**1. Introduction**

The methods for analysis and design of the foundation of buildings and structures in karst areas depend on the complexes of the karst protection measures used. Two possible protection options are suggested:


The choice of protection against karst deformations is determined by the level of karst danger. In Russian Codes (SP 22.13330.2011), the two indicated options are assigned to the corresponding groups of measures of karst protection (structural and geotechnical, respectively) and the requirements for analysis of the karst protection foundations are significantly different.

As the results of the investigations of the karst deformations regularities [1–4], and in accordance with the accepted classification the deformations can be divided into the holes and subsidences (**Figure 1**).

The foundation calculation, providing karst deformations in a base, is the most advisable with due regard for the building and base interaction by the numerical modeling. The most simple decision in the given case is the modeling of the karst hole under the foundation base according to the hole dimensions. In places of the formation of the hole, the soil "goes out" from the foundation base and the load is redistributed to the adjacent parts where the contact of the foundation with the soil is provided. When modeling the building and base interaction with the karst hole, the choice of the base model and the determination of its initial parameters are of great importance.

The more important question is the bridge support pile foundation in the karst areas design. The design of the support pile foundation can be carried out in accordance with the comparison of the load-bearing capacity of the piles and the load transferred to the pile. Studies of the pile behavior during the formation of a karst hole in the base [5–8] show that additional vertical and horizontal loads are transferred to the piles. The additional vertical loads are considered as "negative friction" and it is indicated that they must be taken into account. However, so far there have been no proposals to define such additional loads either in the normative or scientific literature.

The numerical studies for defining additional loads on the bridge support foundation piles during the karst cavity formation in the soil under the pile bottoms, depending on the distance to the karst soil and the karst cavity predicted size, are effective. As a result of the studies performed, the regularities of changes in the additional load transferred to the pile, depending on the variable parameters, are established and formulas for calculating the support foundation piles above the karst cavity are proposed.
