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Seismic Response of Power Transmission Tower-Line System Subjected to Spatially Varying Ground Motions

Vol.2010《Mathematical Problems in Engineering》

Abstract：The behavior of power transmission tower-line system subjected to spatially varying base excitations is studied in this paper. The transmission towers are modeled by beam elements while the transmission lines aremodeled by cable elements that account for the nonlinear geometry of the cables. The real multistation data from SMART-1 are used to analyze the system response subjected to spatially varying ground motions. The seismic input waves for vertical and horizontal ground motions are also generated based on the Code for Design of Seismic of Electrical Installations.Both the incoherency of seismic waves and wave travel effects are accounted for. The nonlinear
time history analytical method is used in the analysis. The effects of boundary conditions, ground motion spatial variations, the incident angle of the seismic wave, coherency loss, and wave travel on the system are investigated. The results show that the uniform ground motion at all supports of system does not provide the most critical case for the response calculations.

Introduction
In China, the west-to-east power transmission project will play an important role in changing the uneven distribution of our country’s energy resources. Transmission projects extend thousands of kilometers and cost billions of dollars to construct and maintain, and most of them will cross high-intensity earthquake zones. However, most of research attentions on it have been paid on the actions of static load, impulsive load, equivalent static wind load and so forth. There are no code provisions for earthquake design of transmission tower-line system. It is unrealistic to assume that the transmission towers and lines are safe to go through earthquakes without adequate analysis. There are several recent cases of damage to power lines during earthquakes. In the 1999 CHI-CHI earthquake, transmission towers and lines was damaged most severely, and a lot of lines were broken and some towers collapsed 1.Sichuan electric network were damaged by the Wenchuan earthquake in China, and some pictures are shown in Figure 1. Therefore, earthquake forces may govern the design in highintensity earthquake zones.
In the past one or two decades, researchers have done some earthquake dynamic analysis on the transmission tower-line system. Noteworthy contributions to the related study of transmission towers include some work that has developed effective approaches to deal with the actual problems. Li et al. 2–4 have completed a number of investigations on seismic problems of coupled system of long-span transmission towers. Ghobarah et al. 5 investigated the effect of multisupport excitations on the lateral responses of overhead power transmission lines. Transmission towers were modeled by space truss elements and the cables were modeled by straight two-node elements. In all these studies, longitudinal and transverse response under uniform excitation and lateral response under multiple-support excitations are obtained.
A major problem that arises in the analysis of the long span structures such as transmission tower-line system is the difference among the ground motion components affecting various support points of the structure. The system response using uniform support excitation is compared with the response using multiple support excitations which is a more realistic assumption. In this paper, spatially varying ground motions of real data from the dense digital arrays of strong motion seismographs in SMART-1 are selected. The seismic input waves for vertical and horizontal ground motions are also generated based on Code for Design of Seismic of Electrical Installations 6. Both the incoherency of seismic waves and wave travel effects are accounted for. Three-dimensional finite tower-line system models are considered in studying the response of this system. The transmission towers are modeled by beam elements while the transmission line is modeled by cable elements that account for the nonlinear geometry of the cable. The primary differences between the present work and previous work include the following: 1 the effect of the boundary condition is studied by three towers and two-span line and three towers and four-span line; 2 the effects of spatially varying ground motions which are obtained from real data are considered in this study; 3 the effect of incident angle of the seismic wave is considered in this paper; 4 the effects of coherency loss and wave travel are also investigated, respectively, in this paper. It should be noted that geometric nonlinear responses are considered but material nonlinear is not included.

Conclusions
The effect of the spatial variation of earthquake ground motion on the response of the transmission tower-line system has been investigated in this paper. The members of transmission tower are modeled by beam elements and the nonlinear dynamic behavior of cables is taken into account. The input of ground motion is taken as displacement time histories. The real data from the close digital arrays of strong motion seismographs in SMART-1 are selected. Artificial ground displacement records are also developed and used in the analysis. The nonlinear time history analytical method is used in the analysis. The influence of the boundary condition, spatially varying ground excitations, incident angle of the seismic wave, coherency, and wave travel on the system are considered. Following conclusions can be obtained based on the above studies.
1 The boundary condition has an obvious effect on the response of the system. In order to obtain accurate results, three towers and four-spans model must be taken in the analysis.
2 The case of uniform support excitation does not produce the maximum response in the system. The multiple support excitations, which is a more realistic assumption,
can result in larger response. The effect of spatially varying ground motions cannot be neglected.
3 The incident angle of the seismicwave has a slight effect on the responses of system.Assuming that the longitudinal of the ground motion and the direction of the wave
propagation coincide with the longitudinal direction of the system could not obtain the maximum responses of the system.
4 The coherency loss has a significant effect on the response of the system. The uncorrelated ground motion gives bigger responses than other cases. In order to obtain a representative analysis, the various degrees of coherency should be considered.
5 The assumed velocity of propagation of seismic waves has a significant effect on the response of system to seismic ground motion. In order to obtain a representative analysis of the system, an accurate estimation of the wave velocity is required. Based on the obtained results, uncorrelated ground motion and the apparent velocity of 200 m/s provide the most critical case for the response calculations. It should be noted that many studies have been reported on the ground motion spatial variation effect on bridges,
viaducts, pipelines, and dams; very limited study on transmission tower-line system can be found in the literature. This study demonstrates that the ground motion spatial variation effect is very important to transmission tower-line system. As many cat head type towers, cup towers, and guyed towers are of transmission systems, more studies are deemed necessary to further investigate the ground motion spatial variation effects on responses of these systems.

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