冲击载荷作用下岩石动态断裂过程机理研究
|
摘要
该文对冲击载荷作用下的岩石断裂机理进行了比较全面和系统的研究,从微观、细观与宏观三个层次对岩石断裂过程特性及其动力响应进行了分析,其主要工作如下:
1、对三种典型应力波分别利用傅立叶变换与小波变换进行了对比分析,得知了它们的频率分布以及能量分布规律;针对冲击载荷的作用特点,提出了由冲击载荷所引起的应力波波长、岩石的缺陷尺寸以及试件尺寸之间的大小关系作为宏观、细观与微观尺度划分标准。
2、针对冲击载荷作用下岩石断裂的微观热力学过程为绝热过程或准绝热过程,利用热力学理论与冲击作用下岩石的物态方程,得出了此状态下的岩石本构关系,并提出了冲击载荷作用下岩石微观热力学破坏条件。
3、通过分析单一有限尺寸裂纹在应力波作用时的近裂纹面应力场,得出了影响其动态应力强度因子的主要因素是应力释放区大小以及应力释放区外的应力分布。在此基础上,构建了用于计算动态应力强度因子的近似表达式。通过对垂直方向、切线方向以及斜向冲击载荷作用下的动态响应进行的数值模拟,得到了各种状况下的动态应力强度因子,同时获悉了最优断裂条件下应力波入射情况。
4、对应力波在软弱结构面以及节理裂隙处传播的特征进行了系统的研究,探讨了岩石动态断裂过程中的应力波波形畸变的问题。针对软弱结构面上的摩擦滑移准则的局限性,引入能量损耗值来表示界面可滑移的程度或趋势大小,把单点上的可滑移条件下的能量动力准则推广到整个结构面上,并从应力准则的角度验证了此方法的可行性。通过对应力波在张开型节理裂隙处传播规律的解析分析,得出了细观缺陷的几何结构、物理特性对应力波传播的影响。通过重点考查SHPB压杆实验中反射波的变化情况,指出其反射波的变化过程能反映岩石的动态累积损伤或动态断裂过程。
5、考虑到岩石动态断裂的相关因素以及应力波作用的特点,以能量
The thesis has systematically investigated the mechanism of dynamic fracture processes of rock subjected to impact loads. The dynamic characteristics and responses of the rock fracture processes have been analyzed from micro, meso and macro levels respectively. The thesis includes the following work.1. Three typical stress waves induced by impact loads were analyzed by both Fast Fourier Transform (FFT) and Wavelet, and the distribution rules of frequency and energy of stress waves were obtained. According to the trait of the impact loading, the paper proposed that the size relation between the wavelength of stress waves induced by impact loads, faults in rock and the samples may be used for the classification criterion among the micro, meso and macro dimensions.2. The dynamic fracture processes of rock under impact loading are regarded as adiabatic or quasi-adiabatic processes in micro thermodynamics. Associated with the state equation of rock subjected to impact loading, the constitutive relation of rock suitable for this situation was obtained, and the breakage condition of micro thermodynamics for rock under the impact loading was proposed.3. The stress field near the crack subjected to impact loads was investigated. The main factors, which have effect on dynamic stress intensity factor (DSIF), are the size of the stress releasing zone and the distribution of the stress out of the release zone. The calculation formula of DSIF was proposed. The dynamic responses of crack subjected several typical impact stresses such as shear, normal and oblique incident stress waves were simulated. According to the results of the simulation the DSIFs were calculated. The angle of initiation of the crack was predicted. The method of
optimizing fracture generating by stress pulses was discussed.4. The propagation characteristics of the stress waves transmitting to the weak interface or opened crack was investigated systematically. For its limitation, the energy criterion under the sliding condition for one point was generalized to the whole interface by inducting the dissipating energy value to indicate the possibility of slide. This method was verified by the stress criterion; The geometry of opened crack and its physical property have effect on the propagation of stress waves according to analytical results; The deformations of reflected stress waves recorded in the SHPB tests were investigated emphatically, and the process of the change of the reflected stress waves refers to the process of dynamic damage cumulation or the dynamic fracture.5. Based upon the study on rock responses to impact load by the principles of energy dissipations and associating with the damage mechanics and the action density of the stress waves as well, the dynamic cumulative damage formula of rock under dynamic cyclic loading at the damage phase was proposed. According to the fractal phenomenon analysis on rock fragments, the iterative relationship expression about the damage fractal value and the number of the fragments of rock subjecting to impact load was obtained. At the same time, the iterative relationship expression about the damage fractal value and the impact energy was proposed basing on the principles of energy dissipations and the criteria of dynamic brittle fracture. The results of tests show that the relation among the impact energy, the damage of rock and the number of fragments lies in a state of mutual coupling.
1、对三种典型应力波分别利用傅立叶变换与小波变换进行了对比分析,得知了它们的频率分布以及能量分布规律;针对冲击载荷的作用特点,提出了由冲击载荷所引起的应力波波长、岩石的缺陷尺寸以及试件尺寸之间的大小关系作为宏观、细观与微观尺度划分标准。
2、针对冲击载荷作用下岩石断裂的微观热力学过程为绝热过程或准绝热过程,利用热力学理论与冲击作用下岩石的物态方程,得出了此状态下的岩石本构关系,并提出了冲击载荷作用下岩石微观热力学破坏条件。
3、通过分析单一有限尺寸裂纹在应力波作用时的近裂纹面应力场,得出了影响其动态应力强度因子的主要因素是应力释放区大小以及应力释放区外的应力分布。在此基础上,构建了用于计算动态应力强度因子的近似表达式。通过对垂直方向、切线方向以及斜向冲击载荷作用下的动态响应进行的数值模拟,得到了各种状况下的动态应力强度因子,同时获悉了最优断裂条件下应力波入射情况。
4、对应力波在软弱结构面以及节理裂隙处传播的特征进行了系统的研究,探讨了岩石动态断裂过程中的应力波波形畸变的问题。针对软弱结构面上的摩擦滑移准则的局限性,引入能量损耗值来表示界面可滑移的程度或趋势大小,把单点上的可滑移条件下的能量动力准则推广到整个结构面上,并从应力准则的角度验证了此方法的可行性。通过对应力波在张开型节理裂隙处传播规律的解析分析,得出了细观缺陷的几何结构、物理特性对应力波传播的影响。通过重点考查SHPB压杆实验中反射波的变化情况,指出其反射波的变化过程能反映岩石的动态累积损伤或动态断裂过程。
5、考虑到岩石动态断裂的相关因素以及应力波作用的特点,以能量
The thesis has systematically investigated the mechanism of dynamic fracture processes of rock subjected to impact loads. The dynamic characteristics and responses of the rock fracture processes have been analyzed from micro, meso and macro levels respectively. The thesis includes the following work.1. Three typical stress waves induced by impact loads were analyzed by both Fast Fourier Transform (FFT) and Wavelet, and the distribution rules of frequency and energy of stress waves were obtained. According to the trait of the impact loading, the paper proposed that the size relation between the wavelength of stress waves induced by impact loads, faults in rock and the samples may be used for the classification criterion among the micro, meso and macro dimensions.2. The dynamic fracture processes of rock under impact loading are regarded as adiabatic or quasi-adiabatic processes in micro thermodynamics. Associated with the state equation of rock subjected to impact loading, the constitutive relation of rock suitable for this situation was obtained, and the breakage condition of micro thermodynamics for rock under the impact loading was proposed.3. The stress field near the crack subjected to impact loads was investigated. The main factors, which have effect on dynamic stress intensity factor (DSIF), are the size of the stress releasing zone and the distribution of the stress out of the release zone. The calculation formula of DSIF was proposed. The dynamic responses of crack subjected several typical impact stresses such as shear, normal and oblique incident stress waves were simulated. According to the results of the simulation the DSIFs were calculated. The angle of initiation of the crack was predicted. The method of
optimizing fracture generating by stress pulses was discussed.4. The propagation characteristics of the stress waves transmitting to the weak interface or opened crack was investigated systematically. For its limitation, the energy criterion under the sliding condition for one point was generalized to the whole interface by inducting the dissipating energy value to indicate the possibility of slide. This method was verified by the stress criterion; The geometry of opened crack and its physical property have effect on the propagation of stress waves according to analytical results; The deformations of reflected stress waves recorded in the SHPB tests were investigated emphatically, and the process of the change of the reflected stress waves refers to the process of dynamic damage cumulation or the dynamic fracture.5. Based upon the study on rock responses to impact load by the principles of energy dissipations and associating with the damage mechanics and the action density of the stress waves as well, the dynamic cumulative damage formula of rock under dynamic cyclic loading at the damage phase was proposed. According to the fractal phenomenon analysis on rock fragments, the iterative relationship expression about the damage fractal value and the number of the fragments of rock subjecting to impact load was obtained. At the same time, the iterative relationship expression about the damage fractal value and the impact energy was proposed basing on the principles of energy dissipations and the criteria of dynamic brittle fracture. The results of tests show that the relation among the impact energy, the damage of rock and the number of fragments lies in a state of mutual coupling.
