Dimensional Analysis and Unified Ultimate Bearing Capacity Expression for I-Wing Piles in Loess: Experimental and Numerical Study

Transmission tower foundations in China’s collapsible loess plateau face severe settlement risks under sustained vertical compression, yet the compressive behavior of winged piles in this metastable soil remains unexplored. This study presents a combined experimental and numerical investigation of I-wing piles in remolded Malan loess, comprising plain (WP0), two-wing (WP2), and four-wing (WP4) configurations. Three-dimensional finite-element models were validated against physical load tests and subsequently used to decompose load transfer into toe, wing-bearing, and side components via a unified hyperbolic interface model. A sixteen-case parametric study isolated the effects of wing geometry and soil properties, and the complete dataset was synthesized into a unified dimensionless capacity expression using Buckingham π theorem. At a normalized settlement of s = 0.1d, the four-wing pile (WP4) exhibited a 69% increase in compressive capacity compared with the plain pile (WP0) in the validated finite-element simulations, while the corresponding physical tests showed a 52% increase. The proportion of pile-base resistance decreased from 59.65% for WP0 to 33.18% for WP4. For WP4, wing-bearing resistance accounted for 18.98% of the total capacity, while total side resistance contributed the largest share at 47.85%. The two-wing pile (WP2) showed capacity increases of 43% in the finite-element simulations and 36% in the physical tests. The investigated reduced-scale baseline had its highest capacity near hw/d ≈ 1.3, an optimum observed only under the investigated soil and geometric conditions. The hyperbolic model captures all interface responses with R2 spanning 0.933 to 0.999. The derived formula achieves an in-sample MAPE of 3.37%, a leave-one-out cross-validation MAPE of 4.66%, and eight independent finite-element blind predictions (full-scale and intermediate-scale prototype winged-pile configurations) within -4.4% to +3.4% (MAPE = 2.63%). Scale calibration used only one numerical monopile reference (FS-M); the eight cases are finite-element predictions, not field tests. Geometric and material similarity are preserved, but strict stress similarity is not achieved under 1 g conditions; the explicit gravity correction factor G represents this mismatch within the investigated numerical domain. These findings demonstrate that winged piles effectively redistribute compressive load away from the pile toe in loess, and the proposed unified expression provides a preliminary prediction tool numerically assessed within the investigated models and parameter ranges for dry, remolded loess.