Slow and very slow landslides can cause severe economic damage to structures. Due to their velocity of propagation, it is possible to take action such as programmed maintenance or evacuation of affected zones. Modeling is an important tool that allows scientists, engineers, and geologists to better understand their causes and predict their propagation. There are many available models of different complexities which can be used for this purpose, ranging from very simple infinite landslide models which can be implemented in spreadsheets to fully coupled 3D models. This approach is expensive because of the time span in which the problems are studied (sometimes years), simpler methods such as depth-integrated models could provide a good compromise between accuracy and cost. However, there, the time step limitation due to CFL condition (which states that the time step has to be slower than the ratio between the node spacing Delta x$\Delta x$ and the physical velocity of the waves results in time increments which are of the order of one-10th of a second on many occasions. This paper extends a technique that has been used in the past to glacier evolution problems using finite differences or elements to SPH depth-integrated models for landslide propagation. The approach is based on assuming that (i) the flow is shallow, (ii) the rheological behavior determining the velocity of propagation is viscoplastic, and (iii) accelerations can be neglected. In this case, the model changes from hyperbolic to parabolic, with a time increment much larger than that of classic hyperbolic formulations.

With the aggravation of climate warming, unstable soil slopes are more and more common in permafrost regions. The long-term monitoring of a slow earthflow (K178 + 530 landslide) in the Xiao Xing'an Mountains permafrost area in Northeast China was carried out. The deformation characteristics and occurrence mechanism of the landslide were studied using field investigation, on-site drilling, sensor monitoring, laboratory test, Google satellite image, unmanned aerial vehicle photogrammetry, and high-density resistivity. To analyze the variation laws of pore water pressure and effective stress and their influence on slope deformation, a coupled hydro-thermo-mechanical model was established to reconstruct the deformation process of the slope. The results show that the groundwater recharge from the permafrost degradation and surface infiltration reduces the soil cohesion and internal friction angle near the main scarp and increases the soil gravity, thus providing dynamic and mechanical conditions for slope deformation. The melting of the continuous segregation ice in the active layer and surface infiltration reduces the soil strength of the sliding surface and provides deformation conditions for the start of the landslide. The combination of these two factors finally led to the occurrence of the landslide. According to its deformation mechanism, it can be judged that the landslide is a thrust-type landslide. In addition, after the melting of the segregation ice, the upper soil slides along the slope under the action of gravity, causing the sliding surface to be parallel to the slope surface. The soil near the main scarp slides downward and accumulates near the toe to form several transverse ridges. The instability of the transverse ridges produces secondary sliding which causes the toe to advance continuously. The numerical simulation results can intuitively reflect the stage deformation characteristics of the slope, pore water pressure changes, and effective stress distributions, which provides a supplement for further understanding the formation mechanism and deformation process of the landslide.