Performance of segmental and shotcrete linings in shallow tunnels crossing a transverse strike-slip faulting
Introduction
Shotcrete and pre-cast concrete segments are widely used as a lining system for shallow tunnels. These lining systems are designed to withstand the static and dynamic forces, such as the gravitational overburden and earthquake loads [19], [28]. Furthermore, they should properly respond against the fault movement if the tunnel crosses it. In fact, any instability and collapse of these tunnels may lead to traffic problems.
For a fault, the block which is positioned above the fault plane is the hanging wall. However, the foot wall is positioned below the fault plane (see Fig. 1).
Generally, fault movement types can be categorized into four groups:
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In a reverse fault (or a thrust fault), the hanging wall moves upward relative to the foot wall, and tectonic forces are compressive (Fig. 1a);
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In a normal fault, unlike the reverse fault, the tectonic forces are tensile. Therefore, the hanging wall moves downward relative to the foot wall (Fig. 1b);
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A strike-slip fault has mostly horizontal motion. In other words, the hanging wall horizontally moves relative to the foot wall (Fig. 1c); and
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An oblique fault has a component of the strike-slip fault, and a component of the dip-slip (reverse or normal) fault (Fig. 1d).
The effects of faulting in a free field (i.e. without considering the existence of above-ground and underground structures) were investigated using centrifuge physical models, and numerical methods [30], [31], [21]. The effects of faulting on some different above-ground and buried structures were addressed in some previous studies. Geotechnical works of several types were studied, like buried pipelines [40], [44], [45], [46], [32], [37], [18] and foundations (deep and shallow ones) with various methods [4], [3], [9], [10], [36], [35], [38]. In the case of tunnels crossing a fault, some investigations have been also carried out using numerical and small-scale physical methods, as discussed in the following.
Gregor et al. [20] numerically modeled the stability of twin tunnels crossing a transverse oblique fault by means of FLAC3D. The results show that the fault can cause the instability of tunnels and therefore the soil mass and water can flow into the segmental tunnels. Considering the issue of reverse faulting, Lin et al. [29] investigated a shotcrete tunnel performance using small-scale centrifuge model tests, as well as numerical simulations (2D plane strain conditions). In their parametric study, the effects of several parameters including the properties of soil and the tunnel layer, the fault angle, and the tunnel position relative to the fault were explored. The results demonstrated that when the tunnel is located far from the fault plane, the tunnel deformation is small. A shotcrete tunnel in a dry sandy soil was modeled by [7], [8] using small-scale centrifuge model tests. Then, they developed a 2D numerical model (plane strain conditions), and verified their results with those of centrifuge models in order to perform parametric studies, in which the effects of the properties of soil and the shotcrete, as well as the tunnel position relative to the reverse fault were evaluated. In these tests, the fault plane (crossing the tunnel section) was parallel to the tunnel axis, and only one dip angle was selected for the faulting. It was found that the soil elastic modulus has a significant effect on tunnel movements and deformations. For the case of normal faulting and reverse faulting, Kiani et al. [23] used small-scale physical centrifuge models to explore the pre-cast concrete segmental tunnel interaction with dry sand. Two various transverse fault dip angles were selected and the tunnel deformation mechanism under faulting was analyzed. The results showed that the number of rings affected by faulting is a function of the tunnel depth and the fault dip angle. However, the effect of soil parameters was not studied due to the limitations associated with the physical tests. Wang et al. [41], using FLAC3D, concisely studied all types of fault movements, except the oblique fault, on the response of the flexible lining of tunnels, and they concluded that strike-slip faults can induce a higher level of damage to deep tunnels than other faults.
This paper investigates the performance of urban tunnels crossing strike-slip faults. The segmental linings performance is investigated. As the literature review showed, this type of faulting has not been sufficiently addressed and nor comprehensively studied. It is why the need arises to investigate it. Furthermore, segmental linings are compared with continuous (i.e. shotcrete) ones in this paper. For this purpose, the interaction between the lining and the surrounding soil when faulting occurs is investigated. Therefore, in addition to the parameters related to the influence of linings and faulting parameters, the tunnel depth and the soil geo-mechanical properties are also studied.
Section snippets
Three dimensional numerical modeling procedure
To investigate the main parameters influencing the tunnel behavior, the finite explicit difference program FLAC3D was employed. The adopted numerical running procedure consists of several following phases:
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Phase 1: Setting up the numerical model, consisting of two parts of a fault, and assigning boundary conditions and initial stresses;
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Phase 2: Excavating the tunnel and installing the tunnel lining (shotcrete or concrete segments); and
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Phase 3: Specifying velocities to the hanging wall to shift
Verification of the numerical model
A numerical model should be calibrated with the results of analytical and/or physical models. However, the case of a strike-slip fault offset influence on tunnels has not been conducted by the aforementioned methods. Therefore, in the absence of data for this fault type, a comparison of the results was made for the case of a dip-slip faulting. The validity of the numerical modeling procedures was carried out by comparing them with those of centrifuge physical modeling by Kiani [24] and Kiani et
The parametric study and input data
A parametric study was conducted to evaluate the effects of multiple parameters on the displacement of the tunnel (tunnel movement), the development of the soil plastic strains, and the deformation of the tunnel cross-section due to the fault movement. According to Table 5, combining of three tunnel depths and two soil types, i.e. dense or loose states (to which were assigned three values of friction angle, one value of elastic modulus (Es)), and one value of density), 18 cases were obtained.
Results and discussion
This section deals with tunnel movements after strike-slip faulting. Fig. 11 shows the final state of the model after 2.5 m fault movement. In this condition, the tunnel cross section is sheared and the segments might be separated. Unlike normal or reverse faulting, the strike-slip fault offset does not impose a great ground surface upward or downward movement, and hence, it is not discussed here.
Conclusion
This paper presented a three-dimensional numerical study of the interaction between the tunnel lining and a strike-slip fault. For this purpose, a parametric study was conducted to investigate the influence of the soil mechanical properties, the layer thickness of the segmental and shotcrete tunnels, the tunnel burial depth, and the fault dip angle. Following main conclusions can be drawn from the present study:
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The shotcrete tunnel layer thickness has no influence on the tunnel movement after
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.
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