基于裂缝扩展细观模拟的堆石料流变特性研究
|
摘要
在深入实施西部大开发战略的背景下,围绕着南水北调及西电东送等重大工程建设,西部地区正在或即将兴建一大批高上石坝工程。随着在建和拟建土石坝的高度跨入300米级,坝体内部高应力区堆石料的颗粒破碎现象更加突出,颗粒破碎引起的应力调整及颗粒位置重排列成为高土石坝变形的重要影响因素之一。
土石坝在填筑及初次蓄水期间的变形主要是由于外荷载施加引起的堆石颗粒挤密以及破碎后的小颗粒填充孔隙。在坝体建成蓄水后,全部荷载已施加上,如果堆石料不存在流变性,坝体变形就不再随时间发展。而国内外多座已建成土石坝的监测资料显示,坝体在竣工蓄水后还将持续地产生后期变形。从时间上看,后期变形可持续几年、十几年甚至更长。从变形量上看,后期变形一般为坝高的0.1%,最大可达3.8%。土石坝后期变形恶化了面板的应力变形性状,导致面板发生挤碎或拉裂,危及大坝安全。但现有知识还不能合理解释后期变形机理及各种实际观测现象。近年来随着高土石坝建设的需要,堆石料的流变特性及机理已成为亟待解决的主要技术问题之一。本文结合国家自然科学基金面上项目(50879007)“基于颗粒破裂细观模拟的堆石料后期变形机理及本构模型研究”,根据亚临界裂缝扩展导致的堆石颗粒破碎具有时间效应的特点来研究堆石料的流变特性,并从细观角度对堆石料的颗粒破碎特性、流变机理等关键问题开展了探索性的研究工作,主要内容有：
(1)数值试样的制备方法研究与数值试验平台构建。针对堆石形状不规则、咬合作用强等特点,发展了多种不规则形状数值颗粒的模拟方法。提出了多种满足一定级配要求的数值试样的生成方法及数值颗粒投放技术。采用fish语言构建数值试验平台,为下一步的研究工作奠定基础。
(2)不考虑时间效应的堆石颗粒破碎研究。筑坝堆石料在填筑、初次蓄水或遭遇地震等极端地质灾害作用后会发生颗粒破碎,该种形式的破碎历时短,多为棱角断裂或劈裂。根据石块在土工试验后表现出的实际破坏形态,研究颗粒破碎的典型模式。总结应用颗粒流方法研究颗粒破碎的思路,将国外学者提出的基于最大拉应力准则的二维圆盘颗粒破碎模型推广至三维条件,建立了三维颗粒脆性破碎的理论模型。将该模型引入颗粒流程序,进行了堆石料三轴剪切数值试验研究,分别从颗粒破碎、颗粒间接触力、孔隙率、破碎颗粒位置分布规律、颗粒运动规律、能量耗散等细观角度初步地探讨了堆石体在三轴条件下受力变形规律及机理。
(3)亚临界裂缝扩展规律及其影响因素研究与堆石料数值流变试验的颗粒流程序设计。基于岩石的亚临界裂缝扩展理论,微裂缝的扩展导致了堆石颗粒的破碎,即堆石的颗粒破碎具有时间效应。通过研究颗粒裂缝面上应力、颗粒及颗粒所含裂缝的几何特征、相对湿度等因素对应力强度因子与裂缝扩展过程的影响,对亚临界裂缝扩展理论进行了提炼、归纳和总结,据此设计了模拟堆石料室内流变试验的颗粒流程序的思路并编写了相关程序。
(4)结合堆石料室内流变试验进行了单轴、三轴流变数值试验研究。确定了合理的数值颗粒破碎模式,直观给出了数值流变过程中颗粒体内部结构参量的变化过程与颗粒破碎情况。综合分析了颗粒破碎规律、颗粒体内部结构变化与流变之间关系,并在此基础上探析了堆石流变的细观机理。
Under the background of the implementation and deepening of the Western Development Strategy, quite a few high rock-fill dams are being or to be built in Western China as an important part of the major engineering items such as South-to-North Water Diversion and West-to-East Power Transmission Project. With the height of dams entering the level of300meters, the rockfill particle breakage in high stress areas of a dam body is more prominent. Therefore, stress adjustment and particle location rearrangement caused by particle breakage becomes one of the controlling factors in deformation of the high rockfill dams.
Deformation of the high rockfill dams during the period of filling and initial impoundment is mainly caused by particle compacting and tiny particles from breakage filling the pores. After completion and impoundment, the deformation won't develop along with time if the rockfills do not possess rheological characteristics. However, the monitoring data of numerous built dams around the world show that the long-term deformation of a high dam would be continued after completion and impoundment, which can last for years, more than a decade or even longer. The deformation rate maintains around0.1%of the height of dam, and the maximum deformation is up to3.8%. Then, the stress and deformation behaviors of the panel are deteriorated, which result in the cracks in the face, even the risk of dam break. Unfortunately, the mechanism and observed phenomena of the long-term deformation still could not be clarified unambiguously. Therefore, the rheology behavior of rockfill has become one of the most important technical issues restricting the construction of high rockfill dams. With the support from National Nature Science Foundation of China under Grant50879007, which titled "Study on Rheological Property and Constitutive Model of Rockfill by Meso-mechanics Simulation Based on Sub-critical Crack Expansion Theory", in-depth research was conducted regarding the critical issues including the characteristics of particle breakage and rock-fill rheology mechanism from the microscopic view. The study includes:
(1) Preparation of numerical samples and construction of numerical experiment platform.
The simulation method for a variety of numerical particles with irregular shape is developed which aims at the characteristics of rockfill, such as irregular shape and prominent interlock behavior. Various types of generation methods for numerical samples and forming techniques for numerical particles are suggested, which can meet certain grading requirements. The numerical experiment platform is built using FISH language to lay the foundation for the next step in this research.
(2) The study of particle breakage for rockfill without considering the time effect.
The rockfill particle breakage can occur after filling, initial impounding or extreme geological disasters like earthquake. Under the high contact stress conditions, the main crushing modes of particles are characterized by angular breakage of particles and cleavage under high contact stress due to the changes of the external loads. Typical crushing modes are studied according to the actual failure modes of rocks in a series of indoor soil tests. In consideration of rockfill particles breaking during filling, a theoretical model of particles' brittle crushing has been extended from two dimensions to three dimensions, and particle flow programs are introduced to conduct triaxial shear numerical study, then the microscopic mechanism of rock-fill deformation under triaxial shear is analyzed.
(3) The study of sub-critical expansion of cracks and the design of particle flow program for numerical rheological test.
According to the theory of sub-critical expansion of cracks, rockfill particles breakage with the time effect is caused by the extension of micro cracks. The influence on the stress intensity factor and extension of crack are studied by discussing the stress on the crack face of particles, geometrical characters of particles and cracks. In order to simulate the rheological lab test of the rockfill, the theory of sub-critical expansion of cracks has been refined, summed up and concluded, and the particle flow programs have been designed and written.
(4) The uniaxial and triaxial numerical rheological tests are carried out according to the rheological lab test. The reasonable particle breakage mode is determined, and the evolution of microscopic characteristics for rockfill samples and particles breakage are presented visually during the process of numerical rheology. The relations among the rule of particles breakage, structure change of particles and rheology are synthetically analyzed. Furthermore, the microscopic mechanism of rock-fill rheology is given qualitatively.
土石坝在填筑及初次蓄水期间的变形主要是由于外荷载施加引起的堆石颗粒挤密以及破碎后的小颗粒填充孔隙。在坝体建成蓄水后,全部荷载已施加上,如果堆石料不存在流变性,坝体变形就不再随时间发展。而国内外多座已建成土石坝的监测资料显示,坝体在竣工蓄水后还将持续地产生后期变形。从时间上看,后期变形可持续几年、十几年甚至更长。从变形量上看,后期变形一般为坝高的0.1%,最大可达3.8%。土石坝后期变形恶化了面板的应力变形性状,导致面板发生挤碎或拉裂,危及大坝安全。但现有知识还不能合理解释后期变形机理及各种实际观测现象。近年来随着高土石坝建设的需要,堆石料的流变特性及机理已成为亟待解决的主要技术问题之一。本文结合国家自然科学基金面上项目(50879007)“基于颗粒破裂细观模拟的堆石料后期变形机理及本构模型研究”,根据亚临界裂缝扩展导致的堆石颗粒破碎具有时间效应的特点来研究堆石料的流变特性,并从细观角度对堆石料的颗粒破碎特性、流变机理等关键问题开展了探索性的研究工作,主要内容有：
(1)数值试样的制备方法研究与数值试验平台构建。针对堆石形状不规则、咬合作用强等特点,发展了多种不规则形状数值颗粒的模拟方法。提出了多种满足一定级配要求的数值试样的生成方法及数值颗粒投放技术。采用fish语言构建数值试验平台,为下一步的研究工作奠定基础。
(2)不考虑时间效应的堆石颗粒破碎研究。筑坝堆石料在填筑、初次蓄水或遭遇地震等极端地质灾害作用后会发生颗粒破碎,该种形式的破碎历时短,多为棱角断裂或劈裂。根据石块在土工试验后表现出的实际破坏形态,研究颗粒破碎的典型模式。总结应用颗粒流方法研究颗粒破碎的思路,将国外学者提出的基于最大拉应力准则的二维圆盘颗粒破碎模型推广至三维条件,建立了三维颗粒脆性破碎的理论模型。将该模型引入颗粒流程序,进行了堆石料三轴剪切数值试验研究,分别从颗粒破碎、颗粒间接触力、孔隙率、破碎颗粒位置分布规律、颗粒运动规律、能量耗散等细观角度初步地探讨了堆石体在三轴条件下受力变形规律及机理。
(3)亚临界裂缝扩展规律及其影响因素研究与堆石料数值流变试验的颗粒流程序设计。基于岩石的亚临界裂缝扩展理论,微裂缝的扩展导致了堆石颗粒的破碎,即堆石的颗粒破碎具有时间效应。通过研究颗粒裂缝面上应力、颗粒及颗粒所含裂缝的几何特征、相对湿度等因素对应力强度因子与裂缝扩展过程的影响,对亚临界裂缝扩展理论进行了提炼、归纳和总结,据此设计了模拟堆石料室内流变试验的颗粒流程序的思路并编写了相关程序。
(4)结合堆石料室内流变试验进行了单轴、三轴流变数值试验研究。确定了合理的数值颗粒破碎模式,直观给出了数值流变过程中颗粒体内部结构参量的变化过程与颗粒破碎情况。综合分析了颗粒破碎规律、颗粒体内部结构变化与流变之间关系,并在此基础上探析了堆石流变的细观机理。
Under the background of the implementation and deepening of the Western Development Strategy, quite a few high rock-fill dams are being or to be built in Western China as an important part of the major engineering items such as South-to-North Water Diversion and West-to-East Power Transmission Project. With the height of dams entering the level of300meters, the rockfill particle breakage in high stress areas of a dam body is more prominent. Therefore, stress adjustment and particle location rearrangement caused by particle breakage becomes one of the controlling factors in deformation of the high rockfill dams.
