岩石加速破裂行为的物理自相似律

杨百存, 秦四清, 薛雷, 陈竑然, 吴晓娲, 张珂. 2017. 岩石加速破裂行为的物理自相似律. 地球物理学报, 60(5): 1746-1760, doi: 10.6038/cjg20170512
引用本文: 杨百存, 秦四清, 薛雷, 陈竑然, 吴晓娲, 张珂. 2017. 岩石加速破裂行为的物理自相似律. 地球物理学报, 60(5): 1746-1760, doi: 10.6038/cjg20170512
YANG Bai-Cun, QIN Si-Qing, XUE Lei, CHEN Hong-Ran, WU Xiao-Wa, ZHANG Ke. 2017. A physical self-similarity law describing the accelerated failure behavior of rocks. Chinese Journal of Geophysics (in Chinese), 60(5): 1746-1760, doi: 10.6038/cjg20170512
Citation: YANG Bai-Cun, QIN Si-Qing, XUE Lei, CHEN Hong-Ran, WU Xiao-Wa, ZHANG Ke. 2017. A physical self-similarity law describing the accelerated failure behavior of rocks. Chinese Journal of Geophysics (in Chinese), 60(5): 1746-1760, doi: 10.6038/cjg20170512

岩石加速破裂行为的物理自相似律

  • 基金项目:

    国家自然科学基金项目(41572311,41302233)资助

详细信息
    作者简介:

    杨百存, 男, 1991年生, 在读博士, 主要从事岩石破裂致灾机理研究.E-mail:yangbaicun@mail.iggcas.ac.cn

    通讯作者: 秦四清, 1964年生, 河北行唐人, 中国科学院地质与地球物理研究所研究员, 主要从事工程地质、非线性岩土力学与岩土工程类研究.目前科研兴趣:强震预测研究.E-mail:qsqhope@mail.iggcas.ac.cn
  • 中图分类号: P313

A physical self-similarity law describing the accelerated failure behavior of rocks

More Information
  • 掌握岩石变形破坏过程中体积膨胀点至峰值强度点之间加速破裂行为的演化规律,是实现地质灾害物理预测的关键.本文考虑裂纹张开和闭合两种情况,基于断裂力学建立了三轴应力作用下裂纹扩展临界尺度与等效应力的关系.对微元体破坏概率,分别采用以等效应力表达的Weibull分布函数和裂纹尺度分形函数,通过对比导出了形状参数m与裂纹分布分维Df关系的表达式.一个有趣的发现是,岩石峰值强度点与体积膨胀点应变比仅与mDf有关.对岩石蠕变或准蠕变破坏,合理的m值范围为[1.0,4.0],在此范围内应变比近似为常数1.48,该常数是描述不同尺度岩石加速破裂规律的物理自相似常数.实例分析表明,基于岩石加速破裂规律构建的多锁固段脆性破裂理论,其适用性广,尤其在崩滑和大地震预测领域,具有良好应用前景.此外,本文给出了b值与m值定量关系,以解释b值的物理意义,并探讨将其用于地震预测的可行性.

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  • 图 1 

    砂岩破坏裂纹分维Df与围压的关系 (杨永明等,2014)

    Figure 1. 

    Relationship between fractal dimension Df of fractured cracks and confined pressure for sandstone (Yang et al., 2014)

    图 2 

    εf/εcm的关系

    Figure 2. 

    Relation between εf/εc and m

    图 3 

    多锁固段概念模型

    Figure 3. 

    A conceptual model of multiple locked patches

    图 4 

    锁固段分层次结构示意图

    Figure 4. 

    Schematic illustration of the hierarchical structure of locked patch

    图 5 

    砂岩在阶梯荷载下的蠕变曲线 (据Tan和Kang (1980)修改)

    Figure 5. 

    Creep curve of sandstone under step load (modified after Tan and Kang (1980))

    图 6 

    盐池河山崩4号裂缝1980年水平位移观测记录 (据孙玉科和姚宝魁 (1983)修改)

    Figure 6. 

    Cumulative horizontal displacement observed at crack No.4 of the Yanchihe avalanche in 1980(modified after Sun and Yao (1983))

    图 7 

    中国及其周边地震区划分图 (秦四清等, 2016b, 2016d)

    Figure 7. 

    Division map of seismic zones in China and its adjacent areas (Qin et al., 2016b, 2016d)

    图 8 

    唐山地震区公元前1767—2015-11-21之间CBS值与时间关系

    Figure 8. 

    Temporal distribution of CBS in the period from B.C. 1767 to 21 November 2015 for the Tangshan seismic zone

    图 9 

    伊斯兰堡—加德满都地震区CBS值与时间关系

    Figure 9. 

    Temporal distribution of CBS for the Islamabad-Kathmandu seismic zone

    图 10 

    单轴压缩下砂岩裂纹分布分维Df与应力关系 (尹小涛等,2008)

    Figure 10. 

    Relation between fractal dimension Df of crack distribution and stress for sandstone subjected to uniaxial compression (Yin et al., 2008)

    图 11 

    唐山地震区b值与时间关系

    Figure 11. 

