is because the slenderness ratio H/B for 40 feet

cell is 1.25 as compared to 0.94 for 63 feet cell. However, below mudline, the deflections in

both cases are of the same order.

Analyses were done for a cofferdam having cell width B = 63 feet and free cell height H = 60

feet (same as Lock and Dam 26 (R)) and depths of embedment, Hd of 10, 21 and 35 feet to study


the deflected shape of cell before collapse under application of lateral loads. Results for depth

of embedment of 35 feet are already discussed in Chapter 7. The soil properties used and

water level were same as described in Chapter 7. The deflected shapes just before collapse

are shown in Figure 8.2.

During lateral loads, outboard sheet piles moved up substantially and inboard sheet pile

moves down very little except for depth of embedment of 10 feet in which case it moves down

by 6 inches (Figure 8.2). The sheet piles on inboard side deflect as cantilever. The outboard

sheet piles move up by approximately 1, 7.8 and 6 feet for depths of embedment of 10, 21 and

35 feet, respectively, before collapse. The horizontal deflection of sheet pile tops are 2.4, 10.8

and 9.4 feet for Hd = 10, 21 and 35 feet, respectively. The movements of sheet piles for Hd

= 21 feet are more than those for Hd = 35 feet. This is because same hydrostatic loading of

7 y,)I was applied before collapse. In fact, for same deflections, the lateral load for Hd = 21

feet would be lesser. Because the loading was applied in steps of 1 y,)I , the load of 7 y,)I

was considered for both cases as a condition before collapse.

Thus, there is a general tendency of lifting up of outboard sheet piles during overturning.

For Hd = 10 feet, the cell can withstand much less deformations before collapse as compared

to Hd = 21 feet and 35 feet.

For loads just before collapse, the cell with Hd = 10 feet has rotating tendency about some

point near center at dredge line. The applied load before collapse is 5 y,)I as compared to 7

y,)I applied for Hd = 21 and 35 feet. For Hd = 21 and 35 feet, the cell rotates about a point very

near to inboard sheet pile just before collapse.


60ft. l 50ft.

35ft.

l

Original shape of 63ft wide cell

Original shape of 40ft wide cell

r-----L--r---if-----=--.., _ - - --, . I

I I

I I I I L_

I

I I

I I I I

I I

/ I

/ I .

r-·-·-1 ·-. . I .

I I

1· JJl'C:-// .. \\C:li·b

l I I I -:..::::.-:_- -

I I

I I

·-·-·; I . I J I / / i I

. I I I

/~•fleeted shape · , of 40ft wide cell

I I / I »""';>1AJ Dredge line

I I

I ~Deflected I 63ft wide I I

shape of cell

·-- ...... :- -....J

I..,.•....---- 40f t. Scale:

._., _____ 63ft.-----~ _z_o_._o_f_t_. _Cell geometry

l.Oinch Cell deflection

Figure 8.1. Deflected shapes of 63 feet and 40 feet wide cells for load 1 ywh

Parametric Studies and Methods to Predict Cell Deformations and Failure Under Lateral Loadingir 181

130

114

.... 98 LLJ LLJ LL

z 82 0 .... < > LLJ _, 66 LLJ

so

35

Ho = 35.0Ft ( 7 x hydrostatic load)

Ho = 21. 0 Ft ( 7 x hydrostatic load)

Ho = 10. 0 Ft ( 5 x hydrostatic load )


Inboard 1~·-------6~0Ft--------~

Deflected· shapes ·~of cell

-~-~ ---, I I I I I I I I I I I I I I I I I I

J.

I I/

Scale

8.0 Ft

2 OFl Geometry

Deflections

Figure 8.2. Deflected shapes of cofferdam cell for collapse lateral load.

Parametric Studies and Methods to Predict Cell Deformations and Failure Under Lateral Loadings 182

: iii 3 ID .. .. n en .. c CL ii Ill II

&. ;: !l ':r'

8. Ill

~ "'O Cil CL ~ n == 0 ~ .. 3 ! 0 :i Ill • :i CL

~ c Cil c :i CL ID .. i !. b g_ ;-~

.... OI w

Deflected of cell

130

114

.....

~ 981 I (/ z 2 82 .... ~

~ 661 ........

so

35

I. 63.0 Ft

t Outboard

sidt

Original shq>t of cell

t ln~rd

Stdt

Out board 1hcct ~Ile

1111111111

I 12>9 ,~· Hft j_

Sea It:

Element 237 to 239 eacovoted to model seour

4 • Hydrost. load wilhout scour

-tt- t, !I Hydrost.load with scour

8.0 fl Gtomttry

2.0 in Otfltctions

Figure 8.3. Deflected shapes of cofferdam cell with and without scour.

Effect of Scour:

To study the impact of scouring on sheet pile deflections and failure, analysis was also

done with excavation of foundation soil up to failure, 20 ft, outside outboard sheet pile and

application of lateral loads. The deflected shape for load 4 y.,jl before collapse is presented

in Figure 8.3. Also shown is the deflected shape for 4 y.,jl without scour effects.

Due to scouring the load before collapse is reduced from 7 y.,jl to only 4 y.,jl for Hd = 35

feet. Outboard sheet pile moves up by 5.0 inch for scouring and 2.8 inches for no scouring for

a load of 4 y.,jl . Inboard sheet piles move down about 2.5 and 2 inches, respectively. The

maximum horizontal deflection of sheet pile top are 16 inches and 11 inches for scouring and

no scouring, respectively.

Thus, scouring substantially reduces the capability of the cell to withstand the overturning

load and to undergo deflections before collapse.

