Reliability Analysis of Circular Foundations on Unsaturated Soils Using Monte Carlo Simulation

This paper presents a reliability analysis of circular footings on unsaturated soils. Two methods were used to capture the unsaturated soil behavior: implementing two elastoplastic constitutive models, including the Barcelona Basic Model (BBM) and the Sun Model (SM), which are explicitly proposed for unsaturated soils, and incorporating the apparent cohesion in the Mohr-Coulomb Model (MCM). The effect of soil suction on the bearing capacity of circular footings was investigated. It was shown that for low values of suction, the bearing capacities obtained from MCM were higher than those obtained from BBM and SM. However, as suction increased, MCM tended to predict lower bearing capacities. In practice, geotechnical engineers are still concerned with the measurement and determination of suction as a key stress state variable of unsaturated soils. In this context, the Monte Carlo simulation technique has been incorporated into numerical modeling for the investigation of the effect of suction uncertainties on the bearing capacity. Uncertainties associated with the suction value were modeled as normally and log-normally distributed random variables. It was shown that assuming a normal distribution for suction resulted in slightly lower probabilistic bearing capacity values (i.e., more conservative design) compared to the log-normal distributions. The results emphasized the important role of the coefficient of variation (COV) of suction in determining the probabilistic bearing capacity. A negative linear correlation was observed between the COV of suction and the probabilistic bearing capacity. Finally, a simple relationship was proposed to estimate the probabilistic bearing capacity of the circular footing in an unsaturated soil when its deterministic value and the COV of suction are known.