The continuous increase in demand for better and more sustainable travel facilities in major cities has led to a significant increase in the interest in routing roads, railways and metros through tunnels. Due to the abundance of existing underground infrastructure at deeper depths, tunnels in urban areas are often being constructed at shallow depths.
A tunnel is considered to be shallow when the height of cover above the tunnel is not much greater than the tunnel diameter. Generally, shallow tunnels are constructed at depths ranging from 9m to 12m (FHWA, 2009). These tunnels can be constructed by mechanised tunnel boring methods (such as TBMs) or by the cut and cover method. The majority of these shallow tunnels are cut and cover arch-shaped concrete tunnels.
The cut and cover construction technique has been used for many years as a means for building underground transportation facilities. This technique may involve one or both of the two following methods: bottom-up construction and top-down construction.
Bottom-up construction involves the excavation of a trench in which the tunnel is erected. Temporary structures, such as sheet pile walls, secant pile walls, tangent pile walls or sheet pile walls are usually required and installed before the excavation takes place to support it. Providing unreinforced side slopes may require the removal of up to six times more material, and spread an additional three tunnel diameters on either side of the excavation for tunnels with depth of cover equal to its diameter. The tunnel is constructed from the bottom slab, up to the tunnel walls and roof. The excavation is covered and the ground level is restored.
The top-down cut and cover construction method is often implemented when the use of the area above the tunnel (e.g., for above-ground transportation systems) is paramount, the side wall deflections must be limited to minimise damage to adjacent structures or if there is limited width of rightof- way for excavation (FHWA, 2009).Excavation support is installed first, consisting of structures such as slurry walls, secant pile walls or sheet pile walls, which usually become the permanent walls of the tunnel. A shallow excavation is created, where the roof of the tunnel is constructed on grade. The excavation is covered for continued use, while the tunnel interior is excavated from below grade with bracing provided to the support walls. The early cover of the excavation allows for quicker turnover from the beginning of construction to the re-availability of the ground surface. In both bottom-up and top-down construction sequences, de-watering of the work area may be necessary before excavation of the ground material.
For shallow tunnels, the cut and cover method is more economical than any other tunnelling method. However, the cost of cut and cover construction increases sharply with increased depth.
Regardless of the construction method, shallow tunnels in major cities will be situated below surfaces that are densely populated with various structures, from bridge piers and abutments to foundations of high-rise buildings. For tunnels constructed using the boring techniques, the tunnel-soilstructure interaction has been modelled extensively (i.e., Morton and King, 1979; Mair et al., 1996; Schroeder, 2002; Leung et al., 2003; Schroeder et al., 2004).
However, the shallow depth of the tunnel in these urban areas will expose it to the zone of influence of many existing and future structure foundations. Shallow tunnels and structure foundations can interact mutually influencing their stability. Hence, it is important to analyse the stress distribution regime around shallow tunnels accounting for tunnel-soilstructure interaction in order to provide an insightful and economic tunnel design. The redistribution of stress around a shallow tunnel depends not only on the characteristic properties of the neighbouring ground, tunnel size, and location, but also on the tunnel lining stiffness.
The scope of this paper will be limited to the effect of the relative stiffness of the backfill and the tunnel lining on the stress redistribution regime around shallow tunnels.
An extensive parametric study was performed to analyse this effect on the stresses experienced in the tunnel lining, the vertical deflection of the tunnel crown and the maximum contact pressure transferred from the tunnel’s foundations to the ground.
NUMERICAL MODEL
In order to investigate this soil-structure interaction problem, an arch-shaped concrete tunnel 10m wide by 8m height with 4m of cover over the crown was considered. The tunnel walls are supported by two 2m-wide and 0.6m-thick strip footings. The considered soil profile consists of a 30m-thick dense sand layer. The tunnel is constructed in a 14m-wide, 12m-deep excavated trench (see Figure 1).
Finite element mesh
The soil continuum was modelled using the 15-noded cubic strain triangular finite element available in the element library of the PLAXIS finite element package (Brinkgreve, 2008). The lateral boundaries were placed at about 10 times the width of the tunnel in each direction to simulate the infinite medium. The bottom boundary was placed at 30m below the ground surface. The size of the model was chosen such that the artificial boundaries and boundary conditions would have little to no impact on the ground stresses around the tunnel.
Soil model
The material constitutive models for both the ground and the granular backfill were assumed to obey the Mohr-Coulomb failure criterion (i.e., elasto-plastic stress-strain relationship). The criterion assumes linear elastic soil behaviour up to the defined Mohr-Coulomb failure surface. If the failure surface is reached, the soil yields, with corresponding stress redistribution to maintain equilibrium, up to the point where the stress conditions in the soil zones do not violate the yield surface and become again acceptable under the failure criterion.
