Yu-Gang Hu

Efficient Evaluation of Reliability for Slopes with Circular Slip Surfaces Using Importance Sampling

Evaluating the reliability of a slope is a challenging task because the possible slip surface is not known beforehand. Approximate methods via the first-order reliability method provide efficient ways of evaluating failure probability of the “most probable” failure surface. The tradeoff is that the failure probability estimates may be biased towards the unconservative side. The Monte Carlo simulation (MCS) is a viable unbiased way of estimating the failure probability of a slope, but MCS is inefficient for problems with small failure probabilities. This study proposes a novel way based on the importance sampling technique of estimating slope reliability that is unbiased and yet is much more efficient than MCS. In particular, the critical issue of the specification of the importance sampling probability density function will be addressed in detail. Three examples of slope reliability will be used to demonstrate the performance of the new method.

Observations on Limit Equilibrium–Based Slope Reliability Problems with Inclined Weak Seams

This study addresses the complexity of slope reliability problems based on limit equilibrium methods (LEMs). The main focus is on the existence of multiple failure modes that poses difficulty to many LEM-based slope reliability methods. In particular, when weak seams are present, the failure modes associated with those seams may be difficult to detect. A systematic way of searching the failure modes is proposed, and its robustness over slopes with or without weak seams is demonstrated. It is found that in the presence of weak seams, assuming circular slip surfaces may cause underestimation of slope failure probability. The conclusion of the study promotes the use of finite elements as the stability method for reliability evaluation because it is not necessary to search for failure surfaces in finite-element stability analysis.

Effect of Element Size in Random Finite Element Analysis for Effective Young’s Modulus

In random finite element analysis (RFEA), continuous random fields must be discretized. The critical element size to achieve acceptable accuracy in effective Young’s modulus for an elementary soil mass is investigated. It is observed that the discrepancy between the continuous and discretized solutions is governed by the discretization strategy (element-level averaging versus midpoint), spatial variability pattern, and the adopted autocorrelation function. With the element-level averaging strategy, RFEA with element size less than (scale of fluctuation)/5 will not induce significant discrepancy from the continuous solution. Moreover, the element-level averaging strategy is more effective than the midpoint strategy.

Effective Young's modulus for a spatially variable soil mass subjected to a simple stress state

ABSTRACT The effect of spatial variability on the effective Youngs modulus of a soil mass is investigated. The soil mass is a two-dimensional plane strain square domain subjected to a simple stress state, with Youngs modulus being modelled as a stationary lognormal random field. The effective Youngs modulus is simulated by random field finite-element analysis. It is found that under the condition of horizontal scale of fluctuation (SOF) = vertical SOF, the effective Youngs modulus can be satisfactorily approximated as the geometric average over the square domain. However, the conclusion changes dramatically when the spatial variability is highly anisotropic, e.g. horizontal scale  vertical SOF. In this case, the effective Youngs modulus can be approximated as the arithmetic average or harmonic average, depending on the direction of loading. A unified spatial averaging model is further proposed in this study. It is shown that the effective Youngs modulus can be satisfactorily approximated by this unified model without the need to switch among arithmetic, geometric and harmonic averages.

On the use of spatially averaged shear strength for the bearing capacity of a shallow foundation

This study examines the validity for representing the mobilized shear strength as the spatial average over a prescribed soil volume. A shallow foundation problem is adopted to demonstrate this. The approach is simple. Two sets of field finite element (FEM) analyses are taken. The first set considers a spatially variable soil mass whose shear strength is simulated by a random field. The bearing capacity simulated by this first set of FEM is the actual (reference) capacity. The same random field is averaged over a prescribed volume of interest to obtain the mobilized value. The second set of FEM then considers a homogeneous soil mass whose shear strength is equal to this mobilized value. The bearing capacity simulated by this second set of FEM is then compared to the reference value. The comparison will be made on two levels. Level I compares the statistics of the two sets of capacities, whereas Level II compares the two sets of capacities on the 1:1 line. Based on these numerical studies, it is observed that the two sets of capacities are at most equal in “distribution”, but not “almost everywhere”.