Study of the Prevention Method of ±800 kV Transmission Tower Foundation Deviation

Abstract

The stability of transmission tower bases is key to ensuring the safe operation of power lines. This paper proposes a joint displacement-control technique for foundation-inclined piles and prestressed foundation tie beams to address the problem of tower base displacement and durability degradation caused by environmental factors. A finite element model of an exposed-pile transmission tower conforming to the structural characteristics of the actual line tower was established based on the current situation of Tower 292 of the ±800 kV Tianzhong line in Xinjiang, China. Three different displacement-control schemes were analyzed under the combined effects of tower line load, ice-cover load, and wind load, including changing exposed pile height, changing inclined pile tilt angle, and increasing the prestressed foundation tie beam. The analysis shows that the combined displacement-control technology of foundation-inclined piles and prestressed foundation tie beams can reduce the horizontal displacement of EHV tower foundations by more than 50%, which greatly reduces safety problems caused by tower displacement and effectively improves tower durability.

1. Introduction

As an important strategy for China, the Hami South-Zhengzhou ±800 kV UHV project is a channel to implement west–east power transmission, and an important guarantee to meet the power load demand in central China. The environment along the Tianzhong line is complex; in the Xinjiang region, as it is affected by the natural environment, the foundation of the transmission-line tower structure is subject to environmental corrosion, and the problem of wind-induced fatigue load on the upper durability of the structure is prominent [1]. Therefore, in the alpine freezing-and-thawing saline land in Xinjiang, how to ensure the durability and safety of transmission-line towers will become an important research topic, and has important theoretical significance and engineering application value.

Numerical simulation methods are developing rapidly; scholars have studied the wind-driven response of transmission-line towers by numerical simulation in recent years. The response of a tower line system to the inclined incident wind is studied in reference [2], and a spatial load model of the tower line system under the action of inclined incident wind is established. Reference [3] establishes a finite element model for two lines and three towers to study the wind-induced response characteristics of a tower line system under different wind-angle and wind-speed conditions, and analyzes the relationship between the maximum stress in the structure and the wind direction and wind speed. Reference [4] details the dynamic response of a transmission-line system under weather wind loads (regular atmosphere, boundary layer) and non-weather wind loads (down-strike storm flow); the gust-induced responses of towers and conductors are also discussed and analyzed. Reference [5] uses the AR method to generate artificial fluctuating wind loads and applies it to a tower line model. Most of the research on wind response is based on the simplified wind-load model to analyze the wind response characteristics of transmission tower line systems, while ignoring the influence of surrounding topography, geology, and environmental conditions on the wind-induced response of transmission lines. In actual projects, especially in Xinjiang, China, the local complex geographical environment can directly affect the wind response of transmission lines. Therefore, it is important to fully consider the local environment in modeling and to establish a model that meets the local reality and structural characteristics. In order to improve the accuracy of the model, reference [6] analyzes historical sample data containing several influencing factors such as elevation, slope, lower pad surface, etc., and then obtains correction coefficients based on data-driven thinking. In reference [7], for mountainous terrain, collection line and suspension chain line equations are used to determine the spatial location of conductors and grounding along pitch direction in any section of the collection line, and modeling and calculation analysis of a three-dimensional electrical geometry model of the whole collection line is completed. Reference [8] considered the effects of real typhoon scenarios, microtopography, and transmission corridor information factors to simulate a transmission-line system. However, these scenarios do not take into account local geological factors and only combine local topography into the model, which does not effectively show the influence of local geology on wind response. Reference [9] considers geological information such as octahedral low-strain shear modulus, geotechnical internal friction angle, and ultimate shear strength in modeling the interaction of geology and structure to assess the safety of high-rise buildings. Reference [10] investigates the interaction of soil information such as geotechnical type and degree of geotechnical weathering with a building structure under vibration and demonstrates that its vibration signal can better characterize structural dynamic properties when geological information is considered. Reference [11] suggests that when conducting risk assessment of buildings, it is necessary to improve the understanding of the interaction between infrastructure and environmental factors, to establish a general coupled model of environment and structure, and to combine numerical simulation and traditional methods to establish a relatively objective and reliable model for risk assessment. Therefore, simulation of the interaction between geological and topographic information and tower bases has become indispensable for analyzing the wind-induced response of transmission-line towers.

