Mobilized shear strength of spatially variable soils under simple stress states

The spatial averaged shear strength is associated with a prescribed finite size spatial domain. It is not intended to cover the mobilized strength along a slip curve arising as a solution to a boundary value problem in a spatially variable medium. Nonetheless, the concept of strength in soil mechanics is fundamentally related to the mobilized strength along a slip curve. In this study, a plane strain soil specimen 12.8 m wide by 48 m high is subjected to undrained compression and shear via finite element analysis (FEA). The yield stress recorded before FEA fails to converge is defined as the mobilized strength. This mobilized strength is compared with spatial average over the entire domain and the line average along the critical slip curve. Numerical results show that the statistics of the mobilized strength is close to the statistics produced by the minimum of line averages along potential slip curves. There are two important details associated with this proposed minimum line average mechanism. First, the orientations of the critical slip curves are primarily controlled by mechanics, rather than spatial variation, but the vertical positions are fairly random, depending on the realizations of the random fields. In other words, the orientations of the slip curves are close to those produced in a homogeneous medium. Spatial variation perturbs the slip curves in two aspects: (1) orientation and (2) regularity of the curve. Both aspects are secondary. As such, potential slip curves can be viewed as roughly parallel to the critical slip curve. Second, the line average for the critical slip curve is the minimum value over the line averages for the potential slip curves. Based on this relatively simple line average mechanism, it is possible to compare the statistics of spatial average with those of the mobilized strength. The spatial variability scenarios under which spatial average is approximately applicable are identified. It is important to note that only simple and uniform stress states are studied in this paper.

▸ Mobilized shear strengths of spatially variable soils are simulated by finite element analysis (FEA). ▸ Simulated mobilized shear strengths are found to be different from the spatial averaging over the entire domain. ▸ Simulated mobilized shear strengths are found to be very close to the line averaging over the actual slip curves. ▸ The correct mechanism in #3 is used to explain the peculiar observations regarding the difference in #2. ▸ The correct mechanism in #3 is used to explain the issue of mesh resolution in FEA for spatial variability.