Mathematical model of landslide stable equilibrium

. A definition of landslide stability condition is given for any sliding surfaces, density, mass, volume, slope, i.e., in general. As a result of mathematical analysis, equilibrium equations in coordinates are obtained. When violating any of these conditions, the landslide movement begins. The problem is in the way of obtaining real parameter values entering the equations. The mechanical and mathematical model of a landslide having an arbitrary sliding surface is the subject of the study. The aim is determining a time of landslide movement beginning and central issues in the task of landslide prediction. Materials and methods. A standard rectangular coordinate system with the origin at the vertex of the landslide body surface was chosen. A derivation of the equation of the landslide body equilibrium in coordinates was given through the equation of surface in general, through the normal friction force vector in components of the coordinate axes and the traction force vector in components of the coordinate axes. Results. The conditions of landslide stability were obtained. The most critical problems were identified. The solution to these problems can lead to the development of theoretical and practical methods for predicting landslide processes, which is very important for solving the problems of ensuring the safety of buildings and structures located on the slope areas. Conclusions. It is necessary to set the real values of all the parameters, to identify the shape of the sliding surface, to determine the real parameters of the landslide body, and correctly position the rectangular coordinate system. The most close approach to solving these problems is possible in case of applying the methods of integrated approach to the analysis of landslide slope area stability, which includes an engineering and geological method (a method of obtaining objective information about the physical and mechanical characteristics of soils on landslide areas of the investigated slope) and an engineering and geodetic method (a method of obtaining objective information about the terrain, area and slope). Acknowledgements: The authors express their gratitude to the reviewers.