## 3 Model Test Results
### Dynamic Strain Responses  
Based on the larger dynamic response produced by z-direction excitation and creep-slip of a normal fault, the longitudinal strain responses of the tunnel lining at section 2-2 under the z-direction El-Centro and Kobe excitation (cases #1-3, #1-6, #2-3, and #2-6) are plotted in Figure 10. The positive and negative values are denoted as tensile and compressive strains, respectively. Figure 10 shows the peak strain responses at the invert (SO-5 monitoring point in Figure 6) were greater than the ones at the crown (SO-1 monitoring point in Figure 6), regardless of the existence of the isolation layer. This indicates that the deformation of the tunnel lining at the invert is more severe than at the crown. Similar responses were also pointed out by the literature [53]. Due to the low strength of the fault, there is extensive interaction between the bottom of the tunnel and the strata, as well as the need to withstand the gravity of the top of the tunnel. This resulted in a considerable strain on the lining invert. In addition, the strain response of the tunnel lining with an isolation layer is distinctly lower than that of the tunnel lining without an isolation layer. In the case of El-Centro excitation, the peak strains of the crown and invert were reduced from 97.7 to 61.1 \(\mu\varepsilon\), with a reduction of 37.5%, and from 212.4 to 124.9 \(\mu\varepsilon\), with a reduction of 42.2%, respectively. Similarly, in the case of Kobe excitation, the peak strains at the crown and invert were also reduced by 47.7% from 140.6 to 73.6 \(\mu\varepsilon\) and by 46.0% from 359.5 to 194.3 \(\mu\varepsilon\), respectively. This indicates that the rubber-sand isolation layer can effectively reduce the strain response of the tunnel under normal fault creep-slip and subsequent seismic excitation. The reason is that the rubber-sand mixture with low modulus properties can accommodate limited deformation and absorb seismic energy [30].  
The irreversible permanent deformation of the tunnel was led by the creep-slip displacement of the fault and subsequent seismic shaking. Referring to the schematic diagram on the sequence of events used by [PERSON] et al. [54], Figure 11 illustrates the variation in permanent strain (accumulated residual strain) in the lining crown and invert (cross-section 2-2), as well as peak strain and seismic strain (peak strain minus residual strain) in each case, respectively. Figure 11 shows the peak strain of the tunnel with the isolation layer was significantly lower than the one without the isolation layer. In terms of the variation pattern of the lining crown, the permanent strain of the tunnel with an isolation layer was significantly lower compared to the tunnel without an isolation layer, while the seismic strain was not much different. From the position of the lining invert, both the permanent strain and the seismic strain were significantly lower in the tunnel with an isolation layer compared to the tunnel without an isolation layer. This also shows that the rubber-sand isolation layer has a favorable aseismic performance. In general, the final tunnel damage was contributed by the seismic strain and the accumulated permanent strain. The permanent strain gradually increases with the working case and increasingly dominates among peak strains. This potentially means that the strain on the tunnel lining cannot be wholly dissipated and gradually accumulates with the continuous effect of fault creep-slip and seismic motion.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multicolumn{3}{c}{**El-Centro Wave**} & \multicolumn{3}{c}{**Kobe Wave**} \\ \cline{2-7}  & **x-Direction** & **y-Direction** & **z-Direction** & **x-Direction** & **y-Direction** & **z-Direction** \\ \hline
1\# (without isolation layer) & 0.26 & 0.40 & 0.65 & 0.20 & 0.30 & 0.45 \\
2\# (with isolation layer) & 0.23 & 0.35 & 0.56 & 0.17 & 0.26 & 0.33 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Indicator of \(\xi\).