基于随机介质理论的偏压隧道地表沉降预测方法

周鹏远; 宋战平; 王军保; 张玉伟; 田小旭

doi:10.11779/CJGE20231121

基于随机介质理论的偏压隧道地表沉降预测方法 English Version

周鹏远^{1, 2,},
宋战平^{1, 2, 3, ,},
王军保^{1, 2},
张玉伟^{1, 2, 3},
田小旭^{1, 2}

1.
西安建筑科技大学土木工程学院, 陕西西安 710055
2.
陕西省岩土与地下空间工程重点实验室, 陕西西安 710055
3.
西安建筑科技大学基础设施智能建造研究院, 陕西西安 710055

基金项目:

国家自然科学基金项目 52178393

陕西省科技创新团队项目 2020TD-005

详细信息

作者简介:
周鹏远(1993—)，男，博士研究生，主要从事城市地下空间及岩土工程方面的研究工作。E-mail: zhoupengyuan@xauat.edu.cn

通讯作者:
宋战平, E-mail: songzhpyt@xauat.edu.cn

中图分类号: TU91
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出版历程
- 收稿日期: 2023-11-20
- 网络出版日期: 2024-08-20
- 刊出日期: 2025-02-28

Prediction method for ground surface settlement induced by bias tunnel based on stochastic medium theory

ZHOU Pengyuan^{1, 2,},
SONG Zhanping^{1, 2, 3, ,},
WANG Junbao^{1, 2},
ZHANG Yuwei^{1, 2, 3},
TIAN Xiaoxu^{1, 2}

1.
School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China
2.
Shaanxi Key Laboratory of Geotechnical and Underground Space, Xi'an University of Architecture and Technology, Xi'an 710055, China
3.
Infrastructure Intelligent Construction Research Institute, Xi'an University of Architecture and Technology, Xi'an 710055, China

摘要

摘要: 隧道开挖引起地表沉降的各种预测方法均假定隧道收敛模式为对称形式，忽略了隧道非对称收敛的影响。为对偏压隧道引起地表沉降进行预测，提出了一种新的隧道偏压收敛模式，定义了相应的偏压参数 $\theta$ ， ${\gamma _1}$ ， ${\gamma _3}$ ，基于随机介质理论，利用坐标变换和二重积分的数值化处理，得到了偏压隧道引起地表沉降的预测模型；通过实际工程案例，验证了该方法的适用性，并分析了相关参数对地表沉降的影响规律。提出的预测模型将传统对称收敛模式拓展至非对称情况，能很好预测地表沉降的非对称趋势，且更接近实际案例的监测数值。
- 偏压隧道 /
- 地表沉降预测 /
- 隧道收敛模式 /
- 随机介质理论
Abstract: The disturbance of the surrounding soil by tunnel excavation will inevitably lead to surface settlement. When calculating the surface settlement caused by tunnel excavation, various prediction methods have assumed that the tunnel convergence mode is bilaterally symmetrical. This assumption ignores the influences of asymmetric convergence of the tunnel, and the resulting surface settlement is also symmetrically distributed. In order to predict the surface settlement caused by a bias tunnel, a new tunnel bias convergence mode is proposed, and the corresponding bias parameters $\theta$ , ${\gamma _1}$ and ${\gamma _3}$ are defined. Based on the stochastic medium theory, a prediction model for the surface settlement caused by the bias tunnel is obtained using the coordinate transformation and double-integral numerical processing. Through actual engineering cases, the applicability of this method is verified, and the influences of the relevant parameters on the surface settlement are analyzed. The proposed model extends the traditional symmetric convergence mode to asymmetric situations, can well predict the asymmetric trend of surface settlement, and it is closer to the monitoring values of actual cases.
- bias tunnel /
- surface settlement prediction /
- tunnel convergence mode /
- stochastic medium theory

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图 1 二维断面开挖收敛示意图

Figure 1. Schematic diagram of 2D section convergence

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图 2 圆形隧道经典不均匀收敛模式

Figure 2. Classical convergence mode for circular tunnel

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图 3 圆形隧道偏压收敛模式

Figure 3. Convergence mode for bias tunnel

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图 4 偏压隧道积分坐标变换示意图

Figure 4. Schematic diagram of coordinate transformation

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图 5 福宁路—五块石区间工程平面图

Figure 5. Layout plan of Funinglu Station-Wukuaishi Station project

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图 6 工程区间地质剖面图

Figure 6. Geological profile map of project

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图 7 各断面偏压隧道地表沉降预测

Figure 7. Prediction of surface settlement of bias tunnel at each section

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图 8 本文方法与传统对称收敛模型的比较

Figure 8. Comparison between proposed method and traditional symmetric convergence model

