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In this paper, an advanced formulation of a time-domain two-dimensional boundary element method (BEM) is presented and

applied to calculate the response of a buried, unlined, and infinitely long cylindrical cavity with a circular cross-section subjected

to SV and P waves. The applicability and efficiency of the algorithm are verified with frequency-domain BEM examples of the

effect of cylindrical cavities on the site response analysis. The analysis results show that acceptable agreements exist between

results of this research and presented examples. For a shallow cavity, the numerical results demonstrate that vertically incident

SV wave reduces the horizontal components of the motion on the ground surface above the cavity, while it significantly increases

the vertical component for a dimensionless frequency (&eta) of 0.5 and h/a=1.5. The maximum values of normalized displacements

in vertical component of P waves are larger than horizontal component of SV waves for &eta=1.0. For a deeply embedded cavity,

the effect of the cavity on the surface ground motion is negligible for incident SV wave, but it increases the vertical component of

the displacement for incident P wave. Additionally, far and near distances from the center of the cavity show different amplitude

patterns of response due to the cavity effect. Increasing the distance from the center of the cavity, the amplitude of displacement

and the effect of the cavity attenuates significantly.

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In this paper, normalized displacement amplitude of the ground surface was presented in the presence of the semi-sine shaped valley above the truncated circular cavity embedded in a homogenous isotopic linear elastic half-plane, subjected to obliquely propagating incident SH waves as Ricker wavelet type. The proposed direct time-domain half-plane boundary element formulation was used and extended to analyze the combined multi-boundary topographic problems. While using it, only boundary of the valley and the surrounding cavity should be discretized. The effect of four geometric parameters including shape ratio of the valley, depth ratio, horizontal location ratio and truncation thickness of the cavity and incident wave angle was investigated on the responses at a single dimensionless frequency. The studies showed that surface behavior was completely different due to complex topographic features, compared with the presence of either valley or cavity alone. In addition, the cavity existence below the surface could play a seismic isolation role in the case of vertical incident waves and vice versa for oblique waves.