Gradient damage models for studying material behavior in underground mining

Block caving is a technique employed in underground mining for the extraction of minerals. It utilizes the force of gravity to facilitate the controlled fracturing of rock, thereby enabling the efficient retrieval of ores from the mine. In our pursuit of numerical simulation of this extraction process and a more profound comprehension of its influence on the mine environment, we examine variational damage models founded upon the gradient damage model proposed by Pham and Marigo in 2010. However, the original theory of Pham and Marigo is insufficient for accurately modeling the complexities of large-scale problems where compression-induced damage is pervasive throughout the rock mass and impedes the recovery of subsidence in the cavity ceiling. To address this limitation, we introduce a variation of the model. This variation incorporates an anisotropic dependence of the damage criterion on the spherical and deviatoric components of the stress tensor, effectively controlling compression damage. The simulations demonstrate the effectiveness of the proposed extension in accurately representing the observed damage in the rock mass and the expected subsidence in a block-caving operation. The new model provides a more comprehensive and realistic representation of the underground mining process, contributing to improved predictive capabilities and more informed mining decision-making.