8.1.2 Effect of Depth of Embedment on Sheet Pile Deflections Due to

Lateral Loading

Maximum sheet pile deflections for cell widths of 63 feet and 40 feet and various loading

levels are plotted in Figure 8.4 against depth of sheet pile embedment. The deflections as a

percentage of free cell height are presented in Figure 8.5 for both cell widths of 63 feet and

40 feet. These results indicate the following:

• For both cell widths, the sheet pile deflections for depth of embedment Hd of 10 feet are

slightly higher than those for Hd of 20 feet and 35 feet. At normal flood load of y.,h , these


-.c u c:

25

!j 20 c: 0 ..... µ u QI

..-1 ~ 15 A QI

r-1 ...... c:i. µ QI

~ 10 Ul

H/B=0.94 , load 3Ywh

0 \

\ \ \ \ \ \ \

\

H = Free cell height B

H/B = Cell Width Slenderness ratio of cell

= Hydrostatic load

\(H/B=l.25,load 3yw11

\ \ \ \ \ \ \

Go--- -- -------e--

H/B=l.25,load lYwh ~ H/B=0.94,load lYwh

---.4-13------L=@ - ---~ 0 ~~~~~~~""-~~~~~~-'-~~~~~~-£--~~~~~~~ o.o 10.0 20.0 30.0 40.0


Figure 8.4. Effect of depth of embedment on sheet pile deflection during lateral loading.


values range from 2 to 2.5 inches. The difference becomes substantially more at high

lateral loads. For example, for load of 3 y.)J , the deflections for cell width of 63 feet are

8.6, 6.2 and 6 inches and for cell width of 40 feet. they are 26.5, 9.3 and 8.4 inches for

embedment depths of 10, 20 and 35 feet, respectively.

• Increase in depth of embedment from 20 feet to 35 feet has insignificant change in sheet

pile deflections.

• At normal flood load of y.)J , the deflection of sheet pile top could be estimated as 0.35%

to 0.28% of free cell height (Figure 8.5) for cell width ranging from 40 feet to 63 feet for

depths of embedment values from 10 to 35 feet. At working flood load, thus, the per-

centage of deflection to cell height is not much influenced either by depth of embedment

or by cell width for usual size of cofferdams. At higher lateral loads, however, the influ-

ence of depth of embedment below 20 feet and the cell width becomes more significant.

8.1.3 Load Deflection Response of Cell

The sheet pile top deflections due to lateral loads for cell widths of 63 feet and 40 feet and

for different depths of embedment are presented in Figures 8.6 and 8. 7, respectively. The

load-deflection curve for Lock and Dam 26 with depth of embedment of 35 feet was discussed

in Chapter 7. These results show that the deflections for depths of embedment of 20 feet and

35 feet are not significantly different, even at high lateral loads. Failure load for depth of

embedment of 10 feet is about 60 percent lower than those for depths of embedment of 20 and

35 feet for cell widths of 64 feet as well as 40 feet.

For working flood load of 1 y.)J , the sheet pile top deflections range from 2 to 2.5 inches

for depths of embedment of 10, 20 and 35 feet for cell widths of 63 and 40 feet.


0 0 -

5.0

~ 4.0 ~ .c: 00 ~ Q)

:::::: ..-4

~ 3.0 u -c: 0

..-4 ~

CJ

~ 2.0 ..... Q) 0 ..-4 ..-4 Q)

~ 1.0

\ \ \ \

B = Cell Width Hydrostatic load

\~ B=40ft.,load

\ \

\ \

\ \

\

' '0----- - - "7-----e---B=6Jft., load 3Ywh

B=40ft.,load lYwh ~B=63ft.,load lYwh ::.::$"----~~----------~


Figure 8.5. Sheet pile deflection as percentage of cell height for different depths of embedment and cell width.


: D1 3 ! .. n ~ c ICI. ii' II DI ~ ICI. 3:: CD ... -:r 0 ICI. II

S' ,. iiJ ICI. !l n ~ 0 CD O' .. 3 a 0 ~ II 1111 ~ ICI.

"" !. c iiJ c ~ ICI. CD .. r-i !. b DI ICI. :r

IQ II

.... m m

7~0r-~-,~~-,.~~-,-~~-,-~~.-~~.-~~r-~--ir--~---i-~~-.-~~-

6.0

'"Cl s.o CIJ 0

...l

CJ

'" "" 4.0 CIJ

"" Cll I .

0 i... yl ~ 3.0

::c:

2.0

1.0

o.o 0 10

/

.>?/' /

20

--- --- -- -..... ~ -- ·~---Hd=35 ft.

/

-· _.0-. - .r- Hdc:lO ft --· . L-. - . ~ -· -· -·-· -·-·-·-·-·0

30

Cell Width B = 63 ft. Hd = Depth of Embedment

40 50 60 70 80 . 90 100 Horizontal Deflections, Ux (Inches)

Figure 8.6. Lateral load vis deflection of sheet pile top for cell width of 63 feet.

110

.,, DI .. DI 3 CD ... .. n (II ... c a. i" • • :I a. i: CD ... -:r 0 a. • ... 0 .,, ; a. fl (")

~ g CD O' .. 3 a 0 :I • DI :I a. "Tl !!. c .. • c: :I a. CD .. ! CD .. !. b DI a. ;-

u:i •

... m co

"C Ill 0

...:i CJ

•r-4 ~

Ill ~ (/) 0 ....

"C >. =

7.0r-~~r-~-y-----,i----.----,,---,~--,~--,.---.----.-~--

6.0

s.o

4.0

3.0

2.0

1.0

Hd=35 ft. _... .... -0"-

// //

// <: :J"r.v',.. Hd=20 ft /p •

Cell Width B ~ 40 ft.

Hd • Depth of embedment

L " =10 f !':\.-. d t. --~ -· _/' ·-/ ·--· yr/ -·-·-·-

o.o~---1----L----L.----'----'----l----'---........ --_._--_._--__. 0 10 20 30 40 50 60 70 80 90 100 110

Horizontal Deflections, Ux (Inches)

figure 8.7. Lateral load v/s deflection of sheet pile top for cell width of 40 feet .

8.1.4 Vertical Displacement of Cell Fill and Slippage of Sheet Piles

As discussed in Chapter 7 for Lock and Dam 26 case with depth of embedment of 35 feet,

vertical displacement of cell fill and possibility of slippage of sheet piles were also investi-

gated for different depths of embedment to study their impact on failure of cell fill.

