Accurately predicting the movement process of high-speed landslides is the prerequisite for their precise prevention and control. The material point method (MPM) has great potential for predicting the movement process of high-speed landslides, but it is rather difficult to handle complex three-dimensional terrain, and thus is still mostly used for two-dimensional landslide simulation. In this paper, by constructing an algorithm for extracting the normal information of the slip surface and constraining the normal momentum of the grid nodes on the slip surface boundary, a three-dimensional material point method model capable of simulating the movement process of high-speed landslides is proposed, and this model is used to simulate and analyze the granular flow curved flume test and the Yanjiagou landslide in Shanyang County, Shaanxi Province. The simulation results of the flume test show that the maximum velocity of the landslide front is about 1.1 m·s−1, and the simulated front and rear edge positions are consistent with the measured results. The simulation results of the Yanjiagou landslide show that the main body of the landslide slides as a whole along the slope; after initiation, a small amount of the rear-edge landslide body is pulled apart and separates from the main sliding body, forming a deposition morphology that branches along the mountain ridge; the maximum velocity of the landslide exceeds 20 m·s−1, and the maximum deposition thickness occurs in the gully at the toe of the slope, about 49 m; under the constraint of the curved gully, the landslide underwent two movement deflections and exhibited a climbing phenomenon; the simulation results are basically consistent with the field conditions.The model in this paper avoids the slip surface embedding problem caused by traditional multi-material contact algorithms, improves the computational efficiency of complex slip surface boundary conditions, and can effectively reproduce the movement process of high-speed landslides under complex terrain. The simulation results can provide a theoretical basis for the risk prevention and control of such landslides.

 Introduction:

  High-speed landslides often exhibit extremely strong mobility and a large disaster-affected range, and thus have attracted widespread attention from the academic community. Effective prediction of the movement process of such landslides is the key to scientifically formulating their prevention and control measures. Since the 1980s, with the improvement of computational power, kinematic simulation technology for high-speed landslides has developed rapidly, and numerical simulation has gradually become the main means of predicting the movement process of such landslides.

  According to the landslide medium, existing kinematic models of high-speed landslides can be mainly divided into three categories: discrete medium models, continuum medium models, and coupled models.Discrete medium models simplify the sliding body into blocks or particles and use the discrete element method (DEM) or the discontinuous deformation analysis (DDA) method to solve the governing equations of the block or particle system; they have been well applied in simulating high-speed landslide-debris flows, but such methods are limited by the number of blocks (particles) when establishing large-scale three-dimensional landslide models. Continuum medium models treat the sliding body as a continuous material, usually establish partial differential governing equations of the landslide based on the principles of mass and momentum conservation, and solve them using numerical methods such as the finite difference method (FDM), finite volume method (FVM), material point method (MPM), or smoothed particle hydrodynamics (SPH). Coupled models are couplings of the former two types of models; some of them, such as the SPH-DEM and CFD-DEM models, have achieved preliminary applications in the analysis of fluid-solid coupling problems. At present, the most widely used continuum medium models mostly adopt the depth-averaged assumption to simplify the equations, that is, ignoring the variation of physical parameters in the depth direction of the landslide. Such models are called depth-averaged models and are suitable for rapid prediction of the disaster-affected range of landslides; some representative models such as LS-RAPID, RAMMS, DAN3D, and Massflow have been widely applied, but due to the depth-averaged assumption, such models are difficult to accurately characterize the internal deformation and forces of landslides.

  In contrast, MPM, as a relatively new continuum numerical method, combines the respective advantages of the Eulerian and Lagrangian methods and has significant advantages in analyzing large deformation problems of rock and soil masses, and therefore has been increasingly applied in high-speed landslide simulation. On the other hand, because the material point method is rather difficult in handling complex three-dimensional slip surface terrain, this method is still mostly used for two-dimensional landslide simulation. Recently, some scholars have attempted to simulate the three-dimensional movement process of high-speed landslides using MPM. For example: Xue et al. considered the constraint effect of the slip surface on the sliding body by fixing all background grid nodes below the slip surface, and carried out a three-dimensional material point method analysis of the movement process of the Hongshiyan landslide; Lei et al. generalized the basal material below the slip surface as multi-layer fixed material points carrying the normal information of the slip surface, and based on the multi-material contact framework, realized three-dimensional material point method simulation of granular flow under complex terrain conditions; Zhao et al. adopted a similar method, mapped the normal information of the basal material points to the background grid nodes, and constructed a three-dimensional material point method model of high-speed landslides; Zhang et al. generalized the slip surface as a triangular mesh surface and, through thepenalty functionconsidered the constraint effect of the slip surface on the material points of the sliding body, and carried out three-dimensional simulation of high-speed landslides under complex terrain.However, existing three-dimensional MPM models usually need to map the terrain information of the basal material points to the grid nodes, or search for the contact between material points and the slip surface, so there is still room for further improvement in computational efficiency.

  Based on the above status quo, this paper proposes a simple algorithm for extracting the normal information of the slip surface and directly assigns the normal information to the grid nodes on the slip surface boundary.By constraining the normal momentum of these nodes, a three-dimensional material point method model capable of simulating the movement process of high-speed landslides under complex terrain is constructed. The model in this paper does not need to map the terrain information of the basal material points to the background grid nodes, nor does it need to search for the contact between material points and the slip surface, thereby simplifying the computational workflow and overcoming the problem of insufficient accuracy in calculating the normal vector of the slip surface under the traditional multi-material contact framework。

Conclusions:

  In this paper, by constructing an algorithm for extracting the normal information of the slip surface and constraining the normal momentum of the grid nodes on the slip surface, a new three-dimensional MPM model capable of simulating the movement process of high-speed landslides is proposed. This model effectively avoids the slip surface embedding problem of multi-material contact models and improves the computational efficiency of complex slip surface boundary conditions. Using this model, simulation analyses were carried out on the granular flow curved flume test and the Yanjiagou landslide in Shanyang County, Shaanxi Province, and the main conclusions are as follows:

  (1) The maximum movement velocity of the sliding body front obtained by the simulation of the granular flow curved flume test is about 1.1 m·s−1, which is consistent with the test results; the front and rear edge positions of the granular flow are close to the test data, indicating that the model in this paper can relatively accurately simulate the constraint effect of curved terrain on the sliding body.

  (2) The simulation results of the Yanjiagou landslide show that the movement stage of the landslide can be divided into three phases: early, middle, and late. In the early stage of movement, the landslide mainly undergoes overall sliding, with a velocity reaching 18 m·s−1. In the middle stage of movement, the landslide collides with the slope on the opposite bank of Daxigou; the left-side sliding body decelerates rapidly, while the right-side sliding body deflects and exhibits a climbing phenomenon. When reaching the location of the mining area construction houses, the maximum velocity still exceeds 20 m·s−1. In the late stage of movement, only the right-side sliding body at the front of the landslide merges into Yanjiagou and undergoes a second movement deflection along the gully. The simulated maximum deposition thickness of the sliding body occurs in Daxigou, about 49 m; the simulated deposition morphology and range of the landslide are basically consistent with the measured results, indicating that the model in this paper has good applicability for simulating the movement process of high-speed landslides under complex terrain.

  (3) The DP yield function adopted by the model in this paper is suitable for simulating granular materials, but the simulation parameters are constants and do not consider changes in the physical properties of the sliding body caused by factors such as landslide disintegration. In the future, more advanced constitutive equations need to be further integrated into the model to improve its accuracy and adaptability.