The Variability of the Void Ratio of Sand and its Effect on Settlement and Infinite Slope Stability

Dissertation

zur Erlangung des akademischen Grades

Doktor-Ingenieur

an der Fakultät Bauingenieurwesen

der

Bauhaus-Universität Weimar

vorgelegt von

M.Sc. Pengtao Zhu

aus Henan (China)

Gutachter:

1. Prof. Dr. -Ing. Karl Josef Witt 2. Prof. Dr. Ren. Nat. Tom Lahmer 3. Prof. Dr. -Ing. Habil. Ivo Hede

Tag der Disputation: 05 März 2018

Contents

Contents

Vorwort des Betreuers

Acknowledgments . 11

Abstract . . iii

Kurzfassung iv

List of Figures . x

List of Tables x1v

Notation . . . xv

1. lntroduction 1 1.1. Background 1 1.2. Motivation . 1 1.3. Study aim . 2 1.4. Thesis scope 3

2. Literature review on soil variability and its efTect on geotechnical practice . 4 2.1. Background of soll variability . . . . 4 2.2. Sources and scales of soll variability 4 2.3. Quantification of soil variability . . . 5

2.3.1. Description of soil variability 5 2.3.2. Mathematical description of inherent spatial correlation 7 2.3.3. Estimation of the correlation structure . . . . . . . 8 2.3.4. Literature review of soil variability quantification 15

2.4. Fluctuation of the generated random field . . . . . . . . . . 18 2.4.1. Local averaging and variance reduction . . . . . . 18 2.4.2. Effect of the dimensionless spatial correlation length on the fluctuation of a

random field . . . . . . . . . . . . . . . . 19 2.5. Methods of reliability analysis . . . . . . . . . . . 21 '2.6. Effect of soil variability on geotechnical practice 22

2.6.1. Settlement . . . . 22 2.6.2. Bearing capacity 25 2.6.3. Slope stability . . 28 2.6.4. Seepage . . . . . 33 2.6.5. Other geotechnical practice 35

3. Effect of stress level on the variability of void ratio related properties of sand 36 3.1. Background and objective . . . . . . . . . 36 3.2. Methodology . . . . . . . . . . . . . . . . 36 3.3. Simulation of the variability of void ratio 37

3.3.1. Model description . . . . . . . . . 37

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3.3.2. Selected best variogram model and weight . . . . . . . . . . 3.3.3. Selected parameters in spatial correlation length calculation 3.3.4. Results and discussion .

3.4. Conclusion from this chapter

38 39 41 48

4. Relative random field generation . 49 4.1. Objective . . . . . . . . . . . . 49 4.2. Stationary random field generation . 50 4.3. Non-stationary random field generation . 51

4.3.1. With depth-dependent mean and/or standard deviation 51 4.3.2. With depth-dependent SCL . . . . . . . . . . . . . . . . . 52

4.4. Mean SCL evaluation of layered random field . . . . . . . . . . 54 4.4.1. Effect of the individual SCL on the mean SCL of the whole random field . 56 4.4.2. Effect of the length of individual random field on the mean SCL of the whole

random field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.4.3. Relation between the mean SCL of the whole random field and both the SCL

and the length of individual random field . 57 4.4.4. Validation of the relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5. ld compression analysis considering the depth-dependent variation of void ratio . 59 5.1. Deterministic compression analysis . . . 59

5.1.1. Deterministic model description 59 5.1.2. Results analysis . . . . . . . . 59

5.2. Stochastic compression analysis . . . . . 60 5.2.1. Stochastic model description . . 60 5.2.2. Effect of the variance reduction . 60 5.2.3. Effect of the depth-dependent mean 62 5.2.4. Effect of the depth-dependent standard deviation 63 5.2.5. Effect of the depth-dependent spatial correlation length . 65

5.3. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . 68

6. Deterministic analysis of infinite slope stability during infiltration 69 6.1. Background of infinite slope stability and objective. 69 6.2. Relevant theory . . . . . . . . . . . . . . . . . . 69

6.2.1. One-dimensional unsaturated seepage . 69 6.2.2. Hydraulic characteristics . . . 70 6.2.3. Infinite slope stability analysis 71

6.3. Infinite slope description . . . . . . . . 72 6.4. Numerical simulation of infiltration . 72

6.4.1. Numerical simulatio!l of the steady state infiltration . 72 6.4.2. Numerical simulation of the transient state infiltration 74 6.4.3. Boundary condition . . . . . . . . . . . . . . . . . . . . 75

6.5. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.5.1. Deterministic analysis without considering the depth-dependent character 76 6.5.2. Deterministic analysis considering the depth-dependent character 80

6.6. Conclusion of this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

7. Probabilistic infinite slope stability analysis during infiltration considering the variation of ks. . . . . . . . . . . . . . 89 7.1. Reliability estimation . 89 7.2. Case description . . . . 89

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7.3. Probabilistic infinite slope stability analysis during infiltration without considering the depth-dependent character . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.3.1. Effect of the variation of ks on the slope stability under steady state infiltration 91 7.3.2. Effect of the CV of ks on the slope stability under steady state infiltration . . 92 7.3.3. Effect of the SCL of ln(ks) on the slope stability under steady state infiltration 95 7.3.4. Effect of the variation of ks on the slope stability under transient state infil-

tration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.3.5. Effect of the CV of ks on the slope stability under transient state infiltration . 101 7.3.6. Effect of the SCL on the slope stability analysis under transient state infiltration104

7.4. Probabilistic infinite slope stability analysis during infiltration considering the depth-dependent character ..................................... 105 7.4.1. Effect of the depth-dependent mean of ks on the slope stability under steady

state infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.4.2. Effect of the depth-dependent mean of ks on the slope stability under tran-

sient state infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.4.3. Effect of the depth-dependent STD of ks on the slope stability under steady

state infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.4.4. Effect of the depth-dependent STD of ks on the slope stability under transient

state infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.4.5. Effect of the depth-dependent mean of ks with CV=l on the slope stability

under steady state infiltration . .. .. .. ...... .... .. ...... ... 117 7.4.6. Effect of the depth-dependent mean of ks with CV=l on the slope stability

under transient state infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.4.7. Effect of the depth-dependent SCL of ks on the slope stability under steady

state infiltration . 122 7.5. Synopsis . . . . . . . . . . . . . 125

8. Conclusions and recommendations 8.1. Summary and conclusions ... 8.2. Recommendations for future study .

Bibliography .................. .

A. Appendix - Method of isotropic RF generation, its validation and limitation A.l. Isotropie RF generation .. A.2. Validation and limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

126 126 129

130

141 141 143

ix