## 1 Introduction  
In recent years, there has been a significant increase in the demand for tunnels in urban areas, especially for public transport purposes. Paralleled twin tunnels that are closely spaced are often adopted to save underground resources [1]. Due to the restriction of construction conditions and the consideration of safety, the second tunnel is not built until the first tunnel is completed for a period of time [2, 3]. Thus, predicting the influence of construction of the following tunnel on the preceding tunnel plays a key role in avoiding any damage to the preceding tunnel and excessive ground settlement during excavation of the following tunnel [4]. In the past, a variety of approaches have been used to study the interaction between paralleled twin tunnels, including physical model testing, field observations, analytical derivation, and finite element modeling. The physical model testing can reflect the spatial relationship of the adjacent tunnels realistically. There are mainly two types of model tests, i.e., 1-g model tests [5, 6] and centrifugal tests [7, 8, 9]. [PERSON] et al. [5] adopted 1-g scale-model experiments to analyze interaction between the following tunnel and the preceding tunnel, emphasizing the influence of the properties of soil and lining, the geometric dimensions of the tunnel, and the excavation method. The simulation of each excavation stage of the tunnel was adopted by [PERSON] et al. [7] using centrifugal experiments. The influence of the size of the existing tunnel, the distance between tunnel centers, and the earth pressure coefficient, \(K\), on the mechanical behavior of new tunnels were investigated and analyzed, and an appropriate distance between tunnel centers was obtained. Field observation is still the key approach to understand the interaction between adjacent tunneling, in which measurement data can be used to explore the influence of construction operation [10], inhomogeneous soil layer [7; 11], and asymmetric parallel tunnels [12; 13]. Unfortunately, however, monitoring points are only placed on specific sections, which often results in incomplete information. In addition, accuracy of the data is also affected by factors such as buried location of transducers and survival rate of transducers [14]. The analytical methods have definite practical significance for investigating the interaction mechanism of parallel tunnels, which are usually based on the theory of beam on elastic foundation. The approaches can be used to predict tunnel deformation from soil deformation [15; 16] and predict tunnel deformation based on the additional load [17; 18]. Finite element modeling seems to be a promising method for addressing this issue. It can simulate shield tunneling realistically, by considering the advancement of tunnel face, shield conicity, grout injection, concrete lining, and ground loss. Many in-depth studies have been carried out on the interaction of adjacent twin tunneling in unimproved soil by means of finite element modeling [19; 20; 21; 22; 23]. [PERSON] et al. [21] established a numerical model for twin tunnels and carried out the study on the influence of factors such as the relative position of tunnels and construction procedure on soil deformation and internal force. [PERSON] et al. [22] presented a refined three-dimensional numerical model, which took into consideration the effects of lining joint patterns, including segmental lining joints and their connections, to assess tunnel lining behavior and displacement fields around the tunnel. [PERSON] et al. [23] established a numerical model using COMSOL Multiphysics to study the influence of excavation of twin tunnels on ground settlement patterns in composite strata. The results indicate that the excavation face stability of parallel tunnels is inferior to that of a single tunnel and degrades as spacing between the two tunnels decreases [24]. In coastal cities, tunnels are often constructed in soft ground.