An improved damage constitutive model for pre-heated rocks under uniaxial compression considering the initial compaction effect and residual strength

Enhancing our understanding of the damage evolution in pre-heated rock is essential for safer design practices. Accordingly, a mechanical damage variable that accurately depicts the initial damage recovery process was proposed. Subsequently, a damage constitutive model is developed based on the generalized equivalent strain principle, enabling the identification of the initial nonlinear characteristics exhibited in the stress-strain curve. By integrating the above constitutive model with a statistical damage model that considers the residual strength based on the Weibull distribution, a comprehensive piecewise damage constitutive model specifically designed for pre-heated rocks was derived. The model consists of eight parameters, which can be directly determined through experimental results or readily obtained by fitting of the stress-strain data. A comparison of experimental data from multiple pre-heated rock types subjected to uniaxial compression is performed to validate the proposed model, revealing a strong agreement between the theoretical and experimental results. The comparison results demonstrate that the proposed model effectively captures the nonlinearity of the stress-strain curve throughout various stages, including the initial compaction, linear elastic, and strain-hardening stages before reaching the peak stress, as well as the subsequent strain-softening and residual stages. Furthermore, the proposed damage constitutive model elucidates the influence of temperature on crucial factors such as the elastic modulus, peak stress, residual strength, and stress-strain curve of pre-heated rocks, thereby enhancing its applicability in the design of deep underground rock projects.