考虑参数空间变异性的隧道结构变形分析简化方法

张晋彰; 黄宏伟; 张东明; 方国光; 唐冲

doi:10.11779/CJGE202201013

考虑参数空间变异性的隧道结构变形分析简化方法 English Version

张晋彰^{1, 2,},
黄宏伟^1, ,,
张东明¹,
方国光²,
唐冲²

1.
同济大学土木工程学院, 上海 200092
2.
新加坡国立大学土木及环境工程系, 新加坡 117576

基金项目:

国家自然科学基金项目 52130805

国家自然科学基金项目 52022070

详细信息

作者简介:
张晋彰(1994—)，男，博士研究生，主要从事地层变异和参数空间变异对隧道结构变形的影响方面的研究工作。E-mail: zhangjz@tongji.edu.cn

通讯作者:
黄宏伟, E-mail: huanghw@tongji.edu.cn

中图分类号: TU43;U45
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出版历程
- 收稿日期: 2021-06-29
- 网络出版日期: 2022-09-22
- 刊出日期: 2021-12-31

Simplified methods for deformation analysis of tunnel structures considering spatial variability of soil properties

1.
College of Civil Engineering, Tongji University, Shanghai 200092, China
2.
Department of Civil and Environmental Engineering, National University of Singapore, 117576, Singapore

摘要

摘要: 土体参数具有空间变异性是被广泛接受的，而这种变异性对岩土中结构性能有着重要的影响。随机场理论是一种常用的用来模拟土体参数空间变异性的方法。基于随机场理论，以土体弹性模量的空间变异性为切入点，采用蒙特卡罗方法和有限差分模拟计算相结合的方法，开展隧道水平收敛的随机分析。在大量蒙特卡罗计算基础上，提出了3种简单易用的简化考虑空间变异性的方法，分别为参数折减法、放大系数法和可靠度分项系数标定法。经过对计算结果的统计分析，给出了在土体弹性模量的水平、竖向相关距离及其变异系数的不同组合下3种简化考虑方法的建议值。提出的简化方法可以为空间变异性研究应用到实际工程提供一定的参考。
- 隧道 /
- 空间变异性 /
- 随机场 /
- 相关距离 /
- 简化方法
Abstract: The spatial variability of soil properties is widely accepted, and the response of a geo-structure can be significantly affected by the spatial variability of the surrounding soil mass. The random field theory is a popularly used method to simulate the spatial variability of soil properties. The stochastic analysis of horizontal convergence of tunnel is carried out using the random field difference method considering the spatial variability of Young's modulus. The random field difference method is combined with the Monte Carlo method and finite difference simulation based on random field theory. A large number of Monte Carlo simulations are adopted in the proposed random field difference method. Meanwhile, three simple and easy-to-use methods for the spatial variability of soil are proposed: reduction factor method, amplification factor method and reliability partial factor calibration method. Based on the statistical analysis of the calculated results, the suggested values of three simplified analysis methods under different combinations of the horizontal scale of fluctuation, the vertical scale of fluctuation and the coefficient of variation are given. This study may provide references for the application of spatial variability research to practical geotechnical engineering.
- tunnel /
- spatial variability /
- random field /
- scale of fluctuation /
- simplified method

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图 1 隧道开挖有限差分模型

Figure 1. Finite difference model of tunnel

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图 2 隧道水平收敛的收敛趋势统计

Figure 2. Converging trend of ΔD_h statistics

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图 3 场地分层土弹性模量云图

Figure 3. E for site-specific case

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图 4 隧道收敛工程实测数据计算结果直方图对比

Figure 4. Comparison of histogram of ΔD_h

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图 5 弹性模量和隧道水平收敛关系

Figure 5. Relationship between Young's modulus and ΔD_h

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图 6 不同空间变异性条件下弹性模量折减系数分布图

Figure 6. Reduction factors incorporating different randomness levels

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图 7 不同空间变异性条件下隧道收敛放大系数分布图

Figure 7. Amplification factors incorporating different randomness levels

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图 8 不同空间变异性条件下隧道收敛可靠度分项系数分布图

Figure 8. Values of partial factors of reliability incorporating different randomness levels

