Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering

First Advisor

James F. Cruise


The probability distribution function for floods and velocity profile in open channel flow are combined with scour theory to present a procedure for determining the risk of bridge failure due to scour. This is accomplished by deriving a probability distribution function for scour at a bridge pier. The theory of entropy and the principle of maximum entropy are used to determine the velocity profile. The constraints used in the entropy maximization are derived from the physical laws of conservation of mass, momentum, and energy. A procedure to approximate the solution to the resulting equations is shown. The vertical velocity is used to determine an effective depth of flow. The specific energy of the flow within this effective depth is used to develop a scour estimation procedure for use at a bridge pier. The probability distribution function for scour at a bridge pier is obtained by applying the procedure for each level of discharge in the flood probability distribution function. The procedure is applied at a pier and the results compared to the actual field measurements.