Seismic Response of Railway Bridges in Active Complex Tectonic Zones Part Ⅱ: Effects of SSI (Soil-Structure Interaction)
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摘要:
目前国家正在复杂艰险构造区修建和规划新的铁路，地震等极限环境耦合作用对铁路交通的影响受到越来越多的关注.本文提出一种列车‒桥梁‒土耦合系统的数值模型，引入车辆简化模型、桥梁结构非线性有限元模型和层状土半解析模型，采用纯时域求解方法.利用p-y曲线、t-z曲线和q-z曲线建立土‒桩基非线性模型，采用双线性模型模拟桥墩及桩基础的滞回特性，计算不良地质体发育区铁路列车‒桥梁‒土耦合系统的弹塑性地震响应，分析SSI对桥梁弹塑性地震响应的影响.研究表明，列车‒桥梁‒土耦合系统的第一弯曲模态通常是临界模态，即梁的一个半波形状导致土桥系统固有频率降低.另外，对于横向地震响应来说，考虑SSI（土‒结构相互作用）后，影响地震响应的频率成分会发生变化，除了频率会变小之外，频段也会变宽.考虑SSI之前，影响频段是1.8~2.0 Hz，考虑SSI之后变为1.2~2.0 Hz之间.对于梁跨中竖向加速度，从考虑SSI之前的4.576 Hz到考虑SSI之后的14.215 Hz，建议考虑SSI进行设计时候应考虑竖向高阶振型影响.
Abstract:When constructing new railways in challenging tectonic zones, the influence of harsh situations like earthquakes on train traffic is increasingly being considered. With a time-domain solution approach, a numerical model of the coupled train-bridge-soil system is provided. In the poor geological development area, the elastic-plastic seismic response of the railroad train-bridge-soil coupled system is calculated using the p-y, t-z, and q-z curves. This means that bending the beam half-wave form reduces the inherent frequency of the coupled train-bridge-soil system, which is discovered to be the initial bending mode. After taking into account soil-structure interaction (SSI), the frequency components impacting the seismic response vary, and the frequency range widens as well as decreasing. The affecting frequency range is 1.8-2.0 Hz before SSI and 1.2-2.0 Hz after SSI, respectively. To design SSI, it is advised that the influence of vertical higher order vibration pattern should be addressed, since it varies from 4.576 Hz to 14.215 Hz before and after SSI consideration.
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图 3 考虑桩土的列车‒桥梁系统简图
a.桥梁-桩基模型示意图；b.土层情况下的地波传播示意图；c.车辆荷载示意图；d.桩基础立面图（单位m）；e.桩基础平面图（单位mm）
Fig. 3. Model of bridges considering SSI
图 4 桥梁振型图
a.无SSI横向振型；b. 有SSI横向振型
Fig. 4. Mode shape of natural vibration of the bridge
图 5 无SSI H+V荷载组合下脉冲/远场非脉冲地震横/竖向梁体加速度傅里叶谱
a.脉冲地震横向加速度；b.远场非脉冲地震横向加速度；c.脉冲地震竖向加速度；d.远场非脉冲地震竖向加速度
Fig. 5. Fourier spectrum of lateral/vertical acceleration at the girder under loading combination of H+V pulse/far field-typed ground motions without considering the SSI
图 6 SSI H+V-塑性脉冲/远场非脉冲地震横/竖向梁体加速度傅里叶谱
a.脉冲地震横向加速度；b.远场非脉冲地震横向加速度；c.脉冲地震竖向加速度；d.远场非脉冲地震竖向加速度
Fig. 6. Fourier spectrum of lateral/vertical acceleration at the mid-span of girder under loading combination of H+V pulse/far field ground motions with considering the SSI
图 7 近/远场非脉冲地震竖向分量傅里叶谱