引文
1. Hudson, J. A., Practical Rock Engineering, Principal of rock engineering consultants, 9, HK Polytechnic University, 2001
2. Brace, W. F. and E. G. Bombolakis, A note on brittle crack growth in compression, J. Geophys. Res., 1963, 68, 3709～3713
3. Cook, N. G. W., The failure of rock, Int. J. Rock Mech. Min. Sci., 1965, 2, 389～403
4. Hoek, E. and Bieniawski, Z. T., Brittle fracture propagation under compression, International Journal of Fracture Mechanics, 1965,1, 137～155
5. T.L. Blanton, Effect of Strain Rates from 10~(-2) to 10 sec~(-1) in Triaxial Compression Tests on Three Rocks. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1981,18, 47～62
6.徐小荷,余静,岩石破碎学,煤炭工业出版社,1984
7.杨善元,岩石爆破动力学基础,煤炭工业出版社,1991
8.唐春安,岩石破裂过程中的灾变,北京:煤炭工业出版社,1993
9.廖振鹏,工程波动理论导引,科学出版社,1996
10.于学馥,郑颖人,刘怀恒,方正昌,地下工程围岩稳定性分析,煤炭工业出版社,1983
11.朱维申,何满潮,复杂条件下围岩稳定性与岩石动态施工力学,科学出版社,1996
12.李夕兵,古德生,岩石冲击动力学,长沙:中南工业大学出版社,1994
13.刘德顺,李夕兵,冲击机械系统动力学,北京:科学出版社,1999
14.王礼立,应力波基础,北京:国防工业出版社,1985
15.赖海辉等,机械岩石破碎学,中南工业大学出版社,1991
16.吴世明,土介质中的波,科学出版社,1997
17.张宗贤,岩石破坏原理及其应用,冶金工业出版社,1994
18.夏蒙棼,柯孚久,吕永华,白以龙,理想微裂纹系统中的随机扩展效应,中国科学,1991,3277～283
19.白以龙,柯孚久,夏蒙棼,固体中微裂纹系统统计演化的基本描述,力学学报,1991,23(3),290～297
20.周维垣,高等岩石力学,北京;水利水电出版社,1990,362～403
21.王礼立,爆炸与冲击载荷下结构和材料动态响应研究的新进展,爆炸与冲击,2001,21(2),81～88
22.王明洋,戚承志,钱七虎 岩体中爆炸与冲击下的破坏研究,辽宁工程技术大学学报(自然科学版),2001,20(4),385～389
23. J.W. Williams, Numerical Methods In Geomechanics[M]. Nsbruck Berkely, 1988, 1799-1803
24.范天佑,断裂动力学引论,北京理工大学出版社,1990
25.赵亚溥,裂纹动态起始问题的研究进展,力学进展,1996,26(3),362～378
26. Mott N F, Brittle fracture in mild steel plates, Engineering, 1948, 165:16
27. Griffith A. A., The phenomena of rupture and flow in solids, Phil. Trans. Roy. Soc., London, 1921, A221, 163～198
28. Irwin, G. R., Fracture, In Handbuch der physik, Springer-Verlag, Berlin, 1958, V. 6, p. 551～585
29.杨卫著,宏微观断裂力学,北京:国防工业出版社,1995
30. Barenblatt, G. I., The mathematical theory of equilibrium cracks in brittle fracture, Sdv. Appl. Mech., 1962, 7,55～129
31. Dugdale, D. S., Yielding of steel sheets containing slits, J. Mech. Phys. Solids, 1960, 8, 100～104
32. Mines R. A. W., Int. J. Impact Engng, 1990, 9, 441～454
33. Steverding B, Lehnigk S.H. Response of cracks to impact, J. Appl. Phys., 1970, 41(5), 2096～2099
34. Steverding B, Lehnigk S.H. Collision of stress pulses with obstacles and dynamic of fracture, J. Appl. Phys., 1971, 42(8), 3231～3238
35. Kalthoff J. F., Shockey D. A., J. Appl. Phys., 1977, 48, 984～993
36.李夕兵,古德生,岩石在不同加载波下的动载强度。中南矿冶学院学报,1994,25(3),301～304
37. Costin L. S., Static and dynamic fracture behavior of oil shale, Fracture mechanics for ceramics, rock and concrete. ASTMSTP745, 1981, 169～184
38. Wu MB., Effects of loading rates on fracture toughness of rock.(in Chinese), Mech Practice 1986, 10 (2), 21～24
39. Bazant Z. P., Bai S. P., Gettu R., Fracture of rock: effect of loading rate. Eng. Fract. Mech, 1993, 45: 393～411
40. Tang C. A., Xu X., A new method for measuring dynamic fracture toughness of rock, Eng. Fract. Mech., 1990, 35, 4～9
41. Z.X. Zhang, S. Q. Kou, J. Yu, Y. Yu, L. G. Jiang, P.-A. Lindqvist, Effects of loading rate on rock fracture, International Journal of Rock Mechanics and Mining Sciences, 36, 1999, 597～611
42. F. V. Donze, J. Bouchez, S. A. Magnier, Modeling Fractures in Rock Blasting, Int. J. Rock Mech. Min. Sci., 1997, Vol. 34, No. 8, pp, 1153～1163
43. Sang Ho Cho, Katsuhiko Kaneko, Influence of the applied pressure waveform on the dynamic fracture processes in rock, International Journal of Rock Mechanics & Mining Sciences, 41, 2004, 771～784
44. Hakailehto K. O., The behaviour of rock under impulse loads-A study using the Hopkinson split bar method, Doctor Thesis, Technical University, Otaniemi-Helsinki, Acta Polytechnica Scandinanca, 1969, NO81, 1～61
45.Rinehart J.S著,固体中的应力瞬变,北京:煤炭工业出版社,1966
46. Miller R. K., Tran H. T., Reflection, refraction, and absorption of elastic waves at a frictional interface: P and SV motion, J. Appl. Mech., 1981, 48, 155～160
47.李夕兵,论岩体软弱结构面对应力波传播的影响,爆炸与冲击,1993,13(4):334～342
48.钱七虎等,与隔振效应有关的断层动力学研究报告1,工程兵工程学内部报告,1991,21～26
49. Walsh J B, The effect of Cracks on the compressibility of rock, J G R, 1965, 70, 381～389
50.尚嘉兰,郭汉彦,岩体裂隙对应力波传播的影响,防护工程学术交流会论文集,1979,91～98
51.李夕兵,赖海辉,古德生,爆炸应力波斜入射岩体软弱结构面的透、反射关系和滑移准则,中国有色金属学报,1992,9～14
52.张奇,应力波在节理处的传递过程,岩土工程学报,1986,8(6),99～105
53.王明洋,钱七虎,爆炸应力波通过节理裂隙带的衰减规律,岩土工程学报,1995,17(2),42～46
54.李宁,张平,段庆伟等,裂隙岩体的细观动力损伤模型,岩石力学与工程学报,2002,21(11),1579～1584
55. Kachanov, L. M., On the time to failure under creep conditions. Izv. AN SSSR, Otd. Tekhn. Nauk, 1958, 8, 26～31
56. Dougill, J. W., Lau, J. C., Burt, N. J., Mechanics in Eng. ASCE. EMD., 1976, 333～355
57. Dragon. A., Mroz, Z., A Continuum Model for Plastic-Brittle Behavior of Rock and Concrete, Int. J. Engng. Sci., 1979, 17, 121～137
58. Krajcinovic D., et al., The Continual Damage Theory of Brittle Materials, Part Ⅰ, J. Appl. Mech. Trans. of ASME, 1981, 48, 809～824
