Effect of compressible layer on time-dependent behavior of soft-rock large deformation tunnels revealed by mathematical analytical method

Abstract

The application of compressible layers is considered to be the most promising solution for solving the problem of large deformations in deep soft-rock tunnels. However, although significant effort has been devoted to understanding its mechanical working, the effect of the compressible layer has not been completely revealed. This study theoretically predicts the mechanical response of a deep soft-rock large deformation tunnel by applying a compressible layer. The theoretical model involves a circular tunnel, which is supported by a compressible layer and concrete lining, and subjected to a non-hydrostatic stress field. The influence of the tunnel face advancement is described by the stress release coefficient, and the three-stage deformation characteristics (elastic–yielding–compaction) of the compressible layer material are considered in this model. The entire tunnel deformation process is divided into unlined and lined (further subdivided into elastic, yielding, and compaction phases of the compressible layer material) phases. A series of complex potential functions in different media (rock, compressible layer, and concrete lining) and at different phases is provided; subsequently, the unknown coefficients in these functions are determined using the stress balance and displacement continuity conditions at different interfaces. Thus, the analytical solutions for tunnel displacement and support pressure at different phases are obtained. Good agreement between the numerical and analytical results is observed after performing the numerical simulation to validate the reliability and feasibility of the proposed analytical derivation. Finally, a parametric sensitivity investigation is conducted by including the yielding stress of the filling material, yielding length of the compressible layer, and installation time of the support. Adequate attention is paid to the tunnel displacement and support pressure on the 100th day and their development laws at the positions of θ = 90°, 45°, and 0° during the first 100 days. Some interesting findings are presented, and useful design suggestions for the compressible layer are provided.