A damage model for modeling the complete stress–strain relations of brittle rocks under uniaxial compression

Based on the “elastic modulus method” derived from the hypothesis of strain equivalence and test data of complete stress–strain curves of marble, granite, and sandstone under uniaxial compression, a damage model in the form of Logistic equation is proposed to simulate the stress–strain relation of rocks. This model can describe the complete deformation process of rocks under uniaxial compression satisfactorily. The used mathematical function is simple with just four model parameters, and each parameter has distinct physical meaning. The validity of the model is demonstrated by a mathematical deduction analysis and the model is further verified using laboratory test data. In addition, this model provides a method for estimating the elastic modulus of undamaged rocks using uniaxial compression test results and it presents a reasonable explanation of the chaos phenomenon occurred in uniaxial compression test.