Stochastic Models for Three-Dimensional Slope Stability Analysis Considering Groundwater Variations

現今隨著全球暖化現象對於氣候條件之影響，暴風雨、洪水、地震等各 種天然災害的數量逐年明顯增加，造成經濟及人民生命財產的極大損失。其 中，邊坡滑動為一種常見的災害，通常由暴雨所引起。目前已有許多方法用以 評估邊坡之穩定性，並分析各種控制因子的影響，其中包含一維至三維的例子 (Lam and Fredlund, 1993)以及簡化至複雜的方法(Duncan, 1996)。然而，極少模 式考慮雨水於邊坡入滲的影響， 亦甚少利用地理資訊系統(Geographic Information System，GIS)資料進行三維分析。因此，本研究欲建立三維邊坡穩 定分析簡化模式，考慮雨水入滲之影響，並模擬不同地下水位的情形，同時亦 將驗證本模式的正確性，與其他方法之結果進行比對，期望對於邊坡穩定的分 析有所裨益。 本研究共建立四種模式，每一模式皆由破壞面與地下水位面位置之間的 關係、地下水位增加高度、以及其他邊坡條件進行定義。在蒐集所需資料並建 立模式後，必須確定所選隨機變數之或然率分佈函數，再由蒙地卡羅模擬方法 (Monte Carlo Simulation Method，MCSM)進行模擬，反覆進行以上步驟直到數 值收斂為止(Rubenstein, 1981)。研究結果可得安全係數之平均值及分佈情形， 由此則可建立以頻率為基礎之評估。結果顯示，所使用的土壤區塊數目(917)足 以得到良好的結果，因此建議以一千或更多的反覆次數來得到收斂之結果。Nowadays, with the effects of global warming to the earth’s atmospheric conditions, the number of various hazardous natural events (i.e. storms, floods, earthquakes, etc.) has increased significantly every year creating large losses to the economy, lives, and properties of people. One of these common disasters is caused by torrential rains or storms, the so-called “landslide”. Numerous methods are available in estimating the stability of slopes against landslides and in analyzing different governing factors involved from one-dimensional approach to three-dimensional cases (Lam and Fredlund, 1993), and from simpler to complex techniques (Duncan, 1996). However, only few models are available that incorporates the effects of rainfall infiltration in slopes and that uses a three-dimensional analysis using data from Geographic Information System (GIS). Thus, this study was established and it aims, generally, to develop simpler models for a 3D slope stability analysis considering the effect of rainfall infiltration by varying groundwater levels; to verify these models; to correlate results with other methods; and, to identify unstable slopes in areas of interests for mitigation purposes. And for this, there were four stochastic models established. Each was defined from the relationship between the location of failure surface and of groundwater table, height of increase in the groundwater table, and from other slope conditions. In the methodology, after gathering the necessary data and establishing the models, first, it is necessary to identify the probability distribution function of the random variables selected. Then, a simulation was conducted by means of a Monte Carlo Simulation Method (MCSM), where iterative process is involved and which will stop not until values converge (Rubenstein, 1981). In the results, the mean value and the distribution of the possible factors of safety is determined, thereby, a probabilistic assessment based on the frequency can be made. It was found that the number of soil columns used (917 columns of 1mx1m cell size) is enough to get satisfactory results and was recommended that the number of iterations be 1000 or higher to meet the convergence criterion.TABLE OF CONTENTS CONTENTS PAGE Preface II Acknowledgment III English Abstract IV Chinese Abstract V List of Tables VI List of Figures VII Notations and Symbols……………………………………………………………………..IX CHAPTER I– INTRODUCTION 1.1 Background of the study 1 1.2 Statement of the objectives 2 1.3 Significance of the study 6 1.4 Scope and limitations of the study 6 Figures in Chapter I 1.1 Damaging storms and floods in the world 3 1.2 Damaging storms and floods in the world 4 1.3 Annual rainfalls in the world 5 CHAPTER II–REVIEW OF RELATED LITERATURE 2.1 Three-dimensional analysis of slope stability 8 2.2 Groundwater variations 15 2.3 Three major approaches of slope analysis 17 2.3.1 Deterministic approach 17 2.3.2 Probabilistic method for slope stability analysis 19 2.3.3 Combined deterministic and reliability approaches 19 2.4 Uncertainty in soil properties 19 2.5 Mechanism of slope failures 20 2.5.1 Shallow sliding 23 2.5.2 Deep-seated sliding 23 Figures in Chapter II 2.1 Considering end effects for φ = 0 12 2.2 Consideration of end effects by Baligh and Azzouz (1975) 13 2.3 Types of slope movements (USGS, 2004) 