## 4 Numerical Calculation of the Stress Change in the Shaft Tower Structure during the DHS Process
### Simulation Results
The freezing project of Chensilou Coal Mine was stopped on 5 July 2020. The peak tensile stresses on the upper surface of L1, L2, L3 and L4 are 0.52 MPa, 0.70 MPa, 0.69 MPa and 0.78 MPa respectively, the lowest values in the construction with the freezing method;  
(4) The shaft tower is prone to structural instability due to the large amount of melting soil and the uncontrolled speed of thaw settlement. At the tha  
Figure 8: Tensile stress curves on the upper surface of the first\(-\)storey concrete main beams in the shaft tower. (**a**) survey line L1; (**b**) survey line L2; (**c**) survey line L3; (**d**) survey line L4. inclination of the shaft tower in the north-south direction first increases and then decreases, resulting in the same change of tensile stress on the upper surface of the main beams; in the same stage, the inclination of the shaft tower in the east-west direction continues to increase, resulting in the continuous rise of the peak tensile stress on L1 and L2. On 13 March 2021, the inclination of L1 to the east was the largest (\(-0.35\) mm/m), and the peak tensile stress on the west side of the L1 reached 1.18 MPa. On 13 April 2021, the inclination of L2 to the east arrived at the largest value (\(-0.32\) mm/m), and the peak tensile stress on the west side of the L2 reached 1.17 MPa;  
(5) It can be seen from the simulation results that the peak tensile stress (at 1.25 MPa) on the upper surface of the main beam appeared on the south side of L4 on 5 January 2020, which is less than the tensile stress limit of C25 concrete (1.78 MPa). Therefore, the safety of the shaft tower structure is effectively guaranteed due to the adoption of protective measures, such as symmetrical drilling, partial freezing protection and hot water circulation in the temperature-control holes. Since there is an obvious positive correlation between the deformation of the shaft tower foundation and the structural stress of the shaft tower, the inclination value of the shaft tower foundation can be used to predict the peak tensile stress on the upper surface of the main beams. The curves of the peak stress and the inclination of the foundation at L1, L2, L3 and L4 that are shown in Figure 9 confirm the high-correlation relationship between the two factors. The fitting equation and correlation coefficient are shown in Table 4. If the upper-surface tensile stress of L1, L2, L3 and L4 is controlled within the strength limit of C25 concrete (1.78 MPa), the inclination values of J1-J2, J3-J4, J1-J3 and J2-J4 will not exceed 0.788, 0.520, 0.835 and 0.723 mm/m, respectively. It is found that the obtained inclination limit value is significantly less than that which is specified in the standard (GB50007-2011 in China: 2.5 mm/m). Therefore, in similar freezing method construction, a numerical calculation model should be established in advance according to the actual conditions, and the building inclination must be controlled according to the limit value that is obtained by the numerical calculation. It can be seen from Figure 9 that the peak value of tensile stress on the upper surface of the main beams increases with the increase in inclination. Therefore, it is necessary to observe the tower inclination in real time when the freezing method is applied to a similar project with a high-rise tower. The observation results of tower inclination can be put into the fitting formula (Table 4) to obtain the maximum tensile-stress values of the main beams, and, therefore, real-time warnings can be offered for the structural safety of the main beams. In the freezing construction process, if the tower inclination is so large that the calculation result of the fitting equation exceeds the strength limit of the concrete main beams, the  
Figure 9: Relationship between the peak tensile stress on the upper surface of the main beams and the inclination of the tower foundation. (**a**) North–south direction; (**b**) east–west direction.