Mathematical modeling and computer simulation of the filtration processes in earth dams

Abstract

We built a mathematical model of the filtration consolidation of the body of an earth dam with engineering inclusions and erosion zone in a two-dimensional setting. It considers the presence of a damaged conduit in the body of a dam. We also took into account the impact of anthropogenic factors: temperature and the concentration of salts, subsidence of the upper boundary and the displacement of internal points in the region of dam over time. The existence of erosion zone (as a result of damage to the conduit) is considered. Taking into account the erosion zone exerts a significant effect on the overall picture of filtration processes occurring in the body of a dam. Erosion zone has the largest impact on the distribution of excess heads and their gradients. We developed a software application to automate the calculation of numerical solution of a boundary problem using the method of radial basis functions that make it possible to conduct numerical experiments by changing the input parameters and the form, as well as represent results of these experiments in the form of charts and numerical data according to each temporal layer. The software application was developed in the integrated programming environment Microsoft Visual Studio 2008 in the language C#. The impact of the existence of a conduit, erosion zone, temperature and the concentration of salts in the body of a dam was explored at different temporal layers. The distribution of all the desired functions and their impact can be displayed graphically. A series of numerical experiments were performed and their analysis conducted. It is shown as a result that the existence of damage in a conduit in the body of a dam leads to the formation of erosion zone. This, in turn, leads to the gradual filtration destruction of soil material of the dam and its possible complete destruction. The results obtained might help to prevent and to evaluate the consequences of possible accidents without conducting field experiments, and, consequently, to save resources and time.