Earthquake-induced soil liquefaction can generate significant damage to low-rise structures, as evidenced in the 2010–2011 Canterbury Earthquake Sequence in New Zealand. In this paper, the structural response of low-rise structures on medium dense granular soils of different permeability (but both nominally liquefiable) was investigated using dynamic centrifuge modelling. In the tests, a series of consecutive motions from the 2010–2011 Canterbury Earthquake Sequence was considered, followed by a long duration ‘double-pulse’ motion from the 2011 Tohoku Earthquake which can potentially apply large inertial loads after liquefaction has been triggered. It was observed that the lower permeability test reached full liquefaction at shallow depth during shaking, while soil of higher permeability was only comparable in response in the first earthquake; in subsequent strong aftershocks excess pore water pressures were substantially reduced. The structural response of higher permeability soil was 10–45% larger due to the increased motion transmission ability of the soil after the initial earthquake. The structure on the higher permeability soil did, however, show reduced post-earthquake tilt in all motions tested. These results suggest that popular liquefaction triggering analyses may be limited in their ability to properly estimate the hazard posed to structures on nominally liquefiable soil when estimating resistance to subsequent motions (aftershocks).