    Relationship between b-value and time for the Tangshan seismic zone

  •  

    Aki K. 1981. A probabilistic synthesis of precursory phenomena.//Simpson D W, Richards P G eds. Earthquake Prediction: An International Review. Washington, D C: AGU, 566-574.

     

    Alexeev A D, Revva V N, Alyshev N A, et al. 2004. True triaxial loading apparatus and its application to coal outburst prediction. Int. J. Coal. Geol., 58(4): 245-250. doi: 10.1016/j.coal.2003.09.007

     

    Allègre C J, Le Mouel J L, Provost A. 1982. Scaling rules in rock fracture and possible implications for earthquake prediction. Nature, 297(5861): 47-49. doi: 10.1038/297047a0

     

    An Z W, Wang L Y, Zhu C Z. 1989. The characteristics of fractal dimension in the temporal-spatial distribution of earthquakes befor and after the occurrence of a large earthquake. Acta Seismologica Sinica (in Chinese), 11(3): 251-258.

     

    Aviles C A, Scholz C H, Boatwright J. 1987. Fractal analysis applied to characteristic segments of the San Andreas fault. J. Geophys. Res., 92(B1): 331-344. doi: 10.1029/JB092iB01p00331

     

    Batdorf S B. 1978. Fundamentals of the statistical theory of fracture.//Bradt R C, Hasselman D P H, Lange F F eds. Proceedings of the International Symposium on Fracture Mechanics of Ceramics. New York: Plenum Press, 1-30.

     

    Benioff H. 1951. Earthquakes and rock creep (Part Ⅰ: Creep characteristics of rocks and the origin of aftershocks). Bull. Seismol. Soc. Am., 41(1): 31-62. https://www.researchgate.net/publication/292136435_Earthquakes_and_rock_creep_Part_I_Creep_characteristics_of_rocks_and_the_origin_of_aftershocks

     

    Cao R L, He S H, Wei J, et al. 2013. Study of modified statistical damage softening constitutive model for rock considering residual strength. Rock and Soil Mechanics (in Chinese), 34(6): 1652-1660, doi: 10.16285/j.rsm.2013.06.018.

     

    Cao W G, Zhang S. 2005. Study on the statistical analysis of rock damage based on Mohr-Coulomb criterion. Journal of Hunan University (Natural Sciences) (in Chinese), 32(1): 43-47. http://en.cnki.com.cn/Article_en/CJFDTOTAL-HNDX200501010.htm

     

    Crosta G B, Agliardi F. 2003. Failure forecast for large rock slides by surface displacement measurements. Can. Geotech. J., 40(1): 176-191, doi: 10.1139/T02-085.

     

    Dai Z X. 2001. Hausdoroff dimension of generalized Cantor sets. Journal of Zhejiang Normal University (Natural Sciences) (in Chinese), 24(2): 143-145.

     

    Das S, Aki K. 1977. Fault plane with barriers: a versatile earthquake model. J. Geophys. Res., 82(36): 5658-5670. doi: 10.1029/JB082i036p05658

     

    Das S, Kostrov B V. 1983. Breaking of a single asperity: rupture process and seismic radiation. J. Geophys. Res., 88(B5): 4277-4288. doi: 10.1029/JB088iB05p04277

     

    Deng R G, Zhou D P, Zhang Z Y, et al. 2001. A new rheological model for rocks. Chinese Journal of Rock Mechanics and Engineering (in Chinese), 20(6): 780-784. https://www.researchgate.net/publication/289399239_A_new_rheological_model_for_rocks

     

    Dobrovolsky I P, Zubkov S I, Miachkin V I. 1979. Estimation of the size of earthquake preparation zones. Pure Appl. Geophys., 117(5): 1025-1044. doi: 10.1007/BF00876083

     

    Dubois J, Novaili L. 1989. Quantification of the fracturing of the slab using a fractal approach. Earth Planet. Sci. Lett., 94(1-2): 97-108. doi: 10.1016/0012-821X(89)90086-1

     

    Gao F, Xie H P, Zhao P. 1993. Fractal properties of Weibull modulus and rock strength. Chinese Science Bulletin (in Chinese), 38(15): 1435-1438. http://www.sciencedirect.com/science/article/pii/S136516099900074X

     

    Gao F, Zhong W P, Li L Y, et al. 2004. Fractal and statistical analysis of strength of jointed rocks. Chinese Journal of Rock Mechanics and Engineering (in Chinese), 23(21): 3608-3612. http://en.cnki.com.cn/Article_en/CJFDTotal-YSLX200421009.htm

     

    Gutenberg B, Richter C F. 1954. Seismicity of the Earth and Associated Phenomena. Princeton: Princeton University Press, 245.