59. Rice J. R., Continuum mechanics and thermodynamics of plasticity in relation to microscale deformations mechanisms, In: Edited by Argon A. S. Constitutive Equations in Plasticity MIT Press, Cambridge, 1975
60.J.勒迈特,损伤力学教程,科学出版社,1996
61. Rubin A M, Ahrens T J. Dynamic Tensile Failure Induced Velocity Deficits in Rock [J]. Geophys. Res. Lett., 1991, 2, 219, 223
62. B. Budiansky and R. J. O'Connell, Elastic Moduli of a cracked solid, Int. J. Solid and Structures, 1976, 12, 81～97
63.谢和平,岩石、混凝土损伤力学,中国矿业大学出版社,1990
64. Sidoroff, F., IUTAM Colloquium, "Physical Nonlinearities in structure Analysis", Berlin, 1981, 237～244
65. Dragon A et al. Localized failure analysis using damage models, In: Chambon R, Desrues J, Vardoulakis I, editors, Localisation and bifurcation theory for soils and rocks, Balkema, 1994, 127～167
66. J.F. Shao, D. Hoxha et al., Modeling of induced anisotropic damage in granites. Int. J. Rock Mech. & Min. Sci., 1999, 36, 1001～1012
67. Ortiz M., A constitutive theory for the inelastic behavior of concrete. Mech. Mater., 1985, 4, 67～93
68. J. W. Ju, On energy based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int. J. Solids Structures, 1989, 25(7), 803～833
69. G. Swoboda, Q. Yang, An energy-based damage model of geomaterials I Formulation and numerical results, Int. J. solids Structures, 1999, 36, 1719～1734
70. Yazdani, S., Schreyer, H. L., Combined plasticity and damage mechanics model for plain concrete, J. Engng. Materials, 1990, 116, 1435～1450
71. Lubarda V. A., Krajcinovic D., Some fundamental issues in rate theory of damage-elastoplasticity, Int. J. Plasticity. 1995, 11,763～797
72. J.C. Simo and J. W. Ju, Strain and stress-based continuum damage models I Formulation, Int. J. Solid Struct., 1987, 23, 7, 821～840
73. Krajcinovic, D., Damage Mechanics, North-Holland, Elsevier, Amsterdam, The Netherlands, 1996
74. Nemat-Nasser, S and Hori M., Micromechanics: Overall Properties of Hetergeneous Materials. Elsevier, The Netherlands, 1993
75. Mark Kachanov, Effective elastic properties of cracked solids: critical review of some basic concepts, Appl. Mech. Rev, 1992, 45(8), 304,335
76. L.G., Margolin, Elastic moduli of a cracked body, Int. J. Frac., 1983, 22, 65～79
77. Krajcnovic D, Basista M, Sumarac D, Micromechanically inspired phenomenological damage model. J. Appl. Mech., 1991, 58, 305～310
78. Tuler, F. R., Butcher, B. M., Int. J. Fract. Mech., 1968, 4, 431
79. Davison, L, Stevens, A. L., J. Appl. Phys., 1972, 43,988
80.朱兆祥,立永池,王肖钧,爆炸作用下钢板层裂的数值计算,应用数学和力学,1981,2,353
81.陈大年,王德生,层裂判据与过程模拟,爆炸与冲击,1982,4,50
82. Eliezer, S., Gilath, I., Laser-induced spall in metals-experiment and simulation, J. Appl. Phys., 1990, 67(2), 715～724
83. Curran, D. R., Shockey, D. A., Seaman, L., J. Appl. Phys., 1973, 44, 4025
84. Seaman, L., Curran, D. R., Shockey, D. A., J. Appl. Phys., 1976, 17, 4814～4826
85. McClintock, F. A., J. Appl. Mech., 1968, 35, 363～371
86. Batdorf, S. B., Nucl. Eng.And Design, 1975, 35, 349
87. L. Seaman, D. R. Curren, W. J. Murri, A Continuum Model for Dynamic Tensile Microfracture and Fragmentation, J. Appl. Mech., 1985, 52,593～600
88. L.N. Taylor, E. P. Chen, and J. S. Kusamaul, Microcrack-Induced Damage Accumulation in brittle rock under dynamic loading. Comput. Meth. Appl. Mech. Eng., 1986, 55, 301～320
89. Grady, D. E. and Kipp, M. E., Mechanisms of Dynamic Fragmentation: Fractors Governing Fragment Size, SAND-84-2304c, 1985
90. A. M. Rajendran and J. L. Kroupa, Impact damage model for ceramic materials, J. Appl. Phys., 1989, 66(8), 3560～3565
91. L.Q. Liu, P. D. Katsabanis, Development of a Continuum Damage Model for Blasting Analysis, Int. J. Rock Mech. Min. Sci., 1997, 34(2), 217～231
92. Hong Hao, A New Constitutive Model for Blast, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1996, 33(3), 245～254
93. Johnson G. R., Holmquist T. J., A Computational constitutive model for brittle materials subjected large strains, high strain rate and high pressures, Proceedings of the ECPLOMET Conference. San Diego, CA, 1990
94. Johnson, G. R., Cook, W. H., Fracture characteristics of three metals subjected to various strains, strain rate, temperatures and pressures, Engen. Fract. Mech. 1985,21 (1), 31～48
95. A. M. Rajendran, M. A. Dietenberger, and D. J. Grove, A void growth-based failure model to describe spallation, J. Appl. Phys., 1989, 65(4), 1521～1527
96. Nicolas Burlion, Fbrice Gatuingt et al, Compaction and Tensile Damage in Concrete: Constitutive Modeling and Application to Dynamics, Comput. Methods Appl. Mech. Engng., 2000, 183, 291～308
97. Gurson, A. L., Continuum theory of ductile rupture by void nucleation and growth Part Ⅰ-yield criteria and flow rules for porous ductile media, ASME J. Eng. Mater. Technol., 1f977, 99, 2～15
98. Grady D. E, Kipp M. E., The micromechanics of impact fracture of rock, Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1979, 16, 293～302
99. Grady D. E., Kipp M. E., Continuum modeling of explosive fracture in oil shale, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1980, 17, 147～157
