Rock Damage Constitutive Model for the Full Deformation Process Based on a Modified Damage Evolution Function and its Experimental Verification
摘要
This study develops a rock damage constitutive model that captures the full deformation process. To improve fidelity for behavior after the peak, we construct a composite damage evolution function by blending a logistic term with a linear term. Guided by the observed evolution of the tangent modulus during compaction and by elastic damage mechanics for the elastic damage stage and the stage after the peak, we formulate a unified model of rock deformation. We benchmark the model against established formulations using published compression tests on intact rock and new compression tests on cracked rock. The model shows substantially smaller deviations from experimental curves than existing models; under uniaxial loading it reproduces abrupt brittle failure after the peak, compared with existing models, it achieves an increase of approximately 98% in the coefficient of determination and improvements of 91%, 90%, and 97.5% in MRE, MAE, and MSE, respectively. Whereas under triaxial loading it predicts brittle behavior after the peak in closer agreement with the data, with an average improvement of 1.51 times in the coefficient of determination over existing models. Two parameters that govern crack evolution, namely the compaction parameter and the expansion parameter, are obtained analytically from characteristic points on the curve of stress versus strain, which supports practical application. The framework can be extended by adding a damage index that controls the convexity of the deformation curve after the peak. Overall, the proposed model provides an effective and practical tool for predicting the full deformation process of rock.