脆性材料钻孔爆炸致裂机理研究
|
摘要
爆破方法具有高效率、低成本等特点,因而在矿山、土木和油气等工程中得到了广泛的应用,因此研究爆破特别是钻孔爆破致裂机理具有很重要的理论意义和应用价值。本文主要研究脆性材料(岩石和混凝土)在爆炸冲击载荷作用下的开裂行为,通过理论分析、数值模拟和实验研究对钻孔爆炸致裂问题进行了较系统的研究,主要内容包括以下几个方面：
钻孔装药爆炸后在距爆源不同的距离会产生破碎区、开裂区和弹性区,根据这三种不同的材料响应行为建立了一种空穴膨胀理论模型,该模型与以前的空穴膨胀模型相比,不同点是空腔初始半径不为0,而是一个有限值。同时在模型中考虑了剪胀效应,这样一来在破碎区内不仅可以描述脆性材料的压缩状态,也可以描述材料的膨胀状态。文中还将理论计算结果与利用实验室自己开发的材料本构模型进行的数值模拟结果进行了比较,发现这两种方法计算得出的空穴壁面处的径向应力大小比较一致。而且通过空穴膨胀模型还可以得出使空穴发生膨胀行为的临界径向应力。
建立了二级钻地弹的侵彻分析模型,研究了靶体中预制孔道直径大小与弹体侵彻深度之间的关系,并与实验结果进行对比,发现两者吻合得很好；优化了二级战斗部系统,并得到了最优侵彻深度与撞击速度、随进弹与前置装药直径之比之间的关系。
数值模拟分析了载荷特性如载荷峰值、加载率和卸载率对钻孔周围破碎区和开裂区范围大小产生的影响。研究发现如果载荷峰值过高会在钻孔周围形成较大范围的破碎区,造成载荷能量的浪费,对宏观连贯性裂纹的扩展延伸没有产生积极的作用；如果载荷峰值过低,钻孔周围介质中的环向应力不足以引起径向裂纹的产生,不利于宏观裂纹的生成。研究还发现在相同冲量的条件下,梯形载荷比三角形载荷的致裂效果好一些,并且载荷的加载率和卸载率对裂纹的数目和长度有很大的影响,加载率越高同时卸载率越低,产生的宏观裂纹越长,但是裂纹数目越少。当使空穴发生膨胀行为的临界径向应力作为载荷峰值的下界时,能够产生较好的致裂效果。
利用实验室自己开发的脆性材料本构模型对花岗岩钻孔爆炸致裂问题进行了数值模拟研究,并与文献中报导的实验结果和实验室自己的实验结果进行了比较。结果表明该本构模型能够较好地模拟脆性材料(岩石、混凝土)在动态冲击载荷下的损伤开裂行为。
采用数值模拟方法研究了裂纹内爆生气体驱使裂纹扩展的过程,并对裂纹内高压气体的分布、裂纹不同位置的张开位移进行了分析,研究发现：裂纹密度越大,驱使裂纹扩展所需要的临界压力也越高；高压气体浸入裂纹内并在孔内膨胀做功的联合作用与只考虑高压气体浸入裂纹内的单独作用相比,前者的致裂效果稍好一些。
Blasting has been widely employed in the areas of excavation, construction, civil engineering, oil and gas industry due to its high efficiency and low cost. It is, therefore, important to investigate the mechanisms of fractures induced by explosion and especially by borehole blasting. The fracture processes in brittle materials by explosion are very complex which involves many areas of sciences. A comprehensive study is carried out in this thesis on fracture mechanisms in brittle materials under borehole blasting, which mainly consists of the following parts:
Three response regions, i.e. comminuted region, cracked region and elastic region were formed in brittle materials such as rocks and concretes subjected to borehole blasting. Based on these observations, spherical and cylindrical cavity expansion models with an initial radius were constrcted, which are different from the previous models without an initial radius. To cater for compressibility or dilatancy of the material in comminuted region, dilatant-kinematic relation is introduced in the models. On the other hand, numerical simulations are performed using LS-DYNA into which a material constitutive relation developed by our group has been incorporated. It is shown that the numerical results are in good agreement with those predictions from the theoretical models. Moreover, from both cavity expansion theoretical models and numerical simulations a critical radial stress can be derived above which a cavity is possible to expand.
An analytical model based upon the above developed cavity expansion theory was proposed to analyze the penetration of a following through bomb (FTB) into concrete targets with pre-drilled hole. It transpires that the model predictions are in good agreement with available test data. It also transpires that the optimized desgn of a dual warhead system can be achieved in terms of penetration depth.vs. impact velocity and ratio of following through bomb (FTB) diameter to forward shaped charge (FSC) diameter.
The effects of pulse parameters such as pulse peak, loading rate and unloading rate on crack initiation and growth in brittlt materials under borehole blasting have been evaluated numerically. It is found that higher peak amplitude induces more extensive comminuted zone which absorbes more energy and is not conducive to crack formulation and propagation, whilst lower peak value is not powerful enough to produce fractures. With the same impulse and peak amplitude, trapezoid pulse is found to more effective than triangle pulse in terms of crack propagation. It is also found that the loading and unloading rates have significant influences on the number and the length of cracks, and that pulse with higher loading rate and lower unloading rate will cause longer but fewer cracks, and that the effect of borehole blasting is satisfactory if the critical radial stress predicted from the cavity expansion model is taken as the lower bound of peak amplitude.
Numerical simulations with LS-DYNA software into which a material constitutive relation developed by our group has been incorporated are performed to examine the cracking patterns. The user subroutine code with the constitutive relation is used to study the dynamic fracture behavior of brittle materials. It is shown that the numerical simulations are in good agreement with the experimental observations for granite subjected to borehole blasting.
Numerical simulations with ABAQUS/STANDARD are performed to invesitigate the behavior of gas driven fracture propogation, the pressure inside crack and the crack width. It is found that the denser the radial cracks are, the higher critical pressure is needed. It is also found that crack caused by the combined effect of gas pressure in borehole and gas pressure penetrated into the crack is longer than that solely caused by gas pressure penetrated into crack.
钻孔装药爆炸后在距爆源不同的距离会产生破碎区、开裂区和弹性区,根据这三种不同的材料响应行为建立了一种空穴膨胀理论模型,该模型与以前的空穴膨胀模型相比,不同点是空腔初始半径不为0,而是一个有限值。同时在模型中考虑了剪胀效应,这样一来在破碎区内不仅可以描述脆性材料的压缩状态,也可以描述材料的膨胀状态。文中还将理论计算结果与利用实验室自己开发的材料本构模型进行的数值模拟结果进行了比较,发现这两种方法计算得出的空穴壁面处的径向应力大小比较一致。而且通过空穴膨胀模型还可以得出使空穴发生膨胀行为的临界径向应力。
建立了二级钻地弹的侵彻分析模型,研究了靶体中预制孔道直径大小与弹体侵彻深度之间的关系,并与实验结果进行对比,发现两者吻合得很好；优化了二级战斗部系统,并得到了最优侵彻深度与撞击速度、随进弹与前置装药直径之比之间的关系。
数值模拟分析了载荷特性如载荷峰值、加载率和卸载率对钻孔周围破碎区和开裂区范围大小产生的影响。研究发现如果载荷峰值过高会在钻孔周围形成较大范围的破碎区,造成载荷能量的浪费,对宏观连贯性裂纹的扩展延伸没有产生积极的作用；如果载荷峰值过低,钻孔周围介质中的环向应力不足以引起径向裂纹的产生,不利于宏观裂纹的生成。研究还发现在相同冲量的条件下,梯形载荷比三角形载荷的致裂效果好一些,并且载荷的加载率和卸载率对裂纹的数目和长度有很大的影响,加载率越高同时卸载率越低,产生的宏观裂纹越长,但是裂纹数目越少。当使空穴发生膨胀行为的临界径向应力作为载荷峰值的下界时,能够产生较好的致裂效果。
利用实验室自己开发的脆性材料本构模型对花岗岩钻孔爆炸致裂问题进行了数值模拟研究,并与文献中报导的实验结果和实验室自己的实验结果进行了比较。结果表明该本构模型能够较好地模拟脆性材料(岩石、混凝土)在动态冲击载荷下的损伤开裂行为。
采用数值模拟方法研究了裂纹内爆生气体驱使裂纹扩展的过程,并对裂纹内高压气体的分布、裂纹不同位置的张开位移进行了分析,研究发现：裂纹密度越大,驱使裂纹扩展所需要的临界压力也越高；高压气体浸入裂纹内并在孔内膨胀做功的联合作用与只考虑高压气体浸入裂纹内的单独作用相比,前者的致裂效果稍好一些。
Blasting has been widely employed in the areas of excavation, construction, civil engineering, oil and gas industry due to its high efficiency and low cost. It is, therefore, important to investigate the mechanisms of fractures induced by explosion and especially by borehole blasting. The fracture processes in brittle materials by explosion are very complex which involves many areas of sciences. A comprehensive study is carried out in this thesis on fracture mechanisms in brittle materials under borehole blasting, which mainly consists of the following parts:
Three response regions, i.e. comminuted region, cracked region and elastic region were formed in brittle materials such as rocks and concretes subjected to borehole blasting. Based on these observations, spherical and cylindrical cavity expansion models with an initial radius were constrcted, which are different from the previous models without an initial radius. To cater for compressibility or dilatancy of the material in comminuted region, dilatant-kinematic relation is introduced in the models. On the other hand, numerical simulations are performed using LS-DYNA into which a material constitutive relation developed by our group has been incorporated. It is shown that the numerical results are in good agreement with those predictions from the theoretical models. Moreover, from both cavity expansion theoretical models and numerical simulations a critical radial stress can be derived above which a cavity is possible to expand.