     

    He M C, Miao J L, Li D J, et al. 2007. Experimental study on rockburst processes of granite specimen at great depth. Chinese Journal of Rock Mechanics and Engineering (in Chinese), 26(5): 865-876. https://www.researchgate.net/publication/279898358_Experimental_study_on_rockburst_processes_of_granite_specimen_at_great_depth

     

    Hirata T. 1987. Omori's power law aftershock sequences of microfracturing in rock fracture experiment. J. Geophys. Res., 92(B7): 6215-6221. doi: 10.1029/JB092iB07p06215

     

    Hirata T. 1989. Fractal dimension of fault systems in Japan: fractal structure in rock fracture geometry at various scales. Pure Appl. Geophys., 131(1-2): 157-170. doi: 10.1007/BF00874485

     

    Huang D, Gu D M, Yang C, et al. 2016. Investigation on mechanical behaviors of sandstone with two preexisting flaws under triaxial compression. Rock Mech. Rock Eng., 49(2): 375-399, doi: 10.1007/s00603-015-0757-3.

     

    Huang R Q. 2007. Large-scale landslides and their sliding mechanisms in China since the 20th century. Chinese Journal of Rock Mechanics and Engineering (in Chinese), 26(3): 433-454. https://link.springer.com/article/10.1007/s10064-011-0403-6

     

    Jia Y, Kang Y M, Wang D, et al. 2010. Research on critical damage for rock subjected to high confining pressure and temperature-change. Journal of Sichuan University (Engineering Science Edition) (in Chinese), 42(6): 79-84. https://www.researchgate.net/publication/293111642_Research_on_critical_damage_for_rock_subjected_to_high_confining_pressure_and_temperature-change

     

    Kanamori H, Anderson D L. 1975. Theoretical basis of some empirical relations in seismology. Bull. Seismol. Soc. Am., 65(5): 1073-1095. http://www.academia.edu/7807233/THEORETICAL_BASIS_OF_SOME_EMPIRICAL_RELATIONS_IN_SEISMOLOGY

     

    King G. 1983. The accommodation of large strains in the upper lithosphere of the earth and other solids by self-similar fault systems: the geometrical origin of b-value. Pure Appl. Geophys., 121(5-6): 761-815. doi: 10.1007/BF02590182

     

    Kong X G, Wang E Y, Hu S B, et al. 2016. Fractal characteristics and acoustic emission of coal containing methane in triaxial compression failure. J. Appl. Geophys., 124: 139-147, doi: 10.1016/j.jappgeo.2015.11.018.

     

    Lei X L, Kusunose K, Satoh T, et al. 2003. The hierarchical rupture process of a fault: an experimental study. Phys. Earth Planet. Inter., 137(1-4): 213-228, doi: 10.1016/S0031-9201(03)00016-5.

     

    Li B, Ma S L, Zhang L. 1993. Fractal dimension of main fractures of marble under different experimental conditions. Seismology and Geology (in Chinese), 15(2): 157-163. http://en.cnki.com.cn/Article_en/CJFDTOTAL-DZDZ199302010.htm

     

    Li S Y, He M T, Yin X C. 2015. Rock Fracture Mechanics (in Chinese). Beijing: Science Press, 537.

     

    Liu T J, Tang C A. 2002. Numerical test on influence of weak & hard touching on fracture model of specimen with inclusion. Journal of Seismological Research (in Chinese), 25(1): 53-57. http://en.cnki.com.cn/Article_en/CJFDTOTAL-DZYJ200201009.htm

     

    Ma H Q. 1982. The spatial distribution of the b-values before large and moderate earthquakes. Acta Seismologica Sinica (in Chinese), 25(2): 163-171. http://manu39.magtech.com.cn/Geophy/EN/abstract/abstract5260.shtml

     

    Ma J, Ma S L, Liu L Q, et al. 1996. Geometrical texture of faults evolution of physical field and instability characteristics. Acta Seismologica Sinica (in Chinese), 18(2): 200-207. https://link.springer.com/article/10.1007/BF02651070

     

    Madden T R. 1983. Microcrack connectivity in rocks: a renormalization group approach to the critical phenomena of conduction and failure in crystalline rocks. J. Geophys. Res., 88(B1): 585-592. doi: 10.1029/JB088iB01p00585

     

    Main I G, Meredith P G, Jones C. 1989. A reinterpretation of the precursory seismic b-value anomaly from fracture mechanics. Geophys. J. Int., 96(1): 131-138. doi: 10.1111/gji.1989.96.issue-1

     

    Mandelbrot B B. 1983. The Fractal Geometry of Nature. New York: W. H. Freeman and Company, 466.

     

    Matsuo Y. 1981. Statistical fracture theory for multiaxial stress states using Weibull's three-parameter function. Eng. Fract. Mech., 14(3): 527-538. doi: 10.1016/0013-7944(81)90040-0

     

    Mei S R. 1995. On the physical model of earthquake precursor fields and the mechanism of precursors' time and space distribution (Ⅰ)—origin and evidences of the strong body earthquake-generating model. Acta Seismologica Sinica (in Chinese), 17(3): 273-282. https://www.researchgate.net/publication/226263254_On_the_physical_model_of_earthquake_precursor_fields_and_the_mechanism_of_precursor%27s_time_and_space_distribution_I-origin_and_evidences_of_the_strong_body_earthquake-generating_model

     

    Mogi K. 1962. Study of elastic shocks caused by the fracture of heterogeneous materials and its relations to earthquake phenomena. Bull. Earthq. Res. Inst., 40(1): 125-173. http://repository.dl.itc.u-tokyo.ac.jp/dspace/handle/2261/12045

     

    Mogi K. 1986. Earthquake Prediction in Japan (in Chinese). Beijing: Seismological Press, 326.