22 CHAPTER III - RELIABILITY APPROACH IN SLOPE STABILITY ANALYSIS 3.1 Reliability approach on slopes 24 3.2 Monte Carlo Random Simulation Method (MCRSM) 27 3.3 Statistical terms used in the three-dimensional slope stability analysis 31 Figures in Chapter III 3.1 Distribution of factor of safety 26 3.2 Simplified simulation process 29 3.3 Some types of probabilistic distribution functions 33 Tables in Chapter II 3.1 List of Probability density functions for random variables 30 3.2 Values of coefficient of variation for geotechnical properties and in situ tests 35 CHAPTER IV- RESEARCH METHODOLOGY 4.1 General methodology 36 4.2 Materials 37 4.3 Models 38 4.3.1 The established models 41 Figures in Chapter IV 4.1 Three-dimensional view of one grid-column 37 4.2 Sliding direction of the main sliding surface 39 4.3 Diagram for Case A 41 4.4 Diagram for Case B 42 4.5 Diagram for Case C 44 4.6 Diagram for Case D 46 CHAPTER V - ANALYSIS AND RESULTS 5.1 Introduction 47 5.2 Results and discussions 49 5.2.1 Effect of the number of soil column to the probability of failure, Pf 50 5.2.2 Effect of number of soil column and number of iteration to the calculated three-dimensional factor of safety, F3 75 5.3 Comparative study 79 Figures in Chapter V 5.1 Composite failure surface used in comparative study 48 5.2 Histogram results of F3 for Case A at 917 soil columns 51 5.3 Histogram results of F3 for Case A at 1500 soil columns 52 5.4 Histogram results of F3 for Case A at 2500 soil columns 53 5.5 Histogram results of F3 for Case A at 3500 soil columns 54 5.6 Histogram results of F3 for Case A at 5000 soil columns 55 5.7 Comparison on the calculated Pf in different number of soil columns for Case A 56 5.8 Histogram results of F3 for Case B at 917 soil columns 57 5.9 Histogram results of F3 for Case B at 1500 soil columns 58 5.10 Histogram results of F3 for Case B at 2500 soil columns 59 5.11 Histogram results of F3 for Case B at 3500 soil columns 60 5.12 Histogram results of F3 for Case B at 5000 soil columns 61 5.13 Comparison on the calculated Pf in different number of soil columns for Case B 62 5.14 Histogram results of F3 for Case C at 917 soil columns 64 5.15 Histogram results of F3 for Case C at 1500 soil columns 65 5.16 Histogram results of F3 for Case C at 2500 soil columns 66 5.17 Histogram results of F3 for Case C at 3500 soil columns 67 5.18 Histogram results of F3 for Case C at 5000 soil columns 68 5.19 Comparison on the calculated Pf in different number of soil columns for Case C 69 5.20 Histogram results of F3 for Case D at 917 soil columns 70 5.21 Histogram results of F3 for Case D at 1500 soil columns 71 5.22 Histogram results of F3 for Case D at 2500 soil columns 72 5.23 Histogram results of F3 for Case D at 3500 soil columns 73 5.24 Histogram results of F3 for Case D at 5000 soil columns 74 5.25 Comparison on the calculated Pf in different number of soil columns for Case D 75 5.26 Comparison on the calculated F3 in different number of soil columns for Case A 76 5.27 Comparison on the calculated F3 in different number of soil columns for Case B 77 5.28 Comparison on the calculated F3 in different number of soil columns for Case C 77 5.29 Comparison on the calculated F3 in different number of soil columns for Case D 78 5.30 Histogram of computed three-dimensional factors of safety for Case A 82 5.31 Histogram of computed three-dimensional factors of safety for Case B 85 5.32 Histogram of computed three-dimensional factors of safety for Case C 89 5.32 Histogram of computed three-dimensional factors of safety for Case D 93 Tables in Chapter V 5.1 Parameters used for the comparative study 49 5.2 List of calculated F3 and Pf for Case A 83 5.3 Results of a comparative study using three-dimensional failure surfaces 83 5.4 List of calculated F3 and Pf for Case C 87 5.5 List of calculated F3 and Pf for Case B 90 5.6 List of calculated F3 and Pf for Case D 93 CHAPTER VI - CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions 95 6.2 Recommendations 96 APPENDIX Notations and Symbols 99 REFERENCES 10