A multi-parametric model for calculating the impact force exerted on cantilevered structures due to the collision of boulder within debris flow

Cantilevered structures, such as slit dams and piers, are vulnerable to destruction caused by boulders within debris flows. Accurately quantifying the boulder impact force within debris flow is essential for ensuring the optimal performance of these structures. Static-based models typically overestimate this force due to their failure to account for structural damping and inertia effects. In contrast, dynamic-based models that incorporate these effects are demonstrated to provide more accurate predictions. However, dynamic-based models are challenged by the difficulty in efficiently obtaining required input parameters during the engineering design process. To address these issues, an implicit multi-parametric model was developed based on similarity theory through the systematic integration of several key parameters including boulder mass, impact velocity, elastic modulus, and cross-sectional moment of inertia. A comprehensive set of numerical experiments was conducted to simulate boulder impacts on cantilevered structures, with structural bending strains being measured and subsequently input into the dynamic-based model for back-calculation of the boulder impact force. Through linear fitting of the calculated results, an explicit expression was successfully derived for the multi-parametric model. Comparative analysis revealed an accuracy loss of approximately 4% relative to the original dynamic-based model, thereby validating the model's effectiveness. The practical application of this model was demonstrated in real-world scenarios involving piers destroyed by boulders entrained in debris flow. The results indicate that the calculated impact forces not only significantly exceed the piers' fracture strength but also closely approximate empirically observed field impact forces.