Nonlinear seismic analysis of a train-tunnel-soil system and running safety assessment of metro vehicles

doi:10.1016/j.soildyn.2021.106772

Soil Dynamics and Earthquake Engineering

Volume 147, August 2021, 106772

https://doi.org/10.1016/j.soildyn.2021.106772 Get rights and content

Highlights

•
Predicting the normal force, separation and derailment factor between wheel and rail.
•
Application of a train-tunnel-soil coupled system due to seismic excitation.
•
Assessing the running safety of a metro train passing through a tunnel under earthquakes.
•
Evaluating the effect of the earthquake intensity and the train speed on the running safety of the subway vehicle.

Abstract

Since earthquakes would pose a serious threat to the safety of underground railway tunnels and subway trains, the seismic analysis of the subway tunnel and the metro train is essential for earthquake-resistant design and construction. This presented study aims to investigate the transient response of a train-tunnel-soil coupled system under various load conditions, and assess running safety of the moving train. Firstly, a simulation model of the train-tunnel-soil system was established, considering interactions between soil and tunnel, rail and train. Secondly, the numerical approaches employed in this paper were verified, and the tunnel-soil model was validated with the available test data. Finally, the nonlinear seismic response of the train-tunnel-soil system is investigated, and running safety indices of the subway vehicle are evaluated. Moreover, the effect of train speed and earthquake intensity on the running safety of the metro train is assessed. The numerical results reveal that compared to the moving-train load, the effect of earthquake action on the dynamic response of the subway tunnel is more prominent, resulting in a significant increase of the wheel-rail force and acceleration of the railway vehicle. Both earthquake loads and train speed have an impact on running safety indices, while the earthquake intensity has a more significant effect on the safety index of the metro vehicle. Moreover, it is worth noticing that with respect to the designed operational speed of 90 km/h for Nanjing Metro Line 10, the ability of the metro train to withstand earthquake excitation is no more than a maximum acceleration of 0.2 g.

Introduction

With the rapidly advancing of the urbanization process around the world, the increasing traffic of urban areas has been a global issue. More and more cities exploit underground space resources to address traffic problems in urban development. As underground railway traffic has become an indispensable part of city transportation, it does not take the safety of underground railway tunnels and subway trains too seriously. The security of earthquake-resistant structures is essential to underground engineering structures such as metro tunnels. In addition to the tunnel lining damage caused by earthquakes, earthquake excitation can pose a severe security risk to the running safety of moving trains as a train passing through a subway tunnel.

Determining the seismic response of the train-tunnel-soil coupled system is a complicated procedure consisting of the nonlinear behaviour of soil, the wheel-rail relationship and the soil-tunnel interaction condition. In recent years, on that note a large number of research work has been implemented to get a better insight into the dynamic response of the tunnel-soil system subjected to ground motions. Some researchers concentrated on the vibration analysis of the tunnel-soil system during an earthquake load. The results of shaking table tests under non-uniform earthquake excitation proposed by Chen et al. [1] reveal that the spatial distribution of earthquake excitation should be taken into account for the earthquake-resistant design of utility tunnel. Anastasopoulos et al. [2] adopted beam-spring element model to capture the seismic response of segmental tunnel lining, and the length and joint properties of the segment was discussed. Hatzigeorgiou et al. [3] presented a new three-dimensional finite element model of a soil-tunnel coupling system to investigate the soil-tunnel interaction under earthquakes. Gomes et al. [4] found that the stratification of the ground determined the dynamic response of shallow circular tunnels during an earthquake load. A new numerical procedure was proposed by Do et al. [5,6] to simulate the dynamic behaviour of the multi-segment linings subjected to earthquake excitation. The results reported by Fabozzi et al. [7] indicated that a proper constitutive law of the soil is vital to simulate the influence of soil-tunnel relationship on the nonlinear response of segmental tunnel linings subjected to an earthquake load.

Several studies took the moving train excitation as an independent load to simulate the vibration performance of the subway tunnel lining. The structure of the foundation and tunnel discretize by using the boundary element approach, and finite element method was adopted by Degrande et al. [8] to study the influence of the vibration induced by the subway vehicle. A 2.5D coupled finite element-boundary element model employed by Galvin et al. [9] concentrated on the ground displacement response induced by moving trains, and the numerical results of the simplified method were validated. A coupled periodic finite element-boundary element model was used to discuss the response of tunnel subjected to the excitation of a Thalys high-speed train in Ref. [10]. Andersen et al. [11] established the 2D and 3D models of the tunnel structure to analyze the vibration from railway tunnels, and the results derived from numerical simulation were validated with the experiment. They concluded that the accuracy and stability of the two-dimensional model were much lower than that of the three-dimensional model.

Some other published papers were related to the running safety assessment of the train vehicle. Tanabe et al. [12] employed a finite element model to simulate the dynamic interaction between a high-speed train and the track structure subjected to earthquake loads. Ju [13] investigated the derailment of the railway vehicle moving on bridge structures numerically, and it was found that a large pier stiffness could ensure the safety of railway vehicles under earthquakes. Xia et al. [14] presented that significant responses of a train-bridge coupling model during collision loads strongly threatened the running safety of high-speed railway vehicles. According to the seismic response of a train-bridge coupled model, Yang et al. [15] proposed critical speeds for running safety of the railway vehicle. The conclusions from the studies [[12], [13], [14], [15]] reveal that the seismic variation has a significant effect on the running safety of moving trains.