100. Shockey D. A., Curran D. R., Seaman L, Rosenberg J.T., et al, Fragmentation of rock under dynamic loads, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1974, 11,303～317
101.李伯功、陈庆寿、徐小荷,分形与岩石破碎特征,地震出版社,1997
102.张济忠,分形,清华大学出版社,1997
103.谢和平,薛秀谦,分形应用中的数学基础与方法,科学出版社,1997
104.谢贤平、谢源,分形理论与岩石爆破块度的预报研究,工程爆破,1995,1,35～41
105. Engleman, R., Rivier, N., Jaeger, Z., Size-distribution in sudden breakage by the use of entropy maximization, J. Appl. Phys. 1988, 63, 4766～4768
106. Nagahama,H., Fractal fragment size distribution for brittle rocks. Int. J. Rock Mech. Miner. Sic. Geomech. Abstr. 1993, 30, 469～471
107. Yong Z, and Hanson, M. T. A rational source of plane fractals and its application to fragmentation analysis of thin plates. Chaos. Solitons and Fractals, 1996, 7, 31～40
108. Aharony, A., Levi, A., Englman, R., et al, Percolation model calculations of fragment properties, Ann. Israel Phys. Soc., 1986, 8, 112～119
109. Matsushita, M., Fractal viewpoint of fracture and accretion, J. Phys. Soc. Jap. 1985, 54, 857～860
110. Turcotte, D. L., Fractals in geology and geophysics, Pure Appl. Geophy., 1989, 131,171～196
111. Rieu, M., Sposito, G., Fractal fragmentation, soil porosity, and soil water properties: I Theory Soil Sci. Soc.Am. J. 1991a, 55, 1231～1238
112. Crawford, J. W., Sleeman, B. D., Young, I. M., On the relation between number-size distributions and the fractal dimension of aggregates. J. Soil Sci., 1993b, 44, 555～565
113. E. Perfect, Fractal models for the fragmentation of rocks and soils: a review, Engineering Geology 1997, 48, 185～198
114.王礼立,高应变率下材料动态力学性能,力学与实践,1982,4(1),9～19
115.陶振宇,岩石力学的理论与实践,北京,水利出版社,1981,257～276
116.刘大安,高级计算机辅助测试技术与岩石断裂力学研究,中南工业大学博士学位论文,1991,94
117. Lindholm U. S., High strain-rate tests, Techniques in Metals Research, New York, 1971, 5
118. Campbell J. D., Material Sci. & Engng, 1973, 12, 3～21
119. C. C. Sih, ed al., Mechanics of Fracture, Noordhoof International Publishing, Leyden, 1977, 4
120.徐国元,古德生,爆炸冲击能和膨胀能破岩作用机理研究,金属矿山,1998,256(7),9～13
121. Cangli Liu and Thomas J. Ahrens, Wave generation from explosions in rock cavities, Pure and Applied Geophysics, 2001, 158: 1909～1949
122.宋光明,爆破振动小波包分析理论与应用研究,中南大学博士学位论文,2001,4
123.王明洋,戚承志,钱七虎等,岩石变形和破坏力学的基本问题,解放军理工大学学报(自然科学版),2000,3(3),33～37
124. Achenbach J. D., Wave Propagation in Elastic Solids. North-Holland, Amsterdam, 1973
125. K. P. Chong, P. M. Hoyt, J. W. Smith & B. Y. Paulsen, Effects of Strain Rate on Oil Shale Fracturing, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 1980, Vol. 17, pp: 35～43
126.张彤,无序材料尺度效应及其微观机理研究,哈尔滨工业大学博士学位论文,2000,2～19
127.谢和平,岩石、混凝土损伤力学,中国矿业大学出版社,1990
128.戚承志,钱七虎,材料变形及损伤演化的微观物理动力机理,固体力学学报,2002,23(3),312～317
129.K.S.P福兰德,T.福兰德等,不可逆热力学—理论及应用,冶金工业出版社,2001,4～6
130.戚承志,王明洋,钱七虎,弹粘塑性孔隙介质在冲击荷载作用下的一种本构关系—第二部分:弹粘塑性孔隙介质的畸变行为,岩石力学与工程学报,2003,22(11),1763～1766
131.耿华运,吴强,谭华,热力学物态方程参数的统计力学表示,物理学报,2001,50(7),1334～1340
132.王平全,破碎性地层概念界定及其破碎的热力学分析,西南石油学院学报,1999,21(1),13～17
133.戚承志,王明洋,钱七虎,弹粘塑性孔隙介质在冲击荷载作用下的一种本构关系—第一部分:状态方程,岩石力学与工程学报,2003,22(9),1405～1410
134. Itou, S. Dynamic stress intensity factors around a rectangular crack in an infinite plate under impact load, Engng Fracture Mechanics, 1983, 18, 145～53
135. Wen, P.H., Aliabadi, M.H. and Young, A. Dual boundary element methods forthree-dimensional dynamic crack problems, Jour Strain Anal, 1999, 34, 373～94
136. Sladek, J. Sladek, V., Mykhas'kiv, V.V. and Stankevych, V.Z. Application of mapping theory to boundary integral formulation of 3D dynamic crack problems, Engineering Analysis with Boundary Elements, 2003, 27, 203～213
137. Sih, G.C. and Loeber, J.F. Journal of the Acoustical Society of America, 1969, Vol. 46, 711～721
138. S. A. Thau and T. H. Lu, Int. J. Solids and Structures, 1971, 7, 731～750
139. Fan, T.Y. Introduction of Dynamic Fracture Mechanics, ed. Fan, T.Y., Publishing House of Bejing Institute of Technology, 1990
140. Grady, D.E. and Lipkin, J. Criteria for impulsive rock fracture, Geophysical Research Letters, 1980, 7(4), 255～258
141. Freund, L.B. Crack propagation in an elastic solid subject to general loading-Ⅲ stress wave loading, Jour. Mech. Phys. Solids, 1973, 21, 47～61
142. Yu Yao-zhong, Qiao Chang-xin and Zhou Qun-li. Fracture Mechanics of Rock and Concrete, ed. Yu Yao-zhong, et. al., Central South University of Technology Press, 1991
143. LI XIBING, Hu LIUQING, and T. S. LOK, Response of rock mass interface to impulsive loads induced by blasting, 2nd Asia conference on rock mechanics, China, 2001, 81～84
144.Rinehart J.S著,固体中的应力瞬变,北京:煤炭工业出版社,1966
145.李夕兵,论岩体软弱结构面对应力波传播的影响,爆炸与冲击,1993,13(4):334～342
146. Li Xibing, Lai HaiHui, Gu Desheng. Reflection and refraction of stress waves at a structural weakness plane in rock mass, Transactions of NF soc., 1992, 2(1): 11～18
147. 1957
148. Bieniawski, Z. T. Rock mass classifications in rock engineering. In Exploration for rock engineering, cape Town: A. A. Bulkema, 1976, No. 1, 97～106
