Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek–Brown failure criterion

Abstract

In this paper, a probabilistic analysis is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a shallow strip footing resting on a rock mass. The rock is assumed to follow the modified Hoek–Brown failure criterion. Vertical and inclined loading cases are considered in the analysis. In this study, the deterministic models are based on the kinematic approach of the limit analysis theory. The polynomial chaos expansion (PCE) methodology is used for the probabilistic analysis. Four parameters related to the modified Hoek–Brown failure criterion are considered as random variables. These are the geological strength index ( GSI), the uniaxial compressive strength of the intact rock ( σ c ), the intact rock material constant ( m i ) and the disturbance coefficient ( D). The results of the vertical load case have shown that (i) the variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random variables; GSI and σ c being of greater effect, (ii) the non-normality of the input variables has a significant effect on the shape of the PDF of the ultimate bearing capacity, (iii) a negative correlation between GSI and σ c leads to less spread out PDF, (iv) the probabilistic footing breadth based on a reliability-based design (RBD) may be greater or smaller than the deterministic breadth depending on the values of the input statistical parameters. Finally, it was shown in the inclined load case that the variability of the ultimate bearing capacity decreases with the increase of the footing load inclination.