内源爆炸荷载作用下无限弹性土体中圆柱形衬砌隧道的瞬态响应解答

高盟; 张继严; 高广运; 陈青生; 晁明颂; 李大勇

doi:10.11779/CJGE201708002

内源爆炸荷载作用下无限弹性土体中圆柱形衬砌隧道的瞬态响应解答 English Version

高盟^{1, 2},
张继严^{1, 2},
高广运³,
陈青生⁴,
晁明颂^{1, 2},
李大勇^{1, 2}

1. 山东科技大学土木建筑学院,山东青岛 266590;
2. 山东科技大学山东省土木工程防灾减灾重点实验室,山东青岛 266590;
3. 同济大学岩土及地下工程教育部重点实验室,上海 200092;
4. 新加坡国立大学土木与环境工程系,新加坡 119077

基金项目: 山东科技大学科研创新团队资助项目（2015KYTD104）

详细信息

作者简介:
高盟(1974- ),男,博士,副教授,硕士生导师,主要从事土动力学、桩基工程及环境土工方面的研究工作。E-mail: gmxyz@tom.com。

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出版历程
- 收稿日期: 2016-05-07
- 发布日期: 2017-08-24

Solution to transient response of a cylindrical lined tunnel in an infinite elastic medium under internal blast load

GAO Meng^{1, 2},
ZHANG Ji-yan^{1, 2},
GAO Guang-yun³,
CHEN Qing-shen⁴,
CHAO Ming-song^{1, 2},
LI Da-yong^{1, 2}

1. Institute of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao 266590, China;
2. Shandong University of Science and Technology, Shandong Province Key Laboratory of Civil Engineering &
Disaster Prevention and Mitigation, Qingdao 266590, China;;
3. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China;
4. Department of Civil and Environmental Engineering, National University of Singapore, Singapore 119077, Singapore

摘要

摘要: 内源爆炸荷载产生的振动响应对地下衬砌隧洞的安全非常重要。采用Fourier 变换和Laplace变换,推导出内源爆炸荷载作用下无限弹性空间中圆柱形衬砌孔洞的瞬态动力响应无量纲解答,利用Fourier和Laplace逆变换数值方法,计算分析内爆炸荷载产生的振动在衬砌和周围弹性介质中的分布和传播衰减规律。计算结果表明,爆源中心处衬砌内表面径向位移、切向应力和衬砌外表面土体径向位移、切向应力最大,向左右两侧迅速衰减,在6倍衬砌内径处衰减为0;衬砌内表面径向位移、切向应力和衬砌外表面土体径向位移、切向应力时程曲线峰值爆源中心处最大,离爆源中心越远,峰值越小,且在t^*=10时衰减为0。
- 内源爆炸荷载 /
- 圆柱形衬砌隧道 /
- 瞬态动力响应 /
- Laplace变换 /
- Fourier变换
Abstract: The vibration response resulting from internal explosion load is very important for the safety of the underground lined tunnels. The dimensionless dynamic transient solution to a cylindrical lined cavity under an internal blast load in an infinite elastic medium is derived by the Fourier transform and the Laplace transform. Utilizing the inverse Fourier transform and the inverse Laplace transform, the distribution and propagation attenuation laws of the vibration response generated by the internal explosion load in the lining and the surrounding elastic medium are calculated and analyzed. The results show that the radial displacement and the hoop stress on the internal lining surface and those of the soil on the interface between the lining and the soil reach the maximum at the explosion source center. The radial displacement and the hoop stress decrease rapidly with z* at both sides of the center, and eventually decay to zero at z*= 6. The peak value of the time history of the radial displacement and the hoop stress at the internal and outer lining surfaces are the maximum at the explosion source center. The further away from the explosion source center, the smaller the peak value. When t^*=10, the radial displacement and the hoop stress decay to zero.
- internal blast load /
- cylindrical lined tunnel /
- transient dynamic response /
- Laplace transform /
- Fourier transform

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参考文献(18)