149. T.S.Lok, X.B.Li, P. J.Zhao, et al, A Large diameter split Hopkinson pressure bar for testing rocks, Frontiers of Rock Mechanics and Sustainable Development in the 21st Century (Ed. By Wang Sijing, Fu Bingjun and Li Zhongkui), A.A. Balkema, Netherlands, 2001, 97～101
150.胡柳青,李夕兵,赵伏军,冲击荷载作用下岩石破裂损伤的耗能规律,岩石力学与工程学报,21(S2):2304～2308,2002
151. Attewell P. B., Response of rocks to high velocity impact, Trans. Inst. Min. Met., 1961～1962, 71, 705～724
152. Attewell P. B., Dynamic fracturing of rocks, Part Ⅰ, Ⅱ, Ⅲ, Colliery Engineering, 1963, 203～210, 248～252, 289～294
153. Kumar A., The effect of stress rate and temperature on the strength of basalt and granite, Geophysics, 1968, 33(3), 501～510
154.章根德。岩石对冲击载荷的动态响应。爆炸与冲击,2(2):1～9,1982
155. Sang Ho Cho, Yuji Ogata, Katsuhiko Kaneko, Strain-rate dependency of the dynamic tensile strength of rock International Journal of Rock Mechanics & Mining Sciences 2003, 40, 763～777
156. X. B. Li, T. S. Lok and J. Zhao, Dynamic characteristics of granite subjected to intermediate loading rate, Rock Mechanics and Rock Engineering, 2005, 38(1): 21～39
157.鲁祖统,郭乙木,岩土材料动态特性参数的内在机理及相互关系的探讨,振动与冲击,1994,49(1):31～40
158.李夕兵,岩石在不同加载波下的σ—ε—ε关系,中国有色金属学报,1994,4(3):16～22
159.邵鹏,张勇,高应变率下砂岩动态特性的研究,建井技术,1997,18(S),83～84
160. M. E. Kipp, D. E. Grady and E. P. Chen, Strain-rate dependent fracture initiation, International Journal of Fracture, 1980, 16(5), 471～478
161. Birkimer, D. L., A possible fracture criterion for the dynamic tensile strength of rock, in Proceedings 12th Symp. On Rock Mech., G. B. Clark, ed., 1971, 573
162.B.H.劳恩,T.R.威尔肖著,陈顺,尹祥础译,脆性固体断裂力学,地震出版社,1985
163.李夕兵,古德生,岩石在不同加载波条件下能量耗散的理论探讨,爆炸与冲击,1994,14(2):129～139
164. X.B.Li, L.Q.Hu and T.S.Lok, Dynami cumulative damage of rock induced by repeated impact loading, Proceedings of the 4th Asia-pacific conference on shock&Impact Loads on Sructures, (Ed. By Lok Tat Seng, Lim Chee Hiong and Li Xibing), Singapore, 2001, 381～388
165. Rubin A M, Ahrens T J. Dynamic Tensile Failure Induced Velocity Deficits in Rock [J]. Geophys. Res. Lett., 1991, 2, 219, 223
166. Nolen Hoeksema R. C., Gordon R. B., Optical detection of crack patterns in the opening mode fracture of marble. Inter. J. Rock. Mech. Min. Sci., 1987, 24, 135～144
167. Botsis J, Kunin B. On self-similarity of crack layer. Inter. Of Fracture, 1987, 35, 51～56
168.谢和平,分形力学的数学基础,力学进展,1995,25(2),174～185 (Xie H P. Mathematical fundamentals to fractal mechanics. Advance in Mechanics, 1995, 25(2), 174～185, (in Chines))
2. Brace, W. F. and E. G. Bombolakis, A note on brittle crack growth in compression, J. Geophys. Res., 1963, 68, 3709～3713
3. Cook, N. G. W., The failure of rock, Int. J. Rock Mech. Min. Sci., 1965, 2, 389～403
4. Hoek, E. and Bieniawski, Z. T., Brittle fracture propagation under compression, International Journal of Fracture Mechanics, 1965,1, 137～155
5. T.L. Blanton, Effect of Strain Rates from 10~(-2) to 10 sec~(-1) in Triaxial Compression Tests on Three Rocks. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1981,18, 47～62
6.徐小荷,余静,岩石破碎学,煤炭工业出版社,1984
7.杨善元,岩石爆破动力学基础,煤炭工业出版社,1991
8.唐春安,岩石破裂过程中的灾变,北京:煤炭工业出版社,1993
9.廖振鹏,工程波动理论导引,科学出版社,1996
10.于学馥,郑颖人,刘怀恒,方正昌,地下工程围岩稳定性分析,煤炭工业出版社,1983
11.朱维申,何满潮,复杂条件下围岩稳定性与岩石动态施工力学,科学出版社,1996
12.李夕兵,古德生,岩石冲击动力学,长沙:中南工业大学出版社,1994
13.刘德顺,李夕兵,冲击机械系统动力学,北京:科学出版社,1999
14.王礼立,应力波基础,北京:国防工业出版社,1985
15.赖海辉等,机械岩石破碎学,中南工业大学出版社,1991
16.吴世明,土介质中的波,科学出版社,1997
17.张宗贤,岩石破坏原理及其应用,冶金工业出版社,1994
18.夏蒙棼,柯孚久,吕永华,白以龙,理想微裂纹系统中的随机扩展效应,中国科学,1991,3277～283
19.白以龙,柯孚久,夏蒙棼,固体中微裂纹系统统计演化的基本描述,力学学报,1991,23(3),290～297
20.周维垣,高等岩石力学,北京;水利水电出版社,1990,362～403
21.王礼立,爆炸与冲击载荷下结构和材料动态响应研究的新进展,爆炸与冲击,2001,21(2),81～88
22.王明洋,戚承志,钱七虎 岩体中爆炸与冲击下的破坏研究,辽宁工程技术大学学报(自然科学版),2001,20(4),385～389
23. J.W. Williams, Numerical Methods In Geomechanics[M]. Nsbruck Berkely, 1988, 1799-1803
24.范天佑,断裂动力学引论,北京理工大学出版社,1990
25.赵亚溥,裂纹动态起始问题的研究进展,力学进展,1996,26(3),362～378
26. Mott N F, Brittle fracture in mild steel plates, Engineering, 1948, 165:16
27. Griffith A. A., The phenomena of rupture and flow in solids, Phil. Trans. Roy. Soc., London, 1921, A221, 163～198
28. Irwin, G. R., Fracture, In Handbuch der physik, Springer-Verlag, Berlin, 1958, V. 6, p. 551～585
29.杨卫著,宏微观断裂力学,北京:国防工业出版社,1995
30. Barenblatt, G. I., The mathematical theory of equilibrium cracks in brittle fracture, Sdv. Appl. Mech., 1962, 7,55～129
31. Dugdale, D. S., Yielding of steel sheets containing slits, J. Mech. Phys. Solids, 1960, 8, 100～104
32. Mines R. A. W., Int. J. Impact Engng, 1990, 9, 441～454
33. Steverding B, Lehnigk S.H. Response of cracks to impact, J. Appl. Phys., 1970, 41(5), 2096～2099
34. Steverding B, Lehnigk S.H. Collision of stress pulses with obstacles and dynamic of fracture, J. Appl. Phys., 1971, 42(8), 3231～3238
35. Kalthoff J. F., Shockey D. A., J. Appl. Phys., 1977, 48, 984～993
36.李夕兵,古德生,岩石在不同加载波下的动载强度。中南矿冶学院学报,1994,25(3),301～304
