Directional Anisotropy of Admissible Tilt in Rectangular Sinking Wells: A Closed-Form Analytical Model

Rectangular sinking wells are widely used in underground and hydraulic engineering, where maintaining vertical alignment during construction is essential for safe serviceability and long-term performance. Even moderate inclination may cause eccentric transfer of the vertical load to the concrete plug, leading to non-uniform contact stresses beneath the base. This study presents a closed-form analytical framework for assessing the admissible tilt of rectangular sinking wells based on stress redistribution under one-axis inclination. The well is modeled as a rigid body, and the resulting load eccentricity is related to the shaft height and tilt angle. Classical eccentric compression theory is then used to derive explicit expressions for the maximum and minimum base stresses, from which a serviceability-based admissibility criterion is formulated. The obtained solution provides the allowable inclination directly as a function of shaft height, plan dimensions, and an adopted stress amplification factor. Parametric analyses show that the admissible tilt decreases with increasing shaft height and increases with larger base dimensions. A distinct directional anisotropy is observed for rectangular plans, whereas square wells recover symmetric behavior with identical limits in both orthogonal directions. This identifies square geometry as the symmetry-preserving limit case of the proposed model. Sensitivity analyses further demonstrate the influence of admissible stress amplification on permissible inclination levels. The proposed formulation offers a transparent screening tool for construction monitoring and post-construction assessment, while also illustrating how geometric symmetry reduction governs the mechanical response of inclined foundation systems.