Research on Foundation Deformation and Structural Stress Variation of Shaft Tower under the Influence of Frost Heave and Thaw Settlement

Abstract

As the laws of structure deformation and structural stress variation under freezing construction around high-rise buildings are not clear and no engineering experience can be referred to, freezing method construction in this situation is paired with huge safety risks. In this paper, freezing construction was successfully carried out around the main shaft tower in Chensilou Coal Mine by taking the following protective measures: symmetrical drilling, local freezing and hot water circulation. The elevation of the shaft tower foundation is continuously measured during the process of drilling, frost heaving and thaw settlement (hereinafter referred to as the DHS process). Benefiting from these protective measures, the maximum inclination value (−0.406 mm/m) of the shaft tower is controlled at well below the allowable value. The observation data informed the settlement and inclination of the tower foundation during the DHS process. A numerical model of the shaft tower is further established based on the observation data to reveal the tower structure’s law of stress variation during the DHS process. In addition, the fitting equation between the tower inclination value and the structural stress is obtained, which can provide a reference for freezing construction of similar high-rise buildings.

1. Introduction

The freezing method is commonly used to prevent the disaster of water inrush in underground excavation in China. This method uses artificial refrigeration technology to form a frozen wall around the underground space in the topsoil section, completely blocking the hydraulic connection between the topsoil aquifer and the excavation space. During freezing method construction, buildings are often on the surface. Freezing method construction has great influence on the stability of a building’s foundation and its structural safety.

The process of freezing method construction includes three stages: drilling, frost heaving and thaw settlement. In the drilling stage, the flushing fluid carries rock powder and sediment away from the formation, which may trigger the settlement of the building foundation. In the freezing stage, the frost heave of rock and soil cause the uplift of the building foundation. In the melting stage, uneven settlement of the foundation makes the shaft tower tilt. In a word, freezing method construction incurs frost heaving and thaw settlement of the soil, and, in turn, the heave or settlement of the building foundation.

A significant amount of research has been conducted on the ground surface movement that is induced by freezing method construction [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. Among them, Li et al. considered the effect of the freezing margin and established a frost-heaving mode to calculate the frost heave deformation of roadbed by a semi-analytical numerical method [1]. Sheng et al. analyzed the influence of horizontal-freezing frost heave on the pile foundation of adjacent buildings in a railway tunnel through a finite element calculation and obtained the influence radius of horizontal-freezing frost heave [2]. Wang et al. analyzed the displacement of upper structures under simultaneous and sequential freezing modes. The results are instructive to the construction of under-passing projects in a water-rich layer [3]. Dubina proposed a mathematical model for the variation and interaction of stress-strain, temperature and humidity fields in the structure and soil layer system in the permafrost region [4]. Liu et al. proposed that the surface frost-heaving amount was the superposition of the frost-heaving rate along the whole freezing depth. According to their research, the normal frost-heave force was the integral of the frost-heaving stress on the frozen front along the influence range of the foundation, which had no direct relation with the surface frost-heaving amount [5]. Huang systematically studied the frost-heaving deformation and its mechanical properties under unloading in freezing envelope engineering. He contended that frost heaving was closely related to the restriction conditions of soil properties, freezing time and degree, and the thickness of frozen soil wall. On this basis, he proposed that the effect of frost-heaving deformation could be alleviated through the pressure relief hole [6]. Lewis and Schrefler focused on multiphase flow and coupled thermo-hydro-mechanical problems in saturated and unsaturated soils [15,16,17]. They offered numerical solutions to soil deformation during fluid flow.

The inclination of the buildings under freezing construction certainly generate the variation of the internal structural stress. At present, finite element numerical calculation is an important method to study the structural stress of buildings. Conventionally, the deformation of a building’s foundation is small, so most numerical simulation uses a linear elastic model [18]. Finite element method (FEM) models of buildings are often created based on experimental data. Szafran et al. established the finite element model of a telecommunication tower structure, according to the actual site conditions. The model carefully analyzed the specific wind velocity-time function, and then, first-order and second-order reliability methods were used to judge the reliability of two particular tower joints [19]. Zhang et al. compared various concrete wall models by finite element analysis, discussed the influence of stress redistribution and load transfer path change on reinforced-concrete shear wall, and put forward some design suggestions for the reinforcement arrangement of reinforced concrete members under a complex stress state [20]. Cocking et al. believed that although the linear elastic finite-element analysis method had its limitations, it was very suitable for evaluating the stability of a masonry arch bridge under service load. They established the finite element numerical calculation model of a masonry arch bridge and compared the monitoring data with numerical results. They found that the monitoring data of low-failure area were quite consistent with the numerical calculation results [21]. Jiang et al. accurately predicted the structural bearing capacity of grid towers under different modes. It is of great significance to accurately evaluate the reliability of transmission lines and power networks and to design effective protection measures [22]. Although many scholars use finite element numerical calculation to study the structural stability of buildings, there is no relevant research on the variation of the structural stress of buildings under the freezing construction method.

