A method is presented for evaluating the risk of failure of bridge structures due to pier scour during flood events. The method takes into account the hydrodynamics of the flow field in the vicinity of the pier. A newly developed entropy-based velocity distribution is used to define the effective depth of the scour-producing activity in the vortex near the pier. This velocity distribution is integrated to obtain an upper bound on the energy in the vortex, which is then used to estimate the local pier scour. The scour-estimation procedure is used with a flood probability distribution to assign an exceedance probability to estimated scour values. This scour probability distribution can be used along with information about the pier parameters to assign a risk of failure corresponding to any discharge value. The procedure allows for the development of a system of risk assessment priorities to aid in scheduling bridge monitoring and repair.