Probabilistic data-driven framework for performance assessment of retaining walls against rockfalls

Rockfall is a significant hazard to sites that are located at the foot of rock slopes. In such sites, there is a notable need to evaluate the potential for rockfall, estimate the extent of areas at risk, and design retaining structures to reduce the risk of rockfall-induced. This paper presents a probabilistic framework for predicting the formation and progression of rockfalls and for evaluating the performance of retaining walls under rockfalls. To this end, first a probabilistic model for the rock projectile motion on a slope is presented. The model accounts for prevailing uncertainties, i.e., the trigger points, rock shape, projectile path, and slope material properties, which include surface roughness, friction angle, and horizontal and normal coefficients of restitution. Next, Monte Carlo sampling is employed to propagate these uncertainties in the proposed model and generate a large dataset of rockfall realizations. The resulting dataset is subsequently utilized to develop an exceedance probability diagram of the rock endpoints, which is in turn used to estimate the location of the retaining wall for a target exceedance probability. Furthermore, the exceedance probability contours of the bounce height and the total kinetic energy of the rock in the projectile path are computed to produce the spatial variation of the exceedance probability at any desired location along the slope. Given the location of the retaining and the target exceedance probability, the probability contours are then employed to approximate the height and the structural capacity of the retaining wall to withstand the rock collision. Finally, a bivariate sensitivity analysis is performed to measure the performance of the retaining wall against the falling rocks and further evaluate the efficiency of the proposed probabilistic design.