||Rainfall characteristics for anisotropic conductivity of soil slope
||Department of Resources Engineering
Anisotropic of hydraulic conductivity
The stability of slopes decreases due to the suction decreases occurring with rainfall infiltration. Traditional studies of slope stability have used a general limit equilibrium method to calculate the safety factors and to determine whether a slope is safe. However, sometimes the failure of slope may occur even though the safety factor is more than unity (FS > 1) because the input soil parameters are considered to be the mean value for slope stability analysis. As a result, when many parameters are used in analysis, the level of uncertainty increases. The probability approach used to study geotechnical issues offers a systematic way to treat uncertainties, especially in the case of slope stability problems. In this study, probability analysis is used to evaluate the stability of unsaturated soil slopes. The geological formation of residual soils is mostly in distinctive layers that may have different hydraulic conductivity (ks) in different directions. Furthermore much of the research on this topic has assumed the ks to be isotropic. Therefore, in this thesis, the effect of anisotropic of ks on the slope seepage under the condition of rainfall infiltration is examined.
In this study, the finite element computer program Geo-Studio is used to simulate the process of rainwater infiltrate to the slope. The pore-water pressure results evaluated from seepage analysis (SEEP/W) are imported into the slope stability program (SLOPE/W). In order to quantify the slope stability results probabilistically, the soil strength parameters are provided with a range.
The results of the designed case study indicated that in the case of sand, the rainfall pattern controlled the time for the occurrence of instability of the slope under consideration. The rate of decrease in safety factor versus time was found to be faster in the case of the advanced pattern, followed by the normal and delayed patterns. The results for the anisotropic ratio of hydraulic conductivity indicated that when the anisotropic ratios become higher, the reduction in the reliability index is insignificant. Cases for the sand slope under different rainfall intensities (I) were designed. It was found that while the ks was greater than I, the reliability index decreased immediately, and there was also a decrease in the reliability index by nearly a quarter because the event after 6 hours remained stable. When, the ks was less than I, the reliability index stayed at the beginning level. About 7 hours later, there was found to be a marked downward trend. The reliability index fell by 65%. In the other case, the simulation results indicated that when the ks was less than I, the percentage probability of the occurrence of a landslide was larger than when the ks was greater than I. Finally, in the cases of anisotropic ks, the stability of the high ratio soil slopes was not found to be sensitive to the reliability index variation during the simulation period. Moreover, when the ks was greater than I, the stability of the slope decreased earlier than was the case in the opposite situation.
Table of Contents
Chapter 1 Introduction 1
1.1 Background and Literature Review 1
1.2 Research Methodology 5
Chapter 2 Theory 8
2.1 Vertical proﬁles of matric suction of unsaturated soils 8
2.2 Evaluating the profile of water content in unsaturated soil 11
2.3 The shear strength of unsaturated soils 15
2.4 Numerical modeling to analyze slope stability problem 17
2.4.1 Conductivity function estimate methods 17
2.4.2 Soil Water Characteristic Curve estimate methods 24
2.4.3 Slope stability analysis 33
2.4.4 Probabilistic slope stability analysis 46
Chapter 3 Influence of Rainfall Patterns on Soil Slopes 53
3.1 Rainfall pattern 54
3.2 Numerical model 56
3.2.1 Geometry and hydraulic boundary conditions 56
3.2.2 Soil properties 57
3.3 Results and discussion 60
3.3.1 The Influence of Rainfall Patterns on the Minimum Factor of Safety of an Isotropic Slope 60
3.3.2 Reliability analysis of the anisotropic hydraulic conductivity of shallow landslides under different rainfall patterns 66
Chapter 4 Rainfall intensity and hydraulic conductivity 74
4.1 Reliability analysis of precipitation variation impact on unsaturated slopes 76
4.1.1 Case 1 (Different hydraulic conductivities) 76
4.1.2 Case 2 (Different rainfall intensity) 79
4.1.3 Summary 81
4.2 Reliability analysis of precipitation variation impact on anisotropic hydraulic conductivity of unsaturated slope 82
4.2.1 Case 1 83
4.2.2 Case 2 85
4.2.3 Summary 87
