Review on Advances in Seismic Research of Large-Span Prestressed-Concrete Continuous Rigid-Frame Bridges
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摘要:
我国已建设大量的大跨PC （prestressed concrete）连续刚构桥，其墩高可达百米及以上，存在遭受强震的可能，尤其是在西部高地震风险区，连续刚构桥主墩与主梁是刚性连接，主梁与桥墩共同承担地震力. 为促进刚构桥的抗震研究，首先，梳理了国内外近期经受地震考验的几座刚构桥的震害表现；然后，从抗震理论及模型试验、减隔震（耗能）设计和震后修复等方面，对连续刚构桥桥墩、上部结构、基础等主要构件以及全桥整体抗震性能等热点问题进行了评述，刚构桥具有良好的抗震性能，高阶效应及墩梁固结处纵桥向弯矩对桥墩地震反映影响较大，模型试验及理论分析中主梁开裂及损伤问题易被忽视，低墩或双柱墩刚构桥已展开墩底及基础隔震研究；最后，对未来可开展研究方向进行了探讨，强震下箱梁的开裂机理及损伤控制，基于新型材料及耗能构件组成的高墩，基础隔震及高墩底部隔震的实用技术，箱梁及空心墩的地震损伤识别及震后修复，（近）跨断层地震作用下刚构桥的渐进倒塌机理与防止.
Abstract:A large number of large-span prestressed concrete (PC) continuous rigid-frame bridges (CRFBs) have been built in China with heights of piers up to 100 m or more. They are likely to suffer strong earthquakes, especially in high seismic risks areas of Western China. The main girder and piers are rigidly connected together in CRFBs, and jointly bear the seismic force in earthquakes. In order to promote the seismic research of CRFB, the seismic damage of several CRFBs which have undergone recent earthquakes at home and abroad was reviewed firstly. Then, from the aspects of seismic theory, model tests, seismic isolation (energy consumption) design and post-earthquake repair, hot issues of the main components such as pier, superstructure, foundation, and the seismic performance of the whole bridge are reviewed. The current research shows that the CRFBs have good seismic performance; the high-order effect and the longitudinal bending moment at the pier-beam consolidation have a greater impact on the seismic response of piers. In the model test and theoretical analysis, the cracking and damage of the main girder are easily ignored, and research on pier bottom and foundation isolation has been carried out for low-pier or double-column CRFBs. Finally, future research directions were explored, including the cracking mechanism and seismic control of box girder under strong earthquakes, the high piers composed of new materials and energy-consuming components, the practical isolation technology of the bottom and foundation of high-piers, the identification of earthquake damage and post-earthquake repair of box girders and hollow piers, the mechanism and prevention of the progressive collapse of rigid frame bridges under the action of (near-fault) cross-fault earthquakes.
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Key words:
- continuous rigid-frame bridge (CRFB) /
- review /
- seismic response /
- seismic design /
- ground motion effect
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随着我国西部大开发的不断开展，高海拔隧道建设越来越多，规划建设的某高原铁路沿线海拔多高于3 km，桥隧比在80%以上，拥有数座长度超过20 km的铁路隧道. 为克服高海拔隧道施工低压低氧的困难，保障施工人员工作效率及生理健康，供氧是最直接的改善措施之一. 众多学者对高海拔供氧进行了相关研究，郭春等[1-2]研究了高海拔供氧标准，得到了不同劳动强度和不同海拔高度下人体最低需氧量；孙志涛[3]对高海拔施工缺氧进行了分级，得到了高海拔隧道施工氧含量的控制标准；王明年等[4-5]对高海拔施工供氧技术进行了总结，得到高海拔供氧技术，包含个人携氧供氧、弥散式供氧、综合供氧、氧吧车供氧和室内鼻息式供氧，在不同隧道施工工序下应组合供氧方法和供氧系统，以适应不同劳动强度下施工人员的供氧需求和心理需求；谢文强[6]对高海拔隧道施工供氧标准进行了研究，得到了不同海拔高度人体所需最小耗氧量和通气量；严涛等[7]对高海拔供氧参数进行研究，建议海拔高度在3 000 m以上施工进行供氧. 目前高海拔隧道施工供氧方面的研究，主要集中在供氧标准及供氧方式两部分，研究手段基本以理论分析与公式推导为主，缺少现场的实际测试.
