Energy driven constitutive modeling of thermally damaged red sandstone under multilevel cyclic loading

This study investigates the mechanical and energy responses of red sandstone subjected to high-temperature treatment and multilevel cyclic loading and develops an energy-driven constitutive model for its deformation behavior. Triaxial cyclic loading tests were conducted on red sandstone treated at different temperatures to examine the effects of thermal treatment and repeated loading on stress–strain response, residual deformation, and energy evolution. The results show that temperature significantly affects the mechanical properties and deformation characteristics of red sandstone. Under repeated loading at the same stress level, the hysteresis-loop area, residual-strain growth, and dissipated energy generally decrease with increasing cycle number, whereas an increase in stress level leads to renewed deformation and energy dissipation. Based on the experimental response, a staged constitutive framework is established for the initial loading, cyclic loading, and subsequent monotonic loading stages by considering compaction deformation, skeleton deformation, and damage evolution. Thermal and mechanical damage are incorporated through a load-carrying ratio, and energy density is introduced to characterize damage accumulation. The proposed model reproduces the main stress–strain characteristics observed in the tests and provides a constitutive description of the mechanical response of thermally treated red sandstone under multilevel cyclic loading.