Two-stage Analysis Method for Influence of Foundation Pit Excavation on Adjacent Existing Roads
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摘要:
针对城市基坑开挖过程中邻近道路沉降开裂问题，基于Winkler理论，将研究对象从一维结构扩展到二维结构. 首先，建立道路在基坑开挖引起沉降场下的计算模型，推导出道路挠曲变形控制方程；其次，采用两阶段分析方法，考虑基坑开挖深度、宽长比、支护刚度以及坑底以上软土层厚度等因素，给出基坑开挖引起沉降场修正公式和地表最大沉降预测方法；接着，将沉降场代入道路挠曲变形控制方程，通过有限差分法求解四阶非线性偏微分方程；最后，通过工程实例对上述关于基坑开挖条件下道路计算分析模型进行验证. 现场监测数据与理论解、数值模拟结果比较发现：道路沉降的误差分别为15%和8.3%，均在合理范围内，确定本文所提出的基坑开挖条件下道路计算分析模型的可靠性.
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关键词:
- 基坑开挖 /
- Winkler地基梁 /
- 土与结构相互作用 /
- 路面沉降
Abstract:To address the issue of settlement and cracking of adjacent roads during the excavation of urban foundation pits, the research object was extended from a one-dimensional structure to a two-dimensional structure based on the Winkler theory. Firstly, a calculation model for the settlement field caused by foundation pit excavation was established, and the control equation for road flexural deformation was derived. Secondly, a two-stage analysis method was adopted by considering factors of foundation pit excavation depth, aspect ratio, support stiffness, and thickness of soft soil layer above the pit bottom, so as to provide a correction formula for settlement field caused by foundation pit excavation and a method for predicting maximum surface settlement. Thirdly, the settlement field was substituted into the control equation for road flexural deformation, and a fourth-order nonlinear partial differential equation was solved by using the finite difference method. Finally, the above road calculation and analysis model under the condition of foundation pit excavation was verified by an engineering example. By comparing the field monitoring data with the theoretical solution and numerical simulation, it was found that the errors in road settlement were 15% and 8.3%, respectively, both of which are within acceptable limits, thereby confirming the reliability of the road calculation and analysis model proposed in this study under the condition of foundation pit excavation.
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图 1 基坑开挖下道路-土相互作用模型
Figure 1. Road-soil interaction model under foundation pit excavation
图 6 基本模型基坑支护结构剖面图（单位：m）
Figure 6. Sectional drawing of foundation pit support structure of basic model （unit: m）
图 7 地表沉降沿基坑长度方向的沉降分布曲线
注：图中实心点表示数值模拟结果，虚线表示拟合结果，R为影响半径，R2为拟合相关系数.
Figure 7. Distribution curves of surface settlement along length of foundation pit
图 8 拟合系数与基坑开挖深度关系
Figure 8. Relationship between fitting coefficient and excavation depth of foundation pit
图 10 限差分法道路节点划分示意
Figure 10. Schematic diagram of road node division by limited difference method
图 12 基坑支护结构剖面图（单位：m）
Figure 12. Sectional drawing of foundation pit support structure （unit: m）
表 1 修正莫尔-库伦模型参数
Table 1. Modified Mohr-Coulomb model parameters
土层名称 γ /（kN•m−3） φ /（°） c/kPa $\mu $ e0 Es/MPa Eoed/MPa E50/MPa Eur/MPa 素填土 18.4 13.6 11.1 0.33 0.914 4.41 4.41 4.41 22.05 淤泥质粉质黏土 17.7 11.8 8.4 0.40 1.100 3.37 3.37 6.74 33.70 粉质黏土夹粉土 17.8 16.4 10.4 0.35 0.953 4.20 4.20 8.20 41.00 粉土夹粉砂 18.5 23.3 8.5 0.31 0.812 6.56 6.56 6.56 32.80 粉细砂 18.5 32.3 2.0 0.27 0.745 10.05 10.05 10.05 50.25 卵石 20.0 35.0 30 0.25 0.650 15.0 15.0 15.0 75.00 风化岩 21.0 35.0 30 0.25 0.600 30.0 30.0 20.0 100.00 注：γ为土体重度；φ为土体内摩擦角；c为土体黏聚力；$\mu $为泊松比；e0为初始孔隙比；Es为土体压缩模量，$ E_{{\text{oed}}} $为固结试验的参考切线模量，$ E_{50}^{} $为三轴排水剪切试验的参考割线模量，$ E_{{\text{ur}}}^{} $为三轴排水剪切试验的参考加卸载模量，四者之间存在经验关系[23,24]. 
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表 2 支护刚度K取值
Table 2. Values of support stiffness K
t（m） EI（Pa） have（m） 支撑层数（层） K 0.6 540 × 103 6.0 3 40 0.8 1280 × 1036.0 3 100 0.8 1280 × 1034.5 4 310 0.8 1280 × 1034.0 5 500 1.0 2500 × 1034.0 5 975
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表 3 影响因素值
Table 3. V Values of influencing factors
影响因素 影响因素取值 K（logK） 40
（1.60）100
（2.00）310
（2.49）500
（2.70）975
（2.99）B/L 0.3 0.5 0.7 0.9 — D/（m） 0 4 8 12 16 H/（m） 1.5 6.0 10.5 15.0 20.0
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表 4 地表最大沉降预测参数
Table 4. Prediction parameters of maximum surface settlement
名称 H/m D/m B/L K 取值 19.75 6.9 0.6 370
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