The Practical Importance of Accounting for Large Deformations in Tunnel Analysis and Design

"INTRODUCTION The small strain assumption routinely made in tunnel analyses remains sufficient from an engineering point of view as long as convergences do not exceed 10%. More specifically, small strain theory assumes that deformations are so small (in relation to the size of the underground opening) that any geometric change in the continuum can be disregarded (Fig. 1a). In fact, however, the geometry is updated during loading (or unloading) according to large strain theory and thus equilibrium and stiffness are evaluated on the deformed configuration of the continuum (Fig. 1b).In problems involving large deformations, where the undeformed and the deformed tunnel geometry differ significantly, small strain theory leads to erroneous and sometimes even nonsensical results (i.e. it can predict wall displacements even greater than the excavated radius under conditions of very low stiffness and strength, high in situ stress and low support pressure). This can easily be verified from the widely applied relationships for the ground response curve. For example, in the ideal case of linearly elastic behaviour, the convergence of an unsupported opening equals (1+?) s0 / E (where E, ? and s0 denote the Young’s modulus, Poisson’s ratio and initial isotropic stress, respectively) and is greater than 100% for E < (1+?) s0. Although convergences are less than 10% in the great majority of tunnelling projects, very large deformations may take place when tunnelling through weak rocks under a high overburden (Fig. 2). This paper will first present a very simple and practicable way to account for large strains, based entirely on the results of routine small strain analyses, and will subsequently show the importance of addressing large strains in tunnel analysis and design with reference to three typical case studies of tunnelling in squeezing ground."