An analytical model based upon the above developed cavity expansion theory was proposed to analyze the penetration of a following through bomb (FTB) into concrete targets with pre-drilled hole. It transpires that the model predictions are in good agreement with available test data. It also transpires that the optimized desgn of a dual warhead system can be achieved in terms of penetration depth.vs. impact velocity and ratio of following through bomb (FTB) diameter to forward shaped charge (FSC) diameter.
The effects of pulse parameters such as pulse peak, loading rate and unloading rate on crack initiation and growth in brittlt materials under borehole blasting have been evaluated numerically. It is found that higher peak amplitude induces more extensive comminuted zone which absorbes more energy and is not conducive to crack formulation and propagation, whilst lower peak value is not powerful enough to produce fractures. With the same impulse and peak amplitude, trapezoid pulse is found to more effective than triangle pulse in terms of crack propagation. It is also found that the loading and unloading rates have significant influences on the number and the length of cracks, and that pulse with higher loading rate and lower unloading rate will cause longer but fewer cracks, and that the effect of borehole blasting is satisfactory if the critical radial stress predicted from the cavity expansion model is taken as the lower bound of peak amplitude.
Numerical simulations with LS-DYNA software into which a material constitutive relation developed by our group has been incorporated are performed to examine the cracking patterns. The user subroutine code with the constitutive relation is used to study the dynamic fracture behavior of brittle materials. It is shown that the numerical simulations are in good agreement with the experimental observations for granite subjected to borehole blasting.
Numerical simulations with ABAQUS/STANDARD are performed to invesitigate the behavior of gas driven fracture propogation, the pressure inside crack and the crack width. It is found that the denser the radial cracks are, the higher critical pressure is needed. It is also found that crack caused by the combined effect of gas pressure in borehole and gas pressure penetrated into the crack is longer than that solely caused by gas pressure penetrated into crack.
引文
[1]Vovk AA, Mikhalyuk AV and Belinskii Ⅳ.1973. Development of fracture zones in rocks during camouflet blasting[J]. Journal of Mining Science,9:383-387.
[2]Isakov AL.1983. Directed fracture of rocks by blasting[J]. Journal of Mining Science, 479-488.
[3]Rossmanith HP, Daehnke A.1997. Knasmillner R E, Kouzniak N, Ohtsu M and Uenishi K. Fracture mechanics applications to drilling and blasting[J]. Fatigue Fract. Engng Mater. Struct,20:1617-1636.
[4]Mandal SK, Singh MM and Dasgupta S.2008. Theoretical concept to understand plan and design smooth blasting pattern[J]. Geotech Geol Eng,26:399-416.
[5]Dehghan Banadaki MM and Mohanty B.2012. Numerical simulation of stress wave induced fractures in rock[J]. Int.J. Impact Engineering,40-41:16-25.
[6]Gebbeken N and Ruppert M.2000. A new material model for concrete in high-dynamic hydrocode simulation[J]. Archive of Applied Mech,70:463-478.
[7]Zhang YQ, Hao H and Lu Y.2003. Anisotropic dynamic damage and fragmentation of rock materials under explosive loading[J]. Int.J. Engng. Sci.41:917-929.
[8]Russell AR and Khalili N.2002. Drained cavity expansion in sands exhibiting particle crushing[J]. Int.J. Numer. Anal. Meth. Geomech.26:323-340.
[9]龙源.1990.条形装药土中爆炸冲击波及空腔的数值模拟[J].爆炸与冲击,10：41-48.
[10]许连坡,金辉,章培德.1982.土中爆炸空腔的发展过程[J].力学学报,5：500-504.
[11]杨人光,庞维泰,秦明武.1984.论黄上中药包爆炸最优空腔比[J].金属矿山,4：6-10.
[12]余永强,杨小林,梁为民,王金星.2007.控制爆破致裂提高矿井瓦斯抽放率试验研究[J].煤炭学报,32：377-381.
[13]颜事龙,冯叔瑜,金孝刚.1998.有机玻璃中条形药包爆炸破碎区发展过程的高速摄影研究[J].爆炸与冲击,18(3)：262-267.
[14]王呼和,佟铮,邢永明,李进福.2009.无限冰介质中爆炸裂纹扩展机理与数值模拟[J].实验力学,24：493-498.
[15]Coates DF.1970. Dynamic Rock Mechanics. Rock Mechanics Principles[Z],8(12):97.
[16]Wu YK, Hao H, Zhou YX and Chong K.1998. Propagation characteristics of blast-induced shock waves in a jointed rock mass[J]. Soil Dynamic and Earthquake Engineering,17:407-412.
[17]Langefors U and Kihlstrom B.1978. The modern techniques of rock blasting (3rd)[C] Wiley, New York.
[18]Duvall WI and Atchison TC.1957. Rock Breakage by Explosives[R]. USBM RI5356.
[19]Hino K.1956. Fragmentation of rock through blasting and shock wave theory of blasting[C]. The 1st U.S. Symposium on Rock Mechanics (USRMS),23-25.
[20]Kutter HK and Fairhurst C.1971. On the Fracture Process in Blasting[J]. Int. J.of Rk Mech.& Min. Sci.8:181-188.
[21]Li CR, Kang LJ, Qi QX. et.al.2009. The numerical analysis of borehole blasting and application in coal mine roof-weaken[J]. Procedia Earth and Planetary Science,1: 451-459.
[22]王仲琦,张奇,白春华.2002.孔深影响爆炸应力波特性的数值模拟分析[J].岩石力学与工程学报,24：550-553.
[23]Zhu ZM, Mohanty B and Xie HP.2007. Numerical investigation of blasting-induced crack initiation and propagation in rocks[J]. Int.J, Rock Mech.& Min. Sci.44:412-424.
[24]Zhu ZM, Xie HP and Mohanty B.2008. Numerical investigation of blasting-induced damage in cylindrical rocks[J]. Int.J, Rock Mech.& Min. Sci.45:111-121.
[25]夏祥,石永强,李海波,马行东,刘博.2007.岩体弹孔及群孔齐发爆破爆炸载荷数值分析[J].岩石力学与工程学报,26：3391-3396.
[26]Fourney WL, Holloway DC and Dally JW.1975. Fracture initiation and propagation from a center of dilatation[J]. Int.J. of Fracture,11:1011-1029.
[27]Isakov AL and Sher EN.1983. Problem of the dynamic for development of directiona cracks during blast-hole firing[J]. Journal of Mining Science,19(3):189-196.
[28]Nilson RH, Proffer W J and Duff RE.1985. Modelling of gas-driven fractures induced by propellant combustion within a borehole[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr.22(1):3-19.
[29]Esen S, Onederra I and Bilgin HA.2003. Modelling the size of the crushed zone around a blasthole[J]. Int.J. Rock Mech & Mining Sci.40:485-495.