Many scholars have now conducted research on control methods for problems such as the deterioration of structural foundation durability. Reference [12] has effectively improved the stability of a structure under the impact of wind and other loads by changing the inclination angle of the inclined piles. Reference [13] finds that horizontal stiffness increases with an increase in inclined pile inclination angle. Although the method of controlling the inclined pile inclination angle has a certain effect of controlling the stability of the tower base, it is not effective enough to be used as a control method alone for improving foundation stress and other aspects. Reference [14] uses anchors to apply external prestress at foundation cracks to limit the width of foundation cracks in wind turbines and to improve the stiffness of the cross-section. Reference [15] has improved phenomena such as foundation cracking and stress concentration by welding cheese-head nails around foundation cracking to strengthen the connection between wind turbine steel rings and foundation concrete. Although foundation cracking control by increasing foundation prestress has a good effect, for extra-high-voltage transmission towers, strengthening prestressing alone is not a good solution for problems such as durability degradation. A complex high-performance organic mineral admixture for high-voltage transmission-line towers was developed in reference [16] as a means to increase compressive strength and tensile strength against bending, frost, water, and corrosion, and to reduce crack expansion width. Reference [17] uses rigid fiber-reinforced concrete to strengthen a turbine tower foundation, which enhances the service life of the foundation and better solves problems such as decreasing durability of the structural foundation. A series of concrete reinforcement measures have been proposed in reference [18] according to the degree of deterioration of different transmission-line tower bases. Therefore, when the durability of the structural foundation declines, not only are inclined piles needed, but they also need to be combined with the application of prestressing and concrete reinforcement for control, which can more effectively solve the safety problems caused by the foundation deflection phenomenon.

The paper proposes a technology for transmission-line tower foundations that uses inclined piles and prestressed tie beams to control displacement. It considers local climate, geology, and site conditions to address wind-driven responses and foundation limitations. Relying on finite element software, concrete reinforcement is simulated by a foundation tie beam, and the pile height, inclined pile angle, and prestressed foundation tie beam are taken as the means, respectively. The displacement-control effect and ability to improve stress concentration of the transmission tower are compared and analyzed under various working conditions.

2. Transmission Tower Structure Characteristics

2.1. Characteristics

The ±800 kV Tianzhong line starts from Hami South Tianshan Converter Station in Hami City in the west, and runs to Zhengzhou Converter Station in Zhongmou County, Henan Province in the east, with a total path length of about 2208.2 km. Some 165.63 km is within Xinjiang, with a total of 327 towers. Tower 292 (construction number Z303) is located near Hongliuhe station, which belongs to the Gobi region, where the natural environment is relatively harsh; there is a long freezing period and extensive distribution of saline soil. Foundation cracks in Tower 292 are shown in Figure 1. Under the coupling effect of various durability damage factors such as the long-term freeze–thaw cycle, saline soil chloride ion erosion, and strong wind load, the tower foundation has a large displacement, and the surrounding soil compression deformation is not recoverable, forming a gap along the foundation around the soil distribution. A crack on the top surface of the foundation is a surface crack, due to the plastic shrinkage of concrete; the crack is small, which has less influence on the bearing capacity and safety of the structure. The foundation side cracks are structural cracks. The tower is in the Gobi area, where the wind speed is high all year round, and transient changes in wind speed and direction in time and space show strong random characteristics. At this time, the foundation will bear the upper structure due to random wind load caused by the loading–unloading–reloading–unloading cycle loading process. In the upper transmission-line tower under wind fatigue load, pulsating wind fatigue load transmitted to the base still maintains pulsating characteristics, and there is a pulsating wind load through the upper structure as well as the soil layer after diffusion propagation. After diffusion of the pulsating wind load through the upper structure and the soil layer, due to the large displacement of the foundation under the wind fatigue load, the deformation of the surrounding soil after compression is not recoverable, and thus a gap forms along the soil around the foundation. As shown in Figure 1b, there are two cracks in the foundation of the tower leg; the width of the cracks is about 2 cm, the length of the cracks in the section of foundation leakage is about 0.9 m, and the leakage of the foundation is about 0.7 m. The cracks have a high impact on the safety of the transmission-line tower in its latter long-term operational state. As the overall height of the tower is about 71.66 m, the total weight of the single tower is nearly 50 t; the main material of the tower leg is arranged at 80° with the ground, and the tower foundation has a large horizontal force and foundation displacement, which has seriously threatened the safe operation of the transmission tower.

2.2. Wind-Induced Vibration Analysis

2.2.1. Field Test

According to 2.1, it is known that under the action of wind load, the lateral cracks of a tower base will be deepened and the durability of transmission tower will be decreased. Therefore, this subsection will test and analyze the wind-induced vibration of Tower 292 based on the acceleration of the tower base, displacement of the tower base, and strain of the tower base under a range of wind speeds over time.