The ground was modelled as purely frictional soil (i.e., c = 0) with Young’s modulus, E = 80MPa, Poisson’s ratio, v = 0.30, and angle of friction, = 38°. Three different sets of material properties were assumed for the granular backfill representing loosely compacted, medium compacted, and well compacted backfill materials. For all considered compaction levels, the unit weight of the backfill was assumed to be constant to isolate only the effect of the stiffness of the material. In all three cases, the backfill was modelled as purely frictional material. Table 1 presents the considered backfill soil properties.
Tunnel lining model
The tunnel lining and its walls and foundations were assumed to obey the linear elasticity model based on Hooke’s law of 0.3m to 1.0m, also the stiffness of the backfill material was varied to correspond to the degree of compaction (i.e., loosely compacted, medium compacted or well compacted backfill materials).
The following sections present the results of the parametric study.
Tunnel side wall stresses
Figures 3 and 4 show the variation in the maximum stresses in the vertical side walls of the tunnel with tunnel lining thickness for three different levels of compaction at the extrados and the intrados locations, respectively.
The degree of compaction was not observed to have a profound impact on the maximum extrados stresses in the side walls as it could be seen from Figure 3. For a lining thickness of 0.3m, the maximum stress experience by the wall varied from 6.2MPa/m when the trench was backfilled with well compacted material to 7.1MPa/m when the trench was backfilled with a loosely compacted material, about 15 per cent change. In general, the extrados stresses were compressive for all levels of lining stiffness and compactions, and were observed to decrease as the lining stiffness increased. The maximum side wall stress decreased from an average 6.6MPa/m for a lining thickness of 0.3m to an average 1.4MPa/m for a lining thickness of 1m, accordingly more than 300 per cent increase in the cross sectional area resulted only in about 80 per cent reduction in the stress.
At the intrados, the degree of compaction is only observed to have a noticeable impact on the intrados stress in flexible tunnel linings. For stiffer tunnel linings (t > 0.5m), the stress state is almost similar for all three levels of compaction as shown in Figure 4. It can be seen that the intrados stress transitioned from tensile to compressive for tunnel thicknesses exceeding roughly 0.8m. It can be concluded here the axial stress due to the thrust exceeds the bending stress induced by the bending moment. Since the compressive strength of concrete is typically much greater than its tensile strength, this situation is favourable. As for typical f’c = 40MPa concrete, the intrados stress was not observed to exceed 60 per cent of the ultimate tensile strength of the concrete (about 4MPa).
Overall, variances in the degree of compaction had a minimal effect on the vertical side wall stresses compared to the effect of the change in lining stiffness.
Tunnel shoulder stresses
The variation in the extrados stress at the tunnel shoulder’s location with the tunnel lining thickness for three different levels of compaction is displayed in Figure 5. For a lining thickness of 0.3m, the maximum stress experienced by the wall varied from 3.8MPa/m when the trench was backfilled with well compacted material to 5.6MPa/m when the trench was backfilled with a loosely compacted material. This trend is expected because as the stiffness of the backfill decreases (loosely compacted backfill), the relative stiffness of the lining increases (with respect to that of the backfill) and thus attracts more stresses. This finding agrees with that of El Naggar et al. (2008). Also, the shoulder extrados stress decreased from an average of 4.7MPa/m for a lining thickness of 0.3m to an average 1.6MPa/m for a lining thickness of 1m. Thus, as the cross sectional area of the lining increase the stress decrease.
Figure 6 shows the variation in the intrados stress experienced in the tunnel’s shoulder with tunnel lining thickness for the three considered levels of compaction. Compaction appears to have had a more profound impact on the shoulder wall intrados stresses than it did for the side wall intrados stresses. Also, compared to the vertical side wall intrados stresses, the shoulder wall intrados stresses were tensile in nature for all lining thicknesses. This is due to the fact that higher magnitude of moments presents at the shoulder location that result in higher tensile bending stresses.
Generally, compaction had much more of an impact on the stresses induced in the shoulder wall than it did for the side wall. It can be concluded that as the stiffness of the backfill increases (with respect to that of the lining) more stresses will be attracted by the backfill and the stresses arching away from the tunnel lining.
