Simulating the grouting process with flowing water based on two-phase flow model using extended numerical manifold method

In this study, an extended cohesive element-based numerical manifold method (Co-NMM) combined with the two-phase flow model is proposed for simulating the migration of the two-phase fluid during the grouting process with flowing water. To achieve this, the two-phase flow model coupled with the Bingham fluid constitutive model is adopted to characterize the displacement process of the multiphase fluid flow. To solve the challenge of simulating the fluid mixing process in the intersecting fracture, the mixed fluid flow algorithm is incorporated into the model to more effectively and accurately capture the flowing and mixing of multiphase fluids. After these improvements, the two-phase flow model coupled with the Bingham fluid constitutive model is verified by reproducing the slurry displacing air and the slurry displacing water in the single fracture against analytical results. The mixed fluid flow algorithm is then validated by reproducing the grouting process in the intersecting fracture under different types of fluid intersection conditions, and comparisons between the results predicted by this proposed method and other numerical methods regarding the diffusion process of slurry and the fluid pressures at the junction are presented. Finally, with the extended Co-NMM, the grouting processes in the fracture network with flowing water are conducted to study the effects of the injection rate (slurry velocity) and the water velocity on the variation of the fluid distribution and slurry diffusion. The results reveal that the injection rate, the water velocity, and the direction of water flow affect the diffusion pattern and diffusion range.