Quantifying Spatial Effects in Row-Pile Support Systems for Loess Deep Excavations: Model Test, Numerical, and Theoretical Study

Three-dimensional spatial effects in deep excavations critically govern the mechanical response of retaining structures and adjacent soils, yet their quantitative characterization remains a challenge. This study systematically investigates the spatial behavior of row-pile-supported foundation pits through an integrated approach combining model tests, theoretical analysis, and numerical simulations. A novel formulation for the spatial effect influence coefficient K is derived from limit equilibrium principles and subsequently validated via ABAQUS-based finite element simulations. Model test results reveal pronounced spatial heterogeneity in earth pressure and bending moment distributions along the pit perimeter: lateral earth pressure at corner regions exceeds that at mid-side locations at equivalent depths, whereas bending moments in mid-side piles are substantially larger than those at corners. Displacement field measurements further demonstrate that corner zones, constrained bidirectionally, undergo minimal deformation, while maximum displacement occurs at the midpoints of the long sides. These observations collectively confirm the existence of a marked corner effect and a subdued side-midpoint effect under three-dimensional confinement. Complementary numerical analyses indicate that the coefficient K decreases monotonically with increasing half-angle corners and distance from the corner, thereby quantitatively capturing the decay of spatial constraint intensity. Together, these findings establish a theoretical framework for assessing excavation-induced spatial effects and provide actionable guidance for the rational design of deep foundation pit support systems.