     

    Molchan G M, Dmitrieva O E. 1990. Dynamics of the magnitude-frequency relation for foreshocks. Phys. Earth Planet. Inter., 61(1-2): 99-112. doi: 10.1016/0031-9201(90)90098-I

     

    Morgan S P, Johnson C A, Einstein H H. 2013. Cracking processes in Barre granite: fracture process zones and crack coalescence. Int. J. Fract., 180(2): 177-204, doi: 10.1007/s10704-013-9810-y.

     

    Mufundirwa A, Fujii Y, Kodama J. 2010. A new practical method for prediction of geomechanical failure-time. Int. J. Rock Mech. Min. Sci., 47(7): 1079-1090, doi: 1079-1090.10.1016/j.ijrmms.2010.07.001.

     

    Nakamura A M, Michel P, Setoh M. 2007. Weibull parameters of Yakuno basalt targets used in documented high-velocity impact experiments. J. Geophys. Res., 112: E02001, doi: 10.1029/2006JE002757.

     

    Ni Y S, Kuang Z B, Yang Y Q. 1992. Fractal study of the fracture surface of grantite caused by triaxial compression. Chinese Journal of Rock Mechanics and Engineering (in Chinese), 11(3): 295-303. http://www.oalib.com/paper/1481513

     

    Peng T R, Zhang Z H. 1989. Distributed functions of fracture size and their applications in fatigue statistical analysis. Journal of Shandong Institute of Building Materials (in Chinese), 3(3): 1-10. http://en.cnki.com.cn/Article_en/CJFDTOTAL-SDJC198903000.htm

     

    Qin S Q, Wang Y Y, Ma P. 2010a. Exponential laws of critical displacement evolution for landslides and avalanches. Chinese Journal of Rock Mechanics and Engineering (in Chinese), 29(5): 873-880. http://www.rockmech.org/EN/abstract/abstract20028.shtml

     

    Qin S Q, Xu X W, Hu P, et al. 2010b. Brittle failure mechanism of multiple locked patches in a seismogenic fault system and exploration on a new way for earthquake prediction. Chinese J. Geophys. (in Chinese), 53(4): 1001-1014, doi: 10.3969/j.issn.0001-5733.2010.04.025.

     

    Qin S Q, Xue L, Huang X, et al. 2010c. A forward prediction of strong earthquakes in the Tibet region. Progress in Geophys. (in Chinese), 25(6): 1879-1886, doi: 10.3969/j.issn.1004-2903.2010.06.001.

     

    Qin S Q, Xue L. 2011. A summary of prediction for the Yingjiang MS5.8 earthquake in Yunnan and the Burma MS7.2 earthquake as well as the analysis on the earthquake situation after the earthquake. Progress in Geophys. (in Chinese), 26(2): 462-468, doi: 10.3969/j.issn.1004-2903.2011.02.010.

     

    Qin S Q, Xue L, Li G L, et al. 2012. The verification of prospective prediction for the Zhaotong earthquakes on 7 September 2012. Progress in Geophys. (in Chinese), 27(5): 1837-1840, doi: 10.6038/j.issn.1004-2903.2012.05.001.

     

    Qin S Q, Xue L, Li G L, et al. 2013. The verification of prospective prediction for the Minxian-Zhangxian MS6.6 earthquake in Gansu province and an analysis on the future earthquake situation. Progress in Geophys. (in Chinese), 28(4): 1860-1868, doi: 10.6038/pg20130427.

     

    Qin S Q, Xue L, Li P, et al. 2014a. A review of prospective prediction for the Jinggu MS6.6 earthquake in Yunnan province and an analysis on future earthquake situation. Progress in Geophys. (in Chinese), 29(5): 2479-2482, doi: 10.6038/pg20140574.

     

    Qin S Q, Xue L, Li G L, et al. 2014b. The verification of prospective prediction for the Lushan MS7.0 earthquake on 20 April 2013 and an analysis on future earthquake situation. Progress in Geophys. (in Chinese), 29(1): 141-147, doi: 10.6038/pg20140118.

     

    Qin S Q, Xue L, Li P, et al. 2014c. A review of prospective prediction for the Yutian 7.3 earthquake in Xinjiang province and an analysis on future earthquake situation. Chinese J. Geophys. (in Chinese), 57(2): 679-684, doi: 10.6038/cjg20140231.

     

    Qin S Q, Li P, Xue L, et al. 2014d. The definition of seismogenic period of strong earthquakes for some seismic zones in southwest China. Progress in Geophys. (in Chinese), 29(4): 1526-1540, doi: 10.6038/pg20140407.