In the Chensilou Coal Mine of Yongmei Group, China, the main shaft repair project is carried out with the freezing method. On the ground of the main shaft there is a high-rise main shaft tower, inside which are installed a guide wheel, friction wheel, hoister, and supporting electronic ventilation equipment. Since the main shaft tower of Chensilou Coal Mine was built 20 years ago, the performance of its structural concrete might have been attenuated. Moreover, if the freezing front develops to the tower foundation, it will pose a serious threat to the safety of the shaft tower structure. Therefore, it is important to ensure the stability of the foundation and the safety of the shaft tower while using the freezing method to repair the main shaft.

When the tilt of the shaft tower exceeds a certain limit, the hoist inside the shaft tower is not be able to operate normally, which could be an immeasurable loss to the company. In addition, the non-uniform settlement of the foundation also leads to changes in the structural stress of the shaft tower. If the stress of the key structure exceeds the strength limit, the structure stability cannot be ensured. Due to the serious safety risks, no other cases of freezing construction around high-rise buildings have been reported, and the foundation deformation and structural stress variation of a shaft tower during the process of drilling, frost heaving and thaw settlement (DHS process) are not well understood.

In view of the above research gap, to ensure the safety of freezing construction around the high shaft tower, effective protection measures must be taken to prevent the tower foundation from being frozen. To achieve this end, it is necessary to continuously observe the deformation of the shaft tower foundation during the DHS process and establish a shaft tower model to analyze the stress variation pattern of the shaft tower structure, in order to ensure the smooth progress of the freezing method construction.

This paper is organized as follows. Section 2 introduces the engineering background of the freezing method repair project on the main shaft of Chensilou Coal Mine. Section 3 analyzes the measurement results of the deformation in the shaft tower foundation during the DHS process. Section 4 builds a numerical model of the shaft tower and reveals the variation law of structural stress during the DHS process. Section 5 is the conclusion.

2. Engineering Background

2.1. The Basic Information of the Main Shaft and Tower

The terrain elevation of Chensilou Coal Mine is 32~35 m, and its design capacity is 2.4 million t/a. The shaft tower, a reinforced concrete box structure with equal sections, is constructed on the upper part of the main shaft. The plane outer edge size is 16.5 × 17.5 m, with a total height of 71 m. Figure 1a shows the exterior of the shaft tower. The walls of the main shaft tower of Chensilou Coal Mine are 350 mm thick below the height of 19 m and 250 mm thick above it. There are eight reinforced concrete pilasters of 600 × 1300 mm inside the tower. All floors of the shaft tower are of a cast-in-place reinforced concrete beam-slab structure, the roof is a cast-in-place concrete well lattice beam-slab structure, and the vertical section size of the concrete main beam is 500 × 1200 mm. The shaft tower is based on a reinforced concrete box foundation whose plane is 25 × 25 m, with a height of 7 m and a burial depth of −7.9 m. The top and bottom of the tower foundation are 250 mm and 500 mm thick, respectively.

2.2. Borehole Layout

The layout of various holes is shown in Figure 1b. Since the foundation size of the shaft tower was 25 × 25 m, a square borehole layout scheme with a side length of 30 × 30 m was adopted for the freezing holes so that a 2.5 m buffer zone was reserved between the freezing wall and the shaft tower foundation. Meanwhile, to ensure that the soil within the tower foundation would not be frozen, temperature-control holes (with a side length of 26 × 26 m) were arranged between the tower foundation and the freezing holes. In order to monitor the temperature around the tower foundation, four thermometer holes were arranged. In order to avoid the impact of drilling on the shaft tower foundation, the symmetrical and synchronous drilling method was adopted to ensure the uniform settlement of the shaft tower foundation as much as possible. Drilling parameters are shown in

Table 1. Drilling parameters.

