The Variability of the Void Ratio of Sand and its Effect ...

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