     

    Qin S Q, Li P, Yang B C, et al. 2016a. The identification of mainshock events for main seismic zones in seismic belts of the Circum-Pacific, ocean ridge and continental rift. Progress in Geophys. (in Chinese), 31(2): 574-588, doi: 10.6038/pg20160209.

     

    Qin S Q, Yang B C, Wu X W, et al. 2016b. The identification of mainshock events for some seismic zones in mainland China (Ⅱ). Progress in Geophys. (in Chinese), 31(1): 115-142, doi: 10.6038/pg20160114.

     

    Qin S Q, Yang B C, Xue L, et al. 2016c. The identification of mainshock events for main seismic zones in the Eurasian seismic belt. Progress in Geophys. (in Chinese), 31(2): 559-573, doi: 10.6038/pg20160208.

     

    Qin S Q, Yang B C, Xue L, et al. 2016d. Revision method of earthquake magnitude. Progress in Geophys. (in Chinese), 31(3): 965-972, doi:10.6038/pg20160305.

     

    Scholz C H. 1968. The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes. Bull. Seismol. Soc. Am., 58(1): 399-415. http://bssa.geoscienceworld.org/content/58/1/399

     

    Shen B T, Stephansson O, Einstein H H, et al. 1995. Coalescence of fractures under shear stresses in experiments. J. Geophys. Res., 100(B4): 5975-5990. doi: 10.1029/95JB00040

     

    Shriki A, Nutov L. 2016. Fractals in the mathematics classroom: the case of infinite geometric series. Learning and Teaching Mathematics, 2016(20): 38-42. https://www.researchgate.net/profile/Atara_Shriki2/publication/304212602_Fractals_in_the_Mathematics_Classroom_The_Case_of_Infinite_Geometric_Series/links/5769713c08ae1a43d23a3414.pdf?origin=publication_list

     

    Smalley R F Jr, Turcotte D L, Solla S A. 1985. A renormalization group approach to the stick-slip behavior of faults. J. Geophys. Res., 90(B2): 1894-1900. doi: 10.1029/JB090iB02p01894

     

    Smalley R F Jr, Chatelain J L, Turcotte D L, et al. 1987. A fractal approach to the clustering of earthquakes: applications to the seismicity of the New Hebrides. Bull. Seismol. Soc. Am., 77(4): 1368-1381. http://www.bssaonline.org/content/77/4/1368.abstract

     

    Smith W D. 1981. The b-value as an earthquake precursor. Nature, 289(5794): 136-139. doi: 10.1038/289136a0

     

    Sun Y K, Yao B K. 1983. Mechanism research on the collapse of Yanchihe mining area. Hydrogeology and Engineering Geology (in Chinese), (1): 1-7. http://www.springerlink.com/index/J351853361011536.pdf

     

    Tan T K, Kang W F. 1980. Locked in stresses, creep and dilatancy of rocks, and constitutive equations. Rock Mechanics, 13(1): 5-22. doi: 10.1007/BF01257895

     

    Wang E Y, He X Q, Wei J P, et al. 2010. The coupling model of stress and electricity of EME of coal or rock. J. Min. Sci., 46(4): 367-374, doi: 10.1007/s10913-010-0046-1.

     

    Wang J A, Park H D. 2001. Comprehensive prediction of rockburst based on analysis of strain energy in rocks. Tunnelling and Underground Space Technology, 16(1): 49-57. doi: 10.1016/S0886-7798(01)00030-X

     

    Wang Q H, Ye Y C, Liu Y Z, et al. 2016. A creep constitutive model of rock considering initial damage and creep damage. Rock and Soil Mechanics (in Chinese), 37(S1): 57-62, doi: 10.16285/j.rsm.2016.S1.007.

     

    Wang S M, Zhu H H, Feng X T, et al. 2006. Influence of heterogeneity on macroscopical crack form of the brittle rock. Rock and Soil Mechanics (in Chinese), 27(2): 224-227. http://en.cnki.com.cn/Article_en/CJFDTOTAL-YTLX200602011.htm

     

    Wang W W. 2009. Study on the interaction and merging condition of multiple [Master's thesis] (in Chinese). Nanjing: Nanjing University of Technology.

     

    Weibull W. 1939. A Statistical Theory of the Strength of Materials. Stockholm: Generalstabens Litografiska Anstalts Föerlag.

     

    Weibull W. 1951. A statistical distribution function of wide applicability. J. Appl. Mech., 18(3): 293-297. http://web.cecs.pdx.edu/~cgshirl/Documents/Weibull-ASME-Paper-1951.pdf

     

    Wen Y T, Li N, Li X Q, et al. 2010. Contrast of disaster losses resulted from the Wenchuan and Tangshan earthquakes and rescue actions in these two events. Journal of Catastrophology (in Chinese), 25(2): 68-72. http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZHXU201002016.htm

     

    Wilson K G. 1979. Problems in physics with many scales of length. Sci. Am., 241(2): 158-179. doi: 10.1038/scientificamerican0879-158

     

    Wu X W, Qin S Q, Xue L, et al. 2016. Physical mechanism of major earthquakes by earthquake cases. Chinese J. Geophys. (in Chinese), 59(10): 3696-3710, doi: 10.6038/cjg20161016.

