An account of the foundation in assessment of earth structure dynamics

An assessment of the dynamic behavior of a plane earth structure with account of its foundation is considered in the paper. A structure with a foundation is considered as an inhomogeneous system, the material of its certain parts is considered elastic or viscoelastic. To assess the effect of the foundation on dynamic behavior of the structure, a finite domain is cut from the foundation and conditions are set at the boundary of this domain that provide energy entrainment from the structure to infinity in the form of the Rayleigh wave. To describe the internal dissipation in material, a linearly hereditary theory of viscoelasticity with the Rzhanitsin kernel is used. A mathematical model, method and algorithm have been developed to assess the dynamic behavior of the structure-finite foundation system. To ensure the adequacy of the mathematical model and to assess the accuracy of the calculation, model problems have been solved when describing the process under consideration. Dynamic behavior of inhomogeneous viscoelastic system of earth dam-foundation with non-reflecting boundary conditions on the boundary of the final domain of the foundation is investigated. In the process of studying the dynamic behavior of inhomogeneous viscoelastic “structure-foundation” systems, a number of mechanical effects