# Seismic Stability of Dual Tunnels in Cohesive-Frictional Soil Subjected to Surcharge Loading
## 1 Introduction  
With the rapid development of urbanization and highway engineering, it is difficult for road construction to avoid encountering hills, especially in the mountainous areas. A detour may lead to creating an unnecessary distance of road and causing an extensive amount of work. In view of this, the tunnel is considered a reasonable construction type to cope with such circumstances. The single tunnel, as the basic tunnel type, was investigated by theoretical methods [1; 2; 3; 4; 5] and numerical methods [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. However, dual parallel tunnels are more economical than the single tunnels, and the stability analysis of dual tunnels is relevant. [PERSON] et al. [17] employed a finite element limit analysis (FELA) to investigate the bearing capacity of double-tube tunnels. The results indicate that the solution of a single tunnel can be adopted to find double-tube solutions. [PERSON] et al. [18] experimentally explored the effects of several factors on the bearing capacity of double tunnels. [PERSON] et al. [19] and [PERSON] et al. [20] conducted centrifuge experiments to investigate the stability of tunnels in sand and soil, respectively. [PERSON] [21] adopted an upper bound limit analysis to investigate the undrained stability of twin tunnels, the variation of shear strength was taken into account. Using upper bound FELA, [PERSON] and [PERSON] [22] presented a series of sensitivity analyses for an insight into the bearing capacity of double tunnels in \(c\)-\(\varphi\) soil. Then, they analyzed the lining pressure of dual tunnels in pure cohesion soil and \(c\)-\(\varphi\) soil, respectively [23]. By combining a FELA and rigid block mechanism, the bearing capacity of circular and square tunnels was investigated by [PERSON] et al. [24] for \(c\)-\(\varphi\) soil and [PERSON] et al. for undrainedsoil. Detailed design charts were offered for engineering use. Recently, [PERSON] et al. [25; 26] and [PERSON] et al. [27; 28] used the upper bound finite element method to propose sensitivity analyses of double tunnels with different shapes, including pure circular, horseshoe and elliptical tunnels. Additionally, adaptive finite element limit analysis (AFELA) was used by [PERSON] et al. [29] to investigate the stability of double tunnels in \(c\)-\(\varphi\) soil at different depths; then, the cases of tunnels in rock mass were considered. In recent years, owing to the frequent earthquakes around the world (e.g., EI Centro, Wenchuan, Loma Prieta, Ancona and Fukushima earthquakes, etc. ), the seismic stability issue of tunnels became a hot topic. [PERSON] and [PERSON] [30] used incremental nonlinear dynamic analysis to evaluate the seismic reliability of RC tunnel-form structures. Then, [PERSON] et al. [31] developed a new method to assess the seismic reliability of RC tunnel-form structures by a combined systems approach. To investigate the seismic responses and damage mechanisms of tunnels, [PERSON] et al. [32] conducted a series of shaking table model tests. The test results offered deep insights into the seismic performance of tunnels with relatively shallower depths. Considering the advantages of numerical simulations, many researchers chose to investigate this problem numerically. [PERSON] et al. [33] adopted finite element analysis code DIANA to explore how RC soil-steel composite tunnels behave under seismic action. [PERSON] and [PERSON] [7; 16] and [PERSON] and [PERSON] [12] combined the FELA and the pseudo-static method to investigate the seismic stability of a single tunnel under various conditions. Their investigations were verified with results from other methods, demonstrating that the FELA can effectively solve seismic stability issues. However, aside from these aforementioned contributions, there is no information regarding the seismic stability of dual tunnels in \(c\)-\(\varphi\) soil.