Simplified lateral free field boundary based on a lumped mass system

After reviewing the studies on the lateral artificial boundaries in dynamic soil-structure interactions,the free field boundary was theoretically analyzed in asymmetric-and symmetric-matrix forms.First,the lumped mass system was combined with viscous or viscoelastic elements to obtain a lumped mass-free field boundary.Second,typical examples were implemented using the finite element software ABAQUS.The incident shear wave was taken to be perpendicular to the bottom to verify the effectiveness of the lumped mass-free field under various sites:underground structures,uniform sites,and layered sites.Finally,the accuracy of the lumped mass-free field boundary was compared with those of the viscoelastic and roller boundaries on different calculation scales,soil damping ratios,structure sizes,and ground motion characteristics.Subsequently,the engineering design values for different damping ratios are given.The results show that the precision of the lumped mass-free field boundary was reasonable,and the operation was simple within the same engineering application.