Chapter 5 Conclusions and recommendations 89
5.1 Conclusions 89
5.2 Recommendations 90
List of Figures
Fig 1 1 An example of changes in the factor of safety with time (Popescu 2005) 3
Fig 1 2 Flowchart for research work 7
Fig 2 1 Matric suction of saturation profiles under various vertical unsaturated flow rates in various representative soils: (a) sand, (b)silt, and (c) clay 10
Fig 2 2 Effective degree of saturation profiles under various vertical unsaturated flow rates in various representative soils: (a) sand, (b)silt, and (c) clay 13
Fig 2 3 Extended Mohr-Coulomb failure envelope for unsaturated soils (Fredlund and Rahardjo 1993) 16
Fig 2 4 Forces acting on a slice through a sliding mass with a circular slip surface (Krahn 2004) 37
Fig 2 5 Forces acting on a slice through a sliding mass with a composite slip surface (Krahn 2004) 37
Fig 2 6 Forces acting on a slice through a sliding mass defined by a fully specified slip surface (Krahn 2004) 38
Fig 3 1 Designed rainfall patterns: (a) advanced rainfall pattern; (b) normal rainfall pattern; (c) delayed rainfall pattern 55
Fig 3 2 Geometry of slope and boundary condition 57
Fig 3 3 SWCC of the three typical soils 58
Fig 3 4 Factor of safety variation with time, for different rainfall patterns: (a) sand slope; (b) silt slope; (c) clay slope 62
Fig 3 5 Pore-water pressure distribution caused by antecedent rainfall at crest (A-A’) and toe (B-B’) cross section for sand slope: (a) advanced rainfall pattern at crest; (b) advanced rainfall pattern at toe; (c) normal rainfall pattern at crest; (d) normal rainfall pattern at toe; (e) delayed rainfall pattern at crest; (f) delayed rainfall pattern at toe. 63
Fig 3 6 Pore-water pressure distribution caused by antecedent rainfall at crest (A-A’) and toe (B-B’) cross section for silt slope: (a) advanced rainfall pattern at crest; (b) advanced rainfall pattern at toe; (c) normal rainfall pattern at crest; (d) normal rainfall pattern at toe; (e) delayed rainfall pattern at crest; (f) delayed rainfall pattern at toe. 64
Fig 3 7 Pore-water pressure distribution caused by antecedent rainfall at crest (A-A’) and toe (B-B’) cross section for clay slope: (a) advanced rainfall pattern at crest; (b) advanced rainfall pattern at toe; (c) normal rainfall pattern at crest; (d) normal rainfall pattern at toe; (e) delayed rainfall pattern at crest; (f) delayed rainfall pattern at toe. 65
Fig 3 8 Flow chart for reliability analysis of the anisotropic hydraulic conductivity of shallow landslides under different rainfall patterns. 67
Fig 3 9 Variation of reliability index of sand at different of anisotropic ratio (a) advanced rainfall; (b) normal rainfall; (c) delayed rainfall 69
Fig 3 10 The pore-water pressure profile of sand slope under the advance rainfall condition (a) kx/ky = 2; (b) kx/ky = 10; (c) kx/ky = 20 70
Fig 3 11 Variation of reliability index under different anisotropic ratios in silt slope (a) advanced rainfall; (b) normal rainfall; (c) delayed rainfall 71
Fig 3 12 Variation of reliability index under different of anisotropic ratios in clay slope (a) advanced rainfall; (b) normal rainfall; (c) delayed rainfall 72
Fig 4 1 Time serial of annual data of (a)Taipei and (b)Tainan stations from 1897 to 2010. (Wu 2012) 75
Fig 4 2 Reliability variation with time considering the same rainfall intensity 78
Fig 4 3 Variation of pore-water pressure with time considering different hydraulic conductivities. (H0 point: surface of the toe, H1 point: depth 1m from the surface of the toe, H2 point: depth 2m from the surface of the toe and H3 point: depth 3m from the surface of the toe.) 79
Fig 4 4 Reliability variation with time under different rainfall intensity 80
Fig 4 5 Pore-water pressure distribution of case 2 at toe of slope (a) ks < I (b) ks > I 81
Fig 4 6 Variation of reliability index under different anisotropic ratios. (ks > I) 84
Fig 4 7 Pore-water pressure profile of different anisotropic ratio with time. 85
Fig 4 8 Variation of reliability index under different anisotropic ratio. (ks < I) 86
Fig 4 9 Pore-water pressure profile of different anisotropic ratio with time. 87
List of Tables
Table 2 1 Representative hydrologic parameters for sand, silt, and clay 14
Table 2 2 Summary of known quantities in solving for a safety factor 39
Table 2 3 Summary of unknown quantities in solving for a safety factor 40
Table 3 1 Representative hydrologic parameters for sand, silt, and clay 59
Table 3 2 Range of strength properties for various soils 59
Table 4 1 Representative hydrologic parameters for sand and silt 76
Table 4 2 Range of strength properties for sand and silt 76
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