# 3D In Situ Stress Estimation by Inverse Analysis of Tectonic Strains
## 3 Application in the In Situ Stress Determination of Three Gorges Dam
### Results of Engineering-Scale In Situ Stress  
Figures 10-12 show the comparison between the measured and calculated values of in situ stress at test points, where the red curve refers to the measured value, the blue curve stands for the calculated value with the stress-based approach, the green curve is for the calculated value using the proposed method, and the gray color means the results with the displacement-based approach. The calculating results using the displacement-based approach were from the previous work [10], and the displacement mode was assumed as the linear displacement when the in situ stress in the region of interest was inversely analyzed. Figure 10 shows the comparison by different approaches for the magnitude and direction of the first principal stress. Similarly, Figure 11 is for the second principal stress, and Figure 12 is for the least principal stress. Figure 11: Comparison with measured values of the second principal stress. Figure 9: Optimization processes using the stress-based and proposed approaches. From the comparison, it can be seen that for the magnitude of principal stress, the calculated values with the proposed approach have better agreement with the measured values than those by the stress-based approach and displacement-based approach. For the stress-based approach, the magnitudes of principal stress differ significantly with the measured values in some test points, especially with respect to the least principal stress. For the displacement-based approach, there are obvious differences among the calculated values at points D4, D6, D7 and the corresponding measured values, which may be caused by the spatial locations of these points close to the faults (Figure 8). For the proposed approach, in the first principal stress, there are significant differences for the comparison between the calculated and the measured value at points D4 and D7. However, in the second principal stress, the obvious difference of the comparison appears at points D6 and D7, and for the least principal stress, the calculated values are obviously inconsistent with the measured values at points D4 and D6. Therefore, some conclusion can be drawn that the main fault has important influence on the inverse calculating results of the in situ stress. For the underground powerhouse of the Three Gorges project, because points D4, D6, and D7 are close to faults F84, F20 and F22, and the calculated results by any approach are significantly different than the measured value at these points. For these approaches, the stress-based approach is worse than others. Though the displacement-based approach is popular, the relative error using this method cannot be ignored. For the proposed method, better estimation for in situ stress can be obtained through comparisons with other approaches. Tables 2 and 3 also showed the comparison among different approaches. In both tables, the positive sign means compression, and the negative sign means tension. Additionally, in Table 4, the calculating results are also shown using the stress-based approach. In both tables, stress-based stands for the stress-based approach, displacement-based represents the displacement-based approach, strain-based is on behalf of the proposed approach, and the measurement means the measured value in field tests. From the comparison of data in both tables, for the principal stresses, the same conclusion can be obtained as those from the above Figures 10-12. Table 4 reveals the corresponding statistical relative errors between the calculating principal stresses by the stress-based approach, displacement-based approach, the proposed approach and the measurement values. Here, for each measurement point, the relative error is the percentage between the absolute error and the measurement value (Equation (30)). In Table 4, the relative error is the mean of the relative errors of all measurement points [25].