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To develop the methods for predicting deformations on floodplain areas in the zone of influence of bridge crossings, a mathematical model of a suspended flow with grass vegetation was developed. The problem of calculating the hydrodynamic fields of velocities and pressure in artificially compressed flows refers to the theory of shallow water since the vertical size (flow depth) is substantially smaller than the horizontal dimensions, such as length and width. In accordance with this, the proposed model is based on the equation of distribution of velocity structure and the depth of a floodplain flow in approximation to two-dimensional dependences taking into consideration force factors. Force factors determine resistance at flowing around vegetation in floodplain areas and resistance of washout of fine-grained soil. To obtain an unambiguous solution of the considered problem, boundary and initial conditions were added to the presented closed system of original equations. These conditions make it possible to determine the level of a free surface of flow and the zone of influence of a bridge crossing at different stages of the estimated flood. Based on finite-difference analogs of transfer equations, the distribution of velocities and depths in estimated sections was calculated. By iteration, the longitudinal velocity in a flood flow with vegetation elements was determined. The results of the calculation of washout on floodplain areas of a sub-bridge watercourse of the lowland river Siversky Donets were obtained. The depth of a flood flow after a washout was determined based on the ratios of actual and flood-free velocities. When compared with the initial bottom marks, the washout of the larger floodplain is 0.96 m, that of the smaller floodplain – 1.28 m. The proposed scientifically substantiated solution for ensuring optimum interaction of floodplain flows with bridge crossings makes a certain contribution to improving the reliability of their operation due to the quality of design works and the corresponding reduction of construction and operating costs

Predicting deformations in the area of impact exerted by a bridge crossing based on the proposed mathematical model of a floodplain flow