Applicability of rock damage model based on power law distribution

Rock damage model is of great significance to the forecast of rock failure in engineering design such as tunnel, drilling, stability of slope, and mine. However, the applicability of statistical damage constitutive models and efficient model selection criteria of rock have not been fully investigated, which leads to difficulties in resolving issues practice via employing models. In the paper, we developed a rock damage constitutive model based on power law distribution and investigated the corresponding applicability in describing rock damage behavior. The uniaxial compression tests for different rocks (e.g., sandstone, granite, mudstone, shale, and marble) are carried out to verify the applicability of the model, and the criterion for model selection is proposed based on the rock porosity strain ratio. The results show that the proposed model exhibits better performance in predicting variation for the brittle rock damage compared with the common damage model based on Weibull distribution. Besides, the applicability of the proposed model can be extended to elastic–plastic rock by adopting the sigmoid function. The research in this study provides an effective model to describe rock damage behavior for brittle and elastic–plastic and presents a criterion for model selection.