Scour at bridge piers is time-dependent. In this paper, temporal evolution of clear-water scour at complex bridge piers is studied experimentally. The pier model has a typical form comprising three components, namely a rectangular column, a rectangular pile-cap, and a group of vertical piles underneath. Various relative pile-cap positions and skew angles ($\alpha$ ) from 0° to 45° were used to investigate their influence on scour evolution. New functions are proposed to fit temporal data and determine the equilibrium scour depth with better accuracy. The results show that the locations for scour initiation and the maximum scour depth may be different, and their relationship varies with pile-cap position and pier skew angle. Highly skewed piers tend to overcome the influence of width ratio of column to pile-cap ($D_c/D_{pc}$ ) on scour evolution, as the column itself becomes dominant. The sensitivity of scour evolution to pier skew angle decreases with higher pile-cap position, especially when it is entirely above the original bed. Four scour development stages were identified for complex piers, including initiation, stagnation, a developing stage, and equilibrium, with each stage being highly dependent on the degree of exposure of each of the pier components. The description of each development stage for different situations is given. The equilibrium time scale $t^{*}$ and the equilibrium scour depth $d_{se}$ for complex piers have similar dependence on flow shallowness ratio ($y_0/D_e$ ) and sediment coarseness ratio ($D_e/d_{50}$ ), as per the equation proposed by an authors’ previous study (Yang et al. 2018). A new equation is proposed to correct the percentage rate of scour development. The correction is especially useful for aligned complex piers, for which the rate of scour time development may be much lower than that for single-column piers. In general, we recommend using the modified Sheppard-Melville method and the corrected time-scale equation in this paper to predict clear-water equilibrium scour depth and scour evolution at complex bridge piers.

An experimental study on flow-induced clear-water local scour at complex bridge piers was conducted using two typical pier models, nine pile-cap elevations, and seven pier skew angles from 0° to 90° with a 15° interval. Results show that a slight skew angle $\alpha$ imposed on an originally aligned pier can significantly increase the equilibrium scour depth $d_{se}$ . When a pier was skewed to the flow, the column made the largest contribution to the scour depth because its wide-pier feature became dominant. Three categories of the pier skewness were defined, namely, an aligned pier (= 0°), a slightly skewed pier ($\alpha \approx 15°$ ), and a highly skewed pier ($\alpha \ge 30°$ ). The influences of the pile cap and the pile group on the scouring process were weakened with increasing $\alpha$ . Additionally, for highly skewed piers with fully submerged pile cap, the equilibrium scour holes tended to equally expose the pier components, no matter the location of the undisturbed bed level. A new scour prediction method is presented, involving modifications for the effect of sediment coarseness. The new method leads to a higher safety margin with significantly reduced underestimation.

An investigation of the characteristics of live-bed scour at circular and skewed rectangular (slab) piers in comparatively shallow flows is presented. The 110 experiments were undertaken in a 2.4-m flume using two circular piers and a slab (long) pier. Based on flow shallowness, that is, the ratio of approaching flow depth ($y_0$ ) to pier diameter ($D$ ), the new data span the wide-pier ($y_0/D<0.2$ ) and transition-pier ($0.2\le y_0/D<1.4$ ) scour ranges. The Sheppard-Melville (S-M) method shows better performance than the other existing predictors and is more readily modified. Modification to the equation for the flow shallowness factor in the S-M method is proposed, based on both the data from the present study and those from literature. The results show the considerable influence of flow shallowness ratio on scour depth at piers in comparatively shallow water, and that, even for non–ripple-forming sediment, the scour depth at the live-bed peak may still exceed that at the clear-water threshold. The modified predictor provides better accuracy than the original Sheppard-Melville method for piers with $y_0/D<1$ , and no significant underestimation of the maximum scour depth is observed.

In this study, we investigated the characteristics of scour at complex bridge piers in close proximity. The experiments were performed under both clear-water and live-bed flow regimes. We compare our results with those for a single complex pier. Further, the performance of existing predictors is discussed. In this study, four typical pier arrangements were adopted, including side-by-side with aligned or 30° skewed flow, staggered, and tandem. The results show that the skew angle for a side-by-side arrangement significantly accelerates the clear-water scour development at all the vertical piles as well as between the piers, and the most scoured pile shifts from the upstream end to the downstream end of the upstream pier flank. The staggered and tandem pier arrangement show significant protection to the downstream pier for both the developing rate and the equilibrium scour depth. When the flow velocity exceeds the threshold for general bed motion, the clear-water scour pattern for all the pier arrangements may be altered significantly due to the upstream sediment supply, the weakened protection effect, and the enhanced flow contraction. The bed-forms migrate via the bridge opening and are damped gradually by the flow, and thus the response of the bed morphology under live-bed conditions is quite unsteady.