## 3 Results Analysis
### Cumulative Damage Under Initial Static Load  
Figure 15 shows the strain evolutionary characteristics of specimens under different initial static loads. This figure indicates that both the tensile and compressive strains increase with the increase of initial static load, and the ultimate compressive strain is much smaller than its ultimate tensile strain, which indicates that the tensile strain, instead of the compressive strain, is the controlling failure factor of the tunnel inverted arch.  
The development of damage extent and strain is also an aspect reflecting the serviceability of the tunnel lining. Both the damage extent and changing ratio of the tensile strain of the tunnel inverted arch are strongly influenced by the stress level of the initial static load. Their relationship curves are obtained and drawn in Figure 16.  
The test results indicate that the damage amount gradually increases with the increase of initial static stress levels. The growth rates of damage amount in the early stage and the damage stage are bigger than that in the middle stage, and the failure stage has obvious nonlinear characteristics. The following is the fitting curve between the damage level and the stress level:  
\[d=1.066-(1-s)^{0.258} \tag{7}\]  
where \(d\) is the damage level, and \(s\) is the stress value.  
Figure 16: Strain and damage curves: (**a**) damage curve; (**b**) changing ratio curve.  
Figure 15: Structural dynamic response with different static loads: (**a**) compressive strain curves; (**b**) tensile strain curves.  
The following is the regression formula between the changing ratio of tensile strain and stress levels:  
\[L=0.35-(1-s)^{25} \tag{8}\]  
where \(L\) is the increasing ratio of tensile strain, and \(s\) is the stress value.  
Table 8 shows the damage value and strain ratio of the tunnel inverted arch under different stress levels.  
This table shows out that strain will increase as the stress level improves. The strain changing rate also has two rapid growth stages, which indicate that there are three stages in the initial damage period of the tunnel lining as shown in Figure 17.  
Test results indicate that the strain amplitude and strain ratio \(\varepsilon/\varepsilon_{0}\) are influenced by the initial static load levels. Figure 17 shows their development characteristic with fatigue life N. The following remarks can be observed from this figure:  
1. The change of strain amplitude and strain ratio would be more significant if the static stress level is higher, and the tunnel inverted arch would be easily damaged in less action times of the dynamic load.
2. When the static load is 25 kN, the corresponding stress level is 0.65 and the change of strain amplitude and strain ratio tends to be stable after growth in the early stage. Once the static load is higher than this value, the strain amplitude and strain ratio are large in the initial stage and failure stage. Therefore, the fatigue life of the tunnel inverted arch would be short if the strain amplitude and strain ratio are significant in the failure stage.  
In order to ensure that the tunnel has a long service capacity, the initial static stress levels should be less than 0.65.