Abstract
Introduction:
Research on vibration mitigation for transmission towers is critical to enhancing the seismic resilience of power grids and ensuring power supply safety.
Methods:
This study investigates the effectiveness of a vibration isolation trench installed around a tower foundation. The trench is backfilled with a composite material consisting of rubber particles and enzyme-induced carbonate precipitation (EICP)-treated loess. The reliability of a finite element model was first validated against shaking table test results. Subsequently, parametric studies were conducted using numerical simulation to analyze the effects of key design parameters—including trench depth, width, and distance from the foundation—on the seismic response of the tower system.
Results:
The optimized trench effectively reduces the transmission of seismic energy to the foundation-structure system, mitigates soil-structure interaction, and significantly decreases the tower’s acceleration and displacement responses. The isolation performance improves with increasing trench width and depth; however, the enhancement plateaus when the depth exceeds 8 meters. Furthermore, a closer proximity to the foundation combined with a greater trench width leads to more pronounced vibration reduction.
Discussion:
This study provides practical guidance for the seismic design of transmission towers in loess regions.
1 Introduction
In China, transmission towers serve as the backbone supporting the national power grid and are critical lifeline infrastructure with direct relevance to public welfare and economic stability. Their structural safety is essential for the reliable implementation of national strategies such as the West-to-East Power Transmission project, as well as for maintaining normal industrial production and daily life. China is located at the intersection of two major global seismic belts and is therefore prone to frequent earthquakes. As a result, transmission lines often pass through regions of high or moderate seismic intensity. Failure or collapse of transmission towers during earthquakes can lead to widespread power outages and substantial economic losses. It can also severely hinder post-earthquake emergency response, rescue operations, and reconstruction efforts. Consequently, improving the seismic performance of transmission towers is a strategic requirement for ensuring national energy security, public safety, and overall societal resilience. At present, China has established seismic design requirements for power facilities that are more stringent than those for ordinary buildings, as specified in standards such as the Code for Seismic Design of Power Facilities (GB 50260-2013). Advanced seismic design methods, including response spectrum and time-history analyses, have been widely adopted in critical transmission projects, such as ultra-high-voltage lines and key crossing sections. These efforts aim to achieve the performance objectives of “no damage under minor earthquakes, repairable damage under moderate earthquakes, and no collapse under major earthquakes.”
Numerous studies have investigated the seismic design of transmission towers from different perspectives. examined the seismic control performance of tuned mass dampers for transmission towers through scaled shaking table tests and finite element simulations, and identified the key influencing factors. further studied a rotational inertia dual tuned mass damper using theoretical modeling and finite element analysis, demonstrating superior multi-hazard vibration control performance compared with conventional tuned mass dampers. analyzed the effectiveness of friction dampers in reducing the seismic response of transmission tower–line systems and determined the optimal design parameters through theoretical and numerical approaches. performed IDA-based fragility analysis of a transmission tower–line system considering bolt slippage. The study showed that joint slippage markedly influences seismic response and that neglecting it may underestimate failure probability under strong earthquakes. investigated the seismic vibration control of a transmission tower using a pounding tuned mass damper (PTMD) through a detailed ABAQUS finite element model. The results showed that the PTMD provides superior bidirectional vibration mitigation compared with conventional TMD, and its effectiveness is mainly governed by mass ratio and incident angle of ground motions. investigated the seismic vulnerability of transmission towers by considering soil–structure interaction, combining finite element modeling with fragility analysis to identify critical influencing factors. evaluated the seismic performance of particle dampers for transmission tower–line systems using shaking table tests and coupled numerical simulations, and reported better robustness than tuned mass dampers. explored the seismic control effects of nonlinear fluid viscous dampers on tall transmission towers located on flat and sloping ground through finite element analysis and earthquake time-history simulations, and found significant vibration reduction. studied the effectiveness of post-tensioned tendons in improving the near-fault seismic performance of base-isolated monopole transmission towers through numerical simulations and parametric analysis. investigated the critical seismic incidence angle of ultra-high-voltage transmission tower–line systems using scaled shaking table tests and numerical simulations, with prediction errors within 10% for their approximate method. These studies mainly enhance seismic performance by modifying the dynamic characteristics of the structure or by introducing additional energy dissipation devices. Although effective, such approaches still face challenges in practical applications, including device durability, model complexity, and parameter uncertainty. On the other hand, most existing studies do not consider the energy absorption capacity of the foundation soil and its contribution to seismic response reduction of transmission towers. To address this gap, this study focuses on energy dissipation and seismic wave control at the source. A vibration isolation trench is constructed near the tower foundation, and the effects of trench geometry and infill materials on the seismic performance of transmission towers are investigated. The fundamental mechanism of the vibration isolation trench is to form a continuous physical barrier within the foundation soil between the seismic source and the protected structure. This barrier attenuates seismic waves through reflection and scattering, thereby dissipating wave energy and reducing the seismic motion transmitted to the foundation. In addition, the trench mechanism does not rely on the dynamic characteristics of the superstructure, requires no post-installation maintenance, and exhibits excellent durability, which makes it more broadly applicable in engineering practice.