在数据拟合方面，BP （back propagation）神经网络目前在多维变量拟合应用中较多，由于BP神经网络自身存在收敛慢、波动大的缺陷[8-10]，大量学者基于BP神经网络做了较多优化，并进行了应用. Wang 等[11]通过MEC-BP神经网络对箱梁施工扰度进行了拟合预测，得到MEC-BP神经网络拟合预测结果优于BP神经网络结构；李步遥等[12]基于MEC-BP神经网络对基坑水平位移进行了反演分析，得到MEC-BP神经网络收敛速度快于GA-BP神经网络[8]，且结果优于GA-BP （genetic algorithms back propagation）神经网络和BP神经网络；王春晓等[13]基于MEC-BP神经网络对群桩轴力进行预测，得到MEC-BP神经网络预测精度及准确度明显高于BP神经网络.
本文通过高海拔隧道供氧实验，对高海拔隧道施工人员进行现场测试，并运用MEC-BP神经网络对现场测试数据进行拟合，研究高海拔人员劳动功率和氧浓度对劳动强度的影响规律，其中劳动强度通过平均能量代谢率表示.
1. MEC-BP神经网络模型简介
1.1 BP神经网络
BP神经网络算法[11]是一种基于输出误差逆向传播的多层前馈神经网络算法，对于三层前馈神经网络，其基本结构由输入层、隐含层、输出层构成，根据神经网络层建立的输入输出函数Q以及误差函数E 分别为
Q=ψ(m∑j=1wjkyi−θk)=ψ(m∑j=1wjkφ(n∑i=1wikxi−θj)−θk), (1) E=12SS∑t=1(Tt−Ot)2, (2) 式中：
$\psi ({\text{•}})$ 和$\varphi ({\text{•}})$ 分别为输出层和隐含层的传递函数；$w_{jk} $ 、$w _{ik}$ 分别为第k个输出层下的第j个隐含层和第i个输入层的连接权重；$\theta _j$ 、$\theta _k$ 分别为第j个隐含层和第k个输出层的阈值；S为样本数量； $ O $ t为第t个样本预测输出值；$x_i$ 和$y_i$ 分别为隐含层输入和输出值；$T_t$ 为实验测试值.由于BP神经网络算法存在收敛慢和局部最小值的缺陷，接下来引入思维进化算法（MEC）对BP神经网络进行优化.
1.2 MEC算法
MEC算法[11]是一种基于遗传算法改进的优化算法，运用MEC算法对BP神经网络的权值和阈值进行最优搜索，能提高BP神经网络的收敛速度和精度. 其基本步骤如下：
步骤1 种群初始化. 先将总体随机分成a个个体(m1，m2，…，ma)，通过式（3）对各个体进行打分，并根据分数将个体分为w个优等子种群（每个优等种群包含b个个体）和r个临时子种群（每个临时种群包含h个个体）两大类，这两个种群分别用Msupi和Mtemi表达，如式（4）所示.
S=11+E, (3) {Msupi={m1,m2,⋯,mb},i=1,2,⋯,w,Mtemi={m1,m2,⋯,mh},i=1,2,⋯,r. (4) 步骤2 种群内竞争. 选出在每个子种群中得分最高的个体，按照正态分布将得分重新排序并再次进行得分计算，当最高得分者保持不变时，该最高得分者所在子种群即视为成熟，最高得分即代表该子种群得分.
步骤3 种群间竞争. 如果临时子种群（Stemi）得分高于成熟的优等子种群（Ssupi），那么成熟的优等种群将会被该临时种群替代. 相反，如果临时种群得分较低，那么该临时种群将会解散，再重新生成新的临时种群，步骤2将产生新的临时种群.
1.3 MEC-BP神经网络拟合预测模型
MEC-BP神经网络拟合预测模型框架如图1所示. 图中：imax、Emax分别为最大迭代次数和最大误差.
其基本流程为根据所选数据结构确定BP神经网络结构，通过MEC方法优化获得BP神经网络权值和阈值，进而得到优化的BP神经网络，通过优化的BP神经网络对给予的测试数据进行验证和预测.
2. 高海拔隧道供氧实验
高海拔供氧实验在西藏拉萨达孜区的圭嘎拉隧道进行，实验地点海拔高度约为4 200 m，实验测试对象为现场6名隧道技术施工人员，年龄在20岁～30岁，现场测试及仪器如图2所示.
