# Digital Twin-Driven Stability Optimization Framework for Large Underground Caverns
## 3 Practical Implementation and Case Study
### Digital Twin Application for Monitoring and Stability Assessment
#### 3.2.3 Virtual Design Optimization (Stress and Convergence Analysis)
The deformation analysis under the same conditions shows that without rock support, the maximum representative deformation of 425 mm occurs in the powerhouse in the mudstone layer, with deformation vectors indicating the most critical areas (Figure 7c). When maximum rock support is applied, the deformation reduces to 280 mm, demonstrating the effectiveness of reinforcement in controlling displacement(Figure 7d). The stress analysis further provides insights into the stability of the cavern. The \(\sigma_{1}\) stress plot reveals that the maximum induced stress ranges between 9 and 12 MPa in the center pillar with maximum rock support, while the stress trajectories illustrate the horizontal and vertical stress distributions (Figure 7e). The \(\sigma_{3}\) stress plot (tensile stress) shows that the minimum stress is zero around the cavern periphery, with negative tensile stress zones (\(\sigma_{3}<0\)) marked in red indicating potential failure regions (Figure 7f). In the second phase (during construction), the feedback from the physical world is provided through the proposed digital twin framework. The behavior of the actual stress required a shift from 2D to 3D numerical modeling, capturing the powerhouse cavern's complex stress interactions more accurately. The transition to 3D modeling was essential due to the irregular niche geometries, excavation-induced stress redistribution, and the interaction between the powerhouse cavern and adjacent structures. The numerical simulation example is shown in Figure 8, where the mesh overview of the powerhouse cavern generated from BIM-based model (Figure 8a) provides a detailed representation of element discretization, ensuring the accurate modeling of stress and deformation responses. The initial stress condition (\(\sigma_{1}\)) at the powerhouse (Figure 8b) highlights pre-existing stress magnitudes and orientations, guiding stability assessments. The total shear strain distribution (Figure 8c) indicates that high-strain zones are concentrated in the buttress and the pillar between draft tube niches 3 and 4, with red zones representing critical strain accumulation. Finally, the deformation pattern in excavation stage 4 (Figure 8d) demonstrates the progressive displacement of the cavern walls and floor, emphasizing the influence of the  
Figure 7: Two-dimensional numerical analysis of power house for K = 1.75 in plane and K = 2.25 out of plane, showing (**a**) deformation without rock support, (**b**) deformation with rock support, (**c**) strength factor without rock support, (**d**) strength factor with rock support, (**e**) \(\sigma_{1}\) (maximum stress), and (**f**) \(\sigma_{3}\) (tensile stress). excavation sequence on stability. The numerical simulations revealed that the pillars between the bonneted gate niches experienced excessive vertical stresses (>40 MPa), leading to cracking and deformation. Furthermore, tensile failure was detected in busbar tunnels and cavern walls, necessitating additional reinforcement. The stress redistribution pattern also indicated that deeper excavation would reduce pillar stresses while increasing stress on the main powerhouse-transformer hall pillar, requiring further stabilization. Due to the digital twin-enabled design optimization, these findings from 3D numerical modeling were implemented, and multiple engineering interventions were implemented. Concrete jackets reinforced with 130 t post-tensioned tie anchors were installed to stabilize niche pillars, while strand anchors (15 m-26 m in length) were strategically placed in the downstream and upstream powerhouse walls to counteract deformation. Additionally, the excavation geometry was optimized, modifying niche layouts and excavation angles to minimize excessive stress concentrations. Drainage and grouting systems were also incorporated to control pore pressure effects, ensuring long-term stability.