Numerical Simulation and Evaluation on Continuum Damage Models of Rocks

Abstract

Damage mechanics play an important role in the analysis of rock deformation and failure. Numerous damage variables have been proposed and the corresponding continuum damage models were suggested. Knowing how to apply these theoretical models appropriately in numerical simulations is the key to whether they can be adopted to solve practical problems. The continuum damage models were grouped into empirical damage models, statistical damage models, and elastoplastic damage models in this article. Their applicability and limitations were studied according to some numerical simulations of the most basic uniaxial compression test of a cylinder rock sample. Three representative damage models were chosen from the literature and applied to FEM numerical simulations by introducing a self-developed program. The stress-strain curves due to damage were obtained from the numerical simulation results and compared to those from the experimental results. The damage distribution and evolution of different damage models were investigated to evaluate their influences on rock deformation. It can be concluded that strain-softening stages presented by both the empirical damage models and the statistical damage models are caused by subtracting the elastic modulus gradually while those presented by the elastoplastic damage models are caused by reducing plastic yield stress gradually. Damage-elastic coupling cannot well reflect the irreversibility of damage. The elastoplastic damage models combine damage with plastic history, and thus the irreversibility of damage can be represented. Furthermore, the compulsory reduction of the elastic modulus can probably lead to extreme element distortion and even an unreasonable negative modulus when damage is very serious, which inevitably causes the numerical simulation to fail prematurely under complex stress states. Although the elastoplastic damage models are recommended at present rather than the other models, a more appropriate definition of the damage variable can be expected that should track the whole deformation and failure process. Knowing how to treat the adverse effect of local deterioration due to damage is the challenge numerical simulations have to face when they are applied in the actual project with complex stress states.

Keywords

• rock damage
• numerical simulation
• damage variable
• stress-strain curve
• strain softening