Reliability Analysis of Bearing Capacity of Square Footing on Soil with Strength Anisotropy Due to Layered Microstructure

The paper deals with reliability analysis of square footing on soil with strength anisotropy. The strength of the soil has been described with identified anisotropic strength criterion dedicated to geomaterials with layered microstructure. The analysis assumes dip angle α and azimuth angle β which define direction of lamination of the structure to be random variables with given probability density functions. Bearing capacity being a function of these variables is approximated based on results of deterministic simulations obtained for variety of orientations. The weighted regression method by Kaymaz and McMahon within the framework of Response Surface Method is used for the approximation. As a result of analysis, global factor of safety that corresponds to assumed value of probability of failure is determined. The value of the safety factor denotes the ratio between the value of the design load and the mean value of bearing capacity which is needed to reduce the probability of failure to the acceptable level. The procedure of calculating the factor has been presented for two different cases. In the first case, no information about lamination direction of the soil has been provided and thus all the orientations are assumed to be equally probable (uniform distribution). In the second case, statistical information including mean, variance and assumed probability distribution for both α and β angle is known. For the latter case, using results obtained for few different values of mean of angle α, also the influence of strength anisotropy on the value of global factor of safety is shown.