Abstract:In the present paper, a three-dimensional problem of bearing capacity of square footing on random soil medium is analyzed. The random fields of strength parameters c and φ are generated using LAS procedure (Local Average Subdivision, Fenton and Vanmarcke 1990). The procedure used is re-implemented by the authors in Mathematica environment in order to combine it with commercial program. Since the procedure is still tested the random filed has been assumed as one-dimensional: the strength properties of soil are random in vertical direction only.Individual realizations of bearing capacity boundary-problem with strength parameters of medium defined the above procedure are solved using FLAC3D Software. The analysis is performed for two qualitatively different cases, namely for the purely cohesive and cohesive-frictional soils. For the latter case the friction angle and cohesion have been assumed as independent random variables. For these two cases the random square footing bearing capacity results have been obtained for the range of fluctuation scales from 0.5 m to 10 m. Each time 1000 Monte Carlo realizations have been performed. The obtained results allow not only the mean and variance but also the probability density function to be estimated. An example of application of this function for reliability calculation has been presented in the final part of the paper.

HDMR (High Dimensional Model Representation) is a relatively new method that is used to form response surface based on results obtained through laboratory experiments or through numerical calculations. So far the method has been used mainly in chemistry, although a few studies conducted in recent years show that it can be considered a useful tool in soil mechanics and foundation engineering.The subject matter of this paper is the application of HDMR method to reliability assessment of bearing capacity of layered soils. Madej's method, widely recognized and used by Polish engineers, is applied to conduct the calculations. In the analysed case bearing capacity is not expressed by means of an explicit formula.To fit the approximate functions of bearing capacity, its values are calculated on a grid of points equally spread on ranges of variables. Finding the relation between input and output data is conducted by means of assessing each variable's influence on response's mean value within a given scope.Approximate functions have been used to calculate reliability indices by means of FORM, SORM and Monte Carlo methods.