SPH modelling of mass detachment processes in overtopped dams. The limits of Froude similarity

We apply Smooth Particle Hydrodynamics (SPH) to simulate mass detachments in an overtopped and breached earth dam. SPH is able to model free surface flows at prototype and laboratory model scales. The flow over the overtopped dam is gravity-driven. Froude similarity is thus employed to scale results from models to prototypes, even if there are fluid-wall interactions. In particular, the processes that govern the interaction between a detached solid from the dam body and the breach flow may not obey Froude similarity. In this paper, we discuss how the geometric scale conditions the effects of mass detachments on the flow field of a breached dam and how SPH simulation tools express these scaling issues. The Navier–Stokes equations for weakly compressible and Newtonian fluids in isothermal flows were used for the water flow. Flow-dam interaction was resolved with dynamic boundary conditions. All simulations were conducted with DualSPHysics, employing the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) scheme. The detached soil mass was modelled as a rigid block. The interaction between the detached block and the fluid flow through the breach was attained by coupling DualSPHysics with the non-smooth multi-body dynamics model (Chrono-Engine). The surface velocity field, determined with Particle Tracking Velocimetry (PTV) during the mass detachment, was used to assess the quality of the SPH solution. The numerical and the observed velocity fields show a reasonable agreement in the time-lapse that encompasses the detachment of the block. However, there are differences in the curvature of streamlines as the flow approaches the breach, suggesting a closer look at the hypotheis of the SPH simulation tool. The impact of the falling block on the flow field varies significantly with the size of the modelled dam. The block is not entirely transported out of the breach in the reduced model. This configures a breakdown of Froude similarity in the sense that hydrodynamic actions on the model are disproportionately smaller in the model relative to the prototype. While there may be physical reasons at play, we note that ensuring mass conservation in the model led to a smaller initial resolution that may have affected how forces are transmitted between the SPH and Chrono simulation tools.