**1. Introduction**

A large number of tunnel projects in China that are under construction or have already been built, are located in earthquake-prone areas, especially in the southwest. The seismic response of tunnels in areas of high earthquake intensity is a problem that must be faced in current tunnel construction, especially for tunnels through fault fracture zones [1–3]. The "5.12" Wenchuan earthquake indicated that tunnels with good engineering geological conditions show good seismic performance, while tunnels with complex geological conditions, including major changes of strata or poor rock properties, are more vulnerable to seismic damage. Therefore, the fault fracture zone is the main area where the tunnel's seismic damage is concentrated [4–6]. Engineering practice indicates that once an earthquake occurs, relative dislocation is easily produced between the rock mass and the fault, which can lead to irreparable damage to the tunnel and can affect its normal operation. This also makes rescue work in the earthquake area much more difficult. Therefore, it is necessary to study the seismic damage characteristics of the tunnel through fault, which will have great practical engineering value and social economic benefit.

**Citation:** Liu, G.; Zhang, Y.; Ren, J.; Xiao, M. Seismic Response Analysis of Tunnel through Fault Considering Dynamic Interaction between Rock Mass and Fault. *Energies* **2021**, *14*, 6700. https://doi.org/10.3390/ en14206700

Academic Editor: Nikolaos Koukouzas

Received: 8 September 2021 Accepted: 12 October 2021 Published: 15 October 2021

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At present, model tests and numerical simulations are the main methods adopted to study the dynamic response laws of the tunnel through fault under seismic action. In a model test, Fang et al. [7] conducted a large-scale shaking table test study of a complex tunnel through fault constructed in Tibet and analyzed the propagation laws of seismic waves and the failure modes of the tunnel. Liu and Gao [8] studied the dynamic failure characteristics of the tunnel through fault compared with ordinary tunnels, using shaking table tests, and they analyzed the development process for lining cracks and the distribution laws of dynamic earth pressure. Fan et al. [9] designed a 3D sliding device representing an active fault and conducted a shaking table test to investigate the seismic performance of a tunnel under normal fault sliding. Although many scholars have achieved a great deal in shaking table test research on the seismic response behavior of the tunnel through fault, the development and application of model tests are still limited by many factors. For example, the engineering geological environment and the boundary conditions are difficult to grasp accurately, and the test cost is very high.

Relatively speaking, the prospects for the application of numerical simulations are more promising than those for model tests, due to their low cost and high efficiency. Li et al. [10] analyzed the displacement difference and plastic zone of a railway tunnel through fault under seismic excitation, using a solid element and a structural plane element to simulate the fault. Yang et al. [11] studied the changing process of stress and strain in a tunnel under the joint action of an earthquake and a fault, using the discrete element method. Ardeshiri et al. [12] conducted a nonlinear dynamic analysis of a cavern–fault system, using the hybrid finite difference–discrete element method. The key to the numerical simulation of seismic damage in the tunnel through fault lies in establishing a reasonable analysis method for the dynamic interaction between the rock mass and the fault. However, most current studies assume that the rock mass and the fault constitute a continuous system, which ignores the influence of discontinuous fault dislocations on the dynamic response of the lining structure. In fact, the dynamic contact force method proposed by Liu and Sharan [13] provides a good method for solving this kind of problem that does not need iteration and is easy to combine with the explicit central difference method [14,15]. However, the traditional dynamic contact force method assumes a small sliding displacement, which is clearly not perfect when simulating large dislocations between rock masses and faults.

In this paper, an improved dynamic contact force method is established that considers the seismic deterioration effect and the large sliding characteristics of the contact interface between the rock mass and the fault. A calculation formula for the vibration deterioration coefficient of the contact interface is obtained, taking into account the deterioration effect of seismic action on the ultimate bearing load of the contact interface. Based on the traditional point-to-point contact type, this method also takes the point-to-surface contact type into account, and the solving strategies for the contact force and methods of judging the contact state in the two cases are expounded. Then, the calculation flow of the improved dynamic contact force method suitable for the tunnel contact system is designed. The simulation results for the engineering case indicate that the proposed method reflects the nonlinear seismic damage characteristics of the tunnel through fault reasonably well.

#### **2. Seismic Deterioration Effect of Contact Interface**

The dynamic deterioration effect of the rock structural plane under seismic action has been confirmed by a large number of rock dynamic tests [16–18]. Through cyclic shear tests on the structural plane for iron-cemented fine sandstone from the Wenchuan earthquake area, Ni et al. [19] obtained a quantitative expression reflecting the vibration deterioration effect of the structural plane. By introducing the vibration deterioration model and making some appropriate modifications, this paper established a mathematical model suitable for studying the deterioration laws of the ultimate bearing load of the contact interface between the rock mass and the fault under seismic action.
