Modeling of Grouting Penetration in Porous Medium with Influence of Grain Distribution and Grout–Water Interaction

In this study, a numerical model of grouting penetration in a porous medium is established. The fluid flow in the interstices of the porous medium is directly modeled by Navier–Stokes equations. The grouting process is considered as a two-phase flow problem, and the level set method is used to characterize the interaction between grout and groundwater. The proposed model has considered the nuances for each grain during grouting penetration, instead of representing the fluid flow as a continuum process. In the simulation, three kinds of porosity (0.3; 0.4; 0.5) and two kinds of grain size distribution (0.5~1 mm; 1~2 mm) are used. Results show that: the pressure drop along penetration distance is approximately in a linear trend. The variation of filling degree along grouting distance approximately obeys a quadratic polynomial function. The injection pressure is influenced by the porosity and grain size of the porous medium, especially by the former. A theoretical analysis is carried out to propose an analytical solution of the grouting penetration. The analytical solution gives a good estimation when the grain amounts in the porous medium are small, and the difference becomes larger as the grain amounts increase.