Borehole Type	Borehole Depth/(m)	Borehole Diameter/(mm)	Borehole Number	Borehole Spacing/(m)
Freezing hole	378	216	70	1.714
Temperature-control hole	46	130	37	2.8
Thermometer hole	46	190	4	-

.

2.3. Measured Results of Temperature-Control Holes

Figure 2 displays the curves of the hot water temperature and monitoring data that were obtained from the thermometer holes (K1, K2, K3, and K4). After 92 days of freezing, the temperature at the deepest point (sensor depth is 45 m) of thermometer holes K1, K2, K3 and K4 reached 2.44, 2.81, 2.50 and 4.50 °C, respectively. At that time, in order to prevent the freezing front from further developing into the tower foundation, hot water circulation in the temperature-control holes was started. As can be seen from Figure 2, when hot water began to circulate in the temperature-control hole, the downward trend of the temperature curve slowed down. Even the temperature at thermometer hole K1 (whose temperature was the lowest in the freezing construction process) remained above 0 °C. This indicates that the freezing of the tower foundation was successfully avoided, thus protecting the tower foundation.

2.4. The Error Analysis

During the freezing construction, OC1820 temperature sensors (with a range between −55 and 125 °C, and error within ±0.5 °C) were installed in the thermometer holes. Their range and accuracy meet the requirements of field engineering. Figure 2 shows that the temperature observed by the sensors near the ground surface is higher than in the lower part of the hole, indicating that small temperature variations can be captured by the sensors. The reduction in temperature at the bottom of the thermometer hole is due to the lack of thermal insulation protection from the polyurethane insulation layer, which is especially obvious at the bottom (a burial depth of 45 m), as the temperature is always kept at the lowest level. The above trend conforms to common sense indicating that the reliability of the measurement data is high, and the error of the equipment itself will not affect the experiment conclusion.

3. Field Measurement of the Deformation of Shaft Tower Foundation during DHS Process

Although partial freezing technology is adopted in the repair project of the main shaft of Chensilou Coal Mine, the deformation of the shaft tower foundation is bound to occur due to drilling, soil freezing and soil melting. The most obvious deformation of the shaft tower are settlement and inclination, among which the inclination values are an important index to measure the non-uniform settlement of the foundation. According to the Allowable Deformation Value of Building Foundation (GB50007-2011 in China), the allowable value for the foundation in Chensilou Coal Mine is 2.5 mm/m. Through the on-site measurement, the deformation values of the shaft tower foundation during the whole process of freezing method construction were obtained to provide an early warning of an over-large inclination of the shaft tower and thus achieve the purpose of safe construction.

3.1. Monitoring Scheme and Equipment

Elevation monitoring points (J1, J2, J3, J4) are arranged at the four corners of the shaft tower, and the benchmarking point in Chensilou Coal Mine is used as the reference point to observe the settlement of the shaft tower foundation. In the case of a high accuracy test, the vibration of the tower foundation affects the accuracy of the monitoring results, so it can only be carried out after the operation in the tower is stopped. Considering the cost of the long-time suspension of the operation and the harsh measurement conditions that are required, high accuracy tests cannot be conducted very often. In order to increase the measurement frequency, rapid measurements are introduced as the supplement. High accuracy tests are performed using RUIDE’s DL-2007 digital level (elevation accuracy is 0.1 mm), and rapid measurements are performed with a DS-3 micro-tilt level (elevation accuracy is 3 mm). The layout of the monitoring points and measuring instruments is shown in Figure 3.

3.2. Shaft Tower Foundation Settlement

We choose a reference point far away from the tower, which is not affected by freezing method construction, and determine the elevation of each measuring point of the tower foundation by round-trip leveling. The measurement starts with drilling, and the settlement data of each monitoring point is shown in Figure 4. The blue solid points in Figure 4 are the monitoring results of the high-precision level, and the red circles are the results of the DS-3. The data analysis is mainly based on the test results of DL-2007, supplemented by the DS-3. It can be seen from Figure 4 that at the drilling stage (A), soil freezing stage (B) and soil melting stage (C), the shaft tower foundation experiences a process of slow settlement, slight heaving, fast settlement and finally, stabilization.

(1) Drilling stage

The drilling stage began on 21 October 2019 and lasted 88 days. A total of 120 holes of various types were drilled, with a total drilling footage of 31,111 m. At the drilling stage, the flushing fluid carried rock powder and sediment away from the stratum, and the rock and soil volume, according to the diameter of the boreholes was estimated at about 950 m³, which caused the settlement of the shaft tower foundation. It can be seen from Figure 4 that at stage A, monitoring points J1 to J4 sank 3 mm, 4 mm, 7 mm, and 7 mm, respectively. The settlement is therefore very limited at the end of stage A, leading to little tilting and disorder in the tower.

