Rock slope damage level prediction by using multivariate adaptive regression splines (MARS)

It is indicated in the literature that current empirical formulas are not able to predict the damage level very accurately for the conventional rubble-mound structures, leading to the unnecessary increase in the construction cost. Therefore, it is imperative to be able to accurately predict the damage level. This study presents a multivariate adaptive regression splines (MARS) approach for predicting the damage level of armor blocks of breakwaters. This technique presents a flexible regression by the use of separate regression slopes in distinct intervals of the independent variable. An experimental dataset of Van der Meer (VDM) containing small- and large-scale tests are employed. Two MARS models, one is for taking into account the main effects and the other for considering two-way interactions, and a multiple stepwise regression model is constructed and compared with each other and widely used empirical formulae of VDM. In the model constructed, variables of permeability, cot α, number of waves, stability number, ξ_m, ξ_m/ξ_mc are found to be most effective ones. The relative error, Nash–Sutcliffe efficiency, mean absolute error, percent bias, and adjusted R² statistics are used for evaluating the accuracy of models. The comparison results indicate that the MARS model with two-way interactions performs better than the other models in the damage level estimation for the particular datasets employed in this study.