A simple nonlinear constitutive model for rocks and its application to the semi-analytical solution of deeply buried tunnels

In this study, a simple yet robust nonlinear constitutive model for rocks is proposed to capture their unique mechanical behaviors under various loading conditions. The model has three key innovations, including an axial strength evolution equation using normalized variables for simulating crack closure, pre-peak, and post-peak responses, a tangent Poisson's ratio formulation for capturing lateral deformation transition, and a strength reduction concept replacing conventional damage parameters. The model provides an analytical solution for stress–strain relationships, facilitating efficient implementation and avoiding complex plasticity-based stress integration. Its accuracy and versatility are validated by comparisons with the experiment on rocks under various loading conditions. Moreover, the model has been applied to calculate the semi-analytical solution for deeply buried tunnels, showing its potential in geotechnical engineering and serving as an effective alternative to conventional elastoplastic models for rock behavior modeling.