Probabilistic analysis of strip footings on spatially variable soils with linearly increasing shear strength

摘要

This paper presents a probabilistic approach to obtain bearing capacities of strip footings resting on spatially variable marine clay deposits of increasing undrained shear strength with depth. A spatially variable feature is generated with a non-stationary random field where the ratio of the mean and standard deviation of undrained shear strength is maintained. The sparse polynomial chaos expansion is adopted to improve the calculation efficiency of random numerical simulation. Similar to the deterministic case, for a given degree of soil heterogeneity kappa, the dimensionless vertical capacity is independent of the change in the slope of undrained shear strength in the stochastic case. The probability density function (PDF) and cumulative distribution function (CDF) curves of normalised bearing capacity for varying kappa are constructed and the effect of soil parameters, such as kappa, coefficient of variations and autocorrelation distances, on the probabilistic bearing capacity is discussed. Results show a remarkable improvement in efficiency in computation with a minimal number of realisations. Parametric studies obtained demonstrate that kappa has the lowest effect on the normalised bearing capacity among the above parameters. In addition, for an anisotropic autocorrelation distance of delta(h)/delta(v) = 5, the greatest reduction in the random vertical capacity v(u,p) at a low p occurs when the dimensionless vertical autocorrelation distance delta(v)/B = 0.5, which offers a guide in the design of offshore shallow foundations.