Loess is characterized by a loose structure, low strength, and pronounced collapsibility. Therefore, the construction of transmission towers and vibration isolation trenches in the Loess Plateau requires improvement of the mechanical properties of the foundation soil. Existing seismic treatment techniques for loess foundations based on physical reinforcement (; ; ; ) often cause significant disturbance to the surrounding soil during construction. In contrast, chemical stabilization methods still face several limitations. The long-term stability and environmental effects of lignin-stabilized loess remain unclear (), while the application of steel slag–stabilized loess is still at an early stage, with uncertain performance under complex environmental conditions (). In addition, studies on existing loess stabilizers are often incomplete and inconsistent, with limited experimental data (). Combined stabilizers and in situ tests have also received insufficient attention. Previous studies have shown that rubber–soil mixtures can absorb incident seismic wave energy and reduce vibration-induced damage (; ). Many researchers have investigated the seismic performance of rubber-mixed soils. studied the mechanical behavior of rubber sand using triaxial tests and found that the inclusion of rubber particles significantly improves liquefaction resistance. conducted model tests to evaluate the dynamic protection effect of rubber–soil mixtures with different rubber contents on buried pipelines, and reported optimal performance at rubber contents of 20%–30%. demonstrated that rubber–soil mixtures used as backfill materials can potentially mitigate dynamic damage induced by soil–structure interaction under seismic loading. verified through geotechnical centrifuge tests using the GSI–RSM system that this approach can prevent soil failure and reduce residual deformation, thereby lowering structural seismic demand by 40%–50% and decreasing structural energy dissipation. investigated the shear behavior of loess modified by rubber particles combined with lime and enzyme-induced calcium carbonate precipitation (EICP) through direct shear tests and SEM observations. The study revealed that rubber–lime treatment markedly enhanced cohesion via C–S–H cementation, while rubber–EICP mainly improved the internal friction angle by carbonate interlocking, demonstrating distinct reinforcement mechanisms. investigated the performance of rubber–soil mixtures as foundation isolation layers using three-dimensional finite element simulations, and showed that rubber content and structural properties significantly influence isolation efficiency. However, the inclusion of rubber particles also introduces adverse effects (). reported that increasing rubber content leads to a reduction in overall soil stiffness. found through resonant column and cyclic torsional shear tests that higher rubber contents increase soil damping but reduce sand strength. Further studies have shown that the combined use of rubber particles and enzyme-induced calcium carbonate precipitation (EICP) can enhance the strength and stiffness of treated loess while effectively improving its energy dissipation capacity ().
The existing research indicates that the addition of rubber particles can effectively enhance the seismic performance of the soil, while the EICP technology can fill the gaps between the particles, thereby improving the soil’s strength and stiffness (). Therefore, this study employs a composite of rubber particles and EICP-treated loess as a damping material to construct isolation trench trenches around a transmission tower. Using shake table tests and numerical simulation—a methodology validated for seismic soil-structure interaction analysis ()—the research investigates the tower’s inter-story displacement and top acceleration responses when trenches of different dimensions are installed (). A detailed investigation was conducted on how the damping performance of the trenches is influenced by key parameters, including their depth, width, and distance from the tower foundation.
2 Test overview
2.1 Shaking table test setup
This study focuses on the drum-type transmission tower, which is the most widely used tower type in loess regions. The analysis is based on the State Grid standardized design model 5E2-SZC3-500 kV double-circuit drum-type tower. The prototype tower has a height of 27 m. The main members are made of Q420 steel tubes, while the bracing and secondary members are made of Q235 steel tubes. The original site of the structure has a seismic fortification intensity of 8° (0.2 g), belongs to the second seismic design group, and is classified as Site Class II. The shaking table tests were conducted using an SZ/ZD-LD electromagnetic shaking table. The main technical specifications are listed in Table 1. The maximum payload of the table is 100 kg, and the maximum achievable acceleration is 20 g. The table can generate sinusoidal excitations in the longitudinal, transverse, and vertical directions. Physical modeling using shaking table tests has been widely recognized as an effective approach for investigating soil-structure interaction under seismic conditions (). The experimental apparatus and the tower model are shown in Figure 1a. A scaled transmission tower model was designed based on geometric similarity, and the acceleration similarity ratio was kept equal to unity. The similarity relationships of the remaining physical quantities were derived according to the Buckingham π theorem [5]. To simulate semi-infinite foundation conditions and radiation damping more realistically, polystyrene foam boards were installed along the inner walls of the rigid model container as flexible boundary layers.
TABLE 1
| No. | Physical quantity | Performance parameter |
|---|---|---|
| 1 | Maximum test load | 100 kg |
| 2 | Frequency range | 1 Hz–600 Hz |
| 3 | Amplitude | 0-5 mm |
| 4 | Maximum acceleration | 20 g |
| 5 | Vibration direction | Vertical, horizontal, and fore-aft |
| 6 | Table size | 750 mm × 750 mm |
| 7 | Vibration waveform | Sine wave |
Technical specifications of SZ/ZD-LD electromagnetic shaking table.
FIGURE 1
To evaluate the boundary effects of the model container, acceleration sensors A11 and A12 were installed at the locations shown in Figure 1b. The acceleration time histories of the two sensors under sinusoidal excitation are presented in Figure 2. The results show good agreement between the two curves, with consistent waveform characteristics. In addition, the ratio of the peak accelerations remains stable at approximately 1. These results indicate that the boundary reflection effects of the model container are effectively controlled and that the test setup satisfies the experimental requirements.
