A numerical solution for unsteady permeation grouting of Bingham grout in saturated porous media considering the threshold pressure gradient

Abstract

To overcome the limitations of steady-state analysis in traditional permeation theory, this study presents an unsteady-state permeation model for Bingham grout flow in saturated porous media under high confining pressures. The model incorporates the threshold pressure gradient (TPG) for Bingham fluid dynamics, which is grounded in two-phase flow principles, to provide a more accurate representation of grout behaviour under these conditions. By utilizing the finite volume method, the fluid partial differential governing equations are discretized, and a custom-designed program is developed to obtain numerical solutions. The program dynamically monitors the pressure gradient at the Bingham grout front, and upon reaching the TPG, adjusts the calculations to accurately track the movement of the grout. The research results indicate the following: (1) The accuracy of numerical solutions depends on the time and spatial step sizes. A time step below 0.1 s limits the errors in the grouting volume and diffusion radius to 2.000 % and 4.32 %, respectively. A spatial step of 0.02 m reduces errors to 4.21 % and 3.85 %, balancing accuracy and efficiency. (2) The numerical solution reveals a nonlinear decrease in grout pressure, with a sharp decrease of up to 74.14 % within 2 m of the grouting pipe before stabilizing near the diffusion front. (3) The slow dissipation of pore water in high-pressure saturated porous media hinders the diffusion and transmission of grouting pressure, thereby limiting the grouting rate. (4) Larger TPGs and smaller pressure ratios hinder grout diffusion, whereas a pressure ratio greater than 2 significantly enhances diffusion, and increasing the TPG from 0.1 MPa/m to 10 MPa/m reduces the maximum diffusion distance by up to 8.11 times. These findings enhance the understanding of grout permeation and diffusion in highly confining pressure-saturated porous media, providing valuable insights for optimizing grouting strategies.