Determining the risk level of ground motions (GM) for structures is crucial for their damage control and resilience enhancement, while the assessment and measurement criteria of GM risk levels for structures isolated by double concave friction pendulum system (DCFPS) remain unclear. Through statistical analysis of the response distribution of DCFPS with various design parameters under 1013 GM records, this study determines an energy dissipation efficacy of 99 %, a floor velocity of 0.35 m/s, a floor velocity of 0.60 m/s, and the displacement capacity of DCFPS as the response criteria for assessing four performance states of efficacy, habitability, functionality, and safety, respectively. In addition, the value of GM intensity in PGA, PGV, PGD, and the equivalent velocity of seismic input energy (VE) for measuring the four GM risk levels corresponding to the four performance states are obtained. Furthermore, a classification of GMs based on earthquake magnitude and fault distance is proposed according to their risk to DCFPS. It is found that the intensity value of each GM risk level varies for different design parameters of DCFPS but fluctuate within a small range, however, great differences exist when using different intensity measures (IM) in classifying GM risk levels. Therefore, based on the correlation between IMs and DCFPS responses, the conservatism of PGA, PGV, PGD and VE in assessing the risk of GMs for DCFPS are evaluated.