## 1 Introduction
[PERSON] [19] implemented the Bingham model into a depth-averaged numerical model to simulate the hyper-concentrated flows. The bottom friction was approximated by a third-order polynomial function to save computational time [19]. [PERSON] [20] developed a two-dimensional two-layer model to simulate the confluence of clear water and mudflow. They used the Harten scheme [21] to solve the depth-averaged equations and the Strang splitting method [22] to manage the friction term. The model was certified by comparing the simulation results with the prediction of [PERSON] [19]. Recently, [PERSON] [16] proposed a first-ever multi-mechanical, multi-phase mass flow model that employed pressure-and rate-dependent Coulomb-viscoplastic rheology, very flexible for the application to the wide range of geophysical mass flow. Given the above studies, theoretical models or two-dimensional depth-averaged numerical models can be used to simulate mudflows in simplified conditions [6; 8; 11; 12; 15; 16]. The depth-integrated model is simplified from Navier-Stokes equations by ignoring the vertical acceleration [23]. The depth-integrated model is suitable to predict the flow without strong vertical acceleration or a sharp velocity shearing [24]. The vertical acceleration and velocity shearing are important in the case of a slope with rugged topography or mudslide overtopping a structure. Inside a complex 3D flow structure, the tailings material will transfer from an un-yield/plug zone to a yield/liquefied/sheared zone if the shear stress is greater than the yield shear stress. Before the tailings reach this plug zone, the liquefied zone might dominate the entire flow field due to strong shear. Adopting a three-dimensional rheology model is an alternative to fully and globally describe the strongly converging and diverging flows [19; 20]. For more detailed results, solving the three-dimensional Navier-Stokes equations is recommended [21; 22]. The Navier-Stokes equation modes were utilized to study a mudflow in the 1990s. Many of these studies concentrated on solving 2D problems [7; 16; 25]. With the advance of computers in the early twentieth century, the 3D Navier-Stokes equations were able to study mudflow by smoothed particle hydrodynamics (SPH) method [22; 26], and projection method [20; 23; 24]. The rheological properties are crucial issues in a slump or a tailings flow simulations. The slump or tailings fluid is a non-Newtonian fluid in nature [27] with complex rheological properties. The travel distance and the spreading of a slump or a tailings flow are affected by the rheological equation [28]. As for the determination of the rheological parameters, [PERSON] [27] determined the yield stress and viscosity of tailings flow by using rheometer and slump tests. The mixture of different materials leads to a complex, yet not well understood rheological behavior [29]. Field observations of mudflow behavior and rheology are challenging and still rare. Numerical modeling is chosen when an assessment of mudflow behavior is needed for planning, zoning, and hazard assessment [28; 30; 31; 32]. Most models require direct calibration to capture site-specific behavior. However, reliable calibration data are scarce, and laboratory experiments are difficult to be upscaled to field situations [29]. This study is divided into two parts. The first part, the main body of this paper, is to build a slump-type landslide model. The slump material is simulated as a homogeneous non-Newtonian material, whose behavior is described by the Bingham model, conventional bi-viscosity model, and modified bi-viscosity model. The failure of the gypsum tailings dam in 1966 is used for the model validation, calibration, sensitivity analysis. The free surface of the slump is tracked by the volume of fluid (VOF) [33] method. In the second part provided in the other paper, tsunamis are generated by a slump on a slope. The slump is described by Bingham model. The accuracy of model is validated by the laboratory data of [PERSON] [34].