# A 3D Two-Phase Landslide Dynamical Model on GIS Platform  
[PERSON]  
1 [EMAIL_ADDRESS] (A.T.); [EMAIL_ADDRESS] (X.G. )1 State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China;
Navier-Stokes equations provides fundamental information such as the velocity, acceleration, and pressure of landslides at different time intervals, enabling the simulation of landslide motion. However, these governing equations are all partial differential equations. A significant challenge lies in solving complicated time-dependent non-linear hyperbolic model equations, thus developing a comprehensive representation of the entire runoff process, where the solutions of these equations should capture the fundamental physical principles underlying the entire process. Regrettably, the development of a comprehensive analytical solution is an arduous task, particularly in intricate scenarios such as geophysical flows. Even under certain simplified conditions, the exact solutions to these equations tend to be either exceedingly intricate to be ascertained in a closed-form manner or, in numerous instances, nonexistent [8; 9; 10; 11]. This predicament stems from the intricate nature of the nonlinear partial differential equations and the dynamic evolution of boundary conditions, collectively delineating the dynamic behavior of landslide flow, spanning the spectrum from simple to complex. In order to solve this equation and simulate the landslide motion process, some scholars have resorted to simplifications. Firstly, [PERSON] was a trailblazer in mass flow modeling. He reshaped avalanche dynamics based on fluid dynamics, derived the model equations and their integrals, and developed the Voellmy model [12]. However, due to the assumption of a mass point, the theoretical formulations of this model are overly simplified, making it incapable of accurately predicting the run-out distances and mass distribution information in the deposition area of geophysical flows [13]. Furthermore, this model is unable to account for the rheological and mechanical properties of materials, is constrained to one-dimensional scenarios, and depends on topographical characteristics and the duration of long-run periods. Subsequently, [PERSON] and [PERSON] established the depth-average theory on this foundation. They assumed that the granular material is an incompressible, frictional Coulomb-like continuum with finite volume similar to [PERSON]'s friction law and thus derived a one-dimensional depth-averaged mass conservation equation and momentum conservation equation. In the depth-averaged model, it is assumed that changes in porosity result in variations in density, and there is no systematic dependence of friction on shear strain rate [14]. The model's governing equations have undergone a significant simplification through depth averaging. However, it comes at the cost of losing some details of the flow field, such as intense fluidization and high shear rates. Following this, scholars such as [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. further refined and extended the model [8; 9; 15; 16; 17; 18; 19]. As most of these models are singularly focused on single-phase behavior, researchers like [PERSON], [PERSON], [PERSON], and [PERSON] later expanded the depth-average model to incorporate the effects of pore fluid [20; 21; 22; 23; 24; 25; 26; 27]. For example, [PERSON] and [PERSON] introduced a fluid-solid mixture model to describe the motion of two-phase mixtures and extended it to two dimensions [22; 28]. [PERSON] divided landslides into liquid and solid phases to depict the landslide motion process [23]. These models are all based on depth-average theory, which simplifies the motion in the Z-axis direction under the assumption of shallow mass flow. This simplification allows for the efficient solution of governing equations within a relatively short timeframe, thereby enhancing the capability to predict landslide movement processes.