1. Introduction
In this section, we briefly describe the convergence-confinement method (CCM), review previous research on the subject and outline the contents and main aims of our research
1.1.The convergence-confinement method
The convergence-confinement method (CCM) is a useful theoretical tool for designing support for underground excavations in rock. It was developed initially in the 1930s, was further refined by various researchers and practitioners [1–5], and has been comprehensively reviewed by Carranza-Torres and Fairhurst [6], who painstakingly developed an application of the method to the design of tunnels in elastic–perfectly plastic rock masses obeying the Hoek–Brown failure criterion
The method consists of three basic graphs: a longitudinal deformation profile (LDP) that relates tunnel deformation to the distance to the tunnel face; a support characteristic curve (SCC) representing the stress–strain relationship in the support system; and a ground reaction or response curve (GRC), which describes the relationship between decreasing inner pressure and increas- ing radial displacement in the tunnel wall
The LDP has been studied by various authors including Panet [4] and Chern et al. [7]. Hoek et al. [8], furthermore, described a technique for obtaining the LDP for different quality rock masses that we apply to the CCM as used in our work. Hoek and Brown [3] have proposed ways of calculating the SCC for different types of support and reinforcement. Other relevant references on this subject are [6,9,10]. The GRC, which is the main object of our research, describes the relationship between the decreasing of inner pressure and the increasing of radial displacement of tunnel wall. It is based on analytical or semi-analytical elasto-plastic analyses
The arrangement and intersection of the LDP, SCC and GRC are considered to represent tunnel behavior in a simple enough way and in a more or less realistic manner. However, tunnel engineers tend not to use the CCM, and the possible reasons why are briefly commented below. Our research, as described here, attempts to overcome some of the problems perceived to be associated with the CCM