Mathematical Simulation of the Stressed-Strained State of the Foundation of Earth Dams with an Open Surface Under the Influence of Heat and Mass Transfer in the Two-Dimensional Case

Abstract

This paper considers the problem of mathematical simulation of the stressed-strained state of the foundation of the earth dam with account for the heat and mass transfer in the presence of a free surface of ground waters. We have obtained a numerical solution of the corresponding boundary-value problem in the two-dimensional case in the inverse formulation with the use of a computational algorithm based on numerical conformal mapping of the composition domain with a curved boundary and the fi nite difference method.Keywords: boundary-value problem, stressed-strained state, heat and mass transfer, earth dam, free surface, conformal mapping, fi nite difference method.Introduction. The problem of estimating the stressed-strained state of earth dams is one of the urgent problems of hydraulic engineering. Earth dams are the most popular type of hydraulic engineering structures. The difference in climatic, geological, topographic, and hydrological conditions determines the different technologies of building dams and their designs. The operation of the earth dam is strongly infl uenced by the fi ltration fl ow which under real conditions is often realized under nonisothermal conditions, as well as by the salt solutions in its foundation.The stressed-strained state of earth masses strongly depends on the above factors. An increase (decrease) in the level of ground waters (underfl ooding of the territory, drainage), the formation of salt solutions, and the presence of various temperature fi elds (seasonal and daily temperature fl uctuations) lead to a redistribution of stresses in the earth of the foundation of the dam. This fact should be taken into account in designing, building, and operating earth dams and other analogous structures.Numerous accidents on hydraulic engineering structures caused by destructions of their foundations are known. Therefore, in order to embody reliability in the design of such structures and provide safety of people working on them, it is necessary to take into account the infl uence of the heat and mass transfer on the strain characteristics of their earth foundations.The stressed-strained state of earth masses has been the subject of many papers. For instance, in [1] the stressedstrained state of earth foundations of hydraulic engineering structures with fi ltration of ground waters, pure waters, and without fi ltration of these waters was considered. Further investigations on these lines with account for the processes of heat and mass transfer under fi ltration of underground waters were carried out in [2][3][4][5]. However, in these works the thermal regime of the earth medium was not taken into account. The solution of the problems of heat and mass transfer and fi ltration consolidation in a porous medium was also the subject of [6][7][8][9].In this connection, the aim of the present work was the mathematical modeling of the stressed-strained state of the foundation of the earth dam with account for the heat and mass transfer in the foundation with fi ltration of salt solutions through ...

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