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Although there is enough knowledge indicating on the influence of frequency content of input motion on the deformation demand of structures, state-of-the-practice seismic studies use the intensity measures such as peak ground acceleration (PGA) which are not frequency dependent. The v max/a max ratio of strong ground motions can be used in seismic hazard studies as the representative of frequency content of the motions. This ratio can be indirectly estimated by the attenuation models of PGA and PGV which are functions of earthquake magnitude, source to site distance, faulting mechanism, and local site conditions. This paper presents new predictive equations for v max/a max ratio based on genetic programming (GP) approach. The predictive equations are established using a reliable database released by Pacific Earthquake Engineering Research Center (PEER) for three types of faulting mechanisms including strikeslip, normal and reverse. The proposed models provide reasonable accuracy to estimate the frequency content of site ground motions in practical projects. The results of parametric study demonstrate that v max/a max increases through increasing earthquake moment magnitude and source to site distance while it decreases with increasing the average shear-wave velocity over the top 30m of the site.

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Currently, there is no reliable design procedure which considers all aspects of liquefaction effects on shallow foundations. There are many light and heavy structures resting on saturated sand with high liquefaction potential in seismic areas. The aim of this experimental and numerical study is to evaluate the performance of two shallow foundations with different contact pressures in liquefaction. The results of the centrifuge experiment of shallow foundations with surcharges of three-story and nine-story buildings on liquefiable sand are presented in detail. Although entire soil profile liquefied, no liquefaction observed under the foundations. There was a clear difference in settlement mechanisms observed beneath the shallow foundation and in the free-field. The heavy foundation fluctuated more strongly compared with the lighter one. The effect of soil permeability and contact pressure on foundation response was investigated during numerical study. The experiment was simulated two dimensionally using a fully coupled nonlinear constitutive model (UBCSAND) implemented in a finite difference program, FLAC-2D. The results show that settlement of foundations increased with the increase of soil permeability. Trends of excess pore water pressure were captured reasonably by the soil model, but the settlement mechanisms were different. The soil model underestimated total liquefaction-induced settlement of shallow foundation, especially for light foundation.