A reliable mitigation of the liquefaction hazard requires an accurate estimation of the consequences of liquefaction in the context of building performance. Knowledge and use of an optimal intensity measure (IM) will reduce variability and improve accuracy of the predicted measure of performance. This paper presents the results of a three-dimensional, fully coupled, nonlinear, dynamic parametric numerical simulation of shallow-founded structures on layered, liquefiable soils, previously validated with centrifuge results. The generation and redistribution of excess pore pressures as well as soil-structure interaction effects were directly considered in the simulations. The influence of different IMs recorded at the base rock, far-field soil surface, and foundation was evaluated and compared on engineering demand parameters (EDP) that relate to structural performance and damage potential, such as foundation settlement and peak, transient, inter-story drift ratios. The IMs identified with the best combination of efficiency, sufficiency, and predictability in predicting the structural EDPs of interest were identified at the base rock as: CAV and CAV5 for permanent settlement, PSA[ T STo] for total and flexural drift ratios, and PGV for rocking drift ratio.