Deformation of the high rockfill dams during the period of filling and initial impoundment is mainly caused by particle compacting and tiny particles from breakage filling the pores. After completion and impoundment, the deformation won't develop along with time if the rockfills do not possess rheological characteristics. However, the monitoring data of numerous built dams around the world show that the long-term deformation of a high dam would be continued after completion and impoundment, which can last for years, more than a decade or even longer. The deformation rate maintains around0.1%of the height of dam, and the maximum deformation is up to3.8%. Then, the stress and deformation behaviors of the panel are deteriorated, which result in the cracks in the face, even the risk of dam break. Unfortunately, the mechanism and observed phenomena of the long-term deformation still could not be clarified unambiguously. Therefore, the rheology behavior of rockfill has become one of the most important technical issues restricting the construction of high rockfill dams. With the support from National Nature Science Foundation of China under Grant50879007, which titled "Study on Rheological Property and Constitutive Model of Rockfill by Meso-mechanics Simulation Based on Sub-critical Crack Expansion Theory", in-depth research was conducted regarding the critical issues including the characteristics of particle breakage and rock-fill rheology mechanism from the microscopic view. The study includes:
(1) Preparation of numerical samples and construction of numerical experiment platform.
The simulation method for a variety of numerical particles with irregular shape is developed which aims at the characteristics of rockfill, such as irregular shape and prominent interlock behavior. Various types of generation methods for numerical samples and forming techniques for numerical particles are suggested, which can meet certain grading requirements. The numerical experiment platform is built using FISH language to lay the foundation for the next step in this research.
(2) The study of particle breakage for rockfill without considering the time effect.
The rockfill particle breakage can occur after filling, initial impounding or extreme geological disasters like earthquake. Under the high contact stress conditions, the main crushing modes of particles are characterized by angular breakage of particles and cleavage under high contact stress due to the changes of the external loads. Typical crushing modes are studied according to the actual failure modes of rocks in a series of indoor soil tests. In consideration of rockfill particles breaking during filling, a theoretical model of particles' brittle crushing has been extended from two dimensions to three dimensions, and particle flow programs are introduced to conduct triaxial shear numerical study, then the microscopic mechanism of rock-fill deformation under triaxial shear is analyzed.
(3) The study of sub-critical expansion of cracks and the design of particle flow program for numerical rheological test.
According to the theory of sub-critical expansion of cracks, rockfill particles breakage with the time effect is caused by the extension of micro cracks. The influence on the stress intensity factor and extension of crack are studied by discussing the stress on the crack face of particles, geometrical characters of particles and cracks. In order to simulate the rheological lab test of the rockfill, the theory of sub-critical expansion of cracks has been refined, summed up and concluded, and the particle flow programs have been designed and written.
(4) The uniaxial and triaxial numerical rheological tests are carried out according to the rheological lab test. The reasonable particle breakage mode is determined, and the evolution of microscopic characteristics for rockfill samples and particles breakage are presented visually during the process of numerical rheology. The relations among the rule of particles breakage, structure change of particles and rheology are synthetically analyzed. Furthermore, the microscopic mechanism of rock-fill rheology is given qualitatively.
引文
[1]彭正光.西北口面板堆石坝蓄水7年变形分析[J].水利水电技术,1999,30(9)：24-27.
[2]杨键.天生桥一级水电站面板堆石坝沉降分析[J].云南水力发电,2001,17(2)：59-63.
[3]赵魁芝,李国英,沈珠江.天生桥混凝土面板堆石坝原型观测资料反馈分析[J].水利水运科学研究,2000,(4)：15-19.
[4]赵魁芝,李国英,沈珠江.天生桥混凝土面板堆石坝面板原型观测资料分析[J].水利水运工程学报,2001,(1)：38-44.
[5]汪明元,何晓民,程展林.粗粒料流变研究的现状与展望[J].岩土力学,2003,10,(24)增刊：451-454.
[6]张亦昭,赵家旺.十三陵抽水蓄能电站上池面板堆石坝体的沉降变形[J].水利水电技术,1997,28(10)：27-31.
[7]Maranda das Neves E, Advances in Rockfill structure[M]. London:Kluwer Academic Publishers,1991.
[8]郦能惠.高混凝土面板堆石坝设计理念探讨[J].岩土工程学报,2007,29(8)：1143-1150.
[9]Cetin H., Laman M. and Ertunc A.. Settlement and slaking problems in the world's fourth largest rock-fill dam, the Ataturk Dam in Turkey [J]. Engineering Geological. 2000,56, No.3,225-242.
[10]花俊杰,周伟,常晓林,周创兵.300m级高堆石坝长期变形预测[J].四川大学学报(工程科学版),2011,43(3)：33-38.
[11]陈立宏,陈祖煜,张进平,赵春.小浪底大坝心墙中高孔隙水压力的研究[J].水利学报,2005,2,36(2)：219-224.
[12]Sowers G. F., Williams R. C. and Wallace T. S.. Compressibility of broken rock and the settlement of rockfills[C]. Proc.6th International Conference Soil Mechanical Foundation Engineering, Montreal 2,1965:561-565.
[13]Fumagalli E. Tests on cohesionless materials for rockfill dams[J]. Journal of Soil Mechanics and Foundation Engineering, ASCE,1969,95(SMI Division):313-330.
[14]Charles J. A.. Geotechnical properties of coarse grained soils[C]. Proceeding of 12th International Conference Soil Mechanical Foundation Engineering, Rio de Janeiro, General Report, Discussion Session 8,1989:2495-2519.
[15]Charles J. A.. Laboratory compression tests and the deformation of rockfill structures [J]. In Advances in Rockfill Structures. NATO ASI Series E,1991, Vol.200: 73-95.
[16]沈珠江,左元明.堆石料的流变特性试验研究[A].第6届土力学基础工程学术会议论文集 [C].上海：同济大学出版社,1991,443-446.
[17]沈珠江.土石料的流变模型及其应用[J].水利水运科学研究,1994,12(4)：335-342.
[18]沈珠江,赵魁芝.堆石坝流变变形的反馈分析[J].水利学报,1998,6(6)：1-6.
[19]蒋鹏,杨淑碧.成都地区卵石土流变特性及长期强度研究[J].地质灾害与环境保护,1998,9(1)：38—4.
[20]郭兴文,王德信,蔡新等.混凝土面板堆石坝流变分析[J].水利学报,1999,11(11)：42-46.
[21]陈峰,杨建贵,蔡新等.土石坝流变非线形分析[J].河海大学学报,1999,27(6)：20-24.
[22]Justo J. L. and Durand P.. Settlement-time behaviour of granular embankments[J]. International Journal of Numerical Analysis Methods Geomechanics,2000,24, No. 3:281-303.
[23]王勇,殷宗泽.一个用于面板坝流变分析的堆石料流变模型[J].岩土力学,2000,21(3)：227-230.
[24]王勇,殷宗泽.面板坝中堆石流变对面板应力变形的影响分析[J].河海大学学报,2000,11(6)：60—64.
[25]王勇.堆石流变的机理及研究方法初探[J].岩石力学与工程学报,2000,7,19(4)：526-530.
[26]Oldecop L. A. and Alonso E. E.. A model for rockfill compressibility[J]. Geotechnique,2001,51,2:127-139.
[27]Marsal R. J.. Mechanical properties of rockfill. In Embankment dam engineering. Casagrande Volume I (eds R. C. Hirschfeld and S. J. Poulos). New York:John Wiley & Sons,1973:110-200.
[28]Veiga Pinto A. A.. Previsa-o do comportamento estrutural de barragens de enrocamento[D]. PhD thesis, Laborato'rio Nacional de Engenharia Civil, Lisbon, 1983.
[29]梁军,刘汉龙.面板坝堆石料的蠕变试验研究[J].岩土工程学报,2002,24(2)：257-259
[30]梁军,刘汉龙,高玉峰.堆石蠕变机理分析与颗粒破碎特性研究[J].岩土力学,2003,6,24(3)：479-483.
[31]程展林,丁红顺.堆石料蠕变特性试验研究[J].岩土工程学报,2004,26(4)：473-476.
[32]汪明元,丁红顺,饶锡保,程展林.高堆石坝粗粒料的流变特性研究[C].中国水利水电工程未来与发展.大连,2002,9：381-385.
[33]李国英,米占宽,傅华,方维凤.混凝土面板堆石坝堆石料流变特性试验研究[J].岩土力学,2004,25(11)：1712-1716.
[34]左永振.粗粒料的蠕变和湿化试验研究[D].武汉：长江科学院,2008.
[35]王海俊,殷宗泽.堆石料长期变形的室内试验研究[J].水利学报,2007,8,38(8)：914-919.
[36]王海俊.土石坝堆石料的长期变形特性研究[D].南京：河海大学,2008.
[37]程展林,丁红顺,吴良平.粗粒土试验研究[J].岩土工程学报,2007,29(8)：1151-1158.
[38]周伟,胡颖,闫生存.高土石坝流变机理的组构理论分析方法[J].岩土工程学报,2007,29(8)：1274-1278.
[39]周伟,胡颖,杨启贵,熊泽斌.高混凝土面板堆石坝流变机理及长期变形预测[J].水利学报,2007,10(增刊)：100-105.
[40]Oldecop L. A. and Alonso E. E.. Theoretical investigation of the time-dependent behaviour of rockfill[J]. Geotechnique,2007,57,5:423-435.
[41]左永振,程展林,丁红顺,姜景山,孔宪勇.堆石料蠕变试验方法研究[J].长江科学院院报,2009,26(12)：63-66.
[42]朱晟,王永明,徐骞.粗粒筑坝材料的增量流变模型研究[J].岩土力学,2011,32(11)：3201-3206.
[43]李海芳,张茵琪,金伟,温彦锋,陈宁.两河口水电站混合料流变模型研究[J].西北地震学报,2011,33(z1)：285-289.
[44]花俊杰,周伟,常晓林,周创兵.300m级高堆石坝长期变形预测[J].四川大学学报(工程科学版),2011,5,34(3)：33-38.