     

    Wyss M, Johnston A C, Klein F W. 1981. Multiple asperity model for earthquake prediction. Nature, 289(5795): 231-234. doi: 10.1038/289231a0

     

    Xie H P. 1996. Fractal-Rock Mechanics (in Chinese). Beijing: Science Press, 369.

     

    Xu J, Li H, Xian X F, et al. 1986. Meso-mechanical experiment of microfracture progress of sandstone under uniaxial stress condition. Mechanics in Engineering (in Chinese), (4): 16-20. http://www.sciencedirect.com/science/article/pii/S136516099900074X

     

    Xue L, Qin S Q, Li P, et al. 2014a. New quantitative displacement criteria for slope deformation process: From the onset of the accelerating creep to brittle rupture and final failure. Eng. Geol., 182: 79-87, doi: 10.1016/j.enggeo.2014.08.007.

     

    Xue L, Qin S Q, Sun Q, et al. 2014b. A quantitative criterion to describe the deformation process of rock sample subjected to uniaxial compression: From criticality to final failure. Physica A, 410: 470-482, doi: 10.1016/j.physa.2014.05.062.

     

    Yang S J, Zeng S, Wang H L. 2005. Experimental analysis on mechanical effects of loading rates on limestone. Chinese Journal of Geotechnical Engineering (in Chinese), 27(7): 786-788. https://www.researchgate.net/publication/290823724_Experimental_analysis_on_mechanical_effects_of_loading_rates_on_limestone

     

    Yang Y M, Ju Y, Mao L T. 2014. Growth distribution laws and characterization methods of cracks of compact sandstone subjected to triaxial stress. Chinese Journal of Geotechnical Engineering (in Chinese), 36(5): 864-872, doi: 10.11779/CJGE201405008.

     

    Yin X T, Wang S L, Dang F N, et al. 2008. Study on fractal characteristics of sandstone damage-fracture under ct test condition. Chinese Journal of Rock Mechanics and Engineering (in Chinese), 27(S1): 2721-2726.

     

    Zhang M, Lu Y J, Yang Q. 2010. Failure probability and strength size effect of quasi-brittle materials. Chinese Journal of Rock Mechanics and Engineering (in Chinese), 29(9): 1782-1789. http://en.cnki.com.cn/Article_en/CJFDTOTAL-YSLX201009007.htm

     

    Zhang Z, Wu K T, Geng N G, et al. 1986. An experimental study of barriers on earthquake fault plane under triaxial compression. Journal of Seismological Research, 9(6): 733-740. http://en.cnki.com.cn/Article_en/CJFDTOTAL-DZYJ198606012.htm

     

    Zhang Z, Wu K T, Jiao Y B. 1987. The changes of b value on samples contained barriers during rupture process. Earthquake Research in China (in Chinese), 3(1): 70-78.

     

    Zhao Y S. 1987. Griffith's criterion for mixed mode crack propagation. Eng. Fract. Mech., 26(5): 683-689. doi: 10.1016/0013-7944(87)90133-0

     

    Zhao Y S. 1990. Elliptic rule criterion for mixed-mode crack-propagation. Eng. Fract. Mech., 37(2): 283-292. doi: 10.1016/0013-7944(90)90041-E

     

    Zheng J. 1992. Nonlinear scientific methods applied to rock rupture and earthquake phenomena. Progress in Geophys. (in Chinese), 7(1): 20-35. http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWJ199201003.htm

     

    Zhou H W, Wang C P, Mishnaevsky L, et al. 2013. A fractional derivative approach to full creep regions in salt rock. Mechanics of Time-Dependent Materials, 17(3): 413-425, doi: 10.1007/s11043-012-9193-x.

     

    Zhu N L, Rao Y G. 2006. Study on constitutive model for quasi-rock materials based on statistical fracture theory. Chinese Journal of Rock Mechanics and Engineering (in Chinese), 25(S2): 3939-3944. http://en.cnki.com.cn/Article_en/CJFDTOTAL-YSLX2006S2093.htm

     

    安镇文, 王琳瑛, 朱传镇. 1989.大震前后地震活动的时空分维特征.地震学报, 11(3): 251-258. http://www.cnki.com.cn/Article/CJFDTOTAL-DZXB198903002.htm

     

    曹瑞琅, 贺少辉, 韦京等. 2013.基于残余强度修正的岩石损伤软化统计本构模型研究.岩土力学, 34(6): 1652-1660, doi: 10.16285/j.rsm.2013.06.018.

