# Shaking Table Array Tests of an Ultra-High-Voltage Cup-Type Transmission Tower-Line System

Authors: Fei Wang; Ke Du; Jingjiang Sun; Fuyun Huang; Zhenghui Xiong
Journal: Shock and Vibration
 (2019)

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## Abstract

Ultra-high-voltage (UHV) cup-type transmission towers supported with long-span transmission lines are unavoidably subjected to the coupling action between the towers and the transmission lines. Therefore, investigating how tower-line coupling affects UHV cup-type transmission towers is important. In this study, three shaking table array tests of an UHV cup-type transmission tower-line system were carried out to investigate the dynamic characteristics of the coupling action between the towers and transmission lines based on the following four comparative models: a single-tower model, a single-tower model with suspended lumped masses, a three-tower-two-line model, and a five-tower-four-line model. The test results demonstrated that the tower-line coupling interaction had a significant effect on the dynamic characteristics and seismic responses, as the suspended conductor line and the suspended lumped mass decreased the frequency of the transmission tower. Under longitudinal ground motion, the model with the suspended lumped mass had the lowest peak acceleration response and the largest peak displacement response. Under the same ground motion, the four models had similar peak strains in the longitudinal direction. Under transverse-the-line ground motion, the model with the suspended lumped mass had the lowest peak acceleration response and the smallest peak responses for displacement and strain in the transverse direction; therefore, this model is inappropriate for the simulation and seismic evaluation of transmission tower-line systems.


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## Body

## 1. Introduction

Electricity transmission systems consisting of transmission towers and transmission lines have been widely recognized as lifeline systems; in the system, the transmission tower is a type of lattice tower that supports the overhead transmission lines. Compared with other power equipment, the ultrahigh voltage (UHV) transmission tower structures are characterized by great heights, long spans, and complex tower-line coupling effects. However, this type of structure is generally considered to be less impacted by seismic action, and relevant studies are rare [1–4]. The mechanical performance of this type of structure under disastrous dynamic wind and ice loads is the main focus of the research performed worldwide [5–9].However, earthquakes have frequently occurred in recent years worldwide, and the power transmission systems have been severely damaged in earthquake-ridden regions [10]. The earthquake damage investigations indicate that transmission line damage is severe [11]. As revealed by the investigations of the damage to transmission lines caused by several typical major earthquakes, seismic damage mainly manifests as tower tilting, insulator breakage, and foundation settling and dislocation. For example, in the 1994 Northridge earthquake in the United States, a few high-voltage transmission towers were damaged; the level of damage to the transmission towers was related to the intensity of the ground motion and the seismic design. In the 1995 Hanshin earthquake in Japan, 23 overhead transmission lines were damaged and 11 steel transmission towers collapsed. During the 1999 Chi-Chi earthquake, transmission lines were severely damaged, including 28 345-kilovolt UHV transmission lines, amounting to a damage rate close to 30%. In the 2008 Wenchuan earthquake, more than 20 over-10-kilovolt transmission towers collapsed, and approximately 16 towers were locally damaged, resulting in severe damage[12]. During the 2013 Lushan earthquake in Sichuan, 265 over-10-kilovolt transmission towers with distribution lines out-of-service and 224 over-35-kilovolt lines were severely damaged, reaching a damage rate of 50% and resulting in huge losses [13]. Considering the harsh and complex geological conditions of the areas along UHV transmission lines, if one tower is damaged or collapses under a strong earthquake, the operation of the whole transmission line will be affected. Therefore, the mechanical mechanism and failure mode of transmission tower structures under strong earthquakes and the corresponding seismic theory and methods have garnered increasing amounts of attention [14, 15].Shaking table tests can reproduce the actual stress state of a structure under an earthquake well and can be used to study the structural dynamic performance, structural response, and failure mode under seismic action. However, the UHV transmission tower-line system is characterized by tall towers (the UHV transmission towers built in China generally exceed 100 m in height) and extremely large spans (e.g., longer than 1000 m), so it is difficult to meet the experimental requirements with single shaking table test equipment. Therefore, shaking table tests of UHV transmission tower-line systems have not often been carried out as conventional civil structures. The earliest known shaking table tests of high-voltage transmission towers were conducted in the 1980s. Kotsubo et al. [16] conducted a shaking table test of three transmission towers in south eastern Kyushu, Japan. The researchers considered the influence of the conductor lines and the ground lines on the adjacent towers, obtained the dynamic characteristics of the transmission towers under earthquakes, and proposed a corresponding seismic calculation method for the transmission towers. Filiatrault [17] conducted a shaking table test of five different electrical substation equipment components, considered the interactions between the conductor lines and insulators with different degrees of relaxation under earthquakes, and concluded that the three flexible conductor lines with different degrees of relaxation had little impact on the insulators under earthquakes. Kempner et al. [18] conducted dynamic tests and theoretical analysis of the modeling of guyed towers. Tian et al. [19] considered the length limitation of the shaking table for the extremely large span of a high-voltage transmission tower-line system and noted that the tower-to-line scale factor for a high-voltage transmission tower-line system is difficult to maintain. Based on numerical analysis, those of the conductor line and ground line were corrected with the similitude ratio of the transmission tower remaining constant. Shi et al. [20] conducted a shaking table test of a simplified long-span transmission tower-line coupling system using steel rods with a diameter of 10 mm to simulate the transmission tower and a steel chain to simulate the conductor line. Three steel rods were connected by two layers of steel chains to form a transmission tower-line coupling system model. This test verified the accuracy of the proposed theoretical calculation method for the transmission line-line coupling system and reflected the dynamic characteristics of a high-voltage transmission tower-line system. However, the experimental model was overly simplified, and the chains that were used to simulate the conductor lines were relaxed and failed to truly reflect the mechanical performance of the tower structure and conductor line. Considering the deficiencies of the shaking table tests by Bai et al., [21, 22] proposed a new model design method for shaking table tests for a UHV transmission tower-line coupling system with double circuits on the same tower and geometric nonlinearity and conducted a shaking table test of a UHV grid transmission tower-line system. Aiming at a coupling system consisting of two different structural forms, i.e., a highly geometrically nonlinear conductor line and ground line and an elastic transmission tower structure, a design method for a separate model with dynamic parameters was proposed in the experimental scheme to address the problem that a tower-line system with a uniform scale cannot meet the length limitation of a shaking table. Xie et al. [23–25] conducted a number of shaking table tests of a high-voltage transmission angle-steel tower-line system and obtained the dynamic response characteristics of UHV angle steel transmission towers, the effects of the mass of the conductor line and ground line on the dynamic response of the tower structure, and the nonlinear vibration responses of the conductor line and ground line of a UHV transmission tower-line coupling system. An improved test method was proposed, and many important conclusions were drawn, which provided a reference for future shaking table tests of tower-line system models. However, most of the research results were obtained based on single shaking tables.The above studies show that the main problem in the shaking table tests of UHV transmission tower-line systems are the length limitations of single shaking tables; the use of an array of shaking tables to capture the interactions in transmission tower-line systems is scarce, making it difficult to consider the effect of tower-line coupling on the transmission towers’ responses. In this paper, an array of three shaking tables are used to test UHV cup-type transmission towers-line systems to investigate the interactions in transmission tower-line systems.


## 2. Model Design of the UHV Cup-Type Transmission Tower-Line System

A typical transmission tower prototype, the ZBC30102A-type self-supporting suspension tower in the Ximeng-Shandong UHV project, is chosen for the shaking table tests. The tower has a height of 73.8 m and a line span of 500 m; the prototype has three conductor lines, which are suspended in the middle and on both sides of the tower head through insulators. The conductor line and the ground line types are JL/G1A-630/45 and JLB20A-170, respectively. The transmission tower prototype is shown in Figure1.Figure 1
UHV cup-type steel tower ZBC30102A.


### 2.1. Design and Manufacture of the Tower

#### 2.1.1. Geometric Similitude Ratio and Material Selection

Considering the size limitations of the shaking tables, which have side lengths of 2.5 m, the geometric similitude ratio of the transmission tower is assumed to be 1 : 15.If all the angle steel members are scaled based on the geometric scale ratio, for the cross section, it is difficult to make the members because their thickness would only be 0.02 mm. Therefore, the transmission tower model uses four specifications of the angle steel (L30 × 3, L25 × 3, L20 × 3, and L10 × 1). The L30 angle steel is used for the main members and diagonal members of the tower leg and tower body, the L25 angle steel is used for the main members and diagonal members of the upper and lower cranks, and the L20 angle steel is used for main members and diagonal members of the ground line supports and crossarms. The auxiliary members of the model tower are made of L10 angle steel, and welded connections are used.


#### 2.1.2. Other Similitude Coefficients

The same material is chosen to use in the towers of the experimental model as is used in the prototype; therefore, the similitude ratio for the elastic modulusE is 1 : 1, and considering the noise and bearing capacity of the shaking tables, the similitude coefficient of acceleration is assumed to be 3 : 1. Then, other similitude coefficients are derived as the preliminary similarity relationships by using dimensional analysis and based on the Buckingham π theorem for the transmission tower model design (Table 1).Table 1
Similitude coefficients of the transmission tower model.
Physical quantity
Ratio of similitude (model/prototype)
Geometric
1 : 15
Elastic modulus
1 : 1
Acceleration
3 : 1
Displacement
1 : 15
Density
5 : 1
Stress
1 : 1
Mass
1 : 130
Time
1 : 6.7
Frequency
6.7 : 1The total mass of the prototype transmission tower is 83544.6 kg, and the total mass of the scaled transmission tower model is 642.65 kg.


