Rockfall phenomena consist of the detachment and downslope movement of rock blocks from steep slopes or fractured rock walls. The study aims to determine the maximum travel distance, most probable trajectories, and maximum impact energy that protective structures must dissipate. Passive protection works include rockfall barriers, interception ditches, and rockfall embankments.

The total kinetic energy of the block is expressed as:

In most engineering applications only the translational component is considered: Ec = ½·m·V²

The penetration depth is estimated using the Kar (1978) relation. The design requires z < embankment thickness. If z > t the embankment is undersized. Two cases:

Penetration depth z is then derived from Z with two candidate values z₁ = 2r√Z and z₂ = (Z+1)·r, selecting the appropriate one based on the ratio z/r.

The impact force is estimated as:

The impact time: T = 3.335 · z / V. With the Impulse theorem method, an equivalent energy factor 1.19×1.1 is applied to Ek.

The factor of safety against sliding is:

where R is the mobilisable sliding resistance (cohesion + friction contributions of fill and reinforcement), Fh is the horizontal impact component, and γR is the resistance partial coefficient (1.0 user / 1.1 NTC).

The total resistance includes fill contribution and, for wall facing, an additional muro component:

Equivalent cohesion: c_eq = c + (Tallow/s)·(sin θ·tan φ + cos θ) where θ = 45 + φ/2. Equivalent friction: tan_eq = (1 + ψ)·tan φ

The software models embankments reinforced with geogrid or geosynthetic elements. Key parameters: