From nominal energy to capacity curves: a probabilistic framework for reliability-based design of flexible rockfall barriers

Flexible rockfall barriers are widely adopted passive protection systems in mountainous regions, yet their design still relies on deterministic criteria based on Maximum Energy Level (MEL) and Service Energy Level (SEL) tests. These standardized procedures provide a single nominal energy value, which does not reflect the variability of real impact scenarios nor the stochastic nature of barrier performance. This limitation hinders the integration of reliability-based principles into design, a cornerstone of modern structural engineering. This work merges a probabilistic framework to estimate the mechanical performance of flexible rockfall barriers under a wide range of impact scenarios into the RockStop software, integrating the resulting capacity curve within the software and enabling its practical use in design workflows. The framework derives capacity curves for flexible rockfall barriers and is built upon a generalized multicomponent analytical model, developed by the authors, that simulates barrier response under arbitrary impact conditions by assembling analytical representations of each component (net, wire ropes, posts, energy dissipators). A Monte Carlo simulation scheme propagates uncertainties in geometry, mechanical properties, impact position, and component variability, generating a probabilistic description of the barrier’s energy absorption capacity. Results show that highly eccentric impacts can significantly alter the nominal capacity. The integration of trajectory outputs, combined with the barrier capacity curve, in RockStop enables site-specific assessment of all possible actions and their frequency, allowing the calculation of failure probability for both newly installed and existing barriers. This framework marks a major advancement toward risk-informed design by enabling the integration of reliability-based safety formats for rockfall barriers, supporting comprehensive lifecycle performance assessment, and providing a robust basis for quantifying residual risk after mitigation.