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 (s 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 s 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 s 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.

International audienceThis paper presents a probabilistic analysis at the ultimate limit state of a shallow strip footing resting on a (c, phi) soil and subjected to an inclined load. The system response considered in the analysis is the safety factor obtained using the strength-reduction technique. The deterministic model makes use of the kinematic approach of the limit analysis theory. The Polynomial Chaos Expansion (PCE) methodology is employed for the probabilistic analysis. The soil shear strength parameters and the footing load components are considered as random variables. A reliability analysis and a global sensitivity analysis are performed. Also, a parametric study showing the effect of the different statistical characteristics of the random variables on the variability of the safety factor is presented and discussed. It is shown that the use of the safety factor (based on the strength-reduction technique) for the system response is of significant interest in the reliability analysis, since it takes into account the simultaneous effect of soil punching and footing sliding and it requires a unique reliability analysis for both failure modes. Furthermore, it allows the rigorous determination of the zones of predominance of soil punching and footing sliding in the interaction diagram for different cases of soil and/or loading uncertainties. Finally, it is shown that the loading configurations located in the zone of the footing sliding predominance exhibit a more significant variability in the safety factor compared to those located in the zone of the soil punching predominance

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A probabilistic analysis using Polynomial Chaos Expansion method is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a rock mass and subjected to a vertical/inclined load. The rock is assumed to follow Hoek-Brown failure criterion. The kinematic approach of the limit analysis theory is used. The results of the vertical load case have shown that: (i) the Geological Strength Index GSI and the uniaxial compressive strength of the intact rock σ c have the most significant weight in the variability of the ultimate bearing capacity, (ii) the non-normality of the input variables has a significant effect on the shape of the PDF of the ultimate bearing capacity and, (iii) a negative correlation between GSI and σ c leads to less spread out PDF. 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.