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Extra info for Dynamic and Transient Infinite Elements: Theory and Geophysical, Geotechnical and Geoenvironmental Applications

Example text

E. e. e. e. ν) is 1 3; the velocities of the P-wave and SV-wave in the medium are 3872 m s−1 and 1936 m s−1 , respectively. 10 shows the distribution of displacement amplitudes along the surface of the half-plane as a result of the vertical incidence of either a plane harmonic SV-wave or a plane harmonic P-wave. In this figure, AU is the amplitude of the horizontal displacement on the surface of the half-plane, while AV is the amplitude of the vertical displacement on the surface of the half-plane.

Station 63) of the embankment dam. Although only horizontal displacements are applied on the wave input boundary of the computational model, vertical displacements appear in the dynamic response of an embankment dam because of the wave scattering effect of the embankment dam. 1 Simulation of Dynamic Gravity Dam–Water–Foundation Interaction Systems Extensive studies on the dynamic response of concrete gravity dams due to earthquake loadings have demonstrated that their dynamic response is mainly affected by the following factors: (1) the interaction between the dam and impounded reservoir water (Chopra 1968; Chakarbarti and Chopra 1974; Liam-Finn et al.

21) Substituting Eqs. 20) into Eq. 23) SW where [L]e is a matrix expressing the pressure–displacement relation on the water– solid interface. [NW ] is the following pressure shape function of the water element: [NW ] = [N1 N2 N3 ]. 24) By assembling the element vector {BWS }e on the water–solid interface, the global matrix {BWS } on this interface can be expressed as {BWS } = −ρW [L] ¨ W . 25) 46 3 Application of Two-Dimensional Dynamic Infinite Elements Substituting Eq. 25) into Eq. 12) yields {PWS } = −ρW [EC ]−1 [L] ¨ W .

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