A computational design optimization method for rockfall protection embankments

In this study, an optimization method based on numerical rockfall simulation is proposed to determine the layout design of a protection embankment, including its position and length on a construction site. Stopping rockfalls farther away from the slope toe requires a lower embankment since the movement of the rockfall decreases with the runout distance and, at the same time, a longer embankment due to the lateral deviation from the central rockfall path. This complicated relation makes the layout design difficult. The proposed method mainly focuses on two design parameters: the distance from the slope toe and the embankment length. With regard to these two decision variables, an optimization problem is formulated, with the aim of minimizing the installation cost of an embankment, which is subject to the global performance requirement for arresting rockfalls. Solving this problem leads to the identification of an optimal layout plan for an embankment at the site of interest. The optimization result is objective and quantitative; therefore, it allows us to choose the best one from several embankment types with different design conditions and costs. To evaluate the performance of the proposed method, an application example was conducted using a virtual rock-slope model. In this application, we employed the discrete element method for the rockfall trajectory simulations. The optimization process was then conducted on 50 different groups of computed trajectories to determine the most economical and stable construction plan among several embankment types and all possible layouts. The reliability of the result was also supported by the fact that the variations in the optimal solutions were reduced with the increase in the sample size.