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The saturated hydraulic conductivity ( K s ) of soil is characterized by strong spatial variability and often decreases with depth. The main objective of this paper is to investigate how the trend function of the mean of saturated hydraulic conductivity ( μ K s ) and its spatial variability affect the distribution of critical failure surfaces and the probability of slope failure during a period of rainfall. A random field method is used to simulate the spatial variability structure in the numerical analysis of a slope, and a numerical procedure for a probabilistic slope stability analysis based on Monte Carlo simulations is presented, in which K s is modeled as a non-stationary lognormal random field. For a hypothetical weathered soil slope subjected to rainfall, a deterministic analysis and a sequence of probabilistic analyses are conducted using an infinite unsaturated slope model. The results show that these shallow failures are attributed to the reduction of matric suction and the development of positive pore pressure. The probability of slope failure increases with an increase in the variation of the trend component (Δ k ), but the rate of increase levels off at the later stage of rainfall. Ignoring the trend component of μ K s would lead to less conservative estimates of the failure probability. The coefficient of variability has a more significant influence on the distribution of the critical failure surfaces and the probability of failure than does the correlation length of K s . [ABSTRACT FROM AUTHOR]

Many soil parameters are highly variable, especially saturated hydraulic conductivity, which is bound to significantly influence the stability of unsaturated soil slopes that are subjected to rainfall infiltration and redistribution. A random variable model is used to characterize the variability of saturated hydraulic conductivity. Random number sequences of saturated hydraulic conductivity are generated following a lognormal distribution using the Monte Carlo Simulation method. Then the closed form of the limit state function is established, based on the combination of the extension of the Green-Ampt model and the infinite slope stability model. The suggested probabilistic method can calculate the time-dependent failure probability of the slope during a process of rainfall infiltration and redistribution. For a hypothetical slope that is subjected to steady-state rainfall infiltration, a series of parameter analyses are conducted and the results indicate that there exists a critical rainfall duration. At different stages of rainwater infiltration–redistribution, the trends between the failure probability of the soil slope and the coefficient of variation of the saturated hydraulic conductivity have a different form. The coefficient of variation of the saturated hydraulic conductivity does not affect the failure time of the slope that is most likely to occur. This paper figures out why some landslides occur after a rainfall event from the perspective of rainwater redistribution, and the corresponding lag times generally depend on the duration of antecedent rainfall. It is very risky to adopt mean safety factors to assess their stabilities for rainfall-induced landslides when the variability of the hydraulic conductivity is considered. [ABSTRACT FROM AUTHOR]

A semi-analytical solution for the groundwater ingress into a lined tunnel in a semi-infinite aquifer is derived based on the conformal mapping technique. The new solution considers the property of the lining, such as the permeability coefficient of the lining as well as the external and internal lining radii. A numerical model is established using the software COMSOL to verify the semi-analytical solution, and a good agreement is found. Parameters including water layer thickness, burial depth of the tunnel, permeability coefficient of the lining and the lining thickness are discussed in detail. This paper explains why the water ingress obtained from early research should be reduced by Heuer’s empirical factor 1/8. Moreover, an optimal burial depth is found when the permeability of the lining is close to the permeability of the aquifer. [ABSTRACT FROM AUTHOR]