#### 2.1.3. The Counterweight of the Model

Because the density similitude ratio is 5 : 1, the total mass of the scaled transmission tower model is 642.65 kg, the weight of the transmission tower without a counterweight is 128.53 kg, and the mass of the actual scaled transmission tower without a counterweight is 129 kg; to evenly apply the counterweight, the actual balancing weight is 555 kg. The actual total mass of the manufactured transmission tower model is 684 kg, and the actual density similitude ratio is 5.3 : 1. In the tests, two counterweights are processed, with masses of 2 kg and 0.25 kg. The counterweights are shown in Figure2.Figure 2
Counterweights of the test model tower. (a) Counterweight No. 1 (b) Counterweight No. 2.
(a)
(b)


### 2.2. Design and Manufacture of the Conductor Line and Ground Line

#### 2.2.1. Similitude Coefficients of the Conductor Line and Ground Line

The tests were carried out using the three-shaking-table array system at Fuzhou University. A 4.1 m × 4.1 m horizontal bidirectional shaking table is in the middle, and two 2.5 m × 2.5 m horizontal bidirectional shaking tables are on each side. The maximum distance between the middle table and the side tables is 10 m, and the horizontal span of the prototype model is 500 m. If the tests are based on a geometric scale ratio of 1 : 15, the dimensions of the shaking tables are unable to meet the requirements. Therefore, in this study, the similitude ratio of the dynamic characteristics and the similitude ratio of the inertial mass are assumed separately to design the similitude coefficients of the conductor lines and ground lines.(1) Design of the Frequency Similitude Ratio of the Conductor Line and Ground Line. When designing the model of the transmission tower-line coupling system, the similitude ratio of the transmission tower should be close to that of the conductor line and ground line.The fundamental natural frequency of the conductor line and ground line is as follows:(1)fC=g4π2s,where fC is the fundamental natural frequency of the conductor line and ground line, g is the gravity acceleration constant, and s is the sag in the conductor line and ground line.The relationship between the frequency similitude ratio and sag similitude ratio of the conductor line and ground line can be derived as follows:(2)Sf=1Ss,Ss=1Sf2.The transmission tower has a frequency similitude ratio of 6.7 : 1, and the conductor line and ground line have a frequency similitude ratio of 6.7 : 1 and a sag similitude ratio of 44.9 : 1.(2) Design of Mass Similitude Ratio of the Conductor Line and Ground Line. If the geometric similitude ratio of the conductor line and ground line is assumed to be the same as that of the transmission tower (1 : 15), since the span of the prototype tower is 500 m, the distance between the model towers would be 33.33 m, exceeding the maximum distance (10 m) between the middle table and the side table and, hence, not meeting the requirements. Therefore, a span similitude ratio of 1 : 55 is selected for the actual tests, and accordingly, the actual distance between the middle tower and the side tower is 9.09 m.The mass similitude ratio of the conductor line and ground line is the same as that of the transmission tower (1 : 130). The total mass of the prototype conductor line is 2.06 × 500 = 1030 kg, so the mass of the model conductor line is 7.92 kg. The total mass of the prototype ground line is 0.49 × 500 = 245 kg. The actual linear densities of the model conductor line and ground line are calculated to be 0.88 kg/m and 0.49 kg/m, respectively (Table2).Table 2
Similitude coefficients of the model conductor line and ground line.
Physical quantity
Ratio of similitude (model/prototype)
Actual horizontal span
1 : 55
Theoretical horizontal span
1 : 15
Acceleration
3 : 1
Mass of conductor line
1 : 130
Mass of ground line
1 : 130
Frequency of conductor line
6.7 : 1
Frequency of ground line
6.7 : 1
Elastic modulus of conductor line
1 : 1
Elastic modulus of ground line
1 : 1
Density of conductor line
1 : 2.34
Density of ground line
1 : 2.34


#### 2.2.2. Manufacture of Conductor Line and Ground Line

Steel wires with the diameters of 4 mm and 2 mm are used for the conductor line and ground line, respectively, in the experimental model. The physical components used for the conductor line and ground line are shown in Figure3.Figure 3
Physical components used for the conductor line and ground line. (a) Conductor line (4-mm steel wire). (b) Ground line (2-mm steel wire).
(a)
(b)According to the mass similitude ratio of the conductor line and ground line models, since the density of the steel wire is lower than that of the design model, counterweights are required. The counterweights of the conductor line and ground line are 8 kg and 4 kg, respectively. The counterweight blocks of the corresponding masses are placed uniformly along the conductor line and ground line.


### 2.3. Design and Manufacture of the Insulator

The V-shaped insulator is simulated by a galvanized plain round steel bar with a diameter of 8 mm and a length of 750 mm, and the I-shaped insulator is simulated by a rigid steel plate with a length of 600 mm and a width of 50 mm. The physical components used for the insulator models are shown in Figure4. To ensure that the insulator is hinged at two ends with the conductor line, a U-shaped steel wire lock is selected to simulate the suspension clamp in the prototype tower, as shown in Figure 5.Figure 4
Physical components used for the insulator models. (a) I-shaped insulator model. (b) V-shaped insulator model.
(a)
(b)Figure 5
Physical components used for the conductor line suspension clamp model.


### 2.4. Equivalent Tower

The equivalent tower is the side tower in the three-tower-two-line model and the five-tower-four-line model. The equivalent tower is used to simulate the boundary conditions without considering the similarity relationship with the tower model. In the tests, two equivalent towers are manufactured using welded L50 × 4, as shown in Figure6. The function of the equivalent tower is similar to that of a corner tower in practical engineering projects.Figure 6
Equivalent generation tower model.


### 2.5. Test Models

#### 2.5.1. Single-Tower Model

The test tower is anchored to the rigid base of the shaking table.


#### 2.5.2. Three-Tower-Two-Line Model

The three-tower-two-line model is a single-tower-two-line model that has a cup-type tower as the middle tower and equivalent towers as the side towers. All three towers are anchored to the rigid base of the shaking table. The conductor line and ground line are fixed on the equivalent towers. The boundary conditions are shown in Figure7, and the physical components used for the three-tower-two-line model are shown in Figure 8.Figure 7
Elevation of the three-tower-two-line model.Figure 8
Physical components used for the three-tower-two-line model.


#### 2.5.3. Five-Tower-Four-Line Model

The five-tower-four-line model is an improved version of the three-tower and two-line model. That is, two new tower models, which are the same as the middle tower, are placed at the locations of the original equivalent towers, which are relocated to the outer side of the new side main towers, along the line direction, and the boundary conditions are simulated through the connection between the equivalent towers and conductor lines, as shown in Figure9. The physical components used for the five-tower-four-line model are shown in Figure 10.Figure 9
Elevation of the five-tower-four-line model.Figure 10
Physical components used for the five-tower-four-line model.


## 2.1. Design and Manufacture of the Tower

### 2.1.1. Geometric Similitude Ratio and Material Selection

Considering the size limitations of the shaking tables, which have side lengths of 2.5 m, the geometric similitude ratio of the transmission tower is assumed to be 1 : 15.If all the angle steel members are scaled based on the geometric scale ratio, for the cross section, it is difficult to make the members because their thickness would only be 0.02 mm. Therefore, the transmission tower model uses four specifications of the angle steel (L30 × 3, L25 × 3, L20 × 3, and L10 × 1). The L30 angle steel is used for the main members and diagonal members of the tower leg and tower body, the L25 angle steel is used for the main members and diagonal members of the upper and lower cranks, and the L20 angle steel is used for main members and diagonal members of the ground line supports and crossarms. The auxiliary members of the model tower are made of L10 angle steel, and welded connections are used.


### 2.1.2. Other Similitude Coefficients

The same material is chosen to use in the towers of the experimental model as is used in the prototype; therefore, the similitude ratio for the elastic modulusE is 1 : 1, and considering the noise and bearing capacity of the shaking tables, the similitude coefficient of acceleration is assumed to be 3 : 1. Then, other similitude coefficients are derived as the preliminary similarity relationships by using dimensional analysis and based on the Buckingham π theorem for the transmission tower model design (Table 1).Table 1
Similitude coefficients of the transmission tower model.
Physical quantity
Ratio of similitude (model/prototype)
Geometric
1 : 15
Elastic modulus
1 : 1
Acceleration
3 : 1
Displacement
1 : 15
Density
5 : 1
Stress
1 : 1
Mass
1 : 130
Time
1 : 6.7
Frequency
6.7 : 1The total mass of the prototype transmission tower is 83544.6 kg, and the total mass of the scaled transmission tower model is 642.65 kg.


### 2.1.3. The Counterweight of the Model

Because the density similitude ratio is 5 : 1, the total mass of the scaled transmission tower model is 642.65 kg, the weight of the transmission tower without a counterweight is 128.53 kg, and the mass of the actual scaled transmission tower without a counterweight is 129 kg; to evenly apply the counterweight, the actual balancing weight is 555 kg. The actual total mass of the manufactured transmission tower model is 684 kg, and the actual density similitude ratio is 5.3 : 1. In the tests, two counterweights are processed, with masses of 2 kg and 0.25 kg. The counterweights are shown in Figure2.Figure 2
Counterweights of the test model tower. (a) Counterweight No. 1 (b) Counterweight No. 2.
(a)
(b)


## 2.1.1. Geometric Similitude Ratio and Material Selection

Considering the size limitations of the shaking tables, which have side lengths of 2.5 m, the geometric similitude ratio of the transmission tower is assumed to be 1 : 15.If all the angle steel members are scaled based on the geometric scale ratio, for the cross section, it is difficult to make the members because their thickness would only be 0.02 mm. Therefore, the transmission tower model uses four specifications of the angle steel (L30 × 3, L25 × 3, L20 × 3, and L10 × 1). The L30 angle steel is used for the main members and diagonal members of the tower leg and tower body, the L25 angle steel is used for the main members and diagonal members of the upper and lower cranks, and the L20 angle steel is used for main members and diagonal members of the ground line supports and crossarms. The auxiliary members of the model tower are made of L10 angle steel, and welded connections are used.


## 2.1.2. Other Similitude Coefficients

The same material is chosen to use in the towers of the experimental model as is used in the prototype; therefore, the similitude ratio for the elastic modulusE is 1 : 1, and considering the noise and bearing capacity of the shaking tables, the similitude coefficient of acceleration is assumed to be 3 : 1. Then, other similitude coefficients are derived as the preliminary similarity relationships by using dimensional analysis and based on the Buckingham π theorem for the transmission tower model design (Table 1).Table 1
Similitude coefficients of the transmission tower model.
Physical quantity
Ratio of similitude (model/prototype)
Geometric
1 : 15
Elastic modulus
1 : 1
Acceleration
3 : 1
Displacement
1 : 15
Density
5 : 1
Stress
1 : 1
Mass
1 : 130
Time
1 : 6.7
Frequency
6.7 : 1The total mass of the prototype transmission tower is 83544.6 kg, and the total mass of the scaled transmission tower model is 642.65 kg.


