Probabilistic geotechnical engineering analysis based on first order reliability method

Limit equilibrium engineering analysis needs the incorporation of probabilistic approaches for the determination of soil strength statistical measures for deterministic and probabilistic analyses. For the commonly used Mohr–Coulomb strength model, the uncertainty and the characteristic values of cohesion (c) and angle of shearing resistance (φ) determination is not straight­­forward. This paper applies the first order reliability method (FORM) to estimate these values from the direct shear and the typical triaxial tests. The method is verified with test data. Furthermore, the FORM is applied to the planar failure limit equilibrium problem to determine the statistical measures of the safety margin (SM) and safety factor (SF). It is observed that the critical slip surface for the best estimate of the mean (SM_m, SF_m), for a 5% probability of exceedance (SM_p=5%, SF_p=5%) and for the characteristic value (SM_k, SF_k) do not coincide. It is interesting that the maximum probability of having a SM<0 or SF<1 does not correspond to the minimum best estimate of the SM or SF. FORM can be a very useful tool for complete probabilistic analyses. Further­more, probabilistic approaches applied to soil properties estimation can set a framework for the selection of their characteristic values for deterministic analyses.