## 3 Validation of the Numerical Model--A Case Study of Fractured
### Laboratory Specimen Simulations  
Building on the successful simulation of the creep behavior in single-element intact and fractured marble under seepage conditions, further investigations were carried out targeting the creep mechanics of cylindrical fractured marble specimens under engineering disturbances at a 2400 m depth. First, following the numerical methodology described in Section 3.1, a pre-existing fracture was idealized as a 10 mm thick fracture zone with a 30\({}^{\circ}\) incline (Figure 4) based on geological investigations of natural fractures in the Jinping area [31], which was deemed a representative fracture for the CJPL area. The actual deformation of the fracture zone was derived from laboratory test data for intact and fractured marble [23], enabling numerical simulation of its time-dependent deformation. The results, shown in Figure 5, demonstrate the strong agreement between the numerical predictions and experimental observations. While this work utilizes a specific fracture geometry (30\({}^{\circ}\) inclination, 10 mm thickness) representative of key observations in the CJPL area to establish a validated baseline model, it is recognized that alternative fracture geometries (e.g., varying dip angles, apertures, or roughness) would likely influence the quantitative creep response, peak strength, and failure patterns observed in the numerical simulations. The primary focus here was demonstrating the capability of the methodology and establishing a benchmark for the specific  
Figure 4: Simulation method for rough fracture zones in specimens. Figure 5: Laboratory experiment vs. numerical calculation results for laboratory specimen. geo-materials and representative fractures under complex multi-physics conditions at this depth. Further investigations into the sensitivity to the fracture's geometric parameters are warranted and planned for future work. A numerical model of cylindrical fractured marble at a 2400 m depth was then developed, incorporating intact marble elements and fracture zone elements. The model (2709 nodes, 2240 C3D8P elements) maintained boundary/loading conditions consistent with those in the single-element case. Engineering disturbance stress paths [12] were applied to simulating the excavation-induced impacts on the rock mechanics, following these steps:  
Step 1: A confining pressure (64 MPa) was applied to the lateral and top surfaces, matching the pre-disturbance in situ horizontal stresses. Step 2: A 10 MPa seepage pressure was imposed on the top surface. To counteract the tensile stresses, we applied an additional 10 MPa compressive stress to preserve the effective stress [27], validated via a uniform seepage distribution and axial stress equilibrium. Step 3: After seepage stabilization, we implemented the engineering disturbance stress path (refer to Section 3.1). Step 4: We maintained the post-disturbance stress levels to compute the 10 h creep deformation. Figure 5(a),b show the normal strain and displacement of the fractured marble specimen after 10 h of creep. The fracture zone exhibits a maximum normal strain 21 times greater than that in the rock matrix, driving localized slip along the fracture and heterogeneous deformation. The total normal strain (\(1.177\times 10^{-4}\)) aligns closely with the single-element experimental/numerical results in Figure 4(b). Figure 5(c),d reveal the horizontal stress/strain patterns after 10 h of creep. The post-disturbance fractured marble develops localized tensile stress concentrations (the red ellipse in Figure 5(c)) due to compression-induced fracturing in the weakened matrix regions. These concentrations intensify with prolonged loading and higher stresses, ultimately forming new shear bands. Figure 5(d) demonstrates the dilatant strain in both the matrix and fracture zones. The significantly higher creep deformation in the fractured zone drives  
Figure 6: Stress/strain contours of laboratory specimen after 10 h of creep.