Stochastic analysis of ultimate bearing capacity of strip footing considering spatial variability of undrained shear strength

The effect of the variation of shear strength parameters of soils with depth on the stability of footing has not been thoroughly studied. A stochastic method is proposed for bearing capacity analysis of strip footing considering the variation of the mean and standard deviation of undrained shear strength parameters with depth. A non-stationary random field model is established, and the random field is discretized by the Karhunen-Loeve (KL) expansion. The effect of spatial variability of the undrained shear strength parameters on the ultimate bearing capacity is investigated. The results of bearing capacity associated with stationary and non-stationary random field models are compared. An undrained clay foundation is presented to demonstrate the effectiveness of the proposed method. The results indicate that both the mean and standard deviation of bearing capacity increase with the increasing correlation length, and that the ultimate bearing capacity is more sensitive to the vertical correlation length than to the horizontal one. The mean of the ultimate bearing capacity decreases but the standard deviation increases as the coefficient of variance increases. The spatial variability of shear strength parameters of soils has a significant influence on the failure probability of foundation. When the factor of safety is large, the failure probability of foundation decreases with the decreasing correlation lengths. Compared with the non-stationary random field, stationary random field will highly overestimate the variation of the ultimate bearing capacity. When the factor of safety against shear failure is low, the stationary random field model will induce a lower probability of failure than the non-stationary random field model. On the contrary, when the factor of safety against shear failure is high, the stationary random field model will induce a higher probability of failure.