[30]Hagan TN.1973. Rock breakage by explosives[C] In:Proc.Nat.Symp. Rock Fragmentation, 1-17.
[31]卢文波,陶振宇.1994.爆生气体驱动的裂纹扩展速度研究[J].爆炸与冲击,14：264-268.
[32]Mchugh S.1983. Crack extension caused by internal gas pressure compared with extension caused by tensile stress[J]. Int. Journ. of Fracture,21:163-176.
[33]Cho SH, Nakamura Y and Kaneko K.2004. Dynamic fracture process analysis of rock subjected to stress wave and gas pressurization[J]. Int. J. Rock Mech. Min. Sci.41:1-8.
[34]杨小林,工梦恕.2001.爆生气体作用下岩石裂纹的扩展机理[J].爆炸与冲击,21：111-116.
[35]Zhou CB and He XG.2004. The rock deep hole blasting new technical progress[M]. China University of Geosciences Press.
[36]Brinkmann JR.1987. Separating shock wave and gas expansion breakage mechanisms[C]. In:Fourney WL, Dick RD, editors. Proc.2nd international symposium on rock fragmentation by blasting. USA:Keystone,6-15.
[37]Mohanty B.1982. Characteristic crack patterns close to an exploding charge[C]. In: Baumgartner P. editor. Proc.14th canadian rock mechanics symposium.Vancouver, Canada: Canadian Institute of Mining and Metallurgy,31-36.
[38]赵新涛,刘东燕,程贵海,李东升.2011.爆生气体作用机理及岩体裂纹扩展分析[J].重庆大学学报,34：75-80.
[39]Sim YJ, Song KI and Cho GC.2005. Evaluation of final fragmentation zone induced by rock blasting[C]. The 18th KKCNN Symposium on Civil Engineering-KAIST12. 18-20:161-168.
[40]徐颖,沈兆武,孟益平. 2003.爆炸载荷作用下刻槽炮孔动态裂纹扩展规律[J].中国科学技术大学学报,33：184-190.
[41]Cho SH, Nakamura Y, Mohanty B and Kaneko K.2006. Study on control of crack-propagation in blasting[C]. In:8th International Symposium on Rock Fragmentation by Blasting, Editec S.A., Santiago, Chile,124-128.
[42]Rathore SS and Bhandari S.2007. Controlled fracture growth by blasting while protecting damages to remaining rock[J]. Rock Mech. Rock Engng.3:317-326.
[43]Dally JW and Fourhey WL.1977. Fracture control in construction blasting[C]. The 18th U.S. Symposium on Rock Mechanics,22-24.
[44]Kutter HK.1970. Stress analysis of a pressurized circular hole with radial cracks in an infinite elastic plate[J]. Int.J. Fracture Mech.6:233-247.
[45]Ramesh K, Shukla S, Dixit PM and Karuppaiah N.1997. Numerical evaluation of SIF for radial cracks in thick annular ring using cyclic symmetry[J]. Engineering Fracture Mech. 56:141-153.
[46]Taran EP and Shapiro VY.1982. Action of the explosion of a blast hole charge in the design of a direct cut with a compensation hole[J]. J. Mining Sci.18:119-122.
[47]张志呈.2000.岩体爆破裂纹扩展速度实验研究[J].爆破器材,1-8.
[48]张志呈,肖正学,郭学彬,林秀英,蒋光明.2001.断裂控制爆破裂纹扩展的高速摄影试验研究[J].西南工学院学报,16：53-57.
[49]张奇.1990.岩石爆破的粉碎区及其空腔膨胀[J].爆炸与冲击,10：68-75.
[50]李端明,唐中华,张志呈.1998.条形药包爆破的最优空强化[J].四川冶金,4：10-14.
[51]徐颖,孟益平,程玉生.2002.装药不耦合系数对爆破裂纹控制的试验研究[J].岩石力学与工程学报,21：1843-1847.
[52]宗琦,李永池,徐颖.2004.炮孔水耦合装药爆破孔壁冲击压力研究[J].水动力学研究与进展,19：610-615.
[53]王志亮,李永池.2005.工程爆破中径向水不耦合系数效应数值仿真[J].岩土力学,26：1926-1930.
[54]龚敏,王德胜,程西江.2004.条形药包不同空腔比试验研究[J].爆破,21：1-4.
[55]Luo Y and Shen ZW.2006. Study on orientation fracture blasting with shaped charge in rock[J]. Journal of USTB.13:193-198.
[56]Wang SL and Yin SD.2011. A closed-form solution for a spherical cavity in the elastic-brittle-plastic medium[J]. Tunneling and Underground Space Technology, 26:236-241.
[57]Zhang CG, Zhang QH, Zhao JH, Xu F and Wu CZ.2010. Unified analytical solution for a circular opening based on non-linear unified failure criterion[J]. Journal of Zhejiang University-Science A (Applied Physics & Engineering).11:71-79.
[58]Eason G.1963. Propagation of waves from spherical and cylindrical cavities[J]. ZAMP. 14:12-23.
[59]许红涛,卢文波,邹奕芳.2003.钻孔爆破中环向裂纹形成机理的研究[J].工程爆破,9：7-11.
[60]Harries G.1973. A mathematical model of cractering and blasting[J]. In National Symposium on Rock Fragmentation, Adelaide,41-45.
[61]Xu BY. and Liu XS.1995. Applying Plasto Elasticity Mechanical[M], Tsinghua University Press.
[62]Curran DR, Seaman L, Shockey DA.1977. Dynamic failure in solids[J]. Physics Today.
[63]Seaman L.1980. A computational model for dynamic tensile microfracture with damage in one plane[R]. SRI Poulter Laboraratory Technical Report001-80, SRI International, Menlo Park.
[64]Margolin LG. 1984. A generalized Griffith criterion for crack propagation[J]. Engineering Fracture Mechanics,19(3):539-543.
[65]Grady DE and Chen ME.1980. Continuum modeling of explosive fracture in oil shale[J]. Int. J. Rock Mech. Min.Sci.Geomech.Abstr.17:147-157.
[66]Kuszmaul JS.1987. A technique for predicting fragmentation and fragment sizes resulting from rock blasting[C]. In:Proc.28th U.S. Symp. Rock Mech.,893-900.
[67]谢和平.1996.分形-岩石力学导论[M].科学出版社.
[68]高峰,谢和平.1996.脆性材料的分形统计强度理论[J].固体力学学报,17(3)：239-244.
[69]Dcik RA.1983. Explosives and blasting procedures mannal [Z]. US Bureau of Mines, IC. No.8929.
[70]宗琦.1994.岩石内爆炸应力波破裂区半径的计算[J].爆破,15-17.
[71]吴亮,卢文波,宗琦.2006.岩石中柱状装药爆炸能量分布[J].岩土力学,27：735-739.
[72]戴俊.2001.柱状装药爆破的岩石压碎圈与裂隙圈计算[J].辽宁工程技术大学学报,20：144-147.
[73]Cao LF, Teh CI and Chang MF.2002. Analysis of undrained cavity expansion in elasto-plastic soils with non-linear elasticity [J]. Int.J. Numer. Anal. Meth. Geomech. 26:25-52.
[74]Collins IF and Yu H S.1996. Undrained cavity expansions in critical state soils [J]. Int. J. Numer. Anal.Meth.Geomech.20:489-516.
[75]Cherry JT, Schock RN and Sweet J.1975. A theoretical model of dilatant behavior of a brittle rock[J]. Pure and Applied Geophysics,113:183-196.
[76]Yuan SC and Harrison JP.2005. Development of a hydro-mechanical local degradation approach and its application to modeling fluid flow during progressive fracturing of heterogeneous rocks[J]. Int.J. Rock Mech.& Min. Sci.42:961-984.
[77]Dunin SZ, Sirotkin VK and Sumin EV.1979. Nature of the state of the medium in the neighboehood of a cavity expanding into a dilating medium[J]. Journal of Applied Mechanics and Technical Physics,20:373-380.
[78]Warren TL, Fossum AF and Frew DJ.2004. Penetration into low-strength (23MPa) concrete:target characterization and simulation [J]. Int. J. Impact Engng.,477-503.
[79]何涛.文鹤鸣.2007.靶体响应力函数的确定方法及其在侵彻力学中的应用[J].中国科学技术大学学报,37：1249-1261.
