Numerical Analysis for the Effect of Heterogeneity on Shear Band Formation

In a natural soil deposit, heterogeneity is the cause of localized failure. Under shear, localization initiates at weak spots and then propagates to form a shear band. The focus of the paper is on modeling the effect of heterogeneity on the formation of shear localization. For this purpose, a higher-order stress strain model is used for the analyses. The higher-order model is within the framework of strain gradient theory developed by Fleck and Hutchinson (1993), in which gradient of rigid-body rotation, couple stress, and material internal length are considered in the constitutive law. Most strain-gradient models have been applied to metal material. Very few are focused on granular soil. In analyses of metal material, the localization is usually assumed to initiate from a single weak spot. For a natural soil deposit, the heterogeneity is associated with its packing structure and the weak spots are randomly distributed. The formation of shear band can be initiated simultaneously at different locations in the material. In this work, the weak spots are modeled in finite element mesh. A shear problem of soil deposit is analyzed using periodic boundary conditions. For different patterns of weak spots spacing, the different localized patterns are obtained. For sparsely distributed weak spots, the finite element solutions have similar patterns to the analytical solutions by Chambon et al. (1998). For densely distributed weak spots, the finite element solutions show complicated behavior. Small shear bands initiate at different weak spots. These small bands propagate and join to form a large shear band. Thus the shear bandwidth is not only a function of material internal length but also of the distribution of weak spots.