A finite-strain procedure for calculating fictitious support pressure of a tunnel based on a re-developed GRC and LDP considering large deformation

Fictitious support pressure on tunnel walls characterizes the face effect as the tunnel advances, necessitating quantification to fully mobilize self-supporting capacity, especially in rock masses undergoing large deformation. This study presents a method for calculating fictitious support pressure along a tunnel profile using a re-developed Ground Reaction Curve (GRC) and Longitudinal Deformation Profile (LDP). It employs a kinematic additive decomposition of the deformation rate tensor based on finite strain and hypoelastic–plastic theory, accounting for the motion of material points. The numerical implementation is provided, with examples for validation demonstrating the accuracy of the re-developed GRC and LDP in scenarios involving both slight deformations and significant large strains. Extensive efforts address practical issues affecting fictitious support pressure, including deformation formulation for large strain analysis, failure criteria, ground conditions, and rock behaviors governed by constitutive relationships and dilatancy. Results indicate that despite displacement deviations from small strain analysis and a simple linear failure criterion, these methods offer reliable approximations for predicting fictitious support pressure and tunnel convergence in suitable rock quality, thus eliminating the need for rigorous large strain elasto-plastic analyses and complex nonlinear failure criteria during the preliminary design stage of tunneling. An application case study is given to illustrate the practical use of the proposed finite-strain Confinement-Convergence Method framework for analyzing the support effect of steel sets during tunnel advancement.