Stratum disturbance induced by shield tunnels based on random field theory
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摘要: 盾构开挖不可避免会造成周围地层扰动，引起地表及深部地层发生变形，变形过大时会威胁到周围建构（筑）物的安全，因而有必要开展隧道施工地表及地层变形扰动方面的研究。首先在土体均质条件下，开展二维数值计算，并分别利用Peck公式拟合优度和多项式拟合优度来评价水平向地层和竖向地层的变形扰动程度；继而考虑土体参数空间变异性，借助Monte Carlo策略，开展盾构施工对地层扰动规律影响研究的随机性分析。研究结果表明：Peck公式拟合优度可以较好地反映施工引起水平地层沉降变形程度；多项式拟合优度可以较好地反映竖向地层水平变形受到施工的影响程度；土体模量空间变异性会对盾构隧道施工地层扰动产生较大的影响，模量较大时会对盾构施工地层扰动有一定的“抑制”作用，但总体上越靠近盾构隧道，地层受到扰动越大。研究可以为类似工程的设计和施工提供有益的参考。Abstract: The shield tunnel will inevitably cause the disturbance of the surrounding stratum and lead to the deformation of the surface and deep strata. Too large deformation of the surface and strata will threaten the safety of the surrounding construction. Therefore, it is necessary to carry out the studies on the disturbance of the surface and strata in tunnel construction. Firstly, under homogeneous soil conditions, two-dimensional numerical calculation is conducted, and the goodnesses of fit of the Peck's formula and polynomials are used to evaluate the degree of deformation disturbance of the horizontal and vertical strata, respectively. Then, considering the spatial variability of soil parameters, within the Monte Carlo framework, the random analysis is performed for the influences of shield construction on stratum disturbance. The results show that the goodness of fit of the Peck's formula can well reflect the degree of settlement of the horizontal strata induced by tunnels. The goodness of fit of the polynomials can well reflect the degree of horizontal deformation of the vertical strata affected by the construction. The spatial variability of soil modulus has a great impact on the stratum disturbance induced by the shield tunnel, and the larger modulus will restrain the disturbance induced by the shield tunnel, but on the whole, the greater stratum disturbance will occur when it is closer to the shield tunnel. The results can provide a useful reference for the design and construction of similar projects.
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Keywords:
- shield tunnel /
- deep stratum /
- deformation and disturbance /
- goodness of fit /
- spatial variability /
- random field
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图 2 地层位移分析剖面示意图
Figure 2. Schematic diagram of analysis section for stratum displacement
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图 4 水平地层沉降曲线及其回归结果对比
Figure 4. Comparison of settlement curves and regression results of horizontal strata
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图 5 竖向地层水平变形曲线及其回归结果对比
Figure 5. Comparison of horizontal deformation curves and regression results of vertical strata
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图 6 竖向地层变形曲线多项式拟合优度对比
Figure 6. Comparison of goodnesses of fit polynomials of deformation curves of vertical strata
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图 7 随机计算结果与确定性计算结果对比（地表沉降）
Figure 7. Comparison between random and deterministic results (surface settlement)
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图 8 水平地层沉降Peck公式拟合优度对比结果
Figure 8. Comparison of goodnesses of fit of Peck formula for settlement of horizontal stratum
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图 9 竖向地层的水平变形随机计算结果（地层c和g）
Figure 9. Random results of horizontal deformation (stratum c and g)
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图 10 竖向地层剖面的水平变形拟合优度对比结果
Figure 10. Comparison results for goodness of fit of horizontal deformation of vertical stratum profile
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图 11 不同模拟时的模量参数分布情况
Figure 11. Distribution of modulus parameters in different simulations
表 1 土体及管片物理力学参数
Table 1 Parameters of soils and segments
材料 密度/(kg·m-3) 弹性模量/MPa 内摩擦角/(°) 黏聚力/kPa 泊松比 土体 1800 24.0 20 13.0 0.35 管片 2450 24.44×103 — — 0.20 
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表 2 地层竖向变形曲线回归分析
Table 2 Regression analysis of vertical deformation curves
多项式回归分析 竖向地层a 竖向地层b 竖向地层c 竖向地层d 三次多项式 0.9801 0.9577 0.8904 0.8520 四次多项式 0.9812 0.9778 0.9556 0.8805 五次多项式 0.9971 0.9922 0.9659 0.8805 六次多项式 0.9998 0.9989 0.9860 0.8951 七次多项式 0.9999 0.9990 0.9862 0.8951
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