Scaling law of piles subjected to dynamic loads for centrifuge model tests. Part Ⅰ: vertical dynamic similarity

In response to the current insufficient in research on dynamic similarity of piles in centrifuge model tests, vertical dynamic similarity conditions through analytical modeling of pile-soil dynamic interaction is obtained in this study. A design approach for model piles is proposed to ensure vertical dynamic response similarity with their prototypes. The errors between the responses of model piles made from commonly used metallic materials and those of a concrete prototype pile are analyzed and further validated by three-dimensional numerical simulations and centrifuge model test. The results show that brass can serve as a suitable substitute for concrete, satisfying the vertical dynamic similarity requirements. The maximum longitudinal phase-velocity error relative to the concrete prototype is only 1.38%; in the impedance comparisons, brass exhibits a frequency-scaling error of approximately 1.6∼1.9% and a maximum normalized stiffness error of approximately 1.4∼2.6%. Furthermore, the error caused by using metal materials instead of prototype concrete to fabricate model piles increases with increasing load frequency and pile diameter, and with decreasing shear wave velocity of the surrounding soil. This work provides a benchmark for using centrifuge tests to investigate soil-pile dynamic interactions and offers a theoretical foundation for the design of model piles subjected to vertical dynamic loading in centrifuge modeling.