Numerical simulation of rock creep and failure using a Norton-Bailey-based four-dimensional lattice spring model

Creep deformation significantly influences the long-term stability of rock structures subjected to sustained loading. This study presents a novel computational framework that integrates the Zienkiewicz-Pande (ZP) plasticity model and the Norton-Bailey (NB) creep law within a four-dimensional lattice spring model (4D-LSM), enabling simulation of the coupled elastic, plastic, and creep responses of geomaterials. To capture tertiary creep characterized by an accelerated deformation rate, the NB model is extended with a strain-based elasto-brittle failure criterion, leveraging the inherent fracture-handling capabilities of the 4D-LSM. The proposed framework is validated against experimental and analytical benchmarks through single-stage uniaxial and multi-stage triaxial compression simulations, demonstrating good agreement and predictive accuracy. The model’s applicability is further demonstrated in tunnel excavation analyses, showcasing its effectiveness in predicting long-term time-dependent deformation. A three-point bending test is also simulated to assess the model’s capability in reproducing creep-induced fracture. Overall, the ZP-NB-4D-LSM framework offers a robust and efficient tool for simulating the full creep-fracture process in rock engineering applications.