Quantification of spatial lag effect on sediment transport around a hydraulic structure using Eulerian–Lagrangian model

•We perform Eulerian–Lagrangian simulation of local scour around a hydraulic structure.•We quantify spatial lag effect of bed load on multi-dimensional simulation.•We find unsaturated and oversaturated bed load around a hydraulic structure.•We find two modes of response of adaptation length depending on clear-water and live-bed scour.•We discuss applicability of linear adaptation equation to multi-dimensional simulation. The spatial lag effect on sediment transport around a hydraulic structure is quantified through numerical simulation using a Eulerian–Lagrangian model. The Eulerian–Lagrangian model uses a deterministic approach of bed load motion and stochastic approach of Einstein's concept, which allows for a reasonable quantification of both non-equilibrium and equilibrium bed load transport rates. Numerical simulations are conducted for local scour around a spur dyke and a weir-type structure. As pointed out in previous experimental studies on the one-dimensional problem, Eulerian–Lagrangian simulation reveals an unsaturated bed load in a scour hole around a hydraulic structure. Furthermore, an oversaturated bed load is also found in the deposition region, particularly behind the structure. The validity of the linear adaptation equation is discussed using numerical results, revealing the possibility that the linear adaptation equation does not appropriately represent the existence of the strong spatial lag effect. The present study finds there are two modes in the response of the adaptation length to the unsaturated bed load, which depend on the clear-water scour condition or the live-bed scour condition. Findings of this study will contribute to multi-dimensional sediment transport simulations that consider the spatial lag effect.