Temperature-dependent hardening and constitutive modelling of frozen rocks: Insights into plastic energy dissipation

Abstract

Fluctuating sub-zero temperatures trigger the phase transitions of ice and water in rocks within cold regions, resulting in a strong temperature-dependent nonlinear stress–strain relationship in frozen rocks. However, existing constitutive models for frozen rocks are established and derived at a given temperature, failing to consider the dynamic impact of temperature changes on plastic hardening and nonlinear mechanical behaviour, thus failing to accurately capture the stress–strain characteristics of rocks under temperature fluctuations. To address this issue, this study derives a hardening law from the perspective of energy dissipation and proposes a unified temperature-dependent constitutive model within a thermodynamic framework to accurately describe the stress–strain behaviour of frozen rocks under continuously changing temperature conditions. To validate its applicability, triaxial tests were conducted at specific temperatures on frozen coal rock and frozen sandstone, along with two multi-temperature uniaxial tests on frozen coal rock. A comparison between the computed results and experimental data reveals a high degree of agreement, demonstrating the reliability and accuracy of the proposed model. The results confirm that the proposed model not only captures the stress–strain behaviour of different frozen rocks at fixed temperatures but also effectively characterizes their mechanical response under dynamic thermal conditions, providing quantitative insights into the relationship between plastic energy dissipation and temperature. The constitutive model proposed in this paper offers new insights into the impact of temperature variations on the mechanical behaviour of frozen rocks and can be integrated into commercial finite element calculation software to provide more reasonable solutions for the mechanical behaviour of cold region rocks under arbitrary temperature changes.