Approximate Analytical Method for Skin Friction of Tunnel-Type Anchorage Used in Suspension Bridge Engineering
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摘要: 为了解析计算悬索桥隧道式锚碇的侧摩阻力，基于弹性理论，并考虑锚碇前、后锚端边界条件，建立了锚碇侧摩阻力的计算表达式。首先，根据实际锚碇受力情况建立了锚碇分析模型；其次，在Mindlin解的剪应力一般表达式基础上，引入锚碇前、后锚端剪应力为0的条件以及锚碇的静力平衡条件予以修正，得到锚碇侧摩阻力的解析式；最后，引用模型试验结果验证了解析方法的合理性，并结合工程实例进一步揭示了锚碇侧摩阻力的分布规律. 研究结果表明：锚碇摩阻应力沿轴向呈单峰曲线分布模式，解析计算与三维数值模拟的最大摩阻应力平均误差约为8.5%；当主缆拉力较小（1倍设计缆力）时，锚碇自重可导致较小的侧摩阻力；当主缆拉力较大（3.5倍设计缆力）时，锚碇自重对侧摩阻力影响相对减弱；随着主缆拉力逐渐增大，锚碇侧表面可能出现局部剪切破坏，侧摩阻力将产生重分布.Abstract: Based on the theory of elasticity, the calculation formulas for the skin friction stress of tunnel-type anchorages used in suspension bridge engineering is provided, taking into account the boundary conditions on the two ends of the anchorage. Firstly, an analysis model is established in light of the practical loading conditions on the anchorage. Then, considering the conditions that the shear stresses on the two ends of the anchorage are individually equal to zero and that the entire anchorage is in a static equilibrium state, a calibrated computation formula for the skin friction stress of the anchorage is proposed based on the shear stress expression of Mindlin solution. Finally, a test model is cited to verify the acceptability of the proposed method, and the distribution characteristics of the skin friction stress are further revealed by using a practical example of tunnel-type anchorage. The analysis results show that the distribution of the skin friction stress along the axial direction of the anchorage is unimodal. The skin friction stress computed using the proposed method agrees well with that obtained using three-dimensional numerical simulation method. The average error between the maximum skin friction stresses of the two methods is about 8.5%. The calculation results also show that the skin friction stress is very small owing to the effect of self-weight load of the anchorage if the actual tension force on the main cable is close to the design value; however, the effect decreases with increase in tension force （e.g. 3.5 times the design value）. In particular, the local interface between the anchorage and the surrounding rock is likely to be in a failure state with increase in the tension force. This causes a corresponding adjustment of the skin friction stress to keep the entire anchorage in balance.
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Key words:
- suspension bridges /
- tunnel-type anchorage /
- skin friction /
- tension force on main cable
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图 3 试验模型锚碇轴向压应力分布曲线
Figure 3. Distribution curves of axial compressive stress on cross section of the anchorage model
图 4 不同缆力工况下锚碇侧表面摩阻应力分布
Figure 4. Distribution curves of skin friction stress on anchorage surface under various tension forces on main cable
图 5 边坡三维数值模型
Figure 5. Three-dimensional numerical simulation model for the practical slope
图 6 主缆拉力为3.5P锚碇侧表面摩阻应力分布
Figure 6. Distribution curve of skin friction stress on anchorage surface under tension force on main cable of 3.5P
图 7 不同荷载工况下锚碇侧表面摩阻应力与抗剪强度分布曲线
Figure 7. Distribution curves of skin friction and shear strength on anchorage surface under various tension forces on main cable
图 8 在7P缆力情况下锚碇侧表面应力重分布曲线
Figure 8. Redistribution curve of skin friction stress under tension force on main cable of 7P
图 9 临塑状态时摩阻应力分布曲线
Figure 9. Distribution curve of skin friction stress if the point maximum shear stress acts on is in critical state
图 10 不同缆力下锚碇轴力分布曲线
Figure 10. Distribution curves of axial force on the anchorage under various tension forces on main cable
表 1 锚碇的相关参数
Table 1. Main parameters of anchorage
弹性模量
/MPa泊松比 重度
/（kN•m–3）前锚面
直径/m后锚面
直径/m轴线与水平面
倾角/（°）几何放大角
/（°）前锚面距坡面
深度/m前后锚面
间距/m31 500 0.2 25 15.7 19.0 36 2.06 117.9 39.2 
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表 2 围岩的相关参数
Table 2. Main parameters of surrounding rock
弹性模量/MPa 泊松比 重度/（kN•m–3） 内摩擦角/（°） 黏聚力/kPa 锚碇-围岩界面综合摩擦因数 16 500 0.2 26 40 1 000 0.577
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表 3 锚碇边坡岩土体物理力学参数
