Simulation of Train Load on Deformation of Big-Diameter Shield Tunnel

Abstract

In order to study the impact of train load on deformation of big-diameter shield tunnel, the Vehicle-Track-Tunnel-Soil coupling dynamic model was established, and the reaction force of fasteners was used to transmit between the Vehicle-Track coupling dynamic model and the Tunnel-Soil finite element model. The results are as follows: the changing of vertical cross section deformation and horizontal cross section deformation has congruent relationship with the changing of train load and there exists a time difference; under the impact of train load, tunnel size increases in vertical direction and shrinks in horizontal direction, cross section shape grows into vertical oval and the deformation is confined to a very small amount. Keywords-shield tunnel; big diameter; cross section deformation; coupling dynamic model I INTRODUCTION With the fast development of urban railway system, more and more shield tunnels have been put into operation. According to the safety inspection on service shield tunnels, cross section deformation is the most common safety problem for tunnel deterioration is close related to it. Wang and Zhang [1] found leakage will be triggered once the cross section deformation exceeds a limiting value, and the worse is that segments will be crushed, bolts lost function, and the collapse of the whole tunnel; the safety problem will be more seriously in large-diameter shield tunnel. Tunnel deformation happens both in construction and operation period, the former is mainly caused by disturbance of shield construction and the latter is influenced by long-term operation load, leakage and surrounding engineering event. Existing research on shield tunnel deformation can be classified into three aspects: the surrounding engineering events and tunnel leakage on tunnel deformation and internal force [2,3,4,5]; the qualitative analysis on tunnel deformation based on field test data[6,7]; the elastic limit radius of curvature based on Modified Routine Method and the relationship between cross section deformation and segment internal force[8]. The impact of operation load on tunnels is mostly given on tunnel vibration: the dynamic response analysis on shield tunnel in operation period using three-dimensional dynamic finite difference method [9]; dynamic response analysis on lining structures of tunnels with three kinds of cross section [10]; the study on the roadbed and standard segments in Shanghai based on monitoring data [11]. Aforementioned research are mainly focus on conventional diameter tunnel and the influence of operation traffic load which is a significant factor on tunnel cross section deformation can be rarely seen. With the Vehicle-Track-Tunnel-Soil coupling dynamic method, this paper studies effect of operation load on cross section deformation of large-diameter shield tunnel. II CALCULATION METHOD AND MODEL The Vehicle-Track-Tunnel-Soil coupled dynamic model consists of two main parts: Vehicle-Track coupling dynamic model and Tunnel-Soil finite element model. The reaction force of fasteners is used to transmit forces between the two constituent parts. A-Train with six cars is adopted and there are three kinds of operation train load: on the right line, on the left line and on both lines, of which the last one is the most unfavorable and is used in the model. A. Vehicle-Track Coupling Dynamic Model The classical model of vehicle-track vertical coupling dynamics, [12], is used. In the vehicle model, each section of the vehicle is modeled as a multi-rigid-body system with seven rigid bodies and 10 degrees of freedom, considering four wheel sets, two bogies and one car body. The dynamic equation of the vehicle can be expressed as unified format: [ ]{ } [ ]{ } [ ]{ } { ()} v v v v M X C X K X Q t    (1) Where {} X , {} X and {} X are, respectively, the generalized acceleration vector, the generalized velocity vector and the generalized displacement vector; [] v M , [] v C and [] v K are, respectively, the mass matrix, damping matrix and the stiffness matrix; { ()} v Qt is the generalized load vector in the vehicle model. In the model, the rail is modeled as an infinite Euler beam lying on the elastic discrete points of support. The elasticity mainly depends on the plate under the rail for the double-block non-ballast track. The equation of vibration mode coordinate for rail is given by: [ ]{ } [ ]{ } [ ]{ } { } r r r r M q C q K q P    (2) where [] r M , [] r C and [] r K are respectively the generalized mass matrix, the generalized damping matrix and the generalized stiffness matrix; {} q , {} q and {} q are International Conference of Electrical, Automation and Mechanical Engineering (EAME 2015)