Analysis of Required Separation Distances of High-Pier Bridges Subjected to Non-stationary Ground Motions
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摘要: 为了研究非平稳地震作用下高墩桥梁体防撞间隙需求，基于随机振动理论及虚拟激励法，对不同烈度下场地条件对非平稳间隙需求的影响进行了分析. 首先，建立了非平稳地震作用下相邻梁体相对位移需求与烈度间的数学关系；其次，基于理论计算的梁体间最大相对位移，确定碰撞间隙宽度需求以达到防止梁体间发生碰撞的目的；最后，以某大跨度连续刚构-连续梁体系为实际工程算例，研究了非平稳地震作用下桥梁结构在一致场地和非一致场地（实际场地）条件下的碰撞间隙需求量，且获得了不同烈度下非平稳碰撞间隙需求谱. 研究结果表明：非平稳地震作用下，硬土场地条件时，相对位移时变均方差的峰值最小，实际场地条件最大，约为硬土场地的4倍；实际场地条件的各烈度下非平稳碰撞间隙宽度需求均值比软土场地、中土场地和硬土场地分别大36%、69%和73%，均方差分别大45%、74%和78%；平稳地震激励比非平稳地震激励时碰撞间隙需求量大20%～30%.Abstract: To investigate the influence of non-stationary ground motions on required separation distances, the influence of site conditions on non-stationary gap under different intensities was analysed based on the random vibration theory and pseudo excitation method. First, the mathematical formulation clarifying the relationship between the required relative displacement and earthquake intensity was derived. Second, the minimum gap required between two adjacent girds to prevent seismic pounding was determined from the maximum relative displacement based on theoretical analysis. Finally, a real continuous rigid bridge was used to obtain the required gap length spectrum between two adjacent decks for considering non-stationary seismic excitations with different intensities under different local site conditions. Furthermore, the influence of actual site conditions and uniform site conditions on the required separation distance was investigated. Numerical results reveal that actual site conditions have the most obvious effect on the time-dependent mean square deviation of relative peak displacement, which is four times the corresponding value for firm site conditions. The mean values of the required separation distance for different intensities are larger than the corresponding values for uniform site conditions by 36%, 69%, and 73% for soft sites, median sites, and firm sites, respectively, whereas the mean square deviation is 45%, 74%, and 78%, respectively. The required separation distance under stationary seismic excitations is 20%–30% larger than that under non-stationary seismic excitations.
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图 2 相对位移时变均方差（7～9度）
Figure 2. Time-dependent mean square deviation of relative displacement (7–9度)
图 3 相对位移时变均方差（10度）
Figure 3. Time-dependent mean square deviation of relative displacement (10度)
表 1 3类场地类型参数
Table 1. Type parameters for three sites
场地类型 ${\omega _{\rm{g}}}$ ${\xi _{\rm{g}}}$ ${\omega _{\rm{f}}}$ ${\xi _{\rm{f}}}$ 硬土 15.0 0.6 1.5 0.6 中土 10.0 0.4 1.0 0.6 软土 5.0 0.2 0.5 0.6 
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表 2 地震动强度比例因子
Table 2. Scale factor of ground motion intensity
场地类型 烈度/度 6 7 8 9 10 硬土 3.69 14.77 59.08 236.31 945.13 中土 3.97 15.89 63.53 254.07 1 016.17 软土 5.22 20.87 83.45 333.76 1 334.86
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表 3 墩底工况分析
Table 3. Analysis of pier bottom condition
工况编号 烈度/度 1# 墩 2# 墩 3# 墩 4# 墩 5# 墩 6S 6 S S S S S 6M 6 M M M M M 6F 6 F F F F F 6R 6 M S F M S 7S 7 S S S S S 7M 7 M M M M M 7F 7 F F F F F 7R 7 M S F M S 8S 8 S S S S S 8M 8 M M M M M 8F 8 F F F F F 8R 8 M S F M S 9S 9 S S S S S 9M 9 M M M M M 9F 9 F F F F F 9R 9 M S F M S 10S 10 S S S S S 10M 10 M M M M M 10F 10 F F F F F 10R 10 M S F M S
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