带裂损隧道在爆炸作用下的二次损伤响应规律

王桂林; 余浩; 翟俊; 陈相宇; 王润秋; 龚晟

doi:10.11858/gywlxb.20230656

带裂损隧道在爆炸作用下的二次损伤响应规律

doi: 10.11858/gywlxb.20230656

王桂林^{1, 2,},
余浩^{1, 2},
翟俊³,
陈相宇^{1, 2},
王润秋^{1, 2},
龚晟^{1, 2}

1.
重庆大学土木工程学院, 重庆　400045
2.
库区环境地质灾害防治国家地方联合工程研究中心, 重庆　400045
3.
重庆大学三峡库区生态环境教育部重点实验室, 重庆　400045

基金项目: 国家重点研发计划（2018YFB2101000）

详细信息

作者简介:
王桂林（1970－），男，博士，教授，主要从事岩土工程研究. E-mail：glw@cqu.edu.cn

中图分类号: O382
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出版历程
- 收稿日期: 2023-05-03
- 修回日期: 2023-06-01
- 录用日期: 2023-06-15
- 网络出版日期: 2023-10-11
- 刊出日期: 2023-11-07

Secondary Damage Response of Cracked Tunnels under Explosion

WANG Guilin^{1, 2
,},
YU Hao^{1, 2},
ZHAI Jun³,
CHEN Xiangyu^{1, 2},
WANG Runqiu^{1, 2},
GONG Sheng^{1, 2}

1.
School of Civil Engineering, Chongqing University, Chongqing 400045, China
2.
National Joint Engineering Research Center of Geohazards Prevention in the Reservoir Areas, Chongqing 400045, China
3.
Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment, Chongqing University, Chongqing 400045, China

摘要

摘要: 服役中的隧道结构通常存在初始裂损，当遇到爆炸作用时，隧道结构性能会受到影响。利用多级背景网格物质点法对爆炸作用下带裂损的地铁隧道的二次损伤响应规律进行了数值模拟。结果表明：在爆炸作用下，初始裂损的存在会导致衬砌结构的刚度下降，轨行区底板产生更大范围的损伤，二次损伤面积增大34.2%，此外，初始裂损会加快隧道结构的损伤速度。初始裂损的深度和长度会显著改变隧道结构及围岩的动力响应，随着衬砌裂缝深度增加，轨行区底板二次损伤面积近线性增加，当裂缝深度为衬砌厚度的一半时，围岩等效塑性应变峰值的增速最快；随着衬砌裂缝长度的增加，轨行区底板二次损伤面积、围岩塑性应变峰值和位移峰值逐渐增大，但增速逐渐减缓。
- 地铁隧道 /
- 初始裂损 /
- 爆炸作用 /
- 二次损伤 /
- 物质点法
Abstract: Tunnel structures in service usually have initial cracking damage, which can affect the tunnel structure when exposed to explosive. In this paper, the secondary damage and response law of the subway tunnel with crack under explosion were simulated by using the material point method with multistage background grid. Under the explosion, the initial crack damage causes a decrease of the stiffness of the lining structure, and increases the damage range of the tunnel floor by 34.2% at the track zone. Besides, the initial crack accelerates the damage speed of the tunnel structure. The depth and length of the initial crack damage significantly alter the dynamic response of the tunnel structure and surrounding rock. The secondary damage area of the track floor increases linearly with the crack depth. When the crack depth reaches half of the lining thickness, the equivalent plastic strain peak increases the fastest. Moreover, the secondary damage area at the track floor, the peak plastic strain, and the peak displacement of the surrounding rock, all increase with the lining crack length, but the growth rate slows down gradually.
- subway tunnel /
- initial crack /
- explosion loading /
- secondary damage /
- material point method

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图 1 地铁隧道基础模型

Figure 1. Foundation model of the subway tunnel

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图 2 验证模型

Figure 2. Validated model

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图 3 FEM与MPM方法获得的爆炸作用下带裂损隧道在拱底和拱顶处的压强结果对比

Figure 3. Comparison of the pressures at arch base and arch vault of the cracked tunnel under explosion obtained by FEM and MPM

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图 4 两种方法获得的带裂损隧道底板中心的损伤因子

Figure 4. Comparison of the damage factors at the central floor of the cracked tunnel obtained by two methods

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图 5 100 ms时隧道及围岩在横、纵截面上的位移分布云图

Figure 5. Displacement distribution at the cross and longitudinal sections of the tunnel and surrounding rock at 100 ms

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图 6 隧道不同位置处的响应压强随时间变化曲线

Figure 6. Pressure versus time at different positions of the tunnel

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图 7 1 ms时隧道在横、纵截面的压强分布

Figure 7. Pressure distribution at the cross and longitudinal sections of the tunnel model at 1 ms

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图 8 100 ms时有裂损隧道的衬砌结构在横、纵截面上的损伤因子分布

Figure 8. Damage distribution at the cross and longitudinal sections of the lining structure of the cracked tunnel at 100 ms

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图 9 100 ms时隧道轨行区底板的损伤因子分布

Figure 9. Damage distribution at the tunnel floor in the track zone at 100 ms

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图 10 隧道轨行区底板中心质点的损伤因子随时间的变化曲线

Figure 10. Damage versus time at the central tunnel floor in the track zone

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图 11 100 ms时横、纵截面上围岩的等效塑性应变分布

Figure 11. Distribution of equivalent plastic strain at the cross and longitudinal sections of the surrounding rock at 100 ms

