Analytical Study for Uncoordinated Deformation of Existing Pipeline and Soil Induced by Tunnel Undercrossing
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摘要:
为分析隧道下穿既有管道施工时既有管道底部脱空对其挠曲响应的影响，提出隧道下穿施工诱发既有管道-土体非协调变形理论模型及其解析解. 首先，将既有管道视为无拉力Pasternak地基上的Euler梁，根据管道与底部土体的接触状态，建立下穿施工引起既有管道-土体非协调变形控制方程，并推导出既有管道挠曲计算式；然后，采用提出的理论方法，探讨了既有管道脱空区上部竖向土压力、抗弯刚度及其所处位置地层沉降槽宽度和最大值等参数对其底部脱空区长度的影响；最后，提出下穿施工引起既有管道底部脱空区长度的参数归一化经验计算式，进一步简化新建隧道下穿施工引起既有管道挠曲的计算方法. 研究结果表明：既有管道底部脱空区长度与2个归一化参数（既有管道抗弯刚度与地基刚度比、既有管道脱空区上部竖向土压力与地层自由沉降槽最大值比）呈较好的相关性，其拟合公式计算值与理论数据的相关系数接近于1.
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关键词:
- 管道-土体非协调变形 /
- 脱空区长度 /
- Pasternak地基 /
- 隧道下穿 /
- 隧道挠曲轨面变形
Abstract:To analyze the effect of a void under the existing pipeline on its deflection response during tunnel undercrossing construction, a theoretical model and an analytical solution of the uncoordinated deformation of the existing pipeline and soil induced by tunnel undercrossing construction were presented. Firstly, the existing pipeline was regarded as an Euler beam on a tensionless Pasternak foundation. According to the contacting condition of the pipeline and soil, the equations for the uncoordinated deformation control of the pipeline and soil caused by the tunnel undercrossing construction were established, and the corresponding formulas for the pipeline deflection were derived. Secondly, the influence of the parameters on the length of the void under the existing pipeline was discussed by using the proposed theoretical method, including the vertical soil pressure acting above the void, the flexural stiffness, and the width and maximum value of the formation settlement trough at the position where the existing pipeline located. Finally, a normalized empirical formula was proposed for calculating the length of the void under the existing pipeline induced by tunnel undercrossing construction, further simplifying the calculation method of existing pipeline deflection induced by the undercrossing construction of new tunnels. The research results show that the length of the void under the existing pipeline has a good correlation with the two normalized parameters (the ratio of the stiffness of the existing pipeline to the foundation, as well as the ratio of the vertical soil pressure acting above the void of the existing pipeline to the maximum value of the formation settlement trough), and the correlation coefficient between the calculated value of the fitting formula and the theoretical data is close to 1.
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图 5 理论计算结果与模型试验数据对比
Figure 5. Comparison of theoretical calculation results and model test data
图 7 地层沉降槽宽度系数对其底部脱空区长度的影响
Figure 7. Influence of width coefficient of formation settlement trough on length of void under existing pipeline
图 8 既有管道底部脱空区长度与其地基沉降最大值的关系
Figure 8. Relationship between length of void under existing pipeline and maximum value of formation settlement
图 9 既有管道抗弯刚度对既有管道底部脱空区长度的影响
Figure 9. Influence of bending stiffness of existing pipeline on length of void
图 10 既有管道底部脱空区长度与各参数关系
Figure 10. Relationship between length of void under existing pipeline and parameters
图 12 计算结果与工程实测数据对比
Figure 12. Comparison of calculated results and measured engineering data
表 1 既有管道试验参数
Table 1. Test parameters of existing pipeline
参数 Dp/mm tp/mm zp/mm E/GPa I/m4 EI/（kN·m2） 数值 31.75 2.08 95.875 69 2.1439 1.4793 
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表 2 新建隧道试验参数
Table 2. Test parameters of new tunnel
参数 Rt/mm zt/mm Vt/% $\kappa $ 数值 50 154.1 3.76 0.558
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表 3 标准砂试验参数
Table 3. Test parameters of standard sand
参数 Es/MPa $ {\nu _{\rm{s}}} $ k/（MN·m−2） G/（MN·m−1） 数值 10 0.3 32 12
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