To accurately test the structure of Tower 292, the dynamic displacement, dynamic strain, and acceleration time curve of the tower structure were tested using environmental random excitation. Four sensors were placed at 8 m from the ground to measure the velocity, acceleration, and displacement time curves, and four dynamic strain sensors were placed at 1 m from the ground, while four dynamic displacement sensors at the tower base were used to monitor the real-time displacement data of the tower base. The specific arrangement of the measurement points is shown in Figure 2. Among them, A and D are the two tower legs that confirm the west and south downward to facilitate the attribution of subsequent experimental data. The main equipment used was the INV9580A bridge dynamic test system—an intelligent wireless tester developed by Beijing Oriental Vibration and Noise Technology Research Institute, and the analysis software is the supporting coinv DASP V11 analysis system.

2.2.2. Test Results

The location of the measurement points was determined according to the site’s environmental conditions and the testing program. Aerial staff in a crane assisted with installing the test instrument in the corresponding location of the measurement point. To ensure its solidity, over a certain period of time the instrument automatically recorded the corresponding data, which were saved to a computer. After the time requirement was reached, the instrument was removed by the ascent operator. Figure 3 shows the results of the upper dynamic displacement test at column D and the lower test results at columns A and D under wind-induced vibration. The upper dynamic displacement measurement points correspond to the acceleration time-course curve in Figure 3a and velocity time-course curve in Figure 3b; the dynamic strain measurement points at the bottom of the tower correspond to the strain time-course curve in Figure 3d, and the base dynamic displacement measurement points correspond to the displacement time-course curve in Figure 3c,d.

2.3. Foundation Displacement Analysis

According to Figure 3a–c, it can be seen that the dynamic displacement measurement point at the upper part of column D of transmission Tower 292 in the Tianzhong line has an acceleration response of 425 mm/s² at a speed of 7 mm/s, and the horizontal displacement value reaches 2.2 mm. According to the local meteorological data survey, the average wind speed in the area where Tower 292 is located is 30.2 m/s at maximum, and the maximum wind speed is 32.2 m/s, while the average wind speed during the field test was 9.5 m/s, which was only 0.3 times more than the regional average wind speed. Therefore, in the long-term operation of the transmission-line tower, it is very easy for an effect of greater tower foundation displacement to occur under the wind load.

From the strain and displacement test data at the tower base at the site in Figure 3d, it can be seen that the base of Tower 292 already possesses a certain displacement under a wind-induced response, and there is already a large safety hazard under the influence of multiple cracks and the harsh environmental conditions at the tower base. In order to guarantee the safe operation of the tower line, it is necessary to conduct a study of the horizontal displacement-control measures of the foundation in line with the current situation of the area.

3. Prevention and Treatment Methods

The tower façade is divided into three parts: tower leg, tower body, and tower head. The bottom leg structure can be approximated as a four-bearing inclined column steel structure, which transmits the static load of the upper structure (tower body self-weight, guide/ground line self-weight, and conductor ice load, etc.). Therefore, this paper mainly focuses on the study of the foundation displacement-control method under the action of a static load, using the extra-high-voltage transmission-line tower as an example.

3.1. Model Building

According to the environment where Tower 292 is located, it is known that under special circumstances such as rainwater washing and rock weathering, the pile body of the transmission-line tower may appear exposed; therefore, it is necessary to use the exposed height of the straight pile as a control group to study the degree of influence of the exposed height of the straight pile on foundation displacement. Three methods are proposed for foundation displacement control, and the change in foundation displacement of the transmission-line tower under a static load is analyzed by finite element simulation. A prestressed foundation tie beam is set at the tower base and tower leg, a Strand1570 steel strand is established, and prestress is applied to control the horizontal displacement of the foundation. Taking No. 292 transmission-line tower as an example, the standard value of the vertical load simulation for the main material of the tower leg is about 1100 kN, and the standard value of the horizontal load is about 140 kN; that is, the ratio of vertical load to horizontal load is about 7.86:1, and the foundation of the tower is a straight-column-type hollow foundation. The transfer path of the overall structure of the transmission-line tower is clear. First of all, the structure of the tower body self-weight, the guide/ground line self-weight, and the conductor ice load are along the tower body to the structure of the tower leg, through the tower leg inclined column structure, transferring to the pile foundation and finally to the independent foundation mainly bearing the upper structure load. The span of the main material of the tower leg along the X and Y directions is 15.6 m, and the angle between the main material and the ground is about 80°. The horizontal force in the X and Y directions increases the outward deformation of the foundation-bearing platform; the foundation displacement-control method is shown in

Table 1. Foundation displacement-control method.

Title 1	Title 2
C0 (control group)	7.0 m straight pile + exposed pile of 0.5 m (design methodology)
C1	7.0 m straight pile + exposed height of pile
C2	7.0 m straight pile + inclined pile tilt angle
C3	7.0 m straight pile + foundation beam + prestress

.

