Shear Stress Distribution in Partially Filled Pipes and its Effect on the Modeling of Sediment Transport in Storm Drains

All traditional sediment transport formulas are derived for steady uniform flow in rectangular flumes or natural rivers. In many cases (flash floods, urban drainage systems) sediment transport however takes place in unsteady flow conditions. From experiments it is known that unsteady sediment transport can not be modeled accurately by the available steady flow formulas, using at each time step the actual water depth and flow velocity and the mean bed shear stress. In particular, different sediment transport rates are found for the same water depth during the rising and the falling limb of the hydrograph, leading to an asymmetric sedimentograph for a symmetric hydrograph. Several empirical studies have therefore tried to adjust the steady state transport formulas for unsteady flow by introducing an additional term related to the slope of the hydrograph. From CFD calculations it has been found that the shear stress distribution over the sediment bed in a pipe with deposited sediments, is quite uniform but larger than the mean shear stress in the cross section. The shear stress is function of the water depth, being larger for lower water depths. This is in accordance with several experimental observations. In this study it is shown that the unsteady behavior of sediment transport can be explained not by changing the transport models, but by including the correct shear stress distribution at each time step, and the phase lag between flow rate, velocity and water depth. Comparisons between numerical calculations and (unsteady) sediment transport measurements confirm these results qualitatively.