A Method to Compute the Ultimate Displacements in Reinforced Earth Rockfall Protection Embankments: A Perspective for the Design

Abstract Rockfall protective embankments (RPEs) offer a cost-effective solution for mitigating rockfall hazards, particularly in scenarios involving high-energy or repeated impacts. Among the available technologies, reinforced earth embankments are widely adopted, although their design methodologies remain a subject of ongoing research. This study investigates the behavior of a reinforced earth RPE, with a focus on characterizing the evolution of the displacement field up to collapse induced by a localized punching force, representing the impact of a falling block, applied to one face of the structure. Two reinforcement configurations are examined: unidirectional geogrid and double-twist steel mesh with metallic clips. Given the scarcity of full-scale experimental data and the practical challenges associated with such tests, a series of reduced-scale tests was designed and conducted. Geometric and mechanical similitude was ensured through the application of the Buckingham Π -theorem. The tests were performed under quasi-static conditions to isolate the displacement field associated with soil layer sliding, neglecting inertial effects. Throughout the tests, both force and displacement histories were continuously recorded and analyzed. The results provide valuable insights into the volume of embankment affected by impact and the pre-collapse displacement patterns for both reinforcement types. Two extended finite element method (XFEM) models were developed to simulate the behavior of each reinforcement configuration. Model calibration was enhanced using photogrammetric reconstruction of the embankment’s downslope face, with point cloud data collected throughout the testing phase, enabling accurate validation of simulated deformation patterns. Finally, a full-scale dynamic impact test from the literature was used to calibrate a real-scale numerical model and to assess the consistency between dynamic and quasi-static responses of the same embankment system.