## 2.1.3. The Counterweight of the Model

Because the density similitude ratio is 5 : 1, the total mass of the scaled transmission tower model is 642.65 kg, the weight of the transmission tower without a counterweight is 128.53 kg, and the mass of the actual scaled transmission tower without a counterweight is 129 kg; to evenly apply the counterweight, the actual balancing weight is 555 kg. The actual total mass of the manufactured transmission tower model is 684 kg, and the actual density similitude ratio is 5.3 : 1. In the tests, two counterweights are processed, with masses of 2 kg and 0.25 kg. The counterweights are shown in Figure2.Figure 2
Counterweights of the test model tower. (a) Counterweight No. 1 (b) Counterweight No. 2.
(a)
(b)


## 2.2. Design and Manufacture of the Conductor Line and Ground Line

### 2.2.1. Similitude Coefficients of the Conductor Line and Ground Line

The tests were carried out using the three-shaking-table array system at Fuzhou University. A 4.1 m × 4.1 m horizontal bidirectional shaking table is in the middle, and two 2.5 m × 2.5 m horizontal bidirectional shaking tables are on each side. The maximum distance between the middle table and the side tables is 10 m, and the horizontal span of the prototype model is 500 m. If the tests are based on a geometric scale ratio of 1 : 15, the dimensions of the shaking tables are unable to meet the requirements. Therefore, in this study, the similitude ratio of the dynamic characteristics and the similitude ratio of the inertial mass are assumed separately to design the similitude coefficients of the conductor lines and ground lines.(1) Design of the Frequency Similitude Ratio of the Conductor Line and Ground Line. When designing the model of the transmission tower-line coupling system, the similitude ratio of the transmission tower should be close to that of the conductor line and ground line.The fundamental natural frequency of the conductor line and ground line is as follows:(1)fC=g4π2s,where fC is the fundamental natural frequency of the conductor line and ground line, g is the gravity acceleration constant, and s is the sag in the conductor line and ground line.The relationship between the frequency similitude ratio and sag similitude ratio of the conductor line and ground line can be derived as follows:(2)Sf=1Ss,Ss=1Sf2.The transmission tower has a frequency similitude ratio of 6.7 : 1, and the conductor line and ground line have a frequency similitude ratio of 6.7 : 1 and a sag similitude ratio of 44.9 : 1.(2) Design of Mass Similitude Ratio of the Conductor Line and Ground Line. If the geometric similitude ratio of the conductor line and ground line is assumed to be the same as that of the transmission tower (1 : 15), since the span of the prototype tower is 500 m, the distance between the model towers would be 33.33 m, exceeding the maximum distance (10 m) between the middle table and the side table and, hence, not meeting the requirements. Therefore, a span similitude ratio of 1 : 55 is selected for the actual tests, and accordingly, the actual distance between the middle tower and the side tower is 9.09 m.The mass similitude ratio of the conductor line and ground line is the same as that of the transmission tower (1 : 130). The total mass of the prototype conductor line is 2.06 × 500 = 1030 kg, so the mass of the model conductor line is 7.92 kg. The total mass of the prototype ground line is 0.49 × 500 = 245 kg. The actual linear densities of the model conductor line and ground line are calculated to be 0.88 kg/m and 0.49 kg/m, respectively (Table2).Table 2
Similitude coefficients of the model conductor line and ground line.
Physical quantity
Ratio of similitude (model/prototype)
Actual horizontal span
1 : 55
Theoretical horizontal span
1 : 15
Acceleration
3 : 1
Mass of conductor line
1 : 130
Mass of ground line
1 : 130
Frequency of conductor line
6.7 : 1
Frequency of ground line
6.7 : 1
Elastic modulus of conductor line
1 : 1
Elastic modulus of ground line
1 : 1
Density of conductor line
1 : 2.34
Density of ground line
1 : 2.34


### 2.2.2. Manufacture of Conductor Line and Ground Line

Steel wires with the diameters of 4 mm and 2 mm are used for the conductor line and ground line, respectively, in the experimental model. The physical components used for the conductor line and ground line are shown in Figure3.Figure 3
Physical components used for the conductor line and ground line. (a) Conductor line (4-mm steel wire). (b) Ground line (2-mm steel wire).
(a)
(b)According to the mass similitude ratio of the conductor line and ground line models, since the density of the steel wire is lower than that of the design model, counterweights are required. The counterweights of the conductor line and ground line are 8 kg and 4 kg, respectively. The counterweight blocks of the corresponding masses are placed uniformly along the conductor line and ground line.


## 2.2.1. Similitude Coefficients of the Conductor Line and Ground Line

The tests were carried out using the three-shaking-table array system at Fuzhou University. A 4.1 m × 4.1 m horizontal bidirectional shaking table is in the middle, and two 2.5 m × 2.5 m horizontal bidirectional shaking tables are on each side. The maximum distance between the middle table and the side tables is 10 m, and the horizontal span of the prototype model is 500 m. If the tests are based on a geometric scale ratio of 1 : 15, the dimensions of the shaking tables are unable to meet the requirements. Therefore, in this study, the similitude ratio of the dynamic characteristics and the similitude ratio of the inertial mass are assumed separately to design the similitude coefficients of the conductor lines and ground lines.(1) Design of the Frequency Similitude Ratio of the Conductor Line and Ground Line. When designing the model of the transmission tower-line coupling system, the similitude ratio of the transmission tower should be close to that of the conductor line and ground line.The fundamental natural frequency of the conductor line and ground line is as follows:(1)fC=g4π2s,where fC is the fundamental natural frequency of the conductor line and ground line, g is the gravity acceleration constant, and s is the sag in the conductor line and ground line.The relationship between the frequency similitude ratio and sag similitude ratio of the conductor line and ground line can be derived as follows:(2)Sf=1Ss,Ss=1Sf2.The transmission tower has a frequency similitude ratio of 6.7 : 1, and the conductor line and ground line have a frequency similitude ratio of 6.7 : 1 and a sag similitude ratio of 44.9 : 1.(2) Design of Mass Similitude Ratio of the Conductor Line and Ground Line. If the geometric similitude ratio of the conductor line and ground line is assumed to be the same as that of the transmission tower (1 : 15), since the span of the prototype tower is 500 m, the distance between the model towers would be 33.33 m, exceeding the maximum distance (10 m) between the middle table and the side table and, hence, not meeting the requirements. Therefore, a span similitude ratio of 1 : 55 is selected for the actual tests, and accordingly, the actual distance between the middle tower and the side tower is 9.09 m.The mass similitude ratio of the conductor line and ground line is the same as that of the transmission tower (1 : 130). The total mass of the prototype conductor line is 2.06 × 500 = 1030 kg, so the mass of the model conductor line is 7.92 kg. The total mass of the prototype ground line is 0.49 × 500 = 245 kg. The actual linear densities of the model conductor line and ground line are calculated to be 0.88 kg/m and 0.49 kg/m, respectively (Table2).Table 2
Similitude coefficients of the model conductor line and ground line.
Physical quantity
Ratio of similitude (model/prototype)
Actual horizontal span
1 : 55
Theoretical horizontal span
1 : 15
Acceleration
3 : 1
Mass of conductor line
1 : 130
Mass of ground line
1 : 130
Frequency of conductor line
6.7 : 1
Frequency of ground line
6.7 : 1
Elastic modulus of conductor line
1 : 1
Elastic modulus of ground line
1 : 1
Density of conductor line
1 : 2.34
Density of ground line
1 : 2.34


## 2.2.2. Manufacture of Conductor Line and Ground Line

Steel wires with the diameters of 4 mm and 2 mm are used for the conductor line and ground line, respectively, in the experimental model. The physical components used for the conductor line and ground line are shown in Figure3.Figure 3
Physical components used for the conductor line and ground line. (a) Conductor line (4-mm steel wire). (b) Ground line (2-mm steel wire).
(a)
(b)According to the mass similitude ratio of the conductor line and ground line models, since the density of the steel wire is lower than that of the design model, counterweights are required. The counterweights of the conductor line and ground line are 8 kg and 4 kg, respectively. The counterweight blocks of the corresponding masses are placed uniformly along the conductor line and ground line.


## 2.3. Design and Manufacture of the Insulator

The V-shaped insulator is simulated by a galvanized plain round steel bar with a diameter of 8 mm and a length of 750 mm, and the I-shaped insulator is simulated by a rigid steel plate with a length of 600 mm and a width of 50 mm. The physical components used for the insulator models are shown in Figure4. To ensure that the insulator is hinged at two ends with the conductor line, a U-shaped steel wire lock is selected to simulate the suspension clamp in the prototype tower, as shown in Figure 5.Figure 4
Physical components used for the insulator models. (a) I-shaped insulator model. (b) V-shaped insulator model.
(a)
(b)Figure 5
Physical components used for the conductor line suspension clamp model.


## 2.4. Equivalent Tower

The equivalent tower is the side tower in the three-tower-two-line model and the five-tower-four-line model. The equivalent tower is used to simulate the boundary conditions without considering the similarity relationship with the tower model. In the tests, two equivalent towers are manufactured using welded L50 × 4, as shown in Figure6. The function of the equivalent tower is similar to that of a corner tower in practical engineering projects.Figure 6
Equivalent generation tower model.


## 2.5. Test Models

### 2.5.1. Single-Tower Model

The test tower is anchored to the rigid base of the shaking table.


### 2.5.2. Three-Tower-Two-Line Model

The three-tower-two-line model is a single-tower-two-line model that has a cup-type tower as the middle tower and equivalent towers as the side towers. All three towers are anchored to the rigid base of the shaking table. The conductor line and ground line are fixed on the equivalent towers. The boundary conditions are shown in Figure7, and the physical components used for the three-tower-two-line model are shown in Figure 8.Figure 7
Elevation of the three-tower-two-line model.Figure 8
Physical components used for the three-tower-two-line model.


### 2.5.3. Five-Tower-Four-Line Model

The five-tower-four-line model is an improved version of the three-tower and two-line model. That is, two new tower models, which are the same as the middle tower, are placed at the locations of the original equivalent towers, which are relocated to the outer side of the new side main towers, along the line direction, and the boundary conditions are simulated through the connection between the equivalent towers and conductor lines, as shown in Figure9. The physical components used for the five-tower-four-line model are shown in Figure 10.Figure 9
Elevation of the five-tower-four-line model.Figure 10
Physical components used for the five-tower-four-line model.


## 2.5.1. Single-Tower Model

The test tower is anchored to the rigid base of the shaking table.


## 2.5.2. Three-Tower-Two-Line Model

The three-tower-two-line model is a single-tower-two-line model that has a cup-type tower as the middle tower and equivalent towers as the side towers. All three towers are anchored to the rigid base of the shaking table. The conductor line and ground line are fixed on the equivalent towers. The boundary conditions are shown in Figure7, and the physical components used for the three-tower-two-line model are shown in Figure 8.Figure 7
Elevation of the three-tower-two-line model.Figure 8
Physical components used for the three-tower-two-line model.


## 2.5.3. Five-Tower-Four-Line Model

The five-tower-four-line model is an improved version of the three-tower and two-line model. That is, two new tower models, which are the same as the middle tower, are placed at the locations of the original equivalent towers, which are relocated to the outer side of the new side main towers, along the line direction, and the boundary conditions are simulated through the connection between the equivalent towers and conductor lines, as shown in Figure9. The physical components used for the five-tower-four-line model are shown in Figure 10.Figure 9
Elevation of the five-tower-four-line model.Figure 10
Physical components used for the five-tower-four-line model.