The results of vertical displacements of cell fill top without and with soil to soil interfaces

for depth of embedment of 21 feet show similar results as for the case of 35 feet. Inclusion

of soil interfaces results into relative soil displacements of about 1.3 inches and formation of

terraces. The load-deflection curve for 21 feet embedment also shows similar behavior as

noticed in case of 35 feet embedment.

The slippage of sheet piles was also investigated for sheet pile embedments of 10 and 21

feet. These results lead to similar observations as noticed in case of 35 feet embedment,

discussed in Chapter 7. As per results, the slippage of sheet piles could only be possible if

a number of sheet piles acts as one unit together, and there is no resistance from intermediate

interlocks.

8.1.5 Failure Mechanisms Under Extreme Lateral Loadings

Possible failure surface and mechanism during lateral loading for Lock and Dam 26 (R)

was discussed in detail in Chapter 7. The lateral loads, failure of different soil elements, the

failure planes and failure surfaces for cell width of 63 feet and depth of embedment of 10 and

21 feet and for cell width of 40 feet and depths of embedment of 10, 20 and 35 feet are given

in Appendix B.


~ 60.0 cu u.. -• ..... cu ~ 'g 40.0

VJ

~ ;:I

~ u.. "lj 20.0

~ 'O ~

B = Cell width

B = 63 fit=> --e--·-----0--- ~--~-8-~·L-------8----- ~ B =· 40 ft.

... o.o· L--~--------r--------,----, ~

-~ 40.0 ........ cu .s

...:l ~

~ 30.0

~ 0 v

c:Q i:: -~ 20.0 cu -0 0:: ..... 0 .... cu

~ ..... 0

10.0

s.o 10.0 20.0

Depth of Embedment Hd (Feet) (A)

3o.o.

B = Cell width

35.0

0.0.L--,---------,-------.-----, s.o 10.0 20.0 30.0 35.0

Depth of Embedment Hd (Feet)

(B)

Figure 8.8. Radius and center of rotation of curved failure surface.


As noticed for Lock and Dam 26 (R) case in Chapter 7, at certain lateral load, the curved

failure surface develops in cell fill near dredge line and vertical shear failure starts near in-

board sheet pile in all the cases studied. The curved failure surfaces are approximated by a

circular surface for simplicity. Although the rotation of cell generally occurs along an axis

passing through points at approximately 8/8 (i.e., 8 feet for 8 = 63 feet) from center of cell to-

wards outboard sheet pile as discussed in Chapter 7, it can be assumed to simplify the ana-

lyses that the center of rotation lies along center line of cell.

The details of circular failure surfaces for different values of cell width, cell height and

depths of embedment are given in Table 8.1. The radius of the curved surface increases as

depth of embedment increases. The center of rotations is lower for higher depth of

embedment. Figures 8.8(A) and 8.8(8) show relationship between depth of embedment Hd to

radius of curved failure surface "r" and distance of center of rotation from dredge line, re-

spectively, for cell width 8 = 63 feet and 40 feet. The relationship is approximately linear.

8.2 Proposed New Method For Determination of Lateral

Capacity of Cellular Cofferdams

Conventional theories devised by Terzaghi (1945) and Schroeder and Maitland (1979) for

vertical shear analyses were discussed in Chapter 2. These methods assume vertical shear

failure plane at center of cell fill. As discussed in Chapter 7 and previous section, the results

of finite element analyses indicate that a curved failure surface develops in cell fill near

dredge line and vertical shear failure surface starts developing in soil near inboard sheet pile

at high lateral loads. A new method is, therefore, proposed in this section for analyses of


Table 8.1

Circular Failure Surfaces

Curved Failure Surface Details Cell Free Depth of Hydrostatic Center of Width Cell Embedment Radius Failure Rotation B H Hd r Load Below Dredge Line (feet) (feet) (feet) (feet) (xywh) (feet)

63 60 10 35 4 to 5 25.0 63 60 21 39 5 to 6 30.0 63 60 35 46 5 to 7 35.0 40 50 10 28 3 20.0 40 50 20 32 4 to 5 25.0 40 50 35 38 4 to 5 33.0


shear distortion failures in cell fill due to lateral loads, accounting for both curved failure sur-

face as well as vertical failure surface.

As indicated in Chapter 7, active and passive failure conditions develop first in foundation

soil outside outboard and inboard sheet piles during lateral loading. The resistance of these

surfaces is, however, neglected in this proposed analysis.

Development of curved failure surface near dredge line generally starts with the develop-

ment of vertical shear planes in the soil near inboard sheet pile. However, the curved failure

surface normally gets formed completely before the vertical shear failure progresses up to

mid-height of the cell (Figure 7.18 and Appendix 8). The resistance due to the curved surface

is computed using Figure 8.9. The center of rotation is assumed to lie on the center line of

cell.

The resultant load P is acting at a distance H1 from dredge line . The computation of

overturning moment Mo due to this load is discussed later.

Radius r of the failure surface is computed using Figure 8.8 and angle 2a in degrees is

determined accordingly.

Approximate distance of top of curved surface from dredge line h = r(1-cosa). Due to

lateral loads, vertical stresses increase on inboard side and decrease on outboard side.

Vertical stress is considered at h/2 from dredge line due to cell fill to compute average re-

sistance of curved surface. Initial vertical stress after cell filling may be considered.

cm = vertical stress <JY at distance h/2 from dredge line

s = length of curved surface = 2ar x n/180 = nar/90


Sheet pile

Resultant Load P

HI

Hd he

B

~

I

Curved failure surface

I

' / './" / ' / ' / ' / ' 2a / ' . /

/

/ /

/

'~ '~/Center of rotation

H

Dredge line

Figure 8.9. Shear failure analysis with curved failure surface.


