A phase-field-based multi-physics coupling numerical method and its application in soil–water inrush accident of shield tunnel

• A multi-physics coupling numerical method for mixed-mode cracks is developed. • The phenomenon of internal force redistribution is revealed by the proposed method. • A safety index is proposed to evaluate the safety state of cracking tunnel linings . The mixed-mode cracking of brittle materials in multi-physics coupling problems has always been a research hotspot. In this study, a phase-field-based multi-physics coupling numerical method is established to simulate the mixed-mode cracking of brittle materials under fluid–structure coupling. The proposed method is available to simulate the mixed-mode cracks of arbitrary topology, and the cracking behavior is governed by a crack evolution equation. To ensure consistency of the crack evolution equation, the crack-driving force is innovatively unified with the critical energy release rate. The phase-field-based multi-physics coupling numerical method is implemented in the finite element framework. Then, the proposed method is applied to simulate the structural discontinuous crack damage (SDCD) induced by soil–water inrush in shield tunnel under complicated geological conditions with confined water. Compared with the field inspection and monitoring, the numerical model performs well in simulating the SDCD and deformation of tunnel lining. It is also found that the soil–water inrush has a significant effect on the distribution of water-earth pressure acting on the tunnel lining, and the internal force of tunnel lining is redistributed during the evolution of SDCD.