[45]夏才初,刘大安.理论流变模型及其统一模型研究[C].中国岩石力学与工程学会第五届学术大会,上海,1998：134-140.
[46]Leung C. F., Lee F. H., and Yet N. S., The role of particle breakage in pile creep in sand[J]. Canada Geotechnology Journal,1996,33:888-898.
[47]Kranz R. L.. The Effects of confining pressure and stress difference on static fatigue of granite[J]. Journal of geophysical research,1980, Vol.85:1854-1866.
[48]Evans A. G..Fracture mechanics determinations [M]. Fracture mechanics of ceramics. Editors:R. C. Bradt, D. P. H. Hasselman, and F. F. Lange, Plenum Press, New York.1974, Vol.21,:17-48.
[49]Tait R. B. and Garrett G. G..A fracture mechanics evaluation of static and fatigue crack growth in cement mortar[C]. Proceedings of conference of fracture mechanics of concrete,1979:18-27.
[50]Taylor P. C. and Tait R. B.. Effects of fly ash on fatigue and fracture properties of hardened cement and mortar[J]. Cement & Concrete Composites,1999, Vol. 21:223-232.
[51]Scholz C. H..Static fatigue of quartz[J]. Journal of geophysical research.1972, Vol.77,No.11:2104-2114.
[52]Wilkins B. J. S.. Slow crack growth and delayed failure of granite[J]. International journal of rock mechanics and mining sciences & geomechanics abstracts,1980, Vol.17:365-369.
[53]Wiederhorn S. M., Fuller E. R. Jr. and Thomson R.. Micromechanisms of crack growth in ceramics and glasses in corrosive environments[J]. Metal Science,1980, August-September:450-458.
[54]Kjaernsli B. and Sande A.. Compressibility of some coarsegrained materials[C]. Proceeding Europa conference soil mechanics foundation engineering.1963,1: 245-251.
[55]Fumagalli E.. Tests on cohesionless materials for rockf ill dams[J]. Journal of soil mechanics foundation engineering.1969, ASCE95, No. SM1:313-330.
[56]Marachi N. D., Chan C. K., Seed H. B. and Duncan, J. M.. Strength and deformation characteristics of rockfill materials. Report No. TE-69-5. Department of Civil Engineering, University of California,1969.
[57]Nobari E. S. and Duncan J. M.. Effect of reservoir filling on stresses and movements in earth and rockfill dams.Report No. TE-72-1. Department of Civil Engineering, University of California,1972.
[58]Veiga Pinto A. A.. Previsa~o do comportamento estrutural de barragens de enrocamento [D]. PhD thesis, Laborato'rio Nacional de Engenharia Civil, Lisbon,1983.
[59]罗勇.土工问题的颗粒流数值模拟及应用研究[D].博士学位论文,2007,12.
[60]Cundall P. A.. A computer model for simulating Progerssive large Scale Movements in Bloeky Rock Systems. In:Proceeding of the symposium of the international society for rock mechanics. Nancy, France,1971,1(8).
[61]魏群.散体单元法的基本原理、数值方法与程序[M].北京：科学出版社,1991.
[62]Cundall, P. A. and Strack,0. D. L..A discrete numerical model for granular assemblies[J]. Geotechnique,1979,vol.29:47-65.
[63]Cundall P. A. & Strack 0. D. L.. The Distinct Element Method as a Tool for Research in Granular Media, Part II. Department of Civil and Mineral Engineering, University of Minnesota National Science Foundation,1979.
[64]Maini T., Cundall P. A..Computer modeling of jointed rock masses[R]. [AD—— A061658]:Defense Technical Information Center,1978.
[65]Lemos, J. V.,Roger, Hart, D.,Cundall, P. A..A Generalized Discrete Eclement Program for Modeling Joined Rock Mass, Proc. Of the Int. Symp. on Fundamentals of Rock Joins, Bjorkliden,1985,335-343.
[66]Lorig, L. J., Brady, B. G. and Cundall, P. A.. Hybrid Distinct Element-Boundary Element Analysis of Jointed Rock. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.,1986,23:303-312.
[67]Lorig, L. J. and Shoi, S. K.. Hydebe-User's Manual, Commonwealth Scientific and Industrial Research Organization, Austrilia,1986.
[68]王泳嘉.离散单元法一种适用于节理岩石力学分析的数值方法.第一届全国岩石力学数值计算及模型实验讨论会文集,1986.
[69]王泳嘉,刑纪波.离散元法及其在岩土力学中的应用.辽宁：东北大学出版社,1991.
[70]Shi, G. H.. Discontinuous Deformation Analysis:A New Numerical Model for the Statics and Dynamics of Block Systems[D]. PhD Thesis. University of California, Berkeley.1988.
[71]石根华.数值流行方法与非连续变形分析[M].裴觉民译.北京：清华大学出版社,1997.
[72]Shi, G. H.. Manifold method of material analysis[C]. Transaction of the 9th Army Conference on Applied Mathematics and Computing, Minneapolis, Minnesota, 1991:57-76.
[73]Shi, G. H.. Manifold metho[C]d. Proceeding of first International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. TSI Press, Albuquerque, NM, Mexico,1996:52-204.
[74]Shi, G. H.. Producing Joint Polygons[J], cutting joint blocks and finding key blocks for general free surfaces. Chinese Journal of Rock Mechanics and Engineering, 2006,25:2161-2170.
[75]Goodman R. E., Shi G. H., Boyle W..Calculation of support for hard, jointed rock using the key block principle[C]. Proceedings of the 23rd US Symposium of Rock Mechanics.1982:883-898.
[76]Goodman R. E.. Block theory and its application[J]. Geotechnique,1995,45 (3):383-423.
[77]Wei Q, Zhang J. J.. Development and application of laser speckle technique in rock tests of hydropower project [C]. Proceedings of ISRM International Symposium on Rock Mechanics and Power Planets.,1988:527-534.
[78]魏群,刘光廷,陈兴华,等.颗粒组合体变形特性的离散元数值模拟方法[C].岩土力学新分析方法讨论会会议文集.上海：同济大学出版社,1989：212-217.
[79]Wei Q.. Discrete element method and its application in jointed rock stability of hydropower projects [C]. Proceedings of the International Symposium on Rock Joints. 1990:759-765.
[80]魏群,陈兴华,刘光廷.颗粒体应力应变的散体元数值计算及验证实验[C].第二届全国岩土工程数值方法的工程应用学术研讨会议文集.上海：同济大学出版社,1990：629-635.
[81]魏群.岩土工程中散体元的基本原理数值方法及实验研究[博士学位论文][D].北京：清华大学,1990.
[82]魏群,张镜剑.颗粒体应力应变的张量表达式在散体元计算中的实施[C].第二届全国岩土工程数值方法的工程应用学术研讨会议文集.上海：上海同济大学出版社,1990：445-451.
[83]魏群,陈兴华.任意形状离散颗粒组合体的计算机模拟方法[C].第四届全国岩石混凝土断裂力学会论文集.1990：1-6.
[84]WEI Q, ZHANG M W. Investigation of crack opening displacement field of concrete beam during stable crack growth with white light speckle method[C]. Proceedings of the 10th Congress on Material Testing, Hungary. [S.1.]:[s. n.],1991:1-6.
[85]魏群.颗粒散体元-散体运动细观分析的一种新方法[C].全国土木工程青年计算机工作者学术论文集.南京：东南大学出版社,1991：599-603.
[86]魏群.椭圆散体元：一种模拟颗粒组合体的新方法[C].水电与矿业工程中的岩石力学问题.北京：科学出版社,1991：224-232.
[87]冯树仁,刘泉声,葛修润等.三维离散单元法及其在滑坡分析中的应用[J].岩土工程学报,2000,22(1)：101—104.
[88]葛修润,焦玉勇.基于静态松弛法求解的三维离散单元法[J].岩石力学与工程学报,200019(4)：451-456.
[89]葛修润,姜清辉,焦玉勇.三维静态同步松弛的离散单元法.中国矿业大学学报,2002,31(4)：338-343.
[90]焦玉勇.三维离散单元法及其应用[D].博士学位论文,中国科学院武汉岩土力学研所,1998.
[91]伍四明,李日国.万县滑坡群形成机制的数值模拟研究[J].水文地质工程地质,1996,6：14-17.
[92]金仁祥,晏鄂川,刘汉超.麻六嘴滑坡成因机制离散元数值模拟[J].地质灾害与环境保护,2000,11(1)：63-66.
[93]毛彦龙,胡广韬,毛新虎等.地震滑坡启程剧动的机理研究及离散元模拟[J].工程地质学报,2001,9(1)：74-80.
[94]安关峰,殷坤龙,唐辉明.黄土坡滑坡的离散元研究[J].中国地质大学学报,2002，27(4)：357-359.
[95]殷坤龙,姜清辉,汪洋.新滩滑坡运动全过程的非连续变形分析与仿真模拟[J].岩石力学与工程学报,2002,21(7)：959-962.
[96]汪洋,姜清辉,殷坤龙.滑坡运动过程仿真分析[J].中国地质大学学报,2002，27(5)：632-636.
[97]Cundall, P. A. and Hart, R. D.. Numerical modeling of discontinua[J]. Engineering Computations,1992,vol.9:101-113.
[98]Bardet J. P., Proubet J. A.. Numerical investigation of stulcture of persistent shear bands in granular media[J].Geotechnique,1991,41(4):599-613.
[99]Bardet J. P., Proubet J. A..Shear-band analysis in idealized granular material [J]. Engineering Mechanics,1992,118(8):397-415.
[100]Ng, T. T..Fabric study of granular materials after compaction[J]. Journal of Engineering Mechanics,1999, vol.125, no.12,1390-1394.
[101]Olivier Tsoungui, Denis Vallet and Jean-Claude Charmet. Numerical model of crushing of grains inside two-dimensional granular materials[J]. Powder Technology, 1999,105:190-198.
[102]Antony, S. J.. Evolution of force distribution in three-dimensional granular media [J].Physical Review,2000, vol.63,011302.
[103]周健,池永,池毓蔚,徐建平.颗粒流方法及PFC2D程序[J].岩土力学,2000,9,21(3)：271-274.
[104]周健,池毓蔚,池永,徐建平.砂土双轴试验的颗粒流模拟[J].岩土工程学报,2000,11,22(6)：701-704.
[105]周健,廖雄华,池永,徐建平.士的室内平面应变试验的颗粒流模拟[J].同济大学学报,2002,9,30(9)：1044-1500.
[106]周健,池永.砂土力学性质的细观模拟[J].岩土力学,2003,12,24(6)：901-906.
[107]McDowell G. R. and Harireche O.. Discrete-element modeling of yielding and normal compression of sand [J]. Geotechnique,2002,52(4):299-304.