The FEM software Midas/GEN was used to build a model of the EHV transmission-line tower. In order to ensure that the FEM model better fits the actual construction situation on site, the specific modeling process is as follows.

In terms of unit type selection, L-shaped angles are mainly used in the main body of the steel structure, and the cross-sectional form is determined by the custom section method; the cross-sectional orientation of the beam and column units is defined by a Beta angle; the steel strength grades are Q235 and Q345; and C30 concrete is used for the foundation bearing. The beam unit is used for the main steel structure, and the solid unit is used for the concrete pile body. To simplify the calculation, ordinary reinforcement inside the foundation pile base was ignored when the model was created.

In the boundary condition simulation, the upper steel nodes of the tower and the tower and the pile foundation are connected in the form of common nodes. The geological information of the tower is shown in

Table 2. Engineering geology information.

Tower Leg Number	Geotechnical Description			Geotechnical Main Indicators
	Geotechnical Name	Degree of Rock Weathering	Layer Bottom Depth (m)	$\mathbf{Severe}\mathit{\gamma }$ (kN/m2)	$\mathbf{Angle}\mathbf{of}\mathbf{Internal}\mathbf{Friction}{\mathit{\varphi }}_{\mathit{k}}\left(\text{°}\right)$	$\mathbf{Characteristic}\mathbf{Value}\mathbf{of}\mathbf{Subsoil}\mathbf{Bearing}\mathbf{Capacity}{\mathit{f}}_{\mathit{a}\mathit{k}}\left(\mathbf{kPa}\right)$	$\mathbf{Critical}\mathbf{Shearing}\mathbf{Strength}{\mathit{\tau }}_{\mathit{s}}\left(\mathbf{kPa}\right)$
Leg A	Gravelly sand	/	0.6	19	30	180	/
	Granite	Strong weathering	4.0	23	40	500	25
		Weathering	7.0	25	50	1000	50
		Breeze-up	8.0	26	60	3000	85
Leg B	Gravelly sand	/	0.8	19	30	180	/
	Granite	Strong weathering	3.0	23	40	500	25
		Weathering	7.0	25	50	1000	50
		Breeze-up	8.0	26	60	3000	85
Leg C	Granite	Strong weathering	4.0	23	40	500	25
		Weathering	7.0	25	50	1000	50
		Breeze-up	8.0	26	60	3000	85
Leg D	Granite	Strong weathering	4.0	23	40	500	25
		Weathering	7.0	25	50	1000	50
		Breeze-up	8.0	26	60	3000	85

Note: During the survey, no groundwater was seen within the survey area.

. Combined with the ground survey report, site conditions, and “Technical Specification for Building Pile Foundation”, the “m method” was used to calculate and apply the elastic support of the pile node to simulate and analyze the effect of the pile soil action of the transmission-line tower. The “m method” assumes that:

(1)

The soil is an elastic medium, so the horizontal resistance coefficient C0 increases linearly with the depth of the pile and is zero at the surface.

(2)

The contact stress (normal elastic resistance) at any point on the pile base is proportional to its normal deformation.

(3)

The adhesion between the pile base and the soil and the resistance of friction to the horizontal force are ignored to simulate the site geological situation [19].

In terms of cell partitioning, this was performed on the constructed model to generate a refined finite element model. According to the cell type, calculation accuracy, and different materials and thickness, the solid cell mesh size was automatically meshed in the form of a 1.0 m quadrilateral + triangle, and the beam cell was automatically meshed in a 1.0 m size.

In terms of static load, the static load in the model used the load group activation/passivation function to simulate the actual load situation, considering the joint action of the tower, guide/ground, and insulator strings and other equipment, with a self-weight factor of 1.2 and a concrete capacity weight of 26 kN/m³.

In terms of transmission-line tower ground/conductor loading, in order to simulate the real working conditions as far as possible, the model also took into account the influence of the tower and ground/conductor self-weight, using the load group activation/passivation function to simulate the actual load situation, where the conductor weight was 3.1 N/m and the ground weight was 1.0 N/m. With a transmission-line tower stall distance of about 500 m, arc drape of about 30 m, and the wire ends’ hanging point approximately equal to the line without height difference, the de-hanging curve equation can be approximated by Equation (1).

$$f=\frac{g{l}^2}{8{\sigma }_{}},$$

(1)

where $f$ is the maximum arc pitch; $l$ is the file distance; $g$ is the acceleration of gravity; and $\sigma$ is the initial stress.

