# A Review of Vertical Shaft Technology and Application in Soft Soil for Urban Underground Space
## 5 Technological Advancements in Design Theory  
### Shaft Section  
In designing vertical shafts, the cross-sectional shape significantly influences structural stability, load distribution, and construction feasibility, particularly in soft UUS. The shaft shape directly affects factors such as lining mobilization and soil-structure interaction. Compared to rectangular or polygonal shafts, circular shafts offer several advantages, including efficient load distribution, reduced lining mobilization, minimized deformation, and decreased shaft reinforcement. In soft UUS, where soil compressibility and settlement are critical concerns, circular shafts present an economical and sustainable solution for shaft construction. The shaft structure section form is the primary consideration in designing the shaft to determine its dimensions and support structure [55]. When designing the shaft section, the shape is determined based on factors such as geological and hydro-geological conditions, shaft depth, and construction costs [56; 57]. Theoretically, shafts can adopt various geometric shapes; however, the most common shapes are circular, square, rectangular, and elliptical. The shaft shape is influenced by its intended purpose and ground conditions [58]. Currently, shaft sections predominantly feature rectangular, circular, oval, and elliptical shapes [59]. In analyzing the prevalence of vertical shafts compared to inclined ones, [PERSON] and [PERSON] [60] reviewed the shapes of vertical shafts sunk over the past sixty years and concluded that the rectangular shape may be phased out, with circular and elliptical shafts becoming the future trend. To develop design guidelines for rectangular- and  
Figure 8: (**a**) Schematic of ACPP; (**b**) automatic track recording system; control interface for an automated excavation, featuring real-time trajectory tracking, depth monitoring, and operational parameters for precise excavation control (**c**) excavation interface; includes multiple parameter settings, directional control buttons, real-time monitoring data, and keys used for adjusting the cutterhead, propulsion system. circular-shaped deep shafts and assess nearby mining effects on shaft stability, [PERSON] et al. [56] investigated an approach to field testing and design for deep mine shafts in the Western U.S.A. High stress concentration occurs at the corners of rectangular vertical shaft cross-sections, leading to the failure of surrounding rock. Therefore, the design of rectangular cross-sections is gradually becoming obsolete and is being replaced by circular vertical shaft cross-section structures [61]. Through numerical calculations, [PERSON] et al. [55] considering factors such as layout, load, function, depth, and construction difficulty of the vertical shaft, provided guidance for engineering scenarios suited for various cross-sectional forms by comparing the cross-sections of vertical shafts. Parametric numerical analysis of shafts with different shapes, construction sequences, stiffness, and embedded lengths concluded that circular shafts resulted in lower lining mobilization than oval and polygonal shafts [62]. According to [PERSON] and [PERSON] [63], circular diaphragm walls represent self-stable structures due to their geometry, which forms a stable ring under compression. Case histories demonstrate that this design usually results in smaller settlements compared to rectangular excavations. Moreover, a circular diaphragm wall can present preferable structural stability compared to a rectangular diaphragm wall due to its inherent rigidity and reduced radial deflection or deformation [64; 65]. Recent project reports of a shaft for an underground car park in Nantes, France, with a diameter of 46 m [66], and a shaft for TBM extraction in Rome, Italy, with a diameter of 15.7 m [67], indicate that such structures remain operational with substantial diameters.