## 3. Shaking Table Test Setup

### 3.1. Selection of Ground Motions

Considering the long span of transmission lines and the different site conditions in the regions that the lines traverse, the El Centro record, Taft record, and artificial waves are selected for site classes II, III, and IV, respectively. The duration of the ground motion is compressed to 1/6.7 of the original, based on the similarity relationship. The original wave is compressed according to the time or frequency similitude ratio and is then applied to the seismic excitation tests of the scale models. The 0.07 g seismic records are shown in Figure11.Figure 11
The 0.07 g seismic records. (a) 0.07 g EL Centro wave. (b) 0.07 g Taft wave. (c) 0.07 g artificial wave.
(a)
(b)
(c)


### 3.2. Sensor Layout

Two types of acceleration sensors, namely, a piezoresistive accelerometer and piezoelectric accelerometer, are used in the tests. The piezoresistive accelerometer has a large measuring range and is mainly used to measure the seismic responses of the top of the tower and the conductor and ground lines. The piezoelectric accelerometer has a slightly smaller measuring range and is mainly used to measure the seismic responses of the tower leg and body. Two types of displacement sensors, namely, a laser displacement sensor and guyed displacement sensor, are used in the tests. Resistive strain gauges are used in the tests to test the strain of the tower model members.


#### 3.2.1. Sensor Layout for the Single-Tower Model

In the single-tower model tests, a total of 22 acceleration sensors, 25 strain gauges, and 14 displacement sensors are deployed. The detailed placements of the sensors are shown in Figures12–14, in which “X” indicates the longitudinal direction, “Y” indicates the transverse direction, as shown by the coordinates in the lower left corner, “A” denotes an acceleration sensor, “S” denotes a strain gauge, and “D” denotes a displacement sensor.Figure 12
Layout of acceleration sensors.Figure 13
Layout of displacement sensors.Figure 14
Layout of strain gauges.


#### 3.2.2. Sensor Layout for the Three-Tower-Two-Line Model

(1) Acceleration Sensors. The layout of the acceleration sensors on the three-tower-two-line model is exactly the same as that on the body of the single-tower model with counterweights. A total of 16 acceleration sensors are deployed on the conductor lines. A total of six acceleration sensors are placed on the ground line. The acceleration sensors are evenly distributed along the conductor and ground lines. The layout of the acceleration sensors on the conductor and ground lines is shown in Figure 15, where C represents the acceleration sensor and the numeral represents the numbering of the sensors.Figure 15
Schematic diagram of the layout of the acceleration sensors on the conductor and ground lines.In the “three-tower-two-line” model, four acceleration sensors are placed on each of the two equivalent towers. Specifically, for each equivalent tower, one acceleration sensor is placed in theX and Y directions on top of the tower, and one acceleration sensor is placed in the X and Y directions on the base of table. Thus, a total of eight acceleration sensors are placed. The detailed layout is shown in Figure 16, where “L” is the left equivalent tower, “R” is the right equivalent tower, “A” is the acceleration, “S” is the strain, “D” is the tower top, “T” is the tower leg, “M” is the table top, and “X” and “Y” are the two vibration directions. The acceleration sensors are placed at the middle point on the top of the equivalent tower, and the strain gages are placed on the tower legs along the line direction.(2) Displacement Sensors. The layout of the displacement sensors on the “three-tower-two-line” model is the same as that on the body of the single-tower model with counterweights. Thus, the detailed layout is the layout of the displacement sensors on the single-tower model (Figure 13).(3) Strain Gauge Layout. The layout of the strain gauges on the “three-tower-two-line” model is the same as that on the body of the single-tower model. The detailed layout is shown in Figure 14, where “S” represents a strain gauge and the numeral represents the numbering of the gauges.


#### 3.2.3. Sensor Layout for the Five-Tower-Four-Line Model

(1) Acceleration Sensor. There are three model towers in the “five-tower-four-line” model. Due to the limitations of the sensors and acquisition channels, in particular, 18 acceleration sensors are deployed in the middle tower. The specific layout is illustrated in Figure 17(a), where A represents an acceleration sensor and the numeral represents the numbering of the sensors.Figure 16
Layout of the accelerator sensors and strain gauges on the equivalent tower model.In the five-tower-four-line model, the layout of the sensors on the two model towers on the left and right small tables reference that on the middle tower. A total of 14 acceleration sensors are placed on the right main tower, as shown in Figure17(b), where R represents the right side, A represents an acceleration sensor, and the numeral represents the numbering of the sensors consistent with that of the middle main tower, indicating that the position of a sensor on the side main tower corresponds with that on the middle tower. A total of 11 acceleration sensors are placed on the left main tower, as shown in Figure 17(c), where L represents the left side, A represents an acceleration sensor, and the numeral represents the numbering of the sensors consistent with that of the middle main tower, indicating that the position of a sensor on the side main tower corresponds to that on the middle tower.The layout of the sensors on the equivalent tower in the five-tower-four-line model is identical to that on the equivalent tower of the three-tower-two-line model. The specific layout is illustrated in Figure16.Figure 17
Acceleration sensor placement of the five-tower and four-line model. Layout of the acceleration sensors on (a) the middle tower, (b) the right model tower, and (c) the left model tower.
(a)
(b)
(c)A total of three acceleration sensors are deployed on the conductor line, and one acceleration sensor is deployed on the ground line. The specific sensor layout is shown in Figure18, where C represents an acceleration sensor, the numeral represents the numbering of the sensors, and the arrow represents the direction of the vibration.Figure 18
Layout of the acceleration sensors on the five-tower-four-line model.(2) Displacement Sensors. The layout of the displacement sensors on the towers of the five-tower-four-line model is identical to that on the tower of the single-tower model with counterweights. The specific layout references the layout of the displacement sensors on the single-tower model (Figure 13), where D represents the displacement and the numeral represents the numbering of the sensors.In the five-tower-four-line model, the layouts of the sensors on the two model towers on the left and right small tables reference that on the middle tower, but the sensors are all deployed above the tower structure, where the layout of the sensors above the structure of the right main tower is consistent with that of the middle tower, with 8 displacement sensors placed (Figure19(a)), while the sensors are symmetrically deployed only on the upper structure of the left main tower, with 4 displacement sensors placed (Figure 19(b)). In the figure, L stands for the left side, R is the right side, D is the displacement sensor, and the numeral is the numbering of the sensors. When the numeral of the main side tower is consistent with that of the middle tower, the location of the sensor on the main side tower corresponds with that on the middle tower. In addition, the direction of the sensor is represented by X or Y. The specific layout is illustrated in Figure 19.Figure 19
Layout of the displacement sensors on the five-tower-four-line model. Layout of the displacement sensors on (a) the right model tower and (b) the left model tower.
(a)
(b)The five-tower-four-line model has a total of 73 strain gauges, including 28 on the middle tower, 23 on the right main tower, 22 on the left main tower, and 2 on the equivalent tower. Figure20 illustrates the specific layout of the strain gages.Figure 20
Layout of the strain gauges on the five-tower-four-line model. (a) Layout of 28 strain gauges on the middle tower. (b) Layout of 23 strain gauges on the right main tower. (c) Layout of 22 strain gauges on the left main tower.
(a)
(b)
(c)


### 3.3. Test Program

The basic dynamic characteristics tests and seismic time-history response tests are conducted on the single-tower model, the single-tower model with suspended lumped masses, the three-tower-two-line model, and the five-tower-four-line model. A total of 21 runs were performed, as listed in Table3.Table 3
Test program.
Test series
Input wave
Peak acceleration (g)
Loading direction
1
White noise
0.07
—
2
El Centro wave
0.07
X
3
Taft wave
0.07
X
4
Artificial wave
0.07
X
5
El Centro wave
0.07
Y
6
Taft wave
0.07
Y
7
Artificial wave
0.07
Y
8
White noise
0.21
—
9
El Centro wave
0.21
X
10
Taft wave
0.21
X
11
Artificial wave
0.21
X
12
El Centro wave
0.21
Y
13
Taft wave
0.21
Y
14
Artificial wave
0.21
Y
15
White noise
0.63
—
16
El Centro wave
0.63
X
17
Taft wave
0.63
X
18
Artificial wave
0.63
X
19
El Centro wave
0.63
Y
20
Taft wave
0.63
Y
21
Artificial wave
0.63
Y


## 3.1. Selection of Ground Motions

Considering the long span of transmission lines and the different site conditions in the regions that the lines traverse, the El Centro record, Taft record, and artificial waves are selected for site classes II, III, and IV, respectively. The duration of the ground motion is compressed to 1/6.7 of the original, based on the similarity relationship. The original wave is compressed according to the time or frequency similitude ratio and is then applied to the seismic excitation tests of the scale models. The 0.07 g seismic records are shown in Figure11.Figure 11
The 0.07 g seismic records. (a) 0.07 g EL Centro wave. (b) 0.07 g Taft wave. (c) 0.07 g artificial wave.
(a)
(b)
(c)


## 3.2. Sensor Layout

Two types of acceleration sensors, namely, a piezoresistive accelerometer and piezoelectric accelerometer, are used in the tests. The piezoresistive accelerometer has a large measuring range and is mainly used to measure the seismic responses of the top of the tower and the conductor and ground lines. The piezoelectric accelerometer has a slightly smaller measuring range and is mainly used to measure the seismic responses of the tower leg and body. Two types of displacement sensors, namely, a laser displacement sensor and guyed displacement sensor, are used in the tests. Resistive strain gauges are used in the tests to test the strain of the tower model members.


### 3.2.1. Sensor Layout for the Single-Tower Model

In the single-tower model tests, a total of 22 acceleration sensors, 25 strain gauges, and 14 displacement sensors are deployed. The detailed placements of the sensors are shown in Figures12–14, in which “X” indicates the longitudinal direction, “Y” indicates the transverse direction, as shown by the coordinates in the lower left corner, “A” denotes an acceleration sensor, “S” denotes a strain gauge, and “D” denotes a displacement sensor.Figure 12
Layout of acceleration sensors.Figure 13
Layout of displacement sensors.Figure 14
Layout of strain gauges.


