Upper Bound Analysis and Application for Shield Supporting Pressure in Vertical Layered Soil Stratum
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摘要: 为确定地铁隧道中竖向分层土质地层盾构掌子面支护力，基于三维楔形体破坏模式，采用极限分析上限法推导支护力计算公式。在一定约束条件下，利用MATLAB编写粒子群算法求得支护力最优解，与已有文献研究对比，验证其适用性。分析各参数对支护力的影响，结果显示：支护力随土体强度值的增加而降低，随隧道埋深比的增加呈现出先增加后逐渐稳定的变化趋势。当上部土体的内摩擦角大于下部土体时，考虑分层的计算结果大于不考虑分层。以深圳地铁12号线怀福区间土压平衡段为例，支护力的理论计算值与土压力测量值相接近。在该土压力值下，盾构掘进平稳，因此支护力上限法可应用于实际工程中。Abstract: In order to determine the shield supporting pressure for subway tunnel face in vertical layered soil stratum, based on wedge failure mode, the calculation formula of supporting pressure was derived by upper bound method of limit analysis. Under certain constraints, the optimal solution of supporting pressure was got by using MATLAB to write particle swarm optimization. The validity of the proposed solution was demonstrated by comparing the calculated results with existing literature research. The influence of various parameters on supporting pressure was analyzed. The results show that the supporting pressure decreases with the increase of soil strength. With the increase of tunnel depth ratio, supporting pressure increases first and then becomes stable. When the internal friction angle of upper soil is larger than that of the lower soil, the calculation result of considering layering is larger than that of not considering layering. Taking the Huai-Fu section of Shenzhen Metro Line 12 as an example, the theoretical calculation value of supporting pressure matches well with the measured value of earth pressure. Under the earth pressure, the EPB is tunneling stably. The upper bound method of supporting pressure can be applied in practical engineering.
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Key words:
- subway tunnel /
- vertical layered /
- wedge failure mode /
- upper bound method /
- supporting pressure /
- earth pressure
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表 1 对比结果
σ 隧道埋深
C/m试验所得极限
支护力Pf/kPa本文计算
结果/kPaθ1/（°） θ2/（°） 0.3 15 32.5 35.11 44.25 58.25 0.4 10 28.5 35.47 45.55 59.55 0.7 15 46.4 45.41 45.97 59.97 
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表 2 地层参数
土层 重度γ
/（kN·m−3）黏聚力
c/kPa内摩擦角
φ/（°）层厚
h/m渗透系数
k/（m·d−1）素填土 17.8 5.0 18.0 4.5 0.5 硬塑状砂质黏性土 18.4 27.5 22.5 9.1 0.1 全风化混合花岗岩 19.0 30 24.5 5.5 0.2 强风化混合
花岗岩（土状）19.5 35 28.5 1.5
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