Design relationships for maximum local scour depth for bridge pier groups.

An investigation of local scour at pier groups has been conducted with the aim of developing design recommendations and scour depth prediction equations for the bridge pier groups. A comprehensive series of steady uniform flow experiments was performed on groups of 2, 3, 4, and 6 model piers. All tests were conducted under clear-water scour conditions. Parameters governing local scour depth around bridge piers include: flow characteristics, sediment properties, and pier size and shape. The effects of these parameters on the maximum local scour depth for a single pier (D$\sb{\rm s}$), have been thoroughly investigated in the past. However, when design criteria developed for single piers are applied directly to pier groups, this approach ignores the following important group effects: (1) sheltering, (2) reinforcement, and (3) horse-shoe vortex (HSV) compression. Furthermore, the group effects will alter with changes in pier spacing, S, and flow angle of attack, $\beta$. This study, which investigates the local scouring process for the aforementioned groups of model bridge piers, and presents design relationships for predicting the corresponding maximum local scour depths, is an attempt to address this limitation in current design practice. Initially the local scour was examined for five different single pier diameters (0.0127 m, 0.018 m, 0.025 m, 0.033 m and 0.05 m). Having established single pier relationships, groups of 2, 3, 4, and 6 equally spaced piers were examined, while altering alignment to the flow and separation distances. For piers in line with the flow direction, downstream piers are sheltered by the upstream ones resulting in reducing scour depth around downstream piers. This effect diminishes with the increasing $\beta$ if there is only one row of piers i.e., 2 and 3 pier groups. In the case of 2 rows of piers aligned to the flow direction (i.e., 4- and 6-pier groups), there is a specific range of $\beta$ in which downstream piers are exposed to the flow. As $\beta$ increases, depending on pier spacing, the piers of one row may shelter the downstream piers of the other row. The reinforcement effect is significant only for small ratios of pier spacing/ pier diameter (S/d) when $\beta \le$ 10$\sp0$. In these ranges of S/d and $\beta$, the front piers are scoured more than that of a single pier. Moreover, the score depth of downstream piers, which are less than that of a single pier, increases with increasing S/d. The compressed (HSV) arms affect the local scour depth significantly if piers are staggered and S/d $\le$ 5. In this range of S/d, the HSV arms are intensified, resulting in a deeper scour hole. However, this effect also becomes insignificant with increasing S/d. The data obtained for each pier group were analysed, using a multiple regression model, to develop local scour depth prediction equations for the front, middle, and rear piers. The regression model includes two important dimensionless parameters ($\beta$ and S/d) associated with group effects, as regressors. The proposed prediction equations estimated the observed data and similar-type published data reasonably well, within marginal errors. From a general practical view-point, the number of prediction equations was reduced to two equations for all pier groups: one for the front piers and the second one for the downstream piers (i.e. combined middle and rear piers)