Maximum ground settlements
The variation in the maximum settlement of the ground surface with the tunnel lining stiffness for three levels of compaction is shown in Figure 7. The settlement was about 20mm for a tunnel lining thickness of 0.3m in loosely compacted backfill, as the thickness increases to 1m the settlement decreases to about 16mm. The same trend was found to hold for all considered levels of compaction. Also, for a lining thickness of 0.3m, the maximum ground settlement was 20mm in the case of loosely compacted backfill and only about 16mm for well compacted backfill case, which is about 20 per cent less than the former settlement. As expected, the settlements for well compacted backfill material were lower than settlements for loosely compacted backfill material. Isolating the effects due to compaction only, it can be seen that a well compacted backfill leads to an average settlement that is about 20 per cent or more lower than it is for loosely compacted backfills.
In general, it can be noticed that the observed settlements decreased with an increase in tunnel lining stiffness. Isolating the effects of tunnel lining stiffness on settlement, it can be observed that the 1m thick lining lead to a ground surface settlement that is about 4mm or 20 per cent less than the settlement when a 0.3m thick lining was used, and is a similar reduction to that obtained by achieving a well compacted backfill. This is likely due to the soil-structure interaction; a stiffer tunnel would lead to reduced tunnel lining deformation and thus reduced volume loss and therefore reduced settlement potential of neighbouringing backfill and soil.
Tunnel crown deflections
Figure 8 shows the variation in the maximum vertical deflection of the tunnel (at the crown location) with tunnel lining stiffness for the three considered levels of compaction. As it can be noticed from Figure 8, the crown deflection is observed to decrease with an increase in both the tunnel lining stiffness and the compaction quality of the backfill. The decrease in deflection is likely due to the fact that the combination of a stiff tunnel lining with a well compacted backfill creates a stiffer medium that is more capable of transferring stresses without inducing as much deformation. A backfill with a poor compaction would be more flexible and would rely more on the lining for support. This can induce more vertical load and thus more deflection of the tunnel crown.
Foundation contact pressure
The variation in maximum tunnel’s foundation contact pressure with tunnel lining thickness for three different levels of backfill compaction is shown in Figure 9. The contact pressure is observed to increase with both an increase in tunnel lining thickness and a decrease in compaction quality. As the tunnel lining becomes stiff relative to the backfill material, it carries a higher potential to transfer stresses to the ground. Therefore, the tunnel will play a larger role in stress transfer when compared to the backfill material. Thus, the tunnel wall foundations will carry a higher contact pressure for a stiffer tunnel lining.
With a better backfill compaction, the backfill material becomes stiff relative to the tunnel lining and thus has more potential to transfer stresses to the ground beneath it through soil arching. This would mean that less stress has to be carried by the tunnel itself, resulting in a lower contact pressure between the tunnel wall foundations and the ground.
The change in relative stiffness between the tunnel lining and the backfill alters the load transfer mechanism. Interaction between the backfill and the tunnel leads to different levels of soil arching, which will alter the amount of stress transferred to the ground via the tunnel wall foundations.
CONCLUSIONS
An extensive parametric study investigated the effects of tunnel lining stiffness and the compaction quality on the stresses in the tunnel lining, ground surface settlement, tunnel crown deflection and the maximum transferred tunnel’s foundations contact pressure. The conclusions of the study can be summarised as follows:
1. Both the extrados and intrados stresses in the tunnel’s vertical side walls decrease with an increase in the compaction quality
2. Compaction quality has a more profound effect on the stresses distribution in the tunnel lining shoulder walls than on the stresses in the vertical side walls
3. The maximum ground surface settlements decrease with both an increase in tunnel lining stiffness and an increase in backfill compaction quality
4. The reduction in contact pressure between the tunnel foundations and the ground as compaction quality increases can be attributed to arching effects
REFERENCES
El Naggar, H., Hinchberger, S. and Lo, K. Y. 2008. A Closed-Form Solution for Tunnel Linings in a Homogenous Infinite Isotropic Elastic Medium, Canadian Geotechnical Journal, Canada. Vol. 45(2), pp. 266-287.
Federal Highway Administration 2009.Technical manual for design and construction of road tunnels- civil elements, Publication number FHWA-NHI-10-034.
Leung, C.F., Lim, J.K., Shen, R.F., Chow, Y.K. 2003. Behavior of pile groups subject to excavation-induced soil movement. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 129 (1), 58- 65.
Mair, R.J., Taylor, R.N., Burland, J.B., 1996. Prediction of ground movements and assessment of risk of building damage due to bored tunnelling. In: Proceedings of the International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, Balkema, Rotterdom, pp. 713-718.
Morton, J.D., King, K.H.1979. Effect of tunnelling on the bearing capacity and settlement of piled foundation. Proceedings of Tunnelling 79, IMM, London, pp. 57- 68.
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Schroeder, F.C., Potts, D.M. and Addenbrooke, T.I. 2004. The influence of pile group loading on existing tunnels, Geotechnique. 54(6): 351-362.