[108]Cheng, Y. P., Nakata, Y. and Bolton, M. D.. Discrete element simulation of crushable soil[J]. Geote-chnique,2003,53(7):633-641.
[109]Potyondy D.0.,Cundall P. A.. Abonded-particle model for rock[J]. International Journal of Rock Mechanics & Mining Sciences,2004,11(41):1329-1364.
[110]Lim W. L. and G. R. McDowell. Discrete element modelling of railway ballast[J]. Granular Matter,2005,7 (1):19-29.
[111]Sebastian Lobo-Guerrero, Luis F. Vesga, Luis E. Vallejo. Discrete element method evaluation of granular crushing under direct shear condit ions[J]. Journal of geotechnical and environmental engineering,2005,131(10):1295-1300.
[112]Sebastian Lobo-Guerrero, Luis E. Vallejo, and Luis F. Vesga. Visualization of crushing evolution in granular materials under compression using DEM[J]. International journal of geomechanics,2006,6(3):195-200.
[113]N. Cho, C.D. Martin, D. C. Sego. A clumped particle model for rock[J]. International Journal of Rock Mechanics & Mining Sciences,2007,44:997-1010.
[114]M. Lu, G. R. McDowell. The importance of modelling ballast particle shape in the discrete element method [J]. Granular Matter,2007,9:69-80.
[115]L. Uthus, M. A. Hopkins and I. Horvli. Discrete element modelling of the resilient behaviour of unbound granular aggregates. International Journal of Pavement Engineering Vol.9, No.6, December 2008,387-395.
[116]N. Belheine, J.-P. Plassiard, F.-V. Donze, F. Darve, A. Seridi. Numerical simulation of drained triaxial test using 3D discrete element model ing[J]. Computers and Geotechnics,2009,36:320-331.
[117]周健,史旦达,贾敏才,闫东霄.砂土单调剪切力学性状的颗粒流模拟[J].同济大学学报(自然科学版),2007,10,35(10)：1299-1304.
[118]史旦达,周健,贾敏才,闫东霄.考虑颗粒破碎的砂土高应力一维压缩特性颗粒流模拟[J].岩土工程学报,2007,5,29(5)：736-742.
[119]吴剑,冯夏庭.高速剪切条件下土的颗粒流模拟[J].岩石力学与工程学报,2008,6,27(1)(增刊)：3054-3059.
[120]张晓平,吴顺川,张志增,胡波.含软弱夹层土样变形破坏过程细观数值模拟及分析[J].岩土力学,2008,5,29(5)：1201-1206.
[121]罗勇,龚晓南,连峰.三维离散颗粒单元模拟无黏性土的工程力学性质[J].岩土工程学报,2008,2,30(2)：292-297.
[122]刘君,刘福海,孔宪京.考虑破碎的堆石料颗粒流数值模拟[J].岩土力学,2009,29(增刊)：107—112.
[123]蒋明镜,李秀梅,孙渝刚,胡海军.考虑颗粒抗转动的砂土双轴试验离散元模拟[J].岩土力学,2009,(12)：514-517.
[124]蒋明镜,李秀梅.双轴压缩试验中砂土剪切带形成的离散元模拟分析[J].山东大学学报(工学版),2010,(4)：52-58.
[125]蒋明镜,肖俞,陈双林,胡海军,吴晓峰.砂土中单桩竖向抗压承载机制的离散元分析[J].岩土力学,2010,(11)：366-372.
[126]蒋明镜,胡海军.密实和松散颗粒材料等吸力三轴剪切试验离散元数值模拟[J].中南大学学报(自然科学版),2010(12)：2350-2359.
[127]井国庆,高亮,邵磊.吹砟车维修机理离散元仿真与应用[J].铁道工程学报,2011(11)：58-62.
[128]Jing, G. Q., Shao, L., Gao, L. Micro-analysis of railway ballast bond effects [J]. Advanced Materials Research,2012:2492-2496.
[129]Mindlin, R. D., Deresiewicz, H.,1953. Elastic spheres in contact under varying oblique forces[J]. ASME J. Appl. Mech.20,327-344.
[130]Hartr, Cundall P. A., Lemos J.. Formulation of a three-dimensional distinct element model——part Ⅱ:Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks[J]. International Journal of Rock Mechanics and Mining Scinces,1998,25(3):117-125.
[131]李广信.高等土力学[M].北京：清华大学出版社,第一版,2004.
[132]Cundall P. A., Strack 0. D. L.. Particle flow code in 3 Dimensions[A]. Itasca Consulting Group, Inc.,1999.
[133]Gye-Chun Cho, Jake Dodds, J. Carlos Santamarina. Particle Shape Effects on Packing Density, Stiffness, and Strength Natural and Crushed Sands[J]. Journal of geotechnical and geoenvironmental engineering,2006,5:591-602.
[134]D.0. Potyondy, P. A. Cundall. A bonded-particle model for rock[J]. International Journal of Rock Mechanics & Mining Sciences,2004,11(41):1329-1364.
[135]周健,池永.土的工程力学性质的颗粒流模拟[J].固体力学学报,2004,25(4)：377—382.
[136]邵磊,迟世春,贾宇峰.堆石料大三轴试验的细观模拟[J].岩土力学,2009,30(增刊)：239-243.
[137]陈希哲.粗粒土强度和咬合力的试验研究[J].工程力学,1994,11(4)：56—62.
[138]马刚,周伟,常晓林,周创兵.堆石体三轴剪切试验的三维细观数值模拟[J].岩土工程学报,2011,33(5)：746-753.
[139]Robertson, D., Bolton, M. D.. DEM simulations of crusha-ble grains and soils [J]. Proc. Powders and Grains,2001,623-626.
[140]Robertson, D.. Computer simulations of crushable aggregates [D]. PhD dissertation, Cambridge University,2000.
[141]邵磊,迟世春,李红军,温州.高心墙堆石坝极限抗震能力初探[J].岩土力学,2011,12,12(32)：3827-3832.
[142]郭熙灵,胡辉,包承纲.堆石料颗粒破碎对剪胀性及抗剪强度的影响[J].岩土工程学报,1997,5,3(19)：83-88.
[143]张启岳,司洪洋.粗颗粒土大型三轴压缩试验的强度与应力应变特性[J].水利学报,1982,9,9：22-31.
[144]傅华,凌华,蔡正银.粗颗粒土颗粒破碎影响因素试验研究[J].河海大学学报(自然科学版),2009,1,1(37)：75-79.
[145]Hardin, B.0. Crushing of soil particles[J].Geotech. Eng.,1985,111(10):1177-1192.
[146]Feda, J. Notes on the effect of grain crushing on the granular soil behavior [J]. Eng. Geol. (Amsterdam),2002,63:93-98.
[147]Lade, P. V., Yamamuro, J. A., Bopp, P. A.. Significance ofparticle crushing in granular materials[J]. J. Geotech. Eng.,1996,122(4):309-316.
[148]Lee, K. L., Farhoomand, I.. Compressibility and crushing ofgranular soil in anisotro-pic triaxial compress ion [J]. Canadian Geotechnical Journal,1967,4(1):68-86.
[149]Hagerty, M. M., Hite, D. R., Ulrich, C. R., and Hagerty, D. J.. One-dimensional high pressure compression of granular media[J]. Geotech. Eng.,1993,119(1):1-18.
[150]王芝银,李云鹏.岩体流变理论及其数值模拟[M].北京：科学出版社,2008.
[151]Kienzler R., Schmitt W.. On single-particle comminution:numerical analysis of compre王芝银d李云鹏heres [J]. Po[M]. Technol.,1990,61:29-38.
[152]沃国纬,王元淳.弹性力学[M].上海：上海交通大学出版社,1998,283-296.
[153]A. W. Larson, The effect of size and contact geometry in single particle crushing[D] Master's thesis, MIT, Boston,1986.
[154]D. Vallet, Jean-Claude Charmet. Mechanical behaviour of brittle cement grains [J]. Journal of Materials Science,1995, (30):2962-2967,
[155]Olivier Tsoungui, Denis Vallet, Jean-Claude Charmet. Numerical model of crushing of grains inside two-dimensional granular materials [J]. PowderTechnol.,1999,105: 190-198.
[156]何满潮,胡江春,熊伟,刘成禹.岩石抗拉强度特性的劈裂试验分析[J].矿业研究与开发,2005,4,25(2)：12-17.
[157]张少华,赵海云.岩石抗拉强度试验方法及其特征[J].矿山压力与顶板管理,1994,3：68-71.
[158]赵旭.不规则岩块抗拉强度的测定与计算[J].不规则岩块抗拉强度的测定与计算技术,1996,4,2：13-16.
[159]王启智,吴礼舟.用平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度—第二部分：试验结果[J].岩石力学与工程学报,2004,1,23(2)：199-204.
[160]贾愚如,范正绮.用水力破裂法测得岩石抗拉强度的统计方法[J].岩石力学与工程学报,1987,6,3：277-286.
[161]ISRM. Suggested methods for determining tensile strength of rock materials. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1978,15(3):99-103.
[162]中华人民共和国国家标准编写组.工程岩体试验方法标准(GB/T50266-99).北京：中国计划出版社,1999.
[163]ASTM. Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens (ASTM C496-86),1986:[s.l.]:[s.n.].
[164]曲嘉.钢纤维混凝土劈拉强度的实验研究[D].博士学位论文.哈尔滨工程大学,2010,6.
[165]Tsoungui 0., Vallet D., Charmet J. C., Roux S..Size efects in single grain fragmentation [J]. Granular Matter,1999,2,19-27.
[166]Alonso E. E., Oldecop L.. Long term behaviour and size effects of coarse granular media[J]. Mechanics of Natural Solids,2009,255-281.
[167]南京水利科学研究院.土工试验规程[M].北京：中国水利水电出版社,1999.
[168]Broek, D.. Elementary engineering fracture mechanics [M]. Dordrecht:Martinus Nijhoff.1986.
[169]Tada H., Paris P. C. and Irwin, G. R.. The stress analysis of cracks handbook[M], 2nd edn. St Louis, MO:Paris Productions,1985.
[170]Speidel M.O..The Theory of Stress Corrosion Cracking in Alloys[M]. Editor:J. C. Scully, North Atlantic Treaty Organization Scientific Affairs Division, Brussels, 1971,289-355.
[171]Charles, R. J.. Static fatigue of glass [J]. Journal of applied physics.1958,29(11), 1549-1560.
[172]Atkinson, B. K.. Subcritical crack growth in geological materials[J]. Journal of Geophysical Research.1984,89(6),4077-4114.
