Bridge headwater afflux estimation using bootstrap resampling method

The bridge structure's development causes a riverbed cross-sections contraction. This influ-ences the flow regime, being visible during catastrophic floods. Then the flow velocity increases and water piles up upstream the bridge, where headwater afflux could be observed. These changes depend on the watercourse geometry and the bridge cross-section properties, especially on the degree of flow con-traction under the bridge. Hydraulic conditions under the bridge depend on flow velocity, dimensions, and shape of abutments, the granulometric composition of bedload, which can be quantitatively char-acterized by hydraulic resistance coefficients. The research subject of headwater afflux is equated with the recognition of morphodynamic processes occurring along the passage route. The headwater afflux could be estimated by empirical formulas and by the energy method using Bernoulli's law. Empirical methods are optimized by adopting various statistical criteria. This paper compares the headwater afflux values calculated using two existing empirical formulas, Rehbock and Yarnell, and compares them with the results of laboratory tests. Following the assumption that the free water surface is influenced by flow resistance, an attempt was made to include friction velocity in the empirical formulas. Based on the Authors' database, the coefficients used were optimized using bootstrap resampling in Monte Carlo simulation. The analyses demonstrated that the formula best describing the phenomenon of headwater afflux upstream the bridge is an empirical formula built based on the historical Yarnell formula, which includes friction velocity value. The optimized equation provides an average relative error of 12.9% in relation to laboratory observations.