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Permanent Displacement Response Spectra

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Permanent seismically-driven deformation of soil occurs when the driving stresses exceed the mobilized capacity of the soil to resist shearing. Soils are flexible and can resonate when excited by earthquake motions. This is especially the case for thick and soft native soils, as well as for landfills and tall engineered-soil embankments. The interaction of earthquake and soil resonance can significantly amplify or de-amplify permanent displacements. Traditional ‘Newmark’-type displacement models assume inflexible (rigid) ground and therefore cannot account for resonance affects on permanent displacements. Comparing the permanent displacements computed by a flexible (compliant) model with those of a rigid model allow us to identify potential amplification. A critical parameter effecting this amplification in flexible soil systems is the site period of the potential slide mass. Permanent Displacement Response Spectra (PDRS) is the amplification ratio of permanent displacements (flexible system displacement/rigid system displacement) plotted against the site period. PDRS is similar to the ‘slope spectra’ concept of Kramer & Smith (1997). PDRS is a useful way to characterize the amplification of permanent displacements in soil due to resonance affects.

Our flexible model for soil deformation is a multi-directional ‘Newmark’-type program that allows the permanently displaced soil mass to deform as a viscously damped oscillator. These oscillations impart added stresses to the shear plane and influence the amplitude of permanent deformations. Incorporating flexibility into our Newmark model, we found that when the natural resonant period of the ground coincides with the mean earthquake period, displacements can greatly exceed those computed by traditional rigid-block Newmark analyses. These amplifications are the peaks of the PDRS plot. On the other hand, when the soils resonant period is out of phase with the earthquake motion, or exceeds it, resultant deformations can be greatly reduced. These de-amplifications are the valleys of the PDRS plot. Rational assessment of permanent deformations in soil requires consideration of motions in the overriding soil mass. PDRS effectively maps the influence of soil resonance on permanent displacement of soil.

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