Overall Shear Strength of Soil Mass With Spatial Variability

Abstract eng:
Spatial variability is a realistic phenomenon for soil shear strengths. Based on statistical analysis, Vanmarcke (1977) showed that the averaged property of a random field over a region has mean value identical to the inherent mean, while the variance of the average is less than the inherent variance. Vanmarcke's derivations for spatial averaging are purely statistical, not involving mechanical principles, e.g., force equilibrium, compatibility, constitutive law, etc. However, the "overall" shear strength of a soil mass should be governed by the mechanical principles. The purpose of this study is therefore to understand the mechanisms that govern the overall shear strength. Random field finite element analyses (FEA) are conducted. The spatially varying shear strength τ_f is simulated by stationary Gaussian random fields. When assigning the simulated τ_f to each element, the local averaging subdivision algorithm developed by Fenton and Vanmarcke (1990) is taken to conduct element-level averaging within each element. What follow are the important findings: 1. Although the spatial averaging of shear strength over a domain D (τ_f^D) has similar statistical behaviors to those predicted by Vanmarcke’s theory, the statistical behaviors of the overall shear strength (τ_f^O) are NOT consistent to those predicted by Vanmarcke’s theory. In fact, the mean value of τ_f^O is always less than that of τ_f^D, and the coefficient of variation (COV) of τ_f^O is always larger than that of τ_f^D. 2. τ_f^O is very close to the line average along the actual slip curve (τ_f^S). The mechanism for τ_f^O is nearly the same as that for τ_f^S – τ_f^O is the result of taking line averaging along the potential slip curves and then taking the minimum value among these averages, rather than taking spatial average of the entire domain D. Due to the action of taking minimum, τ_f^S (or τ_f^O) may have mean value less than that for τ_f^D, especially when the line averaging effect along the potential slip curve is weak, and may have COV larger than that for τ_f^D.

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