Efficient and conservative estimation reliability analysis of strip footing on spatially variable c - ϕ soil using random finite element limit analysis

The study deals with reliability analysis of strip foundation on spatially variable c - ϕ soil. The spatial variability of soil strength parameters, namely cohesion c and friction angle ϕ is modelled using anisotropic uncorrelated random fields, generated with the Fourier series method. Random finite element limit analysis (RFELA) providing a rigorous lower and upper bound for bearing capacity for individual Monte-Carlo simulations is employed. Additional use of adaptive meshing refinement algorithm leads to a significant reduction of the relative difference between statistical moments of obtained lower and upper bound results. The influence of the horizontal and vertical scales of fluctuation and foundation depths on the mean and standard deviation of the obtained bound moments is investigated. Additionally, the rigorousness of the mean and standard deviation of both considered bounds estimation is checked. As a result of the analysis, a novel approach based on a mixed distribution that combines lower and upper bound moments is introduced. As shown, this approach offers significant benefits by providing conservative and relatively precise measures of reliability which can be obtained in reasonable computation time. The proposed method seems to be adequate for practical engineering reliability analysis of foundation bearing capacity and other limits states problems.