Mohr Circles, Stress Paths and Geotechnics

Mohr Circles are a powerful and widely used technique for representing stresses and strains in soil and rock, and for converting test data into design parameters, but they have many other uses in solving geotechnical problems. Mohr Circles, Stress Paths and Geotechnics gives a unified presentation of the theory and application of the techniques, and is the only book to examine the behavior of both soil and rock in a fundamental and comprehensive manner. The second edition of this well established book has been comprehensively updated in line with recent developments. After presenting the fundamentals of stress and strain, and their graphical representation, the book includes chapters on failure states in soils and rocks, observed and elastic paths, and the use of discontinuities. New sections include shear bands and small strain behavior, as well as the use of elastic shear modular stress calculations and discontinuities in plasticity calculations. Expanded coverage is also given to dilitancy ofsoils and roughness of rock joints. Mohr Circles, Stress Paths and Geotechnics will be invaluable for geotechnical engineers in teaching, research and practice.

Worked examples

viii

Preface

x

Historical note

xi

1 Stresses, strains and Mohr circles

1

(39)

1.1 The concept of stress

1

(1)

1.2 Simple axial stress

1

(3)

1.3 Biaxial stress

4

(7)

1.4 Mohr stress circle

11

(2)

1.5 Mohr circles for simple two-dimensional stress systems

13

(3)

1.6 Three-dimensional stress

16

(6)

1.7 Direct shear and simple shear

22

(3)

1.8 Triaxial stress

25

(3)

1.9 Pole points

28

(2)

1.10 Basic failure criteria

30

(2)

1.11 Effective stress and stress history

32

(2)

1.12 Mohr strain circle

34

(3)

1.13 Angle of dilatancv

37

(3)

2 Failure states in soil

40

(38)

2.1 Total and effective stress circles

40

(1)

2.2 The triaxial test

41

(4)

2.3 Triaxial compression tests

45

(18)

2.4 Triaxial extension tests

63

(4)

2.5 Influence of initial stress and structural anisotropy on strength of clays

67

(3)

2.6 Rupture planes in clays

70

(1)

2.7 Shear bands

71

(5)

2.8 Influence of dilatancy on φ' for sands

76

(2)

3 Failure in rock

78

(30)

3.1 The nature of rock

78

(1)

3.2 Intrinsic strength curve

78

(1)

3.3 Griffith crack theory

78

(2)

3.4 Empirical strength criteria for rock masses

80

(3)

3.5 Empirical strength criteria for intact rock

83

(5)

3.6 Strength of rock joints

88

(9)

3.7 Influence of discontinuities in laboratory test specimens

97

(11)

4 Applied laboratory stress paths

108

(32)

4.1 Mohr circles, stresses and stress paths

108

(5)

4.2 Consolidation stresses and stress paths

113

(9)

4.3 Drained triaxial stress paths

122

(3)

4.4 Influence of stress paths on laboratory-measured drained strengths

125

(4)

4.5 Undrained triaxial stress paths

129

(3)

4.6 Influence of stress paths on laboratory-measured undrained strengths

132

(2)

4.7 Relative short-term and long-term field strengths

134

(2)

4.8 Infinite slope stress path

136

(4)

5 Elastic stress paths and small strains

140

(28)

5.1 Elastic behaviour in soils and soft rocks

140

(1)

5.2 Isotropic elastic stress paths

141

(4)

5.3 Undrained triaxial elastic stress paths in anisotropic soil or soft rock

145

(2)

5.4 Observed effective stress paths for undrained triaxial tests

147

(10)

5.5 Small strain behaviour

157

(1)

5.6 Elastic small strain behaviour in isotropic geomaterials

158

(1)

5.7 Elastic small strain behaviour in cross-anisotropic geomaterials

159

(9)

6 The use of stress discontinuities in undrained plasticity calculations

168

(18)

6.1 Lower bound undrained solutions

168

(1)

6.2 Smooth retaining wall

168

(1)

6.3 Stress discontinuity

169

(3)

6.4 Earth pressure on a rough retaining wall

172

(4)

6.5 Foundation with smooth base

176

(7)

6.6 Undrained. flow between rough parallel platens

183

(3)

7 The use of stress discontinuities in drained plasticity calculations

186

(30)

7.1 Lower bound drained solutions

186

(1)

7.2 Smooth retaining wall

186

(4)

7.3 Effective stress discontinuity

190

(4)

7.4 Active earth pressure on a rough retaining wall

194

(1)

7.5 Passive earth pressure on a rough retaining wall

195

(5)

7.6 Smooth foundation on cohesionless soil (φ', c'= 0)

200

(7)

7.7 Silo problem

207

(9)

8 Stress characteristics and slip lines

216

(33)

8.1 Stress characteristics

216

(1)

8.2 Undrained stress characteristics

216

(14)

8.3 Drained stress characteristics

230

(11)

8.4 Rankine limiting stress states

241

(1)

8.5 Slip lines

241

(2)

8.6 Undrained deformation

243

(6)

Appendix: Symbols

249

(5)

References

254

(6)

Index

260

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Mohr Circles, Stress Paths and Geotechnics

Summary

Table of Contents

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