The tunnel may have to be constructed across a faulted zone as it is not always possible to avoid crossing active faults. In these situations, the tunnel lining must tolerate the expected fault displacements and seismic action, and allow only minor damages for the assumed life time. This paper presents a method of designing flexible lining for tunnels within the regions of active faults. The effects of the method are analyzed. The results show the tunnel lining with flexible joints allows the tunnel to distort into S-shape through the fault zone without rupture and thus it can provide reference to the design and construction of tunnels located in the active faulted zones.

1. Introduction

The tunnel may have to be constructed across a fault zone as it is not always possible to avoid crossing active faults. In these situations, the fault movement may subject the tunnel to differential displacments and generate stress concentrations. Looking through the previous studies and relevant cases, it can be concluded that the current methods of designing the safe secitons for the cases of probable deflection along the longitudinal profile of tunnels can principally be classified into fourth kinds of approaches, i.e.:

  1. excavating a larger diameter section in order to provide enough space for the conditions of earthquake or faulting.

  2. The grouting reinforcement technique, which means grouting the ground in order to increase the strength and ductility of the faulted zones.

  3. The isolation technique, which means filling the space gap between the ground and the lining by some soft materials.

  4. the use of flexible joints, which may be considered to increase longitudinal flexibility of the tunnel. For the present study the fourth method is applied.

2. Theoretical analysis

The main loading of tunnels is the deformation imposed by the surrounding ground. For design purpose, this deformation must be somehow predicted. This is a very difficult tast called seismic hazard analysis. Prediction can be attempted based on deterministic or probabilistic analysis. In either case the results are highly uncertain but possibly still the best achievable assumption. Assume now that the wave motion. We consider harmonic waves with the circular frequency w. Non-harmonic waves can be decomposed into harmonic ones. Let the unit vector I denote the direction of wave propagaion and let a be the amplitude of oscillation. Then the displacement u of a point with spatial coordinates x is given by the following expressions. Herein, up and us denotes the p-wave and s-wave displacement vectors, respectively.


cp, cs, ap and as are the corresponding propagation speeds and amplitudes, respectively. Let t be the unit tangential vector at a particular point P of the tunnel axis. Then, the earthquake-induced longitudinal strain and the change of curvature of tunnel can be obtained as:


With α being the angle between I and t. Thus, a joint between two rigid tunnel segments will suffer the elongation s and the rotation θ (see Figure 1) as follows: <>

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