实验通过调节供氧端制氧含量来设置供氧浓度，根据相关资料研究的氧浓度安全上限和实验的安全性[6, 14]，供氧浓度设置为20.9%、25.0%和29.0%，通过调节骑行台设置50、75、100 W的骑行功率. 实验中，每位测试人员需在不同的氧浓度和骑行功率下骑行10 min，最后记录肺通量和相关生理参数. 根据相关肺通量和平均能量代谢率关系式[15-16]，将标准化后的肺通量数值按照式（4）计算平均能量代谢率，现场测试及计算数据如表1所示.
表 1 现场测试及计算数据Table 1. Field test and calculation data测试人员
编号氧浓度/% 功率/W 肺通量/(L·min−1) A/m2 测试环境温度/K 标准肺通气量/
(L·min−1)平均能量代谢率/
(kJ·(min·m2)−1)1 号 20.9 50 10.52 1.86 298.15 5.78 0.57 25.0 50 7.88 1.86 286.15 4.51 0.50 29.0 50 7.29 1.86 284.15 4.20 0.48 20.9 75 20.03 1.86 296.15 11.08 0.96 25.0 75 17.07 1.86 288.15 9.71 0.69 29.0 75 17.02 1.86 290.15 9.61 0.67 20.9 100 32.75 1.86 298.15 18.00 2.21 25.0 100 27.88 1.86 292.15 15.64 1.80 29.0 100 27.94 1.86 292.15 15.67 1.80 2 号 20.9 50 9.75 1.80 299.15 5.34 0.56 25.0 50 7.52 1.80 292.15 4.22 0.49 29.0 50 6.73 1.80 284.15 3.88 0.47 20.9 75 20.45 1.80 298.15 11.24 1.06 25.0 75 18.12 1.80 298.15 9.96 0.81 29.0 75 16.41 1.80 284.15 9.46 0.71 20.9 100 27.54 1.80 298.15 15.13 1.80 25.0 100 23.89 1.80 290.15 13.49 1.50 29.0 100 22.87 1.80 289.15 12.96 1.39 3 号 20.9 50 8.64 1.72 298.15 4.75 0.53 25.0 50 7.39 1.72 291.15 4.16 0.50 29.0 50 6.91 1.72 283.15 4.00 0.49 20.9 75 23.56 1.72 297.15 12.99 1.52 25.0 75 20.45 1.72 298.15 11.24 1.17 29.0 75 19.31 1.72 285.15 11.10 1.14 20.9 100 29.44 1.72 298.15 16.18 2.14 25.0 100 26.56 1.72 289.15 15.05 1.92 29.0 100 25.44 1.72 285.15 14.62 1.84 4 号 20.9 50 10.74 1.85 298.15 5.90 0.59 25.0 50 7.86 1.85 291.15 4.42 0.49 29.0 50 6.66 1.85 282.15 3.87 0.46 20.9 75 18.64 1.85 295.15 10.35 0.83 25.0 75 16.24 1.85 292.15 9.11 0.59 29.0 75 13.52 1.85 284.15 7.80 0.53 20.9 100 25.79 1.85 298.15 14.17 1.55 25.0 100 22.17 1.85 300.15 12.10 1.17 29.0 100 21.25 1.85 283.15 12.30 1.20 5 号 20.9 50 10.22 1.99 298.15 5.62 0.54 25.0 50 8.54 1.99 292.15 4.79 0.49 29.0 50 7.47 1.99 282.15 4.34 0.47 20.9 75 19.39 1.99 298.15 10.66 0.74 25.0 75 18.72 1.99 292.15 10.50 0.71 29.0 75 18.35 1.99 283.15 10.62 0.73 20.9 100 28.27 1.99 298.15 15.54 1.60 25.0 100 25.88 1.99 299.15 14.17 1.37 29.0 100 24.33 1.99 285.15 13.98 1.33 6 号 20.9 50 9.99 1.85 298.15 5.49 0.56 25.0 50 7.35 1.85 291.15 4.14 0.48 29.0 50 6.19 1.85 282.15 3.59 0.45 20.9 75 19.31 1.85 298.15 10.61 0.88 25.0 75 19.17 1.85 294.15 10.68 0.89 29.0 75 18.84 1.85 292.15 10.57 0.87 20.9 100 27.5 1.85 300.15 15.01 1.70 25.0 100 26.09 1.85 299.15 14.29 1.57 29.0 100 25.13 1.85 289.15 14.24 1.56 VE=V1P1TPT1, (5) {lgM=0.0945VEA−0.53394,VE∈(3.0,7.3),M=100.0945VEA−0.53394+13.26−101.1648−0.01258VEA2,lg(13.26−M)=1.1648−0.01258VEA,VE⩾8.0,VE∈[7.3,8.0), (6) 式中：
$V_{\rm{E}} $ 为标准状态肺通气量（L/min）；$V_{1} $ 为相应海拔高度下肺通气量（L/min）；P为标准大气压（101.325 kPa）；P1为相应海拔高度下大气压（实测取60.8 kPa）；T为标准状态温度（273.15 K）；T1为相应海拔高度下温度（K）；M为平均能量代谢率（kJ/（min•m2））；A为体表面积（m2），如式（7）.A=0.0061H+0.0124W−0.0099， (7) 式中：H为身高（cm）；W为体重（kg）.
