The karst protection foundations design

The authors analyze the features of the base modeling for the analysis of a foundation in a karst territory, taking the stiffness of the design parameter of the above‐foundation part of the building into account. Advantages of the contact model of a base (the model of the variable coefficient of subgrade reaction) are analyzed. It is proposed to determine the coefficients of subgrade reaction (stiffness of the piles) around the karst cavity with decreasing these coefficients in relation to the same coefficients calculated using standard methods (i.e., without karst deformations). Analytical solutions for different types of foundations are presented. The method for estimating the thickness of an effective karst protection geotechnical screen is proposed.


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 creation of such a constructive scheme of the underground part of a building or structure that will not allow the forces of the bearing structures to exceed the permissible values if the conditions for the development of karst deformations in the base do not change;  the installation of a protective geotechnical screen, either at the base of the foundation, or above the karsting soils, which will eliminates or substantially reduces the negative influence of karst development on the bearing structures of the building or structure. 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.

REQUIREMENTS FOR ANALYSIS OF THE FOUNDATION AS A CONSTRUCTIVE MEASURE OF KARST PROTECTION
The purpose of constructive measures of karst protection is to prevent the destruction of the structure when karst deformations occurred at the base of the foundation. These measures are designed on the bases of the analyses that ensure a sufficient load bearing capacity of the foundation and abovefoundation structures to accept the additional loads that arise when karst deformations occur in the base. This is usually achieved in two ways: • by carrying out analysis of the foundation in conjunction of the above-foundation structures for the case of the karst deformation occurrence with the specified parameters; • by cutting through the karsting soils and supporting the foundation on monolithic rocks.

