Probabilistic bearing capacity of eccentrically loaded strip footing on spatially random rock mass using correlation-controlled LHS sampling

To examine the heterogeneous behavior of spatially random rock mass, the probabilistic bearing capacity of strip footing subjected to eccentric loading is computed in the present study. The lower bound finite element limit analysis in combination with the power conic optimization technique is employed by assuming the rock mass to follow the generalized Hoek-Brown (GHB) failure criterion at collapse. Geological Strength Index (GSI) is modeled as a spatially random variable. The rock mass material constant (m_i) and uniaxial compressive strength ratio (σ_ci/γB) are modeled as spatially random fields. Correlation-controlled Latin hypercube sampling (LHS) is implemented to create the spatially random discretized rock mass domain. With the help of the Monte Carlo simulation technique, the stochastic responses are determined. The obtained values of bearing capacity factor are found to follow the gamma distribution. The failure probability and mean bearing capacity factor for different ranges of practical cases of rock mass heterogeneity and loading eccentricity conditions are presented in design charts. With the increase in the eccentricity values, the mean bearing capacity factor reduces in all probabilistic cases. The target probability is expressed in terms of the desired factor of safety based on the acquired results for different rock mass and loading parameters.