(1. Key Laboratory of Energy Engineering Safety and Disaster Mechanics，Sichuan University，Chengdu，Sichuan 610065，China；2. School of Architecture and Environment，Sichuan University，Chengdu，Sichuan 610065，China)
Abstract：Tunnels contain radial cracks due to the blasting excavation，and these cracks affect the tunnel stability significantly. In order to study the dynamic fracture behavior of tunnels containing radial cracks under the impact loading，the medium and low speed impact experiment was carried out by using the sandstone tunnel models，and the finite difference code AUTODYN was used for the numerical simulation. The propagation path and the arrest of the crack under the impact loading were studied，and the crack initiation toughness and propagation speed were calculated with the experimental-numerical-analytical methods. The fracturing behaviors of surrounding rock under the static and dynamic loadings are quite different. The damage under the dynamic loading is only the crack initiation and propagation at the crack tips，whereas the damage under the static loading occurrs at the crack tip，arch shoulder，arch foot and sidewalls. The propagation path of the radial crack is along the original direction of the crack under the impact loading，and the crack arrest phenomena was observed clearly in the propagation path. The experimental-numerical-analytical method can be used to determinate the initiation and propagation speed quite well. The curves of the dynamic stress intensity factors of cracks versus the time were obtained by using the displacement extrapolation method. The dynamic initiation toughness was determined using the initiation time measured with the strain gauges.
[1] 杨科之，杨秀敏. 坑道内化爆冲击波的传播规律[J]. 爆炸与冲击，2003，23(1)：37–40.(YANG Kezhi，YANG Xiumin. Shock waves propagation inside tunnels[J]. Explosion and Shock Waves，2003，23(1)：37–40.(in Chinese))
[2] REDDISH D J，STACE L R，VANICHKOBCHINDA P，et al. Numerical simulation of the dynamic impact breakage testing of rock[J]. International Journal of Rock Mechanics and Mining Sciences，2005，42(2)：167–176.
[3] SAKSALA T，HOKKA M，KUOKKALA V T，et al. Numerical modeling and experimentation of dynamic Brazilian disc test on Kuru granite[J]. International Journal of Rock Mechanics and Mining Sciences，2013，59(5)：128–138.
[4] 孔德森，孟庆辉，张伟伟，等. 爆炸荷载作用下地铁隧道的冲击反应研究[J]. 振动与冲击，2012，31(12)：68–72.(KONG Desen，MENG Qinghui，ZHANG Weiwei，et al. Shock responses of a metro tunnel subjected to explosive loads[J]. Journal of Vibration and Shock，2012，31(12)：68–72.(in Chinese))
[5] 孔德森，孟庆辉，史明臣，等. 爆炸冲击波在地铁隧道内的传播规律研究[J]. 地下空间与工程学报，2012，8(1)：863–868.(KONG Desen，MENG Qinghui，SHI Mingchen，et al. The dissemination rule of blasting shock-wave in subway tunnel[J]. Chinese Journal of Underground Space and Engineering，2012，8(1)：863–868.(in Chinese))
[6] XIA K，YAO W. Dynamic rock tests using split Hopkinson(Kolsky) bar system e A review[J]. Journal of Rock Mechanics and Geotechnical Engineering，2015，7(1)：27–59.
[7] 范天佑. 断裂动力学原理与应用[M]. 北京：北京理工大学出版社，2006：24–35.(FAN Tianyou. Principle and application of fracture dynamics[M]. Beijing：Beijing Institute of Technology Press，2006：24–35.(in Chinese))
[8] LI X B，LOK T S，ZHAO J，et al. Oscillation elimination in the Hopkinson bar apparatus and resultant complete dynamic stress–strain curves for rocks[J]. International Journal of Rock Mechanics and Mining Sciences，2000，37(7)：1 055–1 060.
[9] JIANG F，VECCHIO K S. Hopkinson bar loaded fracture experimental technique：a critical review of dynamic fracture toughness tests[J]. Applied Mechanics Reviews，2009，62(6)：1 469–1 474.