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不同 $\theta$ 下地表沉降曲线

Curves of surface settlement under different values of $\theta$

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$\Delta X$ 及S_max随 $\theta$ 变化规律

Variation trends in $\Delta X$ and S_max with $\theta$

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不同 ${\gamma _1}$ 下地表沉降曲线

Curves of surface settlement under different values of ${\gamma _1}$

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$\Delta X$ 及S_max随 ${\gamma _1}$ 变化规律

Variation trends in $\Delta X$ and S_max with ${\gamma _1}$

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不同 ${\gamma _3}$ 下地表沉降曲线

Curves of surface settlement under different values of ${\gamma _3}$

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$\Delta X$ 及S_max随 ${\gamma _3}$ 变化规律

Variation trends in $\Delta X$ and S_max with ${\gamma _3}$

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不同 $H{\text{/}}R$ 下地表沉降曲线

Curves of surface settlement under different values of $H{\text{/}}R$

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$\Delta X$ 及S_max随 $H{\text{/}}R$ 变化规律

Variation trends in $\Delta X$ and S_max with $H{\text{/}}R$

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表 1 偏压隧道收敛模式积分界限表

Table 1 Integral limits of convergence mode of bias tunnel

$\varOmega$ -整体坐标系		$\omega$ -局部坐标系
$a$	$H - R$	$e'$	$- (R - {u_0} - {u_1})$
$b$	$H + R$	$f'$	$R - {u_0} - {u_1}$
$c$	$- \sqrt {{R^2} - {{(\eta - H)}^2}}$	$g'$	$\begin{gathered} - (R - {u_0} + {u_2}) \cdot \hfill \\ \sqrt {1 - {{\left[ {\eta '/(R - {u_0} - {u_1})} \right]}^2}} \hfill \\ \end{gathered}$
$d$	$\sqrt {{R^2} - {{(\eta - H)}^2}}$	$h'$	$\begin{gathered} (R - {u_0} + {u_2}) \cdot \hfill \\ \sqrt {1 - {{\left[ {\eta '/(R - {u_0} - {u_1})} \right]}^2}} \hfill \\ \end{gathered}$

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表 2 土体物理力学参数表

Table 2 Physical and mechanical parameters of soils

土层名称	重度 $\gamma$ /(kN·m^-3)	弹性模量E/MPa	泊松比 $\nu$	黏聚力c/kPa	内摩擦角 $\varphi$ /(°)
人工填土	18	7	0.3	8	10
粉质黏土	19.5	15	0.3	20	16.5
细砂	18.5	4	0.27	0	20
松散卵石	20	20	0.26	0	30
稍密卵石	21	23	0.28	0	35
中密卵石	22	32	0.25	0	40
密实卵石	23	43	0.22	0	45
中砂	19	5.5	0.26	0	22

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表 3 成都地铁五号线典型偏压断面计算参数表

Table 3 Parameters of typical section of Chengdu Metro Line 5

断面	里程	$H{\text{/m}}$	$R{\text{/m}}$	$\beta /(^\circ {\text{ }})$	${V_{\text{l}}}/\%$	$\theta /(^\circ {\text{ }})$	${\gamma _1}/\%$	${\gamma _3}/\%$
DK1	DK15+620	19.5	3	34.5	2	43	0.97	0.33
DK2	DK15+770	26.5	3	34.7	2	45	0.73	0.29
DK3	DK15+830	21.4	3	35.0	2	12	0.76	0.21

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表 4 研究隧道计算参数表

Table 4 Parameters of tunnels

隧道	$H{\text{/m}}$	$R{\text{/m}}$	$\beta /(^\circ {\text{ }})$	${V_{\text{l}}}/\%$	$\theta /(^\circ {\text{ }})$	${\gamma _1}/\%$	${\gamma _3}/\%$
巴西快速交通隧道	14.0	4.8	37.60	8.52	38	0.36	0.17
台湾三义一号隧道	23.5	5.5	41.67	1.77	-29	0.56	0.14
某215工程隧道	19.5	3.0	51.11	0.28	23	0.33	0.09

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