Approximate shear resistance per unit length of curved surface = cm tan <P

where:

<p = friction angle of cell fill.

Total resistance of curved surface F,1 = crn tan <p x n9~ .

Resisting moment MR1 = F,1 x r,

2 MR1 = (crn tan <p) nar

90 [8.1]

Assuming that vertical shear planes could develop in full height of cell due to vertical shear

failure of soil near inboard sheet pile and due to relative displacement of soil in cell fill be-

cause of soil to soil interaction, a modified method of analysis for vertical shear is suggested

as an improvement over Terzaghi's method (1945) of analysis.

This method assumes the development of vertical shear plane near inboard sheet pile

based on the observations made in the analyses. The center of rotation based on analyses

results is considered at a distance of B/8 ( ~ 8 feet for B = 63 feet) from center of cell toward

outboard side. As vertical failure surface would develop at some distance near the inboard

sheet pile, the horizontal distance between this surface and center of rotation could be as-

sumed as B/2. For simplifying the analysis, it could be assumed that the vertical shear plane

would develop at the contact of sheet pile and soil and the center of rotation lies at center of

cell (Figure 8.10).


Resultant Load P

1-11

Hd I I I I I I I -----_;;'

Center of rotation I (Based on analyses)

1 ..

B

(t I

Vertical failure I surface

·I N

~ t ~ ~ ~

H

~ ~ ~

~ ~ ~ ~ ~

J..-Center of ro~tion I (Assumed at center line)

I• 8/2 •I

::::: B/2 • I

Inboard Shcetpile

Dredge line

Figure 8.10. Shear failure analysis with vertical failure surface.


Mo = overturning moment

MRz = total resisting moment of soil and sheet pile interlocks = Q x 8/2

Q =Sc+ Sc'

where:

Q = total shear resistance of soil and sheet pile interlocks

Sc = shear resistance of soil in cell fill and foundation

Sc' = shear resistance of sheet pile interlocks.

Sc = Pc' tan <P'

where:

Pc' = total lateral pressure acting on failure surface N-N

<P' = friction angle of soil in particular reach

Total interlock force T = (Pd - Pu) x R


Total resistance of interlocks T x f = (Pd - Pu) x R x f

where:

Pd = total inside force on inboard side

Pu = total outside force on inboard side

R = radius of cell

f = friction factor = 0.3

This total resistance of interlocks is for one interlock. The failure of soil occurs near in-

board sheet piles, say at distances of about D/8 from inboard sheet pile, where D = cell di-

ameter. Considering an isolated circular cell the total length of chord on which failure is

assumed (Figure 8.11) will be approximately 4/3 R, where R = radius of cell, and since we

considered only one interlock, the applicable length of failure would be 2/3 R.

Thus, average resistance of interlock is Sc' = (Pd - Pu) x R x f x 2~

or Sc' = 3/2 (Pd - Pu) f.

Q = Sc + Sc' = Pc' tan <P + 3/2 (Pd - Pu) x f

MRZ = Q x B/2

= Bl2(Pc' tan <P' + 3/2(Pd - Pu)xf] [8.2]


Sheet piles

OUTBOARD SIDE

Cell fill

D

/ /

/ ol // . -- . _______ ;;:_. __ -· r- ~R

9 RZ mn = .JRz -15

~1-R -3

Failure surface

n INBOARD SIDE

Figure 8.11. Cofferdam circular cell, location of vertical shear failure surface.


Coefficient K of lateral earth pressures used in analysis was 0.75 as during lateral load of

5 yjl average K value adjacent to inboard sheet pile were predicted as approximately 0.75

(Chapter 7).

Free body diagrams considering all forces for both curved and vertical failure surfaces is

shown in Figure 8.12. As cell fill weight "w" passes through center of rotation, it has no effect

on moments.

Considering the resistance due to both curved and vertical failure surfaces, total resisting

moment,

MR = MR1 + MR2 = (crn tan <P) ~~ r 2 + ~[Pc' tan q>' + 3/2(Pd - Pu)f] (8.3]

value off is usually taken as 0.3.

M Factor of safety = M~ .

Figure 8.8(8) can be used to determine depth of center of rotation below dredge line. The

overturning moment is computed about the center of rotation (Figures 8.9 and 8.10).

Overturning moment Mo = P(H1 + he)

P = resultant lateral load

H1 = distance of line of action of P from dredge line.

he = distance of center of rotation below dredge line.


8.2.1 An Example Problem to Compute Failure Load

As an example, consider Lock and Dam 26 (R) cofferdam with B = 63 feet, H = 60 feet,

Hd = 35 feet, water level at 28 feet below top. Cell fill and foundation soil friction angles are

35 and 41 degrees, respectively. The cofferdam is subjected to lateral load.

Curved Failure Surface:

From Figure 8.8, the radius of curved failure surface, r, is 46 feet and location of center of

rotation below dredge line , he, is 35 feet.

2a is angle of curved failure surface.

cosa = h; = ~~ = 0.76

a= 40.5°

h = r - he = 46 - 35 = 11 feet

CJn at 5.5 feet from dredge line

= 123 x 28 + 70.6(32 - 5.5)

= 5315 psf

Resistance of curved surface F,1 = CJn tan <p x ~~

= (5315 x tan 35 x 7t x 40.5 x 46)/90

F,1 = 242kips


Resisting Moment MR, = 242 x 46 = 11132 k. ft.

Vertical Failure Surface:

Using k = 0. 75,

Lateral earth pressures:

At 28 ft from top = 0. 75 x 123 x 28 = 2583 psf

At 60 ft from top = 2583 + (0. 75 x 70.6 x 32) = 4277.4 psf

(At dredge line)

At 35 ft below dredge line = 4277.4 + (0.75 x 70.6 x 35)

(Tip of sheet pile)

= 6130.7 psf

Resistance of cell fill along vertical failure plane:

Sc = (2583 x 14 x tan 35)

( 4277.4 + 6130. 7 x 35 x tan 41) 2

= 260.5 kips

Resistance of sheet pile interlocks:

Sc' = 1._ (Pd - Pu)f 2

+ ( 2583 + 4277.4 x 32 x tan 35) 2 +

Assuming maximum pressure at H/4 from dredge line, and K value near sheet pile as 0.4,

Pd = 0.4 x ~ x 123 x 45 x 95 = 105.2 kips

· Assuming dewatering completed before flooding, Pu = 0.0.