从测试数据中看出，高海拔施工人员平均能量代谢率较低，且在100 W时最大平均能量代谢率为2.21 kJ/（min•m2）；高海拔施工人员平均能量代谢率随着功率增加而增加，在相同骑行功率下，平均能量代谢率随着氧浓度增加有减小趋势，且在100 W骑行功率减小较为明显.
3. MEC-BP神经网络算法拟合结果
根据数据特征，输入神经元选2个（功率、氧浓度），隐藏神经元个数取为10个，输出神经元为1个（平均新陈代谢率），种群规模大小取为100，训练数据取前5个人的45个数据，测试数据取最后1个人的9个数据. 神经网络结构如图3所示. 运用MATLAB R2016a对测试数据进行拟合，MEC-BP迭代次数及拟合优度如图4所示. 图5和图6分别给出了GA-BP和BP神经网络拟合优度及均方误差. 根据式（2）计算出MEC-BP、GA-BP、BP神经网络测试值与预测值均方误差分别为0.0139、0.0130、0.0255. 从拟合优度可以看出，MEC-BP神经网络优化算法相对较好，且均方误差较小，在计算过程中收敛速度快，在第4迭代步时验证集拟合均方根误差达到最小值0.054，在短时间内通过训练能达到较高拟合度，且训练、验证和测试的拟合优度较为平稳.
从图7可以看出：在骑行功率为50 W时，平均能量代谢率随氧浓度变化不明显；在骑行功率为75 W时，平均能量代谢率随着氧浓度增加而减小，减小梯度小于100 W时变化曲率；在功率100 W时，当氧浓度小于25%时，平均能量代谢率随着氧浓度增加逐渐减小，当氧浓度大于25%时，平均能量代谢率随着氧浓度增加趋于平稳.
图 7 MEC-BP拟合平均能量代谢率变化Figure 7. MEC-BP fitting average energy metabolic rate change chart4. 结 论
通过在高海拔进行高原供氧实验，运用MEC-BP神经网络优化算法对高海拔供氧测试数据进行了拟合，得到如下结论：
1） 通过MEC-BP神经网络拟合的测试数据可以看出，拟合曲线变化规律与现场测试数据变化规律基本一致，验证了MEC-BP神经网络拟合的有效性.
2） 通过不同算法对比分析了高原供氧数据拟合结果的准确性，MEC-BP神经网络在测试、验证和训练的拟合优度上相对稳定且精度较高，均方误差较小，拟合效果较好，可为多维数据拟合提供参考.
3） 通过高海拔现场测试和MEC-BP神经网络拟合数据得到，50 W和75 W骑行功率下平均能量代谢率随氧浓度变化较小，100 W骑行功率下平均能量代谢率随氧浓度变化较大；25%供氧浓度可以作为4 200 m高海拔较高劳动强度的供氧浓度参考值.
致谢：成都哲学社会科学规划项目（2019CS107）；成都市科技项目（2019-YFYF-00121-SN）.
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图 1 刚构桥的震害
Figure 1. Seismic damage of prestressed concrete continuous rigid-frame bridges
图 6 钢桁腹板PC刚构桥
Figure 6. Prestressed concrete continuous rigid-frame bridge with steel truss webs
表 1 发生震害的刚构桥基本信息
Table 1. Basic information of continuous rigid-frame bridges damaged in earthquakes
m 大桥名称 跨径 主墩墩高 能登岛大桥 75.0 + 108.5 + 75.0 24.4/24.4 庙子坪特大桥 125.0 + 220.0 + 125.0 102.5/99.5 阿苏长阳大桥 39.3 + 91.0 + 91.0 + 53.3 37.0/68.0/33.0 注：能登岛大桥跨径及墩高为估算值. 
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