[80]蒋明镜,沈珠江.1996.考虑剪胀的弹脆塑性软化柱形孔扩张问题[J].河海大学学报,24：65-72.
[81]蒋明镜,沈珠江.1997.考虑剪胀的线性软化柱形孔扩张问题[J].岩石力学与工程学报,16：550-557.
[82]Mosinets VN and Gorbacheva NP.1972. A seismological method of determining the parameters of the zones of deformation of rock by blasting[J]. Journal of Mining Science, 8:640-647.
[83]葛涛,吴华杰,陶剑青,工明洋.2005.岩石中爆炸破碎区边界参数研究[J].爆破, 22:5-8.
[84]Nakamura Y.1993. Model experiments on effectiveness of fracture plane control method in blasting[J]. Int. J. Blast Fragment.3:59-78.
[85]Nakamura Y, Cho SH, Yoneoka M, Yamamoto M and Kaneko M.2004. Model experiments on crack propagation between two charge holes in blasting[J]. Sci. Technol Energetic Mater.,65:34-39.
[86]Chandar KR and Yang B.1997. On the role of microcracks in the dynamic fracture of brittle materials[J]. J. Mech. Phys. Solid,45:535-563.
[87]Sharon E and Fineberg J.1999. Confirming the continuum theory of dynamic brittle fracture for fast cracks[J]. Nature,397:333-335.
[88]Boudet JF, Ciliberto S and Steinberg V.1995. Experimental study of the instability of crack propagation in brittle materials[J]. Europhys. Lett.30:337-342.
[89]Fineberg J, Gross SP, Marder M and Swinney HL.1992. Instability in the propagation of fast cracks[J]. Physical Review B,45:5146-5154.
[90]Voitenko YI.1995. Fracture of solid by weak blasts[J]. Combustion, Explosion, and Shock Waves,31:492-499.
[91]Sassa K, Ito I, and Hanasaki K.1971. Breakage of brittle material by quasi-static pressure of explosive gas[J]. Journal of the Japan Explosive Society,32(1):9-16. (in Japanese)
[92]Daehnke A, Rossmanith P and Napier JAL.1997. Gas pressurization of blast-induced conical cracks[J]. Int.J. Rock Mech.& Min. Sci.
[93]Dehghan Banadaki MM, Mohanty B.2008. Blast induced pressure in some granitic rocks[C]. In:Majdi A, Ghazvinian A, editors. Proc.5th Asian rock mechanics symposium (ARMS-ISRM):Curran Associates, Inc. Tehran, Iran.,933-939
[94]II'yushin AA.1999. The mechanics of a continuous medium[M]. Izd-vo MGU. Moscow. (Translated in Hustrulid W. Blasting principles for open pit blasting, vol. II. Rotterdam: Balkema,964-1009 [Chapter 21]), [in Russian].
[95]Szuladzinski G.1993. Response of rock medium to explosive borehole pressure[C]. Proceedings of the Fourth International Symposium on Rock Fragmentation by Blasting-Fragblast-4, Vienna, Austria.17-23.
[96]Djordjevic N.1999. Two-component of blast fragmentation[C].Proceedings of the Sixth International Symposium on Rock Fragmentation by Blasting-Fragblast 1999, South African Institute of Mining and Metallurgy, Johannesburg, South Africa..213-219.
[97]Kanchibotla SS, Valery W and Morrell S.1999. Modelling fines in blast fragmentation and its impact on crushing and grinding[C]. Proceedings of Explosive—A Conference on Rock Breaking. The Australasian Institute of Mining and Metallurgy, Kalgoorlie, Australia. 137-44.
[98]Tesarik DR and Hustrulid WA.2009. A hydrodynamics-based approach for predicting the blast damage zone in drifting as demonstrated using concrete block data[J]. Blast. Fragm.
[99]Cho SH.2003. Dynamic fracture process analysis of rock and its application to fragmentation control in blasting[D], Ph. D. Eng. Thesis, Hokkaido University at Sapporo, Japan.
[100]Cho SH, Nakamura Y, Mohanty B, Yang HS and Kaneko K.2008. Numerical study of fracture plane control in laboratory-scale blasting[J]. Engineering Fracture Mech. 75:3966-3984.
[101]Papanastasiou P and Thiercelin M.1993. Influence of inelastic rock behavior in hydraulic fracturing[J]. Int.J.Rock Mech.Min.Sci.& Geomech. Abstr.30:1241-1247.
[102]Wawrzynek PA and Ingraffea AR.1987. Interactive finite element analysis of fracture processing:an integrated approach[J]. Theo. App. Fract. Mech.,8:137-150.
[103]Tang CA and Kaiser PK.1998. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure-Part I:Fundamentals[J]. Int. J. Rock Mech. Min. Sci.,35(2):113-121.
[104]Kaiser PK and Tang CA.1998. Numerical simulation of damage accumulation and seismic energy release during brittle rock failure-Part H:Rib Pillar Collapse[J]. Int. J. Rock Mech. Min. Sci.,35(2):123-134.
[105]Ma GW and An XM.2008. Numerical simulation of blasting-induced rock fractures[J]. Int.J.Rock Mech.Min.Sci.45:966-975.
[106]Cho SH and Kaneko K.2004. Influence of the applied pressure waveform on the dynamic fracture processes in rock[J]. Int. J. Rock Mech. Min. Sci.41:771-784.
[107]Shi GH.1993. Block system modelling by discontinuous deformation analysis[R]. Computational Mechanics Publication:Southampton, U.K.
[108]Zhao ZY and Gu J.2008. Fracture propagation in rock under blast load-a numerical investigation[R]. NTU. Civil Engineering Research.21:75-78.
[109]Zhao ZY and Zhang Y.2010. Rock blast simulation by discontinuous deformation analysis[R]. Civil Engineering.
[110]夏祥,李海波,李俊如,肖克强,唐海马国伟.2006.岩体爆生裂纹的数值模拟[J].岩上力学,27：1987-1991.
[111]王志亮,郑明新.2008.基规范TCK损伤本构的岩石爆破效应数值模拟[J].岩土力学,29：230-234.
[112]Wang ZL, Li YC and Shen RF.2007. Numerical simulation of tensile damage and blast crater in brittle rock due to underground explosion[J]. Int. J. Rock Mech.& Min. Sci.44: 730-738.
[113]Beppu M, Miwa K, Itoh M, Katayama M and Ohno T.2008. Damage evaluation of concrete plates by high-velocity impact[J]. Int.J. Impact Engineering.35:1419-1426.
[114]Tu ZG and Lu Y.2009. Evaluation of typical concrete material models used in hydrocodes for high dynamic response simulations[J]. Int.J. Impact Engineering.36:132-146.
[115]Shahani AR and Fasakhodi MRA.2009. Finite element analysis of dynamic crack propagation using remeshing technique[J]. Materials and Design,30:1032-1041.
[116]Song J and Kim K.1996. Micromechanical modeling of the dynamic fracture process during rock blasting[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr.33(4):387-394.
[117]Donze FV, Bouchez J and Magnier SA.1997. Modeling fractures in rock blasting[J]. Int.J.Rock Mech.Min.Sci.34:1153-1163.
[118]Munjiza A, Latham JP and Andrews KRF.2000. Detonation gas model for combined finite-discrete element simulation of fracture and fragmentation[J]. Int. J. for Numerical Methods in Engineering,49:1495-1520.
[119]Bishop RF, Hill R and Mott NF.1945. The theory of indentation and hardness tests[J]. Proceedings of the Physical Society,57:147.-159.
[120]Hunter SC and Crozier RJM.1968. Similarity solution for the rapid uniform expansion of a spherical cavity in a compressible elastic-plastic solid[J]. Q. J. Mechanics Appl.&Math., 21(4):467-486.
[121]Foresstal MJ and Luk Vk.1988. Dynamic spherical cavity-expansion in a compressible elasic-platic solid[J]. J.Appl.Phys.,55:275-279.
[122]Durban D. and Fleck NA.1997. Spherical Cavity Expansion in a Drucker-Prager Solid[J]. J. Appl. Mech.,64:743-750.
[123]Foresstal MJ, Longcope DB and Norwood FR.1981. A model to estimate forces on conical penetrators into dry porous rock[J]. ASME J. Appl. Mech.,48:25-29.
