Mean and Variance of Mobilized Shear Strength for Spatially Variable Soils under Uniform Stress States

This study proposes a set of simple equations for the mean value and variance of the mobilized shear strength for spatially variable soil masses subjected to uniform stress states. These equations are fairly effective in explaining the complicated behaviors for the mobilized shear strengths, regardless of stress states (e.g., compression or shear), spatial variability patterns (e.g., isotropic or anisotropic), and inherent mean and variance of the random field. Two mechanisms that affect the behaviors of the mobilized shear strength are identified: (1) the averaging effect along the potential slip curves, and (2) the emergent feature of a critical slip curve. The emergence is associated with the slip curve with the minimum averaged strength. In any realization of the random field, it is not possible to know a priori the location of the minimum average; hence, it would not coincide with a prescribed average. It is shown that the well-known phenomenon of critical scale of fluctuation is the result of the trade-off between these two mechanisms.