Group efficiency and load transfer mechanisms of semi-rigid soil–cement piles: integrated experimental, 3D numerical, and analytical evaluation

Understanding the group behavior of semi-rigid soil–cement piles remains a major challenge in deep-mixed foundation engineering. Unlike conventional displacement piles, soil–cement columns exhibit transitional stiffness and composite interaction with the surrounding ground, leading to settlement-dependent mechanisms that are not captured by existing group-efficiency approaches. This study integrates rare full-scale load tests, carefully calibrated three-dimensional finite-element analysis (3D FEA), and systematic analytical benchmarking to establish a mechanistic basis for evaluating group efficiency in soil–cement pile groups. Instrumented field tests on single, three-pile, and five-pile groups (S/D = 2) reveal pronounced stress overlap, non-uniform shaft mobilisation, and significant reductions in per-pile capacity. A high-fidelity 3D FEA model, incorporating a physically justified transitional zone and enhanced interface stiffness, reproduces both the load–settlement response and axial force transfer with high accuracy. Parametric analyses over a wide range of spacings and group sizes demonstrate that group efficiency is not a constant parameter but increases with settlement due to progressive mobilisation of shaft resistance and pile–cap–soil interaction. Benchmarking against eight widely used empirical equations confirms that traditional rigid–pile formulations systematically misrepresent the behavior of semi–rigid pile groups. Motivated by these findings, a new settlement–dependent analytical expression for group efficiency is proposed, combining a geometry-based interaction term with a nonlinear mobilisation function. The model reproduces numerical trends with an average error of only 6.8 % and captures the physical behavior observed in both field and numerical results. The study provides a unified, experimentally validated framework for interpreting soil–cement pile group behavior and offers improved guidance for serviceability-based design of deep-mixed foundations.