[124]Nikolaevskij VN.1990. Mechanics of porous and fractured media[M]. World Scientific Press.
[125]何涛.2007.动能弹在不同材料靶体中的侵彻行为研究[D].中国科学技术大学博士论文.
[126]Durban D and Masri R.2004. Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium[J]. Int.J Solids Struct.41:5697-5716.
[127]Hanchak SJ, Foresttal MJ, Young ER and Ehrgott JQ.1992. Perforation of concrete slabs with 48MPa and 140MPa unconfined compressive strengths[J]. Int.J.Impact Eng.,12(1):1-7.
[128]He T, Wen HM and Guo XJ.2011. A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy[J]. Acta Mechanica Sinica,27(6):1001-1012.
[129]Rosenberg Z and Dekel E.2008. A numerical study of the cavity expansion process and its application to long-rod penetration mechanics[J]. Int. J. Impact Engng.35:147-154.
[130]Zhang LL and Huang FL.2006. Analysis on the penetration performance of a following projectile based on modified cavity expansion theory[J]. Transactions of Beijing Institute of Technology,26:1038-1042.
[131]Folsom Jr EN.1987. Projectile penetration into concrete with an inline hole[D]. Master's Thesis. Lawrence Livermore National Laboratory, UCRL-53786.
[132]Murphy MJ.1984. Performance analysis of two-stage munitions[C]. Proceedings of the 8th International Symposium on Ballistics, Orlando, Florida, Oct.23-25, TB 23-29.
[133]Teland JA.2001. Cavity expansion theory applied to penetration of targets with pre-drilled cavities[C].19th International Symposium of Ballistics. Switzerland,1329-1335.
[134]Frew DJ, Forrestal MJ, Cargile JD.2005. The effect of concrete target diameter on projectile deceleration and penetration depth[J]. Int J Impact Eng.,1-11.
[135]Teland JA, Sj(?)l H.2000.Boundary effects in penetration into concrete[R]. FFI/RAPPORT-2000/05414.
[136]Guo XJ and Wen HM.2012. Performance analysis and optimization of a dual warhead system[J]. IJNSNS,13(1):49-54.
[137]Forrestal MJ, Tzou DY.1997. A spherical cavity-expansion penetration model for concrete targets[J]. Int J Solids Struct,34(31-32):4127-4146.
[138]Guo XJ, He T and Wen HM.2012. A cylindrical cavity expansion penetration model for concrete targets with shear dilatancy[J]. ASCE.Eng.Mech.
[139]LS-DYNA 2007. KEYWORD USER'S MANUAL.LSTC[Z].
[140]Willam K and Warnke E.1975. Constitutive model for the triaxial behavior of concrete[C]. in, ISMES, Bergamo, Italy,1-30.
[141]Gebbeken N and Ruppert M.2000. A new material model for concrete in high-dynamic hydrocode simulations[J]. Archive of Applied Mechanics,70:463-478.
[142]Malvar LJ, Crawford JE, Wesevich JW and Simons D.1997. A plasticity concrete material model for DYNA3D[J]. Int J Impact Eng,19:847-873.
[143]Hartmann T, Pietzsch A and Gebbeken N.2010. A Hydrocode Material Model for Concrete[J]. International Journal of Protective Structures,1:443-468.
[144]Weerheijm J and Van Doormaal JCAM.2007. Tensile failure of concrete at high loading rates:New test data on strength and fracture energy from instrumented spalling tests[J]. Int J Impact Eng,34:609-626.
[145]Herrmann W.1969. Constitutive equation for the dynamic compaction of ductile porous materials[J]. Journal of Applied Physics,40:2490-2499.
[146]许红涛,卢文波.2003.爆破破岩过程中的动态卸载效应探讨[J].岩土力学,24：969-973.
[147]卢文波,陶振宇.1994.预裂爆破中炮孔压力变化历程的理论分析[J].爆炸与冲击,14：140-147.
[148]Dehghan Banadaki MM and Mohanty B.2012. Numerical simulation of stress wave induced fractures in rock[J]. Int.J. Impact Engineering,40-41:16-25.
[149]颜事龙,徐颖,宗琦,傅菊根.2009.空气垫层装药爆破过程中爆炸应力场衰减规律的初步探讨[J].南华大学学报(自然科学版),23：9-11.
[150]杨汉武.2002.爆炸磁压缩发生器及其脉冲功率调制研究[D].国防科学技术大学博士论文.
[151]Nilson RH, Proffer WJ and Duff RE.1985. Modelling of gas-driven fractures induced by propellant combustion within a borehole[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr.,22(1):3-19.
[152]Detournay E.2004. Propagation regimes of fluid-driven fractures in impermeable rocks[J]. Int. J. Geomech.4, SPECIAL ISSUE:PETROLEUM GEOMECHANICS,35-45.
[153]Savitski AA and Detournay E.2002. Propagation of a penny-shaped fluid-drivenfracture in an impermeable rock:asymptotic solutions[J]. International Journal of Solids and Structures,39(26):6311-6337.
[154]Lecampion B and Detournay E.2007. An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag[J]. Computer Methods in Applied Mechanics and Engineering,196(49-52):4863-4880.
[155]Adachi J, Siebrits E, Peirce A and Desroches J.2007. Computer simulation of hydraulic fractures[J]. International Journal of Rock Mechanics and Mining Sciences, 44(5):739-757.
[156]Wittmann FH and Hu XZ.1991. Fracture process zone in cementitious materials[J]. Int. J. Fracture,51:3-18.
[157]Papanastasiou P.1999. An efficient algorithm for propagating fluid-driven fractures[J]. Computational Mechanics,24:258-267.
[158]连志龙等.2008.水力压裂扩展的流固耦合数值模拟研究[J].岩土力学,20：3021-3026.
[159]徐浩.2013.混凝土动态计算本构新模型[D].中国科学技术大学博士论文.
[2]Isakov AL.1983. Directed fracture of rocks by blasting[J]. Journal of Mining Science, 479-488.
[3]Rossmanith HP, Daehnke A.1997. Knasmillner R E, Kouzniak N, Ohtsu M and Uenishi K. Fracture mechanics applications to drilling and blasting[J]. Fatigue Fract. Engng Mater. Struct,20:1617-1636.
[4]Mandal SK, Singh MM and Dasgupta S.2008. Theoretical concept to understand plan and design smooth blasting pattern[J]. Geotech Geol Eng,26:399-416.
[5]Dehghan Banadaki MM and Mohanty B.2012. Numerical simulation of stress wave induced fractures in rock[J]. Int.J. Impact Engineering,40-41:16-25.
[6]Gebbeken N and Ruppert M.2000. A new material model for concrete in high-dynamic hydrocode simulation[J]. Archive of Applied Mech,70:463-478.
[7]Zhang YQ, Hao H and Lu Y.2003. Anisotropic dynamic damage and fragmentation of rock materials under explosive loading[J]. Int.J. Engng. Sci.41:917-929.
[8]Russell AR and Khalili N.2002. Drained cavity expansion in sands exhibiting particle crushing[J]. Int.J. Numer. Anal. Meth. Geomech.26:323-340.
[9]龙源.1990.条形装药土中爆炸冲击波及空腔的数值模拟[J].爆炸与冲击,10：41-48.
[10]许连坡,金辉,章培德.1982.土中爆炸空腔的发展过程[J].力学学报,5：500-504.
[11]杨人光,庞维泰,秦明武.1984.论黄上中药包爆炸最优空腔比[J].金属矿山,4：6-10.
[12]余永强,杨小林,梁为民,王金星.2007.控制爆破致裂提高矿井瓦斯抽放率试验研究[J].煤炭学报,32：377-381.
[13]颜事龙,冯叔瑜,金孝刚.1998.有机玻璃中条形药包爆炸破碎区发展过程的高速摄影研究[J].爆炸与冲击,18(3)：262-267.
[14]王呼和,佟铮,邢永明,李进福.2009.无限冰介质中爆炸裂纹扩展机理与数值模拟[J].实验力学,24：493-498.
[15]Coates DF.1970. Dynamic Rock Mechanics. Rock Mechanics Principles[Z],8(12):97.
