The bridge structure’s development causes a riverbed cross-sections contraction. This influences 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 contraction 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 characterized 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.

This paper conducts research based on the hollow slab members in the reconstruction and expansion project of expressways, two types of numerical finite element models with and without considering bond-slip relationship of reinforcement and concrete are established, and verified by tests. The distribution characteristics of crack spacing in reinforced concrete beams are studied. The results show that the bond-slip characteristics of reinforced concrete have little effect on the load-deflection characteristics of 8m hollow slab beam. Due to the influence of the bond-slip relationship of reinforced concrete, the load-deflection curve is partially serrated, while without considering the bond-slip relationship of reinforced concrete, the load-deflection curve is smooth. In the numerical model without considering the bond-slip characteristics, almost all damage occurs in the longitudinal direction, and the distribution characteristics of cracks can’t be accurately determined. Regardless of whether the bond-slip is considered or not, the macroscopic characteristics of the stress distribution is: smaller near the support and larger at the mid-span. As secondary flexural cracks expand, models with and without consideration of bond-slip characteristics can’t calculate crack spacing based on the stress distribution characteristics of the reinforcement.