Thermal–Mechanical Coupled Creep Characteristics and a Fractional-Order Nonlinear Damage Model for Red Sandstone under Impact Disturbance

Abstract

Deep rock masses in geothermal engineering, nuclear waste disposal, and deep mining are often subjected to the coupled effects of high temperatures and dynamic disturbances, leading to a significant deterioration in their long-term mechanical stability. However, existing research has rarely explored the coupled effects of thermal damage and impact loading on creep characteristics, and there is a lack of constitutive models capable of capturing the evolution of such coupled damage. In this study, uniaxial compressive strength tests and physical measurements were conducted on red sandstone after heat treatment (200°C–800°C), followed by impact creep tests under various temperatures and impact energies. A critical thermal threshold of approximately 400°C was identified, above which mass loss, volume expansion, and density reduction accelerated significantly, and the failure mode transitioned from splitting to shear-dominated patterns. Under impact loading, the first impact contributed the largest proportion of creep deformation, and cumulative creep deformation increased exponentially with rising temperature, while the steady-state creep rate exhibited a gradually slowing growth trend. Based on the Burgers model, a fractional-order nonlinear damage-creep constitutive model was developed by introducing a viscoplastic element and replacing the Newtonian dashpot with a fractional-order Abel dashpot. This model can effectively capture the entire creep process under coupled thermal and impact effects. The identified critical temperature of 400°C provides a practical reference for assessing the thermal stability of underground engineering, while the proposed constitutive model offers an effective tool for predicting time-dependent deformation of rock masses under the coupled effects of high temperatures and dynamic loads.