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The double impulse is introduced as a substitute of the fling-step near-fault ground motion. A closed-form solution of the elastic–plastic response of a structure on compliant (flexible) ground by the “critical double impulse” is derived for the first time based on the solution for the corresponding structure with fixed base. As in the case of fixed-base model, only the free vibration appears under such double impulse and the energy approach plays an important role in the derivation of the closed-form solution of a complicated elastic–plastic response on compliant ground. It is remarkable that no iteration is needed in the derivation of the critical elastic–plastic response. It is shown via the closed-form expression that in the case of a smaller input level of double impulse to the structural strength, as the ground stiffness becomes larger, the maximum plastic deformation also becomes larger. On the other hand, in the case of a larger input level of double impulse to the structural strength, as the ground stiffness becomes smaller, the maximum plastic deformation becomes larger. The criticality and validity of the proposed theory are investigated through the comparison with the response analysis to the corresponding one-cycle sinusoidal input as a representative of the fling-step near-fault ground motion. The applicability of the proposed theory to actual recorded pulse-type ground motions is also discussed

Closed-Form Critical Earthquake Response of Elastic–Plastic Structures on Compliant Ground under Near-Fault Ground Motions