外圆内椭管片结构内力计算模型

谷拴成; 孙冠临; 苏培莉

doi:10.19818/j.cnki.1671-1637.2021.04.006

外圆内椭管片结构内力计算模型

doi: 10.19818/j.cnki.1671-1637.2021.04.006

谷拴成^1,,
孙冠临^1, ,,
苏培莉^{1, 2}

1.
西安科技大学建筑与土木工程学院，陕西西安 710054
2.
西安科技大学西安市岩土与地下工程重点实验室，陕西西安 710054

基金项目:

国家自然科学基金项目 41672305

西安市岩土与地下工程重点实验室开放基金项目 XKLGUEKF20-03

中国博士后科学基金项目 2017M623330XB

详细信息

作者简介:
谷拴成(1963-)，男，陕西扶风人，西安科技大学教授，工学博士，从事岩土加固理论与技术及地下结构抗震研究

通讯作者:
孙冠临(1993-)，男，江苏淮安人，西安科技大学工学博士研究生

中图分类号: U451.4
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出版历程
- 收稿日期: 2021-02-12
- 网络出版日期: 2021-09-16
- 刊出日期: 2021-08-01

Computational model of outer-circle and inner-ellipse shield tunnel lining structure

GU Shuan-cheng^1
,,
SUN Guan-lin^{1
, ,},
SU Pei-li^{1, 2}

1.
School of Architecture and Civil Engineering, Xi'an University of Science and Technology, Xi'an 710054, Shaanxi, China
2.
Xi'an Key Laboratory of Geotechnical and Underground Engineering, Xi'an University of Science and Technology, Xi'an 710054, Shaanxi, China

Funds:

National Natural Science Foundation of China 41672305

Open Foundation of Xi'an Key Laboratory of Geotechnical and Underground Engineering XKLGUEKF20-03

China Postdoctoral Science Foundation 2017M623330XB

More Information

Author Bio:
GU Shuan-cheng(1963-), male, professor, PhD, 790480485@qq.com

Corresponding author: SUN Guan-lin(1993-), male, doctoral student, sunguanlin067@163.com

摘要

摘要: 为了使地铁隧道适应地层荷载的不均匀性，参考异形管片结构形式，同时兼顾制作与施工等因素，提出外圆内椭管片结构，以保证管片结构最不利位置的刚度满足安全要求，并适当降低管片其他位置的刚度，充分利用材料特性；采用刚度阶梯折算法求解外圆内椭管片的柔度系数与自由项，建立外圆内椭管片的计算模型；参照实际工程地质条件，研究外圆内椭管片的内力分布特点；利用《铁路隧道设计规范》(TB 1003—2016)对外圆内椭管片的安全性进行评价。计算结果表明：相比于等刚度管片，在相同的荷载条件下，外圆内椭管片减小了管片结构拱顶与拱底的弯矩，将最大弯矩与最大轴力转移至拱腰，在验算时重点分析管片结构拱腰处的内力能否满足安全条件即可，简化了安全验算内容；在稳定性方面，等刚度管片在拱顶、拱肩与拱腰处的安全系数分别为3.07、18.05和2.45，外圆内椭管片在拱顶、拱肩与拱腰处的安全系数分别为2.79、14.86和2.21，虽然较之等刚度管片略有降低，但仍然大于安全验算要求规定的最小值2.0，可充分发挥混凝土的材料特性；在内部空间方面，外圆内椭管片在外径与等刚度管片一致的情况下，等刚度管片的内部空间面积为22.9m²，而外圆内椭管片的内部空间面积为23.76 m²，明显大于等刚度管片面积，因此，可在不扩大外径的条件下，增加了内部空间面积，提高了内部空间利用率。
- 隧道工程 /
- 盾构隧道 /
- 外圆内椭管片 /
- 阶梯折算法 /
- 力学特性 /
- 安全性
Abstract: In order to adapt the metro tunnel to the inhomogeneity of stratum load, referring to the structural form of special-shaped shield tunnel lining and taking into account the factors such as production and construction, the outer-circle and inner-elliptic shield tunnel lining structure was proposed, ensuring that the stiffness of the most unfavorable position of the lining structure meets the safety requirement, appropriately reducing the stiffness of the rest of the lining structure, and taking advantage of material properties. The flexibility coefficient and free term of outer-circle and inner-elliptic shield tunnel lining were solved by the stiffness step discounting method, and the calculation model of the lining was established. Referring to the actual engineering geological condition, the internal force distribution characteristics of outer-circle and inner-elliptic shield tunnel lining were studied. The safety of outer-circle and inner-elliptic shield tunnel lining was evaluated by the Code for Design of Railway Tunnel (TB 1003—2016). Calculation results show that compared with the equal stiffness shield tunnel lining, under the same loading condition, the outer-circle and inner-elliptic shield tunnel lining reduces the bending moments at the top and bottom of the lining structure, and transfers the maximum bending moment and maximum axial force to the arch waist, which simplifies the safety test by focusing on whether the internal force at the arch waist of the lining structure can meet the safety condition during the test. In terms of stability, the safety factors of equal stiffness shield tunnel lining are 3.07, 18.05 and 2.45 at the vault, arch shoulder and arch waist, respectively. The safety factors of outer-circle and inner-elliptic shield tunnel lining are 2.79, 14.86 and 2.21 at the vault, arch shoulder and arch waist, respectively, and slightly lower than those of the equal stiffness shield tunnel lining, but still greater than the minimum value 2.0 stipulated by the safety checking requirement, giving full play to the material characteristics of concrete. In terms of internal space, when the outer-circle and inner-elliptic shield tunnel lining and the equal stiffness shield tunnel lining have the same outer radius, the internal space area of the equal stiffness shield tunnel lining is 22.9 m², and the value of the outer-circle and inner-elliptic shield tunnel lining is 23.76 m² and significantly larger than that of the equal stiffness shield tunnel lining. Therefore, the area and utilization rate of internal space of the proposed lining increase without expanding the outer radius. 8 tabs, 11 figs, 31 refs.
- tunnel engineering /
- shield tunnel /
- outer-circle and inner-ellipse lining /
- step discounting method /
- mechanical property /
- security

