Buoyancy of tunnels in soft soils

Abstract

INTRODUCTION The construction of bored tunnels in soft soils is one of the major achievements of civil engineering in the 20th century. The process minimises the disturbance in the environment, especially in built-up areas, but there may still be some disturbance of the stress field, and some deformation of the soil surrounding the tunnel. In particular, some subsidence above the tunnel may occur, because of the excavation process at the front of the tunnel, and because the dimensions of the tunnel-boring machine are necessarily somewhat larger than the tunnel constructed in its interior. The latter effect is often reduced by the injection of grout between the tunnel elements and the soil, but experience shows that there is usually some subsidence above the tunnel. The simplest problem for theoretical analysis arises when considering the ground loss problem: the deformations caused by a uniform reduction of the radius of a cylindrical cavity. For the surface subsidence due to ground loss, various methods of analysis have been suggested, ranging from analytic solutions assuming elastic or elasto-plastic behaviour to numerical solutions using advanced material modelling of soil behaviour, and empirical methods using some assumed subsidence curve (Peck, 1969). In most of the elastic methods (Sagaseta, 1987; Verruijt & Booker, 1996) the problem considered is an imposed deformation of a circular ring in a half-plane, ignoring other effects. It has been observed (e.g. Loganathan & Poulos, 1998) that the subsidence curve predicted by such elastic solutions is wider than the subsidence curve observed in engineering practice, with the observed subsidence curves being some 50% narrower than the curves predicted from elastic solutions for the ground loss problem. To improve the predictions, various improved methods of analysis have been suggested. Loganathan & Poulos (1998) considered the possible ovalisation of the tunnel and, preferably, the addition of a semi-empirical correction factor. Other possible causes for deviations from an elastic solution are differences between the excavation face pressure and the in situ stresses, plastic deformations of the soil (Osman et al., 2006), and consolidation or creep of the soil after the construction process of the soil. Perhaps the ultimate solution is to use a numerical method, for instance based upon the finite element method, in which elasto-plastic soil behaviour and creep can be incorporated, and even the effect of grouting (Van Jaarsveld et al., 1999; Brinkgreve et al., 2006). Buoyancy will automatically be included in such a model if it starts with an initial state of stress due to gravity of the soil, and then considers the construction of the tunnel as a removal of the soil, the installation of the tunnel, and consolidation or creep of the soil after the construction process, taking into account the effective weight of the various components. If desired, the grouting process can also be included. The effect to be considered in this paper is the difference in weight of the completed tunnel and the excavated soil, to be denoted as the buoyancy effect (Strack, 2002; Strack & Verruijt, 2002). Because the weight of the tunnel is usually less than the weight of the excavated soil, an upward force is exerted on the surrounding soil, and this will affect the deformation and stress field, including a reduced subsidence. The purpose of the present paper is to investigate the influence of the buoyancy effect on the subsidence curve at the surface, and in particular the width of this curve, using a simple homogeneous isotropic elastic model for the soil. Of course, other effects, such as plasticity, consolidation and creep, may also influence the shape of the subsidence curve, but this paper considers the ground loss and buoyancy effects only.