[173]Alonso E. E., Oldecop L.. Long term behaviour and size effects of coarse granular media[J]. Mechanics of Natural Solids,2009,255-281.
[174]Freiman, S. W.. Effects of chemical environments on slow crack growth in glasses and ceramics. J. Geophys. Res.,1984,89, No. B6:4072-4076.
[175]Sun, Z. and Ouchterlony, F,.Fracture toughness of stripa granite cores[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1986,Vol.23:399-409.
[176]Thiercelin, M. and Roegiers, J. C.. Toughness determination with the modified ring test[C]. Proceeding of 27th U.S. Symposium on rock mechanics:key to energy production,1986:615-622.
[177]Ouchterlony, F.. Suggested methods for determining the fracture toughness of rock[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1988, Vol.25, No.1:71-96.
[178]Singh, R.N. and Sun, G. X.. Relationships between fracture toughness, Hardness Indices and Mechanical Properties of Rocks, Mining Department Magazine, Department of Mining Engineering, University of Nottingham, England,1989:49-62.
[179]Singh, R. N. and Sun, G. X.. A Numerical and Experimental Investigation for Determining Fracture Toughness of Welsh Limestone, Mining Science & Technology, 1990a, Vol.1, No.10:61-70.
[180]Singh, R. N. and Sun, G. X.. An Investigation into the Factors Affecting the Fracture Toughness of Coal Measures Sandstones, Journal of Mines, Metals and Fuels,1990b, 7:11-118.
[181]Guo, H.. Rock Cutting using Fracture Mechanics Principles[D], PhD Dissertation, University of Wollongong, Australia,1990.
[182]Whittaker, B. N., Singh, R. N., and Sun, G.. Rock Fracture Mechanics-Principles[M] Design and Applications. Amsterdam:Elsevier,1992.
[183]Basham, K. D., Chong, K. P., and Boresi, A. P.. A New Method to Compute Size Independent Fracture Toughness Values for Brittle Materials[J]. Engineering Fracture Mechanics,1993,Vol.46, No.3:357-363.
[184]Baek, H.. Evaluation of Fracture Mechanics Properties and Microstructural Observa-tions of Rock Fractures [D], PhD Dissertation, University of Texas at Austin,1994.
[185]Haberfield, C.M. and I.W. Johnston. Determination of the Fracture Toughness of a Saturated Soft Rock [J], Canadian Geotechnical Journal,1990, Vol.27, No.6, pp. 276-284.
[186]Lim, I.L., Johnston, I.W., Choi, S. K., and Boland J. N.. Fracture Testing of a Soft Rock with Semi-Circular Specimens under Three Point Bending, Part 1:Mode-I [J]. International Journal of Rock Mechanics and Mining Sciences & GeomechanicsAbstracts,1994a, Vol.31, No.3:185-197.
[187]Lim, I.L., Johnston, I.W., Choi, S. K., and Boland J. N.. Fracture Testing of A Soft Rock with Semi-Circular Specimens under Three Point Bending, Part 2: Mixedmode, [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1994b,Vol.31, No.3, pp.199-212.
[188]Krishnan, G. R., Zhao, X. L., Zaman, M., and Roegiers, J. C.. Fracture Toughness of a Soft Sandstone[J]. International Journal of Rock Mechanics and Mining Sciences,1998, Vol.35, No.6:695-710.
[189]Nakagawa, S. and L. R. Myer. Mechanical and Acoustic Properties of Weakly Cemented Granular Rocks[C]. Proceedings of 38th U.S. Symposium on Rock Mechanics:Rock Mechanics in the National Interest,7-10, July, Washington D. C.,2001, Vol. 1:3-10.
[190]Atkinson, B. K. and Meredith, P. G.. Experimental Fracture Mechanics Data for Rocks and Minerals[M]. Fracture Mechanics of Rock, Editor:B. K. Atkinson, Academic Press Geology Series,1987:477-525.
[191]徐世娘.混凝土断裂机理[D].博士学位论文,大连理工大学,1988,4. (Xu Shi-lang. The mechanisms of concrete fracture[D]. PhD thesis, Dalian University of Technology, 1988,4.)
[192]黄达海,宋玉普.混凝土起裂韧度与断裂韧度的关系[J].水力发电学报,2000,1：92-100.
[193]Atkinson, B. K.. Subcritical crack growth in geological materials[J]. Journal of Geophysical Research.1984,89(6),4077-4114.
[194]Alonso E. E., Oldecop L.. Long term behaviour and size effects of coarse granular media[J]. Mechanics of Natural Solids,2009,255-281.
[195]Cundall P. A., Strack O. D. L.. Particle flow code in 3D Dimensions[A]. Itasca Consulting Group, Icn.,1999.
[196]于浩,李海芳,温彦锋,徐泽平.九甸峡堆石料三轴蠕变试验初探[J].岩土力学,2007,10,(S1)：103-106.
[197]黄宝涛.振动压实对道路材料空间组构及其力学性能演化的离散元模拟[D].博士学位论文.东南大学,2009,10.
[198]吴剑.滑带剪切过程的离散元模拟研究[D].博士学位论文.中国科学院武汉岩土力学研究所,2007,6.
[199]张锐.基于离散元细观分析的土壤动态行为研究[D].博士学位论文.吉林大学,2005,6.
[200]曾远.土体破坏细观机理及颗粒流数值模拟[D].博士学位论文.同济大学,2006,4.
[201]高红.岩土材料屈服破坏准则研究[D].博士学位论文.中国科学院武汉岩土力学研究所,2007,6.
[202]王者超,李术才.高应力下颗粒材料—维力学特性研究(Ⅰ)：压缩性质[J].岩士力学,2010,31(10)：3051-3057.
[203]杨新辉.脆性/韧性断裂机理与判据及裂尖变形理论研究[D].博士学位论文,大连理工大学2005,4.
[204]万琳辉,曹平,黄永恒,文有道,汪亦显.岩石亚临界裂纹扩展及其应用研究[J].科技导报,2010,9：42-46.
[205]肖洪天,杨若琼,周维垣.三峡船闸花岗岩亚临界裂纹扩展试验研究[J].岩石力学与工程学报,1999,18(4)：447-450.
[206]黎振兹,张静宜,刘大安,徐纪成,易建国,孙宗硕.岩石断裂力学测试与理论研究[J].中国有色金属学报,1994,12,4,(4)：18-21.
[207]贾学明,王启智.标定ISRM岩石断裂韧度新型试样CCNBD的应力强度因子[J].岩石力学与工程学报,2003,22(8)：1227-1233.
[208]肖洪天,周维垣.脆性岩石变形与破坏的细观力学模型研究[J].岩石力学与工程学报,2001,20(2)：151-155.
[209]袁海平,曹平,周正义.金川矿岩亚临界裂纹扩展试验研究[J].中南大学学报(自然科学版),2006,Vo1.37,No.2：381-384.
[210]谢其泰,王建力.石材亚临界裂纹扩展量测之研究[C].第一届中国水利水电岩土力学与工程学术讨论会论文集.2006：117-120.
[211]李江腾,曹平,袁海平.岩石亚临界裂纹扩展试验及门槛值研究[J].岩土工程学报,2006,Vo1.28,No.3：415-418.
[2]杨键.天生桥一级水电站面板堆石坝沉降分析[J].云南水力发电,2001,17(2)：59-63.
[3]赵魁芝,李国英,沈珠江.天生桥混凝土面板堆石坝原型观测资料反馈分析[J].水利水运科学研究,2000,(4)：15-19.
[4]赵魁芝,李国英,沈珠江.天生桥混凝土面板堆石坝面板原型观测资料分析[J].水利水运工程学报,2001,(1)：38-44.
[5]汪明元,何晓民,程展林.粗粒料流变研究的现状与展望[J].岩土力学,2003,10,(24)增刊：451-454.
[6]张亦昭,赵家旺.十三陵抽水蓄能电站上池面板堆石坝体的沉降变形[J].水利水电技术,1997,28(10)：27-31.
[7]Maranda das Neves E, Advances in Rockfill structure[M]. London:Kluwer Academic Publishers,1991.
[8]郦能惠.高混凝土面板堆石坝设计理念探讨[J].岩土工程学报,2007,29(8)：1143-1150.
[9]Cetin H., Laman M. and Ertunc A.. Settlement and slaking problems in the world's fourth largest rock-fill dam, the Ataturk Dam in Turkey [J]. Engineering Geological. 2000,56, No.3,225-242.
[10]花俊杰,周伟,常晓林,周创兵.300m级高堆石坝长期变形预测[J].四川大学学报(工程科学版),2011,43(3)：33-38.
[11]陈立宏,陈祖煜,张进平,赵春.小浪底大坝心墙中高孔隙水压力的研究[J].水利学报,2005,2,36(2)：219-224.
[12]Sowers G. F., Williams R. C. and Wallace T. S.. Compressibility of broken rock and the settlement of rockfills[C]. Proc.6th International Conference Soil Mechanical Foundation Engineering, Montreal 2,1965:561-565.
[13]Fumagalli E. Tests on cohesionless materials for rockfill dams[J]. Journal of Soil Mechanics and Foundation Engineering, ASCE,1969,95(SMI Division):313-330.
[14]Charles J. A.. Geotechnical properties of coarse grained soils[C]. Proceeding of 12th International Conference Soil Mechanical Foundation Engineering, Rio de Janeiro, General Report, Discussion Session 8,1989:2495-2519.
[15]Charles J. A.. Laboratory compression tests and the deformation of rockfill structures [J]. In Advances in Rockfill Structures. NATO ASI Series E,1991, Vol.200: 73-95.
[16]沈珠江,左元明.堆石料的流变特性试验研究[A].第6届土力学基础工程学术会议论文集 [C].上海：同济大学出版社,1991,443-446.
[17]沈珠江.土石料的流变模型及其应用[J].水利水运科学研究,1994,12(4)：335-342.
[18]沈珠江,赵魁芝.堆石坝流变变形的反馈分析[J].水利学报,1998,6(6)：1-6.
[19]蒋鹏,杨淑碧.成都地区卵石土流变特性及长期强度研究[J].地质灾害与环境保护,1998,9(1)：38—4.
[20]郭兴文,王德信,蔡新等.混凝土面板堆石坝流变分析[J].水利学报,1999,11(11)：42-46.
[21]陈峰,杨建贵,蔡新等.土石坝流变非线形分析[J].河海大学学报,1999,27(6)：20-24.
[22]Justo J. L. and Durand P.. Settlement-time behaviour of granular embankments[J]. International Journal of Numerical Analysis Methods Geomechanics,2000,24, No. 3:281-303.
