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With the UPM, 2D and 3D mass/energy transport problems can be transformed into equivalent 1D problems, similar to the lattice element method (LEM). The unified pipe-network method (UPM) is one of these simplified methods it uses equivalent pipe networks to simulate the mass/energy transport processes within a porous/fractured medium. However, when focusing only on mass/energy transport within existing fractures and not their mechanical evolution, much simpler models can be used instead of these sophisticated techniques. Generally, fractures exist naturally within rock-like materials thus, the initiation and propagation of such fracture need to be modelled by sophisticated numerical tools, such as the eXtended Finite Element Method (XFEM), the strong discontinuity embedded approach, the mixed-mode FEM, and the phase-field model. Moreover, research has been presented on the simulation of grout flow considering filtration effects in a fractured, porous medium. Finally, the grout filtration process in a complex 3D fractured network is simulated, indicating that the size of the grout penetration region is limited due to filtration. Then sensitivity analysis is conducted, showing the influences of grout injection pressures, the water–cement ratios of grout (W/C) and the grout injection rates on filtration effect. By comparing the model with the experimental results, we firstly verify the proposed numerical model. The grout is assumed to exhibit two-phase flow, and the filtration effects depend on not only the concentration and rheology of the grout but also the porosity and permeability of the fractured porous medium. In this paper, the 3D unified pipe-network method (UPM) is adopted for simulating 3D grout penetration process in a fractured porous medium, considering filtration effects. Taking into account filtration effects is essential for accurately estimating the grout penetration region.

Filtration partly/even completely blocks the transportation channels in the medium, greatly decreasing its permeability. In grouting process, filtration is the retention and adsorption of cement-grout particles in a porous/fractured medium.