Numerical modeling of tunnel excavation in weak sandstone using a time-dependent anisotropic degradation model

This paper presents a shear-induced anisotropic degradation model involving time-dependent behavior to simulate the deformational characteristics of weak sandstone. The stress–strain relationship of the proposed model was originated from the degradation of moduli K and G subjected to different loading conditions. An anisotropic factor β is introduced to indicate the tendency of shear-induced volumetric deformation. Furthermore, to incorporate time-dependent deformation behavior of sandstone, this anisotropic degradation model is further extended using a generalized Burger’s model. As a result, the proposed model is characterized by the following features: (1) being capable of describing shear-induced volumetric deformation, either compression or dilation, prior to the failure state; (2) being versatile in the time-dependent (creep) deformations; and (3) the anisotropic factor β serves as a convenient index regarding whether shear-induced volumetric deformation dilates or not. Afterward, the proposed model has been verified by comparing to experimental results. It is found that the proposed model is versatile in simulating short-term and long-term deformations of sandstone under different stress paths. Moreover, this model has been incorporated into finite element program and used to analyze a case of tunnel squeezing. Comparing with other existing models, it is found that the prediction of the proposed model is closer to reality and reveals a larger crown settlement, namely a squeezing condition, owing to larger extent of dilation zones. Overall, although the proposed model is a simple variable moduli model, it is capable of describing the key deformation behavior of weak sandstone reasonably-well, including time-dependent and shear-induced deformations.