Probabilistic assessment of bearing capacity of strip footings seated on heterogeneous slopes using finite element limit analysis (FELA) and response surface method (RSM)

This paper demonstrates the use of the response surface method (RSM) to carry out probabilistic assessment of the bearing capacity of shallow footings seated near naturally occurring heterogeneous slopes. The method substantially reduces the number of Monte Carlo simulations required to carry out cumbersome probabilistic slope stability analyses. A finite element limit analysis model based on the lower bound theorem is developed. The soil behaviour in this model has been assumed to follow the associated plastic flow rule by conforming to the perfectly plastic Mohr-Coulomb failure criterion. The model then used to generate a large synthetic database of numerical results for the bearing capacity of shallow foundations resting on inherently variable natural slopes. To this end, a permutation of the key parameters is formed and lower bound FELA-based limit loads are sought through optimization in MATLAB. A closed-form solution is formulated using RSM-based polynomials. The response surface method equations, which are acquired from least squares regression analyses, are used to carry out probabilistic Monte Carlo simulations. The results of the current study clearly show that the earth slope angle of 75o would give rise to the diminished factor of safety, or in other words, the substantially augmented probability of failure compared to the other two slope angles considered. On the other hand, the slope angle of 45o renders higher factor of safety and lower probability failure as compared to the slope angle of 60o. Moreover, it is observed that constructing the foundation at a farther distance relative to the slope would cause the probability of failure to substantially diminish while leading the reliability index to enhance for the majority of the safety factor scenarios considered. Indeed, targeting a particular probability of failure or a specific reliability index would demand smaller factor of safety for greater soil-footing distances.