[23]王勇,殷宗泽.一个用于面板坝流变分析的堆石料流变模型[J].岩土力学,2000,21(3)：227-230.
[24]王勇,殷宗泽.面板坝中堆石流变对面板应力变形的影响分析[J].河海大学学报,2000,11(6)：60—64.
[25]王勇.堆石流变的机理及研究方法初探[J].岩石力学与工程学报,2000,7,19(4)：526-530.
[26]Oldecop L. A. and Alonso E. E.. A model for rockfill compressibility[J]. Geotechnique,2001,51,2:127-139.
[27]Marsal R. J.. Mechanical properties of rockfill. In Embankment dam engineering. Casagrande Volume I (eds R. C. Hirschfeld and S. J. Poulos). New York:John Wiley & Sons,1973:110-200.
[28]Veiga Pinto A. A.. Previsa-o do comportamento estrutural de barragens de enrocamento[D]. PhD thesis, Laborato'rio Nacional de Engenharia Civil, Lisbon, 1983.
[29]梁军,刘汉龙.面板坝堆石料的蠕变试验研究[J].岩土工程学报,2002,24(2)：257-259
[30]梁军,刘汉龙,高玉峰.堆石蠕变机理分析与颗粒破碎特性研究[J].岩土力学,2003,6,24(3)：479-483.
[31]程展林,丁红顺.堆石料蠕变特性试验研究[J].岩土工程学报,2004,26(4)：473-476.
[32]汪明元,丁红顺,饶锡保,程展林.高堆石坝粗粒料的流变特性研究[C].中国水利水电工程未来与发展.大连,2002,9：381-385.
[33]李国英,米占宽,傅华,方维凤.混凝土面板堆石坝堆石料流变特性试验研究[J].岩土力学,2004,25(11)：1712-1716.
[34]左永振.粗粒料的蠕变和湿化试验研究[D].武汉：长江科学院,2008.
[35]王海俊,殷宗泽.堆石料长期变形的室内试验研究[J].水利学报,2007,8,38(8)：914-919.
[36]王海俊.土石坝堆石料的长期变形特性研究[D].南京：河海大学,2008.
[37]程展林,丁红顺,吴良平.粗粒土试验研究[J].岩土工程学报,2007,29(8)：1151-1158.
[38]周伟,胡颖,闫生存.高土石坝流变机理的组构理论分析方法[J].岩土工程学报,2007,29(8)：1274-1278.
[39]周伟,胡颖,杨启贵,熊泽斌.高混凝土面板堆石坝流变机理及长期变形预测[J].水利学报,2007,10(增刊)：100-105.
[40]Oldecop L. A. and Alonso E. E.. Theoretical investigation of the time-dependent behaviour of rockfill[J]. Geotechnique,2007,57,5:423-435.
[41]左永振,程展林,丁红顺,姜景山,孔宪勇.堆石料蠕变试验方法研究[J].长江科学院院报,2009,26(12)：63-66.
[42]朱晟,王永明,徐骞.粗粒筑坝材料的增量流变模型研究[J].岩土力学,2011,32(11)：3201-3206.
[43]李海芳,张茵琪,金伟,温彦锋,陈宁.两河口水电站混合料流变模型研究[J].西北地震学报,2011,33(z1)：285-289.
[44]花俊杰,周伟,常晓林,周创兵.300m级高堆石坝长期变形预测[J].四川大学学报(工程科学版),2011,5,34(3)：33-38.
[45]夏才初,刘大安.理论流变模型及其统一模型研究[C].中国岩石力学与工程学会第五届学术大会,上海,1998：134-140.
[46]Leung C. F., Lee F. H., and Yet N. S., The role of particle breakage in pile creep in sand[J]. Canada Geotechnology Journal,1996,33:888-898.
[47]Kranz R. L.. The Effects of confining pressure and stress difference on static fatigue of granite[J]. Journal of geophysical research,1980, Vol.85:1854-1866.
[48]Evans A. G..Fracture mechanics determinations [M]. Fracture mechanics of ceramics. Editors:R. C. Bradt, D. P. H. Hasselman, and F. F. Lange, Plenum Press, New York.1974, Vol.21,:17-48.
[49]Tait R. B. and Garrett G. G..A fracture mechanics evaluation of static and fatigue crack growth in cement mortar[C]. Proceedings of conference of fracture mechanics of concrete,1979:18-27.
[50]Taylor P. C. and Tait R. B.. Effects of fly ash on fatigue and fracture properties of hardened cement and mortar[J]. Cement & Concrete Composites,1999, Vol. 21:223-232.
[51]Scholz C. H..Static fatigue of quartz[J]. Journal of geophysical research.1972, Vol.77,No.11:2104-2114.
[52]Wilkins B. J. S.. Slow crack growth and delayed failure of granite[J]. International journal of rock mechanics and mining sciences & geomechanics abstracts,1980, Vol.17:365-369.
[53]Wiederhorn S. M., Fuller E. R. Jr. and Thomson R.. Micromechanisms of crack growth in ceramics and glasses in corrosive environments[J]. Metal Science,1980, August-September:450-458.
[54]Kjaernsli B. and Sande A.. Compressibility of some coarsegrained materials[C]. Proceeding Europa conference soil mechanics foundation engineering.1963,1: 245-251.
[55]Fumagalli E.. Tests on cohesionless materials for rockf ill dams[J]. Journal of soil mechanics foundation engineering.1969, ASCE95, No. SM1:313-330.
[56]Marachi N. D., Chan C. K., Seed H. B. and Duncan, J. M.. Strength and deformation characteristics of rockfill materials. Report No. TE-69-5. Department of Civil Engineering, University of California,1969.
[57]Nobari E. S. and Duncan J. M.. Effect of reservoir filling on stresses and movements in earth and rockfill dams.Report No. TE-72-1. Department of Civil Engineering, University of California,1972.
[58]Veiga Pinto A. A.. Previsa~o do comportamento estrutural de barragens de enrocamento [D]. PhD thesis, Laborato'rio Nacional de Engenharia Civil, Lisbon,1983.
[59]罗勇.土工问题的颗粒流数值模拟及应用研究[D].博士学位论文,2007,12.
[60]Cundall P. A.. A computer model for simulating Progerssive large Scale Movements in Bloeky Rock Systems. In:Proceeding of the symposium of the international society for rock mechanics. Nancy, France,1971,1(8).
[61]魏群.散体单元法的基本原理、数值方法与程序[M].北京：科学出版社,1991.
[62]Cundall, P. A. and Strack,0. D. L..A discrete numerical model for granular assemblies[J]. Geotechnique,1979,vol.29:47-65.
[63]Cundall P. A. & Strack 0. D. L.. The Distinct Element Method as a Tool for Research in Granular Media, Part II. Department of Civil and Mineral Engineering, University of Minnesota National Science Foundation,1979.
[64]Maini T., Cundall P. A..Computer modeling of jointed rock masses[R]. [AD—— A061658]:Defense Technical Information Center,1978.
[65]Lemos, J. V.,Roger, Hart, D.,Cundall, P. A..A Generalized Discrete Eclement Program for Modeling Joined Rock Mass, Proc. Of the Int. Symp. on Fundamentals of Rock Joins, Bjorkliden,1985,335-343.
[66]Lorig, L. J., Brady, B. G. and Cundall, P. A.. Hybrid Distinct Element-Boundary Element Analysis of Jointed Rock. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.,1986,23:303-312.
[67]Lorig, L. J. and Shoi, S. K.. Hydebe-User's Manual, Commonwealth Scientific and Industrial Research Organization, Austrilia,1986.
[68]王泳嘉.离散单元法一种适用于节理岩石力学分析的数值方法.第一届全国岩石力学数值计算及模型实验讨论会文集,1986.
[69]王泳嘉,刑纪波.离散元法及其在岩土力学中的应用.辽宁：东北大学出版社,1991.
[70]Shi, G. H.. Discontinuous Deformation Analysis:A New Numerical Model for the Statics and Dynamics of Block Systems[D]. PhD Thesis. University of California, Berkeley.1988.
[71]石根华.数值流行方法与非连续变形分析[M].裴觉民译.北京：清华大学出版社,1997.
[72]Shi, G. H.. Manifold method of material analysis[C]. Transaction of the 9th Army Conference on Applied Mathematics and Computing, Minneapolis, Minnesota, 1991:57-76.
[73]Shi, G. H.. Manifold metho[C]d. Proceeding of first International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. TSI Press, Albuquerque, NM, Mexico,1996:52-204.
[74]Shi, G. H.. Producing Joint Polygons[J], cutting joint blocks and finding key blocks for general free surfaces. Chinese Journal of Rock Mechanics and Engineering, 2006,25:2161-2170.
[75]Goodman R. E., Shi G. H., Boyle W..Calculation of support for hard, jointed rock using the key block principle[C]. Proceedings of the 23rd US Symposium of Rock Mechanics.1982:883-898.
[76]Goodman R. E.. Block theory and its application[J]. Geotechnique,1995,45 (3):383-423.
[77]Wei Q, Zhang J. J.. Development and application of laser speckle technique in rock tests of hydropower project [C]. Proceedings of ISRM International Symposium on Rock Mechanics and Power Planets.,1988:527-534.
[78]魏群,刘光廷,陈兴华,等.颗粒组合体变形特性的离散元数值模拟方法[C].岩土力学新分析方法讨论会会议文集.上海：同济大学出版社,1989：212-217.
[79]Wei Q.. Discrete element method and its application in jointed rock stability of hydropower projects [C]. Proceedings of the International Symposium on Rock Joints. 1990:759-765.
[80]魏群,陈兴华,刘光廷.颗粒体应力应变的散体元数值计算及验证实验[C].第二届全国岩土工程数值方法的工程应用学术研讨会议文集.上海：同济大学出版社,1990：629-635.
[81]魏群.岩土工程中散体元的基本原理数值方法及实验研究[博士学位论文][D].北京：清华大学,1990.
[82]魏群,张镜剑.颗粒体应力应变的张量表达式在散体元计算中的实施[C].第二届全国岩土工程数值方法的工程应用学术研讨会议文集.上海：上海同济大学出版社,1990：445-451.
[83]魏群,陈兴华.任意形状离散颗粒组合体的计算机模拟方法[C].第四届全国岩石混凝土断裂力学会论文集.1990：1-6.
[84]WEI Q, ZHANG M W. Investigation of crack opening displacement field of concrete beam during stable crack growth with white light speckle method[C]. Proceedings of the 10th Congress on Material Testing, Hungary. [S.1.]:[s. n.],1991:1-6.