(2) Soil freezing stage

The freezing stage was put into trial operation on 22 January 2020, and after 164 days, the freezing station was shut down on 4 July 2020. It can be seen from Figure 4 that in the first 58 to 61 days of soil freezing, the elevation of the monitoring points was still decreasing, indicating that the shaft tower foundation settlement caused by drilling did not stop. The rock-soil expansion that was caused by soil freezing slowed down the settlement of the shaft tower foundation but did not compensate the settlement from drilling. Compared with the starting point of drilling construction, J1 to J4 sank 8 mm, 9 mm, 10 mm, and 10 mm, respectively. After 61 days of freezing operation, the foundation of the shaft tower trended in reverse, starting to rise at all four monitoring points. This phenomenon showed that after the soil was frozen for 61 days, the frozen walls began to form a complete circle, and the soil strength and expansion in the frozen area continued to increase, which stopped the drilling-induced settlement of the foundation.

(3) Soil melting stage

On 4 July 2020, the repair project stopped freezing and entered the thaw settlement stage. After the freezing station was shut down, the elevation of the shaft tower foundation started to show some typical features of the settlement stage (the blue point on the timeline is the result of 5 July). In the early stage of soil melting, the settlement rate of the shaft tower foundation was relatively fast, but 113 days after soil melting (26 October 2020), it began to slow down, and 281 days after soil melting (13 April 2021) the settlement stopped. During the whole melting period, monitoring points J1 to J4 sank 39.2 mm, 46.0 mm, 40.0 mm, and 43.7 mm, respectively. From the monitoring results of foundation settlement, it can be seen that the thaw settlement amount is much greater than the frost-heaving amount.

3.3. Inclination of the Shaft Tower Foundation

The inclination value of the shaft tower foundation can be calculated from the high-precision levels’ monitoring results. The results in the DHS process are shown in Figure 5, where a positive value means that the shaft tower inclines to the south or west, and a negative value means it tilts to the north or east. Figure 5 shows that the shaft tower foundation first inclines northeastward at the drilling stage, and then recovers towards southwest due to frost heaving, and the shaft tower tilts further eastward at the thaw settlement stage.

(1) Drilling stage

After drilling, the shaft tower foundation began to sink and the shaft tower started to incline due to the inconsistency of the settlement speed at the four corners of the shaft tower. Figure 5 shows that the shaft tower inclines towards northeast immediately after the drilling operation. The maximum inclination rate in the north–south direction is −0.343 mm/m (5 January 2020), and that in the east–west direction is −0.171 mm/m (5 January 2020), which are less than the allowable value (2.5 mm/m) for the inclination of the shaft tower foundation. Measured against the shaft tower height (71 m), the maximum inclination value towards the north at the top of the shaft tower is 24.4 mm, and the maximum value towards the east is 12.1 mm in the drilling stage.

(2) Soil freezing stage

During the freezing construction period, the northeastward inclination of the shaft tower continued to decrease, which means the shaft tower was returning to the southwest direction. After the freezing construction, the inclination value of the shaft tower in the north–south direction was close to 0 mm/m (5 July 2020). Although the soil strength and expansion in the frozen area continued to increase, which prevented the shaft tower foundation from sinking, the decrease in the inclination value was not under human control, but the result of a combination of factors.

(3) Soil melting stage

At the soil melting stage, the inclination value of the shaft tower foundation in the north–south direction increased first and then decreased. After 281 days of soil melting (13 April 2021), the inclination value of the shaft tower in the north–south direction almost decreased to 0 mm/m. In addition, at the stage of soil melting, the shaft tower foundation further inclined to the east, and the maximum inclination was −0.406 mm/m (10 January 2021). Measured against the shaft tower height (71 m), the maximum inclination value towards the north at the top of the shaft tower was 11.6 mm, and the maximum value towards the east was 28.83 mm.

Benefiting from the protective measures, such as symmetrical drilling, partial freezing and hot water circulation in temperature-control holes, the stability of the shaft tower foundation was ensured with the maximum inclination value (−0.406 mm/m) well below the allowable value (2.5 mm/m) in the DHS process.

