Numerical simulation of dike breaching by overtopping. Influence of the bank erosion operator.

We employ a physically-based in-house 2D multi-layered depth and time averaged shallow water model with the capacity to simulate morphology and sediment transport (HiSTAV) to model the erosion of dikes subjected to overtopping. Its conceptual model is based on conservation laws for shallow flows and requires closures for flow resistance, and sources and sinks of transported substances. The conservation laws are discretized within a Godunov-type Finite Volume scheme. HiSTAV design is entirely cross-compatible between CPUs and GPUs, through an intuitive object-oriented approach. HiSTAV requires the parametrization of the processes expressing hydraulic erosion, slope failure and mass detachment. The latter are modelled as sudden collapses of cells of dam body, dry but adjacent to the flow, a process akin to river bank collapse. A secondary mesh is defined to group the cells that form the detached mass. We investigate the effects of the dimension of the group and the values of the parameters (velocity and shear stress) that trigger the collapse. As expected, the bulk erosion rate increases with the size of the detached group. The results of the model were compared with data from laboratory models. Three laboratory tests were carried out in a medium-scale facility located at the Fluvial Facilities of the Hydraulics and Environment Department (DHA) of LNEC. The facility operates in closed circuit and is composed by a 1.40 m wide and 19 m long channel where the river stream is simulated. It allows testing dikes up to 0.50 m height and 2.0 m long. The water level upstream the dike is controlled by a sluice gate placed at the downstream end of the channel. The dike site and the main channel where constructed in an elevated platform, after which there a settling basin (2.10W x 4.5L (m)) where the eroded soil from the failure tests is deposited. A Bazin spillway exists at the end of this structure to measure the dike outflow discharge. We performed 3-D reconstructions of the evolving dike geometry, monitored the water levels in the main channel, the flow discharges in the main channel and across the breach and calculated the surface velocity fields in the vicinity and breach (LSPIV). The rate of breach erosion and the velocities near the breach were compared with the results of the model. It was observed that the size of the detachment group should scale with the breach crest and is influenced by the type of soil.

Acknowledgements: This work was partially funded by the Portuguese Foundation for Science and Technology (FCT) through Project DikesFPro PTDC/ECI-EGC/7739/2020 and through CERIS funding UIDB/04625/2020