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

Abstract

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

Devising a procedure for integrated modeling of riverbed shape in the area of bridge crossing in order to avoid dangerous washing erosion

“…In work [8], in order to determine the average depth of the flow under the bridge under the calculation conditions, the calculation of the total erosion is performed for the predicted cross-sections of the riverbed. The quasi-three-dimensional form of steady-state finite-difference flood flow equations proposed by the authors allows taking into account the law of distribution of the averaged hydrostatic pressure vertically and the distribution of suspended sediments, the influence of the cohesion of fine-grained soils and the resistance of vegetation on general and local erosion of the bottom, but it makes it difficult to determine the redistribution of water flows and sediments between river and floodplain sections of the river.…”

“…Our review of the literature [1][2][3][4][5][6][7][8][9][10][11] revealed that in the cases of solving complex problems of studying riverbed processes for the practical purposes of designing bridges and other important hydraulic structures, it is necessary to use and improve numerical methods that make it possible to simulate hydromorphodynamic processes in riverbeds. Therefore, it is expedient to study the specific problem of river processes, namely the hydromorphodynamics of bottom and bank changes, through the integrated application of modern computer technologies with the use of GIS for the grid approximation of the calculation area and analysis of the calculation results.…”

Devising a procedure to calculate and analyze parameters for passing the flood and breakthrough wave taking into consideration the topographical and hydraulic riverbed irregularities

“…The calculation of the total erosion under bridges is carried out for the projected cross-sections of a riverbed [7] in order to determine, under the estimated conditions, the average depth of a flow under the bridge. This is done by comparing the total erosion coefficient with the permissible one Р dop and the hydraulic characteristics of the flow (velocity V, depth H) on the verticals of the sub-bridge section.…”

“…where L і is the length of the river section with the velocity of breakthrough wave movement V. For example, for a river with a well-formed riverbed, with narrow floodplains without large heads, at a slope of the bottom i=0.0012, the average velocity of movement along the riverbed and floodplain sections, according to [7], is V 1 =10 km/h. In this case, according to Table 1, this is a riverbed with a characteristic of 2 at a slope i=0.0015 and an average roughness n=0.140.…”