## 3 Validation of the Numerical Model--A Case Study of Fractured  
### Single-Element Crep Behavior Simulation  
First, the UMAT subroutine was utilized to simulate the long-term mechanical behavior of a single hexagonal element (dimensions: 1 m \(\times\) 1 m \(\times\) 1 m; element type: C3D8P), representing both fractured and intact marble under in situ stress conditions at a 2400 m depth. In this section, the fractured marble was modeled as an equivalent continuous medium, with the material parameters adopted from existing studies [23]. The parameters for intact marble were determined based on laboratory creep test results for Jinping intact  
Figure 2: The implementation workflow for customized constitutive models using the Abaqus/UMAT subroutine.  
marchle [24]. The seepage parameters for fractured and intact marble were derived from studies on post-excavation damaged zones and intact rock masses [25; 26], with detailed values listed in Table 1.  
To ensure numerical-empirical consistency, the following workflow was aligned with prior laboratory testing steps:  
Step 1: A confining pressure (19.5 MPa) was applied to the element's lateral and top surfaces to simulate the post-excavation stresses at a 2400 m depth.  
Step 2: A seepage pressure boundary condition (10 MPa) was set for the element's top surface. To counteract the tensile stresses induced by seepage, an additional 10 MPa compressive stress was applied to the top to maintain a constant effective stress [27].  
Step 3: After seepage stabilization, a deviatoric stress of 145.9 MPa [12] was applied to the element's top surface to simulate the creep behavior over a 10 h period.  
For the boundary condition settings, the fixed boundary conditions during confining pressure loading are the horizontal displacements at the lateral boundaries (U1 = U2 = 0) and the vertical displacement at the base (U3 = 0). During the subsequent seepage pressure loading and creep phases, full constraints are applied to the element base (U1 = U2 = U3 = 0) which coincide with the real engineering conditions.  
Figure 3 compares the numerical and experimental results on the axial strain for intact and fractured marble. The simulations effectively replicate the decaying creep and steady-state creep phases observed in both intact and fractured marble after engineering disturbances, with the strain magnitudes closely matching the experimental data. To assess the model's robustness under parameter variations, we compared the 30\({}^{\circ}\) fracture baseline against the intact specimens. And the model maintained high accuracy with low RMSE values for both samples, as shown in Figure 3.  
It should be noted that while the equivalent continuum model assumed for the fractured marble in this research efficiently captures the macroscale creep behavior of fractured marble, its simplification introduces two primary uncertainties. On the one hand is the issue of fracture geometry homogenization. The fracture geometry selected in our manuscript was a representative fracture in the Jinping area, which made it difficult to reflect the  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Type** & **E\({}_{0}\)/GPa** & **E\({}_{1}\)/GPa** & **\(\eta_{1}\)/GPa-h** & **\(\sigma\)/MPa** & **\(p\)/MPa** \\ \hline Intact Marble & 135.5 & 1133 & 1665 & & \\ \hline Fractured Marble & 87.9 & 2650 & 3320 & & \\ \hline \end{tabular}
\end{table}
Table 1: Parameters for numerical simulation of creep mechanical behavior in marble at 2400 m depth.  
Figure 3: Comparison of numerical calculation and laboratory test results [23; 24].  
differences in the fracture network across the entire Jinping area, and the discrete fracture networks may have overestimated the rock mass's stiffness, which may have resulted in the higher strain in the numerical simulation results shown in Figure 3b. The other is the depth-dependent parameter variability: with an increase in the engineering depth, the mechanical and seepage parameters may change [28; 29; 30], which should be considered further in subsequent research.