“…Most recent numerical method verifications (Rayamajhi, et al, 2014;and Rayamajhi, et al, 2016) as well as dynamic centrifugal testing results (Rayamajhi, et al, 2015) supported Goughnour and Pestana (1998) arguments. Based on comparing the ground response of the improved and unimproved soil, the ratio of seismic shear stress in improved and unimproved sand, R rd , is (Rayamajhi, 2014): (1) where G r is the shear modulus ratio of the inclusion and sand (= G pc/sc /G s ), A r is the ratio of the inclusion area to the total area (= A pc/sc /A), g r is the ratio of shear strain in the inclusion to the strain in the sand (= g pc/sc /g s ), and C G is a shear factor (= 1.0 for circular inclusions, and ~ 0.5 for rectangular grids).…”