Sc' = ~ x 105.2 x 0.3 = 47.3 kips


Total resistance:

Q = sc + sc'

= 260.5 + 47.3 = 307.8 kips

Resisting moment MR 2 = Q x ~

= 307.8 x 623 = 9695.7 k. ft.

Total resisting moment MR = MR, + MR2

= 11132 + 9695.7

= 20827.7 k.ft.

Considering that there are n units of hydrostatic load required for failure:

Overturning moment M0 = n x ~ x 62.4 x 602 x (20 + 35)

= n x 6177.6 k.ft.

At failure, M0 = MR

n x 6177.6 = 20827.7

n = 3.4

Therefore, 3.4 times the normal flood load (3.4 y.jl) will result in shear failure in cell fill.


~~ -t:o m,.. :Os: )."' r- -t r-:o o-,..n 0(1) --1 Zc a o (I)-m

(I)

). z 0 s: ~ p 0 0 (I)

6 H, ,, :0

"' 0 ii -t n "' r- he r-0 m .,, 0 :0 s: ). ::! 0 z (II

). z 0 .,, ~ r-c :0

"' c z 0 m :0

~ "'

i r i B ·1 I I I I w

I · center of I rotation 14 ~s12 •I

(a) Failure surfaces and forces

p

(H1+hc)

~ I I

I I I I !w

( b) Free body diagram

Figure 8.12. Schematic representation of failure surfaces and free body diagram showing forces.

Q

8.3 Comparison of Shear Failure Analyses Methods

Load-deflection curves for cell widths of 63 and 40 feet and for different depths of

embedment were discussed in Chapter 7 and earlier in this chapter. On these curves are

plotted the predictions of failure loads based on Terzaghi (1945), Schroeder and Maitland

(1979) and proposed new method for analysis of shear distortion failure, and the results are

shown in Figures 8.13 and 8.14 for cell widths of 63 and 40 feet. respectively. These results

suggest following:

Terzaghi and Schroeder and Maitland methods give same failure load for all depths of

embedments because overturning moments are computed at the end of sheet pile or the point

of fixity, and the vertical shear resistance is calculated for cell fill and foundation up to same

depth. In case of new proposed method, the failure load is higher for higher depth of

embedment because the overturning moment is computed about center of rotation and shear

resistance is calculated up to depth of embedment. Logically also, the higher depth of

embedment should give higher failure load. For cell width of 63 feet, the predicted failure

loads (Figure 8.13) based on proposed new method are 2. 7 to 3.4 y.)1 which are about 23 to

52 percent higher for different depths of embedment than the failure load based on Schroeder

and Maitland method. The resulting deflections for depth of embedment of 21 or 35 feet are

2, and 3.3 inches based on Terzaghi, and Schroeder and Maitland method, respectively, and

are 5.5 and 8 inches for depth of embedment of 21 and 35 feet, based on proposed new

method.

In case of cell width of 40 feet, the predicted failure loads (Figure 8.14) based on new

method are 2.3 to 2.5 y.)1 , which are about 30 to 50 percent higher for different depth of

embedments than the failure load based on Schroeder and Maitland method. The corre-


!;:~ "1;u ;u )lo )lo s: ,..~ ,.. ::0 o-:Pn c en z~ "c en -'" en

)lo z c s: ~ 0 c en d '11 ::0

'" c r; ~ (") m ,.. ,.. c m "Tl 0 ::0 s: )lo ::I 0 z (I)

)> z CJ "Tl ~ r-c ::0 m c: z CJ m ::0

N 0 ...,

"'O C1I 0

..J

u ·~ ~

C1I ~

Cll 0 ...

"'O >. ::r:

7.0--~---,.--~--.~___, ........ ___,~--___,~--___,~--___,___,..,_~~.--~--.___,___,__.~~--

6.0

s.o

4.0

3.0

2.0

.~---- ______ ............ -,...~~-21 ft.

.,.. .,.. ~.,...,...

.,...,.. Hd•lO ft. __..0-·-·~-·-·-·-·-·-·--·-·--·0 ...-· ,,,..

/ /

~· /

_L_Hd•".lc:F .. _}

!f..'_~ H;;: _ (New Propo:ed Method) ------·- . F.S. 1.0

I Hd•lOft ·-----(Schroeder Method, F.S.=1.0)

Cell Width B • 93 ft.

Hd • Depth of Embedment

l.O ldi'l------(Terzaghi Method, F.S.=1.0)

o.o 0 10 20 30 40 50 60 70 80 90


Figure 8.13. Comparison of shear failure analyses methods, load-deflection curves for cell width 63 feet.

100 l l 0

~~ ... :u '"» :u 3:

~m o-»n CHll zc! C>o en-m

(II

)> z CJ 3:

~ 0 0 (II

cj -0 :u m CJ n ... n m ,... ,... CJ m ,, 0 :u 3: ~ 0 z (II

)> z 0 .,.. )> ;= c :u '" c z CJ

'" :u

N 0 00

'tJ t'O 0 ~

u •.-1 4..1 t'O 4..1 (/) 0

'"' 'tJ >. :I:

7.0--~--..--~-.-~~---~~..,..-~~-.-~~--~~....-~--..--~--..~~-.....~~~

6.0

Cell Width B = 40 ft. 5.0 Hd•3~ ft.

Hd • Depth of embedment

4.0

Hd=lO ft.

.--G·-·-·L-·-·-·-·-·-'/ - . ,/' -~-===}New Proposed Method, F. S .•l. O -r----- ( Hd=l0,20 and 35 ft.)