37. Costin L. S., Static and dynamic fracture behavior of oil shale, Fracture mechanics for ceramics, rock and concrete. ASTMSTP745, 1981, 169～184
38. Wu MB., Effects of loading rates on fracture toughness of rock.(in Chinese), Mech Practice 1986, 10 (2), 21～24
39. Bazant Z. P., Bai S. P., Gettu R., Fracture of rock: effect of loading rate. Eng. Fract. Mech, 1993, 45: 393～411
40. Tang C. A., Xu X., A new method for measuring dynamic fracture toughness of rock, Eng. Fract. Mech., 1990, 35, 4～9
41. Z.X. Zhang, S. Q. Kou, J. Yu, Y. Yu, L. G. Jiang, P.-A. Lindqvist, Effects of loading rate on rock fracture, International Journal of Rock Mechanics and Mining Sciences, 36, 1999, 597～611
42. F. V. Donze, J. Bouchez, S. A. Magnier, Modeling Fractures in Rock Blasting, Int. J. Rock Mech. Min. Sci., 1997, Vol. 34, No. 8, pp, 1153～1163
43. Sang Ho Cho, Katsuhiko Kaneko, Influence of the applied pressure waveform on the dynamic fracture processes in rock, International Journal of Rock Mechanics & Mining Sciences, 41, 2004, 771～784
44. Hakailehto K. O., The behaviour of rock under impulse loads-A study using the Hopkinson split bar method, Doctor Thesis, Technical University, Otaniemi-Helsinki, Acta Polytechnica Scandinanca, 1969, NO81, 1～61
45.Rinehart J.S著,固体中的应力瞬变,北京:煤炭工业出版社,1966
46. Miller R. K., Tran H. T., Reflection, refraction, and absorption of elastic waves at a frictional interface: P and SV motion, J. Appl. Mech., 1981, 48, 155～160
47.李夕兵,论岩体软弱结构面对应力波传播的影响,爆炸与冲击,1993,13(4):334～342
48.钱七虎等,与隔振效应有关的断层动力学研究报告1,工程兵工程学内部报告,1991,21～26
49. Walsh J B, The effect of Cracks on the compressibility of rock, J G R, 1965, 70, 381～389
50.尚嘉兰,郭汉彦,岩体裂隙对应力波传播的影响,防护工程学术交流会论文集,1979,91～98
51.李夕兵,赖海辉,古德生,爆炸应力波斜入射岩体软弱结构面的透、反射关系和滑移准则,中国有色金属学报,1992,9～14
52.张奇,应力波在节理处的传递过程,岩土工程学报,1986,8(6),99～105
53.王明洋,钱七虎,爆炸应力波通过节理裂隙带的衰减规律,岩土工程学报,1995,17(2),42～46
54.李宁,张平,段庆伟等,裂隙岩体的细观动力损伤模型,岩石力学与工程学报,2002,21(11),1579～1584
55. Kachanov, L. M., On the time to failure under creep conditions. Izv. AN SSSR, Otd. Tekhn. Nauk, 1958, 8, 26～31
56. Dougill, J. W., Lau, J. C., Burt, N. J., Mechanics in Eng. ASCE. EMD., 1976, 333～355
57. Dragon. A., Mroz, Z., A Continuum Model for Plastic-Brittle Behavior of Rock and Concrete, Int. J. Engng. Sci., 1979, 17, 121～137
58. Krajcinovic D., et al., The Continual Damage Theory of Brittle Materials, Part Ⅰ, J. Appl. Mech. Trans. of ASME, 1981, 48, 809～824
59. Rice J. R., Continuum mechanics and thermodynamics of plasticity in relation to microscale deformations mechanisms, In: Edited by Argon A. S. Constitutive Equations in Plasticity MIT Press, Cambridge, 1975
60.J.勒迈特,损伤力学教程,科学出版社,1996
61. Rubin A M, Ahrens T J. Dynamic Tensile Failure Induced Velocity Deficits in Rock [J]. Geophys. Res. Lett., 1991, 2, 219, 223
62. B. Budiansky and R. J. O'Connell, Elastic Moduli of a cracked solid, Int. J. Solid and Structures, 1976, 12, 81～97
63.谢和平,岩石、混凝土损伤力学,中国矿业大学出版社,1990
64. Sidoroff, F., IUTAM Colloquium, "Physical Nonlinearities in structure Analysis", Berlin, 1981, 237～244
65. Dragon A et al. Localized failure analysis using damage models, In: Chambon R, Desrues J, Vardoulakis I, editors, Localisation and bifurcation theory for soils and rocks, Balkema, 1994, 127～167
66. J.F. Shao, D. Hoxha et al., Modeling of induced anisotropic damage in granites. Int. J. Rock Mech. & Min. Sci., 1999, 36, 1001～1012
67. Ortiz M., A constitutive theory for the inelastic behavior of concrete. Mech. Mater., 1985, 4, 67～93
68. J. W. Ju, On energy based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int. J. Solids Structures, 1989, 25(7), 803～833
69. G. Swoboda, Q. Yang, An energy-based damage model of geomaterials I Formulation and numerical results, Int. J. solids Structures, 1999, 36, 1719～1734
70. Yazdani, S., Schreyer, H. L., Combined plasticity and damage mechanics model for plain concrete, J. Engng. Materials, 1990, 116, 1435～1450
71. Lubarda V. A., Krajcinovic D., Some fundamental issues in rate theory of damage-elastoplasticity, Int. J. Plasticity. 1995, 11,763～797
72. J.C. Simo and J. W. Ju, Strain and stress-based continuum damage models I Formulation, Int. J. Solid Struct., 1987, 23, 7, 821～840
73. Krajcinovic, D., Damage Mechanics, North-Holland, Elsevier, Amsterdam, The Netherlands, 1996
74. Nemat-Nasser, S and Hori M., Micromechanics: Overall Properties of Hetergeneous Materials. Elsevier, The Netherlands, 1993
75. Mark Kachanov, Effective elastic properties of cracked solids: critical review of some basic concepts, Appl. Mech. Rev, 1992, 45(8), 304,335
76. L.G., Margolin, Elastic moduli of a cracked body, Int. J. Frac., 1983, 22, 65～79
77. Krajcnovic D, Basista M, Sumarac D, Micromechanically inspired phenomenological damage model. J. Appl. Mech., 1991, 58, 305～310
78. Tuler, F. R., Butcher, B. M., Int. J. Fract. Mech., 1968, 4, 431
79. Davison, L, Stevens, A. L., J. Appl. Phys., 1972, 43,988
80.朱兆祥,立永池,王肖钧,爆炸作用下钢板层裂的数值计算,应用数学和力学,1981,2,353
81.陈大年,王德生,层裂判据与过程模拟,爆炸与冲击,1982,4,50