### 3.2.2. Sensor Layout for the Three-Tower-Two-Line Model

(1) Acceleration Sensors. The layout of the acceleration sensors on the three-tower-two-line model is exactly the same as that on the body of the single-tower model with counterweights. A total of 16 acceleration sensors are deployed on the conductor lines. A total of six acceleration sensors are placed on the ground line. The acceleration sensors are evenly distributed along the conductor and ground lines. The layout of the acceleration sensors on the conductor and ground lines is shown in Figure 15, where C represents the acceleration sensor and the numeral represents the numbering of the sensors.Figure 15
Schematic diagram of the layout of the acceleration sensors on the conductor and ground lines.In the “three-tower-two-line” model, four acceleration sensors are placed on each of the two equivalent towers. Specifically, for each equivalent tower, one acceleration sensor is placed in theX and Y directions on top of the tower, and one acceleration sensor is placed in the X and Y directions on the base of table. Thus, a total of eight acceleration sensors are placed. The detailed layout is shown in Figure 16, where “L” is the left equivalent tower, “R” is the right equivalent tower, “A” is the acceleration, “S” is the strain, “D” is the tower top, “T” is the tower leg, “M” is the table top, and “X” and “Y” are the two vibration directions. The acceleration sensors are placed at the middle point on the top of the equivalent tower, and the strain gages are placed on the tower legs along the line direction.(2) Displacement Sensors. The layout of the displacement sensors on the “three-tower-two-line” model is the same as that on the body of the single-tower model with counterweights. Thus, the detailed layout is the layout of the displacement sensors on the single-tower model (Figure 13).(3) Strain Gauge Layout. The layout of the strain gauges on the “three-tower-two-line” model is the same as that on the body of the single-tower model. The detailed layout is shown in Figure 14, where “S” represents a strain gauge and the numeral represents the numbering of the gauges.


### 3.2.3. Sensor Layout for the Five-Tower-Four-Line Model

(1) Acceleration Sensor. There are three model towers in the “five-tower-four-line” model. Due to the limitations of the sensors and acquisition channels, in particular, 18 acceleration sensors are deployed in the middle tower. The specific layout is illustrated in Figure 17(a), where A represents an acceleration sensor and the numeral represents the numbering of the sensors.Figure 16
Layout of the accelerator sensors and strain gauges on the equivalent tower model.In the five-tower-four-line model, the layout of the sensors on the two model towers on the left and right small tables reference that on the middle tower. A total of 14 acceleration sensors are placed on the right main tower, as shown in Figure17(b), where R represents the right side, A represents an acceleration sensor, and the numeral represents the numbering of the sensors consistent with that of the middle main tower, indicating that the position of a sensor on the side main tower corresponds with that on the middle tower. A total of 11 acceleration sensors are placed on the left main tower, as shown in Figure 17(c), where L represents the left side, A represents an acceleration sensor, and the numeral represents the numbering of the sensors consistent with that of the middle main tower, indicating that the position of a sensor on the side main tower corresponds to that on the middle tower.The layout of the sensors on the equivalent tower in the five-tower-four-line model is identical to that on the equivalent tower of the three-tower-two-line model. The specific layout is illustrated in Figure16.Figure 17
Acceleration sensor placement of the five-tower and four-line model. Layout of the acceleration sensors on (a) the middle tower, (b) the right model tower, and (c) the left model tower.
(a)
(b)
(c)A total of three acceleration sensors are deployed on the conductor line, and one acceleration sensor is deployed on the ground line. The specific sensor layout is shown in Figure18, where C represents an acceleration sensor, the numeral represents the numbering of the sensors, and the arrow represents the direction of the vibration.Figure 18
Layout of the acceleration sensors on the five-tower-four-line model.(2) Displacement Sensors. The layout of the displacement sensors on the towers of the five-tower-four-line model is identical to that on the tower of the single-tower model with counterweights. The specific layout references the layout of the displacement sensors on the single-tower model (Figure 13), where D represents the displacement and the numeral represents the numbering of the sensors.In the five-tower-four-line model, the layouts of the sensors on the two model towers on the left and right small tables reference that on the middle tower, but the sensors are all deployed above the tower structure, where the layout of the sensors above the structure of the right main tower is consistent with that of the middle tower, with 8 displacement sensors placed (Figure19(a)), while the sensors are symmetrically deployed only on the upper structure of the left main tower, with 4 displacement sensors placed (Figure 19(b)). In the figure, L stands for the left side, R is the right side, D is the displacement sensor, and the numeral is the numbering of the sensors. When the numeral of the main side tower is consistent with that of the middle tower, the location of the sensor on the main side tower corresponds with that on the middle tower. In addition, the direction of the sensor is represented by X or Y. The specific layout is illustrated in Figure 19.Figure 19
Layout of the displacement sensors on the five-tower-four-line model. Layout of the displacement sensors on (a) the right model tower and (b) the left model tower.
(a)
(b)The five-tower-four-line model has a total of 73 strain gauges, including 28 on the middle tower, 23 on the right main tower, 22 on the left main tower, and 2 on the equivalent tower. Figure20 illustrates the specific layout of the strain gages.Figure 20
Layout of the strain gauges on the five-tower-four-line model. (a) Layout of 28 strain gauges on the middle tower. (b) Layout of 23 strain gauges on the right main tower. (c) Layout of 22 strain gauges on the left main tower.
(a)
(b)
(c)


## 3.2.1. Sensor Layout for the Single-Tower Model

In the single-tower model tests, a total of 22 acceleration sensors, 25 strain gauges, and 14 displacement sensors are deployed. The detailed placements of the sensors are shown in Figures12–14, in which “X” indicates the longitudinal direction, “Y” indicates the transverse direction, as shown by the coordinates in the lower left corner, “A” denotes an acceleration sensor, “S” denotes a strain gauge, and “D” denotes a displacement sensor.Figure 12
Layout of acceleration sensors.Figure 13
Layout of displacement sensors.Figure 14
Layout of strain gauges.


## 3.2.2. Sensor Layout for the Three-Tower-Two-Line Model

(1) Acceleration Sensors. The layout of the acceleration sensors on the three-tower-two-line model is exactly the same as that on the body of the single-tower model with counterweights. A total of 16 acceleration sensors are deployed on the conductor lines. A total of six acceleration sensors are placed on the ground line. The acceleration sensors are evenly distributed along the conductor and ground lines. The layout of the acceleration sensors on the conductor and ground lines is shown in Figure 15, where C represents the acceleration sensor and the numeral represents the numbering of the sensors.Figure 15
Schematic diagram of the layout of the acceleration sensors on the conductor and ground lines.In the “three-tower-two-line” model, four acceleration sensors are placed on each of the two equivalent towers. Specifically, for each equivalent tower, one acceleration sensor is placed in theX and Y directions on top of the tower, and one acceleration sensor is placed in the X and Y directions on the base of table. Thus, a total of eight acceleration sensors are placed. The detailed layout is shown in Figure 16, where “L” is the left equivalent tower, “R” is the right equivalent tower, “A” is the acceleration, “S” is the strain, “D” is the tower top, “T” is the tower leg, “M” is the table top, and “X” and “Y” are the two vibration directions. The acceleration sensors are placed at the middle point on the top of the equivalent tower, and the strain gages are placed on the tower legs along the line direction.(2) Displacement Sensors. The layout of the displacement sensors on the “three-tower-two-line” model is the same as that on the body of the single-tower model with counterweights. Thus, the detailed layout is the layout of the displacement sensors on the single-tower model (Figure 13).(3) Strain Gauge Layout. The layout of the strain gauges on the “three-tower-two-line” model is the same as that on the body of the single-tower model. The detailed layout is shown in Figure 14, where “S” represents a strain gauge and the numeral represents the numbering of the gauges.


## 3.2.3. Sensor Layout for the Five-Tower-Four-Line Model

(1) Acceleration Sensor. There are three model towers in the “five-tower-four-line” model. Due to the limitations of the sensors and acquisition channels, in particular, 18 acceleration sensors are deployed in the middle tower. The specific layout is illustrated in Figure 17(a), where A represents an acceleration sensor and the numeral represents the numbering of the sensors.Figure 16
Layout of the accelerator sensors and strain gauges on the equivalent tower model.In the five-tower-four-line model, the layout of the sensors on the two model towers on the left and right small tables reference that on the middle tower. A total of 14 acceleration sensors are placed on the right main tower, as shown in Figure17(b), where R represents the right side, A represents an acceleration sensor, and the numeral represents the numbering of the sensors consistent with that of the middle main tower, indicating that the position of a sensor on the side main tower corresponds with that on the middle tower. A total of 11 acceleration sensors are placed on the left main tower, as shown in Figure 17(c), where L represents the left side, A represents an acceleration sensor, and the numeral represents the numbering of the sensors consistent with that of the middle main tower, indicating that the position of a sensor on the side main tower corresponds to that on the middle tower.The layout of the sensors on the equivalent tower in the five-tower-four-line model is identical to that on the equivalent tower of the three-tower-two-line model. The specific layout is illustrated in Figure16.Figure 17
Acceleration sensor placement of the five-tower and four-line model. Layout of the acceleration sensors on (a) the middle tower, (b) the right model tower, and (c) the left model tower.
(a)
(b)
(c)A total of three acceleration sensors are deployed on the conductor line, and one acceleration sensor is deployed on the ground line. The specific sensor layout is shown in Figure18, where C represents an acceleration sensor, the numeral represents the numbering of the sensors, and the arrow represents the direction of the vibration.Figure 18
Layout of the acceleration sensors on the five-tower-four-line model.(2) Displacement Sensors. The layout of the displacement sensors on the towers of the five-tower-four-line model is identical to that on the tower of the single-tower model with counterweights. The specific layout references the layout of the displacement sensors on the single-tower model (Figure 13), where D represents the displacement and the numeral represents the numbering of the sensors.In the five-tower-four-line model, the layouts of the sensors on the two model towers on the left and right small tables reference that on the middle tower, but the sensors are all deployed above the tower structure, where the layout of the sensors above the structure of the right main tower is consistent with that of the middle tower, with 8 displacement sensors placed (Figure19(a)), while the sensors are symmetrically deployed only on the upper structure of the left main tower, with 4 displacement sensors placed (Figure 19(b)). In the figure, L stands for the left side, R is the right side, D is the displacement sensor, and the numeral is the numbering of the sensors. When the numeral of the main side tower is consistent with that of the middle tower, the location of the sensor on the main side tower corresponds with that on the middle tower. In addition, the direction of the sensor is represented by X or Y. The specific layout is illustrated in Figure 19.Figure 19
Layout of the displacement sensors on the five-tower-four-line model. Layout of the displacement sensors on (a) the right model tower and (b) the left model tower.
(a)
(b)The five-tower-four-line model has a total of 73 strain gauges, including 28 on the middle tower, 23 on the right main tower, 22 on the left main tower, and 2 on the equivalent tower. Figure20 illustrates the specific layout of the strain gages.Figure 20
Layout of the strain gauges on the five-tower-four-line model. (a) Layout of 28 strain gauges on the middle tower. (b) Layout of 23 strain gauges on the right main tower. (c) Layout of 22 strain gauges on the left main tower.
(a)
(b)
(c)


## 3.3. Test Program

The basic dynamic characteristics tests and seismic time-history response tests are conducted on the single-tower model, the single-tower model with suspended lumped masses, the three-tower-two-line model, and the five-tower-four-line model. A total of 21 runs were performed, as listed in Table3.Table 3
Test program.
Test series
Input wave
Peak acceleration (g)
Loading direction
1
White noise
0.07
—
2
El Centro wave
0.07
X
3
Taft wave
0.07
X
4
Artificial wave
0.07
X
5
El Centro wave
0.07
Y
6
Taft wave
0.07
Y
7
Artificial wave
0.07
Y
8
White noise
0.21
—
9
El Centro wave
0.21
X
10
Taft wave
0.21
X
11
Artificial wave
0.21
X
12
El Centro wave
0.21
Y
13
Taft wave
0.21
Y
14
Artificial wave
0.21
Y
15
White noise
0.63
—
16
El Centro wave
0.63
X
17
Taft wave
0.63
X
18
Artificial wave
0.63
X
19
El Centro wave
0.63
Y
20
Taft wave
0.63
Y
21
Artificial wave
0.63
Y


## 4. Test Results

To study the influence of the coupling effect of the transmission tower-line system on the transmission tower, dynamic characteristics tests and the shaking table tests are performed on the single-tower model, the single-tower model with suspended lumped masses, the three-tower-two-line model, and the five-tower-four-line model. The results of the frequency, damping, acceleration, displacement, and strain of the middle tower are obtained from the tests.


