## 4 Effect from the Rheology Parameters  
To understand the effect of the rheology parameters on the wave generation, three rheological variables sets used in Equation (1) are proposed. They are un-yield viscosity \(\mu_{A}\), yield viscosity \(\mu_{B}\), and yield stress \(\tau_{y}\). The un-yield viscosity \(\mu_{A}\) plays a role in constraining the deformation of the slumps. The effect of \(\mu_{A}\) is expected to be marginal as long as the stress is larger than the yield stress [56; 57]. In the Bingham model, the yield stress \(\tau_{y}\) and yield viscosity \(\mu_{B}\) are the key rheological parameters. In this study, however, the influence of three rheological variables, \(\mu_{A}\), \(\mu_{B}\), and \(\tau_{y}\), are discussed in detail. A series of sensitivity analyses is conducted with a wide range of the variable sets. The results are compared with the laboratory data of [PERSON] [16]. While dealing with a landslide problem, the role of un-yield viscosity \(\mu_{A}\) is to stop the landslide deformation, which is discussed in Part I [42]. Figure 6 shows the free-surface profiles of four different un-yield viscosities: \(\mu_{A}=10^{2},~{}10^{4},10^{6},10^{10}\) Pa s. The yield viscosity \(\mu_{B}=50\) Pa s and the yield stress \(\tau_{y}=1000\) Pa are kept the same. The differences between the 4 simulated results are indistinguishable. This indicates that adopting \(\mu_{A}=10^{10}\) in this study guarantees a converged result in terms of un-yield viscosity \(\mu_{A}\). The sensitivity analysis of the yield viscosity \(\mu_{B}\) is presented in Figure 7 with a range of \(0\leq\mu_{B}\leq 500\) Pa s. The result of NASA-VOF2D-Bingham (Assier Rzadkiewicz [16]) (\(\mu_{B}=0\) Pa s, \(\tau_{y}=1000\) Pa) are presented as a reference. In this sensitivity analysis, the un-yield viscosity \(\mu_{A}=10^{10}\) Pa s and the yield stress \(\tau_{y}=1000\) Pa are kept the same. In Figure 7, the four results from Splash3D have no obvious differences in terms of free-surface profiles at the early stage of t = 0.4 s. However, the differences become more obvious at t = 0.8 s at x = \(-0.1\) m. This phenomenon is affected by the yield viscosity \(\mu_{B}\). The larger yield viscosity slows down the sliding speed of the slump, resulting in a shallow wave trough. The effect of the yield stress \(\tau_{y}\) is presented in Figure 8 with a range of \(0\leq\tau_{y}\leq 2000\) Pa. In this analysis, the un-yield viscosity \(\mu_{A}=10^{10}\) Pa s and the yield viscosity \(\mu_{B}=50\) Pa s are kept the same. The results of NASA-VOF2D-ideal ([PERSON] [16]) and Fluidity ([PERSON] [10]) are presented as references. In 0, the result of Splash3D (\(\tau_{y}=0\) Pa) is similar to the results of NASA-VOF2D-ideal [16] and Fluidity [10]. This is no surprise since \(\tau_{y}=0\) indicates the Newtonian-type slump, which has a similar behavior to the assumptions of NASA-VOF2D-ideal and Fluidity results. Compared to the effects of the un-yield viscosity \(\mu_{A}\) and yield viscosity \(\mu_{B}\), the effect of yield stress \(\tau_{y}\) is more significant to the free-surface profile. The larger yield stress \(\tau_{y}\) delays the yield processes and results in a milder free-surface displacement. As seen in 0, the case of \(\tau_{y}=1000\) Pa has the best fit to the laboratory data. Overall, the yield viscosity \(\tau_{y}\) of the slump is an important variable in the wave generation and slump movement. It is the key rheological variable in the Bingham model, which distinguishes the Newtonian or non-Newtonian fluid. Figure 9 is the assembly of the free-surface profiles as well as the slump surface profiles of all simulated cases with the combinations of un-yield viscosity \(\mu_{A}\), yield viscosity \(\mu_{B}\), and yield stress \(\tau_{y}\).