[16]Wu YK, Hao H, Zhou YX and Chong K.1998. Propagation characteristics of blast-induced shock waves in a jointed rock mass[J]. Soil Dynamic and Earthquake Engineering,17:407-412.
[17]Langefors U and Kihlstrom B.1978. The modern techniques of rock blasting (3rd)[C] Wiley, New York.
[18]Duvall WI and Atchison TC.1957. Rock Breakage by Explosives[R]. USBM RI5356.
[19]Hino K.1956. Fragmentation of rock through blasting and shock wave theory of blasting[C]. The 1st U.S. Symposium on Rock Mechanics (USRMS),23-25.
[20]Kutter HK and Fairhurst C.1971. On the Fracture Process in Blasting[J]. Int. J.of Rk Mech.& Min. Sci.8:181-188.
[21]Li CR, Kang LJ, Qi QX. et.al.2009. The numerical analysis of borehole blasting and application in coal mine roof-weaken[J]. Procedia Earth and Planetary Science,1: 451-459.
[22]王仲琦,张奇,白春华.2002.孔深影响爆炸应力波特性的数值模拟分析[J].岩石力学与工程学报,24：550-553.
[23]Zhu ZM, Mohanty B and Xie HP.2007. Numerical investigation of blasting-induced crack initiation and propagation in rocks[J]. Int.J, Rock Mech.& Min. Sci.44:412-424.
[24]Zhu ZM, Xie HP and Mohanty B.2008. Numerical investigation of blasting-induced damage in cylindrical rocks[J]. Int.J, Rock Mech.& Min. Sci.45:111-121.
[25]夏祥,石永强,李海波,马行东,刘博.2007.岩体弹孔及群孔齐发爆破爆炸载荷数值分析[J].岩石力学与工程学报,26：3391-3396.
[26]Fourney WL, Holloway DC and Dally JW.1975. Fracture initiation and propagation from a center of dilatation[J]. Int.J. of Fracture,11:1011-1029.
[27]Isakov AL and Sher EN.1983. Problem of the dynamic for development of directiona cracks during blast-hole firing[J]. Journal of Mining Science,19(3):189-196.
[28]Nilson RH, Proffer W J and Duff RE.1985. Modelling of gas-driven fractures induced by propellant combustion within a borehole[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr.22(1):3-19.
[29]Esen S, Onederra I and Bilgin HA.2003. Modelling the size of the crushed zone around a blasthole[J]. Int.J. Rock Mech & Mining Sci.40:485-495.
[30]Hagan TN.1973. Rock breakage by explosives[C] In:Proc.Nat.Symp. Rock Fragmentation, 1-17.
[31]卢文波,陶振宇.1994.爆生气体驱动的裂纹扩展速度研究[J].爆炸与冲击,14：264-268.
[32]Mchugh S.1983. Crack extension caused by internal gas pressure compared with extension caused by tensile stress[J]. Int. Journ. of Fracture,21:163-176.
[33]Cho SH, Nakamura Y and Kaneko K.2004. Dynamic fracture process analysis of rock subjected to stress wave and gas pressurization[J]. Int. J. Rock Mech. Min. Sci.41:1-8.
[34]杨小林,工梦恕.2001.爆生气体作用下岩石裂纹的扩展机理[J].爆炸与冲击,21：111-116.
[35]Zhou CB and He XG.2004. The rock deep hole blasting new technical progress[M]. China University of Geosciences Press.
[36]Brinkmann JR.1987. Separating shock wave and gas expansion breakage mechanisms[C]. In:Fourney WL, Dick RD, editors. Proc.2nd international symposium on rock fragmentation by blasting. USA:Keystone,6-15.
[37]Mohanty B.1982. Characteristic crack patterns close to an exploding charge[C]. In: Baumgartner P. editor. Proc.14th canadian rock mechanics symposium.Vancouver, Canada: Canadian Institute of Mining and Metallurgy,31-36.
[38]赵新涛,刘东燕,程贵海,李东升.2011.爆生气体作用机理及岩体裂纹扩展分析[J].重庆大学学报,34：75-80.
[39]Sim YJ, Song KI and Cho GC.2005. Evaluation of final fragmentation zone induced by rock blasting[C]. The 18th KKCNN Symposium on Civil Engineering-KAIST12. 18-20:161-168.
[40]徐颖,沈兆武,孟益平. 2003.爆炸载荷作用下刻槽炮孔动态裂纹扩展规律[J].中国科学技术大学学报,33：184-190.
[41]Cho SH, Nakamura Y, Mohanty B and Kaneko K.2006. Study on control of crack-propagation in blasting[C]. In:8th International Symposium on Rock Fragmentation by Blasting, Editec S.A., Santiago, Chile,124-128.
[42]Rathore SS and Bhandari S.2007. Controlled fracture growth by blasting while protecting damages to remaining rock[J]. Rock Mech. Rock Engng.3:317-326.
[43]Dally JW and Fourhey WL.1977. Fracture control in construction blasting[C]. The 18th U.S. Symposium on Rock Mechanics,22-24.
[44]Kutter HK.1970. Stress analysis of a pressurized circular hole with radial cracks in an infinite elastic plate[J]. Int.J. Fracture Mech.6:233-247.
[45]Ramesh K, Shukla S, Dixit PM and Karuppaiah N.1997. Numerical evaluation of SIF for radial cracks in thick annular ring using cyclic symmetry[J]. Engineering Fracture Mech. 56:141-153.
[46]Taran EP and Shapiro VY.1982. Action of the explosion of a blast hole charge in the design of a direct cut with a compensation hole[J]. J. Mining Sci.18:119-122.
[47]张志呈.2000.岩体爆破裂纹扩展速度实验研究[J].爆破器材,1-8.
[48]张志呈,肖正学,郭学彬,林秀英,蒋光明.2001.断裂控制爆破裂纹扩展的高速摄影试验研究[J].西南工学院学报,16：53-57.
[49]张奇.1990.岩石爆破的粉碎区及其空腔膨胀[J].爆炸与冲击,10：68-75.
[50]李端明,唐中华,张志呈.1998.条形药包爆破的最优空强化[J].四川冶金,4：10-14.
[51]徐颖,孟益平,程玉生.2002.装药不耦合系数对爆破裂纹控制的试验研究[J].岩石力学与工程学报,21：1843-1847.
[52]宗琦,李永池,徐颖.2004.炮孔水耦合装药爆破孔壁冲击压力研究[J].水动力学研究与进展,19：610-615.
[53]王志亮,李永池.2005.工程爆破中径向水不耦合系数效应数值仿真[J].岩土力学,26：1926-1930.
[54]龚敏,王德胜,程西江.2004.条形药包不同空腔比试验研究[J].爆破,21：1-4.
[55]Luo Y and Shen ZW.2006. Study on orientation fracture blasting with shaped charge in rock[J]. Journal of USTB.13:193-198.
[56]Wang SL and Yin SD.2011. A closed-form solution for a spherical cavity in the elastic-brittle-plastic medium[J]. Tunneling and Underground Space Technology, 26:236-241.
[57]Zhang CG, Zhang QH, Zhao JH, Xu F and Wu CZ.2010. Unified analytical solution for a circular opening based on non-linear unified failure criterion[J]. Journal of Zhejiang University-Science A (Applied Physics & Engineering).11:71-79.
[58]Eason G.1963. Propagation of waves from spherical and cylindrical cavities[J]. ZAMP. 14:12-23.
[59]许红涛,卢文波,邹奕芳.2003.钻孔爆破中环向裂纹形成机理的研究[J].工程爆破,9：7-11.
[60]Harries G.1973. A mathematical model of cractering and blasting[J]. In National Symposium on Rock Fragmentation, Adelaide,41-45.
[61]Xu BY. and Liu XS.1995. Applying Plasto Elasticity Mechanical[M], Tsinghua University Press.
[62]Curran DR, Seaman L, Shockey DA.1977. Dynamic failure in solids[J]. Physics Today.
[63]Seaman L.1980. A computational model for dynamic tensile microfracture with damage in one plane[R]. SRI Poulter Laboraratory Technical Report001-80, SRI International, Menlo Park.
[64]Margolin LG. 1984. A generalized Griffith criterion for crack propagation[J]. Engineering Fracture Mechanics,19(3):539-543.
