A finite-strain viscoelastic-damage numerical model for time-dependent failure and instability of rocks

Abstract

Understanding the time-dependent behavior of rocks has long been an essential topic, obstructed predominantly by not only complex multiscale failure and instability mechanisms but also their time effects. Existing research stops short of explaining the interaction effect between these mechanisms, and there is still a lack of a unified numerical scheme to comprehensively consider the above factors. Here, we focus on the long-term strength and time-dependent deformation, failure and instability mechanism of rocks. The numerical Finite-Strain Viscoelastic-Damage Model (FSVDM) is proposed within the framework of irreversible thermodynamics. Material heterogeneity is considered at the mesoscale, and a continuum damage constitutive relationship is utilized to describe the material failure process. The finite strain formulation is adopted to capture large deformation and buckling instability. The generalized Maxwell model is employed to represent the viscoelastic behavior over time. The FSVDM is calibrated with laboratory-scale creep and stress relaxation tests, and then applied to analyze the time-dependent collapse of rock slabs. Meanwhile, the Small-Deformation Viscoelastic-Damage Model (SDVDM) is performed as a comparison. The long-term strength depends on not only the typical long-term failure strength but also long-term instability strength. Collapse occurs due to competition and synergy between the time-dependent failure and buckling instability mechanisms. The findings are expected to supply guidance for the assessment of the rheological behavior of rocks and crust.