# Seismic Stability of Dual Tunnels in Cohesive-Frictional Soil Subjected to Surcharge Loading
## 4 Results and Discussions
It can be seen that the seismic bearing capacities of Figure 5c are greater than those of Figure 5a, which corresponds to Figure 4. Regarding the effect of \(\varphi\) on the critical interaction distance, it can be observed that, in cases of small seismic action (\(k_{h}=0.05\), \(0.1\)), the critical distance of different \(\varphi\) is almost maintained as equal, whereas if the seismic action becomes larger (\(k_{h}=0.15\), \(0.2\)), the critical interaction distance between tunnels would increase with  
To present a deeper and more visualized insight of the critical distance, Figure 6 depicts the variation of \(N_{cs}\) with different internal friction angle. It can be seen that for all subfigures, the critical distance decreases with the increase in \(\varphi\). Through comparisons between Figure 6a,b, it can be seen that the critical distance would decrease with the increase in \(\gamma D/c\). Additionally, by contrasting the data of Figure 6b,c, it is clear that the deeper the tunnel depth is, the greater the critical distance becomes. The critical distance of tunnels would also increase with a stronger seismic action. This trend is revealed through comparisons of Figure 6c,d. Figure 7 depicts the variation of seismic bearing capacity with different internal friction angle \(\varphi\). As expected, all curves of Figure 7 show an uptrend, which means the bearing capacity increases with the increase in \(\varphi\). Additionally, for all figures, the gradient of the curves becomes steeper with the deeper depth of tunnels. This indicates that, for cases with a deeper depth of tunnels, the internal friction angle would have a more significant influence on seismic bearing capacity. Furthermore, it can be seen from Figure 7a-c that, when \(\gamma D/c=0\), the difference values of \(N_{cs}\) between different \(H/D\) tend to be greater with the increase in \(\varphi\), while the difference values become smaller with the increase in \(\varphi\) with \(\gamma D/c=2\). This phenomenon indicates that, for cases of small \(\gamma D/c\) (Figure 7a), the depth of tunnels has a greater effect on the seismic bearing capacity with a greater \(\varphi\), whereas for cases of high \(\gamma D/c\) (Figure 7c), the effect of the tunnel depths on the seismic bearing capacity attenuates with the increase in \(\varphi\). Additionally, this trend of \(\gamma D/c=1\) is in between cases of \(\gamma D/c=0\) and \(\gamma D/c=2\). The \(H/D\) has almost no effect on seismic bearing capacity at the overlapped part in Figure 7b. Through comparisons between Figure 7b,d, it is clear that the seismic bearing capacity of cases with \(S/D=5\) is greater than cases with \(S/D=3\). Additionally, the variations in the internal friction angle would incur a greater influence on seismic bearing capacity with a further distance between tunnels. This tendency is more distinct with the deeper depth of tunnels. Figure 8 depicts the variation trend of seismic bearing capacity with different depths of the tunnels. It can be seen that, for all cases, the curves are straight, which means the \(H/D\) would have a linear impact on \(N_{cs}\). Additionally, the gradients of curves with different \(k_{h}\) are almost the same. This indicates that seismic action affects the seismic bearing capacity almost proportionally. In addition, for cases of \(\gamma D/c=0\), the values of \(N_{cs}\) increase repeatedly with the apparent increase in \(H/D\). Additionally, a trend can be observed from the curve gradients that the variation in \(H/D\) has a strong influence on the \(N_{cs}\) for cases of greater internal friction angles. By contrast, in Figure 8b, the seismic bearing capacity increases with the increase in the tunnel depth for large \(\varphi\), while for cases of small internal friction angle (\(\varphi\leq 15^{\circ}\)), the seismic bearing capacity decreases with an increasing \(H/D\).