[10] ZHANG M，WU H J，LI Q M，et al. Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part I：Experiments[J]. International Journal of Impact Engineering，2009，36(12)：1 335–1 345.
[11] 王 蒙，朱哲明，谢 军. 岩石I–II复合型裂纹动态扩展SHPB实验及数值模拟研究[J]. 岩石力学与工程学报，2015，34(12)：2 474–2 485.(WANG Meng，ZHU Zheming，XIE Jun. Experimental and numerical studies of the mixed-mode I and II crack propagation under dynamic loading using SPHB[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(12)：2 474–2 485.(in Chinese))
[12] 王 蒙，朱哲明，胡 荣. 基于SCSCC试样的岩石复合型裂纹动态扩展特征研究[J]. 四川大学学报：工程科学版，2016，(2)：57–65.(WANG Meng，ZHU Zheming，HU Rong. Rock experiments study of crack propagation under I and II mixed-mode dynamic loading using SCSCC specimens[J]. Journal of Sichuan University：Engineering Science Edition，2016，(2)：57–65.(in Chinese))
[13] 王 蒙，朱哲明，王 雄. 冲击荷载作用下的I/II复合型裂纹扩展规律研究[J]. 岩石力学与工程学报，2016，35(7)：1 323–1 332. (WANG Meng，ZHU Zheming，WANG Xiong. The growth of mixed-mode I/II under impacting loads[J]. Journal of Rock Mechanics and Engineering，2016，35(7)：1 323–1 332.(in Chinese))
[14] ZHANG Q B，ZHAO J. Effect of loading rate on fracture toughness and failure micro-mechanisms in marble[J]. Engineering Fracture Mechanics，2013，102(2)：288–309.
[15] ZHANG Q B，ZHAO J. Determination of mechanical properties and full-field strain measurements of rock material under dynamic loads[J]. International Journal of Rock Mechanics and Mining Sciences，2013，60(8)：423–439.
[16] JAVED R A，ZHU S，GUO C，et al. Investigation into dynamic response of a three-point bend specimen in a Hopkinson bar loaded fracture test using numerical methods[J]. Advances in Mechanical Engineering，2015，7(7)：1–13.
[17] WANG Q Z，FENG F，NI M，et al. Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar[J]. Engineering Fracture Mechanics，2011，78(12)：2 455–2 469.
[18] 张财贵，周 妍，杨井瑞，等. 用边裂纹平台圆环试样测试岩石的I型动态断裂韧度[J]. 水利学报，2014，(6)：691–700.(ZHANG Caigui，ZHOU Yan，YANG Jingrui，et al. Determination of mode-I dynamic fracture toughness of rock using edge cracked flattened ring (ECFR) specimen[J]. Journal of Hydraulic Engineering，2014，(6)：691–700.(in Chinese))
[19] 杨井瑞，张财贵，周 妍，等. 用SCDC试样测试岩石动态断裂韧度的新方法[J]. 岩石力学与工程学报，2015，34(2)：279–292. (YANG Jingrui，ZHANG Xin，ZHOU Yan，et al. A new method for determining dynamic fracture toughness of rock using SCDC specimens[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(2)：279–292.(in Chinese))
[20] ZHU Z M. Numerical prediction of crater blasting and bench blasting[J]. International Journal of Rock Mechanics and Mining Sciences，2009，46(6)：1 088–1 096.
[21] ZHU Z M，WANG C，KANG J M，et al. Study on the mechanism of zonal disintegration around an excavation[J]. International Journal of Rock Mechanics and Mining Sciences，2014，67(4)：88–95.
[22] ZHU Z M，MOHANTY B，XIE HP. Numerical investigation of blasting-induced crack initiation and propagation in rocks[J]. International Journal of Rock Mechanics and Mining Sciences，2007，44(3)：412–424.