[65]Grady DE and Chen ME.1980. Continuum modeling of explosive fracture in oil shale[J]. Int. J. Rock Mech. Min.Sci.Geomech.Abstr.17:147-157.
[66]Kuszmaul JS.1987. A technique for predicting fragmentation and fragment sizes resulting from rock blasting[C]. In:Proc.28th U.S. Symp. Rock Mech.,893-900.
[67]谢和平.1996.分形-岩石力学导论[M].科学出版社.
[68]高峰,谢和平.1996.脆性材料的分形统计强度理论[J].固体力学学报,17(3)：239-244.
[69]Dcik RA.1983. Explosives and blasting procedures mannal [Z]. US Bureau of Mines, IC. No.8929.
[70]宗琦.1994.岩石内爆炸应力波破裂区半径的计算[J].爆破,15-17.
[71]吴亮,卢文波,宗琦.2006.岩石中柱状装药爆炸能量分布[J].岩土力学,27：735-739.
[72]戴俊.2001.柱状装药爆破的岩石压碎圈与裂隙圈计算[J].辽宁工程技术大学学报,20：144-147.
[73]Cao LF, Teh CI and Chang MF.2002. Analysis of undrained cavity expansion in elasto-plastic soils with non-linear elasticity [J]. Int.J. Numer. Anal. Meth. Geomech. 26:25-52.
[74]Collins IF and Yu H S.1996. Undrained cavity expansions in critical state soils [J]. Int. J. Numer. Anal.Meth.Geomech.20:489-516.
[75]Cherry JT, Schock RN and Sweet J.1975. A theoretical model of dilatant behavior of a brittle rock[J]. Pure and Applied Geophysics,113:183-196.
[76]Yuan SC and Harrison JP.2005. Development of a hydro-mechanical local degradation approach and its application to modeling fluid flow during progressive fracturing of heterogeneous rocks[J]. Int.J. Rock Mech.& Min. Sci.42:961-984.
[77]Dunin SZ, Sirotkin VK and Sumin EV.1979. Nature of the state of the medium in the neighboehood of a cavity expanding into a dilating medium[J]. Journal of Applied Mechanics and Technical Physics,20:373-380.
[78]Warren TL, Fossum AF and Frew DJ.2004. Penetration into low-strength (23MPa) concrete:target characterization and simulation [J]. Int. J. Impact Engng.,477-503.
[79]何涛.文鹤鸣.2007.靶体响应力函数的确定方法及其在侵彻力学中的应用[J].中国科学技术大学学报,37：1249-1261.
[80]蒋明镜,沈珠江.1996.考虑剪胀的弹脆塑性软化柱形孔扩张问题[J].河海大学学报,24：65-72.
[81]蒋明镜,沈珠江.1997.考虑剪胀的线性软化柱形孔扩张问题[J].岩石力学与工程学报,16：550-557.
[82]Mosinets VN and Gorbacheva NP.1972. A seismological method of determining the parameters of the zones of deformation of rock by blasting[J]. Journal of Mining Science, 8:640-647.
[83]葛涛,吴华杰,陶剑青,工明洋.2005.岩石中爆炸破碎区边界参数研究[J].爆破, 22:5-8.
[84]Nakamura Y.1993. Model experiments on effectiveness of fracture plane control method in blasting[J]. Int. J. Blast Fragment.3:59-78.
[85]Nakamura Y, Cho SH, Yoneoka M, Yamamoto M and Kaneko M.2004. Model experiments on crack propagation between two charge holes in blasting[J]. Sci. Technol Energetic Mater.,65:34-39.
[86]Chandar KR and Yang B.1997. On the role of microcracks in the dynamic fracture of brittle materials[J]. J. Mech. Phys. Solid,45:535-563.
[87]Sharon E and Fineberg J.1999. Confirming the continuum theory of dynamic brittle fracture for fast cracks[J]. Nature,397:333-335.
[88]Boudet JF, Ciliberto S and Steinberg V.1995. Experimental study of the instability of crack propagation in brittle materials[J]. Europhys. Lett.30:337-342.
[89]Fineberg J, Gross SP, Marder M and Swinney HL.1992. Instability in the propagation of fast cracks[J]. Physical Review B,45:5146-5154.
[90]Voitenko YI.1995. Fracture of solid by weak blasts[J]. Combustion, Explosion, and Shock Waves,31:492-499.
[91]Sassa K, Ito I, and Hanasaki K.1971. Breakage of brittle material by quasi-static pressure of explosive gas[J]. Journal of the Japan Explosive Society,32(1):9-16. (in Japanese)
[92]Daehnke A, Rossmanith P and Napier JAL.1997. Gas pressurization of blast-induced conical cracks[J]. Int.J. Rock Mech.& Min. Sci.
[93]Dehghan Banadaki MM, Mohanty B.2008. Blast induced pressure in some granitic rocks[C]. In:Majdi A, Ghazvinian A, editors. Proc.5th Asian rock mechanics symposium (ARMS-ISRM):Curran Associates, Inc. Tehran, Iran.,933-939
[94]II'yushin AA.1999. The mechanics of a continuous medium[M]. Izd-vo MGU. Moscow. (Translated in Hustrulid W. Blasting principles for open pit blasting, vol. II. Rotterdam: Balkema,964-1009 [Chapter 21]), [in Russian].
[95]Szuladzinski G.1993. Response of rock medium to explosive borehole pressure[C]. Proceedings of the Fourth International Symposium on Rock Fragmentation by Blasting-Fragblast-4, Vienna, Austria.17-23.
[96]Djordjevic N.1999. Two-component of blast fragmentation[C].Proceedings of the Sixth International Symposium on Rock Fragmentation by Blasting-Fragblast 1999, South African Institute of Mining and Metallurgy, Johannesburg, South Africa..213-219.
[97]Kanchibotla SS, Valery W and Morrell S.1999. Modelling fines in blast fragmentation and its impact on crushing and grinding[C]. Proceedings of Explosive—A Conference on Rock Breaking. The Australasian Institute of Mining and Metallurgy, Kalgoorlie, Australia. 137-44.
[98]Tesarik DR and Hustrulid WA.2009. A hydrodynamics-based approach for predicting the blast damage zone in drifting as demonstrated using concrete block data[J]. Blast. Fragm.
[99]Cho SH.2003. Dynamic fracture process analysis of rock and its application to fragmentation control in blasting[D], Ph. D. Eng. Thesis, Hokkaido University at Sapporo, Japan.
[100]Cho SH, Nakamura Y, Mohanty B, Yang HS and Kaneko K.2008. Numerical study of fracture plane control in laboratory-scale blasting[J]. Engineering Fracture Mech. 75:3966-3984.
[101]Papanastasiou P and Thiercelin M.1993. Influence of inelastic rock behavior in hydraulic fracturing[J]. Int.J.Rock Mech.Min.Sci.& Geomech. Abstr.30:1241-1247.
[102]Wawrzynek PA and Ingraffea AR.1987. Interactive finite element analysis of fracture processing:an integrated approach[J]. Theo. App. Fract. Mech.,8:137-150.
[103]Tang CA and Kaiser PK.1998. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure-Part I:Fundamentals[J]. Int. J. Rock Mech. Min. Sci.,35(2):113-121.
[104]Kaiser PK and Tang CA.1998. Numerical simulation of damage accumulation and seismic energy release during brittle rock failure-Part H:Rib Pillar Collapse[J]. Int. J. Rock Mech. Min. Sci.,35(2):123-134.
[105]Ma GW and An XM.2008. Numerical simulation of blasting-induced rock fractures[J]. Int.J.Rock Mech.Min.Sci.45:966-975.
[106]Cho SH and Kaneko K.2004. Influence of the applied pressure waveform on the dynamic fracture processes in rock[J]. Int. J. Rock Mech. Min. Sci.41:771-784.
[107]Shi GH.1993. Block system modelling by discontinuous deformation analysis[R]. Computational Mechanics Publication:Southampton, U.K.
[108]Zhao ZY and Gu J.2008. Fracture propagation in rock under blast load-a numerical investigation[R]. NTU. Civil Engineering Research.21:75-78.
[109]Zhao ZY and Zhang Y.2010. Rock blast simulation by discontinuous deformation analysis[R]. Civil Engineering.