Nevertheless, in most of the research work related to the tunnel-soil system, the existing studies in which laboratory experiments, theoretical analysis and numerical simulations were carried out to get a main insight into the seismic response of the tunnel structure without considering the effect of train excitation, instead the moving train load was taken as an independent load to simulate the vibration of the underground tunnel structure. On the other hand, earthquakes can pose a severe security threat to the safety of subway trains in the underground tunnel, while little research concerns the running safety of the subway vehicle due to earthquake action. Therefore, this paper develops a train-tunnel-soil coupled system to investigate the dynamic response of the tunnel and the railway vehicle under various load conditions, and running safety of the moving train is also evaluated in this work.

In this paper, using the finite element method, a full three-dimensional train-tunnel-soil model based on the subway tunnel in respect of Nanjing Metro Line 10 is established. The nominal orthotropic constants of the tunnel lining structure are verified by comparing the dynamic response of the load test regarding the equivalent lining and the segmental lining. And the penalty method is used to investigate the wheel-rail relationship and the interaction condition between tunnel and soil. Then, numerical simulations were performed to verify the wheel-set contact model, calibrated the equivalent lining model and validate a tunnel-soil coupling model. Furthermore, with respect to the train-tunnel-soil coupled model, the dynamic response of the tunnel and moving train has been simulated. In addition, the running safety of a moving railway vehicle passing through the subway tunnel during an earthquake has been studied in detail. Moreover, due to the enormous computational effort [16,17], the simulation is performed based on the high-performance computer Magic Cubic-Ⅱ using LS-DYNA FE (finite element) code.

Section snippets

Explicit dynamic analysis

As the schematic of a train-tunnel-soil system is illustrated in Fig. 1, the dynamic model consists of the train vehicle submodel, the tunnel submodel and the soil submodel, with the external excitation of an earthquake load applied at the bottom of the foundation.

The interaction between the rail and the tunnel is assumed to be bonded, and the equations of motion can be given by: $[\begin{array}{l} M_{V V} & 0 & 0 \\ 0 & M_{T T} & 0 \\ 0 & 0 & M_{S S} \end{array}] {\begin{cases} {\ddot{U}}_{V} \\ {\ddot{U}}_{T} \\ {\ddot{U}}_{S} \end{cases}} + [\begin{array}{l} C_{V V} & C_{V T} & 0 \\ C_{T V} & C_{T T} & C_{T S} \\ 0 & C_{S T} & C_{S S} \end{array}] {\begin{cases} {\dot{U}}_{V} \\ {\dot{U}}_{T} \\ {\dot{U}}_{S} \end{cases}} + [\begin{array}{l} K_{V V} & K_{T V} & 0 \\ K_{V T} & K_{T T} & K_{T S} \\ 0 & K_{S T} & K_{S S} \end{array}] {\begin{cases} U_{V} \\ U_{T} \\ U_{s} \end{cases}} = {\begin{cases} F_{V T} \\ F_{T V} + F_{T S} \\ F_{S T} \end{cases}} + {\begin{cases} 0 \end{cases}$

Wheel-rail force under normal operation

A wheel-rail coupled model was established to verify the accuracy of the penalty function method for the wheel-rail contact. Fig. 5 shows the 3D model of the wheel-rail contact. The rails were composed of 8-node solid elements, and the fastener was represented as a linear spring damping element. The nodes at the bottom of the fastener structure were constrained. The irregularities of the track are neglected. A lumped mass of 14 tons is applied at wheel sets, and the wheels travel at a constant

Train model details

Fig. 16 shows the metro train of Nanjing Metro Line 10. The subway vehicle consists of six carriages which a car body, two bogies, four wheel sets and four spring-dashpot systems are attached to.

Fig. 17 indicates the dynamic analysis model of the carriage body. The subway train modeled by multi rigid-bodies connected with spring-dashpot relationships, and the interaction between wheel and rail is defined as a penalty contact algorithm. The following conditions are assumed during the modeling

Effect of various excitation conditions

As the underground tunnel structure is deeply immersed, the tunnel lining structure is subject to the gravity of the soil, resulting in the initial stress and deformation. For this reason, the dynamic relaxation method is adopted to assign the initial state of the train-tunnel-soil system before the dynamic response simulation. Fig. 23 illustrates the vertical-displacement and stress-response time histories at the cross-section C1 when the metro train is traveling in the tunnel at a constant

Conclusions

In this paper, a 3D finite element model of the train-tunnel-soil coupled system during earthquakes is established. On the one hand, the explicit algorithm is applied to numerically simulate the dynamic response of the underground tunnel and the subway vehicle. On the other hand, running safety of moving trains in the tunnel during earthquakes is calculated based on the numerical results. Furthermore, the effect of train speed and earthquake intensity on the running safety of the metro train is

Author statement

I have made substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; AND.

I have drafted the work or revised it critically for important intellectual content; AND.

I have approved the final version to be published; AND.

I agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

All persons who

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by the National Key Research and Development Program of China (Grant no. 2016YFB0201800) and the National Natural Science Foundation of China (Grant no. 11772192).

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Nonlinear seismic analysis of a train-tunnel-soil system and running safety assessment of metro vehicles

Highlights

Abstract

Introduction

Section snippets

Explicit dynamic analysis

Wheel-rail force under normal operation

Train model details

Effect of various excitation conditions

Conclusions

Author statement

Declaration of competing interest

Acknowledgement

Soil Dynam Earthq Eng

Soil Dynam Earthq Eng

Soil Dynam Earthq Eng

Soil Dynam Earthq Eng

Soil Dynam Earthq Eng

Procedia engineering

J Sound Vib

Soil Dynam Earthq Eng

Soil Dynam Earthq Eng

J Sound Vib

Eng Struct

Comput Struct

Eng Struct

Soil Dynam Earthq Eng

J Sound Vib

Eng Struct

Comput Struct

Soil Dynam Earthq Eng

Eur J Mech Solid