[23] ERARSLAN N，WILLIAMS D J. The damage mechanism of rock fatigue and its relationship to the fracture toughness of rocks[J]. International Journal of Rock Mechanics and Mining Sciences，2012，56：15–26.
[24] ALIHA M R M，AYATOLLAHI M R. Rock fracture toughness study using cracked chevron notched Brazilian disc specimen under pure modes I and II loading-A statistical approach[J]. Theoretical and Applied Fracture Mechanics，2014，69(2)：17–25.
[25] FUNATSU T，KURUPPU M，MATSUI K. Effects of temperature and confining pressure on mixed-mode(I-II) and mode II fracture toughness of Kimachi sandstone[J]. International Journal of Rock Mechanics and Mining Sciences，2014，67(2)：1–8.
[26] HAERI H，SHAHRIAR K，MARJI M F，et al. Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks[J]. International Journal of Rock Mechanics and Mining Sciences，2014，67(4)：20–28.
[27] 周 磊，朱哲明，刘 邦. 隧道周边不同位置径向裂纹对隧道围岩稳定性影响规律的研究[J]. 岩土工程学报，2016，38(7)：1 230–1 237.(ZHOU Lei，ZHU Zheming，LIU Bang. Influence of radial cracks on stability of surrounding rocks at different locations around tunnel[J]. Chinese Journal of Geotechnical Engineering，2016，38(7)：1 230–1 237.(in Chinese))
[28] 解 德，钱 勒，李长安. 断裂力学中的数值计算方法及工程应用[M]. 北京：科学出版社，2009：3–5.(XIE De，QIAN Le，LI Chang?an. Numerical calculation method and engineering application in fracture mechanics[M]. Beijing：Science Press，2009：3–5.(in Chinese))
[29] 郭伟国，李玉龙，索 涛. 应力波基础简明教程[M]. 西安：西北工业大学出版社，2007：44–52.(GUO Weiguo，LI Yulong，SUO Tao. Stress wave basic tutorial[M]. Xi′an：Northwestern Polytechnical University Press，2007：44–52.(in Chinese))
[30] 叶卫平. Origin9.1科技绘图及数据分析[M]. 北京：机械工业出版社，2015：299–319.(YE Weiping. Origin9.1 science and technology drawing and data analysis[M]. Beijing：Mechanical Industry Press，2015：299–319.(in Chinese))
[31] 杨井瑞，张财贵，周 妍，等. 用CSTBD试样确定砂岩的动态起裂和扩展韧度[J]. 爆炸与冲击，2014，34(3)：264–271.(YANG Jingrui，ZHANG Caigui，ZHOU Yan，et al. Determination of dynamic initiation toughness of sandstone using CSTBD specimens[J]. Explosion and Shock Waves，2014，34(3)：264–271.(in Chinese))
[32] KONOKMAN H E，ÇORUH M M，KAYRAN A. Computational and experimental study of high-speed impact of metallic Taylor cylinders[J]. Acta Mechanica，2011，220(1)：61–85.
[33] WU C，HAO H. Numerical prediction of rock mass damage due to accidental explosions in an underground ammunition storage chamber[J]. Shock Waves，2006，15(1)：43–54.
[34] ZAIDI AMA，KOSLAN MFS，OTHMAN M Z，et al. Appropriate coupling solvers for the numerical simulation of rolled homogeneous armor plate response subjected to blast loading[J]. Advances in Mechanical Engineering，2013，(3)：1–12.
[35] HU R，ZHU Z M，XIE J，et al. Numerical study on crack propagation by using softening model under blasting[J]. Advances in Materials Science and Engineering，2015，(2015)：1–9.
[36] 郦正能. 应用断裂力学[M]. 北京：北京航空航天大学出版社，2012：12–16.(LI Zhengneng. Application of fracture mechanics[M]. Beijing：Beijing University of Aeronautics and Astronautics Press，2012：12–16.(in Chinese))
2017, Vol. 36 