[110]夏祥,李海波,李俊如,肖克强,唐海马国伟.2006.岩体爆生裂纹的数值模拟[J].岩上力学,27：1987-1991.
[111]王志亮,郑明新.2008.基规范TCK损伤本构的岩石爆破效应数值模拟[J].岩土力学,29：230-234.
[112]Wang ZL, Li YC and Shen RF.2007. Numerical simulation of tensile damage and blast crater in brittle rock due to underground explosion[J]. Int. J. Rock Mech.& Min. Sci.44: 730-738.
[113]Beppu M, Miwa K, Itoh M, Katayama M and Ohno T.2008. Damage evaluation of concrete plates by high-velocity impact[J]. Int.J. Impact Engineering.35:1419-1426.
[114]Tu ZG and Lu Y.2009. Evaluation of typical concrete material models used in hydrocodes for high dynamic response simulations[J]. Int.J. Impact Engineering.36:132-146.
[115]Shahani AR and Fasakhodi MRA.2009. Finite element analysis of dynamic crack propagation using remeshing technique[J]. Materials and Design,30:1032-1041.
[116]Song J and Kim K.1996. Micromechanical modeling of the dynamic fracture process during rock blasting[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr.33(4):387-394.
[117]Donze FV, Bouchez J and Magnier SA.1997. Modeling fractures in rock blasting[J]. Int.J.Rock Mech.Min.Sci.34:1153-1163.
[118]Munjiza A, Latham JP and Andrews KRF.2000. Detonation gas model for combined finite-discrete element simulation of fracture and fragmentation[J]. Int. J. for Numerical Methods in Engineering,49:1495-1520.
[119]Bishop RF, Hill R and Mott NF.1945. The theory of indentation and hardness tests[J]. Proceedings of the Physical Society,57:147.-159.
[120]Hunter SC and Crozier RJM.1968. Similarity solution for the rapid uniform expansion of a spherical cavity in a compressible elastic-plastic solid[J]. Q. J. Mechanics Appl.&Math., 21(4):467-486.
[121]Foresstal MJ and Luk Vk.1988. Dynamic spherical cavity-expansion in a compressible elasic-platic solid[J]. J.Appl.Phys.,55:275-279.
[122]Durban D. and Fleck NA.1997. Spherical Cavity Expansion in a Drucker-Prager Solid[J]. J. Appl. Mech.,64:743-750.
[123]Foresstal MJ, Longcope DB and Norwood FR.1981. A model to estimate forces on conical penetrators into dry porous rock[J]. ASME J. Appl. Mech.,48:25-29.
[124]Nikolaevskij VN.1990. Mechanics of porous and fractured media[M]. World Scientific Press.
[125]何涛.2007.动能弹在不同材料靶体中的侵彻行为研究[D].中国科学技术大学博士论文.
[126]Durban D and Masri R.2004. Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium[J]. Int.J Solids Struct.41:5697-5716.
[127]Hanchak SJ, Foresttal MJ, Young ER and Ehrgott JQ.1992. Perforation of concrete slabs with 48MPa and 140MPa unconfined compressive strengths[J]. Int.J.Impact Eng.,12(1):1-7.
[128]He T, Wen HM and Guo XJ.2011. A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy[J]. Acta Mechanica Sinica,27(6):1001-1012.
[129]Rosenberg Z and Dekel E.2008. A numerical study of the cavity expansion process and its application to long-rod penetration mechanics[J]. Int. J. Impact Engng.35:147-154.
[130]Zhang LL and Huang FL.2006. Analysis on the penetration performance of a following projectile based on modified cavity expansion theory[J]. Transactions of Beijing Institute of Technology,26:1038-1042.
[131]Folsom Jr EN.1987. Projectile penetration into concrete with an inline hole[D]. Master's Thesis. Lawrence Livermore National Laboratory, UCRL-53786.
[132]Murphy MJ.1984. Performance analysis of two-stage munitions[C]. Proceedings of the 8th International Symposium on Ballistics, Orlando, Florida, Oct.23-25, TB 23-29.
[133]Teland JA.2001. Cavity expansion theory applied to penetration of targets with pre-drilled cavities[C].19th International Symposium of Ballistics. Switzerland,1329-1335.
[134]Frew DJ, Forrestal MJ, Cargile JD.2005. The effect of concrete target diameter on projectile deceleration and penetration depth[J]. Int J Impact Eng.,1-11.
[135]Teland JA, Sj(?)l H.2000.Boundary effects in penetration into concrete[R]. FFI/RAPPORT-2000/05414.
[136]Guo XJ and Wen HM.2012. Performance analysis and optimization of a dual warhead system[J]. IJNSNS,13(1):49-54.
[137]Forrestal MJ, Tzou DY.1997. A spherical cavity-expansion penetration model for concrete targets[J]. Int J Solids Struct,34(31-32):4127-4146.
[138]Guo XJ, He T and Wen HM.2012. A cylindrical cavity expansion penetration model for concrete targets with shear dilatancy[J]. ASCE.Eng.Mech.
[139]LS-DYNA 2007. KEYWORD USER'S MANUAL.LSTC[Z].
[140]Willam K and Warnke E.1975. Constitutive model for the triaxial behavior of concrete[C]. in, ISMES, Bergamo, Italy,1-30.
[141]Gebbeken N and Ruppert M.2000. A new material model for concrete in high-dynamic hydrocode simulations[J]. Archive of Applied Mechanics,70:463-478.
[142]Malvar LJ, Crawford JE, Wesevich JW and Simons D.1997. A plasticity concrete material model for DYNA3D[J]. Int J Impact Eng,19:847-873.
[143]Hartmann T, Pietzsch A and Gebbeken N.2010. A Hydrocode Material Model for Concrete[J]. International Journal of Protective Structures,1:443-468.
[144]Weerheijm J and Van Doormaal JCAM.2007. Tensile failure of concrete at high loading rates:New test data on strength and fracture energy from instrumented spalling tests[J]. Int J Impact Eng,34:609-626.
[145]Herrmann W.1969. Constitutive equation for the dynamic compaction of ductile porous materials[J]. Journal of Applied Physics,40:2490-2499.
[146]许红涛,卢文波.2003.爆破破岩过程中的动态卸载效应探讨[J].岩土力学,24：969-973.
[147]卢文波,陶振宇.1994.预裂爆破中炮孔压力变化历程的理论分析[J].爆炸与冲击,14：140-147.
[148]Dehghan Banadaki MM and Mohanty B.2012. Numerical simulation of stress wave induced fractures in rock[J]. Int.J. Impact Engineering,40-41:16-25.
[149]颜事龙,徐颖,宗琦,傅菊根.2009.空气垫层装药爆破过程中爆炸应力场衰减规律的初步探讨[J].南华大学学报(自然科学版),23：9-11.
[150]杨汉武.2002.爆炸磁压缩发生器及其脉冲功率调制研究[D].国防科学技术大学博士论文.
[151]Nilson RH, Proffer WJ and Duff RE.1985. Modelling of gas-driven fractures induced by propellant combustion within a borehole[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr.,22(1):3-19.
[152]Detournay E.2004. Propagation regimes of fluid-driven fractures in impermeable rocks[J]. Int. J. Geomech.4, SPECIAL ISSUE:PETROLEUM GEOMECHANICS,35-45.
[153]Savitski AA and Detournay E.2002. Propagation of a penny-shaped fluid-drivenfracture in an impermeable rock:asymptotic solutions[J]. International Journal of Solids and Structures,39(26):6311-6337.
[154]Lecampion B and Detournay E.2007. An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag[J]. Computer Methods in Applied Mechanics and Engineering,196(49-52):4863-4880.
[155]Adachi J, Siebrits E, Peirce A and Desroches J.2007. Computer simulation of hydraulic fractures[J]. International Journal of Rock Mechanics and Mining Sciences, 44(5):739-757.
[156]Wittmann FH and Hu XZ.1991. Fracture process zone in cementitious materials[J]. Int. J. Fracture,51:3-18.
[157]Papanastasiou P.1999. An efficient algorithm for propagating fluid-driven fractures[J]. Computational Mechanics,24:258-267.
[158]连志龙等.2008.水力压裂扩展的流固耦合数值模拟研究[J].岩土力学,20：3021-3026.
[159]徐浩.2013.混凝土动态计算本构新模型[D].中国科学技术大学博士论文.