Dimensionless Analysis and Scaling of Helical Piles Using the Buckingham Pi Theorem

https://doi.org/10.46610/JoRAIS.2026.v011i01.002

Abstract

Helical piles are widely used in modern foundation engineering due to their high load-bearing efficiency and suitability across diverse soil conditions. However, due to the complex interaction that exists between the geometries of the pile and soil, scaling the behavior of helical piles from the laboratory model to full-scale applications remains a dominant challenge. This study applies the Buckingham Pi theorem to develop a dimensionless framework for scaling helical piles that enables the consistent replication of prototype behavior in reduced-scale models. Eleven geometric, material, and loading parameters were identified as key parameters and transformed to eight independent dimensionless Π-terms, which control the load–settlement response of helical piles. Using these Π-terms, a theoretical scaling law was established to relate the prototype and laboratory-scale models by geometric, load, and settlement similitude. The proposed methodology was then validated through model preparation and load-scaling analysis for both cohesive and cohesionless soils. The results from the dimensionless approach indicate an accurate preservation of the physical behavior of helical piles across scales, thus ensuring reliable prediction of load capacity and settlement. This research provides a systematic and cost-effective framework for model testing; offering engineers a robust tool for analyzing and optimizing helical pile performance under varying soil conditions.