After Equation (2) curve integration, the total length of the conductor per file distance was calculated to be about 561.2 m.

$$L={{\displaystyle \int }}_{-250}^{250}\sqrt{\left(1+f^2\right)}dl,$$

(2)

With the ground at the same time and a ground/conductor safety factor of 2.5, the conductor gravity loads are 26.1 kN and 4.4 kN, respectively. Taking into account that the tower is in the 10 mm ice area, the conductor-equivalent diameter is about 42 mm and the ice density is 0.9 kg/m [20]. The ice load of each ground/wire is 38.1 kN. In terms of prestressing load, a prestressed foundation tie beam is set at the foundation and tower leg to establish steel strand, and prestressing is applied to control the horizontal displacement of the foundation. The Strand1570 steel strand was used from the material library. The finite element model is shown in Figure 4.

3.2. Testing Location

According to the structural characteristics of the transmission-line tower, when the tower base undergoes horizontal displacement, the main material of the tower leg will produce a large stress change, so five displacement simulation analysis points were selected along the transmission-line tower foundation, and five strain simulation analysis points were arranged at 2.0 m from the top of the foundation pile; a simulation analysis point layout diagram is shown in Figure 5 (A–D) are denoted as the four tower bases of the transmission tower.

As the transfer characteristics of the transmission tower forces are clear, the transmission-line tower construction phase is initially divided into eight analysis conditions; the specific analysis conditions are shown in

Table 3. Transmission-line tower analysis working conditions.

Analysis Condition	Structure Group (m)	Load Group
Condition 1	main frame under 10.0	self-weight, wind load 1
Condition 2	main frame under 21.1	wind load 2
Condition 3	main frame under 32.3	wind load 3
Condition 4	main frame under 42.0	wind load 4
Condition 5	main frame under 51.0	wind load 5
Condition 6	main frame under 57.0	wind load 6
Condition 7	main frame under 66.0	wind load 7
Condition 8	main frame under 71.55	conductor load, wind load, prestressing

.

4. Analysis of Wind-Load Effects on Transmission-Line Towers

Due to the high wind speed in most areas of Xinjiang all year round, the influence of wind load is large, and the wind load is transferred to the foundation after the inclined column falls to the ground with a large horizontal-component force; therefore, it is necessary to use a displacement-control method to control the horizontal displacement of the transmission-line tower inclined column structure foundation under the joint action of line self-weight under ice and wind loads.

4.1. Equivalent Static Wind-Load Simulation

The transfer path of the overall structural forces of the transmission tower is clear. First the structure of the tower self-weight, the guide/ground line self-weight, and the conductor ice load are along the tower body to the structure tower leg, through the tower leg inclined column structure, transferring to the pile foundation and finally to the independent foundation mainly bearing the upper structure load, so the transmission tower can be applied to the segmental load [21]. According to the relevant specifications, the equivalent static load acting on the windward side of the transmission-line tower is calculated according to the following equation:

$$W_k=W_0\cdot {\mu }_z\cdot {\mu }_s\cdot {\beta }_z\cdot B_2\cdot A_s,$$

(3)

where W_k is the tower wind-load standard value (kN); W₀ is the benchmark wind-pressure standard value (kN/m²), taken as 0.6 kN/m², according to the “hydro-meteorological survey report”; ${\mu }_z$ is the height z at the wind-pressure height-change coefficient; ${\mu }_s$ is the wind-load body coefficient; ${\beta }_z$ is the tower wind-load adjustment coefficient; B₂ is the tower body after the ice component wind-load increase coefficient, taken as 1.2 for the tower in the 10 mm ice area; A_S is the component of the calculated value of the wind-pressure-bearing projection area (m²).

The wind-load body shape factor can be set to qualify structures with different height-to-width ratios, and thus cross-sectional shapes.

The wind-pressure height-change coefficient is shown in

Table 4. Wind-pressure height-change coefficient.

Simulation Point Height (m)	5.00	15.55	26.70	37.15	46.50	54.00	61.5	68.78
${\mu }_z$	1.17	1.532	1.744	1.886	1.991	2.066	2.132	2.190

.

The transmission-line tower wind-carrier-type coefficient should be based on the value of the tower blocking wind coefficient; that is, the tower blocking wind coefficient, by calculation, is less than 0.1. For a single-angle steel frame body, regardless of the wind direction, a conservative value for the body coefficient is 2.9 [22]. The wind-load adjustment factor of the tower and the background component factor R of the pulsating wind load are calculated according to Equations (4) and (5), respectively:

$${\beta }_z=1+2g{I}_{10}{B}_z\sqrt{1+R^2},$$

(4)

$$R=\sqrt{\frac{\pi }{6{\zeta }_1}\cdot \frac{x_1^2}{{\left(1+x_1^2\right)}^{4/3}}},$$

(5)

where $g$ is the peak factor, taken to be 2.5; $I_{10}$ is the nominal turbulence intensity at 10 m height and class-A ground roughness, taken to be 0.12; R is the background component factor of the pulsating wind load; B_z is the background component factor of the pulsating wind load; ${\zeta }_1$ is the structural damping ratio, taken to be 0.01.

