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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