### 4.1. Dynamic Characteristics Test Results

Figure21 shows the spectral analysis results of the acceleration time-history curve at the midpoint of the middle tower model head in the transverse direction (first-order) and the longitudinal direction (second-order) of the four models. Table 4 compares the basic dynamic characteristics of the middle towers of the four models. The results show that the suspension of the conductor lines and lumped masses decreases the frequency of the middle tower. Compared with the single-tower model, the first-order frequency of the single tower with suspended lumped masses model decreases by 5.08%, and the second-order frequency decreases by 4.03%. The frequencies of the two models with suspended conductor lines are very close. Compared with those of the single-tower model, the first-order frequency of the model with suspended conductor lines decreases by 0.82%, and the second-order frequency decreases by 4.0%. In terms of structural damping, the suspension of clumped masses and conductor lines increase the damping ratio of the structure, with the damping ratio of the three-tower-two-line model reaching a maximum of 2.99%. These results show that there is no significant difference regarding the effect of tower-line coupling for the dynamic characteristics between the three-tower-two-line model and the five-tower-four-line model. The effect of tower-line coupling decreases the frequency of the tower and increases the damping ratio. The single-tower model with suspended lumped masses can simulate the effect of tower-line coupling on the longitudinal dynamic characteristics of the transmission tower well, but this model faces difficulty in satisfactorily simulating the effect of tower-line coupling on the transverse characteristics of the transmission tower.Figure 21
Spectrum analysis curves of the middle towers of the four counterweight models. (a) First-order frequency spectrum analysis curves. (b) Second-order frequency spectrum analysis curves.
(a)
(b)Table 4
Comparison of the basic dynamic characteristics of the middle towers of the four models.
Model
Frequency
Damping ratio
f1 (Hz)
f2 (Hz)
C1 (%)
C2 (%)
Single-tower model
7.202
7.568
0.92
2.40
Single tower with suspended lumped masses
6.836
7.263
1.06
1.18
Three-tower-two-line model
7.143
7.265
2.99
2.58
Five-tower-four-line model
7.143
7.265
2.38
1.65


### 4.2. Comparative Analysis of the Dynamic Results of the Middle Towers from the Shaking Table Tests

(1) Comparative Analysis of the Acceleration Response. Figure 22 shows the longitudinal peak acceleration responses under the unidirectional input of a 0.21 g artificial wave. The results show that the peak acceleration response curves of the tower accelerations of the different models basically coincide, and the trends are similar. The peak acceleration response gradually increases from the base of the tower to the top, reaching the maximum at the top of the tower.Figure 22
Longitudinal peak acceleration responses of the middle tower of the four models under a 0.21 g artificial wave.Table5 shows the longitudinal peak acceleration responses of the middle towers of the four models under each wave. The results show that the peak acceleration response is the largest under the artificial wave and the smallest under the El Centro wave. The model with the suspended lumped mass has the smallest acceleration response. Therefore, the use of a single-tower model with suspended lumped masses to simulate a three-tower-two-line model or a five-tower-four-line model is inaccurate. Except for the 0.63 g test condition, the effect of the tower-line coupling increases the longitudinal peak acceleration response of the tower.Table 5
Longitudinal peak acceleration responses of the middle towers of the four models.
Test series
Single-tower model (m/s2)
Single-tower model with suspended lumped masses (m/s2)
Three-tower-two-line model (m/s2)
Five-tower-four-line model (m/s2)
0.07 g artificial wave
5.966
5.278
5.905
7.310
0.07 g El Centro wave
4.563
4.122
4.456
4.096
0.07 g Taft wave
5.137
4.202
5.961
5.810
0.07 g average
5.222
4.534
5.441
5.739
0.21 g artificial wave
16.738
16.166
18.663
17.921
0.21 g El Centro wave
14.291
11.379
16.815
11.809
0.21 g Taft wave
15.791
13.880
17.458
16.866
0.21 g average
15.607
13.808
17.646
15.532
0.63 g artificial wave
64.671
41.566
46.214
57.260
0.63 g El Centro wave
46.165
36.703
45.403
38.731
0.63 g Taft wave
53.828
41.161
41.546
49.032
0.63 g average
54.888
39.810
44.388
48.341Figure23 shows the transverse peak acceleration response under the unidirectional input of a 0.21 g artificial wave. The results show that except for the single tower with suspended lumped masses model, the peak acceleration response curves of the towers of the other models basically coincide and have similar trends. The comparison shows that the peak accelerations are relatively close within the lower portion of the tower structure, while the peak acceleration responses at the crossarm vary noticeably. The peak acceleration of the single-tower model with suspended lumped masses is the smallest at the crossarm, and the peak acceleration of the single-tower model is the largest at the crossarm.Figure 23
Transverse peak acceleration responses of the four counterweight models under a 0.21 g artificial wave.Table6 shows the transverse peak accelerations of the middle towers of the four models under each wave. The results show that the peak acceleration response is the largest under the artificial wave and is the smallest under the El Centro wave. The model with suspended lumped masses has the lowest peak acceleration response, and the single-tower model with counterweights has the highest peak acceleration response. Therefore, the suspended masses and conductor lines are decreasing the transverse seismic response of the model tower. In comparison, the single tower with suspended lumped masses tested using a single shaking table has the lowest seismic response, so the use of this model to simulate the tower-line system is inaccurate. Under the three seismic conditions of the same seismic intensity level, the average transverse peak acceleration response of the three-tower-two-line model is greater than that of the five-tower-four-line model; the effect of tower-line coupling decreases the transverse peak acceleration response of the tower.Table 6
Vertical peak acceleration responses of the middle towers of the four models.
Test series
Single-tower model (m/s2)
Single-tower model with suspended lumped masses (m/s2)
Three-tower-two-line model (m/s2)
Five-tower-four-line model (m/s2)
0.07 g artificial wave
4.612
2.563
3.662
4.059
0.07 g El Centro wave
1.795
1.192
1.716
1.538
0.07 g Taft wave
3.349
2.236
2.996
2.333
0.07 g average
3.252
1.997
2.791
2.643
0.21 g artificial wave
13.710
7.441
11.511
10.878
0.21 g El Centro wave
5.827
4.911
5.669
4.603
0.21 g Taft wave
10.963
6.676
9.522
7.003
0.21 g average
10.167
6.343
8.901
7.495
0.63 g artificial wave
35.349
21.697
32.248
26.287
0.63 g El Centro wave
17.258
13.433
18.088
13.516
0.63 g Taft wave
29.543
20.806
24.010
20.001
0.63 g average
27.383
18.645
24.782
19.935(2) Comparative Analysis of the Displacement Responses. Figure 24 shows the longitudinal peak displacement responses under the unidirectional input of a 0.21 g artificial wave. The results show that except for that of the single-tower model with suspended lumped masses, the peak displacement response gradually increases from the base of the tower to the top, reaching the maximum peak displacement at the top of the tower.Figure 24
Longitudinal peak displacement responses of the four models under a 0.21 g artificial wave.Table7 shows the longitudinal peak displacements of the main towers of the four models under each wave. The results show that the peak displacement response is the largest under the artificial wave and is the smallest under the El Centro wave. The single-tower model with suspended lumped masses has the maximum displacement response. Under the three test conditions at the same seismic level, the average of the longitudinal peak displacement responses of the three-tower-consistency model is larger than that of the five-tower-consistency model. Except for 0.63 g test condition, the effect of tower-line coupling increases the longitudinal peak displacement response of the tower.Table 7
Longitudinal peak displacement responses of the middle towers of the four models.
Test series
Single-tower model (mm)
Single-tower model with suspended lumped masses (mm)
Three-tower-consistency model (mm)
Five-tower-consistency model (mm)
0.07 g artificial wave
1.737
2.963
2.456
2.021
0.07 g El Centro wave
0.989
0.979
1.389
1.329
0.07 g Taft wave
1.161
1.474
1.149
1.304
0.07 g average
1.296
1.805
1.665
1.551
0.21 g artificial wave
5.936
10.072
7.516
6.681
0.21 g El Centro wave
4.155
6.321
4.876
3.799
0.21 g Taft wave
3.619
5.076
3.710
4.593
0.21 g average
4.570
7.156
5.368
5.024
0.63 g artificial wave
30.041
35.823
27.151
19.555
0.63 g El Centro wave
15.137
22.200
14.378
12.541
0.63 g Taft wave
14.462
15.054
10.921
13.204
0.63 g average
19.880
24.359
17.483
15.100Figure25 shows the transverse peak displacement responses under the unidirectional input of a 0.21 g artificial wave. The results show that the trends of the peak displacement response curves of the towers are similar. The peak displacement response gradually increases from the base of the tower to the top, reaching the largest peak displacement at the top of the tower.Figure 25
Transverse peak displacement responses of the four models under a 0.21 g artificial wave.Table8 shows the transverse peak displacements of the main towers of the four models under each wave. The results show that the peak displacement response is the largest under the artificial wave and is the smallest under the El Centro wave. The single-tower model with suspended lumped masses has the smallest peak displacement response, and the three-tower-two-line model has the largest peak displacement response. Therefore, the use of the single-tower model with suspended lumped masses to simulate the tower-line system is inaccurate. Under the three test conditions at the same seismic level, the average of the transverse peak displacement response of the three-tower-two-line model is larger than that of the five-tower-four-line model; the effect of the three-tower-two-line model’s tower-line coupling increases the transverse peak displacement response of the tower, while the effect of the five-tower-four-line model’s tower-line coupling decreases the transverse peak displacement response of the tower.Table 8
Transverse peak displacement responses of the middle towers of the four models.
Test series
Single-tower model (mm)
Single-tower model with suspended lumped masses (mm)
Three-tower-two-line model (mm)
Five-tower-four-line model (mm)
0.07 g artificial wave
2.134
1.687
3.126
1.848
0.07 g El Centro wave
0.811
0.543
0.720
0.736
0.07 g Taft wave
1.127
0.883
0.824
0.897
0.07 g average
1.357
1.038
1.557
1.161
0.21 g artificial wave
7.258
5.223
9.663
6.032
0.21 g El Centro wave
2.148
2.447
2.514
2.089
0.21 g Taft wave
3.962
2.233
2.976
3.130
0.21 g average
4.456
3.301
5.051
3.750
0.63 g artificial wave
21.152
16.141
26.785
16.364
0.63 g El Centro wave
7.513
7.250
8.162
6.549
0.63 g Taft wave
12.204
7.045
7.768
8.783
0.63 g average
13.623
10.146
14.238
10.565(3) Comparative Analysis of the Strain Responses. Figure 26 shows that for the four models under a 0.21 g unidirectional seismic input, the longitudinal peak strain variation curves of the towers under the crank arms are consistent in both shape and magnitude, and the strain is relatively large at the locations of the tower head, crank arm, and tower legs.Figure 26
Longitudinal peak strain responses of the four models under a 0.21 g artificial wave.Table9 shows the longitudinal peak strain values of the main tower strains of the four models under each wave. The results show that the peak strain response is the largest under the artificial wave and is the smallest under the El Centro wave. The longitudinal peak strains of the main towers of the four models are relatively close under the same wave. Except for the 0.63 g test condition, the effect of tower-line coupling increases the longitudinal peak strain response of the tower.Table 9
Longitudinal peak strain responses of the middle towers of the four models.
Test series
Single-tower model (με)
Single-tower model with suspended lumped masses (με)
Three-tower-two-line model (με)
Five-tower-four-line model (με)
0.07 g artificial wave
53.546
59.655
56.044
56.169
0.07 g El Centro wave
28.017
33.378
33.323
33.819
0.07 g Taft wave
33.187
37.373
33.432
34.995
0.07 g average
38.250
43.469
40.933
41.661
0.21 g artificial wave
148.616
171.750
167.730
150.257
0.21 g El Centro wave
101.668
108.935
129.404
104.848
0.21 g Taft wave
106.910
117.344
111.988
122.553
0.21 g average
119.065
132.677
136.374
125.886
0.63 g artificial wave
450.086
426.452
442.957
513.300
0.63 g El Centro wave
358.235
359.335
394.204
347.420
0.63 g Taft wave
394.345
347.076
306.438
377.690
0.63 g average
400.888
377.621
381.200
412.803Figure27 shows the curves of the transverse peak strain values of the tower body structure for the four models under a 0.21 g unidirectional seismic input. The curves are consistent in shape, with parallel decreasing trends. The largest peak strain occurs in the single-tower model, reaching approximately 200 με, and the smallest peak strain occurs in the single-tower model with suspended lumped masses, which is approximately 1/2 of that of single-tower model without suspended lumped masses.Figure 27
Transverse peak strain responses of the four counterweight models under a 0.21 g artificial wave.Table10 shows the transverse peak strain values of the main tower of the four models under each wave. The results show that the peak strain response is the largest under the artificial wave and the smallest under the El Centro wave. Except for the 0.21-g test condition, the model with suspended lumped masses has the smallest peak strain response, and the single-tower model has the largest peak strain response. Therefore, the suspended masses and conductor lines reduce the transverse seismic response of the model tower. The effect of tower-line coupling decreases the transverse peak strain response of the tower.Table 10
Transverse peak strain responses of the middle towers of the four models.
Test series
Single-tower model (με)
Single-tower model with suspended lumped masses (με)
Three-tower-two-line model (με)
Five towers and four lines (με)
0.07 g artificial wave
60.648
40.017
58.052
57.997
0.07 g El Centro wave
19.677
17.108
23.169
19.698
0.07 g Taft wave
37.271
30.922
35.836
41.472
0.07 g average
39.199
29.349
39.019
39.722
0.21 g artificial wave
192.680
115.984
147.565
178.187
0.21 g El Centro wave
65.084
62.486
65.149
64.533
0.21 g Taft wave
129.431
88.464
110.259
118.373
0.21 g average
129.065
88.978
107.658
120.364
0.63 g artificial wave
573.068
359.498
410.263
469.876
0.63 g El Centro wave
193.587
174.849
178.199
197.560
0.63 g Taft wave
384.188
253.697
298.134
351.734
0.63 g average
383.614
262.681
295.532
339.723