The first-order self-oscillation frequency of the structure $f_1=1/T_1$, according to the Code for Structural Loads of Buildings; the empirical formula for the first-order self-oscillation frequency of the structure is $T_1=0.013$ H, so that $f_1=0.175$ Hz; that is, $x_1=36.8, R=2.174$.

The background component factor of the pulsating wind load shall be calculated according to the following equation:

$$B_z=k{H}^{a_1}{\rho }_x{\rho }_z\frac{{\phi }_1\left(z\right)}{{\mu }_z},$$

(6)

where ${\phi }_1\left(z\right)$ is the first-order vibration coefficient of the structure; H is the total height of the structure (m); ${\rho }_x$ is the horizontal-direction correlation coefficient of pulsating wind load; ${\rho }_z$ is the vertical-direction correlation coefficient of pulsating wind load; k and $a_1$ are coefficients obtained by checking the table, which are 1.276 and 0.186, respectively.

The values of the first-order vibration coefficients of the structure are shown in

Table 5. First-order vibration coefficients of the structure.

Simulation Point Height (m)	5.00	15.55	26.70	37.15	46.50	54.00	61.5	68.78
${\phi }_1\left(z\right)$	0.020	0.081	0.219	0.388	0.559	0.760	0.856	1.000

.

Pulsating wind-load horizontal-direction correlation coefficients ${\rho }_x$ and ${\rho }_z$ should be calculated according to Equations (7) and (8), respectively:

$${\rho }_x=\frac{10\sqrt{B+50e^{-B/50}-50}}{H},$$

(7)

$${\rho }_z=\frac{10\sqrt{H+60e^{-B/60}-60}}{H},$$

(8)

where B is the width of the windward side of the structure, which is taken to be 13.85 m, so that ${\rho }_x$= 0.956; H is the total height of the structure, so that ${\rho }_z$= 0.762.

Therefore, the values are taken as in

Table 6. Wind-load adjustment factor.

Height above Ground z (m)	5.00	15.55	26.70	37.15	46.50	54.00	61.5	68.78
$B_z$	0.035	0.108	0.256	0.420	0.573	0.750	0.819	0.932
${\beta }_z$	1.050	1.155	1.368	1.603	1.822	2.078	2.176	2.338

.

In summary, the basic parameters of the wind-load loading of the tower calculated according to the following equation are shown in

Table 7. Tower wind-load loading basic parameters.

Simulation Point Height (m)	5.00	15.55	26.70	37.15	46.50	54.00	61.5	68.78
${\omega }_k$ (kN/m2)	0.075	0.332	1.063	2.207	3.616	5.605	6.612	8.298

.

The tower static wind load is applied in the form of an instantaneous nodal load on the tower segmental bars, and the combined force of each tower segment is calculated according to the following formula.

$$W_k={\omega }_k{A}_s,$$

(9)

where A_S is the windward area of each segmental bar of the tower.

In summary, Figure 6 shows the side view of the segmental equivalent static wind-load loading of the 292 transmission-line tower, which visualizes the loading of the maximum design-equivalent static wind load of the tower; the specific loading of the wind load of the tower is shown in

Table 8. Specific wind load on the tower.

Height Range (m)	5.00	15.55	26.70	37.15	46.50	54.00	61.5	68.78
${\omega }_k$ (kN/m2)	0.075	0.332	1.063	2.207	3.616	5.605	6.612	8.298
$A_s$ (m2)	15.76	18.12	12.69	9.34	10.73	14.06	6.74	22.71
Number of nodes (number)	22	33	31	27	27	25	25	97
Node load (kN)	0.054	0.182	0.435	0.763	1.437	3.152	1.782	2.203

.

4.2. Analysis of the Influence of the Exposed Height Factor of Straight Piles

As can be seen from Table 1, the idea for the base displacement control of model C1 is to control the base displacement by adjusting the exposed height of straight piles. Variation in the horizontal displacement of the model C1/C0 base and the maximum stress at the overall structure of the tower leg are compared, and the optimized ratio of the straight pile exposed height on foundation horizontal displacement under a wind load are analyzed. For model C1, four groups of models with different heights (C1-1, C1-2, C1-3, and C1-4) were set up for control, for which parameter adjustment of the comparison model is shown in

Table 9. Model C1 parameter adjustment.

