Prediction of Coefficient of Restitution of Limestone in Rockfall Dynamics Using Adaptive Neuro-Fuzzy Inference System and Multivariate Adaptive Regression Splines

Document Type : Regular Paper

Authors

1 Assistant Professor, Faculty of Civil Engineering and Architecture, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 Assistant Professor, Department of Civil Engineering, Dariun Branch, Islamic Azad University, Dariun, Iran

Abstract

Rockfalls are a type of landslide that poses significant risks to roads and infrastructure in mountainous regions worldwide. The main objective of this study is to predict the coefficient of restitution (COR) for limestone in rockfall dynamics using an adaptive neuro-fuzzy inference system (ANFIS) and Multivariate Adaptive Regression Splines (MARS). A total of 931 field tests were conducted to measure kinematic, tangential, and normal CORs on three surfaces: asphalt, concrete, and rock. The ANFIS model was trained using five input variables: impact angle, incident velocity, block mass, Schmidt hammer rebound value, and angular velocity. The model demonstrated strong predictive capability, achieving root mean square errors (RMSEs) of 0.134, 0.193, and 0.217 for kinematic, tangential, and normal CORs, respectively. These results highlight the potential of ANFIS to handle the complexities and uncertainties inherent in rockfall dynamics. The analysis was also extended by fitting a MARS model (degree 2, 8 basis functions) to the same dataset. The MARS model achieved MAE ≈ 0.095 and RMSE ≈ 0.118—marginally improving over ANFIS—while delivering a fully explicit algebraic form and an intrinsic ranking of variable importance.

Highlights

  • A novel application of ANFIS was employed to predict the coefficients of restitution for rockfall events, using parameters such as impact angle, incident velocity, block mass, surface hardness, and angular velocity.
  • A comprehensive dataset of 931 field tests was collected, with 571 tests deemed suitable for determining coefficients of restitution on various surfaces (asphalt, concrete, rock) under different seasonal conditions.
  • The study identified a decreasing trend of kinematic and normal coefficients of restitution with increasing impact angle and incident velocity, providing insights into rockfall dynamics and behavior.
  • The ANFIS model demonstrated robust predictive capabilities, effectively handling the inherent uncertainties in field data and offering a reliable method for predicting rockfall behavior and mitigating hazards.

Keywords

Main Subjects

References

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History

  • Receive Date: 19 October 2024
  • Revise Date: 30 May 2025
  • Accept Date: 01 July 2025

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