Table 3. Rock and soil properties of the slope with anchorage in the practical engineering
坡体材料 黏聚力/kPa 内摩擦角/（°） 重度/（kN•m–3） 弹性模量/MPa 泊松比 含砾黏土 30 25 19 20 0.38 漂卵石层 15 38 22 300 0.20 强风化闪长岩 250 37 25 500 0.23 中风化闪长岩 1 500 45 26 19 800 0.20 强风化蚀变二长花岗岩 250 30 25.5 600 0.23 中风化蚀变二长花岗岩 1 000 40 26 16 500 0.20
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孙振. 隧道式锚碇受力机理研究[D]. 成都: 西南交通大学, 2005 赵克烈,李光耀. 乌江大桥隧道锚围岩承载特性研究[J]. 西南交通大学学报,2012,47(增刊): 213-216ZHAO Kelie, LI Guanyao. Research on bearing properties of surrounding rocks of the tunnel anchor of Wu river bridge[J]. Journal of Southwest Jiaotong University, 2012, 47(Sup.): 213-216 汤华,熊晓荣,吴振君,等. 隧道锚抗拔作用机理的室内模型试验[J]. 上海交通大学学报,2015,49(7): 935-939TANG Hua, XIONG Xiaorong, WU Zhenjun, et al. Laboratory model test study of pullout mechanism of tunnel anchorage[J]. Journal of Shanghai Jiaotong University, 2015, 49(7): 935-939 夏才初,程鸿鑫,李荣强. 广东虎门大桥东锚旋现场结构模型试验研究[J]. 岩石力学与工程学报,1997,16(6): 571-576XIA Caichu, CHENG Hongxin, LI Rongqiang. Testing study of field structure model of the east anchorage of Guangdong Humen bridge[J]. Chinese Journal of Rock Mechanics and Engineering, 1997, 16(6): 571-576 朱杰兵,邬爱清,黄正加,等. 四渡河特大悬索桥隧道锚模型拉拔试验研究[J]. 长江科学学院院报,2006,23(4): 51-55ZHU Jiebing, WU Aiqing, HUANG Zhengjia, et al. Pulling test of anchorage model of Siduhe suspension bridge[J]. Journal of Yangtze River Scientific Research Institute, 2006, 23(4): 51-55 邬爱凊,彭元诚,黄正加,等. 超大跨度悬索桥隧道锚承载特性的岩石力学综合研究[J]. 岩石力学与工程学报,2010,29(3): 433-441WU Aiqing, PENG Yuancheng, HUANG Zhengjia, et al. Rock mechanics comprehensive study of bearing capacity characteristics of tunnel anchorage for super large span suspension bridge[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(3): 433-441 周火明,李维树,王帅,等. 软岩隧道锚变形破坏机理缩尺模型试验研究[J]. 长江科学院院报,2016,33(10): 67-71ZHOU Huoming, LI Weishu, WANG Shuai, et al. Scale model test on the deformation and failure mechanism of tunnel-type anchorage surrounded by soft rock[J]. Journal of Yangtze River Scientific Research Institute, 2016, 33(10): 67-71 朱玉,廖朝华,彭元成,等. 大跨径悬索桥隧道锚设计及结构性能评价[J]. 桥梁建设,2005(2): 44-46, 73ZHU Yu, LIAO Chaohua, PENG Yuancheng, et al. Design and structure capacity assessment of tunnel-type anchorage for long-span suspension bridge[J]. Bridge Construction, 2005(2): 44-46, 73 汪海滨,高波,孙振. 悬索桥隧道式锚碇系统力学行为研究[J]. 岩石力学与工程学报,2005,24(15): 2728-2735WANG Haibing, GAO Bo, SUN Zhen. Study on mechanical behavior of tunnel anchorage system for suspension bridge[J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(15): 2728-2735 余家富,曹春明. 悬索桥隧道锚抗拉承载力公式探讨[J]. 交通科技,2015(2): 21-24YU Jiafu, CAO Chunming. Discussion on the formula of tensile bearing capacity of tunnel anchorage for suspension bridge[J]. Transportation science and technology, 2015(2): 21-24 廖明进,王全才,袁从华,等. 基于楔形效应的隧道锚抗拔承载能力研究[J]. 岩土力学,2016,37(1): 185-192LIAO Mingjin, WANG Quancai, YUAN Conghua, et al. Research on the pull-out capacity of the tunnel-type anchorage based on wedge-effect[J]. Rock and Soil Mechanics, 2016, 37(1): 185-192 中华人民共和国交通运输部. JTG1T D 65—2015 公路悬索桥设计规范[S]. 北京: 人民交通出版社, 2015 张奇华,胡建华,陈国平,等. 矮寨大桥基础岩体稳定问题研究[J]. 岩石力学与工程学报,2012,31(12): 2420-2430ZHANG Qihua, HU Jianhua, CHENG Guoping, et al. Study of rock foundation stability of Aizhai bridge[J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(12): 2420-2430 MINDLIN RAYMOND D. Force at point in the Interior of a semi-infinite solid[J]. Physics, 1936, 7(5): 195-202 江南. 铁路悬索桥隧道式锚碇承载机理及计算方法研究[D]. 成都: 西南交通大学, 2014 肖世国,周德培. 非全长粘结型锚索锚固段长度的一种确定方法[J]. 岩石力学与工程学报,2004,23(9): 1530-1534XIAO Shiguo, ZHOU Depei. Calculation method of length of anchoring segment for partial-cohesive cable[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(9): 1530-1534 赵晓彦,黄金河,周一文,等. 坡面锚索与坡脚抗滑桩联合加固边坡设计方法[J]. 西南交通大学学报,2017,52(3): 489-495ZHAO Xiaoyan, HUANG Jinhe, ZHOU Yiwen, et al. Joint reinforcement design method of tieback anchors on slope surface and anti-slide piles at slope toe[J]. Journal of Southwest Jiaotong University, 2017, 52(3): 489-495 程富强. 大吨位悬索桥隧道式锚碇承载性能研究[D]. 成都: 西南交通大学, 2015 -
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