Rainfall infiltration in an unsaturated soil slope induces loss of suction (and even positive pore-water pressures), which can eventually lead to failure. This paper investigates the probability and the size of failure of an unsaturated slope with spatially variable void ratio, subjected to a constant intensity rainfall. The random finite element method is employed in conjunction with a Monte Carlo simulation to stochastically evaluate the factor of safety and the size of the sliding mass. The results indicate that the mean value and the variability of these two quantities depend on both correlation length and coefficient of variation of the void ratio field. This dependency is more prominent during the transient regime than at steady states. Notably, the factor of safety in some cases can be low but the corresponding sliding mass is relatively small, while in other instances, the factor of safety might remain large though the associated sliding mass is very sizeable. The correlation between the factor of safety and the size of the sliding mass shifts from positive to negative as the rainfall progresses. A simple quadrant plot is suggested to assess the risk associated with slope failure, taking into account both the factor of safety and the size of failure, rather than the factor of safety alone as it is usually the case. The study also demonstrates an application of a numerical approach to assess stability of geostructures composed of complex multiphase materials such as unsaturated soils or frozen soils.

This paper presents an approach for reliability analysis of engineering structures, referred to as Metamodel Line Sampling (MLS). The approach utilizes a metamodel of the performance function, within the framework of the Line Sampling method, to reduce computational demands associated with the reliability analysis of engineering structures. Given a metamodel of the performance function, the failure probability is estimated as a product of a metamodel-based failure probability and a correction coefficient. The correction coefficient accounts for the error in the metamodel estimate of failure probability introduced by the replacement of the performance function with a metamodel. Computational efficiency and accuracy of the MLS approach are evaluated with the Kriging metamodel on analytical reliability problems and a practical reliability problem of a monopile foundation for offshore wind turbine. The MLS approach demonstrated efficient performance in low to medium-dimensional reliability problems.

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