Probabilistic analysis and design at the ultimate limit state of obliquely loaded strip footings

Abstract

This paper presents a probabilistic approach for the analysis and design of a strip footing subjected to an inclined load. Both the punching and sliding modes of failure were considered. The deterministic model of the soil punching mode was based on the kinematic approach of limit analysis using a non-symmetrical translational multiblock failure mechanism. The vertical and horizontal components of the footing load were considered as random variables. The soil shear strength parameters were first modelled as random variables and then as random fields to take into account the soil spatial variability. Spatial averaging was used to transform the random field problem to a simple problem of correlated random variables. The reliability index of each failure mode and the system failure probability were calculated. When the soil shear strength parameters were modelled as random variables, it was shown that the coefficient of variation of the angle of internal friction and that of the horizontal footing load have a non-negligible effect on the system failure probability. On the other hand, when the shear strength parameters were modelled as random fields, it was found that the case of (a) a finite (i.e. non-infinite) autocorrelation distance and/or (b) an anisotropic soil regarding the autocorrelation distance, leads to a greater reliability of the foundation with respect to the reference case of isotropic and infinite autocorrelation distances (i.e. the case of random variables). For both cases of random variables or random fields, it was shown that the negative correlation between the shear strength parameters gives a greater reliability of the foundation in comparison to the uncorrelated shear strength parameters. Finally, for design, an iterative procedure was performed to determine the breadth of the footing for a target system failure probability.