## 3 Failure Characteristics and Numerical Analysis
### Numerical Simulation  
The surrounding rock mass failure in LPL5-1 had obvious stress-dominated characteristics. To study the excavation-induced stress evolution in the surrounding rock mass, a numerical simulation of the underground powerhouse excavation was conducted using ANSYS. The numerical model includes the left bank underground powerhouse and surrounding rock mass, with faults and internal and interlayer shear zones also generated (Figure 7). The dimensions of the model are 600 m \(\times\) 600 m \(\times\) 600 m (in the axial, water flow and vertical directions). The element type used in the model is hexahedron SOLID185. The model contains 742,701 nodes and 1,487,340 elements. In general, the range of the model should cover main caverns and geological structures; meanwhile, the dimension of elements should take into account computational accuracy and efficiency. Thus, the model adopts the aforementioned dimension setting. The mesh size is smaller near the periphery of cavern and away from the cavern it is larger. The in situ stress field is simulated by inverse analysis based on field measurement results. According to the stratified excavation scheme, the simulation of excavation is carried out in layers. The constitutive model employed in the calculation is the Mohr-Coulomb model; the mechanical properties adopted are listed in Table 1.  
After the model is established, it is verified. The simulated magnitude of in situ stress is consistent with the measured value. During the simulated excavation of layer L, compressive stress is concentrated at the upstream spandrel of the main powerhouse, which is consistent with the location of the spalling on site. Moreover, the calculated magnitude of the surrounding rock mass deformation is in general accord with the monitoring results. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Materials** & **Parameters** & **Values** \\ \hline \multirow{6}{*}{Intact rock} & Elasticity modulus (GPa) & 5–19 \\  & Poisson’s ratio & 0.25 \\  & Friction angle & 1.2 \\  & Cohesion (MPa) & 10 \\  & Density (g/cm\({}^{3}\)) & 2.7 \\ \hline \multirow{2}{*}{Interlayer shear zone} & Deformation modulus (GPa) & 0.25–0.3 \\  & Friction angle & 0.46–0.5 \\  & Cohesion (MPa) & 0.1–0.17 \\ \hline \multirow{2}{*}{Internal shear zones} & Deformation modulus (GPa) & 0.15–0.3 \\  & Friction angle & 0.36–0.5 \\  & Cohesion (MPa) & 0.05–0.1 \\ \hline \multirow{2}{*}{Faults} & Deformation modulus (GPa) & 0.15–0.3 \\  & Friction angle & 0.36–0.5 \\ \cline{1-1}  & Cohesion (MPa) & 0.05–0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of the surrounding rock masses used for the numerical simulation. Figure 7: Numerical model: (**a**) outside of the model, (**b**) main components of the model, (**c**) a side view of the underground powerhouse and (**d**) a three-dimensional diagram of the underground powerhouse. MP, TC, DTBGC, TSC and TCP are abbreviations for the main powerhouse, transformer chamber, draft tube bulkhead gate chamber, tailrace surge chamber and tailrace connection pipe, respectively. These agreements prove that the numerical model is valid and the simulation results are reliable. The simulation results indicate that the surrounding rock mass stress is adjusted and redistributed during excavation, with the radical stress unloading and the tangential stress increasing near free face. Since the direction of the in situ maximum principal stress intersects with the axis of the main powerhouse at a large angle and slightly inclines to the upstream side, a stress concentration zone (SCZ) is generated at the upstream arch of the main powerhouse. As shown in Figure 8a, after the excavation of layer I, the maximum principal stress in the SCZ is 38-44 MPa, which exceeds the crack initiation stress of the Baihetan basalt (34 MPa) [16]. Accordingly, stress-dominated surrounding rock mass failures occur near the free face, such as spalling and splitting. As the stratified excavation is progressed, the stress concentration is intensified and the SCZ scope expands.