Application of the boundary element method for soil structure interaction problems
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Soil-structure interaction problems are those in which the behavior of the structure and the behavior of the soil surrounding it are interdependent, and the solution requires the analysis of both the structure and the soil in a compatible manner. Modeling of soil is very complicated and approximations are made purely on the experience and judgment of the engineer. So far, because of the simplicity of the concept, Winkler's Model is being used extensively in soilstructure interaction problems. Closed form solutions are available only for simple geometry and loading conditions, thereby restricting the analysts to idealize the problem. There are improved models developed by Pasternak, Vlasov and Leontiev, adding complexities in calculations. The drawback in these analyses is the nonunique value of the coefficient of subgrade reaction of the soil. Recently, the finite element method has been used to solve these problems. Here the advantage of modeling the problem is offset by the tedium in the preparation of input data for the analysis. It is in this context that the boundary element method is used in this research for application in some soil-structure interaction problems. In this work, the structure is represented by finite elements and the soil medium by boundary elements. The soil stiffness matrix is developed and condensed up to the interface. This matrix is efficiently transformed and coupled to the structure stiffness matrix for complete analysis. Computer programs have been developed in two and three dimensional elasticity for application to typical soilstructure interaction problems. Also, a condensation procedure has been suggested for analyzing layered soil media. The results compare favorably with complete finite element analysis. The elastic constants of the materials are sufficient for the analysis, thereby totally avoiding the value of the coefficient of subgrade reaction. Thus, the codes developed establish their superiority for implementation in soil-structure interaction problems. This procedure is a starting step in geotechnical problems for an accurate and rational analysis to replace the semiempirical relations presently in use.