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图 9 不同埋深对隧道收敛的影响

Figure 9. Effects of tunnel depth on horizontal convergence

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表 1 数值模型中接触面参数表

Table 1 Parameters of interface in numerical model

对应节点层	抗拉刚度/(GPa·m^-1)	抗压刚度/(GPa·m^-1)	剪切刚度(GPa·m^-1)
2，3	5.40	0	0
6，7	5.40	120	10000
1，4，5	0.08	0	0

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表 2 模拟工况设置

Table 2 Case design of random field

工况	δ_h/m	δ_v/m	δ_h/δ_v	δ_h/D	δ_v/D
ANI-1	60	1.5	40.00	9.68	0.24
ANI-2	60	3.1	19.35	9.68	0.50
ANI-3	60	6.2	9.68	9.68	1.00
ANI-4	60	15	4.00	9.68	2.42
ANI-5	60	30	2.00	9.68	4.84
ANI-6	60	60	1.00	9.68	9.68
ANI-7	90	1.5	60.00	14.52	0.24
ANI-8	29.03	1.5	19.35	4.68	0.24
ANI-9	14.52	1.5	9.68	2.34	0.24
ANI-10	6	1.5	4.00	0.97	0.24
ANI-11	3	1.5	2.00	0.48	0.24
ANI-12	1.5	1.5	1.00	0.24	0.24

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表 3 均质模型工况的设置和计算结果

Table 3 Case design and results of deterministic analysis

E/MPa	2.5	5	7.5	10	15	20
ΔD_h /mm	86.18	52.82	38.49	30.43	21.75	17.24

E/MPa	25	30	35	40	45	50
ΔD_h /mm	14.31	12.17	10.76	9.71	8.73	7.97

E/MPa	55	60	65	70	80	90
ΔD_h /mm	7.31	6.76	6.25	5.80	5.09	4.49

E/MPa	100	110	120	130
ΔD_h /mm	4.03	3.63	3.29	3.01

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表 4 竖向相关距离变化下的弹性模量折减系数(δ_h=60 m)

Table 4 Reduction factors of E with δ_v (δ_h=60 m)

置信区间	COV	竖向相关距离δ_v/m
置信区间	COV	1.5	3.1	6.2	15	30	60
95%	0.1	0.88	0.86	0.85	0.83	0.79	0.80
	0.3	0.73	0.68	0.65	0.59	0.53	0.55
	0.5	0.60	0.55	0.54	0.42	0.36	0.34
99%	0.1	0.86	0.84	0.84	0.80	0.75	0.77
	0.3	0.69	0.62	0.55	0.52	0.48	0.46
	0.5	0.54	0.49	0.45	0.36	0.31	0.29

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表 5 水平相关距离变化下的弹性模量折减系数(δ_v=1.5 m)

Table 5 Reduction factors of E with δ_h (δ_v=1.5 m)

置信区间	COV	水平相关距离δ_h/m
置信区间	COV	1.5	3	6	14.52	29.03	60	90
95%	0.1	0.91	0.89	0.89	0.88	0.87	0.88	0.88
	0.3	0.81	0.77	0.74	0.75	0.74	0.73	0.72
	0.5	0.72	0.68	0.62	0.59	0.58	0.60	0.59
99%	0.1	0.90	0.89	0.87	0.86	0.86	0.86	0.87
	0.3	0.79	0.72	0.66	0.72	0.70	0.69	0.69
	0.5	0.69	0.62	0.58	0.53	0.46	0.54	0.54

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表 6 竖向相关距离变化下的隧道收敛放大系数(δ_h=60 m)

Table 6 Amplification factors of ΔD_h with δ_v (δ_h=60 m)

置信区间	COV	竖向相关距离δ_v/m
置信区间	COV	1.5	3.1	6.2	15	30	60
95%	0.1	1.07	1.09	1.10	1.13	1.18	1.16
	0.3	1.26	1.34	1.38	1.52	1.64	1.59
	0.5	1.50	1.61	1.64	2.00	2.31	2.41
99%	0.1	1.09	1.11	1.12	1.17	1.23	1.20
	0.3	1.32	1.44	1.61	1.67	1.81	1.88
	0.5	1.64	1.76	1.89	2.30	2.65	2.77

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表 7 水平相关距离变化下的隧道收敛放大系数(δ_v=1.5 m)

Table 7 Amplification factor of ΔD_h with δ_h (δ_v=1.5 m)

