## 4 Numerical Calculation of the Stress Change in the Shaft Tower Structure during the DHS Process
### Simulation Results  
The concrete main beams (shown in Figure 6) can stand compressive or shear stress, but not tensile stress, and the tensile strength is maximum at the upper surface of the beams that are especially close to the pilaster. Considering that the deformation of the shaft tower foundation had the greatest influence on the first-storey concrete main beams, survey lines (L1, L2, L3, L4) to monitor the tensile stress were arranged on their upper surface. The stress distribution of the upper surface is given in Figure 8. It could be inferred from Figure 8 that (1) The peak tensile stress appears at the joint between the pilaster and the main beams. When the shaft tower inclines to the east, the peak tensile stress appears on the west surface of the main beams; when the shaft tower inclines to the north, the peak tensile stress appears on the south surface of the main beams. The inclination value of the shaft tower foundation is positively correlated with the peak value of the tensile stress;  
(2) The influence of various types of drilling construction on the deformation of the shaft tower foundation and structural stress distribution cannot be ignored, because drilling around high-rise shaft tower lasts for a long time and has a significant impact on its foundation. On 5 January 2020, just before the end of the drilling period, the inclination value of the shaft tower to the north was the largest. The inclination value of the L3 main beam was at \(-\)0.24 mm/m, and that of L4 reached \(-\)0.31 mm/m. The peak tensile stresses \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Date** & **J1/m** & **J2/m** & **J3/m** & **J4/m** & **Displacement** & **Displacement** & **Displacement** \\  & & & & **Equation z\({}_{2}\)/m** & **Equation z\({}_{2}\)/m** & **Equation z\({}_{2}\)/m** \\ \hline
5 January 2020 & 0.0010 & 0.0010 & 0.0040 & 0.0010 & & \\ \hline
31 March 2020 & 0.0060 & 0.0093 & 0.0082 & 0.0060 & & \\ \hline
13 June 2020 & 0.0020 & 0.0030 & 0.0022 & 0.0020 & & \\ \hline
5 July 2020 & 0.0038 & 0.0030 & 0.0040 & 0.0038 & & \\ \hline
19 August 2020 & 0.0113 & 0.0143 & 0.0128 & 0.0113 & \((\chi/17.5)\)\((\mathrm{J}4-\mathrm{J}3)\) + J3 & \((\chi/17.5)\)\((\mathrm{J}4-\mathrm{J}2)\) + J2 & \((\chi/17.5)\)\((\mathrm{J}2-\mathrm{J}1)\) + J1 & \((\chi/16.5)\)\((\mathrm{J}3-\mathrm{J}1)\) + J1 \\ \hline
20 September 2020 & 0.0196 & 0.0232 & 0.0210 & 0.0196 & & \\ \hline
26 October 2020 & 0.0270 & 0.0314 & 0.0286 & 0.0270 & & \\ \hline
10 January 2021 & 0.0373 & 0.0440 & 0.0400 & 0.0373 & & \\ \hline
13 March 2021 & 0.0424 & 0.0491 & 0.0443 & 0.0424 & \\ \hline
13 April 2021 & 0.0427 & 0.0494 & 0.0444 & 0.0427 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Monitoring results of relative displacement at each monitoring point and predefined displacement equation on the bottom frames of the model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Elastic Modulus/(GPa)** & **Poisson’s Ratio** & **Density/(kg/m3)** & **Data Sources** \\ \hline C-30 Concrete & 30.00 & 0.18 & 2400 & GB/T 50107-2010 \\ C-25 Concrete & 28.00 & 0.20 & 2360 & GB/T 50107-2010 \\ M7.5 machine brick & 5.65 & 0.15 & 1700 & JGJ-T 110-2017 \\ M5 mixed mortar & 4.00 & 0.17 & 1560 & JGJ-T 110-2017 \\ Steel bar & 205.00 & 0.30 & 7850 & GB50017-2014 \\ Cold rolled steel plate & 210.00 & 0.28 & 7900 & GB50017-2014 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measurement results of the material properties of the Chensilou shaft tower. on the south side of L3 and L4 came to 1.09 MPa and 1.25 MPa, respectively. Therefore, in the drilling process around tall buildings, the principle of symmetrical and synchronous construction should be followed to ensure the safety of the building structure;  
(3) With the thickening of frozen walls, the stratum strength in the freezing range continues to increase, which alleviates the uneven settlement of the tower. The shaft tower gradually recovers to the southwest, and the peak tensile stresses decrease to varying degrees.