[85]魏群.颗粒散体元-散体运动细观分析的一种新方法[C].全国土木工程青年计算机工作者学术论文集.南京：东南大学出版社,1991：599-603.
[86]魏群.椭圆散体元：一种模拟颗粒组合体的新方法[C].水电与矿业工程中的岩石力学问题.北京：科学出版社,1991：224-232.
[87]冯树仁,刘泉声,葛修润等.三维离散单元法及其在滑坡分析中的应用[J].岩土工程学报,2000,22(1)：101—104.
[88]葛修润,焦玉勇.基于静态松弛法求解的三维离散单元法[J].岩石力学与工程学报,200019(4)：451-456.
[89]葛修润,姜清辉,焦玉勇.三维静态同步松弛的离散单元法.中国矿业大学学报,2002,31(4)：338-343.
[90]焦玉勇.三维离散单元法及其应用[D].博士学位论文,中国科学院武汉岩土力学研所,1998.
[91]伍四明,李日国.万县滑坡群形成机制的数值模拟研究[J].水文地质工程地质,1996,6：14-17.
[92]金仁祥,晏鄂川,刘汉超.麻六嘴滑坡成因机制离散元数值模拟[J].地质灾害与环境保护,2000,11(1)：63-66.
[93]毛彦龙,胡广韬,毛新虎等.地震滑坡启程剧动的机理研究及离散元模拟[J].工程地质学报,2001,9(1)：74-80.
[94]安关峰,殷坤龙,唐辉明.黄土坡滑坡的离散元研究[J].中国地质大学学报,2002，27(4)：357-359.
[95]殷坤龙,姜清辉,汪洋.新滩滑坡运动全过程的非连续变形分析与仿真模拟[J].岩石力学与工程学报,2002,21(7)：959-962.
[96]汪洋,姜清辉,殷坤龙.滑坡运动过程仿真分析[J].中国地质大学学报,2002，27(5)：632-636.
[97]Cundall, P. A. and Hart, R. D.. Numerical modeling of discontinua[J]. Engineering Computations,1992,vol.9:101-113.
[98]Bardet J. P., Proubet J. A.. Numerical investigation of stulcture of persistent shear bands in granular media[J].Geotechnique,1991,41(4):599-613.
[99]Bardet J. P., Proubet J. A..Shear-band analysis in idealized granular material [J]. Engineering Mechanics,1992,118(8):397-415.
[100]Ng, T. T..Fabric study of granular materials after compaction[J]. Journal of Engineering Mechanics,1999, vol.125, no.12,1390-1394.
[101]Olivier Tsoungui, Denis Vallet and Jean-Claude Charmet. Numerical model of crushing of grains inside two-dimensional granular materials[J]. Powder Technology, 1999,105:190-198.
[102]Antony, S. J.. Evolution of force distribution in three-dimensional granular media [J].Physical Review,2000, vol.63,011302.
[103]周健,池永,池毓蔚,徐建平.颗粒流方法及PFC2D程序[J].岩土力学,2000,9,21(3)：271-274.
[104]周健,池毓蔚,池永,徐建平.砂土双轴试验的颗粒流模拟[J].岩土工程学报,2000,11,22(6)：701-704.
[105]周健,廖雄华,池永,徐建平.士的室内平面应变试验的颗粒流模拟[J].同济大学学报,2002,9,30(9)：1044-1500.
[106]周健,池永.砂土力学性质的细观模拟[J].岩土力学,2003,12,24(6)：901-906.
[107]McDowell G. R. and Harireche O.. Discrete-element modeling of yielding and normal compression of sand [J]. Geotechnique,2002,52(4):299-304.
[108]Cheng, Y. P., Nakata, Y. and Bolton, M. D.. Discrete element simulation of crushable soil[J]. Geote-chnique,2003,53(7):633-641.
[109]Potyondy D.0.,Cundall P. A.. Abonded-particle model for rock[J]. International Journal of Rock Mechanics & Mining Sciences,2004,11(41):1329-1364.
[110]Lim W. L. and G. R. McDowell. Discrete element modelling of railway ballast[J]. Granular Matter,2005,7 (1):19-29.
[111]Sebastian Lobo-Guerrero, Luis F. Vesga, Luis E. Vallejo. Discrete element method evaluation of granular crushing under direct shear condit ions[J]. Journal of geotechnical and environmental engineering,2005,131(10):1295-1300.
[112]Sebastian Lobo-Guerrero, Luis E. Vallejo, and Luis F. Vesga. Visualization of crushing evolution in granular materials under compression using DEM[J]. International journal of geomechanics,2006,6(3):195-200.
[113]N. Cho, C.D. Martin, D. C. Sego. A clumped particle model for rock[J]. International Journal of Rock Mechanics & Mining Sciences,2007,44:997-1010.
[114]M. Lu, G. R. McDowell. The importance of modelling ballast particle shape in the discrete element method [J]. Granular Matter,2007,9:69-80.
[115]L. Uthus, M. A. Hopkins and I. Horvli. Discrete element modelling of the resilient behaviour of unbound granular aggregates. International Journal of Pavement Engineering Vol.9, No.6, December 2008,387-395.
[116]N. Belheine, J.-P. Plassiard, F.-V. Donze, F. Darve, A. Seridi. Numerical simulation of drained triaxial test using 3D discrete element model ing[J]. Computers and Geotechnics,2009,36:320-331.
[117]周健,史旦达,贾敏才,闫东霄.砂土单调剪切力学性状的颗粒流模拟[J].同济大学学报(自然科学版),2007,10,35(10)：1299-1304.
[118]史旦达,周健,贾敏才,闫东霄.考虑颗粒破碎的砂土高应力一维压缩特性颗粒流模拟[J].岩土工程学报,2007,5,29(5)：736-742.
[119]吴剑,冯夏庭.高速剪切条件下土的颗粒流模拟[J].岩石力学与工程学报,2008,6,27(1)(增刊)：3054-3059.
[120]张晓平,吴顺川,张志增,胡波.含软弱夹层土样变形破坏过程细观数值模拟及分析[J].岩土力学,2008,5,29(5)：1201-1206.
[121]罗勇,龚晓南,连峰.三维离散颗粒单元模拟无黏性土的工程力学性质[J].岩土工程学报,2008,2,30(2)：292-297.
[122]刘君,刘福海,孔宪京.考虑破碎的堆石料颗粒流数值模拟[J].岩土力学,2009,29(增刊)：107—112.
[123]蒋明镜,李秀梅,孙渝刚,胡海军.考虑颗粒抗转动的砂土双轴试验离散元模拟[J].岩土力学,2009,(12)：514-517.
[124]蒋明镜,李秀梅.双轴压缩试验中砂土剪切带形成的离散元模拟分析[J].山东大学学报(工学版),2010,(4)：52-58.
[125]蒋明镜,肖俞,陈双林,胡海军,吴晓峰.砂土中单桩竖向抗压承载机制的离散元分析[J].岩土力学,2010,(11)：366-372.
[126]蒋明镜,胡海军.密实和松散颗粒材料等吸力三轴剪切试验离散元数值模拟[J].中南大学学报(自然科学版),2010(12)：2350-2359.
[127]井国庆,高亮,邵磊.吹砟车维修机理离散元仿真与应用[J].铁道工程学报,2011(11)：58-62.
[128]Jing, G. Q., Shao, L., Gao, L. Micro-analysis of railway ballast bond effects [J]. Advanced Materials Research,2012:2492-2496.
[129]Mindlin, R. D., Deresiewicz, H.,1953. Elastic spheres in contact under varying oblique forces[J]. ASME J. Appl. Mech.20,327-344.
[130]Hartr, Cundall P. A., Lemos J.. Formulation of a three-dimensional distinct element model——part Ⅱ:Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks[J]. International Journal of Rock Mechanics and Mining Scinces,1998,25(3):117-125.
[131]李广信.高等土力学[M].北京：清华大学出版社,第一版,2004.
[132]Cundall P. A., Strack 0. D. L.. Particle flow code in 3 Dimensions[A]. Itasca Consulting Group, Inc.,1999.
[133]Gye-Chun Cho, Jake Dodds, J. Carlos Santamarina. Particle Shape Effects on Packing Density, Stiffness, and Strength Natural and Crushed Sands[J]. Journal of geotechnical and geoenvironmental engineering,2006,5:591-602.
[134]D.0. Potyondy, P. A. Cundall. A bonded-particle model for rock[J]. International Journal of Rock Mechanics & Mining Sciences,2004,11(41):1329-1364.
[135]周健,池永.土的工程力学性质的颗粒流模拟[J].固体力学学报,2004,25(4)：377—382.
[136]邵磊,迟世春,贾宇峰.堆石料大三轴试验的细观模拟[J].岩土力学,2009,30(增刊)：239-243.
[137]陈希哲.粗粒土强度和咬合力的试验研究[J].工程力学,1994,11(4)：56—62.
[138]马刚,周伟,常晓林,周创兵.堆石体三轴剪切试验的三维细观数值模拟[J].岩土工程学报,2011,33(5)：746-753.
[139]Robertson, D., Bolton, M. D.. DEM simulations of crusha-ble grains and soils [J]. Proc. Powders and Grains,2001,623-626.
[140]Robertson, D.. Computer simulations of crushable aggregates [D]. PhD dissertation, Cambridge University,2000.
[141]邵磊,迟世春,李红军,温州.高心墙堆石坝极限抗震能力初探[J].岩土力学,2011,12,12(32)：3827-3832.
[142]郭熙灵,胡辉,包承纲.堆石料颗粒破碎对剪胀性及抗剪强度的影响[J].岩土工程学报,1997,5,3(19)：83-88.
[143]张启岳,司洪洋.粗颗粒土大型三轴压缩试验的强度与应力应变特性[J].水利学报,1982,9,9：22-31.
[144]傅华,凌华,蔡正银.粗颗粒土颗粒破碎影响因素试验研究[J].河海大学学报(自然科学版),2009,1,1(37)：75-79.
[145]Hardin, B.0. Crushing of soil particles[J].Geotech. Eng.,1985,111(10):1177-1192.
[146]Feda, J. Notes on the effect of grain crushing on the granular soil behavior [J]. Eng. Geol. (Amsterdam),2002,63:93-98.
[147]Lade, P. V., Yamamuro, J. A., Bopp, P. A.. Significance ofparticle crushing in granular materials[J]. J. Geotech. Eng.,1996,122(4):309-316.
[148]Lee, K. L., Farhoomand, I.. Compressibility and crushing ofgranular soil in anisotro-pic triaxial compress ion [J]. Canadian Geotechnical Journal,1967,4(1):68-86.
