Rapid assessment of the mechanical response of deeply-buried tunnels: Governing equations, parameter calibration, and GUI design

Rapid and reliable evaluation of rock deformation around deeply buried tunnels remains a major challenge in underground engineering. This study presents Tunnel Solver , an integrated framework that couples a non-linear analytical rock (NAR) constitutive model with a semi-analytical boundary value problem (BVP) solver for deep tunnels. An automated calibration strategy is developed to identify model parameters directly from conventional triaxial data, employing an unconstrained Levenberg–Marquardt optimisation with an adaptive branch-switching scheme to accommodate highly non-linear responses. For data-scarce scenarios, an empirical method is employed to enable parameter estimation. The framework is then implemented in a graphical user interface (GUI), providing a unified workflow for parameter identification, tunnel analysis, and visualisation. Numerical examples demonstrate its capability to capture the deformation behaviour of rocks with distinct characteristics, offering an efficient and transparent tool for deep tunnel assessment.