3.4. The Error Analysis

The high-precision measurement of the foundation elevation of the shaft tower is performed by using the DL-2007 digital level of RUIDE, and its measurement accuracy reaches 0.1 mm. When the high-precision measurement is performed, operations around the shaft tower foundation are suspended to avoid the impact of vibration on the measurement results, thus ensuring the measurement accuracy. Since each high-precision measurement demands strict measurement conditions and takes a long time, the normal coal mine production is affected, so high-precision measurement is not frequently performed. In order to supplement the monitoring frequency, a DS-3 micro-tilt level with a precision of 3 mm is used in rapid measurement. It can be seen from Figure 4 that the rapid measurement results fluctuate on both sides of the high-precision monitoring curve. Although there is a certain degree of error in the monitoring results, it is still acceptable and will not affect the experiment conclusion.

4. Numerical Calculation of the Stress Change in the Shaft Tower Structure during the DHS Process

4.1. Simulation Scheme

The solid mechanics module in the COMSOL software was used to carry out the numerical calculation of the stress in the shaft tower, and the geometric model was established according to the on-site conditions. Moreover, the boundary conditions were determined according to the elevation change of the shaft tower foundation, and the material properties of each part of the shaft tower were determined based on the existing measurement results.

(1) Geometric model

According to the structure and size of the shaft tower, a geometric model was established. Inside the pilasters of the shaft tower, the longitudinal reinforcing bars were six steel bars of 28 mm in diameter, the stirrups were steel bars of 10 mm in diameter, and the spacing between the stirrups was 120 mm. The section size of the concrete main beam was 440 × 1500 mm; the reinforcing bars were six steel bars of 32 mm in diameter, the stirrups were steel bars of 12 mm in diameter, and the spacing between the stirrups was 140 mm. In order to protect the concrete main beams of the shaft tower, steel plates with a thickness of 8 mm were wrapped on its surface. Since the objects in the established model varied greatly in size, the sub-regional meshing method was adopted. The reinforcing bars, steel plates, pilasters, and main beams used ultra-fine meshes, and the tower walls adopted fine meshes. The model generated a total of 0.73 million free-tetrahedron meshes, and the geometry and mesh diagrams of the model are shown in Figure 6. The model is calculated by a steady-state solver, and the number of degrees of freedom to calculate reaches 3,490,206.

(2) Constitutive equations

Since the shaft tower deformation is in a small range, it can be assumed that the shaft tower structure is linear elastic, and its deformation follows Hooke’s law:

$${\sigma }_{ij}=\lambda {\delta }_{ij}{\epsilon }_{\mathrm{V}}+2G{\epsilon }_{ij}$$

(1)

where σ_ij is the total stress tensor; λ is the Lame constant; δ_ij is the Kronecker function; G is the shear modulus; and ε_ij is the strain tensor.

(3) Geometric deformation equation

The deformation of the shaft tower is within a small range, and its geometric equation can be written as:

$${\epsilon }_{ij}=\frac{1}{2}(u_{ij}+u_{ji})$$

(2)

where: u_ij and u_ji are the displacement components.

(4) Boundary conditions

Since the bottom frame is in contact with the shaft tower foundation, this paper simulates the different inclination states of the shaft tower by changing the displacement on the bottom frame. Since the model is established according to the actual situation of the shaft tower, the remaining boundaries can be set as free boundaries, so that the shaft tower can tilt in different directions.

The bottom of the model includes the frames that are shown in Figure 7, whose boundary conditions are set to predefined displacement boundaries. The other boundaries of the model are set to free boundaries.

Since only the elevations of monitoring points J1, J2, J3, and J4 were observed but the tower foundation was quite rigid, it was assumed that the predefined displacements on the bottom frames were distributed linearly along the frames. Under this assumption, the displacement along all the structural frames can be extracted from the monitoring data that were obtained from J1, J2, J3, J4 using the equations presented in

Table 2. Monitoring results of relative displacement at each monitoring point and predefined displacement equation on the bottom frames of the model.

