Effects of random heterogeneity of soil properties on bearing capacity

This study examines the effect of random heterogeneity of soil properties on bearing capacity. The stochastic soil property considered is the undrained shear strength and two major sources of uncertainty are identified with it: inherent spatial variability (modeled as a non-Gaussian, homogeneous stochastic field) and uncertainty in the estimation of its expected value (modeled as a random variable). The two sources of uncertainty are treated separately, before being eventually combined. A Monte Carlo simulation approach is followed in combination with non-linear finite element analysis. It is demonstrated that the inherent spatial variability of soil shear strength can drastically modify the basic form of the failure mechanism in this bearing capacity problem. Consequently, there is no 'average' failure mechanism (surface) in this problem, leading to the conclusion that Monte Carlo simulation is the only methodology capable of providing a solution to this geomechanics problem. It is further demonstrated that this behavior of the failure mechanism translates into a substantial reduction in the ultimate bearing capacity (in an average sense), compared to the corresponding deterministic (homogeneous soil) case. In addition, differential settlements are computed in the stochastic analysis, something impossible in a deterministic analysis of a symmetric problem. A parametric study is performed using fragility curves to investigate the effects of various probabilistic parameters involved in the problem. It is found that the coefficient of variation and the marginal probability distribution of the soil's shear strength (both controlling the amount of loose pockets in the soil mass) are the two most important parameters in reducing the bearing capacity (in an average sense) and producing substantial differential settlements in heterogeneous soils (compared to homogeneous soils). A technique is finally introduced for determining 'overall' fragility curves that account for both inherent soil spatial variability and uncertainty in the expected value of soil strength. Based on such 'overall' fragility curves obtained at failure (ultimate bearing capacity), nominal values of the bearing capacity of a heterogeneous soil deposit corresponding to an exceedance probability of 5% are established for a range of probabilistic characteristics.