Grouting is widely used for mitigating the seepage of underground water and enhancing the stability of fractured rock mass. After injection, the viscosity of the grout gradually increases until solidification. Conventional multifield analysis models ignoring such effects greatly overestimate the penetration region of the grout and the stability of the grouted rock structures. Based on the 3D unified pipe-network method (UPM), we propose a novel numerical model considering the time-dependent viscosity of the grout, therein being a quasi-implicit approach of high efficiency. The proposed model is verified by comparing with analytical results and a time-wise method. Several large-scale 3D examples of fractured rock mass are considered in the numerical studies, demonstrating the effectiveness and robustness of the proposed method. The influence of the time-dependent viscosity, fracture properties, and grouting operation methods are discussed for the grout penetration process.

In grouting process, filtration is the retention and adsorption of cement-grout particles in a porous/fractured medium. Filtration partly/even completely blocks the transportation channels in the medium, greatly decreasing its permeability. Taking into account filtration effects is essential for accurately estimating the grout penetration region. 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. 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. By comparing the model with the experimental results, we firstly verify the proposed numerical model. 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. 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.

The cracking elements method (CEM) is a novel numerical approach for simulating fracture of quasi-brittle materials. This method is built in the framework of conventional finite element method (FEM) based on standard Galerkin approximation, which models the cracks with disconnected cracking segments. The orientation of propagating cracks is determined by local criteria and no explicit or implicit representations of the cracks' topology are needed. CEM does not need remeshing technique, cover algorithm, nodal enrichment or specific crack tracking strategies. The crack opening is condensed in local element, greatly reducing the coding efforts and simplifying the numerical procedure. This paper presents numerical simulations with CEM regarding several benchmark tests, the results of which further indicate the capability of CEM in capturing complex crack growths referring propagations of existed cracks as well as initiations of new cracks.