Phase-field fracture modeling and energy-based stability analysis of cemented paste backfill

Abstract

Cemented paste backfill is widely used in underground mining to provide ground support and enable the sustainable disposal of mine tailings. As mining operations encounter increasingly complex stope geometries, the fracture behaviour and stability of exposed CPB structures become critical concerns. Conventional stability analyses generally rely on strength-based elastoplastic models that cannot explicitly represent the initiation, propagation, and coalescence of cracks governing the quasi-brittle failure of CPB. They also rarely account for the continuous evolution of fracture properties caused by cement hydration. This dissertation therefore develops two hydration-dependent phase-field fracture models and an energy-based method for assessing the stability of CPB structures. First, an evolutive phase-field model is developed for tensile fracture by linking cement hydration and binder content to the elastic modulus and tensile fracture resistance of CPB. The model is validated against direct tensile, split-tensile, and semi-circular bending tests conducted at different curing ages and binder contents. The results demonstrate its ability to reproduce tensile crack initiation and propagation, load-displacement responses, and the transition from diffuse early-age damage to increasingly localized fracture with continued hydration. Second, a phase-field model is developed for mixed-mode fracture by decomposing the crack-driving energy into tensile and shear components and introducing distinct tensile and shear critical energy release rates. Experimental tests on single- and double-notched specimens, together with additional tensile and mixed-mode validation cases, demonstrate that the model captures crack initiation, propagation, interaction, and coalescence under complex loading conditions. Based on the proposed mixed-mode model, an Energy Limitation Method is developed for three-dimensional, field-scale stability assessment. The method progressively reduces the tensile and shear fracture resistance until unstable, through-going crack propagation occurs, thereby defining an energy-based stability index. Increasing cement content from 4.5% to 8% increased the stability index from 1.6 to 4.0, while increasing curing time from 28 to 120 days increased it from 1.75 to 2.65. In contrast, increasing backfill height from 30 to 60 m reduced the index from 5.35 to 1.25. Overall, the developed framework integrates hydration-dependent tensile and mixed-mode fracture modeling with energy-based stability assessment, providing a physically consistent approach for investigating crack-dominated failure and supporting the design of CPB structures.