Reliability assessment of concrete walls as rockfall protection systems in mountainous areas

Rockfall protection systems are essential for safeguarding infrastructure and human activities in mountainous regions, where falling rock masses pose persistent hazards that can cause severe damages. Structural mitigation measures, such as energy-dissipating barriers, are commonly installed near roads, buildings, and industrial facilities to reduce impact forces. These systems function by either absorbing the kinetic energy of falling blocks through deformation or resisting impact via mass and frictional dissipation. Two main energy dissipation strategies characterize these systems. Flexible barriers, such as net fences, absorb energy through large deformations and are widely used for their adaptability and effectiveness across varying block sizes. However, they require sufficient clearance between the barrier and protected infrastructure, which limits their application in narrow corridors. To overcome this constraint, rigid systems, such as L-shaped reinforced concrete walls, have been developed. For high-impact energies, a cushion layer of granular material is often added to the upslope face of the wall. However, this solution requires a large footprint, which is not always feasible, and in steep areas, the added weight can even lead to overall slope instability. Therefore, for expected impact energies up to approximately 800 kJ, a rigid system alone can represent an effective and economical solution. These structures rely on mass and bending resistance to dissipate energy without requiring buffer space, making them suitable for constrained environments. Nevertheless, their long-term reliability under diverse impact conditions remains an open question. This study introduces a time-integrated reliability analysis of rigid rockfall protection systems, focusing on performance under variable loading over extended periods. The approach incorporates the frequency–magnitude distribution of rockfall events, acknowledging that smaller blocks occur more frequently than larger ones. Variability in block mass, impact velocity, and kinetic energy is modelled within a probabilistic framework that accounts for uncertainties in material properties and structural response. The analysis is applied to a real-world slope with documented rockfall activity, evaluating the reliability of a concrete wall system under cumulative low-energy impacts and rare high-energy events. Using limit state functions, failure probabilities and critical performance thresholds are estimated. Results emphasize the importance of integrating temporal and probabilistic dimensions into design, showing that rigid barriers, while effective in constrained spaces, exhibit reliability sensitivity to impact frequency, energy dissipation capacity, and degradation over time.