Analysis of Limit Support Pressure Due to Shield Tunnelling with a Shallow Overburden Under Seepage
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摘要: 基于半承压水模型综合考虑土压盾构穿越渗透性地层时覆土层及下卧层的渗透性，推导了盾构穿越层中沿掘进方向的水头分布的解析解，将其与现有的二维渗流场的解析解结合扩展为相应的三维近似解，同时采用数值仿真得到稳态渗流条件下浅埋渗透性地层的主、被动破坏模式，建立了相应的柱体+弧形转角体模型，将前述三维渗流场引入该模型，通过力矩平衡法得到了相应两种极限状态下开挖面支护压力的计算公式，与既有结果进行对比，此计算方法更接近数值解. 研究结果表明：施工对开挖面前方渗流场的扰动基本局限在三倍洞径以内，主、被动极限支护压力的值随水头差的增大均线性增加，盾构直径和水头差是影响主动极限支护压力的主要因素，拱顶埋深与盾构直径是影响被动极限支护压力的主要因素；实际施工过程中，支护压力值应尽可能接近水土分算下的土体原始地层侧压力值，并在其附近（最好在其上方）小幅度波动，波动范围应以变形控制标准为依据.Abstract: Based on the semi-contained water model, the permeability of shield-crossing soil and overburden layers when the shield passed through the permeable soil was comprehensively analysed. The analytical solution of the head distribution along the tunnelling direction in the shield-crossing soil layer was derived, and the analytical solution of the two-dimensional seepage field was extended to the corresponding three-dimensional approximate solution. The active and passive failure modes of shallow-buried soil under steady-state seepage were determined using numerical modelling, and a corresponding cylinder-arc-corner-shaped model was established. Subsequently, the formulas of the two-limit support pressures at the tunnel face were obtained by introducing the above-mentioned three-dimensional seepage solution, and the newly calculated results were compared with those of the existing model. The results derived from the developed model were closer to the numerical solution. In addition, disturbance of the seepage field in front of the tunnel face was limited to three times the tunnel diameter and the values of the active and passive limit support pressure increased linearly with increasing head difference. The shield diameter and head difference were found to be the two main factors affecting the active limit pressure. The overburden thickness and shield diameter were the two major factors affecting the passive limit pressure. During tunnelling, the support pressure should be as close as possible to the in-situ transverse earth pressure using the approach that separately calculated the values for soil and water and should slightly fluctuate in the vicinity (preferably above it). The fluctuation range should be determined according to the deformation control standard.
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Key words:
- Shield tunnelling /
- permeable soil /
- seepage /
- limit support pressure
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图 1
$y = D$ 处孔隙水压力分布（单位：Mpa）Figure 1. Distribution of pore water pressure at
$y = D$ （unit：Mpa）
图 2
$AB$ 线孔压解析解与数值解对比 （$y = D$ 单位：Mpa）Figure 2. Comparison between analytical solution and numerical solution of pore water pressure on line
$AB$ （$y = D$ unit：Mpa，）
图 3
$MN$ 线孔压解析解与数值解对比（单位：Mpa）Figure 3. Comparison between analytical solution and numerical solution of pore water pressure on line
$MN$ （unit：Mpa）
图 4 模型最大塑性剪切应变率（变形放大50倍）
Figure 4. Maximum plastic shearing strain rate of numerical model （The deformation is magnified 50 times）
图 6 极限支护压力与水头差的关系
Figure 6. Relationship between limit support stress and water head difference
表 1 隧道几何参数及围岩力学参数
Table 1. Geometric parameters of tunnel and mechanics parameters of surrounding soil
D/m C/m H/m c/kPa $\varphi $/（°） $\gamma $/（kg•m–3） ${\gamma _{{\rm{sat}}}}$/（kg•m–3） 5 5 5/10/15 1 30 1 611 1 920 
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表 2 各影响参数取值及主、被动极限支护压力敏感度因子
Table 2. Selection of parameters and its sensitivity to active and passive limit support pressures
参数 取值 参数变化范围/m 敏感度因子 主动 被动 $D$ 10 m 5 m～15 m 0.66 0.94 $C$ 10 m 5 m～15 m 0.08 1.44 $H$ 5 m 0～10 m 0.24 0.19 $\gamma $ 20 kN•m – 3 15 kN•m–3～25 kN•m–3 0.10 0.35 ${\eta _\gamma }$ 0.525 0.4～0.65 0.41 0.17 $\varphi $ 30° 5°～55° 0.05 0.42 ${\eta _\varphi }$ 0.75 0.5～1.0 0.17 0.55 $c$ 5 kPa 0 ～ 10 kPa 0.02 0.05 ${\eta _c}$ 0.75 0.5～ 1.0 0.15 0.06 $\Delta h$ 10 m 0～20 m 0.56 0.23 $q$ 25 kPa 0 ～50 kPa 0.02 0.13
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表 3 地层力学参数
Table 3. Mechanical parameters of soil
土层编号 名称 饱和重度/（kN•m–3） 黏聚力/kPa 内摩擦角/（°） 渗透系数/（cm•s–1） 侧压力系数 （1） 杂填土 19.1 12.32 12.50 3.43 × 10–6 0.65 （2） 粉质黏土 19.3 16.57 18.54 4.63 × 10–6 0.52 （3） 粉质黏土 19.3 15.21 22.35 3.36 × 10–6 0.55 （4） 粘质黏土 19.2 14.64 24.16 3.64 × 10–5 0.55 （5） 粘质黏土 20.0 16.32 18.36 5.73 × 10–4 0.53 （6） 粉质黏土 20.2 15.68 19.83 4.62 × 10–6 0.52
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