a.脉冲地震；b.远场非脉冲地震
Fig. 7. Fourier spectrum of vertical near fault/ far field ground motions
图 8 近场/远场非脉冲地震墩底第1单元转角时程图及其对应的傅里叶谱图
时程图：a. Kobe 1995地震KJMA波地震；b. Duzce 1999地震Bolu波；c. Kobe 1995地震Shin-Osaka波. 傅里叶谱图：d. Kobe 1995地震KJMA波地震；e. Duzce 1999地震Bolu波；f. Kobe 1995地震Shin-Osaka波
Fig. 8. Rotation angle time-history diagrams and its corresponding Fourier spectra at first element of the pier bottom subjected to the NF/FF ground motions
表 1 脉冲近场地震
Table 1. Pulse-typed near-fault ground motion database
地震名称 台站 震级 断层距(km) 场地 Tp
(s)PGAH
(g)PGVH (cm/s) PGAV
(g)$ {\partial }_{PGA} $ Ap/
vpKobe 1995 KJMA 6.9 1.0 粘土 1.09 0.854 105.6 0.342 0.401 8.08 Northridge1994 Rinaadi 6.7 0.0 粘土 1.25 0.869 149.0 0.834 0.959 5.84 Kobe 1995 Takatori 6.9 1.4 粘土 1.55 0.682 153.2 0.271 0.398 4.45 Imperial Valley06 1979 Agrarias 6.53 0.6 粘土 2.34 0.311 53.5 0.834 2.679 5.82 Duzce 1999 Bolu 7.1 6.6 粘土 5.94 0.775 65.8 0.202 0.261 11.79 Chi-Chi 1999 TCU059 7.62 3.6 粘土 7.78 0.168 64.1 0.056 0.334 2.63 注：Tp为脉冲周期；PGAH为横向峰值地震加速度；PGVH为横向峰值地震速度；PGAV为竖向峰值地震加速度；竖向峰值地震加速度与横向峰值地震加速度比值$ {\partial }_{PGA}=PG{A}_{\mathrm{V}}/PG{A}_{\mathrm{H}} $；Ap/vp是横向峰值加速度与横向峰值速度的比值. 
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表 2 远场非脉冲地震
Table 2. Far field ground motion database
地震名称 台站 震级 断层(km) 场地 PGAH
(g)PGVH (cm/s) PGAV
(g)$ {\partial }_{PGA} $ Ap/
vpChi-Chi 1999 CHY036 7.6 16.1 粘土 0.322 36.31 0.104 0.322 8.89 Kobe 1995 Shin-Osaka 6.9 19.2 粘土 0.186 29.96 0.058 0.314 6.23 Imperial Valley 1979 El Centro Array #13 6.5 21.9 粘土 0.138 14.23 0.045 0.330 9.70 Loma Prieta 1989 Coyote Lake Dam (Downst) 6.9 20.8 粘土 0.159 10.30 0.0947 0.593 15.50 Chi-Chi 1999 CHY092 7.6 22.7 粘土 0.111 60.71 0.119 1.076 1.83 Loma Prieta 1989 Capitola 6.9 15.2 粘土 0.371 34.55 0.541 1.455 10.75
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表 3 桥墩/桩柱弯矩‒曲率骨架曲线响应计算值
Table 3. Calculated value of skeleton-frame curves of moment-curvature relation of pier/pile
地震方向 屈服转角(10-3 rad) 屈服弯矩(103 kN·m) 极限转角(10-3 rad) 极限弯矩(103 kN·m) 桥墩 横桥向 0.47 56.40 17.87 97.90 顺桥向 1.45 24.80 52.63 35.80 桩柱 横桥向 2.10 5.51 47.50 6.42 顺桥向 2.18 5.71 44.30 6.96
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表 4 地质参数
Table 4. Soil column properties
层序号 到桩顶距离(m) 土层厚度(m) 岩土名称 密度
(g/cm3)剪切波速
(m/s)泊松比 剪切模量(MPa) 弹性模量(MPa) 1 0~3.5 3.5 淤泥、淤泥质土 1.85 85 0.46 13.37 49.47 2 3.5~11.0 7.5 含淤泥粉砂 1.94 191 0.35 70.77 274.59 3 11~29 18 全风化花岗片麻岩 2.05 311 0.27 198.28 812.95 4 29~31 2 强风化花岗片麻岩 2.00 1 200 0.25 2 880 11 250 5 31~34 3 弱风化花岗片麻岩 2.10 1 500 0.22 4 725 16 601
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