FIGURE 2
2.2 Shaking table test results
Owing to the limitations of the available model container, bidirectional or three-dimensional seismic excitation could not be applied. Moreover, as the primary objective of this study is to investigate the vibration mitigation performance of a vibration isolation trench filled with rubber particles and EICP-treated loess, the experiments were conducted under unidirectional seismic loading only. First, low-amplitude broadband white noise excitation was applied to the model to identify the dynamic characteristics of the tower–soil system and to verify the operational status of the sensors. Subsequently, sinusoidal sweep tests with constant amplitude were performed. The natural frequencies of the transmission tower model were determined by identifying resonance peaks in the response amplitude–frequency curves. To effectively monitor the evolution of structural dynamic properties, white noise scans were conducted before and after the tests, as well as at key loading stages. Changes in dynamic response characteristics were analyzed based on the variations in natural frequency and damping ratio. An acceleration sensor was installed at the top of the transmission tower model to measure the absolute acceleration response, with a sampling frequency of 1,000 Hz. A sinusoidal excitation with an amplitude of 0.005 g was applied to the shaking table, with the frequency continuously swept from 0.5 Hz to 20 Hz. The acceleration response at the tower top was recorded in real time. The power spectral density of the tower-top acceleration time history was obtained from the sinusoidal sweep tests, as shown in Figure 3. The first three natural frequencies of the transmission tower model were identified as 1.4087 Hz, 5.7362 Hz, and 11.0562 Hz, respectively.
FIGURE 3
Compared with natural earthquake ground motions, sinusoidal excitations with the same intensity can induce larger structural deformations. Therefore, sinusoidal waves were adopted as dynamic loads in the model tests to obtain more pronounced dynamic responses of the superstructure under different test conditions. Based on the identified natural frequencies of the transmission tower model, the excitation frequencies were approximately set to 1.4 Hz and 5.7 Hz, with an acceleration amplitude of 0.2 g. The loading results are presented in Figures 4, 5.
FIGURE 4
FIGURE 5
3 Validation of the finite element model
3.1 Numerical model setup
A finite element model corresponding to the shaking table test model was established in ABAQUS: beam elements were adopted for the main members and diagonal members of the upper tower structure, while truss elements were used for the secondary members. A pile foundation was adopted for the transmission tower, of which the material was C40 concrete. The longitudinal reinforcement was made of HRB400 steel bars, and the stirrups were made of HRB300 steel bars. The foundation soil was defined as loess ground, with the detailed material parameters listed in Table 2. The geostatic step and dynamic implicit step were employed for the analysis. A tie constraint was applied between the tower foundation and the ground, and then a surface-to-surface contact was defined on their contact interface. The normal contact behavior was set as hard contact, while the tangential contact behavior was governed by the penalty friction formulation with a friction coefficient of 0.3. To simulate the absorption and scattering of seismic waves by the soil under the condition of a semi-infinite medium, a viscoelastic artificial boundary was set at the foundation boundary (). The dynamic load was applied to the bottom of the soil mass, and the constraints in the corresponding directions were removed simultaneously. Since the primary focus was on the seismic mitigation effect of the improved loess isolation trench on the transmission tower, the transmission line load was simplified as a concentrated mass point acting on the corresponding position of the tower head in the model.
TABLE 2
| Material | Density/(kg/m3) | Young’s modulus (E)/MPa | Damping ratio | Damping ratio |
|---|---|---|---|---|
| 40 MPa concrete | 2,500 | 32,500 | 0.05 | 0.2 |
| Steel section | 7,850 | 2.06 × 105 | 0.04 | 0.3 |
| Foundation soil | 1960 | 109.87 | 0.26 | 0.05 |
Material parameters.
The mesh generation result is shown in Figure 6. In this model, local mesh refinement was applied to the soil region surrounding the pile foundation and along the pile shaft. This approach follows established practices in geotechnical finite element analysis, where finer elements are used in key areas to capture stress concentrations while maintaining computational efficiency. Similar strategies have been widely adopted in pile-soil interaction studies to balance accuracy and computational cost (). The mesh generation result is shown in Figure 6.
FIGURE 6
3.2 Comparison between shaking table test results and finite element model results
To validate the reliability of the finite element model, a comparative approach was adopted using the shaking table test results as a benchmark. First, modal analysis was performed on the numerical model to extract the natural frequencies of the transmission tower, which were then compared with the experimental values obtained from white noise sweeps. Subsequently, time-history analyses were conducted under sinusoidal excitations at frequencies corresponding to the identified natural modes. The acceleration and displacement responses at the tower top were compared with the shaking table test measurements. Quantitative evaluation was carried out using the root mean square (RMS) error to assess the overall agreement in response amplitude and waveform characteristics (). This validation framework ensures that the numerical model accurately captures both the dynamic characteristics and the seismic response behavior of the transmission tower-soil system.
3.2.1 Comparison of dynamic characteristics
The modal analysis results of the transmission tower, as summarized in Table 3, indicate that the errors between the first three dynamic characteristics obtained from the finite element model and the experimental measurements are within 5%. This agreement confirms that the numerical model can accurately represent the actual dynamic behavior of the structure.
TABLE 3
| Modal | Experiment/Hz | Simulation/Hz | Error/(%) |
|---|---|---|---|
| The first order | 1.4087 | 1.4164 | −0.54 |
| The second order | 5.7362 | 5.6955 | 0.71 |
| The third order | 11.0652 | 10.929 | 1.24 |
Comparison of natural frequencies for the transmission tower.
The first two vibration modes of the transmission tower are illustrated in Figure 7. The first-order mode is characterized by the first-order bending in the X-direction, where the entire structure sways along the X-direction with an obvious bending component. The second-order mode is characterized by the second-order bending in the X-direction, where an inflection point occurs in the structure along the X-direction, resulting in a more complex bending configuration.
FIGURE 7
3.2.2 Comparison of time-history analysis results for tower-top acceleration
To quantitatively evaluate the agreement between the shaking table test results and numerical simulation results, the Root Mean Square (RMS) of acceleration was adopted as the comparison index. It can objectively characterize the overall vibration energy level through mathematical calculation and thus quickly and effectively evaluate the overall response level of the model. The RMS of acceleration obtained from the shaking table test and numerical simulation under sine wave excitation is presented in Table 4. It can be observed that the error between the numerical simulation results and the test results is within 5%, indicating a good agreement between them.
