Global Reliability Analysis of Transmission Tower–Line Coupling System Considering Soil-Structure Interaction
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摘要:
为研究土-结构相互作用和塔线耦合作用对输电塔整体可靠度的影响，建立随机风荷载作用下考虑土-结构相互作用的输电塔-线耦合系统简化力学模型，其中，输电塔、绝缘子、导线和基础4个结构采用多质点力学模型进行模拟，地基土对耦合系统动力响应的影响采用S-R （swing-rocking）模型进行模拟，耦合系统所处随机风场则采用谱表示-降维方法进行模拟；其次，基于耦合系统简化力学模型和概率密度演化方法（PDEM），提出适用于考虑土-结构相互作用的输电塔-线耦合系统整体可靠度分析方法；最后，以某特高压交流输变电线路的直线塔为例，分别计算塔顶位移的概率密度函数、均值和标准差，并以塔顶位移极值为控制变量求解耦合系统的整体可靠度. 分析结果表明：考虑塔线耦合作用后，塔顶位移响应极值的分布函数明显右移，结构失效概率由1.605 × 10−38增加至0.932；考虑土-结构相互作用后，塔顶位移响应极值的分布函数轻微右移，结构失效概率有所增加，与固定端工况相比，中硬土、中软土和软弱土工况下的结构失效概率增幅分别为4.44%、5.22%和11.76%；与蒙特卡洛方法相比，所提方法可高效获得塔顶位移的概率信息，其计算时间仅为蒙特卡洛方法的1/33，而均值与标准差的二范数相对误差在3%以内.
Abstract:To investigate the influence of soil-structure interaction and tower-line coupling effect on global reliability of transmission towers, a simplified mechanical model of a transmission tower–line coupling system considering soil-structure interaction under stochastic wind excitation was established. A multi-mass mechanical model was adopted to simulate the transmission tower, insulator, conductor, and foundation. The effect of the subsoil on the dynamic response of the coupling system was modeled using the swing-rocking (S-R) model, and the stochastic wind field was generated using the spectrum representation–dimension reduction method. The simplified mechanical model and the probability density evolution method (PDEM) were employed to develop a global reliability analysis method for transmission tower–line coupling systems considering soil-structure interaction. Finally, intermediate support from an ultra-high voltage alternating current transmission line was used as an example. The probability density function (PDF), mean, and standard deviation of the tower-top displacement were calculated, and the global reliability was evaluated with the tower-top displacement extremum as the control variable. The results show that after considering tower-line coupling effect, the cumulative distribution function (CDF) of tower-top displacement extremum shifts noticeably to the right, and the failure probability increases from 1.605 × 10−38 to 0.932. After soil-structure interaction is taken into account, the CDF of tower-top displacement extremum shows a slight rightward shift, and the failure probability increases. Compared with the fixed-base condition, the increase ratios of failure probability under medium-hard soil, medium-soft soil, and weak soil conditions are 4.44%, 5.22%, and 11.76%, respectively. Compared with the Monte Carlo method, the proposed method efficiently obtains the probabilistic information of the tower-top displacement. The computational time is only 1/33 of that of the Monte Carlo method, while the two-norm relative errors of the mean and standard deviation are within 3%.
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图 1 输电塔-线耦合系统简化模型
Figure 1. Simplified model of transmission tower–line coupling system
图 2 考虑土-结构相互作用的输电塔-线耦合系统简化力学模型
Figure 2. Simplified mechanical model of transmission tower–line coupling system with soil-structure interaction
图 4 耦合系统风场模拟点（单位：m）
Figure 4. Wind field simulation points of coupling system (unit: m)
图 5 塔顶脉动风速样本均值功率谱与目标值
Figure 5. Mean power spectral density of tower-top turbulence wind speed samples and target values
图 6 塔顶脉动风速样本均值和标准差
Figure 6. Mean and standard deviation of tower-top turbulence wind speed samples
图 11 不同结构体系下塔顶位移极值的PDF和CDF
Figure 11. PDF and CDF of tower-top displacement extremum under different structure systems
图 12 不同工况下塔顶位移极值的PDF和CDF
Figure 12. PDF and CDF of tower-top displacement extremum under different conditions
表 1 不同地基土参数
Table 1. Parameters of different subsoil types
土体类型 ρ/（ kg·m−3） v VS/（m·s−1） G/（×108 N·m−2） 中硬土 2000 0.30 400 3.20 中软土 1900 0.40 200 0.76 软弱土 1800 0.49 100 0.18 
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表 2 不同结构体系的失效概率
Table 2. Failure probabilities of different structure systems
结构体系 失效概率 单塔 1.1974 × 10−59地基-单塔 1.6052 × 10−38塔线 0.7589 地基-塔线 0.9321
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表 3 不同工况下耦合系统的失效概率
Table 3. Failure probabilities of coupling system under different conditions
工况 失效概率 变化率/% 固定端 0.7589 中硬土 0.7926 4.44 中软土 0.8340 5.22 软弱土 0.9320 11.76
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