Spatial shape determination method of horizontal soil arching between single-row piles

Horizontal soil arching is a critical stress redistribution mechanism developing between pile rows under lateral loads from adjacent excavations or embankments. This phenomenon significantly affects the performance of pile-based protection systems, yet its spatial formation and depth-dependent geometry remain insufficiently understood. In this study, a comprehensive methodology is developed for determining the spatial shape of horizontal soil arching through an integrated experimental–numerical approach. Laboratory model tests on single-row piles under controlled lateral loading were complemented by validated three-dimensional (3D) finite-element simulations. The investigation revealed that soil arching efficiency is primarily controlled by pile spacing-to-diameter ratio and pile diameter as geometric parameters, along with soil cohesion and internal friction angle as strength parameters. A methodology was developed to determine arch geometry by analysing horizontal stress distributions, identifying the leading edge through stress peaks and the trailing edge through maximum stress gradients. This approach enabled systematic characterisation of the 3D arch morphology. Numerical analyses established that horizontal soil arches exhibit parabolic geometry, with the leading edge maintaining constant geometry with depth while the trailing edge shows progressive expansion. Mathematical equations were developed to predict arch geometry based on pile and soil parameters, providing a scientific basis for optimising pile row design in urban excavation projects.