## 2 Acquisition of the Original Database
### Designation of Representative Measurement Points
At this slip surface, it could be considered that the first principal stress is the main cause of the slip of the rock and soil mass. According to the ultimate equilibrium condition, the first principal stress could be used to determine whether the rock and soil body has yielded or not. The consideration of the first principal stress as a target variable is of certain investigative worth. On the basis of Figure 4a,c, the first principal stresses at the vault, arch bottom, and both sides of haunch of the tunnel entrance under Case 1 and Case 19 are significant. The  
Figure 3: Vertical displacement curve: (**a**) Case 1; (**b**) Case 10; (**c**) Case 19. Figure 2: Finite-element modelling of karst tunnel: (**a**) tunnel model; (**b**) karst cave model. first principal stresses in the both sides of haunch of the tunnel cross-section at 30 m from the tunnel entrance are more significant. In Figure 4b, the first principal stresses in both sides of the haunch of the tunnel are greater under Case 10. Stress concentration occurs in areas with higher values of the first principal stress, which enter the stress yielding phase earlier than other areas, and stress redistribution occurs. In summary, the location of the tunnel haunch at a distance of 30 m from the tunnel entrance was chosen as the measurement point. According to Mohr-Coulomb strength theory, the Mohr-Coulomb criterion of rock failure is the maximum principal shear stress theory. The difference between the first principal stress and the third principal stress is twice the shear strength of that rock and soil mass. Consequently, the occurrence of the destruction of the tunnel surrounding rock could be determined by the difference in principal stresses in the complex stress state in which the tunnel is located. When the rock and soil body is in ultimate equilibrium, the relationship between the first principal stress and the third principal stress is  
\[\sin\varphi=\frac{(S1-S3)/2}{c\cdot\cot\varphi+(S1+S3)/2}=\frac{(S1-S3)}{S1+S3 +2c\cdot\cot\varphi} \tag{1}\]  
The meaning of each symbol in the expression is as follows: S1--the first principal stress, S3--the third principal stress, \(c\)--cohesion of rock and soil masses, \(\varphi\)--internal friction angle. As illustrated in Figure 5, by comparing the magnitude of the principal stress difference at each measurement point of the tunnel cross-section at the tunnel entrance and 30 m from the tunnel entrance for Case 1, Case 10, and Case 19, the measurement point that best describes the stress state of the tunnel was selected. In Figure 5a, the principal stress difference curves in the cross-section at the tunnel entrance and 30 m from the tunnel entrance for Case 1 and the cross-section at 30 m from the tunnel entrance for Case 19 were shown as \"fan-shaped\" closed curves. The principal stress difference at the tunnel haunch is larger than at the other measurement points, which is more susceptible to shear damage, and is therefore more appropriately adopted as a representative measurement point for evaluating the stability of the tunnel surrounding rocks. The principal stress difference in the cross-section at the tunnel entrance in Case 1 and Case 19 and in the cross-section at 30 m from the tunnel entrance in Case 10 reveal a \"butterfly shaped\" closed curve, as shown in Figure 5. At that moment, the principal stress difference on both sides of the tunnel shoulder and both sides of the tunnel arch footing is greater than the measured value of other measurement points. Therefore, it is more appropriate to designate one of the four points as the measurement point for both sides of the tunnel shoulder and both sides of the tunnel arch footing. Figure 4: First principal stress curve: (**a**) Case 1; (**b**) Case 10; (**c**) Case 19. To sum up, different measurement points should be selected for different target variables in order to effectively reflect the degree of stability of the tunnel surrounding rock and the support of the tunnel.