## 3 Analysis of Active Earth Pressure in Circular Shafts
### Validation and Comparison with Other Theoretical and Experimental Results  
[PERSON] et al. [34] employed a circular shaft model with a uniformly decreasing diameter to investigate the distribution of active earth pressure on the shaft wall. The relevant parameters of the model test are: \(\varphi=41^{\circ},\delta=0,\ c=0,\ \gamma=14.7\ \text{kN}/\text{m}^{3},\ r_{0}/H=0.075\). Figure 7 compares the calculation results obtained in this study with the experimental results of [PERSON] et al. [34], and further compares and analyzes them alongside the theoretical predictions of [PERSON] [16], [PERSON] et al. [19], and [PERSON] et al. [29]. As shown in Figure 7, the calculated values from this study and those of [PERSON] et al. [29] are generally consistent with the model test results. It is noteworthy that this study incorporates the spatial arching effect of the soil in the calcula  
Figure 7: Comparison of the calculated active earth pressure with the experimental results of [PERSON] et al. [34] and other theoretical results [16; 19; 29]. a more accurate representation of the trend where the soil pressure intensity first increases and then decreases with depth. In contrast, the calculation results of [PERSON] (16) and [PERSON] et al. (19) show significant deviations from the experimental values. The primary reason is that both studies assume the circumferential stress coefficient \(\lambda\) to be constant (1 and \(K_{0}\), respectively), neglecting the fact that the circumferential stress continuously varies with position. By comparison, this study accounts for the variation of the circumferential stress coefficient \(\lambda\) along the radial coordinate, resulting in calculated values that are closer to the experimental results and thereby verifying the rationality and effectiveness of the proposed calculation method. To further analyze the influence of the radius-to-height ratio and wall-soil friction angle on the distribution of active earth pressure intensity, Figure 8 presents the distribution curves of active earth pressure intensity under different radius-to-height ratios and wall-soil friction angles. Additionally, to investigate the role of the interlayer shear effect of the soil, the calculation results of this study are compared with the values reported by [PERSON] et al. (2021). For ease of analysis, both the horizontal and vertical axes in the figure are normalized. As shown in the figure, the active earth pressure intensity obtained in this study exhibits a curved distribution. The smaller the radius-to-height ratio and the larger the wall-soil friction angle, the more pronounced the influence of the soil arching effect on the distribution of active earth pressure intensity, and the more evident the curved distribution characteristics. In addition, when the radius-to-height ratio is less than 1, the calculated active earth pressure intensity in the middle and lower portions of the shaft is significantly lower than the theoretical value predicted by [PERSON]'s earth pressure theory. As the radius-to-height ratio increases, the circumferential arching effect gradually weakens, and the active earth pressure intensity at the same depth progressively increases; however, the rate of increase gradually diminishes. Further comparative analysis of the calculation results of [PERSON] et al. (2021) reveals that the shear stress between soil layers has a substantial impact on the distribution of active earth pressure along the depth direction. This effect is primarily reflected in the reduction of active earth pressure in the middle and upper portions of the shaft and the increase of active earth pressure at the shaft bottom. Moreover, the larger the radius-to-height ratio and the larger the wall-soil friction angle, the more pronounced the influence of interlayer shear on the active earth pressure distribution. Figure 8: Parametric analysis.