## 3 Establishment of Hydro-Mechanical Properties Creep Damage Constitutive Model
### Model Validation  
Based on the creep test results of [PERSON] et al. [27] on the coupled characteristic of rock hydro-mechanical properties, the rock hydro-mechanical properties creep damage constitutive model established in this paper is validated. The parameters in the hydro-mechanical properties model are given in the paper, as shown in Table 1 in Section 2.2, and the model parameters can be determined through the experimental results in the paper. The parameter values and definitions of the constitutive model are shown in Table 2.  
The simulated rock specimens are chosen from the test specimens of creep mechanical properties of granitic gneiss under the coupling effect of hydro-mechanical properties in the literature [27]. Namely, the confining pressure is 4 MPa, and the pore pressure is 1 MPa, 2 MPa, and 3 MPa, respectively. The program of rock creep damage constitutive model of hydro-mechanical properties is written in Fortran language. The model is verified by numerical simulation analysis of the creep mechanical property test curve of granite gneiss under different seepage pressure conditions. The specific numerical simulation results are shown in Figure 1.  
It can be seen from Figure 1 that the creep mechanical behavior of granite gneiss under different seepage pressures can be well described. The numerical simulation result based on the hydro-mechanical properties creep damage coupled constitutive model is in good agreement with the corresponding experimental results. Granite gneiss is a homogeneous rock material with consistent triaxial mechanical behavior under the same conditions. The model parameters in Table 2 are determined by the basic mechanical properties of granite gneiss and do not change with external force conditions, only related to the mechanical properties of the rock material itself. From the simulation results, it can be seen that this model is suitable for simulating the creep mechanical behavior of granite gneiss under the coupling effect of hydro-mechanical properties. [PERSON] et al. [30] and [PERSON] et al. [31] simulated salt rock by establishing corresponding constitutive models, defined parameters based on different rock material properties, and simulated them. The simulation results were good, which is consistent with the phenomenon presented in the manuscript. In general, the coupled constitutive model of rock hydro-mechanical property creep damage can accurately describe the instantaneous damage, time-dependent damage and creep deformation characteristics of rocks under the coupling effect of hydro-mechanical properties, further verifying the accuracy of the theory and simulation of this model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Values** & **Definition** \\ \hline \(A_{0}\) & 950 & They are obtained by obtaining the trajectories of the peak strength of each rock sample in the plane of average stress p and deviator stress q from triaxial tests under different confining pressure conditions. \\ \(\alpha_{p}^{0}\) & 0.021 & It describes the initial yield surface position of rocks. \\ \(B\) & 0.0005 & It is a parameter characterizing the plastic hardening rate of rock. \\ \(\eta\) & \(-\)0.0025 & It represents the slope of the boundary line between the compression and expansion regions of the rock sample. \\ \(d_{c}\) & 0.9 & It represents the maximum critical value of the damage variable. \\ \(B_{d}\) & 125 & It can be determined by the relationship between the damage driving force and the damage variable. \\ \(\gamma\) & 5.0 \(\times\) 10\({}^{-7}\)/s & It is determined by the creep rate. \\ \hline \hline \end{tabular}
\end{table}
Table 2: The lists of model parameters.