~ fl --r----- Schroeder & Maitland, F. S .=1. O

3.0

2.0

1.0 Terzaghi, F.S.=1.0

o.00~---,1;~--;;;;---~::-----:-7-----::-!---~-----1-----L---__L ____ .L_ __ _J 10 20 30 40 50 60 70 80 100 90 110


Figure 8.14. Comparison of shear failure analyses methods, load-deformation curves for cell width 40 feet.

spending deflections are 2, 3.3 and 7.3 inches based on Terzaghi, Schroeder and Maitland and

new method of analysis for depths of embedment of 20 and 35 feet. For embedment depth of

10 feet, the deflections are 3.5, 5.5 and 11 inches based on Terzaghi, Schroeder and Maitland

and new method, respectively.

Thus, the proposed new method yields substantially higher failure loads for shear dis-

tertian failure and larger deflections at failure in cofferdams as compared to conventional

methods.


Chapter IX

SUMMARY AND CONCLUSIONS

9.1 Summary

Cellular cofferdams have primarily been used as temporary systems which serve to allow

construction of facilities in open bodies of water. Applications for these structures have been

increasing and today they may serve as permanent retaining walls or as navigation or

waterfront structures. Conventional design methods for cellular cofferdams are based on

semi-empirical approaches largely developed in the 1940s and 1950s. None of the available

traditional procedures are capable of predicting cofferdam deformations, a parameter of key

importance to the cofferdam performance, and which is often observed during construction for

purposes of safety monitoring. Also, there is evidence that much of the conventional design

technology is conservative, in some cases predicting loading by more than twice that which

actually occurs.

SUMMARY AND CONCLUSIONS 210

One method which has shown promise as a means to incorporate the process of soil-

structure interaction, and to reduce design conservatism is the finite element method. In

theory, this approach allows the cell, fill and foundation system to be considered in one

analysis, and incorporates the interaction between these key elements. Recent work has

shown that realistic results are only obtained if allowances are made for the nonlinear be-

havior of the soil and the local yielding of the sheet pile system at the interlocks between the

sheet piles. Finite element techniques with the appropriate characteristics have been devel-

oped to account for these behavioral aspects, and incorporated into the program

SOILSTRUCT. However, certain key elements of the structural system of the cofferdam remain

to be provided in this program. One of the major objectives of this work is directed at resol-

ution of this deficiency. In particular, this involved adding better bending elements to the

program to represent the sheet pile systems in axisymmetric and plane strain analyses. Also,

in the case of the plane strain program, a new method is developed to allow for stress transfer

through the sheet pile system. Through case history and theoretical analyses, the enhanced

programs are demonstrated to yield accurate and realistic results.

This investigation also included other objectives beyond that of simply improving the finite

element program. These related to using parametric studies of the filling, dewatering and

flooding stages to evaluate conventional design procedures and develop new, simplified

methods which could be used in design. All of the parametric studies focused on cofferdams

founded on sandy soils, and filled with free-draining sandy soil.

In the effort to improve the structural response of the axisymmetric version of the finite

element program, a shell element was added. This allows for modeling of the sheet piles

using their actual thicknesses, and accounts for their bending characteristics. The accuracy

of the shell element is tested by comparing predicted results to those from closed form and

finite element solutions. The plane strain version of the program was modified first by adding

a beam element to represent the front and back walls of the cofferdam. The beam element


allows the sheet pile response in the plane strain program to be consistent with that in the

axisymmetric program. Also, special shear transfer elements were added to the plane strain

program. These elements model the effects of the portion of the cofferdam which is not

physically present in the plane strain analysis of a cofferdam.

Design of the shear transfer elements to model the cofferdam response involved the de-

velopment of two modulus reduction factors. Application of these factors to the modulus of

steel and use of the resulting modulus for the shear transfer elements results in a structural

performance which models the larger cofferdam system. The first of the modulus reduction

factors accounts for the fact that the actual cofferdam cell is round as opposed to the planar

shape used in the analyses. The second modulus reduction factor incorporates the influence

of the nonlinear aspects of the cofferdam introduced by the cell fill and the sheet pile system

itself. Where the first modulus reduction factor is derived theoretically, the second is based

on case history analyses.

Using the modified finite element programs, parametric analyses were performed. Rela-

tive to the cell filling stage, the parametric analyses were directed to assess the effects of cell

embedment, cell dimensions, and cell fill and foundation properties on cell behavior. Effects

of differential water loading on the cofferdam were studied to evaluate the influence of the

same factors as for cell filling, but also including level of the differential loading.

9.2 Conclusions

The conclusions derived from this research on modification of finite element programs and

parametric analyses for cofferdams on sand are as follows.


9.2.1 Modifications in SOILSTRUCT Programs

1. The modifications to include better bending elements (shell and beam elements) in

axisymmetric and plane strain programs and shear transfer elements in plane strain

program make it possible to model cofferdams more realistically.

2. To determine appropriate value of modulus for shear transfer elements, two reduction

factors are applied to modulus of steel. First modulus reduction factor (RF1) is computed

based on a comparison of theoretical results to finite element analyses. Curves are de-

veloped to determine this factor for a particular value of cell height (H) to cell width (8)

ratio. A second modulus reduction factor (RF2) is needed to account for nonlinear be-

havior. A value of 25 is determined for RF2 based on case history studies.

3. Using shear transfer element results in smoother transfer of lateral load from outboard

sheet pile through cell fill as well as through shear transfer elements as compared to

when springs are used.

9.2.2 Cell Filling

1. Conventional design methods yield higher values of maximum interlock force than those

from finite element analyses. Interlock forces based on Schroeder and Maitland (1979)

method are higher by 36 percent as compared to finite element prediction for free cell

height of 60 feet. Conventional methods as well as finite element analyses for cell filling

show that maximum interlock forces increase as free cell height increases. The differ-

ence between conventional method and finite element predictions grows larger as the

free cell height increases.


