ИЗМЕНЕНИЕ НАПРЯЖЕННОГО СОСТОЯНИЯ СКЛОНА ГОРЫ С УСТУПОМ ПОД ДЕЙСТВИЕМ ВНЕШНЕЙ НАГРУЗКИ С УБЫВАЮЩЕЙ ТРЕУГОЛЬНОЙ ЭПЮРОЙ

Abstract

The Kyrgyz Republic covers an area of – 198,5 thousand km2. Mountains and mountain slopes occupy more than 94 % of the country. For this reason, in mountainous areas, mountain slopes are used for conducting various types of human economic activity ledges at different heights of the mountain slope, from hundreds of meters to 4–5 km. The object of the study is the ledges of the mountain slope, which are necessary for economic activity, located at different heights of the slope. The subject of the study is the initial and changed stress-strain state of the massif near the scarp of the mountain slope from the action of gravitational and tectonic forces. The aim of the study is to create a mathematical model and calculate the stress-strain state of the massif near the scarps of the mountainside to check the boundary conditions with the load of a decreasing triangular epure. The objective of the study is to establish the laws of stress distribution in each point of the massif by solving the differential equation of equilibrium using the Kolosov-Muskhelishvili method. Ledges are formed either by nature or created by man, technogenically, and are mated with the mountain slope at a different angle of inclination at different heights of the slope. To assess the stability and safety from landslide processes of structures located in the ledge zone, it becomes necessary to carefully study the stress-strain state of the massifs. To study the stress state of a rock mass, the following main methods have been used: the unloading method, the finite element method, the finite difference method, as well as the analytical methods of Kolosov-Muskhelishvili in the version where the conformal mapping is used [Gulnara]. Thus, to study the state of massifs in the zone of ledges of the mountain slope, it is necessary to create an analytical model of the stress-strain state of massifs of ledges of the mountain slope, in which the zones of conjugation of the ledge and the mountain slope, the possible heights of the ledge, the effect of volumetric and surface loads would be taken into account in a single analytical model. In this case, the authors consider the problem when the stress state of a mountain massif with a symmetrical scarp in natural conditions, which is formed under the combined action of gravitational, horizontal tectonic forces and external distributed loads with a triangular epure. The problem is solved using the Kolosov-Muskhelishvili method and the MATNCAD software environment. As a result of the calculations, the patterns of stress distribution in the massifs of the mountain slope with a ledge have been created, where the actions of gravitational, horizontal tectonic forces were taken into account each separately. To check the boundary conditions with a load with a decreasing triangular diagram, the stresses are calculated for the contour points in the vicinity of the loaded section of the contour. The patterns of distribution of the initial stress state of the slope mass with ledges are presented for each stress component in the form of stress isolines.