## 3 Application to the Shuangjiangkou Hydropower Station
### Inversion Analysis of the In Situ Stress Distribution  
3.2.1. Numerical Model  
The inversion model should provide a comprehensive analysis of the impact of topography, geomorphology, lithology, and geological structures on the engineering field. After considering the precise locations of the testing points, a numerical model centered on the main powerhouse was established. As shown in Figure 5a, the 3D model can be mainly divided into three layers. The upper layer, represented by the color red, consists of strongly weathered granite. The middle layer, depicted in blue, is composed of moderately weathered granite. Finally, the lower layer, shown in green, comprises fresh rock. The geological structures, namely the F1 fault and lamprophyre, are simulated in the model through the fine mesh with specific thicknesses, as shown in Figure 5b. Besides, the spatial relationships between the F1 fault, lamprophyre, and underground caverns were determined based on a geological survey report. The underground cavern group of the Shuangjiangkou hydropower station consists of three parallel caverns (the main powerhouse, transformer chamber, and tailrace surge chamber) and some auxiliary caverns such as the penstock and generatrix tunnels. The range of the model requires an adequate length to minimize boundary effects and ensure an appropriate distance between the underground caverns and boundaries. The Flac(3D) model has dimensions of 700 m in the x-axis (vertical axial direction), 700 m in the y-axis (axial direction), and 1100 m in the z-axis (elevation direction). The model has been extended to include the ground surface above the underground caverns, consisting of 477,685 nodes and 753,151 brick elements. The mesh is primarily composed of eight-node hexahedral elements, which exhibit uniform size and excellent morphology. Besides, to improve the computational accuracy, the mesh in the underground cavern area was further refined, with a minimum mesh density of 0.5m. In FLAC(3D) software, the Mohr-Coulomb criterion is commonly used to model the behavior of rock under different loading conditions, which is the criterion utilized in this back analysis. The required mechanical parameters of all materials for this criterion, such as Young's modulus, Poisson's ratio, and strength parameters, are listed in Table 2, according to the geological survey report of Shuangjiangkou Hydropower Station.  
3.2.2. Orthogonal Design Experiment  
Obtaining accurate in situ stress distribution through neural networks requires a sufficient number of comprehensive training samples. Therefore, the in situ stress at the measurement points under different boundary conditions was generated through FLAC(3D) software. The training sample scheme was established using an orthogonal design. Firstly, the six boundary condition coefficients of in situ stress inversion in FLAC(3D) were determined according to the inversion theory in Section 2.1. Then, the test data in Table 3 was used as the base values for each parameter. The weight coefficient \(k_{\rm g}\) was 1.3, the horizontal stress coefficients \(k_{\rm x}\) and \(k_{\rm y}\) were 1.3 and 1.6, respectively, and the shear stress coefficients were 2.3 MPa, \(-\)3.7 MPa, and 2.8 MPa, respectively. The weight coefficient, the horizontal stress structure coefficients, and the shear stress coefficients were varied within a range of 10%, 20%, and 30%, respectively, based on the base values. As shown in Table 4, an L49 (76) orthogonal scheme was designed. The 49 sets of boundary condition schemes were then input into FLAC(3D) software. The boundary conditions and the simulated in situ stress at the testing points constitute the training samples for the network.