## 4.1. Dynamic Characteristics Test Results

Figure21 shows the spectral analysis results of the acceleration time-history curve at the midpoint of the middle tower model head in the transverse direction (first-order) and the longitudinal direction (second-order) of the four models. Table 4 compares the basic dynamic characteristics of the middle towers of the four models. The results show that the suspension of the conductor lines and lumped masses decreases the frequency of the middle tower. Compared with the single-tower model, the first-order frequency of the single tower with suspended lumped masses model decreases by 5.08%, and the second-order frequency decreases by 4.03%. The frequencies of the two models with suspended conductor lines are very close. Compared with those of the single-tower model, the first-order frequency of the model with suspended conductor lines decreases by 0.82%, and the second-order frequency decreases by 4.0%. In terms of structural damping, the suspension of clumped masses and conductor lines increase the damping ratio of the structure, with the damping ratio of the three-tower-two-line model reaching a maximum of 2.99%. These results show that there is no significant difference regarding the effect of tower-line coupling for the dynamic characteristics between the three-tower-two-line model and the five-tower-four-line model. The effect of tower-line coupling decreases the frequency of the tower and increases the damping ratio. The single-tower model with suspended lumped masses can simulate the effect of tower-line coupling on the longitudinal dynamic characteristics of the transmission tower well, but this model faces difficulty in satisfactorily simulating the effect of tower-line coupling on the transverse characteristics of the transmission tower.Figure 21
Spectrum analysis curves of the middle towers of the four counterweight models. (a) First-order frequency spectrum analysis curves. (b) Second-order frequency spectrum analysis curves.
(a)
(b)Table 4
Comparison of the basic dynamic characteristics of the middle towers of the four models.
Model
Frequency
Damping ratio
f1 (Hz)
f2 (Hz)
C1 (%)
C2 (%)
Single-tower model
7.202
7.568
0.92
2.40
Single tower with suspended lumped masses
6.836
7.263
1.06
1.18
Three-tower-two-line model
7.143
7.265
2.99
2.58
Five-tower-four-line model
7.143
7.265
2.38
1.65