2. The depth of embedment does not influence maximum cell deflection and maximum

interlock force significantly during cell filling. The cell embedment is, therefore, provided

for reasons other than for reducing interlock forces.

3. Location of maximum cell deflection and maximum interlock force for free cell height of

60 feet is at about one-fourth of free cell height from dredge line for depth of embedment

of 10 to 25 feet. For depth of embedment of 35 feet or more, they occur at about one-sixth

of free cell height from dredge line.

4. Location of maximum cell deflection and maximum interlock force remains constant at

about one-sixth of free cell height from dredge line for all cell heights, ranging from 20 to

80 feet for same depth of embedment of 35 feet.

5. Changing friction angle of the cell fill from 35 degrees to 41 degrees results in reductions

of about 30% in maximum radial deflection and 35% in maximum interlock force for all

free cell heights.

6. Changing the friction angle of the foundation soil from 41 degrees to 35 degrees has little

to no effect on maximum cell deflection and maximum interlock force. This confirms the

approach of conventional theories, which do not consider the effect of foundation material

on interlock forces.

9.2.3 Differential Loading

1. The conventional methods are conservative in predicting internal shear failure. For a

case of cofferdam with cell width of 63 feet, free cell height of 60 feet and depth of

embedment of 35 feet, the conservatism factors based on failure loads are 2.75 and 5.5

for Schroeder and Maitland (1979) and Terzaghi (1945) methods, respectively.

2. The load-deflection response of cofferdam is strongly nonlinear at high lateral loads. At

typical working loads, the factors of safety are large enough that the load-deflection re-


sponse is essentially linear. The load-deflection response is a function of cell width, cell

height, and depth of embedment for given cell fill and foundation soils.

3. Terzaghi (1945) recommended the use of 0.5 for lateral earth pressure coefficient (K) for

performing vertical shear analysis for cell fill. Based on finite element analyses, it is

concluded that at failure loads lateral earth pressure coefficient (K) values in center of

cell fill and near outboard sheet pile could reach unity, as suggested by Schroeder and

Maitland (1979) for vertical shear analysis.

4. Under lateral loading, cofferdam cell tends to rotate along axis passing through some

point on the dredge line which may be at a distance of B/5 to B/8 (B is cell width) from

center of cell towards outboard sheet pile.

5. At normal working lateral loads equivalent to flood loads on full height of cell, the lateral

deflections of sheet pile top are estimated as 0.35 to 0.28% of free cell height for cell width

of 40 feet to 63 feet and depth of embedment varying from 10 to 35 feet.

6. During high lateral loads, a curved (convex upward) failure surface develops in cell fill

near dredge line. Simultaneously, vertical shear failure also starts in cell fill and foun-

dation soil first near inboard sheet pile.

7. The possibility of slippage of sheet piles due to lateral loading is remote except if there

are interlock misalignment and other installation defects.

8. Proposed new method for analysis of shear distortion failure in cell fill results in allowable

loads which are 20 to 50 percent higher compared to those predicted by Schroeder and

Maitland (1979) method for different cell widths and embedment depths.


Appendix A

Appendix A 216

0.1

II

o. 01

Appendix A

B = 63. 0 Ft H = 81. .O Ft H/B =1.33

sFEM : Horizontal deflection of top of cell using finite element prog

Stheory = Horiz~tal deflection of top of cell using beam theory

Es/ Eshear

Deflection ratio versus modulus ratio for shear transfer elements.

217

1.0

>-.... 0 0.1 a.

.c:. -c.o '-... ~ UJ LL.

co II

~

0.01

Appendix A

B = 63.0 Ft H = 48.8 Ft H/B = 0.775


218

>-L-0 Cl .c ...... ~

............. :E w u..

(/J

II

:E

1 o.o

1.0

H = 37. 6 Ft.

8 = 63.0 Ft.

H/B=0.597

------

0.01 __ ~~--~~~..._~~_._~~~-'--~~--1.~~~-L-~~~ 0 20 1.0 60 80 100 120

Es /Eshear


Appendix A 219

>-... 0 Cll

..t::.

<.o --ai LL

tO

"

0.1

Appendix A

H = 25. 0 B = 6 3. 0 Ft H/B = 0.397

Es / E shear

---


220

100.0

10.0

>-... 0 GI = co --~ UJ LL

t()

II

~

t. 0

Appendix A

H = 12. 5 Ft B = 6 3 Ft H/B = 0.198

0

a

Top of cell

Mid-height of cell


221

>-'-0 Cll ~ -w --~ UJ lL.

co II

~

1. 0

0.1 I

I I

I

H : 50 Ft B : 40 Ft

H/8 = 1.25

, , /

~

, ,,

,. ,,, ,,, , ,. -

e.shr~l~ ~-..... e.s\ M .,.o

\ c.e\\ tor - --. ~\ o ------i,G

.. i·,"'-~e'~ -- -- \Esnr=~ ""' u e\\ --- Es "': ,.o ' c._-- tor "''

.,,,.. O'-,o~--.,,.

o. o10L---2...1.0 ___ 4l...o---6~0:------:::s:1=0---:,~o--o---:-:,2~0:-----;-:, 40

Es/ Eshear


Appendix A . 222

>-... 0 • .c -co --~

lJ.. co II

0.1

Appendix A

H = 40 Ft B = 40 Ft H/B = 1.0

20 40 60 80 100 120


140

223

1. 0

>-~

0 Cll

.s::. -<o ~

lJJ LL c.o

" :l:

I I

I 0.1

Appendix A

H : 30 Ft

B : 1.0 Ft H/8:0.75

~ --... .:,~"" (.~,--~· o\.,, \O~"" ,,-'

;'"' ;'

"' ~ , , /

/

-----

Es/ E shear

------------


224

,,

0.1

Appendix A

H = 20 Ft B : 40 Ft

H/B = 0.5

Es/ E shear


225

100.0r----.---r---,----,--__:__,-,--~

10.0

>-... 0 GI

.&; -co --. ::i: IJJ IJ..

co II

I

H : 10 Ft B : I. 0 Ft

H/B=0.25

"'~ (,~ --c} .,,.,,,.'

