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Spatial variability in soil shear strength affects the occurrence of the ultimate limit state not only by the spatial averaging along the potential slip curve but also by seeking out mechanically admissible weak zones. The former factor (spatial averaging) reduces the variance of the mobilised shear strength, whereas the latter factor (weak-zone seeking) reduces the mean of the mobilised shear strength among others. Existing simplified formulas for determining the characteristic value of shear strength consider statistical spatial averaging only, not weak-zone seeking. This paper calibrates the weakest-path model (WPM) using simulation results from the random finite element method (RFEM). The calibrated WPM captures both spatial averaging and weak-zone seeking. Moreover, the behaviours for the calibrated WPM are similar to those for the RFEM. Based on the calibrated WPM, a simplified formula is proposed to determine a mobilisation-based characteristic value. The effectiveness of this formula is showcased by real case studies. It is found that for problems whose uncertainty is dominated by spatial variability and whose slip curve is not highly constrained by mechanical admissibility, the proposed formula provides significant improvements over existing simplified formulas in the literature that consider only statistics and do not consider mechanics at a detailed level.

Mobilisation-based characteristic value of shear strength for ultimate limit states