In consideration of the influence of energy dissipation on the rock compression process, the traditional elastic stress-strain relationship was improved by adding the energy release rate. The microintensity of the rock was assumed to satisfy the Weibull distribution. The improved stress-strain relationship was transformed into a triaxial stress-strain model in consideration of the loading damage combined with mesodamage mechanics. The characteristic points of the stress-strain curve and the experimental data were utilized to calculate the distribution parameters of the rock under different conditions. The model curve was compared with the experimental data. Results showed that the stress-strain curve of the rock has peak points in the conventional triaxial compression test, but the radial peak of the rock was not evident in the unloading test. The energy of the rock under the loading path was smaller than that under the unloading path. The model curve exhibited a high degree of fitting with the experimental data, and its correlation coefficient was relatively large (> 0.90), which indicated that the model can clearly represent the actual damage and evolution law of the surrounding rock. Furthermore, the established model can also reflect the rock’s stress-strain relationship, which can serve as a practical guide for relevant applications. Finally, the distribution parameters also reflected the evolution law of rock energy and provided a method for the assessment of rock energy and damage trend.

In order to study the creep behavior of the surrounding rock of Hengda coal mine in Fuxin under different temperatures, the triaxial creep test of sandstone is carried out by the MTS815.02 test system. The relationship between damage variables and temperature is constructed based on the Weibull distribution of the meso-probability voxel intensity. Aiming at the nonlinear characteristics of rock creep, a nonlinear viscous pot element and a nonlinear spring element are proposed. The two linear viscous pot elements and one linear spring element in the Nishihara model can be replaced separately. Thus, an unsteady parameter creep model is established. The comparison between the Nishihara model curve and the model and the experimental curves in this article has been added to the article. Furthermore, the superiority of this model can be proved. The results show that the established variable-time aging creep model not only can describe the rock attenuation creep and stable creep deformation characteristics but also can make up for the shortcomings of the traditional creep model that cannot describe the accelerated creep characteristics. Moreover, it predicts the development law of creep deformation well. The model is in good agreement with the test curve, which shows the correctness and rationality of the model. It has guiding significance for actual engineering support and prediction of long-term deformation of surrounding rock.

Stress relaxation is a key time-dependent response that governs the long-term stability of deep underground rock engineering. In this study, staged uniaxial and triaxial stress relaxation tests on sandstone were carried out using an MTS815.02 triaxial rheological servo system. Based on the Hausdorff derivative, a fractal-order dashpot was introduced to replace the Newtonian dashpot in the classical Poynting–Thomson model, yielding a nonlinear viscoelastic relaxation model with a time-fractal parameter α. By decomposing stress/strain into spherical and deviatoric parts, the model was further extended to a three-dimensional stress state and verified against triaxial relaxation data. Model parameters were identified by the Levenberg–Marquardt algorithm, and the fitting correlation coefficient for all strain levels exceeded 0.95. A parameter sensitivity analysis quantified the roles of elastic moduli, viscosity, and α in controlling the initial stress level, relaxation magnitude, and relaxation rate. The proposed formulation provides a practical constitutive description for relaxation-dominated deformation of sandstone under high in-situ stress and offers a basis for time-dependent stability assessment and support design in deep rock engineering.

To address the shortcomings of traditional rock creep models, including neglecting the time-varying cumulative effect of thermal damage, low accuracy in describing accelerated creep, and failing to reflect the thermo-mechanical coupling rheological mechanism of deep high-temperature rock mass, this paper proposes a fractional-order rock creep damage model considering temperature influence, based on continuum damage mechanics and fractional calculus theory. Firstly, a time-varying thermal damage evolution equation dependent on both temperature level and heating duration is developed, and a temperature-coupled stress creep damage equation is established synchronously to realize the synergistic evolution of dual time-varying damage, with damage only acting on the fractional viscosity coefficient to keep the elastic modulus unchanged. Then, combined with the improved fractional-order Kelvin element and optimized Nishihara model, the uniaxial creep damage model is derived via rigorous equation derivation and integration, and the corresponding triaxial model is further deduced for complex engineering stress conditions. Finally, model verification and comparison are conducted based on rock creep tests under 25 °C, 50 °C, 75 °C and 100 °C. The results indicate that the model can accurately characterize the full three-stage creep behavior of rock, with the predicted curves in excellent agreement with test data and all correlation coefficients exceeding 0.95. Compared with the classical Nishihara model and existing models, the proposed model has higher fitting precision and better performance in capturing accelerated creep inflection points, verifying its superiority and reliability, and providing theoretical support for long-term stability analysis of deep high-temperature rock engineering.

Aiming at the problem that the traditional creep model is difficult to reflect the characteristics of accelerated creep stage of rock, the influence of stress state on accelerated creep is fully considered, and a constitutive model which can describe viscoplastic creep is established based on strain energy density function. In order to comprehensively improve the accurate description of the three stages of rock creep, based on the traditional Nishihara model, an improved creep model is proposed by connecting a nonlinear viscoplastic element in series. The continuous medium strain energy theory is used to analyze the sudden change process of creep macroscopic mechanical behavior, and the critical strain energy density value is defined as the control parameter to predict the occurrence time of accelerated creep. At the same time, the origin software is used to introduce different creep data for fitting. The results show that the creep constitutive model can fit the rock creep test curve well and identify the parameters. It can better simulate the creep deformation characteristics of rock under different stress levels. It can accurately reflect the nonlinear creep characteristics of the whole process of rock creep. It shows that the newly established creep constitutive model has strong applicability and correctness. It provides a new creep constitutive model for future geotechnical engineering.