黏弹性围岩纵向变形曲线及其释放系数演化规律

doi:10.16183/j.cnki.jsjtu.2023.350

上海交通大学学报 ›› 2025, Vol. 59 ›› Issue (4): 513-524.doi: 10.16183/j.cnki.jsjtu.2023.350

黏弹性围岩纵向变形曲线及其释放系数演化规律

王嘉琛¹, 孟令赞¹^,², 张顶立¹(), 卢松¹, 文明³

1.北京交通大学城市地下工程教育部重点实验室,北京 100044
2.北京城建设计发展集团股份有限公司北京市轨道结构工程技术研究中心,北京 100037
3.北京市应急管理科学技术研究院城市运行安全研究中心,北京 101101

收稿日期:2023-07-28 修回日期:2024-02-20 接受日期:2024-03-27 出版日期:2025-04-28 发布日期:2025-05-09
通讯作者: 张顶立 E-mail:zhang_dingli@263.net
作者简介:王嘉琛(1998—),博士生,从事隧道与地下工程研究.
基金资助:
中央高校基本科研业务费专项资金(2023YJS049)

Evolution Law of Longitudinal Deformation Curve and Release Coefficient of Viscoelastic Rock

WANG Jiachen¹, MENG Lingzan¹^,², ZHANG Dingli¹(), LU Song¹, WEN Ming³

1. Key Laboratory for Urban Underground Engineering of the Ministry of Education, Beijing Jiaotong University, Beijing 100044, China
2. Beijing Engineering Research Center of Track Structure, Beijing Urban Construction Design and Development Group Co., Ltd., Beijing 100037, China
3. Urban Operation Safety Research Center, Beijing Academy of Emergency Management Science and Technology, Beijing 101101, China

Received:2023-07-28 Revised:2024-02-20 Accepted:2024-03-27 Online:2025-04-28 Published:2025-05-09
Contact: ZHANG Dingli E-mail:zhang_dingli@263.net

摘要/Abstract

摘要：

常规的弹性解无法对具有强蠕变特性的软岩隧道变形规律提出合理解释.因此,针对软岩隧道施工的时间-空间效应,引入Burgers模型揭示其时空演化规律,并通过数值计算探究不同因素对黏弹性围岩纵向变形规律的影响.同时基于响应面法得到位移释放系数的经验公式,与现场监测和其他理论比较验证了本文方法的可行性.研究结果表明地应力对位移释放系数影响可忽略,Kelvin切变模量、Kelvin黏滞系数、Maxwell切变模量和开挖速度显著影响位移释放系数,而根据延滞时间的不同可分为低延滞系数、中延滞系数和高延滞系数3类;针对时间效应影响型、空间效应影响型和时空效应影响型3种黏弹性围岩纵向变形曲线类型拟合得到相应的经验公式.研究结论可为软岩隧道变形预测提供更简便的方法.

关键词: 黏弹性, 纵向变形曲线, 软岩隧道, 时空效应, 位移释放系数

Abstract:

Conventional elastic solutions cannot explain the deformation characteristics of soft rock tunnels exhibiting creep behavior. Therefore, a Burgers model is introduced to demonstrate the space-time effects in the construction period of soft rock tunnel. The influences of different factors on the longitudinal deformation behavior of viscoelastic rock as well as the spatiotemporal evolution patterns have been revealed through numerical simulations. An empirical formula for the displacement release coefficient is derived using the response surface method. The feasibility of the proposed method is validated by comparing the results with on-site monitoring data and other theoretical values. The findings indicate that geostress has a negligible effect on the displacement release coefficient. In constrast, the Kelvin shear modulus, viscosity coefficient, Maxwell shear modulus, and excavation speed significantly affect the displacement release coefficient. According to viscosity time, the hysteresis coefficient can be divided into three categories: low, medium, and high. Empirical formulas are fitted for the longitudinal deformation curve, including time, spatial, and spatiotemporal factors. The research conclusion can provide a more convenient method for predicting the deformation of soft rock tunnels.

Key words: viscoelasticity, longitudinal deformation profile, soft rock tunnel, time-space effect, displacement release coefficient

中图分类号:

TU432

王嘉琛, 孟令赞, 张顶立, 卢松, 文明. 黏弹性围岩纵向变形曲线及其释放系数演化规律[J]. 上海交通大学学报, 2025, 59(4): 513-524.