TABLE 4
| Control scheme | Experiment/(m·s−2) | Simulation/(m·s−2) | Error/(%) |
|---|---|---|---|
| 1.4 Hz | 4.6732 | 4.6098 | 1.3 |
| 5.7 Hz | 0.3826 | 0.3719 | 2.7 |
Comparison of RMS acceleration.
Under sine wave excitation at 1.4 Hz and 5.7 Hz, the tower-top acceleration time-history and displacement time-history curves obtained from the shaking table test and ABAQUS finite element simulation are illustrated in Figures 8, 9. The two sets of results show good agreement in terms of the overall fluctuation trend, vibration frequency, and peak response, with errors within an acceptable range. This verifies the effectiveness of the finite element model in simulating the dynamic behavior of the structure under sine wave excitation. However, the response deviations observed at certain time points are caused by a combination of multiple factors, including test system errors, material discreteness, and non-idealities in the loading waveform. The simulation accuracy can be further improved in subsequent studies by optimizing test precision, refining the damping and constitutive assumptions of the model, and other such measures.
FIGURE 8
FIGURE 9
4 Analysis of the influence of damping trench design parameters on the vibration reduction performance of transmission towers
4.1 Model construction
Based on the results of numerical simulation and shaking table tests, the finite element simulation model established in ABAQUS can accurately reflect the dynamic response of the transmission tower under dynamic loads, with the error within an acceptable range. Due to the limitations of test conditions, the numerical simulation approach is adopted to investigate the seismic mitigation effects of design parameters for loess vibration-damping trenches improved by rubber particles combined with EICP on the transmission tower. In the numerical model, the rubber particle-EICP composite was treated as a homogeneous continuum with equivalent macroscopic material properties. The particle size of the rubber was selected as 0–1 mm, with a content of 7% (). The density of the composite was 1,460 kg/m3, the elastic modulus was 128.38 MPa as determined from laboratory tests on the composite material, and Poisson’s ratio was 0.3. These parameters were directly assigned to the trench region in the finite element model to represent the integrated mechanical behavior of the composite. It should be noted that the individual contributions of rubber particles and EICP to vibration mitigation were not distinguished in the numerical framework; rather, the composite was considered as a unified damping material whose overall isolation performance was evaluated through parametric analysis of trench geometry. The underlying energy dissipation and stiffening mechanisms, attributed respectively to rubber deformation and EICP cementation, are discussed based on experimental observations and existing literature. A 1:1 scale model of the 5E2-SZC3 500 kV double-circuit drum-type transmission tower is established in ABAQUS. Its nominal height is 48 m, the base dimensions are 14.75 m × 14.75 m, the foundation embedment depth is 13 m, the pile length is 10 m, and the pile diameter is 1.2 m. The spatial configuration of the pile–soil–structure–isolation trench system is shown in Figure 10. The piles are embedded in the soil, and the transmission tower structure is supported on the pile foundation. The isolation trench is arranged in the soil area adjacent to the pile foundation.
FIGURE 10
4.2 Loading regime
To systematically investigate the influence of design parameters of damping trenches filled with rubber particles combined with EICP-modified loess on the seismic mitigation performance of transmission towers, the depth, width, and distance from the pile foundation of the damping trench are selected as the key variables. Numerical simulation analysis is carried out. The specific design of each working condition is shown in Table 5. Among them, h, b, and s represent the optimal depth, optimal width, and optimal distance from the pile foundation of the damping trench in the listed working conditions, respectively. In the numerical simulation, the El Centro 1940 NS seismic wave was adopted as the input load, and, moreover, in accordance with the requirements of seismic fortification intensity eight in Xi’an, its peak ground acceleration (PGA) was scaled to 0.2 g. Given that the primary objective of this parametric study is to evaluate the influence of trench geometry (depth, width, and distance) on vibration mitigation performance, the El Centro 1940 NS wave scaled to 0.2 g was selected as a representative seismic input. This approach minimizes the number of variables and allows for a clearer assessment of the geometric effects. Moreover, the dominant frequencies of this wave (1–8 Hz) encompass the first two natural frequencies of the transmission tower (1.42 Hz and 5.70 Hz), rendering it particularly suitable for evaluating the isolation efficiency under near-resonance conditions. The acceleration time-history curve and Fourier spectrum of this seismic wave are shown in Figure 11.
TABLE 5
| Control scheme | Depth/m | Width/m | Distance/m | Optimal |
|---|---|---|---|---|
| H-1 | 4 | 1 | 2 | h |
| H-2 | 6 | 1 | 2 | |
| H-3 | 8 | 1 | 2 | |
| H-4 | 10 | 1 | 2 | |
| H-5 | 12 | 1 | 2 | |
| B-1 | h | 0.6 | 2 | b |
| B-2 | h | 0.8 | 2 | |
| B-3 | h | 1.0 | 2 | |
| B-4 | h | 1.2 | 2 | |
| S-2 | h | b | 2 | s |
| S-3 | h | b | 3 | |
| S-4 | h | b | 4 |
Working condition table.
FIGURE 11
It can be seen from the Fourier spectrum analysis that the seismic energy is mainly concentrated in the frequency band of 1–8 Hz. This frequency range covers the first and second natural frequencies of the transmission tower. This indicates that the seismic excitation is prone to inducing structural resonance, thereby enabling a more effective evaluation of the isolation effect of the damping trench.
