Probabilistic Analysis of Shallow Foundations on c-φ Soils Using 2nd Order Response Surface Methods

Abstract

The HL-Reliability Index is utilized to investigate the applicability of several linear and nonlinear response surface models based on design experiments techniques to evaluate the safety under random loading, against bearing capacity failure of shallow foundations resting on c-φ soils with multivariate correlated variables. The reliability results obtained using FORM/SORM coupled with these models, are checked by Monte Carlo simulation method. It is demonstrated that the application of these models significantly reduces the execution time and memory requirements, with the central composite design scheme being the most accurate. It is also concluded, that consideration of correlation, significantly affects the reliability index for large values of soil friction angle uncertainty. The reliability index is found to be highly sensitive to uncertainties of soil friction angle more than the cohesion and the loading which have approximately the same influence, especially for the case of lognormally distributed variables. In addition, the probabilistic results show that reliability index decreases substantially with the increase of the applied pressure, and that there is significant difference between the reliability indices values computed, based on the assumption of normal distribution as compared to lognormal distribution, especially for the lower ranges of applied loading.