Analytical spatiotemporal distribution equations of viscous slurry grouting pressure during the grouting process in rock fissures

To give a simpler theoretical solving approach for modeling the grouting process of viscous slurry in porous/broken rocks, this work derives two theoretical spatiotemporal distribution equations of viscous slurry penetration in rock fissures based on the Darcy seepage model (DM) and the Bingham fluid model (BM) through a hypothetical micro-element model. Through a two-dimensional (2D) conceptual grouting hole model with porous media, the applicability of the two proposed theoretical spatiotemporal distribution equations of viscous slurry pressure is validated by comparing the analytical results with the numerical results obtained from the two-phase flow simulation. The results indicate that the analysis results obtained from two proposed theoretical spatiotemporal distribution equations are well consistent with the simulation results at different times and under different grouting velocities. That means the time-consuming numerical simulation of the porous/broken rocks grouting process can be replaced by two proposed theoretical spatiotemporal distribution equations, which will greatly reduce the difficulty of real-time evaluation of the grouting effects in engineering practice and shorten the assessment time.