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algorithm amplitude analysis applied augmentation axis beam behaviour Beskos body boundary conditions Boundary Element Boundary Element Method calculation computational considered constraint contact force contact problems contactor node convergence coordinates coupled defined deflection deformation denotes derivative discretized displacement dynamic Earthquake effect eigenvalue elastic Elem equations finite difference finite element method flow fluid fluid-structure interaction formulation foundation frequency function geometrical grid half-space integration interface iteration Lagrange multipliers Lagrangian linear load loop material mechanical mesh motion nodal line nodes nonlinear normal numerical solution obtained Papadrakakis parameters particle pavement pipeline plate PLEXIS-3C Poisson's ratio POUNDING POUNDING SCENARIO present procedure radial Rayleigh wave rotationally periodic scheme second-order shear shown in Figure soil solved space-time step stiffness equation stiffness matrix strain stress structural domain structure structured grid substructure tangential target segment technique temperature thermal tion transient values variables variation vector velocity vertical vibrations wave