| Summary: | 碩士 === 國立臺灣大學 === 土木工程學研究所 === 100 === Soil shear strengths vary in space. For most foundation engineering problems, resistances provided by soil mass are the overall shear strengths, which are typically related to spatial averaging over certain region. For example, the failure region for an embankment typically consists of three regions (active, transient, and passive), and the overall resistance is related to the averaging over these three regions.
Spatial variabilities of soil properties can be simulated by random fields. Random fields are consisted by random functions and modeled by inherent mean value, inherent variance, and scale of fluctuation. 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 theories of spatial averaging are purely statistical, not involving mechanisms. However, the overall shear strength of a soil mass should be governed by the mechanisms, hence the first purpose of this study is to understand the difference between the spatial average of Vanmarcke’s theories and the overall shear strength.
After simulating the samples from MATLAB and ABAQUS, this study proposes a set of simple equations to predict the mean value and variance of the overall shear strength for spatially variable soil masses subjected to uniform stress states. These equations are rather effective in explaining the complicated behaviors for the overall shear strengths, regardless of stress states (e.g., compression or shear), spatial variability patterns (e.g., isotropic or anisotropic). Two factors that affect the behaviors of the overall shear strength are identified: (a) the line averaging effect along the potential slip curves, and (b) uncertain failure path, It is shown that the slip curve is associated with the minimum line averaged strength of potential slip curves, and the critical scale of fluctuation is the result of the tradeoff between these two factors.
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