[1]	FORRESTAL M J, SAGARTZ M J. Radiated pressure in an acoustic medium produced by pulsed cylindrical and spherical shells[J]. Journal of Applied Mechanics, 1971, 38(4): 1057-1060.
[2]	DUFFEY T A. Transient response of visco-plastic and visooelastio shells[J]. Journal of Applied Mechanics, 1976, 98: 137-143.
[3]	KARPP R R, DUFFEY T A, NEAL T R. Response of containment vessels to explosive blast loading[J]. Journal of Pressure Vessel Technology, 1983, 105(1): 23-27.
[4]	ABO-ZENA A M. Radiation from a finite cylindrical explosive source[J]. Geophysics, 1977, 42(7): 1384-1393.
[5]	ZAKOUT U, AKKAS N. Transient response of a cylindrical cavity with and without a bonded shell in an infinite elastic medium[J]. International Journal of Engineering Science, 1997, 35(12): 1203-1220.
[6]	高盟, 高广运, 王滢, 等. 均布突加荷载作用下圆柱形衬砌振动响应的解析解[J]. 岩土工程学报, 2010(2): 237-242. (GAO Meng, GAO Guang-yun, WANG Ying, et al. Analytical solution on dynamic response of lining subjected to sudden internal uniform loading[J]. Chinese Journal of Geotechnical Engineering, 2010(2): 237-242. (in Chinese))
[7]	SENJUNTICHAI T, RAJAPAKSE R. Transient response of a circular cavity in a poroelastic medium[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1993, 17(6): 357-383.
[8]	杨峻, 宫全美, 吴世明, 等. 饱和土体中圆柱形孔洞的动力分析[J]. 上海力学,1996, 17(1): 37-45. (YANG Jun, GONG Quan-mei. WU Shi-ming, et al. Transient response of a cylindrical cavity in a saturated soil body[J]. Shanghai Journal of Mechanics, 1996, 17(1): 37-45. (in Chinese))
[9]	XIE K, LIU G, SHI Z. Dynamic response of partially sealed circular tunnel in viscoelastic saturated soil[J]. Soil Dynamics and Earthquake Engineering, 2004, 24(12): 1003-1011.
[10]	刘干斌, 谢康和, 施祖元. 黏弹性饱和多孔介质中圆柱孔洞的频域响应[J]. 力学学报, 2004, 36(5): 557-563. (LIU Gan-bin, XIE Kang-he, SHI Zu-yuan. Frequency response of a cylindrical cavity in poro-viscoelastic saturated medium[J]. Acta Mechanica Sinica, 2004, 36(5): 557-563. (in Chinese))
[11]	徐长节, 马晓华. 黏弹性准饱和土中球空腔的动力响应[J]. 岩土力学, 2005, 26(8): 1189-1194. (XU Chang-jie, MA Xiao-hua. Dynamic response of spherical cavity in nearly saturated viscoelastic soils[J]. Rock and Soil Mechanics, 2005, 26(8): 1189-1194. (in Chinese))
[12]	HASHEMINEJAD S M, KOMEILI M. Effect of imperfect bonding on axisymmetric elastodynamic response of a lined circular tunnel in poroelastic soil due to a moving ring load[J]. International Journal of Solids and Structures, 2009, 46(2): 398-411.
[13]	高盟, 高广运, 王滢, 等. 饱和土与衬砌动力相互作用的圆柱形孔洞内源问题解答[J]. 固体力学学报, 2009(5): 481-488. (GAO Meng, GAO Guang-yun, WANG Ying, et al. A solution on the internal source problem of a cylindrical cavity considering the dynamic interaction between lining and saturated soil[J]. Chinese Journal of Solid Mechanics, 2009(5): 481-488. (in Chinese))
[14]	高盟, 高广运, 李大勇. 考虑耦合质量影响的均布突加荷载作用下衬砌结构的瞬态响应[J]. 岩土工程学报, 2011, 33(6): 862-868. (GAO Meng, GAO Guang-yun, LI Da-yong. Transient response of lining structure subjected to sudden internal uniform loading considering effects of coupling mass[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(6): 862-868. (in Chinese))
[15]	蔡袁强, 陈成振, 孙宏磊. 爆炸荷载作用下饱和土中隧道的瞬态动力响应[J]. 岩土工程学报, 2011, 33(3): 361-367. (CAI Yuan-qiang, CHEN Cheng-zhen, SUN Hong-lei. Transient dynamic response of tunnels subjected to blast loads in saturated soil [J]. Chinese Journal of Geotechnical Engineering, 2011, 33(3): 361-367. (in Chinese))
[16]	曾晨, 孙宏磊, 蔡袁强, 等. 简谐荷载作用下饱和土体中圆形衬砌隧道三维动力响应分析[J]. 岩土力学, 2014, 35(4): 1147-1156. (ZENG Chen, SUN Hong-lei, CAI Yuan-qiang, et al. Analysis of three-dimensional dynamic response of a circularlining tunnel in saturated soil to harmonic loading[J]. Rock and Soil Mechanics, 2014, 35(4): 1147-1156. (in Chinese))
[17]	王滢, 高广运. 准饱和土中圆柱形衬砌的瞬态动力响应分析[J]. 岩土力学, 2015, 36(12): 3400-3409. (WANG Ying, GAO Guang-yun. Analysis of transient dynamic response of cylindrical lined cavity in nearly saturated soil [J]. Rock and Soil Mechanics, 2015, 36(12): 3400-3409. (in Chinese))
[18]	杨桂通, 张善元. 弹性动力学[M]. 北京：中国铁道出版社, 1988: 199-203. (YANG Gui-tong, ZHANG Shan-yuan. Elastic dynamics[M]. Beijing: China Railway Publishing House, 1988: 199-203. (in Chinese))