A generalized mathematical model predicting the mechanical response of tunnel yielding supports in extremely large deformation environments

Abstract

“Radial–circumferential” combined yielding supports can tolerate extremely large deformations of the surrounding rock without being damaged. However, to date, the coordinated deformation mechanism of combined yielding supports remains unclear, and a well-established design model is still unavailable. This study analyzed the mechanical responses of tunnels with combined yielding supports using a mathematical analytical method. First, the mechanical characteristics of the compressible layer and primary lining with highly deformable elements were introduced, and their deformation processes were divided into three stages in the analytical model. Second, the deformation modes of the combined yielding supports were proposed, and their mechanical responses were classified into three cases. A mechanical model of the interaction between the surrounding rock and combined yielding supports was established. In the proposed analytical model, the rock geomaterial exhibited viscoelastic behaviour, and the effects of tunnel face advancement and support installation delay were considered. An analytical solution corresponding to each deformation mode of the combined yielding supports was provided to predict the rock displacement and interface contact stresses. Furthermore, numerical modelling was conducted for comparison with the analytically predicted results, indicating the reliability and feasibility of the proposed analytical model. Finally, a quick and convenient parametric investigation was performed to determine the sensitivity of the model output results to three design parameters: the yielding lengths of both the compressible layer and primary lining, and the yielding stress of the compressible layer. The analysis revealed that within a certain range, the tunnel displacement and interface contact stresses were highly sensitive to these three parameters. Below or beyond this range, changes in these parameters did not significantly affect the output results of the model. Based on the results of the parametric analysis, several design insights into the combined yielding supports were obtained.