Model Number	C0	C1-1	C1-2	C1-3	C1-4
Exposed height of straight pile (m)	0.5	0	0.25	0.75	1.0
Maximum positive stress (MPa)	187.50	186.98	187.23	187.78	188.07
Maximum negative stress (MPa)	−259.20	−258.70	−258.94	−259.47	−259.90

.

From the analysis in Table 9, it can be seen that the maximum positive stress of the model C1 tower leg inclined column steel structure is about 187.0 MPa, and the maximum negative stress is about −259.0 MPa; the maximum stresses are concentrated in the main material of the tower leg. Under the same construction conditions, even if the exposed height of the straight pile reaches 1 m, the stress change of the inclined column steel structure will not be greater than 1.0 MPa, so the degree of stress change is small. The stress in the critical section of the structural inclined column structure increases by about 0.25 MPa with each 0.25 m increase in exposed height of the straight pile, which shows that the use of the exposed height of the straight pile has a small effect on the stress in the inclined column steel structure under the wind load.

Under the eight working conditions shown in Table 3, the ANSYS software was used to analyze the ability of different schemes in C1 to affect tower base displacement, where W2, W3, W4, and W5 are the four displacement measurement points as shown in Figure 5. From the analysis of Figure 7, under working condition 8, it can be seen that with each 0.25 m increase in exposed height of the straight pile, the foundation displacement increases by about 0.5 mm, and the changes in the foundation displacement of the model C1/C0 structure are −20.0%, −10.7%, 11.1%, and 23.4%, respectively, compared with model C0, which shows that the excessive exposed height of the straight pile is not conducive to the control of the horizontal displacement of the structural foundation under wind load.

4.3. Analysis of the Impact of Inclined Pile Foundation

The idea for the base displacement control of model C2 is to carry out base displacement control by adjusting the inclination angle of the 7.0 m inclined pile, comparing the base horizontal displacement of model C2/C0 and the stress change of the key section of the inclined column structure, and analyzing the optimized ratio of inclined piles on the horizontal displacement of the foundation and the stress variation at the tower leg structure. The comparison model parameter adjustment is shown in

Table 10. Model C2 parameter adjustment.

Model Number	C0	C2-1	C2-2	C2-3	C2-4
Inclined pile tilt angle (°)	0	3	6	9	12
Maximum positive stress (MPa)	187.50	186.34	185.33	184.35	183.52
Maximum negative stress (MPa)	−259.20	−258.03	−257.03	−256.06	−255.15

.

From the analysis of Table 10, it can be seen that the maximum positive stress of the model C2 tower leg inclined column steel structure is about 187.0 MPa on average, and the maximum negative stress is about −259.0 MPa on average; under the same construction conditions, for every 3° increase in tilt angle, the stress change of the inclined column steel structure is not more than 1.0 MPa, and the degree of stress change is small; due to the small influence of inclined pile foundation on the horizontal component of the foundation, with each 3° increase in the inclination angle of the model-C2 inclined column, the stress of the main material section decreases by about 1.0 MPa. This allows for the mitigation of fatigue problems at the base of transmission towers; although this method has a better effect than the straight pile exposure method, it still has less effect on the stress change of the tower leg inclined column structure.

From the analysis of Figure 8, and the ability to analyze the effect of different scenarios in ANSYS software C2 on the displacement of the tower base, it can be seen that the inclined pile foundation has a certain resistance effect on the structural uplift force and the upper horizontal component force. For working condition 8, with each 3° increase in pile tilt angle, the maximum reduction of the foundation horizontal displacement is about 2.3 mm; relative to model C0, the reduction of the foundation displacement of the model-C2 structure is 46.4%, 89.2%, 135.5%, and 186.1%, respectively. The foundation horizontal displacement decreases with an increase in the inclined pile. The foundation horizontal displacement decreases with an increase in inclination angle [23], so displacement control is more effective.

4.4. Analysis of the Impact of Prestressed Foundation Tie Beams

The idea for the base displacement control of model C3 is to apply prestress for displacement control by adding a concrete base tie beam in the tower base, comparing the horizontal displacement of the model C3/C0 base and the stress change of the key section of the inclined column structure, and to analyze the optimized ratio of the inclined pile base on the horizontal displacement of base and stress change of the tower structure. The comparison model parameters are adjusted as shown in

Table 11. Model C3 parameter adjustment.

Model Number	B0	B3-1	B3-2	B3-3	B3-4	B3-5	B3-6
Section size (mm)	—	600 × 200	600 × 400	800 × 400	800 × 200	1000 × 200	600 × 200
Prestress value (kN)	—	0	0	0	0	0	100
Maximum positive stress (MPa)	187.50	182.28	182.02	181.99	185.27	182.14	185.27
Maximum negative stress (MPa)	−259.20	−260.27	−260.02	−259.98	−257.10	−260.12	−258.91

.