     

    曹文贵, 张升. 2005.基于Mohr-Coulomb准则的岩石损伤统计分析方法研究.湖南大学学报 (自然科学版), 32(1): 43-47. http://www.cnki.com.cn/Article/CJFDTOTAL-HNDX200501010.htm

     

    戴振祥. 2001.一类广义Cantor集的Hausdorff维数.浙江师大学报 (自然科学版), 24(2): 143-145. http://www.cnki.com.cn/Article/CJFDTOTAL-ZJSZ200102010.htm

     

    邓荣贵, 周德培, 张倬元等. 2001.一种新的岩石流变模型.岩石力学与工程学报, 20(6): 780-784. http://www.cnki.com.cn/Article/CJFDTOTAL-CJKB201407011.htm

     

    高峰, 谢和平, 赵鹏. 1993. Weibull模量和岩石强度的分形性质.科学通报, 38(15): 1435-1438. doi: 10.3321/j.issn:0023-074X.1993.15.016

     

    高峰, 钟卫平, 黎立云等. 2004.节理岩体强度的分形统计分析.岩石力学与工程学报, 23(21): 3608-3612. doi: 10.3321/j.issn:1000-6915.2004.21.009

     

    何满潮, 苗金丽, 李德建等. 2007.深部花岗岩试样岩爆过程实验研究.岩石力学与工程学报, 26(5): 865-876. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200705000.htm

     

    黄润秋. 2007. 20世纪以来中国的大型滑坡及其发生机制.岩石力学与工程学报, 26(3): 433-454. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200703000.htm

     

    贾延, 康亚明, 王东等. 2010.高围压与变温环境下大理岩的临界损伤度研究.四川大学学报 (工程科学版), 42(6): 79-84. http://www.cnki.com.cn/Article/CJFDTOTAL-SCLH201006016.htm

     

    李彪, 马胜利, 张流. 1993.不同实验条件下大理岩主破裂的分数维.地震地质, 15(2): 157-163. http://www.cnki.com.cn/Article/CJFDTOTAL-DZDZ199302010.htm

     

    李世愚, 和泰名, 尹祥础. 2015.岩石断裂力学.北京:科学出版社, 537.

     

    刘庭金, 唐春安. 2002.软硬接触对含包体试样破裂模式影响的数值试验.地震研究, 25(1): 53-57. http://www.cnki.com.cn/Article/CJFDTOTAL-DZYJ200201009.htm

     

    马鸿庆. 1982.大、中地震前b值的区域分布.地球物理学报, 25(2): 163-171. http://manu39.magtech.com.cn/Geophy/CN/abstract/abstract5260.shtml

     

    马瑾, 马胜利, 刘力强等. 1996.断层几何结构与物理场的演化及失稳特征.地震学报, 18(2): 200-207. http://www.cnki.com.cn/Article/CJFDTOTAL-DZXB602.006.htm

     

    茂木清夫. 1986.日本的地震预报.北京:地震出版社, 326.

     

    梅世蓉. 1995.地震前兆场物理模式与前兆时空分布机制研究 (一)——坚固体孕震模式的由来与证据.地震学报, 17(3): 273-282. http://www.cnki.com.cn/Article/CJFDTOTAL-DZXB503.000.htm

     

    倪玉山, 匡震邦, 杨英群. 1992.常规三轴压缩下花岗岩断裂表面的分形研究.岩石力学与工程学报, 11(3): 295-303. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX199203007.htm

     

    彭图让, 张泽华. 1989.裂纹尺寸分布函数及其在疲劳统计分析中的应用.山东建材学院学报, 3(3): 1-10. http://www.cnki.com.cn/Article/CJFDTOTAL-SDJC198903000.htm

     

    秦四清, 王媛媛, 马平. 2010a.崩滑灾害临界位移演化的指数律.岩石力学与工程学报, 29(5): 873-880. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201005005.htm

     

    秦四清, 徐锡伟, 胡平等. 2010b.孕震断层的多锁固段脆性破裂机制与地震预测新方法的探索.地球物理学报, 53(4): 1001-1014, doi: 10.3969/j.issn.0001-5733.2010.04.025. http://manu39.magtech.com.cn/Geophy/CN/abstract/abstract3019.shtml

     

    秦四清, 薛雷, 黄鑫等. 2010c.西藏地区未来强震预测.地球物理学进展, 25(6): 1879-1886, doi: 10.3969/j.issn.1004-2903.2010.06.001.

     

    秦四清, 薛雷. 2011.云南盈江MS5.8级地震和缅甸MS7.2级地震预测总结及震后趋势分析.地球物理学进展, 26(2): 462-468, doi: 10.3969/j.issn.1004-2903.2011.02.010.

     

    秦四清, 薛雷, 李国梁等. 2012.云南昭通"9·7地震"的前瞻性预测验证.地球物理学进展, 27(5): 1837-1840, doi: 10.6038/j.issn.1004-2903.2012.05.001.

     

    秦四清, 薛雷, 李国梁等. 2013.甘肃岷县漳县6.6级地震的前瞻性预测验证及震后趋势分析.地球物理学进展, 28(4): 1860-1868, doi: 10.6038/pg20130427.

