Investigation of the Mechanism of Fault Formation Using Bifurcation Analysis

摘要

We investigate a mechanism of fault formation by detecting the surface instability of ground using bifurcation analysis based on finite deformation theory. The bifurcation analysis is carried out in the case of a simple boundary value problem - the plane strain compression test of half-space made of incompressible isotropic and anisotropic hypo-elastic materials. Closed form solutions of bifurcation stress are obtained for many diffuse deformation modes defined by the number of the half wavelength of sine wave. The bifurcation stress of any diffuse deformation mode decreases with decreasing Young's modulus of horizontal direction compared to that of the vertical direction. In several diffuse modes, ground movement and the contour of maximum shear strain are examined to predict where fault formation occurs. The ground movements obtained by the bifurcation analysis show the surface instability of ground as sine waves, the amplitude of which decays rapidly with depth. In many cases, maximum shear strain is strongly localized beneath areas of ground sinking, due to bifurcation phenomenon. Moreover, comparatively large maximum shear strains appear in the deep parts of heaving grounds. The mechanism of fault formation can be explained using the distributions of localized maximum shear strains.