## 4.2. Comparative Analysis of the Dynamic Results of the Middle Towers from the Shaking Table Tests

(1) Comparative Analysis of the Acceleration Response. Figure 22 shows the longitudinal peak acceleration responses under the unidirectional input of a 0.21 g artificial wave. The results show that the peak acceleration response curves of the tower accelerations of the different models basically coincide, and the trends are similar. The peak acceleration response gradually increases from the base of the tower to the top, reaching the maximum at the top of the tower.Figure 22
Longitudinal peak acceleration responses of the middle tower of the four models under a 0.21 g artificial wave.Table5 shows the longitudinal peak acceleration responses of the middle towers of the four models under each wave. The results show that the peak acceleration response is the largest under the artificial wave and the smallest under the El Centro wave. The model with the suspended lumped mass has the smallest acceleration response. Therefore, the use of a single-tower model with suspended lumped masses to simulate a three-tower-two-line model or a five-tower-four-line model is inaccurate. Except for the 0.63 g test condition, the effect of the tower-line coupling increases the longitudinal peak acceleration response of the tower.Table 5
Longitudinal peak acceleration responses of the middle towers of the four models.
Test series
Single-tower model (m/s2)
Single-tower model with suspended lumped masses (m/s2)
Three-tower-two-line model (m/s2)
Five-tower-four-line model (m/s2)
0.07 g artificial wave
5.966
5.278
5.905
7.310
0.07 g El Centro wave
4.563
4.122
4.456
4.096
0.07 g Taft wave
5.137
4.202
5.961
5.810
0.07 g average
5.222
4.534
5.441
5.739
0.21 g artificial wave
16.738
16.166
18.663
17.921
0.21 g El Centro wave
14.291
11.379
16.815
11.809
0.21 g Taft wave
15.791
13.880
17.458
16.866
0.21 g average
15.607
13.808
17.646
15.532
0.63 g artificial wave
64.671
41.566
46.214
57.260
0.63 g El Centro wave
46.165
36.703
45.403
38.731
0.63 g Taft wave
53.828
41.161
41.546
49.032
0.63 g average
54.888
39.810
44.388
48.341Figure23 shows the transverse peak acceleration response under the unidirectional input of a 0.21 g artificial wave. The results show that except for the single tower with suspended lumped masses model, the peak acceleration response curves of the towers of the other models basically coincide and have similar trends. The comparison shows that the peak accelerations are relatively close within the lower portion of the tower structure, while the peak acceleration responses at the crossarm vary noticeably. The peak acceleration of the single-tower model with suspended lumped masses is the smallest at the crossarm, and the peak acceleration of the single-tower model is the largest at the crossarm.Figure 23
Transverse peak acceleration responses of the four counterweight models under a 0.21 g artificial wave.Table6 shows the transverse peak accelerations of the middle towers of the four models under each wave. The results show that the peak acceleration response is the largest under the artificial wave and is the smallest under the El Centro wave. The model with suspended lumped masses has the lowest peak acceleration response, and the single-tower model with counterweights has the highest peak acceleration response. Therefore, the suspended masses and conductor lines are decreasing the transverse seismic response of the model tower. In comparison, the single tower with suspended lumped masses tested using a single shaking table has the lowest seismic response, so the use of this model to simulate the tower-line system is inaccurate. Under the three seismic conditions of the same seismic intensity level, the average transverse peak acceleration response of the three-tower-two-line model is greater than that of the five-tower-four-line model; the effect of tower-line coupling decreases the transverse peak acceleration response of the tower.Table 6
Vertical peak acceleration responses of the middle towers of the four models.
Test series
Single-tower model (m/s2)
Single-tower model with suspended lumped masses (m/s2)
Three-tower-two-line model (m/s2)
Five-tower-four-line model (m/s2)
0.07 g artificial wave
4.612
2.563
3.662
4.059
0.07 g El Centro wave
1.795
1.192
1.716
1.538
0.07 g Taft wave
3.349
2.236
2.996
2.333
0.07 g average
3.252
1.997
2.791
2.643
0.21 g artificial wave
13.710
7.441
11.511
10.878
0.21 g El Centro wave
5.827
4.911
5.669
4.603
0.21 g Taft wave
10.963
6.676
9.522
7.003
0.21 g average
10.167
6.343
8.901
7.495
0.63 g artificial wave
35.349
21.697
32.248
26.287
0.63 g El Centro wave
17.258
13.433
18.088
13.516
0.63 g Taft wave
29.543
20.806
24.010
20.001
0.63 g average
27.383
18.645
24.782
19.935(2) Comparative Analysis of the Displacement Responses. Figure 24 shows the longitudinal peak displacement responses under the unidirectional input of a 0.21 g artificial wave. The results show that except for that of the single-tower model with suspended lumped masses, the peak displacement response gradually increases from the base of the tower to the top, reaching the maximum peak displacement at the top of the tower.Figure 24
Longitudinal peak displacement responses of the four models under a 0.21 g artificial wave.Table7 shows the longitudinal peak displacements of the main towers of the four models under each wave. The results show that the peak displacement response is the largest under the artificial wave and is the smallest under the El Centro wave. The single-tower model with suspended lumped masses has the maximum displacement response. Under the three test conditions at the same seismic level, the average of the longitudinal peak displacement responses of the three-tower-consistency model is larger than that of the five-tower-consistency model. Except for 0.63 g test condition, the effect of tower-line coupling increases the longitudinal peak displacement response of the tower.Table 7
Longitudinal peak displacement responses of the middle towers of the four models.
Test series
Single-tower model (mm)
Single-tower model with suspended lumped masses (mm)
Three-tower-consistency model (mm)
Five-tower-consistency model (mm)
0.07 g artificial wave
1.737
2.963
2.456
2.021
0.07 g El Centro wave
0.989
0.979
1.389
1.329
0.07 g Taft wave
1.161
1.474
1.149
1.304
0.07 g average
1.296
1.805
1.665
1.551
0.21 g artificial wave
5.936
10.072
7.516
6.681
0.21 g El Centro wave
4.155
6.321
4.876
3.799
0.21 g Taft wave
3.619
5.076
3.710
4.593
0.21 g average
4.570
7.156
5.368
5.024
0.63 g artificial wave
30.041
35.823
27.151
19.555
0.63 g El Centro wave
15.137
22.200
14.378
12.541
0.63 g Taft wave
14.462
15.054
10.921
13.204
0.63 g average
19.880
24.359
17.483
15.100Figure25 shows the transverse peak displacement responses under the unidirectional input of a 0.21 g artificial wave. The results show that the trends of the peak displacement response curves of the towers are similar. The peak displacement response gradually increases from the base of the tower to the top, reaching the largest peak displacement at the top of the tower.Figure 25
Transverse peak displacement responses of the four models under a 0.21 g artificial wave.Table8 shows the transverse peak displacements of the main towers of the four models under each wave. The results show that the peak displacement response is the largest under the artificial wave and is the smallest under the El Centro wave. The single-tower model with suspended lumped masses has the smallest peak displacement response, and the three-tower-two-line model has the largest peak displacement response. Therefore, the use of the single-tower model with suspended lumped masses to simulate the tower-line system is inaccurate. Under the three test conditions at the same seismic level, the average of the transverse peak displacement response of the three-tower-two-line model is larger than that of the five-tower-four-line model; the effect of the three-tower-two-line model’s tower-line coupling increases the transverse peak displacement response of the tower, while the effect of the five-tower-four-line model’s tower-line coupling decreases the transverse peak displacement response of the tower.Table 8
Transverse peak displacement responses of the middle towers of the four models.
Test series
Single-tower model (mm)
Single-tower model with suspended lumped masses (mm)
Three-tower-two-line model (mm)
Five-tower-four-line model (mm)
0.07 g artificial wave
2.134
1.687
3.126
1.848
0.07 g El Centro wave
0.811
0.543
0.720
0.736
0.07 g Taft wave
1.127
0.883
0.824
0.897
0.07 g average
1.357
1.038
1.557
1.161
0.21 g artificial wave
7.258
5.223
9.663
6.032
0.21 g El Centro wave
2.148
2.447
2.514
2.089
0.21 g Taft wave
3.962
2.233
2.976
3.130
0.21 g average
4.456
3.301
5.051
3.750
0.63 g artificial wave
21.152
16.141
26.785
16.364
0.63 g El Centro wave
7.513
7.250
8.162
6.549
0.63 g Taft wave
12.204
7.045
7.768
8.783
0.63 g average
13.623
10.146
14.238
10.565(3) Comparative Analysis of the Strain Responses. Figure 26 shows that for the four models under a 0.21 g unidirectional seismic input, the longitudinal peak strain variation curves of the towers under the crank arms are consistent in both shape and magnitude, and the strain is relatively large at the locations of the tower head, crank arm, and tower legs.Figure 26
Longitudinal peak strain responses of the four models under a 0.21 g artificial wave.Table9 shows the longitudinal peak strain values of the main tower strains of the four models under each wave. The results show that the peak strain response is the largest under the artificial wave and is the smallest under the El Centro wave. The longitudinal peak strains of the main towers of the four models are relatively close under the same wave. Except for the 0.63 g test condition, the effect of tower-line coupling increases the longitudinal peak strain response of the tower.Table 9
Longitudinal peak strain responses of the middle towers of the four models.
Test series
Single-tower model (με)
Single-tower model with suspended lumped masses (με)
Three-tower-two-line model (με)
Five-tower-four-line model (με)
0.07 g artificial wave
53.546
59.655
56.044
56.169
0.07 g El Centro wave
28.017
33.378
33.323
33.819
0.07 g Taft wave
33.187
37.373
33.432
34.995
0.07 g average
38.250
43.469
40.933
41.661
0.21 g artificial wave
148.616
171.750
167.730
150.257
0.21 g El Centro wave
101.668
108.935
129.404
104.848
0.21 g Taft wave
106.910
117.344
111.988
122.553
0.21 g average
119.065
132.677
136.374
125.886
0.63 g artificial wave
450.086
426.452
442.957
513.300
0.63 g El Centro wave
358.235
359.335
394.204
347.420
0.63 g Taft wave
394.345
347.076
306.438
377.690
0.63 g average
400.888
377.621
381.200
412.803Figure27 shows the curves of the transverse peak strain values of the tower body structure for the four models under a 0.21 g unidirectional seismic input. The curves are consistent in shape, with parallel decreasing trends. The largest peak strain occurs in the single-tower model, reaching approximately 200 με, and the smallest peak strain occurs in the single-tower model with suspended lumped masses, which is approximately 1/2 of that of single-tower model without suspended lumped masses.Figure 27
Transverse peak strain responses of the four counterweight models under a 0.21 g artificial wave.Table10 shows the transverse peak strain values of the main tower of the four models under each wave. The results show that the peak strain response is the largest under the artificial wave and the smallest under the El Centro wave. Except for the 0.21-g test condition, the model with suspended lumped masses has the smallest peak strain response, and the single-tower model has the largest peak strain response. Therefore, the suspended masses and conductor lines reduce the transverse seismic response of the model tower. The effect of tower-line coupling decreases the transverse peak strain response of the tower.Table 10
Transverse peak strain responses of the middle towers of the four models.
Test series
Single-tower model (με)
Single-tower model with suspended lumped masses (με)
Three-tower-two-line model (με)
Five towers and four lines (με)
0.07 g artificial wave
60.648
40.017
58.052
57.997
0.07 g El Centro wave
19.677
17.108
23.169
19.698
0.07 g Taft wave
37.271
30.922
35.836
41.472
0.07 g average
39.199
29.349
39.019
39.722
0.21 g artificial wave
192.680
115.984
147.565
178.187
0.21 g El Centro wave
65.084
62.486
65.149
64.533
0.21 g Taft wave
129.431
88.464
110.259
118.373
0.21 g average
129.065
88.978
107.658
120.364
0.63 g artificial wave
573.068
359.498
410.263
469.876
0.63 g El Centro wave
193.587
174.849
178.199
197.560
0.63 g Taft wave
384.188
253.697
298.134
351.734
0.63 g average
383.614
262.681
295.532
339.723


## 5. Conclusions

In this study, three-shaking-table array system tests of UHV cup-type transmission tower-line systems were carried out, and the dynamic characteristics and seismic responses of a single-tower model, a single-tower model with suspended lumped masses, a three-tower-two-line model, and a five-tower-four-line model were studied. The test results demonstrated the following:(1)
The suspended conductor lines and suspended lumped masses reduce the frequency of the middle tower. The single-tower model with suspended lumped masses can simulate the effect of tower-line coupling on the longitudinal dynamic characteristics of the transmission tower well but cannot simulate the transverse dynamic characteristics of the transmission tower. The dynamic characteristics of the three-tower-two-line model are very close to those of the five-tower-four-line model. The effect of tower-line coupling decreased the frequency of the tower but increased the damping ratio.(2)
Under longitudinal ground motion, except for the single-tower model with suspended lumped masses, the peak accelerations and peak displacements of the other models gradually increase from the base of the tower to the top, reaching the highest peak acceleration and peak displacement at the top of the tower. The peak strain curves of the four models below the crank arm are consistent in shape and magnitude, and the strains are relatively large at the tower head, crank arms, and tower legs. The model with suspended lumped masses has the lowest peak acceleration response and the largest peak displacement response. The longitudinal peak strains of the main towers of the four models under waves are relatively close. Except for 0.63 g seismic condition, the effect of tower-line coupling increased the longitudinal peak acceleration, displacement, and strain response of the tower.(3)
Under transverse ground motion, except for the single-tower model with suspended lumped masses, the peak acceleration responses and peak displacements of the other models gradually increase from the base of the tower to the top, reaching the highest peak acceleration and peak displacement values at the top of the tower. The transverse peak strain curves of the tower structure are consistent in shape, with a parallel decreasing trend, and the model with counterweights has the largest peak strain. The model with suspended lumped masses has the smallest transverse peak acceleration responses for acceleration, displacement, and strain, and use of this model to simulate the tower-line system is inaccurate. Under the three seismic conditions of the same seismic intensity level, the effect of tower-line coupling decreases the transverse peak acceleration response of the tower, the effect of the three-tower-two-line model’s tower-line coupling increases the transverse peak displacement response of the tower, while the effect of the five-tower-four-line model’s tower-line coupling decreases the transverse peak displacement response of the tower. Except for 0.21 g seismic condition, the effect of tower-line coupling decreased the transverse peak strain response of the tower.



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*Source: 2350675-2019-12-11.xml*