4.3 Results and analysis of finite element simulation
4.3.1 Seismic response of transmission towers with varying trench depths
To investigate the regulatory mechanism of damping trench depth on the seismic dynamic response of transmission towers, the acceleration and displacement responses of the transmission tower under different damping trench depths (denoted H-1 to H-6) and without damping trench (denoted H-0) were obtained via numerical simulation, and the results are shown in Figures 12, 13. It can be seen from Figure 12 that the relationship between damping trench depth and the maximum floor absolute acceleration of the tower exhibits obvious nonlinear characteristics: as the depth increases from 4 m to 8 m, the damping trench’s capacity for seismic wave reflection, diffraction, and seismic energy absorption gradually enhances. The acceleration response of the tower decreases continuously. When the trench depth exceeds 8 m, the isolation effect plateaus because the trench has already intercepted the primary wave propagation path. Beyond this depth, seismic waves are naturally attenuated by geometric and material damping, yielding diminishing returns. This threshold depends on site-specific soil properties (e.g., shear wave velocity and impedance contrast) and the dominant frequency of the input motion. Therefore, the optimal depth should be determined based on actual site and seismic conditions. Figure 13 shows the variation trend of the maximum relative displacement of each floor of the tower under different trench depths, which is consistent with the law of acceleration response on the whole.
FIGURE 12
FIGURE 13
4.3.2 Seismic response of transmission towers with different trench widths
Five width gradients 0 m (no trench, denoted as B-0), 0.6 m (B-1), 0.8 m (B-2), 1.0 m (B-3), and 1.2 m (B-4) are set to analyze the influence of damping trench width on the dynamic response of the tower. The results are shown in Figures 14, 15. With the increase in damping trench width, the maximum floor absolute acceleration and relative displacement of the tower decrease gradually: compared with the case without a damping trench, the dynamic response of the tower is significantly reduced after the damping trench is installed; furthermore, as the width increases from 0.6 m to 1.2 m, the acceleration response of the tower and the maximum relative displacement of each floor decrease continuously. This is mainly attributed to the seismic mitigation mechanism of the damping trench filled with loess improved by rubber particles combined with EICP: on the one hand, it can reflect and diffract seismic waves; on the other hand, it can absorb the energy of seismic waves through the deformation of rubber particles. With the increase in the width of the damping trench, its capacity to absorb seismic wave energy is further enhanced, thereby reducing the seismic response more effectively.
FIGURE 14
FIGURE 15
4.3.3 Seismic performance of transmission towers at different trench–tower distances
To investigate the effect of damping trench layout positions, three working conditions 2 m (S-2), 3 m (S-3), and 4 m (S-4) from the tower foundation and the non-trench condition (S-0) were selected. The maximum absolute acceleration responses of floors 1 to 20 of the tower under each condition were analyzed, and the results are shown in Figure 16. The study finds that the installation of damping trenches can effectively reduce the acceleration response of transmission towers under seismic action, and the seismic mitigation effect is closely related to the distance between the trenches and the tower foundation. Overall, the greater the layout distance of the damping trench, the weaker its seismic mitigation effect on the tower. Specifically, when the damping trench is 2 m away from the foundation, the peak acceleration of each floor of the tower reaches the minimum value, which is significantly lower than that of the non-trench S-0 condition. As the layout distance increases to 3 m (S-3) and 4 m (S-4), the acceleration response values increase successively, yet they are still generally lower than those under the S-0 condition. This clearly indicates that the seismic mitigation effect gradually weakens with the increase in layout distance. This is because damping trenches weaken the seismic ground motion input by reflecting and scattering seismic waves, as well as dissipating energy through the deformation of their own materials. When the damping trench is close to the tower foundation, it can more effectively intercept and dissipate seismic waves before they propagate to the foundation, thereby reducing the seismic energy transmitted to the superstructure to a greater extent.
FIGURE 16
4.3.4 Tower-top peak acceleration and relative displacement under different trench geometries
The influences of different depths (H) and widths (B) of damping trenches on the maximum absolute acceleration and maximum relative displacement of the tower top are shown in Figures 17, 18. The results show that with the increase in trench depth or width, both the maximum absolute acceleration and maximum relative displacement of the tower top exhibit a continuous attenuation trend. When the depth of the damping trench is in the range of 8–12 m, the decreasing trend of the tower top acceleration and displacement tends to flatten out; whereas with the increase in the width of the damping trench, the tower top response continues to attenuate, and the attenuation rate increases to some extent. This is mainly attributed to the fact that the increase in trench depth and width enhances the reflection, diffraction and energy absorption of seismic waves; meanwhile, it strengthens the frictional energy dissipation effect between granular materials and extends the propagation and dissipation path of vibration energy, thereby effectively weakening the transmission of seismic energy to the tower top. In addition, the time instant corresponding to the maximum tower-top acceleration under the condition without a damping trench is taken as the reference. The Von Mises stress contours of the tower for different trench depths (H-0 to H-5) at this time instant are presented in Figure 19. The results show that increasing the trench depth leads to a reduction in stress concentration at the tower legs, accompanied by a decrease in the maximum equivalent stress. These results are consistent with those obtained in the previous analysis.
FIGURE 17
FIGURE 18
FIGURE 19
In engineering design, it is necessary to determine the optimal dimensions of damping trenches through parameter optimization (e.g., within the range of 8–10 m for depth and 1.0–1.2 m for width) by combining site conditions, so as to achieve efficient control of the dynamic response of tower tops.