[149]Hagerty, M. M., Hite, D. R., Ulrich, C. R., and Hagerty, D. J.. One-dimensional high pressure compression of granular media[J]. Geotech. Eng.,1993,119(1):1-18.
[150]王芝银,李云鹏.岩体流变理论及其数值模拟[M].北京：科学出版社,2008.
[151]Kienzler R., Schmitt W.. On single-particle comminution:numerical analysis of compre王芝银d李云鹏heres [J]. Po[M]. Technol.,1990,61:29-38.
[152]沃国纬,王元淳.弹性力学[M].上海：上海交通大学出版社,1998,283-296.
[153]A. W. Larson, The effect of size and contact geometry in single particle crushing[D] Master's thesis, MIT, Boston,1986.
[154]D. Vallet, Jean-Claude Charmet. Mechanical behaviour of brittle cement grains [J]. Journal of Materials Science,1995, (30):2962-2967,
[155]Olivier Tsoungui, Denis Vallet, Jean-Claude Charmet. Numerical model of crushing of grains inside two-dimensional granular materials [J]. PowderTechnol.,1999,105: 190-198.
[156]何满潮,胡江春,熊伟,刘成禹.岩石抗拉强度特性的劈裂试验分析[J].矿业研究与开发,2005,4,25(2)：12-17.
[157]张少华,赵海云.岩石抗拉强度试验方法及其特征[J].矿山压力与顶板管理,1994,3：68-71.
[158]赵旭.不规则岩块抗拉强度的测定与计算[J].不规则岩块抗拉强度的测定与计算技术,1996,4,2：13-16.
[159]王启智,吴礼舟.用平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度—第二部分：试验结果[J].岩石力学与工程学报,2004,1,23(2)：199-204.
[160]贾愚如,范正绮.用水力破裂法测得岩石抗拉强度的统计方法[J].岩石力学与工程学报,1987,6,3：277-286.
[161]ISRM. Suggested methods for determining tensile strength of rock materials. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1978,15(3):99-103.
[162]中华人民共和国国家标准编写组.工程岩体试验方法标准(GB/T50266-99).北京：中国计划出版社,1999.
[163]ASTM. Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens (ASTM C496-86),1986:[s.l.]:[s.n.].
[164]曲嘉.钢纤维混凝土劈拉强度的实验研究[D].博士学位论文.哈尔滨工程大学,2010,6.
[165]Tsoungui 0., Vallet D., Charmet J. C., Roux S..Size efects in single grain fragmentation [J]. Granular Matter,1999,2,19-27.
[166]Alonso E. E., Oldecop L.. Long term behaviour and size effects of coarse granular media[J]. Mechanics of Natural Solids,2009,255-281.
[167]南京水利科学研究院.土工试验规程[M].北京：中国水利水电出版社,1999.
[168]Broek, D.. Elementary engineering fracture mechanics [M]. Dordrecht:Martinus Nijhoff.1986.
[169]Tada H., Paris P. C. and Irwin, G. R.. The stress analysis of cracks handbook[M], 2nd edn. St Louis, MO:Paris Productions,1985.
[170]Speidel M.O..The Theory of Stress Corrosion Cracking in Alloys[M]. Editor:J. C. Scully, North Atlantic Treaty Organization Scientific Affairs Division, Brussels, 1971,289-355.
[171]Charles, R. J.. Static fatigue of glass [J]. Journal of applied physics.1958,29(11), 1549-1560.
[172]Atkinson, B. K.. Subcritical crack growth in geological materials[J]. Journal of Geophysical Research.1984,89(6),4077-4114.
[173]Alonso E. E., Oldecop L.. Long term behaviour and size effects of coarse granular media[J]. Mechanics of Natural Solids,2009,255-281.
[174]Freiman, S. W.. Effects of chemical environments on slow crack growth in glasses and ceramics. J. Geophys. Res.,1984,89, No. B6:4072-4076.
[175]Sun, Z. and Ouchterlony, F,.Fracture toughness of stripa granite cores[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1986,Vol.23:399-409.
[176]Thiercelin, M. and Roegiers, J. C.. Toughness determination with the modified ring test[C]. Proceeding of 27th U.S. Symposium on rock mechanics:key to energy production,1986:615-622.
[177]Ouchterlony, F.. Suggested methods for determining the fracture toughness of rock[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1988, Vol.25, No.1:71-96.
[178]Singh, R.N. and Sun, G. X.. Relationships between fracture toughness, Hardness Indices and Mechanical Properties of Rocks, Mining Department Magazine, Department of Mining Engineering, University of Nottingham, England,1989:49-62.
[179]Singh, R. N. and Sun, G. X.. A Numerical and Experimental Investigation for Determining Fracture Toughness of Welsh Limestone, Mining Science & Technology, 1990a, Vol.1, No.10:61-70.
[180]Singh, R. N. and Sun, G. X.. An Investigation into the Factors Affecting the Fracture Toughness of Coal Measures Sandstones, Journal of Mines, Metals and Fuels,1990b, 7:11-118.
[181]Guo, H.. Rock Cutting using Fracture Mechanics Principles[D], PhD Dissertation, University of Wollongong, Australia,1990.
[182]Whittaker, B. N., Singh, R. N., and Sun, G.. Rock Fracture Mechanics-Principles[M] Design and Applications. Amsterdam:Elsevier,1992.
[183]Basham, K. D., Chong, K. P., and Boresi, A. P.. A New Method to Compute Size Independent Fracture Toughness Values for Brittle Materials[J]. Engineering Fracture Mechanics,1993,Vol.46, No.3:357-363.
[184]Baek, H.. Evaluation of Fracture Mechanics Properties and Microstructural Observa-tions of Rock Fractures [D], PhD Dissertation, University of Texas at Austin,1994.
[185]Haberfield, C.M. and I.W. Johnston. Determination of the Fracture Toughness of a Saturated Soft Rock [J], Canadian Geotechnical Journal,1990, Vol.27, No.6, pp. 276-284.
[186]Lim, I.L., Johnston, I.W., Choi, S. K., and Boland J. N.. Fracture Testing of a Soft Rock with Semi-Circular Specimens under Three Point Bending, Part 1:Mode-I [J]. International Journal of Rock Mechanics and Mining Sciences & GeomechanicsAbstracts,1994a, Vol.31, No.3:185-197.
[187]Lim, I.L., Johnston, I.W., Choi, S. K., and Boland J. N.. Fracture Testing of A Soft Rock with Semi-Circular Specimens under Three Point Bending, Part 2: Mixedmode, [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1994b,Vol.31, No.3, pp.199-212.
[188]Krishnan, G. R., Zhao, X. L., Zaman, M., and Roegiers, J. C.. Fracture Toughness of a Soft Sandstone[J]. International Journal of Rock Mechanics and Mining Sciences,1998, Vol.35, No.6:695-710.
[189]Nakagawa, S. and L. R. Myer. Mechanical and Acoustic Properties of Weakly Cemented Granular Rocks[C]. Proceedings of 38th U.S. Symposium on Rock Mechanics:Rock Mechanics in the National Interest,7-10, July, Washington D. C.,2001, Vol. 1:3-10.
[190]Atkinson, B. K. and Meredith, P. G.. Experimental Fracture Mechanics Data for Rocks and Minerals[M]. Fracture Mechanics of Rock, Editor:B. K. Atkinson, Academic Press Geology Series,1987:477-525.
[191]徐世娘.混凝土断裂机理[D].博士学位论文,大连理工大学,1988,4. (Xu Shi-lang. The mechanisms of concrete fracture[D]. PhD thesis, Dalian University of Technology, 1988,4.)
[192]黄达海,宋玉普.混凝土起裂韧度与断裂韧度的关系[J].水力发电学报,2000,1：92-100.
[193]Atkinson, B. K.. Subcritical crack growth in geological materials[J]. Journal of Geophysical Research.1984,89(6),4077-4114.
[194]Alonso E. E., Oldecop L.. Long term behaviour and size effects of coarse granular media[J]. Mechanics of Natural Solids,2009,255-281.
[195]Cundall P. A., Strack O. D. L.. Particle flow code in 3D Dimensions[A]. Itasca Consulting Group, Icn.,1999.
[196]于浩,李海芳,温彦锋,徐泽平.九甸峡堆石料三轴蠕变试验初探[J].岩土力学,2007,10,(S1)：103-106.
[197]黄宝涛.振动压实对道路材料空间组构及其力学性能演化的离散元模拟[D].博士学位论文.东南大学,2009,10.
[198]吴剑.滑带剪切过程的离散元模拟研究[D].博士学位论文.中国科学院武汉岩土力学研究所,2007,6.
[199]张锐.基于离散元细观分析的土壤动态行为研究[D].博士学位论文.吉林大学,2005,6.
[200]曾远.土体破坏细观机理及颗粒流数值模拟[D].博士学位论文.同济大学,2006,4.
[201]高红.岩土材料屈服破坏准则研究[D].博士学位论文.中国科学院武汉岩土力学研究所,2007,6.
[202]王者超,李术才.高应力下颗粒材料—维力学特性研究(Ⅰ)：压缩性质[J].岩士力学,2010,31(10)：3051-3057.
[203]杨新辉.脆性/韧性断裂机理与判据及裂尖变形理论研究[D].博士学位论文,大连理工大学2005,4.
[204]万琳辉,曹平,黄永恒,文有道,汪亦显.岩石亚临界裂纹扩展及其应用研究[J].科技导报,2010,9：42-46.
[205]肖洪天,杨若琼,周维垣.三峡船闸花岗岩亚临界裂纹扩展试验研究[J].岩石力学与工程学报,1999,18(4)：447-450.
[206]黎振兹,张静宜,刘大安,徐纪成,易建国,孙宗硕.岩石断裂力学测试与理论研究[J].中国有色金属学报,1994,12,4,(4)：18-21.
[207]贾学明,王启智.标定ISRM岩石断裂韧度新型试样CCNBD的应力强度因子[J].岩石力学与工程学报,2003,22(8)：1227-1233.
[208]肖洪天,周维垣.脆性岩石变形与破坏的细观力学模型研究[J].岩石力学与工程学报,2001,20(2)：151-155.
[209]袁海平,曹平,周正义.金川矿岩亚临界裂纹扩展试验研究[J].中南大学学报(自然科学版),2006,Vo1.37,No.2：381-384.
[210]谢其泰,王建力.石材亚临界裂纹扩展量测之研究[C].第一届中国水利水电岩土力学与工程学术讨论会论文集.2006：117-120.
[211]李江腾,曹平,袁海平.岩石亚临界裂纹扩展试验及门槛值研究[J].岩土工程学报,2006,Vo1.28,No.3：415-418.