A simple model for stress-induced anisotropic softening of weak sandstones

Weak sandstones possess deformational behavior different from hard rocks; these phenomena include shear dilation and softening of the deformational moduli. It has been found previously that under hydrostatic loading, the bulk modulus increases as confining pressure arises; and that under shear loading, the weak sandstone may transform from its original isotropy to a stress-induced anisotropic material, and the deformational modulus can accordingly be softened as well. These phenomena contribute to the increase of crown settlements during tunnel excavations, and account for several cases of tunnel squeezing. Consequently, a model capable of simulating major deformational characteristics of weak sandstones is needed for engineering purposes. A simple yet innovative constitutive model is accordingly proposed. This proposed model is characterized during the simulation as having: (1) non-linear volumetric deformation under hydrostatic loading; (2) significant shear dilation prior to the failure state; (3) isotropic stiffening of deformational moduli under hydrostatic loading; and (4) anisotropic softening of deformational moduli under shearing condition. The proposed model was formulated based on the linear elastic model, and it accounts for the variations of moduli E and G through different loading conditions. It was found that the proposed model is able to closely simulate the actual deformational characteristics of weak sandstones. In addition, the proposed model only needs six material parameters, and all these parameters can be easily obtained from experiments. This model was then incorporated into a finite element program and was used to analyze a squeezing tunnel case.