Date	J1/m	J2/m	J3/m	J4/m	Displacement Equation z1/m	Displacement Equation z2/m	Displacement Equation z3/m	Displacement Equation z4/m
5 January 2020	0.0010	0.0010	0.0040	0.0010	(x/17.5) (J4 − J3) + J3	(y/16.5) (J4 − J2) + J2	(x/17.5) (J2 − J1) + J1	(y/16.5) (J3 − J1) + J1
31 March 2020	0.0060	0.0093	0.0082	0.0060
13 June 2020	0.0020	0.0030	0.0022	0.0020
5 July 2020	0.0038	0.0030	0.0040	0.0038
19 August 2020	0.0113	0.0143	0.0128	0.0113
20 September 2020	0.0196	0.0232	0.0210	0.0196
26 October 2020	0.0270	0.0314	0.0286	0.0270
10 January 2021	0.0373	0.0440	0.0400	0.0373
13 March 2021	0.0424	0.0491	0.0443	0.0424
13 April 2021	0.0427	0.0494	0.0444	0.0427

. Compared with the monitoring data on the start date of the drilling project (21 October 2019), the relative displacement of each monitoring point and the predefined displacement equations on the bottom frame are shown in Table 2.

(5) Material properties

Tower body and pilasters: C30 concrete was applied below the elevation of 19 m, and C25 concrete was used above 19 m. Floor: C30 concrete was used below the elevation of 19 m, and C25 concrete was used above 19 m. C25 concrete was used for the roof, and M7.5 machine bricks and M5 mixed mortar were used for the walls. Reinforcing steel plates covering the main beams: cold-rolled steel plates with a thickness of 8 mm were used.

Since the main shaft tower was built 20 years ago, the structural strength of each part may have been attenuated to varying degrees. However, the measurement results reveal that the carbonization depth of the concrete components is less than 10 mm, and the corrosion degree of the internal steel skeleton is small; the compressive strength of C30 concrete tested by an ultrasonic detector is 33.7 MPa (standard = 34.5 MPa), and the strength of C25 concrete is 27.3 MPa (standard = 28.75 MPa). The results show that the current concrete strength is slightly lower than the standard value, but the difference is small. Therefore, the standard value is accepted as the concrete property in the simulation. The material properties of each part of the shaft tower are shown in

Table 3. Measurement results of the material properties of the Chensilou shaft tower.

Material	Elastic Modulus/(GPa)	Poisson’s Ratio	Density/(kg/m3)	Data Sources
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

. In the solid mechanics module, the material properties of different well tower structures are assigned according to Table 3.

4.2. 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 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. 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 thaw settlement stage, the 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. Fitting equation and correlation coefficient between the peak tensile stress on the upper surface of the main beams and the inclination of the shaft tower foundation.

Monitoring Line for Inclination	Fitting Equation	Correlation Coefficient R2
J1-J2	σ1 = 1.6124T + 0.5086	0.9792
J3-J4	σ2 = 2.4831T + 0.4907	0.9736
J1-J3	σ3 = 1.3936T + 0.6156	0.9173
J2-J4	σ4 = 1.3883T + 0.7776	0.9126

Note: T is the inclination of the concrete main beam, mm/m.

. 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 freezing construction should be stopped immediately, and grouting reinforcement measures should be adopted to slow down the tower inclination.

5. Conclusions

Freezing method construction around high-rise buildings is paired with great safety risks and there is no engineering experience to refer to at present. This paper successfully carried out the freezing method construction around the main shaft tower of Chensilou Coal Mine by taking protection measures, such as symmetrical drilling, local freezing and hot water circulation. The following conclusions can be drawn.

(1) The change patterns of the settlement and inclination of the shaft tower foundation were obtained by measuring its elevation continuously during the DHS process. The measurement results showed that the shaft tower foundation experienced four stages, namely, slow settlement, slight heaving, rapid settlement and stabilization through the DHS process. The thaw settlement amount is much greater than the frost-heaving amount, and the tower foundation deformation in the thaw settlement stage deserves engineers’ attention.

(2) During the DHS process, the shaft tower foundation first inclined northeastward at the drilling stage, and then recovered towards southwest due to frost heaving, and the shaft tower tilted further eastward at the thaw settlement stage. Benefiting from the abovementioned protective measures, the stability of the shaft tower foundation was ensured with the maximum inclination value (−0.406 mm/m) well below the allowable value (2.5 mm/m).

(3) According to the on-site conditions, a numerical model of the shaft tower was established. The model results showed that the peak tensile stress on the upper surface of the main beams existed at the joint between the pilaster and the main beams of the shaft tower. When the tower tilted to one side, the peak value of tensile stress appeared on the other side of the main beam.

(4) The fitting equation between the peak tensile stress on the upper surface of the main beams and the inclination of the shaft tower was obtained. If the safety of the shaft tower was to be ensured, the inclination values of J1-J2, J3-J4, J1-J3 and J2-J4 could not exceed 0.788, 0.520, 0.835, and 0.723 mm/m, respectively. 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.