82. Eliezer, S., Gilath, I., Laser-induced spall in metals-experiment and simulation, J. Appl. Phys., 1990, 67(2), 715～724
83. Curran, D. R., Shockey, D. A., Seaman, L., J. Appl. Phys., 1973, 44, 4025
84. Seaman, L., Curran, D. R., Shockey, D. A., J. Appl. Phys., 1976, 17, 4814～4826
85. McClintock, F. A., J. Appl. Mech., 1968, 35, 363～371
86. Batdorf, S. B., Nucl. Eng.And Design, 1975, 35, 349
87. L. Seaman, D. R. Curren, W. J. Murri, A Continuum Model for Dynamic Tensile Microfracture and Fragmentation, J. Appl. Mech., 1985, 52,593～600
88. L.N. Taylor, E. P. Chen, and J. S. Kusamaul, Microcrack-Induced Damage Accumulation in brittle rock under dynamic loading. Comput. Meth. Appl. Mech. Eng., 1986, 55, 301～320
89. Grady, D. E. and Kipp, M. E., Mechanisms of Dynamic Fragmentation: Fractors Governing Fragment Size, SAND-84-2304c, 1985
90. A. M. Rajendran and J. L. Kroupa, Impact damage model for ceramic materials, J. Appl. Phys., 1989, 66(8), 3560～3565
91. L.Q. Liu, P. D. Katsabanis, Development of a Continuum Damage Model for Blasting Analysis, Int. J. Rock Mech. Min. Sci., 1997, 34(2), 217～231
92. Hong Hao, A New Constitutive Model for Blast, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1996, 33(3), 245～254
93. Johnson G. R., Holmquist T. J., A Computational constitutive model for brittle materials subjected large strains, high strain rate and high pressures, Proceedings of the ECPLOMET Conference. San Diego, CA, 1990
94. Johnson, G. R., Cook, W. H., Fracture characteristics of three metals subjected to various strains, strain rate, temperatures and pressures, Engen. Fract. Mech. 1985,21 (1), 31～48
95. A. M. Rajendran, M. A. Dietenberger, and D. J. Grove, A void growth-based failure model to describe spallation, J. Appl. Phys., 1989, 65(4), 1521～1527
96. Nicolas Burlion, Fbrice Gatuingt et al, Compaction and Tensile Damage in Concrete: Constitutive Modeling and Application to Dynamics, Comput. Methods Appl. Mech. Engng., 2000, 183, 291～308
97. Gurson, A. L., Continuum theory of ductile rupture by void nucleation and growth Part Ⅰ-yield criteria and flow rules for porous ductile media, ASME J. Eng. Mater. Technol., 1f977, 99, 2～15
98. Grady D. E, Kipp M. E., The micromechanics of impact fracture of rock, Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1979, 16, 293～302
99. Grady D. E., Kipp M. E., Continuum modeling of explosive fracture in oil shale, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1980, 17, 147～157
100. Shockey D. A., Curran D. R., Seaman L, Rosenberg J.T., et al, Fragmentation of rock under dynamic loads, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1974, 11,303～317
101.李伯功、陈庆寿、徐小荷,分形与岩石破碎特征,地震出版社,1997
102.张济忠,分形,清华大学出版社,1997
103.谢和平,薛秀谦,分形应用中的数学基础与方法,科学出版社,1997
104.谢贤平、谢源,分形理论与岩石爆破块度的预报研究,工程爆破,1995,1,35～41
105. Engleman, R., Rivier, N., Jaeger, Z., Size-distribution in sudden breakage by the use of entropy maximization, J. Appl. Phys. 1988, 63, 4766～4768
106. Nagahama,H., Fractal fragment size distribution for brittle rocks. Int. J. Rock Mech. Miner. Sic. Geomech. Abstr. 1993, 30, 469～471
107. Yong Z, and Hanson, M. T. A rational source of plane fractals and its application to fragmentation analysis of thin plates. Chaos. Solitons and Fractals, 1996, 7, 31～40
108. Aharony, A., Levi, A., Englman, R., et al, Percolation model calculations of fragment properties, Ann. Israel Phys. Soc., 1986, 8, 112～119
109. Matsushita, M., Fractal viewpoint of fracture and accretion, J. Phys. Soc. Jap. 1985, 54, 857～860
110. Turcotte, D. L., Fractals in geology and geophysics, Pure Appl. Geophy., 1989, 131,171～196
111. Rieu, M., Sposito, G., Fractal fragmentation, soil porosity, and soil water properties: I Theory Soil Sci. Soc.Am. J. 1991a, 55, 1231～1238
112. Crawford, J. W., Sleeman, B. D., Young, I. M., On the relation between number-size distributions and the fractal dimension of aggregates. J. Soil Sci., 1993b, 44, 555～565
113. E. Perfect, Fractal models for the fragmentation of rocks and soils: a review, Engineering Geology 1997, 48, 185～198
114.王礼立,高应变率下材料动态力学性能,力学与实践,1982,4(1),9～19
115.陶振宇,岩石力学的理论与实践,北京,水利出版社,1981,257～276
116.刘大安,高级计算机辅助测试技术与岩石断裂力学研究,中南工业大学博士学位论文,1991,94
117. Lindholm U. S., High strain-rate tests, Techniques in Metals Research, New York, 1971, 5
118. Campbell J. D., Material Sci. & Engng, 1973, 12, 3～21
119. C. C. Sih, ed al., Mechanics of Fracture, Noordhoof International Publishing, Leyden, 1977, 4
120.徐国元,古德生,爆炸冲击能和膨胀能破岩作用机理研究,金属矿山,1998,256(7),9～13
121. Cangli Liu and Thomas J. Ahrens, Wave generation from explosions in rock cavities, Pure and Applied Geophysics, 2001, 158: 1909～1949
122.宋光明,爆破振动小波包分析理论与应用研究,中南大学博士学位论文,2001,4
123.王明洋,戚承志,钱七虎等,岩石变形和破坏力学的基本问题,解放军理工大学学报(自然科学版),2000,3(3),33～37
124. Achenbach J. D., Wave Propagation in Elastic Solids. North-Holland, Amsterdam, 1973
125. K. P. Chong, P. M. Hoyt, J. W. Smith & B. Y. Paulsen, Effects of Strain Rate on Oil Shale Fracturing, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 1980, Vol. 17, pp: 35～43