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图 12 轨行区损伤面积及围岩塑性应变峰值随裂缝深度的变化情况

Figure 12. Variations of the damage area in the track zoneand the peak value of equivalent plastic strainof the surrounding rock with crack depth

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图 13 轨行区损伤面积及隧道结构响应压强峰值随裂缝长度的变化

Figure 13. Variations of the damage area in the track zone and the peak value of response pressure of tunnel structre with crack depth

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图 14 围岩等效塑性应变峰值和位移峰值随裂缝长度的变化

Figure 14. Variations of the peak values of equivalent plastic strain and displacement of the surrounding rock with crack length

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表 1 混凝土结构的物理力学参数

Table 1. Physical and mechanical parameters of the concrete structure

$f'{_{ \mathrm{c} } ^{ { {} } } }$/MPa	$\rho /(\rm{kg\cdot {m}^{-3}})$	$ E/{\rm{GPa}} $	$ \nu $	$ A $	$ B $	$ n $	$ C $	${S}_{ \mathrm{m}\mathrm{a}\mathrm{x} }$	${D}{_{1} }$	${D}{_{2} }$
40	2400	32.5	0.2	0.79	1.6	0.61	0.007	7.0	0.04	1.0

${\varepsilon }{_{\mathrm{m}\mathrm{i}\mathrm{n} }^{\mathrm{f} } }$	${p}{_{\mathrm{c}\mathrm{r}\mathrm{u}\mathrm{s}\mathrm{h} }}/{\rm{GPa}}$	${p} {_{\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k} } }/{\rm{GPa}}$	${\mu }{_{\mathrm{c}\mathrm{r}\mathrm{u}\mathrm{s}\mathrm{h} }}$	${\mu }{_{\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k} } }$	${K}{_{1}}/{\rm{GPa}}$	${K}{_{2}}/{\rm{GPa}}$	${K}{_{3}}/{\rm{GPa}}$	$ T/{\rm{GPa}} $	${v }{_{\mathrm{p} } }/(\rm{m\cdot {s}^{-1}})$	${v }{_{\mathrm{s} } }/(\rm{m\cdot {s}^{-1}})$
0.01	0.016	0.8	0.001	0.1	85	−171	208	0.004	3870	2375

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表 2 围岩的物理力学参数

Table 2. Physical and mechanical parameters of the surrounding rock mass

${\rho }{_{\mathrm{} } }/(\mathrm{g}\cdot{\mathrm{c}\mathrm{m} }^{-3})$	${E}{_{\mathrm{} } }/{\rm{GPa} }$	${\nu }{_{\mathrm{} } }$	${q}{_{\mathrm{\phi } } }$	${k}{_{\mathrm{\phi } }}/{\rm{kPa}}$	${q}{_{\mathrm{\psi }} }$/(°)	${\sigma }{_{\mathrm{t} } }/{\rm{kPa} }$	${v}{_{\mathrm{p} } }/(\rm{m\cdot {s}^{-1} })$	${v}{_{\mathrm{s} }}/(\rm{m\cdot {s}^{-1} })$
1.85	0.1	0.35	0.404	11.11	0	0.1	185	89

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表 3 空气的物理力学参数

Table 3. Physical and mechanical parameters of the air model

${\rho }_{ }/(\mathrm{k}\mathrm{g}\cdot {\mathrm{m} }^{-3})$	${D}_{\mathrm{} }/(\rm{m\cdot{s}^{-1} })$	$ \kappa $	${E}_{0}^{\mathrm{} }/(\mathrm{M}\mathrm{J}\cdot {\mathrm{m} }^{-3})$	${v}{_{\mathrm{p} } }/(\rm{m\cdot {s}^{-1} })$	${v}{_{\mathrm{s} } }/(\rm{m\cdot {s}^{-1} })$
1.29	340	1.4	0	340	0

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表 4 固体炸药的JWL状态方程参数

Table 4. Parameters of the solid explosive in JWL equation of state

${\rho }{_{0} }/(\mathrm{k}\mathrm{g}\cdot{\mathrm{m} }^{-3})$	${p}_{\mathrm{C}\mathrm{J} }/\rm{GPa}$	${D}_{\mathrm{J} }/(\rm{m\cdot{s}^{-1} })$	$ \gamma $	${E}_{0}/(\mathrm{k}\mathrm{J}\cdot{\mathrm{c}\mathrm{m} }^{-3})$
1500	21.0	6930	2.727	7.0

${A}_{\mathrm{J} }/\rm{GPa}$	${B}_{\mathrm{J} }/\rm{GPa}$	$ {R}_{1} $	$ {R}_{2} $	$ \omega $
371.2	3.23	4.15	0.95	0.30

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表 5 有、无裂损情况下爆炸作用下地铁隧道结构和围岩的响应情况对比

Table 5. Comparison of responses of tunnel structure and surrounding rock under explosion charge for the cases of cracked tunnel and complete tunnel

Condition	$ {p}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{s}} $/MPa	$ {d}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{r}} $/m	${\varepsilon }_{\mathrm{p,}\mathrm{m}\mathrm{a}\mathrm{x} }^{\mathrm{r} }$	$ {d}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{s}} $/m	$ {S}_{\mathrm{f}} $/m²
Complete tunnel	3.8	0.22	0.29	0.04	1.21
Cracked tunnel	4.3	0.24	0.59	0.06	1.60
Variation/%	13.15	9.09	103.40	50.00	33.05

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