Effect of drainage conditions on porewater pressure distributions and lining stresses in drained tunnels

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Abstract

This study deals with the effect of drainage conditions on porewater pressure distributions and lining stresses in drained tunnels. Firstly, simple closed-form analytical solutions for the steady-state porewater pressure are re-derived within a common theoretical framework for two different boundary conditions (one for zero water pressure and the other for a constant total head) along the tunnel circumference by using the conformal mapping technique. The difference in porewater pressure distributions among the analytical solutions is investigated. The numerical simulation of a drained circular tunnel under the steady-state groundwater flow condition is made to investigate the effect of porewater pressure distributions on lining stresses. Secondly, the case study of the planned South Blue Line Extension subway tunnel under the steady-state groundwater flow condition is performed for four different drainage conditions (sealed, fully-drained with zero water pressure or a constant total head, and invert only-drained) along the tunnel circumference. The effects of different drainage conditions on porewater pressure distributions, flow nets, and lining stresses are investigated.

Introduction

Bangkok crams more than 10 million people into a rapidly growing area. Anyone, traveling through the city, braces for an ordeal of wasting hours in impenetrable traffic. Concern about Bangkok’s increasing heavy traffic led to the implementation of the first phase of the Bangkok Blue Line Subway project, which was completed and opened in 2004. However, the initial phase was only 20 km long and mainly concentrated in the heart of the city. This only mitigates the traffic problem to some degree. The coming South Blue Line Extension subway project is the second phase and expected to mitigate traffic problem in the southern part of the metropolitan area. This project will be about 5.5 km twin-tunnel and excavated underneath the Chao Phraya River, which is the main river pass through the center of Bangkok city.

One of the important issues in the construction of underwater tunnels is the design of the linings with the consideration of groundwater flow into the tunnels. The lining of sealed tunnels is designed to withstand full hydrostatic pressures as well as the earth pressures. For the design of the lining of drained tunnels, estimations of the seepage force acting on the lining and the stress in the lining due to the seepage force must be considered. Usually two approaches, numerical methods and analytical methods, are used to estimate the porewater pressure, the seepage force and the lining stresses in a drained tunnel.

For deep tunnels, Atkinson and Mair (1983) mentioned that, using an elastic approach, loads on the tunnel linings are the same, considering impermeable or fully-drained lining. For shallow tunnels, Schweiger et al. (1991) and Lee and Nam (2001) obtained less stresses in the linings with the consideration of the seepage force. Schweiger et al. (1991) showed that the lining stresses in the drained condition were about 75% of the value obtained when the full hydrostatic pressure is applied. In the case study of Seoul Subway line 5 under the steady-state groundwater flow condition, Lee and Nam (2001) showed that the lining stresses in the tunnel reached approximately 30% of those of the sealed tunnel. By applying the drained condition at the tunnel invert only, Bilfinger (2005) mentioned the possibility of significant reductions in lining loads due to the water level.

In drained tunnels, however, two different boundary conditions (one for zero water pressure and the other for a constant total head) along the tunnel circumference are used in the existing solutions and analyses (Park et al., 2008a, Park et al., 2008b). Through the comparison of the analytical results for steady-state groundwater inflow and seepage force, Park et al., 2008a, Park et al., 2008b showed the difference in the predictions of groundwater inflow and seepage force for two different boundary conditions in a shallow drained circular tunnel. Therefore, it is required to investigate the effect of different drainage conditions (sealed, fully-drained, and invert only-drained) on lining stresses.

This study consists of two parts. First, we shall revisit the closed-form analytical solution for the steady-state porewater pressure in a drained circular tunnel with focus on two different boundary conditions along the tunnel circumference. The solutions for two different boundary conditions are re-derived on a theoretically consistent way by using the conformal mapping technique. Porewater pressure predictions by analytical solutions are compared with numerical results. The difference in porewater pressure distributions among the analytical solutions is also investigated. The numerical simulation of a drained circular tunnel under the steady-state groundwater flow condition is performed using the finite element software ABAQUS/Standard (2004). The effect of different porewater pressure distributions on lining stresses is investigated.

The second part focuses on the case study of the planned South Blue Line Extension subway tunnel under the steady-state groundwater flow condition to investigate the effect of different drainage conditions for the twin-tunnel. Four different drainage conditions (sealed, fully-drained with zero pressure or a constant total head, and invert only-drained) along the tunnel circumference are considered. The effects of different drainage conditions on porewater pressure distributions, flow nets, and lining stresses are investigated.

Section snippets

South Blue Line Extension subway

The first MRT Blue Line subway of the city of Bangkok, opened in 2004, consists of 18 underground stations, running from central main railway station called Hualamphong station (S1), going through the business area, passing the bus terminal and ending at the Bangsue station (S21) (Fig. 1). The South Blue Line Extension subway project will be extended from Hualamphong station to Thapra station. This line will pass through the old china town district and underneath the Chao Phraya River. In the

Definition of the problem

Underwater tunnels can be designed to either be sealed or drained, according to groundwater control methodology. The lining of sealed tunnels is designed to withstand full hydrostatic pressures as well as earth pressures.

For drained tunnels, using Darcy’s law and mass conservation, the two-dimensional steady-state groundwater flow around the tunnel can be described by the following Laplace equation:2ϕx2+2ϕy2=0where ϕ is the total head (or hydraulic head), being given by the sum of the

Analytical solutions for steady-state porewater pressure

By considering two different boundary conditions along the tunnel circumference, two different solutions for the steady-state porewater pressure in a drained circular tunnel are re-derived in this section.

Numerical simulation

In order to validate the analytical solutions and investigate the effect of porewater pressure distributions on lining stresses, the numerical simulation is made using the finite element software ABAQUS/Standard (2004), which can address the continuum stress and seepage problems. Fig. 5 shows a circular tunnel of 5.0 m diameter with the conditions of C/D = 4 and the varying ratio of F/D (Lee et al., 2007). Typical modeling mesh and boundary conditions are shown in Fig. 6. The ground is discretized

Numerical simulation

The numerical analysis of the South Blue Line Extension subway tunnel has been performed for the single tunnel and the twin-tunnel with four different drainage conditions, using the finite element software ABAQUS/Standard (2004).

Plane strain condition is used in the analysis. Fig. 14 shows the modeling mesh for the twin-tunnel. The model geometry used is 120 m wide and 80 m deep. The ground is discretized using four-node bilinear displacement and pore pressure plane strain element, while the

Conclusions

Simple closed-form analytical solutions for the steady-state porewater pressure in a drained circular tunnel have been revisited by re-deriving the solutions within a common theoretical framework for two different boundary conditions (one for zero water pressure and the other for a constant total head) along the tunnel circumference. The effect of porewater pressure distributions on lining stresses is investigated by numerical simulation. The following conclusions can be drawn:

  • (1)

    While the

Acknowledgements

The authors gratefully acknowledge the financial and other support provided by the Royal Thai Government, Korea Institute of Construction Technology (Environmental-friendly Geospace Development) and Korea University (BK-21 Global Leaders in Construction Engineering).

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