From the analysis in Table 11, it can be seen that the stresses in the tower leg inclined column steel structure were changed by changing the section width and height of the foundation tie beam in models C3-1 and C3-2 and models C3-1, C3-4, and C3-5, respectively; compared with model C0, the maximum stress in the tower leg inclined column steel structure changed by no more than 5.0 MPa, and the stresses decreased with an increase in the section size of the foundation tie beam, except for C3-3 and C3-5, where the change was smaller; the stresses in the foundation tie beam and the prestressed foundation tie beam in models C3-1, C3-2, C3-3, and C3-5 decreased by about 3.0% compared with model C0. The stresses in the foundation tie beam and prestressed foundation tie beam in models C3-1 to C3-6 reduced by about 3.0% compared with model C0, and the stresses in the inclined column structure were better controlled by the straight pile exposed height and inclined pile inclination angle method, so fatigue problems at the base of transmission towers can be better mitigated.

From the analysis of Figure 9, and the ability of different schemes in the ANSYS software to analyze the effect on the displacement of the tower base in C3, it can be seen that under the same construction conditions, the maximum reduction of the base displacement of models C3-1 to C3-5 and model C0 is about 30%, and the maximum reduction of the horizontal displacement of the base of W4 is about 100%, which shows that the effect of the base tie beam on the control of the horizontal displacement of the base is more significant; models C3-1 and C3-2 and models C3-1, C3-4, and C3-5 adjust the base tie beam width and height, respectively. The maximum increase of the horizontal displacement of the foundation is about 20% with each increase of 0.2 m in the cross-sectional size of the foundation tie beam; under the action of prestressing, the horizontal displacement of the foundation of the inclined column structure of models C3-1 and C3-6 decreases about 1.6 mm, and changes from 4.1 mm to 2.5 mm in the forward direction to the outside, which shows that the control of the prestressing of the foundation tie beam has a better effect on the control of horizontal displacement.

Combined with the effect of considering three kinds of displacement control under the joint action of tower line self-weight, ice-cover load, and wind load, this paper proposes a joint displacement-control scheme based on inclined pile tilt control and pre-stressed foundation tied beam control. According to the above theoretical analysis, after optimizing the key parameters such as inclined pile tilt angle, foundation tie beam cross-sectional size, and prestressing, the horizontal displacement of the foundation can reach more than 50% for extra-high-voltage transmission towers, and can reduce the structural stress in part of the tower legs, which effectively alleviates the status of the horizontal displacement of the tower base of transmission towers and the fatigue problem of transmission tower bases.

5. Conclusions

Through a wind-induced vibration test and displacement-control theory analysis of Tower 292 of the ±800 kV Tianzhong line, a joint displacement-control technology of foundation-inclined piles and prestressed foundation tie beams is researched. It has good application prospects and promotion value for tower displacement caused by the harsh natural environment in Xinjiang, and greatly reduces the problem of durability degradation of the extra-high-voltage tower of the Tianzhong line. The main conclusions are as follows.

(1)

Combining the site condition factors with the wind-induced vibration load test on the site of Tower 292 of the Tianzhong line, the tower was tested for foundation and safety assessment; at only 0.3 times the average wind speed in the region, the horizontal displacement value had reached 2.2 mm, under the influence of multiple cracks in the tower base and harsh environmental conditions, so there was already a large safety hazard.

(2)

For the Tianzhong line Tower 292, detailed modeling was carried out in terms of unit type selection, boundary condition simulation, static load, transmission-line tower ground/conductor load calculation, ground/conductor ice-load calculation, and prestress load, taking into account not only the actual structure type of the tower, but also the local ice cover, and using the “m” method to equate the specific geological conditions at the base of the tower, so that the model could fully represent the actual structural characteristics of the tower.

(3)

Displacement-control analysis was carried out by three different displacement-control methods, namely: controlling the exposed height of the pile, inclined pile tilt angle, and prestressed foundation tie beam, respectively. In working condition 8, with each 3° increase of pile inclination angle, the maximum reduction of foundation horizontal displacement is about 2.3 mm; and under the prestressing effect, the foundation horizontal displacement of models C3-1 and C3-6 inclined column structures is reduced by about 1.6 mm. To derive a joint displacement-control technique of foundation-inclined piles and prestressed foundation tie beams under the action of a tower’s own load and wind-induced load can significantly improve the displacement status of tower bases and the fatigue problems of transmission tower bases.