Modified Logarithmic Law for Velocity Distribution Subjected to Upward Seepage

A modified logarithmic law is derived to describe the velocity distribution in open-channel flow with an upward seepage. The derived function agrees well with the experimental measurements conducted in a laboratory flume. The roughness function included in the modified logarithmic law is found to be dependent on the boundary Reynolds number and the ratio of the seepage velocity to the shear velocity. With the integration of the modified logarithmic law, the bed-shear stress subjected to upward seepage can be computed based on the depth-averaged velocity, water depth, boundary roughness, and seepage velocity. Using this method, variations of the bed-shear stress over the seepage zone are studied. The results show that the bed-shear stress decreases rapidly from the leading section of the seepage zone and then increases gradually toward the downstream end of the seepage zone.