Nonlinear Dimensional Analysis of Trapezoidal Valleys Subjected to Vertically Propagating SV Waves

This paper studies the seismic response of soil basins emphasizing the sensitivity of 2D dynamic response to geometric and material properties. This is accomplished through a formal dimensional analysis accounting for fully inelastic soil response thus augmenting the generalization potential of the results, and providing a novel framework for future research on the subject. It is shown that 2D valley response may be described through the following key dimensionless parameters: (1) the valley shape factor s, expressing the slope inclination; (2) the impedance ratio i, which expresses the stiffness of the soil relative to the bedrock; (3) the wavelength ratio lambda(S), which is a function of soil stiffness and seismic excitation frequency; (4) the rigidity ratio v, expressing the stiffness of the soil relative to its strength; and (5) the resistance ratio r, which expresses the degree of soil nonlinearity. The effectiveness of the dimensional formulation is verified through the numerical analysis of equivalent valleys, assuming elastic and nonlinear soil response. Finally, a parametric study is conducted to gain insight on the effects of the introduced dimensionless parameters on the dynamic response of trapezoidal alleys. It is shown that decreasing the valley slope or the wavelength ratio promotes wave reflections within the wedge, thus enhancing the possibility of wave interferences and subsequently leading to 2D aggravation on the valley surface. On the other hand, the geometry-dependent parasitic vertical acceleration increases as the valley slope becomes steeper. As the degree of soil nonlinearity increases, 2D phenomena tend to become localized close to the valley edges.