~ ~,,,"" ·~ (,fl,/ e '/ ~ o'/ .'b 7

.~ ~ ~~

I I

I I

1.oWZ'--------------------=1

0.1 0L----=2-'=-0 ----=,-k0--~5t;o:----~atro\--,1r1o;no--1:12ffiol--


Appendix A 226

Appendix B

Appendix B . 227

FAILURE LOAD

lxywH [2ZJ

2xywH -

3xywH E

SxY H ~ w

Loaded side

i...1·-------63.Q Ft

=-- ..... -..... --_ __, -- -- -----:,......,--- -- _,,.,.. - - --- --::;... - ...,,,_

60.0Ft

Failed elements and failure loads, (B = 63 ft, Hd = 10 ft).

Appendix B 228

T 10.0 FT

..L

, ..... 1------63· 0 Ft EL 130.0 --

Outboard Inboard side side

LOAD 60.QFt

rFailure Surfaces\

\ ' v ........ ~ N ' - I ~ '

~ ~ \ ............... ~ r"....

-\-- -\- """' ""' i

Dredge Ii ne 4 // ~ ~ EL 70.0 ~T 'X / ~ ' ~ ~'\ ~ ">9 '

"!'... ... , ·~

""" ~ - ' K,,. ' -->< ......... ~

' .. ~~'- -\-. i'b ~ ~K"'" ~ 'Li~ ./

,~ ~·'o'.'.:·/ Center of Rotation

'//////////////// / ////////////////

Failure plane directions and failure surfaces (B = 63 ft, Hd = 10 ft).

Appendix B 229

FAILURE LOAD

6xy H "'

Loaded side

Appendix B

... 1-------63.Q Ft

60.0Ft

Failed elements and failure loads (B = 63 ft, Hd = 21 ft).

230

I l-l•------63.0 Ft EL 130.0

x -.--

~ Outboard lnboar d

side side

-LOAD 60.0Ft

~Failure Surfaces~

) ~ !""'-~~ ' ,,,, .......

f"'.. ~ ~

I ,, ~~~-- ...... ~· ~ JI'

T 21.0 FT

Dredge Ii ne ""'"'\ )R' -\- -\-- ........ ....... ~ EL 70.0 r--.... ~

l'\ x ?~ -\- ~ ....... ~ ~ rsy r--....

I~ ~ -\- -\-- - ........ ~ ' v~ t"""'- / ~

1 ~ "' ~~ -\- v

-\-::><"" - ,,' ......... " ~ p-;..

~---~w ,.,,

~ >< ~~~c:Y . , -\-['-.. -cen1er of Rotafion

ELO. 0 ///// '///////////// ///////////////


Appendix B 231

FAlLU~E LOAD

lxywH EZ:J 2xywH -

)xywH ~

Loaded side

Dredge tine\

i--r-----1.0.0Ft ---~1

--I

50.0Ft

I


Appendix B

.. :·::

}~¥!/

. 232

,._r----1.0.0Ft ----1 --

""" Outboard Inboard

side side

- 50.0Ft LOAD r Failure Surfaces'\

J ' ~ ~ --t< ' ~

-1- j~ ~ ........ .........

' I ' >< ~ ~ "-- ........ ~ l ' ~ ' ............

~ ~A- ~ ...... ~ Dredge line\ ..........

~ ' 1FT ~~ 'K I ,

......... ' '/ ~ >< ~~ .......... ~ .... ~ ~1' ~- '/......... ' ~ .""\ "'-...~ >< ........

\-/ ' \ I L__

20 ft >< ~ ~ >K ~ 6>~' " +J.-~./ .

Center of Rotation


Appendix B · 233

LOAD rt------1.0.0 Ft ---.-t1

50.0Ft

Loaded Side

-.,.... '"";:~ - ......... - - -~-==--............ -=-=..-


Appendix B 234

i-r----~O.OFt ----1 --

Outboard x Inboard side side

LOAD 50.0Ft ~

Failure Surfaces r ---r--. . . \ ,.

~ ~ ' >< ~ _J ........... ' ~ -:::-.. '

Dredge line\ x ~-\- ............ .......... ~ ......... .......... ' 'f..'- I"' ,, ~

_j ........... " I ~7 ~ ' r-- '-.. '

~ -~ ~ + -.l ........ /~ ,-~

~ ..... ~ !'--.. r--.. " 20 ft ~·~ ' ' / \' l

25ft "- // j\ ~~, II..

' '

-'-- VCenter of Rotation

.


Appendix B 235

lxy H 'W

Jxy H 'W

-1-----,0.0Ft ----~ LOAD I I

50.0Ft

Loaded Side


Appendix B 236

t--r----J..O.OFt-----1 --x I

Outboard -t- In boar side side

d

+ LOAD

50.0Ft Failure Surfaces ........

""' ~

~ ~ ~ ~

" :>< -+- J' ' ~ ' >< --\- -\-- It ......... ~ I~

' --\-- ~ ~ ~ I

Dredge line\ ~ ~ ~

" ~ - ~ ,, .

~ ~ ' rJ -~ ~ ........ \. ~

·~ ~ ~ ~ ~ I ,

' ~ "" i--

\~ ~ I --\--><."" '

~ ,I 35 ft 33ft ~

-1-~ ~ I

I I\ . I

-L ~ ~ ¥ Center of Rotation

I

Faiiure plane directions and failure surfaces (B = 40 ft, Hd = 35 ft).

Appendix B 237

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REFERENCES 239

Maitland, J.K. , "Behavior of Cellular Bulkheads in Deep Sands", thesis presented to Oregon State University, Corvallis, OR, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, 1977.

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REFERENCES 241

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Documents

n. ae=-.. · increasing and today they may serve as permanent retaining walls or as navigation or waterfront structures. Conventional design methods for cellular cofferdams are based