4.3.5 Evaluation of vibration mitigation provided by damping trenches
4.3.5.1 Analysis of hysteresis curves and equivalent viscous damping coefficient
Based on the comparative test results, the optimal vibration damping effect for the transmission tower is achieved with a damping trench configuration of 8 m in depth, 1 m in width, and 2 m in distance from the foundation. The base shear force versus tower-top displacement hysteresis curves were compared for this optimal case and the case without a trench. This analysis aims to investigate the influence of the damping trench on the tower’s dynamic response and energy dissipation capacity. The results are shown in Figure 20 (). The results indicate that the dynamic response of the tower is significantly reduced after installing the damping trench. Compared to the condition without a trench, the maximum tower-top displacement decreases from 115.53 mm to 91.47 mm, representing a reduction of approximately 20.8%. The maximum base shear force decreases from 123.86 kN to 91.83 kN, a reduction of about 25.9%. These results demonstrate the trench’s effective vibration mitigation performance. The Equivalent Viscous Damping Coefficient describes the equivalent viscous damping characteristics related to energy dissipation of a structure during vibration. It can be calculated using Equation 1:where is the energy dissipated per hysteresis cycle, and is the equivalent elastic strain energy.
FIGURE 20
In terms of hysteresis characteristics, the hysteresis curve under the condition without a damping trench is relatively full, with a larger loop area, as shown in Figure 20a. The corresponding equivalent viscous damping ratio is approximately 10.4%. After installing the damping trench, the hysteresis curve becomes noticeably narrower and the loop area decreases, as shown in Figure 20b. The equivalent viscous damping ratio drops to 3.4%. These results indicate that the damping trench can effectively control the dynamic deformation and internal force response of the transmission tower. This is achieved by weakening the transfer of dynamic loads to the foundation and superstructure, thereby reducing the overall structural response level.
4.3.5.2 Analysis of acceleration amplification factor
Following the aforementioned analysis of hysteresis characteristics, the acceleration amplification factor is introduced as an evaluation metric to further investigate the acceleration response characteristics of the transmission tower before and after the installation of the damping trench (). The acceleration amplification factor is defined as the ratio of the maximum tower-top acceleration to the peak ground surface input acceleration. The ground surface acceleration (shown in Figures 21, 22) is obtained from a free-field location unaffected by the structure. The acceleration amplification factor can be calculated using Equation 2:where is the tower-top maximum acceleration, and is the peak free-field ground surface input acceleration.
FIGURE 21
FIGURE 22
The calculation yields values of = 2.3706 and = 1.5143. The installation of the damping trench reduces the acceleration amplification factor by approximately 36%. This result indicates that the trench effectively reduces the transmission of seismic waves to the tower foundation and superstructure. It thereby suppresses the dynamic response amplification of the tower and improves its seismic performance.
5 Conclusion
Through shaking table tests and numerical simulations, this study systematically investigates the enhancement effect of damping trenches filled with rubber particle-reinforced EICP-modified loess on the seismic performance of transmission tower systems, with a focus on analyzing the influence of three key design parameters: trench depth, width, and layout distance. The main research conclusions are as follows.
The arrangement of damping trenches filled with rubber particle-reinforced EICP-modified loess around the tower foundation can reduce the peak acceleration of the tower top and the interlayer displacement of the tower under seismic action. Its seismic mitigation mechanism can be attributed to three aspects: the reflection and scattering of incident seismic waves, the energy absorption capacity brought by the deformation of rubber particles, and the enhancement of the integrity of trench materials by the cementation effect of EICP, which jointly weaken the seismic energy transmitted to the structure.
The depth of the damping trench has a significant nonlinear effect on the seismic mitigation performance. Within the range of working conditions studied, the mitigation effect improves with the increase of trench depth and reaches the optimum at a depth of 8 m (Case H-3). Therefore, there exists an optimal depth range in engineering applications, which is recommended to be determined according to specific project conditions.
The seismic mitigation efficiency of damping trenches increases continuously with the expansion of their width. When the width increases from 0.6 m to 1.2 m, the dynamic response of transmission towers shows a monotonically decreasing trend, as wider trenches can dissipate seismic wave energy more effectively. If feasible, it is recommended to adopt a relatively large width (e.g., 1.0–1.2 m) to achieve a better seismic mitigation effect.
The layout position of damping trenches is crucial to the exertion of their efficiency. Studies have shown that the closer the damping trench is to the foundation, the more significant the seismic mitigation effect will be. When the distance is 2 m (Case S-2), the isolation and dissipation of seismic excitation are most effective. As the distance increases to 3 m and 4 m, the seismic mitigation effect weakens significantly. Therefore, while ensuring the requirements of construction and stability, the damping trench should be arranged as close to the transmission tower foundation as possible.
The hysteresis analysis demonstrates that the damping trench reduces both the seismic energy input into the foundation-structure system and the soil-structure interaction, thereby effectively mitigating the seismic response. This finding is corroborated by the observed decrease in the acceleration amplification factor.
Compared with conventional measures such as pile reinforcement and base isolation, the proposed isolation trench provides a complementary wave-barrier mechanism that mitigates seismic energy at its propagation path. It achieves notable reductions in structural response—20.8% in tower-top displacement and 25.9% in base shear—while offering advantages in durability, ease of construction, and retrofitting suitability. Although this study focuses on a drum-type transmission tower in loess regions, the underlying vibration mitigation mechanism is largely independent of superstructure configuration, as the trench functions by reflecting, scattering, and absorbing seismic waves at the foundation level. Therefore, the observed performance trends are expected to apply to other tower types and soil conditions, though optimal trench dimensions may require adjustment based on site-specific characteristics. By integrating flexible energy dissipation from rubber particles with chemical cementation via EICP, the trench material exhibits both high damping and adequate stiffness, presenting an environmentally friendly and effective solution for enhancing seismic resilience of lifeline infrastructure.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
LeL: Writing – original draft, Investigation, Conceptualization, Methodology, Resources, Project administration, Formal Analysis. YX: Writing – original draft, Formal Analysis, Software, Funding acquisition, Resources, Methodology, Data curation, Validation, Writing – review and editing. LvL: Writing – original draft, Data curation, Investigation, Software. XC: Formal Analysis, Investigation, Writing – review and editing, Software. YZ: Writing – review and editing, Methodology, Project administration, Supervision, Conceptualization, Funding acquisition, Resources. NX: Investigation, Supervision, Writing – review and editing. SC: Writing – review and editing, Methodology, Funding acquisition.
