# 3D In Situ Stress Estimation by Inverse Analysis of Tectonic Strains
## 3 Application in the In Situ Stress Determination of Three Gorges Dam  
### Forward Numerical Model  
The Three Gorges Dam cross the Yangtze River in China's Hubei Province is the largest hydroelectric project ever constructed, starting in 1994 and completed in 2009. Figure 5 shows the main component of the project, and from 1 to 5, there are the corresponding underground powerhouse, right dam, flood discharge dam, left dam and ship lift. In this project, the underground powerhouse of this project located at the right bank of the project is inside a small mountain, named Baiyanjian, which is indicated by 1 in Figure 5.  
The results of the field tests for the in situ stress field demonstrated that the tectonic stress should be paid more attention than gravity stress in the underground powerhouse of the project. Before the construction of the underground powerhouse, the in situ stress field was simulated based on the measured values [10; 23]. In order to verify the reasonability of the proposed approach, it is used to inversely analyze the in situ stress field; moreover, the result of the proposed approach is compared with the results of traditional approaches.  
The underground powerhouse is inside a small mountain named Baiyanjian, and the top elevation of the mountain is 243 m. The underground powerhouse is 240 m long, 37 m wide, and 66.8 m high (Figure 6). The powerhouse is mainly composed of the main powerhouse, diversion tunnel, tailrace tunnel and busbar tunnel. The rock masses around the area of the underground powerhouse are mainly granite and diorite, and in this area four main faults are distributed (Figure 7); they are, respectively, named F20, F22, F32 and F84. Faults F20, F22 and F32 are filled with cataclastic rock masses, which are well cemented, and the structural planes are rough and dry. For the spatial distribution of F20, F22 and F32 with yellow color in Figure 8, the strike angle is about N240\({}^{\circ}\)-250\({}^{\circ}\) W, the dip angle is approximately 65\({}^{\circ}\)-70\({}^{\circ}\), the extension length is greater than 300 m, and the general width is 2-5 m. For F84 (Figure 7), the fault appears as a breccia-brittle fracture zone controlled by two cross-sections, and it is sometimes wide and sometimes narrow. The fracture zone is composed of calcite caves, clusters and gaps with poor cementation and intensified weathering, and there is dripping water or flowing water along many areas of the fault. With respect to spatial distribution, the strike angle is approximately N340\({}^{\circ}\)-10\({}^{\circ}\) W, the dip angle is approximately 60\({}^{\circ}\)-80\({}^{\circ}\), and the general width is 0.5-4 m.  
Figure 5: Overall view of the Three Gorges Project.  
Figure 6: Main caverns of underground powerhouse.  
According to the topography data and geologic materials of the powerhouse, the computing coordinate system and 3-D calculating model was established as in the following. The \(X\) axis is along the central line of generating units from the first to the sixth generating unit, and the \(Y\) axis is perpendicular to the axis of the powerhouse, horizontally pointing downstream. The \(Z\) axis coincides with the vertical coordinate. The origin of the coordinate system is at the intersection point between the axis of the powerhouse and the sidewall near the 1\(\#\) generating unit. The scope of the coordinate system is corresponding to the following: it is \([-247~{}573]\) for the \(X\) axis, \([-300~{}400]\) for the \(Y\) axis, and \([-250\) mountaintop] for the \(Z\) axis. In this calculating model, there are 7033 nodes and 19,497  
Figure 8: _Cont._