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• Framework to assess the fragility of RC buildings to ground shaking and liquefaction. • Nonlinear incremental dynamic analysis under effective stresses of the soil. • Consideration of soil-structure interaction and soil liquefaction potential. • Conventional fragility curves for buildings due to ground shaking and liquefaction. • Fragility surfaces for buildings due to combined ground shaking and liquefaction. The recent strong seismic events have demonstrated that most damage to coastal buildings is often associated with liquefaction effects. The occurrence of earthquake-induced ground shaking and liquefaction may be dramatic for buildings and poses a considerable threat to people. However, the influence of the simultaneous action of ground shaking and soil liquefaction considering soil-structure interaction (SSI) effects on the structural behaviour of buildings has not been adequately studied yet. In this respect, we propose a methodology for the fragility assessment of non-ductile reinforced concrete (RC) moment-resisting frame buildings exposed to combined ground shaking and soil liquefaction, based on a fully coupled numerical approach considering SSI. A fully coupled (u-P) formulation is employed, which can capture in cohesionless soils the permanent shear-strain accumulation during dilation and soil liquefaction. Two-dimensional incremental dynamic analysis of the nonlinear SSI systems is conducted for the estimation of the building response. The proposed methodology yields either conventional fragility curves, or coupled fragility surfaces, which are a function of more than one intensity measures and provide useful and important information for an integrated fragility assessment. It is shown that the height of the building resting on liquefiable soil may significantly affect its vulnerability to combined ground shaking and soil liquefaction, with the non-ductile low-rise RC frame buildings suffering more structural damages compared to the mid- and high-rise ones. Also, the high-rise buildings, even susceptible to liquefaction, do not sustain severe structural damages but only sink or tilt. The proposed fragility models can be adapted to estimate the risk of typical non-ductile RC frame buildings exposed to ground shaking and soil liquefaction. [ABSTRACT FROM AUTHOR]