Funding
The author(s) declared that financial support was received for this work and/or its publication. The work described in this paper was funded by the Shaanxi Province Key Research and Development Plan Project (No. 2025SF-YBXM-539) and Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No. 20230118).
Conflict of interest
Authors LeL, LvL, YZ, and NX were employed by State Grid Hubei Electric Power Co, Ltd. Author XC was employed by State Grid Hubei Electric Power Co, Ltd. Huangshi Power Supply Company.
The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
1
AbbasS.FatimaA.KazmiS. M. S.MunirM. J.AliS.RizviM. A. (2022). Effect of particle sizes and dosages of rubber waste on the mechanical properties of rubberized concrete composite. Appl. Sci.12, 8460. 10.3390/app12178460
2
AnQ.ZhangQ.ZhangX.ZhangJ. (2021). Bridging the gap between engineering properties and grouting reinforcement mechanisms for loess in eastern China: taking jinan loess as an example. Bull. Eng. Geol. Environ.80, 4125–4141. 10.1007/s10064-021-02201-w
3
ArgyroudisS.PalaiochorinouA.MitoulisS.PitilakisD. (2016). Use of rubberised backfills for improving the seismic response of integral abutment bridges. Bull. Earthq. Eng.14, 3573–3590. 10.1007/s10518-016-0018-1
4
AtashfarazB.TaiyariF.RaadH. H.FormisanoA. (2021). Post-tensioned tendons for enhancing the seismic behaviour of base-isolated monopole transmission towers. Eng. Struct.247, 113222. 10.1016/j.engstruct.2021.113222
5
BiswasR.KonarT.GhoshA. D. (2025). Nonlinear fluid viscous dampers for seismic vibration control of tall transmission towers on flat and sloped ground. J. Constr. Steel Res.232, 109634. 10.1016/j.jcsr.2025.109634
6
ChaiS.LiX.LiT.LiuJ.QuanD.FanZ. (2024). Experimental study on dynamic properties of loess improved by rubber particles and EICP technology. Adv. Eng. Sci.56, 134–146. 10.15961/j.jsuese.202300961
7
ChenB.WengS.ZhiL.LiD. (2017). Response control of a large transmission tower-line system under seismic excitations using friction dampers. Adv. Struct. Eng.20, 1155–1173. 10.1177/1369433216679999
8
ChenY.ChaiS.CaiD.WangW.LiX.LiuJ. (2023). Experimental study on shear mechanical properties of improved loess based on rubber particle incorporation and EICP technology. Front. Earth Sci.11, 1270102. 10.3389/feart.2023.1270102
9
DingY.ZhangJ.ChenX.WangX.JiaY. (2021). Experimental investigation on static and dynamic characteristics of granulated rubber-sand mixtures as a new railway subgrade filler. Constr. Build. Mater.273, 121955. 10.1016/j.conbuildmat.2020.121955
10
DushimimanaA.DushimimanaC.MbereyahoL.NiyonsengaA. A. (2023). Effects of building height and seismic load on the optimal performance of base isolation system. Arab. J. Sci. Eng.48, 13283–13302. 10.1007/s13369-023-07660-9
11
GhassemiS.EkraminiaS. S.Hajialilue-BonabM.TohidvandH. R.AzarafzaM.DerakhshaniR. (2025). Innovative insights into micropile seismic response: shaking table tests reveal critical dependencies and liquefaction mitigation. Bull. Eng. Geol. Environ.84, 206. 10.1007/s10064-025-04225-y
12
HouY.LiP.WangJ. (2021). Review of chemical stabilizing agents for improving the physical and mechanical properties of loess. Bull. Eng. Geol. Environ.80, 9201–9215. 10.1007/s10064-021-02486-x
13
HouJ.LuY.WangJ.YuK. (2023). Calculation model of compaction coefficient of soil among SP−PSC pile group on collapsible loess foundation. Appl. Sci.13, 4003. 10.3390/app13064003
14
JeonB.-G.ChangS.-J.KimS.-W.ParkD.-U.ChunN. (2024). Experimental study on the acceleration amplification ratio of cable terminations for electric power facilities. Energies17, 5641. 10.3390/en17225641
15
LeeC.TruongQ. H.LeeW.LeeJ.-S. (2010). Characteristics of rubber-sand particle mixtures according to size ratio. J. Mater. Civ. Eng.22, 323–331. 10.1061/(ASCE)MT.1943-5533.0000027
16
LiX.WangX.DiaoH.ZhangH.ZhuC. (2023). Influence of depth and position of vibration-isolating slot on damping effect of blasting vibration. Shock Vib.2023, 1–11. 10.1155/2023/8492360
17
LiJ.-X.ZhangC.ChengJ.-P. (2024). Seismic fragility analysis of the transmission tower-line system considering bolt slippage. Appl. Sci.14, 10909. 10.3390/app142310909
18
LuS.LinG.WangZ.MaY.ZhaoH. (2024). A numerical research on dynamic interaction of the rubber soil foundation and structure. KSCE J. Civ. Eng.28, 5647–5664. 10.1007/s12205-024-0086-8
19
LuZ.ShenY.ZhouM.RongK.TianL. (2025). Experimental and numerical study on the seismic mitigation performance of particle dampers on transmission tower-line system. Soil Dyn. Earthq. Eng.195, 109394. 10.1016/j.soildyn.2025.109394