The karst protection foundations design GOTMAN Natalia 1 , GOTMAN Alfred 2
Examples from the practice of design and construction show that the foundations designed for the karst deformations occurrence provide protection of the building or structure from destruction when the karst processes in the base are activated.
However, the inclusion of a foundation that provides effective karst protection of a building can only be guaranteed if it is designed on the basis of calculated positions and initial data corresponding to the nature of the development of karst deformations. The main initial data in this case are the design parameters of karst deformations. The design parameters of karst deformations are determined (predicted) depending on their type. There are three types of the karst and suffusion deformations development: -"Hole", when the karst cavity develops in karsting soils and "floats" under the foundation base; -"Subsidence" as the result of the karst and suffusion processes development in the cover mass; -"Local subsidence", when the karst cavity develops in karsting soils or in the cover layer, but does not "float" under the foundation base.
The decision which kind of karst deformations is critical is determined by the soil conditions and design features of the projected building or structure. The most dangerous variant of development of deformations is accepted for design.
For shallow buildings or structures, it is advisable to perform calculations for the occurrence of a karst hole under the foundation base (the design diameter of the karst hole is taken as the design parameter of the karst deformation) or for the formation of a cauldron with the specified parameters.
For buildings or structures with the underground part, the most dangerous can be a karst deformation of the type "local subsidence", since the foundation is approaching karsting soils and the growth of the cavity in them, even if the stability of the arch is maintained, can cause significant additional forces in the bearing structures of the underground part. At the same time, the size of the karst cavity can be adopted as the design parameter of karst deformation, for which its arch is stable. Figure 1 shows an example of determining the size of such a cavity. In this case, the mathematical modeling of the karst cavity growth is performed using the finite element model of the soil mass by eliminating the weakened zones (zones of the local loss of stability) around the karst cavity while maintaining the constant control of the equilibrium conditions of the arch. The growth of the cavity occurs before the maximum value of its diameter is attained, at which the equilibrium condition of the system is satisfied in the pre-limit state of the cover mass soil. Figure 1 shows the lines of equal soil shear strains with the cavity width increase from value b 1 to b 3 in karsting soils.
To design the reliable and economical foundations, it is important to take the effect of the occurrence of karst deformations on the stress-strain state of the base and bearing structures into account.
Taking into the consideration the fact that the geometric dimensions of karst cavities in karstic rocks are not strictly defined, and the modeling of karst occurrence at the foundation base of a building or structure cannot guarantee the reliability of the results of the foundation analysis, the simplest solution is to model a karst hole under the foundation base in accordance with the dimensions determined by the statistical -probabilistic methods. At the same time, in the places of the holes formation, the ground "leaves" from under the foundation base, and the load is redistributed to adjacent areas, in which there is a contact of the foundation with the base. The modeling of the base behavior when karst  where E P is the p cavity oc Analysis of the pile-raft foundation in karsted areas is usually performed for karst deformations of a "hole" type. The stiffness ratio of the piles is equated to zero within the boundaries of the karst hole, and outside these boundaries it is assumed to be constant, and is determined by the standard methods, that is, without taking into account the formation of a karst hole. Due to the peculiarities of the pile-raft foundation behaviour, namely the effect of pile pre-stressing in the soil, a situation is possible when the soil mass, stabilized with piles, accepts stresses of karst deformations and the karst cavity under the pile tips does not develop to the foundation base. In this case, karst deformations should be considered as "local subsidence". In this case the forces in the raft sections and, accordingly, the reinforcement of the raft, can be significantly reduced. Considering these features of the pile-raft foundation behaviour, a method was developed for analysis of the stiffness coefficient of the pile foundation above the karst cavity located under the pile tips. Analytical solutions were obtained to determine the pressures in the base and the settlements of the raft over the karst hole (Gotman , 2008). Analysis of the pile strip foundation when a karst hole occurre is usually performed by mathematical modeling of the foundation on an unevenly deformed base. For modeling of the base and foundation in this case, it is advisable not to complicate the calculation model, but, on the contrary, to apply the simplified models. Such a calculation model of the pile strip foundation base when a karst hole occurre is the contact base model, according to which the piles are modeled by constraints of finite stiffness, and the stiffness of the bonds is determined quantitatively by analogy with the stiffness ratio of the piles. Based on the results of the experimental and theoretical studies of the stress-strain state of the "pile strip foundation -base" interaction, the regularities of the change in pile behavior around the karst hole were obtained, on the basis of which an analytical solution was developed to determine the stiffness ratio of piles, providing for introduction of the decreasing ratio ξ with respect to the stiffness ratio, determined without taking the karst hole into attention (Gotman , Davletyarov,2017). The decreasing stiffness ratio ξ is suggested to be determined depending on the pile length (L), the hole depth (H), the distance from the pile to the hole boundary (B): (4)

REQUIREMENTS TO ANALYSIS OF THE FOUNDATION 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 karsting soils. Schemes of karst protection cementation of the foundation are developed on the basis of the Russian Code [SP 22.13330.2011], which recommend cementation of the cavities and the entire thickness of the karsting soils. However, in practice these strata often reach considerable sizes (from 15to 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 made it possible to establish that the most efficient method was the cementation of the soil mass in the roof of the karsting soils. In this case, the additional deformations in the foundation base are minimal when cavities occurrence in karsting 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 karsting 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 the 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 is met.

CONCLUSION
1. To design the reliable and economical foundations, the practical design experience of Russian engineers-researchers confirms the efficiency of a combined approach use in the foundations analysis while karst deformations occurrence based on the use of an elastoplastic soil model for calculating stresses, deformations and coefficient of subgrade reaction of the base.
2. The most effective way to determine the coefficients of subgrade reaction is to use the lowering coefficients with respect to the coefficients of subgrade reaction defined by standard methods without taking karst deformation into account.
3. Based on the results of numerical and field studies with the elastoplastic soil model, methods for determining of the lowering coefficients for raft, pile-raft and pile strip foundations, including very deep foundations, have been developed.
4. One of the most effective geotechnical karst-protection measures is the grouting of the cover mass above the karsting soils. In this case, the soil collapse into the karst cavity will not occur if the height of the probable collapse area above the cavity does not exceed the thickness of the artificially strengthened soil layer. The boundaries of a possible collapse area can be defined as the locus of the Mohr-Coulomb failure criteria points.