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This paper investigates topographic effects of rocky valleys with irregular topographic conditions subjected to vertically propagating SV waves of Ricker type using a boundary element code. Valleys with two intersecting slopes, [Formula: see text] and [Formula: see text], are modelled in order to study their combined effects on ground motion. Presented in the form of pseudo-acceleration response spectra, results of this work can be extended to similar topographies. The main findings are: (i) [Formula: see text] (the first slope angle) and [Formula: see text] (L is the half width of the valley and [Formula: see text] is its corresponding height) have amplifying effects, and [Formula: see text] (the second slope angle) has de-amplifying effects on the site response. (ii) [Formula: see text] has a straight effect on intensifying the effects of both [Formula: see text] and [Formula: see text]. (iii) The combined effects of slope angles have been found to be important in modifying the response so more than a single slope should be considered for seismic analysis. (iv) Engineers should use the maximum amplification of 2.4 in case of valleys with the first and second slope angles below [Formula: see text].

This paper presents an advanced formulation of the time-domain two-dimensional (2D) boundary element method (BEM) for an elastic, homogeneous unsaturated soil subjected to dynamic loadings. Unlike the usual time-domain BEM, the present formulation applies a convolution quadrature which requires only the Laplace-domain instead of the time-domain fundamental solutions. The coupled equations governing the dynamic behavior of unsaturated soils ignoring contributions of the inertia effects of the fluids (water and air) are derived based on the poromechanics theory within the framework of a suction-based mathematical model. In this formulation, the solid skeleton displacements [Formula: see text], water pressure [Formula: see text] and air pressure [Formula: see text] are presumed to be independent variables. The fundamental solutions in Laplace transformed-domain for such a dynamic [Formula: see text] theory have been obtained previously by authors. Then, the BE formulation in time is derived after regularization by partial integrations and time and spatial discretizations. Thereafter, the BE formulation is implemented in a 2D boundary element code (PORO-BEM) for the numerical solution. To verify the accuracy of this implementation, the displacement response obtained by the boundary element formulation is verified by comparison with the elastodynamics problem.