126.张彤,无序材料尺度效应及其微观机理研究,哈尔滨工业大学博士学位论文,2000,2～19
127.谢和平,岩石、混凝土损伤力学,中国矿业大学出版社,1990
128.戚承志,钱七虎,材料变形及损伤演化的微观物理动力机理,固体力学学报,2002,23(3),312～317
129.K.S.P福兰德,T.福兰德等,不可逆热力学—理论及应用,冶金工业出版社,2001,4～6
130.戚承志,王明洋,钱七虎,弹粘塑性孔隙介质在冲击荷载作用下的一种本构关系—第二部分:弹粘塑性孔隙介质的畸变行为,岩石力学与工程学报,2003,22(11),1763～1766
131.耿华运,吴强,谭华,热力学物态方程参数的统计力学表示,物理学报,2001,50(7),1334～1340
132.王平全,破碎性地层概念界定及其破碎的热力学分析,西南石油学院学报,1999,21(1),13～17
133.戚承志,王明洋,钱七虎,弹粘塑性孔隙介质在冲击荷载作用下的一种本构关系—第一部分:状态方程,岩石力学与工程学报,2003,22(9),1405～1410
134. Itou, S. Dynamic stress intensity factors around a rectangular crack in an infinite plate under impact load, Engng Fracture Mechanics, 1983, 18, 145～53
135. Wen, P.H., Aliabadi, M.H. and Young, A. Dual boundary element methods forthree-dimensional dynamic crack problems, Jour Strain Anal, 1999, 34, 373～94
136. Sladek, J. Sladek, V., Mykhas'kiv, V.V. and Stankevych, V.Z. Application of mapping theory to boundary integral formulation of 3D dynamic crack problems, Engineering Analysis with Boundary Elements, 2003, 27, 203～213
137. Sih, G.C. and Loeber, J.F. Journal of the Acoustical Society of America, 1969, Vol. 46, 711～721
138. S. A. Thau and T. H. Lu, Int. J. Solids and Structures, 1971, 7, 731～750
139. Fan, T.Y. Introduction of Dynamic Fracture Mechanics, ed. Fan, T.Y., Publishing House of Bejing Institute of Technology, 1990
140. Grady, D.E. and Lipkin, J. Criteria for impulsive rock fracture, Geophysical Research Letters, 1980, 7(4), 255～258
141. Freund, L.B. Crack propagation in an elastic solid subject to general loading-Ⅲ stress wave loading, Jour. Mech. Phys. Solids, 1973, 21, 47～61
142. Yu Yao-zhong, Qiao Chang-xin and Zhou Qun-li. Fracture Mechanics of Rock and Concrete, ed. Yu Yao-zhong, et. al., Central South University of Technology Press, 1991
143. LI XIBING, Hu LIUQING, and T. S. LOK, Response of rock mass interface to impulsive loads induced by blasting, 2nd Asia conference on rock mechanics, China, 2001, 81～84
144.Rinehart J.S著,固体中的应力瞬变,北京:煤炭工业出版社,1966
145.李夕兵,论岩体软弱结构面对应力波传播的影响,爆炸与冲击,1993,13(4):334～342
146. Li Xibing, Lai HaiHui, Gu Desheng. Reflection and refraction of stress waves at a structural weakness plane in rock mass, Transactions of NF soc., 1992, 2(1): 11～18
147. 1957
148. Bieniawski, Z. T. Rock mass classifications in rock engineering. In Exploration for rock engineering, cape Town: A. A. Bulkema, 1976, No. 1, 97～106
149. T.S.Lok, X.B.Li, P. J.Zhao, et al, A Large diameter split Hopkinson pressure bar for testing rocks, Frontiers of Rock Mechanics and Sustainable Development in the 21st Century (Ed. By Wang Sijing, Fu Bingjun and Li Zhongkui), A.A. Balkema, Netherlands, 2001, 97～101
150.胡柳青,李夕兵,赵伏军,冲击荷载作用下岩石破裂损伤的耗能规律,岩石力学与工程学报,21(S2):2304～2308,2002
151. Attewell P. B., Response of rocks to high velocity impact, Trans. Inst. Min. Met., 1961～1962, 71, 705～724
152. Attewell P. B., Dynamic fracturing of rocks, Part Ⅰ, Ⅱ, Ⅲ, Colliery Engineering, 1963, 203～210, 248～252, 289～294
153. Kumar A., The effect of stress rate and temperature on the strength of basalt and granite, Geophysics, 1968, 33(3), 501～510
154.章根德。岩石对冲击载荷的动态响应。爆炸与冲击,2(2):1～9,1982
155. Sang Ho Cho, Yuji Ogata, Katsuhiko Kaneko, Strain-rate dependency of the dynamic tensile strength of rock International Journal of Rock Mechanics & Mining Sciences 2003, 40, 763～777
156. X. B. Li, T. S. Lok and J. Zhao, Dynamic characteristics of granite subjected to intermediate loading rate, Rock Mechanics and Rock Engineering, 2005, 38(1): 21～39
157.鲁祖统,郭乙木,岩土材料动态特性参数的内在机理及相互关系的探讨,振动与冲击,1994,49(1):31～40
158.李夕兵,岩石在不同加载波下的σ—ε—ε关系,中国有色金属学报,1994,4(3):16～22
159.邵鹏,张勇,高应变率下砂岩动态特性的研究,建井技术,1997,18(S),83～84
160. M. E. Kipp, D. E. Grady and E. P. Chen, Strain-rate dependent fracture initiation, International Journal of Fracture, 1980, 16(5), 471～478
161. Birkimer, D. L., A possible fracture criterion for the dynamic tensile strength of rock, in Proceedings 12th Symp. On Rock Mech., G. B. Clark, ed., 1971, 573
162.B.H.劳恩,T.R.威尔肖著,陈顺,尹祥础译,脆性固体断裂力学,地震出版社,1985
163.李夕兵,古德生,岩石在不同加载波条件下能量耗散的理论探讨,爆炸与冲击,1994,14(2):129～139
164. X.B.Li, L.Q.Hu and T.S.Lok, Dynami cumulative damage of rock induced by repeated impact loading, Proceedings of the 4th Asia-pacific conference on shock&Impact Loads on Sructures, (Ed. By Lok Tat Seng, Lim Chee Hiong and Li Xibing), Singapore, 2001, 381～388
165. Rubin A M, Ahrens T J. Dynamic Tensile Failure Induced Velocity Deficits in Rock [J]. Geophys. Res. Lett., 1991, 2, 219, 223
166. Nolen Hoeksema R. C., Gordon R. B., Optical detection of crack patterns in the opening mode fracture of marble. Inter. J. Rock. Mech. Min. Sci., 1987, 24, 135～144
167. Botsis J, Kunin B. On self-similarity of crack layer. Inter. Of Fracture, 1987, 35, 51～56
168.谢和平,分形力学的数学基础,力学进展,1995,25(2),174～185 (Xie H P. Mathematical fundamentals to fractal mechanics. Advance in Mechanics, 1995, 25(2), 174～185, (in Chines))