In order to assess the damage condition of bridge components for a large-span rigid bridge in a soft clay site in a mountainous area in China southwest, a finite element model of a large-span rigid bridge is established based on the OpenSees software, and the joint probability density distribution function of the ground motion strength and seismic demand and the marginal distribution function of the ground motion are introduced into the kernel density function. As a basis to get the method of calculating the fragility of the bridge members, and the method is verified for its feasibility, on this basis, the damage condition of the bridge components are analyzed, and finally the damage condition of the bridge system are analyzed by the first-order bounds method and the improved PCM method (IPCM). The results showed that: (1) Kernel density method (KDE) can effectively calculate the damage probability of each component, for example, under ground motions with PGA equal to 0.2 g, the probability of slight damage of the 1# pier is 29%, that of the intermediate consolidation pier (2# pier ~ 4# pier) is about 90%; the probability of slight damage of the 1# bearing is 48%, and that of the 2# bearing is 87%. (2) Reasonable value of the expansion joints can effectively reduce the probability of main beam collision. In this investigation, the value is taken as 0.18 m ~ 0.24 m. (3) The bridge system is more likely to be damaged than a single component in the system, and the damage probability of a single component cannot be used as a criterion for the bridge system in the actual working condition. Comparing the first-order boundary law with the IPCM method, the IPCM method has higher accuracy.