An Improved Design Method for Basal Heave Resistance and Embedded Depth of Circular Shafts Under Spatial Confinement

Circular shafts are widely used in shield launching and receiving, metro ventilation, municipal utilities, and underground energy facilities. In practical shaft construction, embedded depth design directly affects basal heave safety, material consumption, construction cost, and construction duration. However, conventional design methods for basal heave stability are mostly derived from wide pit assumptions, which may lead to conservative designs when they are directly applied to circular shafts. The scientific challenge lies in the fact that the basal heave mechanism of circular shafts is governed not only by excavation unloading and soil strength, but also by spatial confinement and circumferential arching induced by the closed annular retaining system. To address this issue, this study develops a 2D plane-strain equivalent model and a 3D full-scale numerical model using FLAC3D based on an actual circular shaft project. The spatial evolution of basal heave, retaining wall deformation, support internal force, and plastic zone development is systematically investigated. On this basis, spatial confinement and the arching effect are introduced as quantitative correction coefficients within narrow foundation pit theory, and an improved design method for basal heave resistance and critical embedded depth is proposed by combining the foundation bearing capacity failure mode and circular slip failure mode. The results show that circular shafts with width–depth ratios of 0.3–1.0 exhibit typical narrow excavation behavior. Compared with the 2D plane-strain equivalent model, the 3D model produces smaller deformation, lower support internal force, and more localized plastic zones because the closed circular structure can mobilize circumferential compression and spatial load transfer. The proposed method increases the calculated basal heave safety factor by approximately 15–40% and reduces the required embedded depth by approximately 15–30% compared with conventional code-based methods under the investigated conditions. The study provides an improved theoretical and practical approach for basal heave stability assessment and embedded depth optimization of circular shafts, contributing to safer, more economical, and more sustainable shaft construction.