Abstract.The results of the analysis of probabilistic methods that are used to assess the deformed state of the foundations of engineering structures are presented. A finite element analysis of the stress-strain state of the "man made soil ground -foundation -structure" system was carried out. A method for probabilistic calculation using the finite element method is proposed. On a real example, the level of reliability of a design decision based on a deterministic calculation is estimated by probabilistic calculation. On the basis of the statistic data obtained by imitational modeling, the probability of failure and no-failure operation of the structure regarding the absolute value of settlement and regarding the value of tilt against the reinforcement ratio of soft soil grounds settlements was determined. The probability of failure regarding the value of tilt against the reinforcement ratio was taken (15 to 25%), which is 0.03 -0.05.

In this article the possibility of applying the warping model offered by V. G. Piskunov, A. V. Goryk and V. N IntroductionComposite structures based on light concretes with profiled steel sheeting have been widely applied recently, especially in construction. Most often, these structures are used as lapping in construction of new low-rise buildings as well as in reconstruction of the existing buildings. The use of the light concretes with profiled steel sheeting ensures several advantages, such as the possibility of slab production directly on a building site, structure lightweight and its sufficient strength. However, one of the main problems which limits the application of concrete structures with profiled sheeting is the absence of a sufficiently reliable method for its analysis.The accounting for a combined action of sheeting and concrete, as well as the determination of the moment of their separation and the coming loss of load-carrying capability of the slab are the most difficult and interesting tasks here. Since separation of the profiled sheeting from the concrete occurs due to transverse stresses at the boundary of contacting materials, determination of the transverse stresses is the main task of such a method. Herewith, shear deformations should be taken into account as they cause cross-section warping. One of the models which combines all those features is a model developed by V. G. Piskunov and co-authors. Accounting for inhomogeneous structure of the cross-section is a distinctive feature of this model. Existing models [1][2][3][4][5][6][7][8][9][10] are used for analyzing layered beams and slabs with a simple cross-sectional shape without inclusions, so the considered model enables us to take into account any inhomogeneous structure of cross-section. However, this model has not yet been applied for analyzing reinforced concrete structures.To assess the applicability of checking and verify the model, offered by V. G. Piskunov and co-authors in [11][12][13] for studying steel reinforced concrete structures, it is necessary to carry out an analysis of a real structure, and to compare the obtained results with the experimental data. To do so, a polystyrene concrete slab with profiled steel sheeting (PCSPSS) for which experimental results were known has been taken as the object of research.

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The light concrete (polystyrene concrete) composite slab with profiled steel sheeting was considered. In this slab, the flexible reinforcement (PMA-2) was used as strengthening. Previous experimental studies have shown that this slab has increased carrying capacity in 2.4 times compared with a similar slab without additional anchoring means. The finite element method (FEM) was used for a detailed study of the PMA-2 slab work and its components. The calculations of light concrete composite slab allowed to investigate the work of profiled steel sheeting, material contact, their bundles, as well as the work of the reinforcement and its influence on the stress-strain state parameters of polystyrene concrete and profiled steel sheeting. Comparison by FEM calculations with experimental data confirmed the accuracy and adequacy of the developed model for PMA-2 slab.