Beam on poroelastic foundation
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The beam on elastic foundation problem has been studied by previous researchers for several decades. They have developed various kinds of models using different solving techniques for this purpose and studied the immediate (elastic) settlement of the foundation under an appUed loading. In the present study, the idea of the modified Vlasov model developed by VaUabhan and Das (1988) is extended to include time-dependent behavior of fine-grained (clayey) soils, a common foundation problem in geotechnical engineering. The concept of poroelasticity (time-dependent elasticity related to pore water dissipation) is also used here in developing a technique to study the long term behavior of the soU which is assumed to be normally consolidated and saturated with pore water, that follows the immediate deformation. This problem has been studied by many engineers assuming that the beam is relatively rigid. However, when the beam becomes long and flexible a very complex interaction occurs between the beam and clayey soil. This behavior of soil-structure interaction was weU enlightened in the study of the elastic settlement of modified Vlasov model. In the present study, this behavior is combined with one-dimensional consolidation analysis. To the knowledge of the author, this type of interaction has not been done in the past. For investigating the consolation settlement of soil medium, Sandhu and Pister 1970) developed a linear, coupled field theory between the deforming porous solid and the pore water flow. Following their concept, and assuming some simplified variation of the displacement and pore pressure whhin the soil, a total energy functional was developed. Applying the minimum theory of energy functional, four differential field equations that represent the deformation of soil and pore pressure distribution, at a certain time during the consolidation, are developed. The equations are solved using the classical finite difference method in the spatial domain. A finite difference approximation similar to the Crank-Nicolson scheme is used here to solve the flow continuity equations in time domain. The results from the analysis provide the settlement of the beam and pore pressure variation in the soil at each time step.