HTML全文

图 1 外圆内椭管片截面

Figure 1. Section of outer-circle and inner-ellipse lining

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图 2 外圆内椭管片荷载模型与力法基本结构

Figure 2. Load model and force method's basic structure of outer-circle and inner-ellipse lining

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图 3 单位阶梯函数

Figure 3. Unit step function diagram

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图 4 内轮廓阶梯化处理的基本结构

Figure 4. Basic structure of inner contour stepping treatment

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图 5 西安地铁隧道管片

Figure 5. Xi'an metro shield tunnel linings

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图 6 外圆内椭管片

Figure 6. Outer-circle and inner-ellipse lining

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图 7 外圆内椭管片阶梯化基本结构

Figure 7. Outer-circle and inner-ellipse lining's stepwise basic structure

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图 8 等刚度管片与外圆内椭管片内力分布对比

Figure 8. Comparison of internal force distributions between equal stiffness lining and outer-circle and inner-ellipse lining

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图 9 管片与配筋的有限元模型

Figure 9. Finite element models of lining and reinforcement

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图 10 平均Mises应力云图

Figure 10. Average Mises stress cloud

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图 11 数值模拟与理论分析结果对比

Figure 11. Comparison of numerical simulation and theoretical analysis results

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表 1 土层参数

Table 1. Soil parameters

土层编号	土层类别	重度/(kN· m^-3)	层厚/m	位置
1-2	素填土	15.9	1.7	隧道覆土
2-1-1	黄土状土	5.3	16.4
2-1-2	黄土	18.5	4.6
2-1-2	黄土	18.5	2.5	隧道所处地层
2-2	古土壤	19.4	3.5	隧道所处地层

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表 2 荷载计算值

Table 2. Calculated values of loads

q/ (kN·m^-2)	P₁/ (kN·m^-1)	P₂/ (kN·m^-1)	P₃/ (kN·m^-1)	P₄/ (kN·m^-1)	_γ/ (kN·m^-3)
30.00	229.05	252.61	103.07	154.44	25

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表 3 阶梯化结构的几何数据与计算参数

Table 3. Geometric data and calculated parameters of stepped structure

i	θ/(°)	r_c/m	h/m	I(θ)/m⁴	1/ I(θ)
0	0	2.890 0	0.220 0	0.000 887	1 126.972 2
1	15	2.887 9	0.224 1	0.000 938	1 065.615 0
2	30	2.882 3	0.235 4	0.001 087	920.278 8
3	45	2.874 8	0.250 5	0.001 310	763.493 8
4	60	2.867 3	0.265 4	0.001 557	642.171 6
5	75	2.861 9	0.276 1	0.001 754	570.130 9
6	90	2.860 0	0.280 0	0.001 829	546.647 2

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表 4 结构危险截面内力

Table 4. Internal forces of dangerous sections of structures

结构类型	θ /(°)	M /(kN·m)	N/kN	Q/kN
等刚度管片	0	233.353 9	335.943 3	0.000 0
	45	4.106 8	540.567 8	-163.778 4
	90	-227.581 7	686.468 3	5.587 3
外圆内椭管片	0	195.877 5	341.652 7	0.000 0
	45	-3.532 2	515.913 3	-162.505 8
	90	-263.693 3	683.161 0	6.591 1

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表 5 结构安全系数

Table 5. Safety factors of structures

结构类型	校核位置安全系数
结构类型	正弯矩最大处	剪力最大处	负弯矩、轴力最大处
等刚度管片	3.07	18.05	2.45
外圆内椭管片	2.79	14.86	2.21

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表 6 安全验算参数

Table 6. Safety verification parameters

D/kN	A₃/mm²		e₂/mm	σ/MPa	G/mm⁴
D/kN	拱顶	拱腰	e₂/mm	σ/MPa	拱顶	拱腰
1 500	1.76× 10⁵	2.24× 10⁵	10	18.2	7.10× 10⁸	1.46× 10⁹

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表 7 混凝土与钢筋材料参数

Table 7. Material parameters of concrete and reinforcement

材料	泊松比	弹性模量/GPa	密度/(kg·m^-3)
混凝土(C50)	0.2	34.5	2 600
钢筋(HPB400)	0.3	200.0

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表 8 ABAQUS与理论分析结果对比

Table 8. Comparison of ABAQUS and theoretical analysis results

内力	0°		45°		90°		135°		180°
内力	理论	ABAQUS	理论	ABAQUS	理论	ABAQUS	理论	ABAQUS	理论	ABAQUS
弯矩/(kN·m)	195.878	195.544	-44.243	-45.446	-263.69	-262.953	-33.608	-36.882	185.274	185.168
轴力/kN	341.653	336.712	515.913	518.135	683.161	686.228	540.915	540.202	402.558	400.921
剪力/kN	0.000	5.160	-162.51	-156.600	6.591	1.626	154.037	153.562	0.000	0.392

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