**3. Requirements to analysis as a geotechnical measure of karst protection**

One of the most effective geotechnical karst protection measures is the cementation of the cover soils above the karst soils. Schemes of karst protection cementation of the foundation are developed on the basis of the Russian Code (SP 22.13330.2011), which recommends cementation of the cavities and the entire thickness of the karst soils. However, in practice, these strata often reach considerable sizes (from 15 to 20 m), and their cementation to the full depth to monolithic rock soils where karst cavities do not form is not possible due to a significant rise in the cost of construction and technological problems of cementation and control its quality at great depths.

Investigations of the stress–strain state of the artificially strengthened foundation base over the karst cavity [10] made it possible to establish that the most efficient method was the cementation of the soil mass in the roof of the karst soils. In this case, the additional deformations in the foundation base are minimal when cavities occurrence in karst soils. Also, soil collapse into the karst cavity is not allowed if the height of the probable collapse area above the cavity does not exceed the thickness of the artificially strengthened soil layer.

The design forecast of the possibility of soil collapse into the karst cavity is based, as a rule, on the classical view of the distribution of stresses and the mechanism of the arches formation above the karst cavities. The arch above the cavity in the equilibrium state (up to the moment of its collapse) can be considered as an area of increased stresses and deformations, the size of which is determined by the strength and deformation characteristics of the soils. When cementing a soil layer of a given thickness over the karst soils in which the cavity growth is predicted, this area depends on the thickness and characteristics of the cemented soils, as well as on the maximum predicted cavity size for the standard operating life of the building and on the building loads.

The state of the collapse process characterizes the excess of the boundary values of the tensile and compressive stresses around the cavity that can be obtained from Mohr's circle of stress. Therefore, the boundaries of the region of increased stresses and the formation of shear strains can be determined using the strength condition according to Mohr-Coulomb failure criteria, taking it as the boundary condition of rock flow and its collapse. Thus, the boundaries of a possible collapse area are defined as the locus of points at which the Mohr-Coulomb failure criteria are met.

Determination of additional load on the bridge foundation pile under karst deformation.

During the formation of a karst hole in the base of the bridge support pile foundation the additional loads are transferred to the piles. The additional vertical loads can be taken into account as the tangential stresses on the lateral surface of the piles, directed to the pile base.
