A method for rockfall risk quantification and optimal arrangement of protection structures along a road

•Optimal arrangement of rockfall protection structures combined with risk analysis.•Risk quantification considering several rock block sizes and their frequencies.•Hazard and exposure analysis based on three-dimensional trajectory simulation.•Determination of positions and types of countermeasures that minimize road risk.•Optimization subject to budget constraints and changes in traffic volume. The purpose of this study is to introduce a novel framework that aids in the installation of rockfall protection structures for the risk reduction of rockfall-related damage. In this study, we propose a computational method that performs risk analysis for a road and plans an optimal arrangement of rockfall protection structures. First, a rockfall trajectory simulation is performed using a three-dimensional numerical analysis method to obtain sufficient data for risk analysis. Then, the risk to motorized traffic during a certain period is quantified considering the relationship between rock block volume and rockfall frequency, the movement of rock blocks, the vulnerability of elements at risk, and some other factors. Finally, a knapsack problem that aims to minimize the total risk on a road while satisfying a budget constraint is solved. The proposed method is applied to an actual site and represents that it can derive a layout for protection structures to maximize the cost-benefit performance depending on the road traffic and budget conditions. The obtained results of the structural protection plan can be used to support road managers in decision making.