     

    秦四清, 薛雷, 李培等. 2014a.云南景谷MS6.6级地震前瞻性预测回顾及其震后趋势分析.地球物理学进展, 29(5): 2479-2482, doi: 10.6038/pg20140574.

     

    秦四清, 薛雷, 李国梁等. 2014b.四川省芦山"4·20"7.0级地震的前瞻性预测验证及震后趋势分析.地球物理学进展, 29(1): 141-147, doi: 10.6038/pg20140118.

     

    秦四清, 薛雷, 李培等. 2014c.新疆于田7.3级地震前瞻性预测回顾及其震后趋势分析.地球物理学报, 57(2): 679-684, doi: 10.6038/cjg20140231. http://manu39.magtech.com.cn/Geophy/CN/abstract/abstract10101.shtml

     

    秦四清, 李培, 薛雷等. 2014d.中国西南地区某些地震区强震孕育周期界定.地球物理学进展, 29(4): 1526-1540, doi: 10.6038/pg20140407.

     

    秦四清, 李培, 杨百存等. 2016a.环太平洋、大洋海岭与大陆裂谷地震带主要地震区主震事件判识.地球物理学进展, 31(2): 574-588, doi: 10.6038/pg20160209.

     

    秦四清, 杨百存, 吴晓娲等. 2016b.中国大陆某些地震区主震事件判识 (Ⅱ).地球物理学进展, 31(1): 115-142, doi: 10.6038/pg20160114.

     

    秦四清, 杨百存, 薛雷等. 2016c.欧亚地震带主要地震区主震事件判识.地球物理学进展, 31(2): 559-573, doi: 10.6038/pg20160208.

     

    秦四清, 杨百存, 薛雷等. 2016d.地震震级修订方法.地球物理学进展, 31(3): 965-972, doi:10.6038/pg20160305.

     

    孙玉科, 姚宝魁. 1983.盐池河磷矿山体崩坍破坏机制的研究.水文地质工程地质, (1): 1-7. http://www.cnki.com.cn/Article/CJFDTOTAL-SWDG198301000.htm

     

    王其虎, 叶义成, 刘艳章等. 2016.考虑初始损伤和蠕变损伤的岩石蠕变全过程本构模型.岩土力学, 37(S1): 57-62, doi: 10.16285/j.rsm.2016.S1.007.

     

    王士民, 朱合华, 冯夏庭等. 2006.细观非均匀性对脆性岩石材料宏观破坏形式的影响.岩土力学, 27(2): 224-227. http://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200602011.htm

     

    汪微微. 2009. 多裂纹相互作用及其合并条件的研究[硕士论文]. 南京: 南京工业大学.

     

    温玉婷, 李宁, 刘雪琴等. 2010.汶川地震与唐山地震损失与救助之对比.灾害学, 25(2): 68-72. http://www.cnki.com.cn/Article/CJFDTOTAL-ZHXU201002016.htm

     

    吴晓娲, 秦四清, 薛雷等. 2016.基于震例探讨大地震的物理机制.地球物理学报, 59(10): 3696-3710, doi: 10.6038/cjg20161016. http://manu39.magtech.com.cn/Geophy/CN/abstract/abstract13145.shtml

     

    谢和平. 1996.分形-岩石力学导论.北京:科学出版社, 369.

     

    许江, 李贺, 鲜学福等. 1986.对单轴应力状态下砂岩微观断裂发展全过程的实验研究.力学与实践, (4): 16-20. http://www.cnki.com.cn/Article/CJFDTOTAL-LXYS198604003.htm

     

    杨仕教, 曾晟, 王和龙. 2005.加载速率对石灰岩力学效应的试验研究.岩土工程学报, 27(7): 786-788. http://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200507012.htm

     

    杨永明, 鞠杨, 毛灵涛. 2014.三轴应力下致密砂岩裂纹展布规律及表征方法.岩土工程学报, 36(5): 864-872, doi: 10.11779/CJGE201405008.

     

    尹小涛, 王水林, 党发宁等. 2008. CT实验条件下砂岩破裂分形特性研究.岩石力学与工程学报, 27(S1): 2721-2726. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2008S1024.htm

     

    张明, 卢裕杰, 杨强. 2010.准脆性材料的破坏概率与强度尺寸效应.岩石力学与工程学报, 29(9): 1782-1789. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201009007.htm

     

    张智, 吴开统, 焦远碧. 1987.含有障碍体的岩石样品破裂发展过程中的b值变化.中国地震, 3(1): 70-78. http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZD198701011.htm

     

    郑捷. 1992.研究地震和岩石破裂现象的非线性科学方法.地球物理学进展, 7(1): 20-35. http://www.cnki.com.cn/Article/CJFDTOTAL-DQWJ199201003.htm

     

    朱乃龙, 饶云刚. 2006.基于统计断裂理论的岩石类材料本构模型的研究.岩石力学与工程学报, 25(S2): 3939-3944. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2006S2093.htm

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收稿日期:  2016-11-26
修回日期:  2017-03-16
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