## 6 Conclusions and Future Work  
This study applied the rheology models, BM, CBM, and MBM, to the mudslide simulation. The rheology models were integrated into the 3D Navier-Stokes equations coupled with the LES turbulent model to give a detailed description of the vertical acceleration. The free-surface kinematic was described by the VOF method with a PLIC surface tracking scheme. The BM results were validated by the channel flow and the spreading slow data, which received good agreements in both cases. The Bingham model (BM) and conventional bi-viscosity model (CBM) were then used to simulate FGT66. The predicted inundation distance was 220 m with accuracy at about 73% of the observed data. To improve the result, a modification to CBM was raised. A large viscosity number of un-yield region, \(\mu_{A}=10^{10}\) Pa s, was applied to representing a more rigid behavior of the material as suggested by [PERSON] [34], [PERSON] [45], and [PERSON] [28]. A series of sensitivity analyses on the yield strain rate \(\dot{\dot{y}}_{y}\) was performed by matching the simulated tailings' boundary to the field observation. A larger yield strain rate indicated the tailings with sturdier behavior. The yield strain rate was suggested to be  
Figure 16: The stoppage boundary profiles for sensitivity analysis of concentration \(C_{\text{p}}\). (**a**) Kaolinite simulated by BM; (**b**) kaolinite simulated by MBM; (**c**) typical soils simulated by BM; (**d**) typical soils simulated by MBM. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & **Kaolinite** & & & **Typical Soils** & \\ \hline C\({}_{\text{p}}\) & 0.42 & 0.44 & 0.46 & 0.48 & 0.5 & 0.65 & 0.7 & 0.75 & 0.8 \\ \hline Yield stress & 301.28 & 456.00 & 690.19 & 1.04\(\times 10^{3}\) & 1.58\(\times 10^{3}\) & 374.95 & 889.14 & 2.11\(\times 10^{3}\) & 5000.00 \\ \hline Yield viscosity & 2.29 & 3.31 & 4.79 & 6.92 & 10.00 & 158.49 & 398.11 & 1000.00 & 2.51\(\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The yield stress and yield viscosity of kaolinite and typical soils. \(\dot{\gamma}_{y}=0.2\) s\({}^{-1}\) in the MBM to simulate the FGT66. By the sensitivity analysis, the material of FGT66 was close to the kaolinite with concentration \(C_{\triangledown}=0.5\). The results show that the modified bi-viscosity model (MBM) could provide a better prediction than BM and CBM in terms of the flood distance and the spreading width. The development of the flood free-surface, velocity, strain rate, and un-yield/yield zone were presented and discussed. The important results and conclusions are listed as follows:  
* The Bingham model was successfully integrated into the 3D CFD model to simulate a mudslide by adopting the implicit scheme for the viscosity term;
* If the yield strain was small enough, the conventional bi-viscosity model would converge into the Bingham model numerically;
* The flood distance predicted by BM and CBM was 220 m, with the accuracy at about 73% of the field observation;
* To improve the result, MBM was introduced by giving a large viscosity to the un-yield phase and adjusting the yield strain rate with a sensitivity analysis;
* The flood distance predicted by MBM was 310 m, which was closer to the filed observation with 97% of the accuracy;
* Not only did the flood distance improve, the spreading width improved in the result of MBM;
* The free-surface, velocity, strain rate, and the un-yield/yield profiles were presented and discussed;
* The sensitivity analysis of the grid resolution was performed. The grid resolution in the BM was less sensitive than that in the MBM;
* The analysis of the yield strain rate was carried out. A larger yield strain rate indicated the tailings with sturdier behavior. The yield strain rate was suggested to be \(\dot{\gamma}_{y}=0.2\) s\({}^{-1}\) in the MBM in the case of FGT66;
* The un-yield zone in MBM was sturdier than that in the pure BM.