A general framework for probabilistic damage in rock using maximum entropy theory is proposed to describe the failure process of marble from hydropower station at Jinping II, China. In this paper, the failure process of marble is divided into three stages. In the first stage, a parameter D0 is employed to describe the compaction of rock before elastic period which can be calculated by maximum entropy theory. In the second stage, elastic theory is used to express no damage in the rock. In the last stage, a parameter D is performed to define and calculate the damage of rock based on maximum entropy theory. The proposed model is used to simulate the failure process of marble under uniaxial compression. The simulated result is well agreement with experimental data, validating the proposed computational framework.
The failure process of rock generally experiences compaction, elastic, pre-peak damage and post peak damage or failure stages. A model suitable to describe such a process helps to understand the failure mechanism of rock. The probabilistic damage model is widely used to describe the process of rock failure which can be easily introduced to computer code for numerical simulation. This method is performed to characterize the process of rock failure from a mesoscopic view to a macro view and has achieved some success (Tang et al. 1998, Tang et al. 1998, Tang et al. 2000, Zhu et al. 2004). In those methods, many probabilistic distributions have been employed to characterize the strength distribution of rock elements. Some researchers have made many discussions about those methods (Zhang et al. 2005, Li et al. 2012, Liu et al. 2007, Wong et al. 2006, Basu et al. 2009). In those methods, it's hard to describe the complete process (e.g., compaction stage) of rock under mechanical loading. It's easily to observe the phenomenon of compaction in conventional experiment especially in some hard rock such as marble. In this paper, the maximum entropy theory is combined with probabilistic damage method to compensate the disadvantage above. Based on the experiment of marble failure process, a new model is proposed to describe the whole process of marble failure and the failure mechanism is explained.