Using experience and data from recent tunnel construction in Japan and the United States the authors propose a method to find the appropriate range of maximum allowable convergence of rock based on tunnel convergence measurements. Two types of geologic conditions are discussed: (1) expansive mudstone of Japan, and (2) schistosegneiss, containing many shear zones in Washington, D.C. The behavior of these rock types in response to tunneling are discussed in terms of the stress-strain behavior, actual deformations, maximum allowable convergence (MAC), practical design and monitoring. The emphasis is placed on the importance of the stress-strain behavior for the determination of the MAC for weak rocks.
In the consideration of the tunnel stability and the determination of support it is necessary to improve the understanding of rock support interaction. The fundamental stresses and displacements in the rock surround the tunnels and in the support/lining are governed by the in-situ stress field, type and stiffness of the support lining, and the timing of its installation. The relationship between the support reaction (i.e., support load) and radial displacement of the wall is also of concern. Fenner (1938) and Talobre (1957) proposed support reaction curves based on ideal elastic and elasto-plastic behavior of rock, respectively. Pacher (1964) corrected these curves from his experience to show a minimum support pressure corresponding to some limited displacement of the tunnel walls. Other models for ground support (e.g., Kastner, 1949; La Basse, 1949; Hendron & Aiyer, 1972; Ladanyi, 1974; Hoek and Brown, 1980) are summarized by Brown et al. (1983). These solutions are based on an assumed behavior of the rock. They are helpful only in the design stages of tunneling because the relationship between the minimum support load and the corresponding magnitude of displacement has yet to be clearly defined. Currently the allowable deformation accepted in tunneling is often too large, resulting in support loads larger than necessary. This is partially the result of incorrect assumptions regarding the material behavior. Conventional elastic and elasto-plastic theories are not always best suited for many geologic and tunneling conditions. For example, a strain-softening analysis is best suited for weak rock. Without the proper assumptions a quantitative limit for the allowable deformation cannot be defined. If the stress-strain behavior can be determined through laboratory tests and the actual deformation can be monitored during construction, it should be possible to minimize the support loads, thus optimize the design.
OBSERVED DEFORMATIONS IN TUNNELLING
The most popular and practical measurement of deformation in tunneling is the convergence measurement. It is defined as the reduction in the distance between the floor and roof of an opening, or by the inward displacement of the tunnel walls. It is a simple measurement which can be made during construction, and yields information on the displacement of the tunnel walls and change in the radial stress corresponding to the displacements. In most cases the results of convergence measurements are plotted on a deformation -time graph, which gives the apparent deformation rate. However, because of the dependence of deformation on the position of the mining face, it is more informative to plot the results of the convergence survey relative to the distance to the face and tunnel walls.