On Some Aspects of Reliability Computations in Bearing Capacity of Shallow Foundations

Abstract

The chapter deals with bearing capacity of spread foundations in the context of reliability computations. In the first part evaluations base on the recommendations given by Polish Standard (1981). Consequently some most important ideas concerning bearing capacity suggested by this standard are presented and compared with analogical statements of Eurocode EC7 (1997). Next some reliability computations are carried out under an assumption that each individual soil property is modelled by a single random variable throughout the earth body considered. But such approach seems to be too simple. In order to evaluate credible reliability indices when bearing capacity of a shallow foundation is considered it is reasonable to describe soil strength properties in terms of random field’s theory. As a next step the selected random field can be spatially averaged by means of a procedure introduced by (1977). Earlier experiences have proved that, without applying spatial averaging procedure, reliability computations carried out in the context of foundation’s bearing capacity had given significantly small values of reliability indices (large values of failure’s probability) even for foundations which were considered as relatively safe. On the other hand the volume of the area under averaging strongly affects results of reliability computations. Hence the selection of the averaged area constitutes a vital problem and has to be dependent on the failure mechanism under consideration. In the present study local averages associated with kinematically admissible mechanism of failure proposed by (1920) are considered. Soil strength parameters are assumed to constitute anisotropic random fields with different values of vertical and horizontal fluctuation scales. These fields are subjected to averaging along potential slip lines within the mechanism under consideration. Next examples of equations for variances of random variables resulting from averaging procedure are shown. By numerical examples it is demonstrated that for reasonable proportions (from practical viewpoint) between horizontal and vertical fluctuation scales the reliability indices resulting in two-dimensional case only slightly differs from resulting that obtained in one-dimensional. This means that the simpler one-dimensional approach can be usually utilised when reliability measures of shallow strip foundation are carried out.