Uncontrolled overtopping during flood events can endanger embankment dams. Erosion of the downstream slope and scouring of its base caused by the high velocity and energy of the overflow can indeed lead to breach formation until complete failure. In this context and faced with the important number of overtopped embankment dams to be rehabilitated, since the early eighties, researchers have investigated surface protection solutions for downstream slope. Overlays against erosion such as seeded goetextile or cable-tied cellular concrete blocks, are not sufficient. In fact, they can resist only short events with low discharge and velocity. Solution to overcome more severe overflow lies in overlays which dissipate flow energy along the downstream embankment slope. Conventional steps resulting from Roller Compacted Concrete (RCC) techniques fulfill efficiently this challenge. However, flows over steep stepped chutes are quite complex, characterizing by great aeration, high turbulence and confused wavy free surface. Then, most of hydraulic studies of such flows are performed on physical model. Yet, understanding and definition of flow behaviour and accurate approach to estimate energy dissipation are still lacking. General guidelines of hydraulics of aerated flows over stepped macro-roughness chutes and for optimal design of protection overlay remain confusing. To contribute to reduce these uncertainties, experimental study of flow over stepped chutes equipped with macro-roughness elements is performed in a laboratory gated flume for mild (~ 1:7H : 1V ) and weak (~ 3H : 1V ) chutes. Thus, they are representative of the range of embankment dams and spillways slopes. Three types of stepped macro-roughness overlays are assessed, namely rectangular conventional steps, steps equipped with endsills fixed on their nose over all the flume width and steps equipped with rectangular spaced blocks. Endsills overlays were characterized with different longitudinal distributions whereas blocks overlays consisted in different transverse patterns. Tests were conducted for the three nappe, transition and skimming flow regimes. Results can be extrapolated to 1/5 to 1/15 scaled prototypes using the Froude similarity with negligible scale effects. Flow depth, local air concentration and longitudinal velocities are measured with a double fiber-optical probe. Pressures at macro-roughness faces are taken with piezo-resistive sensors. Sequent depths of the hydraulic jump forced in the stilling basin at the flume base are measured with ultrasound sensors. Thus, this experimental phase of the thesis has allowed: to define flow parameters (regimes, depths, velocity and air concentration distributions, hydrodynamic forces) for tested overlays, to highlight that air-water flow depth is divided into: a rough boundary layer influenced by shear stress and by drag form (macro-turbulence) caused by macro-roughness, a homogeneous aerated layer which represents the main portion of flow involved in energy dissipation mechanism, a free surface layer which must be considered in the side walls design, to stress that energy dissipation is mainly a question of drag losses, to validate indirect method of hydraulic jump for energy dissipation estimation, to estimate relative energy loss for several stepped macro-roughness overlays. Tests finally show that an optimal alternative to dissipate the overflow energy during an overtopping event consists in spaced blocks, with transverse space larger than the width of block and fixed alternately on conventional steps. However, experimental results remain related and limited to their tested domains. Then, in order to provide more general governing equations of aerated flows over macro-roughness stepped chutes, a numerical modeling of two phase flows over conventional stepped flume was performed in collaboration with the Laboratory of Applied Hydrodynamics and Hydraulic Constructions at University of Liège. A quasi-2D numerical model based on the finite volume method was developed. It consists in applying the classical depth-averaged simplified Navier-Stokes equations (viscosity and Coriolis terms neglected) to a 1D incompressible air-water mixture flow over mild and steep slopes with a stepped topography. Self-aeration process is modeled by a transport equation of depth-averaged air concentration whereas turbulent structures are indirectly implemented through the Boussinesq coefficient. This first 1D-approach of semi-theoretical description of aerated flow over steps is tested for a 30o gated stepped flume and a 52° crested spillway laboratory model. This numerical model leads to realistic results regarding mixture depth, mean flow velocity, air concentration and wave amplitudes of the flow free surface. Finally, on the basis of existing protections of embankment dams and previous studies, the present experimental and numerical results contribute to extend the knowledge of high velocity aerated flows over macro-roughness and to provide elements of guidelines to optimize stepped macro-roughness overlays for embankment dams safety.