WANG Jiachen, MENG Lingzan, ZHANG Dingli, LU Song, WEN Ming. Evolution Law of Longitudinal Deformation Curve and Release Coefficient of Viscoelastic Rock[J]. Journal of Shanghai Jiao Tong University, 2025, 59(4): 513-524.

图/表 26

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表2

表3

图5

图6

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图9

图10

图11

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表4

图14

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表5

图16

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表6

图18

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图20

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系列	G_K/GPa	η_K/(GPa·h)	G_M/GPa	K/MPa	系列	G_K/GPa	η_K/(GPa·h)	G_M/GPa	K/MPa
1	3.72	0.13	8.90	95.14	8	3.23	16.7	0.410	160.32
2	2.38	0.11	5.16	65.79	9	0.94	9.7	0.088	74.36
3	0.23	0.03	0.68	47.44	10	4.21	155.2	9.770	58.33
4	9.75	0.23	16.66	60.42	11	2.27	185.3	1.660	168.00
5	3.65	0.13	8.42	70.83	12	2.27	182.4	2.020	178.79
6	2.38	0.11	4.85	48.48	13	0.28	91.1	0.160	50.79
7	12.61	286.20	22.54	186.31	14	0.07	44.6	0.058	111.73

系列	k×10⁴	u_max/σ⁰×10⁴	系列	k×10⁴	u_max/σ⁰×10⁴
1	5.23	5.49	8	37.72	39.40
2	8.45	8.86	9	170.05	176.79
3	79.90	83.40	10	4.67	4.88
4	2.19	2.29	11	14.44	15.09
5	5.32	5.59	12	12.83	13.33
6	8.56	8.97	13	141.55	146.02
7	1.69	1.76	14	428.45	445.90

工况	G_K/GPa	η_K/(GPa·h)	G_M/GPa	K/MPa	工况	G_K/GPa	η_K/(GPa·h)	G_M/GPa	K/MPa
K-1	12.61	286.20	22.54	18.63	η_K-1	12.61	28.62	22.54	186.31
K-2	12.61	286.20	22.54	93.16	η_K-2	12.61	143.10	22.54	186.31
K-3	12.61	286.20	22.54	279.47	η_K-3	12.61	429.30	22.54	186.31
K-4	12.61	286.20	22.54	1 863.10	η_K-4	12.61	28620	22.54	186.31
G_K-1	1.261	286.20	22.54	186.31	G_M-1	12.61	286.20	2.254	186.31
G_K-2	6.31	286.20	22.54	186.31	G_M-2	12.61	286.20	11.27	186.31
G_K-3	18.92	286.20	22.54	186.31	G_M-3	12.61	286.20	33.81	186.31
G_K-4	126.10	286.20	22.54	186.31	G_M-4	12.61	286.20	225.40	186.31

系列	t_d/d	v/(m·d^-1)	系列	t_d/d	v/(m·d^-1)	系列	t_d/d	v/(m·d^-1)
1	1.47×10^-3	16	6	1.93×10^-3	16	11	3.40	0.8
2	1.93×10^-3	16	7	0.946	4	12	3.35	0.8
3	5.44×10^-3	16	8	0.215	8	13	13.56	0.4
4	9.83×10^-4	16	9	0.431	4	14	26.55	0.2
5	1.48×10^-3	16	10	1.54	2

工况	a	b	c
7-1	-0.814	-0.203	0.974
7-2	-0.823	-0.358	0.993
10-1	-0.801	-0.136	0.943
10-2	-0.838	-0.233	0.988
10-3	-0.835	-0.321	0.998
11-1	-0.539	-0.276	0.771
11-3	-0.698	-0.359	0.963

黏弹性围岩纵向变形曲线及其释放系数演化规律

Evolution Law of Longitudinal Deformation Curve and Release Coefficient of Viscoelastic Rock

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位置	模型	a	b	c
掌子面前方		0.231	1.94	0
掌子面后方	空间效应控制型	基于图14进行上下限求解
	时空效应控制型	基于表5进行插值求解
	时间效应控制型	式(9)	式(8)	式(10)

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