置信区间	COV	水平相关距离δ_h/m
置信区间	COV	1.5	3	6	14.52	29.03	60	90
95%	0.1	1.04	1.06	1.06	1.08	1.08	1.07	1.08
	0.3	1.15	1.20	1.24	1.23	1.25	1.26	1.27
	0.5	1.28	1.34	1.45	1.50	1.53	1.50	1.50
99%	0.1	1.05	1.07	1.08	1.09	1.09	1.09	1.08
	0.3	1.18	1.27	1.37	1.27	1.30	1.32	1.32
	0.5	1.32	1.44	1.54	1.64	1.85	1.64	1.62

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表 8 竖向相关距离变化下可靠度分项系数标定(δ_h=60 m)

Table 8 Partial factors of reliability with δ_v (δ_h=60 m)

竖向相关距离/m	COV=0.1			COV=0.3			COV=0.5
竖向相关距离/m	$\beta =$ 2.7	$\beta =$ 3.2	$\beta =$ 3.7	$\beta =$ 2.7	$\beta =$ 3.2	$\beta =$ 3.7	$\beta =$ 2.7	$\beta =$ 3.2	$\beta =$ 3.7
1.5	1.11	1.13	1.15	1.34	1.41	1.47	1.69	1.82	1.97
3.1	1.13	1.15	1.18	1.50	1.60	1.72	1.88	2.07	2.29
6.2	1.14	1.17	1.20	1.62	1.76	1.92	2.03	2.28	2.56
15	1.19	1.23	1.26	1.76	1.94	2.14	2.52	2.94	3.43
30	1.26	1.31	1.36	1.99	2.24	2.53	3.02	3.64	4.40
60	1.27	1.32	1.38	2.01	2.27	2.57	3.32	4.08	5.00

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表 9 水平相关距离变化下可靠度分项系数标定(δ_v=1.5 m)

Table 9 Partial factors of reliability with δ_h (δ_v=1.5 m)

竖向相关距离/m	COV=0.1			COV=0.3			COV=0.5
竖向相关距离/m	$\beta =$ 2.7	$\beta =$ 3.2	$\beta =$ 3.7	$\beta =$ 2.7	$\beta =$ 3.2	$\beta =$ 3.7	$\beta =$ 2.7	$\beta =$ 3.2	$\beta =$ 3.7
1.5	1.06	1.07	1.08	1.19	1.22	1.26	1.37	1.43	1.49
3	1.08	1.09	1.10	1.28	1.33	1.38	1.45	1.53	1.61
6	1.09	1.11	1.12	1.34	1.40	1.46	1.59	1.70	1.82
14.5	1.10	1.12	1.14	1.35	1.41	1.48	1.70	1.85	2.00
29	1.11	1.13	1.15	1.34	1.41	1.47	1.73	1.88	2.04
60	1.11	1.13	1.15	1.34	1.41	1.47	1.69	1.82	1.97
90	1.11	1.13	1.15	1.36	1.42	1.50	1.67	1.81	1.95

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表 10 不同埋深下3种方法结果对比(δ_h=60 m, δ_v=1.5 m)

Table 10 Comparison of results of three methods at different depths (δ_h=60 m, δ_v=1.5 m)

置信区间	方法		浅埋	中埋	深埋	浅埋误差/%	深埋误差/%
95%	参数折减法		0.76	0.73	0.77	4.10	5.48
	放大系数法		1.26	1.26	1.25	0	0.79
	可靠度分项系数法	β=2.7	1.36	1.34	1.33	1.49	0.75
		β=3.2	1.43	1.41	1.40	1.42	0.71
		β=3.7	1.50	1.47	1.46	2.04	0.68

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考虑参数空间变异性的隧道结构变形分析简化方法 English Version

作者简介: 张晋彰(1994—)，男，博士研究生，主要从事地层变异和参数空间变异对隧道结构变形的影响方面的研究工作。E-mail: zhangjz@tongji.edu.cn

通讯作者: 黄宏伟, E-mail: huanghw@tongji.edu.cn

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出版历程

Simplified methods for deformation analysis of tunnel structures considering spatial variability of soil properties

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出版历程

目录

作者简介:
张晋彰(1994—)，男，博士研究生，主要从事地层变异和参数空间变异对隧道结构变形的影响方面的研究工作。E-mail: zhangjz@tongji.edu.cn

通讯作者:
黄宏伟, E-mail: huanghw@tongji.edu.cn