Calculation of displacement response induced by tunnel excavation considering restraint effects of in-service piles and soil stiffness hardening
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摘要: 忽略桩-土相互作用中的在役桩牵制效应与土体刚度应力相关性，可能导致隧道开挖位移响应的理论计算结果与实际值之间存在一定程度偏差。鉴于此，采用两阶段分析法，建立了考虑在役桩牵制效应和土体刚度硬化的桩-土相互作用模型，并引入考虑土体黏聚力的等效内摩擦角修正了Loganathan-Poulos（L & P）公式，求解邻近在役桩基隧道开挖诱发的土体位移；进一步基于非线性土弹簧的Winkler地基梁模型，求解盾构隧道开挖引起的既有桩基位移；应用所提计算方法，探究了桩隧间距、地层损失率、隧道埋深和桩径对隧道开挖诱发桩基位移的响应规律。结果表明：所提方法对地表沉降的计算结果与既有理论计算结果、离心机试验数据及现场监测数据吻合良好，有效改进了传统L & P公式；深层土体位移计算结果与既有理论计算结果的规律基本一致；考虑在役桩牵制效应及土体刚度硬化所得的桩基位移均小于既有解析解计算结果；考虑不同地层损失率工况下，桩基位移计算结果与有限元模拟结果整体趋势一致，隧道轴线深度处，桩基竖向位移计算结果均小于有限元模拟值2%左右，而桩基水平位移小于有限元模拟值10%左右。Abstract: Neglecting the restraint effect of in-service piles and the stress-dependency of soil stiffness in pile-soil interaction may lead to a certain degree of discrepancy between the theoretically calculated values and the realistic values of displacement responses induced by tunnel excavation. Therefore, a two-stage analysis method (TSAM) was adopted to develop a pile-soil interaction model incorporating both the restraint effect of in-service piles and soil stiffness hardening. Moreover, an equivalent internal friction angle integrating soil cohesion was introduced to correct the Loganathan-Poulos (L & P) formula and calculate soil displacements induced by tunnel excavation adjacent to in-service piles. Using a Winkler model with nonlinear soil springs, the displacement of existing piles resulting from tunnel excavation was subsequently determined. Finally, the proposed solution was utilized to explore the rules of pile displacement responses induced by tunnel excavation, taking into account the influence of pile-tunnel spacing, ground loss ratio, tunnel depth, and pile diameter. The results demonstrate that the proposed solution exhibits excellent agreement with the existing theoretical solutions, centrifuge test data, and field monitoring results for surface settlement, offering a significant improvement over the traditional L & P formula. The change law of in-depth soil displacement solution shows strong consistency with that of existing theoretical solutions. Notably, the pile displacements predicted by considering the restraint effect of in-service piles and soil stiffness hardening are smaller than those estimated by existing theoretical solutions. Under different ground loss ratio scenarios, the calculated pile displacement exhibits consistent overall trends with finite element (FE) results. At the tunnel axis elevation, the calculated vertical pile displacements are about 2% lower than the FE results, with horizontal displacements being 10% smaller than the FE results.
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图 1 隧道移动及桩隧相关参数示意
Figure 1. Schematic of tunnel movement and pile-tunnel related parameters
图 2 桩-土相互作用机理模型及相互作用力
Figure 2. Pile-soil interaction mechanism model and interaction force
图 3 Mindlin解及转换坐标后通解
Figure 3. Mindlin solution and general solution after coordinate transformation
图 5 地表沉降预测值与既有解对比
Figure 5. Comparison of the surface settlements obtained by the proposed and existing analytical solutions
图 6 地表沉降预测值与离心机试验对比
Figure 6. Comparison of the surface settlements obtained by the proposed and centrifuge test
图 7 地表沉降预测值与监测数据对比
Figure 7. Comparison of the surface settlements obtained by the proposed and measured data
图 8 与既有解析解对比桩周土体竖向位移
Figure 8. Vertical displacement of the surrounding soil of the pile compared with existing analytical solutions
图 9 与既有解析解对比桩周土体水平位移
Figure 9. Horizontal displacement of the surrounding soil of the pile compared with existing analytical solutions
图 12 不同隧道埋深下桩身竖向位移
Figure 12. Vertical displacement of the pile body under different tunnel burial depths
图 13 不同隧道埋深下桩基水平位移
Figure 13. Different tunnel burial depth pile foundation lateral displacement
图 14 不同地层损失比下桩身竖向位移
Figure 14. Vertical displacement of the pile body under different gap conditions
图 15 不同地层损失率下桩身水平位移
Figure 15. Lateral displacement of pile shaft under different ground loss ratios
图 16 不同桩径下桩身竖向位移
Figure 16. Vertical displacement of the pile body under different pile diameters
图 17 不同桩径下桩身水平位移
Figure 17. Lateral displacement of pile shaft under different pile diameters
图 18 不同桩基隧道距离下桩身竖向位移
Figure 18. Vertical displacement of the pile body under different pile-tunnel distances
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