20
MaY.HeX.GuanY.FanD.GaoR.LuoF.et al (2025). Sensitivity analysis of foundation soil physical–mechanical properties on pile foundation stability. Buildings15, 4001. 10.3390/buildings15214001
21
NiW.NieY.LüX.FanM. (2024). Mechanical behavior and microstructure evolution of malan loess under dynamic compaction. Environ. Earth Sci.83, 76. 10.1007/s12665-023-11361-9
22
OkurD. V.UmuS. U. (2018). Dynamic properties of clean sand modified with granulated rubber. Adv. Civ. Eng.2018, 5209494. 10.1155/2018/5209494
23
PanH.LiC.TianL. (2021). Seismic fragility analysis of transmission towers considering effects of soil-structure interaction and depth-varying ground motion inputs. Bull. Earthq. Eng.19, 4311–4337. 10.1007/s10518-021-01124-x
24
PistolasG. A.PitilakisK.AnastasiadisA. (2020). A numerical investigation on the seismic isolation potential of rubber/soil mixtures. Earthq. Eng. Eng. Vib.19, 683–704. 10.1007/s11803-020-0589-3
25
TianL.RongK.ZhangP.LiuY. (2017). Vibration control of a power transmission tower with pounding tuned mass damper under multi-component seismic excitations. Appl. Sci.7, 477. 10.3390/app7050477
26
TianL.DongX.PanH.GaoG.XinA. (2020). Critical seismic incidence angle of transmission tower based on shaking table tests. Struct. Eng. Mech.76, 251–267. 10.12989/SEM.2020.76.2.251
27
TsangH. (2008). Seismic isolation by rubber–soil mixtures for developing countries. Earthq. Engng Struct. Dyn.37, 283–303. 10.1002/eqe.756
28
TsangH.LoS. H.XuX.Neaz SheikhM. (2012). Seismic isolation for low‐to‐medium‐rise buildings using granulated rubber–soil mixtures: numerical study. Earthq. Engng Struct. Dyn.41, 2009–2024. 10.1002/eqe.2171
29
TsangH.TranD.HungW.PitilakisK.GadE. F. (2021). Performance of geotechnical seismic isolation system using rubber‐soil mixtures in centrifuge testing. Earthq. Engng Struct. Dyn.50, 1271–1289. 10.1002/eqe.3398
30
VidaN.MasoudH. B. (2024). Seismic response analysis of tunnels using a coupled polygonal finite element method. Civ. Geoengin. Lett., 1(1), e100009. 10.22034/CGEL.1.1.e100009
31
WangZ.BaiZ.LuW.WuX.YinY.LiD. (2025). Experimental study on the dynamic response of lignin-modified loess under traffic vibration and seepage wetting. Case Stud. Constr. Mater.22, e04419. 10.1016/j.cscm.2025.e04419
32
WuH.WuM.WuX.ZhangF.ZhangJ.QiaoH.et al (2024). Study on the performance of collapsible loess subgrade improved by steel slag. J. Build. Eng.84, 108642. 10.1016/j.jobe.2024.108642
33
XieZ.LiuX.XiongT.ZhouY.ChaiS. (2026). Experimental study on the shear mechanical properties of loess modified by rubber particles combined with cementing material. Appl. Sci.16, 697. 10.3390/app16020697
34
XuX.YanX. (2024). Experiment on MICP-Solidified calcareous sand with different rubber particle contents and sizes. Front. Mater.11, 1425653. 10.3389/fmats.2024.1425653
35
ZengC.ZhangZ.SuN. (2025). Enhanced vibration control on transmission towers with rotational inertial double tuned mass dampers for seismic and wind hazards. Structures73, 108326. 10.1016/j.istruc.2025.108326
36
ZhangF.DongJ.YangX.LianB.WangX. (2021). Study on the hydro‐thermal‐mechanical characteristics of the lime‐soil compaction pile in the forming process. Adv. Mater. Sci. Eng.2021, 7701423. 10.1155/2021/7701423
37
ZhaoB.WuD.LuZ. (2021). Shaking table test and numerical simulation of the vibration control performance of a tuned mass damper on a transmission tower. Struct. Infrastructure Eng.17, 1110–1124. 10.1080/15732479.2020.1800755
38
ZhouE.CuiL.ZuoX.WangL. (2023). Dynamic behaviour of pipe protected by rubber–soil mixtures. Geosynth. Int.30, 285–295. 10.1680/jgein.21.00071
Summary
Keywords
EICP technique, improved loess, isolation trench, rubber particles, shock reduction and isolation, transmission tower
Citation
Liu L, Xu Y, Li L, Chen X, Zhou Y, Xiao N and Chai S (2026) Influence of rubber particle-EICP composite improved loess as a seismic isolation trench on the vibration response of high-voltage transmission towers. Front. Earth Sci. 14:1799038. doi: 10.3389/feart.2026.1799038
Received
29 January 2026
Revised
02 March 2026
Accepted
02 March 2026
Published
19 March 2026
Volume
14 - 2026
Edited by
Manoj Khandelwal, Federation University Australia, Australia
Reviewed by
Mohammad Azarafza, University of Tabriz, Iran
Djamalddine Boumezerane, University of the West of Scotland, United Kingdom
Updates
Copyright
© 2026 Liu, Xu, Li, Chen, Zhou, Xiao and Chai.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Shaobo Chai, shbchai@chd.edu.cn
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.