## 4 Numerical Modeling of Da'anshan Landslide
### Numerical Simulation Results and Analysis
#### 4.3.3 Comparison of Flow Depth Characteristics in Different Simulations  
To analyze the effect of rigid-like sliding duration (\(t_{s}\)) on the dynamic characteristics of the landslide, two additional simulations with different \(t_{s}\) were carried out. Except for the sliding duration (\(t_{s}\)), all other parameters have the same values in all simulations. For simulation (II) and (III), \(t_{s}\) = 2 s and 6 s, respectively.  
The initial area of the source zone is about 4175 m\({}^{2}\), and the different evolutions of the simulated impact areas are shown in Figure 11. The impact areas of simulation (II), (I), and (III) increased to 4625 m\({}^{2}\), 4693 m\({}^{2}\), and 5367 m\({}^{2}\), respectively in 2 s, 4 s, and 6 s, which increased by 10.8%, 12.4%, and 28.6% relative to the initial area. Therefore, the impact areas increase slowly during the period of the multi-block model. The maximum impact areas for \(t_{s}\) = 2 s, 4 s, and 6 s are 14,399 m\({}^{2}\), 13,961 m\({}^{2}\), and 13,415 m\({}^{2}\), respectively. Within a few seconds of the triggering stage, if the occurrence of disintegration is advanced by 2 s, the maximum impact area will increase by about 3.1% to 4.1%. It can be seen that the smaller the \(t_{s}\) value, the greater the peak value of the impact area. As the block sliding duration (\(t_{s}\)) decreases, the simulation results of the integrated dynamic model should be closer to the single depth-averaged model.  
Most depth-averaged models are based on fluid dynamics; these models include the influence of the lateral earth pressure coefficient, which constitutes the diffusion term in the model equations. The larger the lateral earth pressure coefficient, the more obvious the diffusion will be. In a multi-block model, multiple blocks within a group have the same acceleration component, the interaction between blocks is ignored, and there is no lateral diffusion effect between blocks within the group. The greater the spatial extent of a group, the more masses with the same acceleration component are contained within the group. The lower lateral diffusion and the larger group dimension are the main reasons for the low kinetic energy of landslides in the multi-block stage.  
In Figure 12, the flow height distributions along the profile line (the green dashed line in Figures 4a and 9a) in three simulations were compared. At 4 s (Figure 12a), simulation (I) and (III) have the same distribution of flow height because they are both in the multi-block model stage. Only simulation (II)experienced a depth-averaged model stage of 2 s; its landslide front edge is about 20 m ahead of the others, and its flow heights are lower than the others. At 6 s (Figure 12b), simulation (II) and (I)experienced the depth-averaged model stage of 2 s and 4 s, respectively. Therefore, after the outward spreading, the flow height obviously decreased. Since simulation (III) was at the end of the multi-block model stage, the height of the flow did not decrease significantly. The gaps between the three landslide fronts further increased.  
Figure 11: Comparison of landslide impact areas of three simulations.