This study presents a multidimensional compliant model for block displacement that allows the overriding displaced block to deform as a flexible viscously-damped oscillating mass. These oscillations impart additional stresses to the shear plane and influence the amplitude of deformation. Plastic yielding and permanent deformations occur when the resultant vector from strike and dip earthquake-stresses and resonance-stresses exceed the mobilized capacity of the soil to resist shearing. The portion of the model that describes the strength of soil is formulated within the frameworks of critical state soil mechanics and normalized soil properties. We found that traditional Newmark-type displacement models neglect the strike component of motion and resonance of the displaced mass. Taken together, these omissions lead to considerable errors in computing displacements. Our model includes these important elements.

Incorporating compliance into our model, we found that when the natural resonant frequency of the sheared flexible-mass coincides with multiples of the mean motion frequency, displacement can dramatically exceed those of traditional rigid-block Newmark analyses. On the other hand, when block resonant frequencies are out of phase with earthquake motions reduced deformations are predicted. When the mean frequency of the earthquake motion exceeds the resonance frequency of the displaced ground, traditional rigid Newmark models tend to over-predict deformation. A rigorous assessment of shear deformation in deposits of soft soil requires consideration of oscillatory motions in the overriding sheared block.