| Grouting is one of the treatment methods for groundwater hazard.However,the spatiotemporal variation of paste viscosity has not been accurately described,and the existing numerical methods cannot simulate the paste-water mixing process.Above defects limited the application of numerical simulation in grouting.In order to solve this problem,the following work is developed in this paper:(1)Based on the Volume-of-Fluid method,the governing equations of water-paste system are carried out.In this framework,following the spirit Continuous-Species-Transfer method,the time transfer equation which can describe the viscosity of paste phase at any position in the domain independently is derived.This equation solves the residence time of paste phase in the computational domain,namely the transport time.Reference previous research,the numerical approach of transport time tracking for flowing water grouting is proposed.(2)Based on the miscibility assumption,a mathematical model considering the interfacial dispersion in two-phase system was developed.The corresponding volume fraction equation and momentum equation were also derived.Thus,the mixture formed by two-phase miscibility could be properly considered in numerical simulation.Based on the above work,by implanting the governing equation proposed in this study with appropriate finite volume discretization and the using of PIMPLE algorithm,the corresponding solvers for flowing water grouting are proposed.(3)In order to solve the numerical diffusion of above time transfer equation,the counter-gradient transfer method was employed and an artificial convection term was added to the time transfer equation to suppress the numerical diffusion error.Through validation,the reconstructed time transfer equation shows better accuracy at the phase interface and the transport time in the domain can be effectively tracked.A two-dimensional droplet falling case is also set up to discuss effect of the artificial coefficient H and the influence of its value.Through two-dimensional cavity case,the influence of different material properties on transport time is studied.It is found that the expansion of the viscosity difference between two phases will aggravate numerical diffusion.Finally,a study on mixing process of water and paste was carried out to verify the mathematical model considering the dispersion effect.(4)According to previous experiments,the numerical simulation research on the still/flowing water grouting of flat fracture is carried out.For still water grouting,it is found that this method can accurately predict the grouting pressure variation by comparing with the experimental results.In the case of flowing water grouting,the calculated results are in good agreement with the paste diffusion behavior presented in the experiments.The blocking behavior in the fracture was also investigated.The paste viscosity near the wall is higher and the will be blocked earlier,the blocking region gradually expands to the interior,then the paste phase loses its fluidity.(5)The numerical simulation of still/flowing water conduit grouting is carried out,different cases were set up according to whether the dispersion effect is considered or not.Compared with previous experiments,it is found that the numerical simulation of conduit grouting is more accurate when considering the dispersion of two-phase interface,whether it’s still water or flowing water.The blocking behavior is also investigated.It is found that when a slice of the conduit is completely filled with paste,its blocking behavior is similar to fracture grouting.Otherwise,the blocking will start at the bottom of the conduit and develop upward. |
