(1. CNNC/BRIUG Division of Environment Engineering,Beijing 100029,China;2. College of Water Resources and Hydropower,Sichuan University,Chengdu,Sichuan 610065,China,3. University of Lille1,Lille 59660,France)
Abstract:Based on the mechanical investigation,a coupled elastoplastic damage model is proposed to simulate the mechanical behaviour and damage evolution process of the intact deep granite in Beishan area. The experimental results revealed that Beishan granite exhibits typical brittle failure mode under low confining pressure. With the increase of confining pressure,the brittle-ductile transition of the mechanical behaviour took place;and significant plastic deformation and volumetric dilatation are noticed. The damage evolution process is also analyzed according to the initiation and propagation characteristics of the stress-induced microcracks. It is indicated that the failure and nonlinear mechanical behaviour of Beishan granite are essentially related to the coupling effect between the damage and plastic deformation. Based on this acknowledgement,a coupled elastoplastic damage model is proposed. In the model,a non-associated plastic flow rule is used to describe the compression-dilatation transition of the volumetric deformation. The coupling between the damage and plastic deformation is realised by introducing the independent damage variable in the plastic yield surface. The comparison between the predictive result and experimental data suggests that the proposed model is capable to reproduce the main mechanical performances of Beishan granite under compressive stress condition,especially the brittle-ductile transition of mechanical behaviour with the increase of confining pressure.
[1] 潘自强,钱七虎. 高放废物地质处置战略研究[M]. 北京:原子能出版社,2009:37–39.(PAN Ziqiang,QIAN Qihu. Strategic research for deep geological disposal of high level radioactive waste[M]. Beijing:Atomic Energy Press,2009:37–39.(in Chinese))
[2] 王 驹,范显华,徐国庆,等. 中国高放废物地质处置十年进展[M]. 北京:原子能出版社,2004:1–12.(WANG Ju,FAN Xianhua,XU Guoqing,et al. Geological disposal of high-level radioactive waste in China:progress in last decade[M]. Beijing:Atomic Energy Press,2004:1–12.(in Chinese))
[3] SHAO J F,CHAU KT,FENG X T. Modeling of anisotropic damage and creep deformation in brittle rocks[J]. International Journal of Rock Mechanics and Mining Sciences,2006,43(4):582–592.
[4] 刘泉生,胡云华,刘 滨. 基于试验的花岗岩渐进破坏本构模型研究[J]. 岩土力学,2009,30(2):289–296.(LIU Quansheng,HU Yunhua,LIU Bin. Progressive damage constitutive models of granite based on experimental results[J]. Rock and Soil Mechanics,2009,30(2):289–296.(in Chinese))
[5] NAWROCKI P A,DUSSEAULT M B. Modeling of damaged zones around openings using radius dependent Young?s modulus[J]. Rock Mechanics and Rock Engineering,1995,28(4):227–239.
[6] 杨 强. 岩体损伤力学发展现状和面临的问题[C]// 中国岩石力学与工程学会第七次学术大会论文集. 西安:中国科学技术出版社, 2002:46–50.(YANG Qiang. The state of art and problems in rock damage mechanics[C]// Proceedings of the 7th Symposium of the Institute of Chinese Rock Mechanics and Engineering. Xi?an:Chinese Science and Technology Press,2002:46–50.(in Chinese))
[7] JU J W. On energy based coupled elastoplastic damage theories:constitutive modeling and computational aspects[J]. International Journal of Solids and Structures,1989,25(7):803–833.
[8] SHAO J F,JIA Y,KONDO D,et al. A coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions[J]. Mechanics of Materials,2006,38(3):218–232.
[9] CHEN L, SHAO J F,HUANG H W. Coupled elastoplastic damage modeling of anisotropic rocks[J]. Computers and Geotechnics,2010,37(1/2):187–194.
[10] 胡云华. 高应力下花岗岩力学特性试验及本构模型研究[博士学位论文][D]. 武汉:中国科学院武汉岩土力学研究所,2008.(HU yunhua. Study on mechanical properties of granites under high pressure conditions and its constitutive models[Ph. D. Thesis][D]. Wuhan:Institute of Rock and Soil mechanics,Chinese Academy of Sciences,2008.(in Chinese))
[11] 余寿文,冯西桥. 损伤力学[M]. 北京:清华大学出版社,1997:78–92.(YU Shouwen,FENG Xiqiao. Damage mechanics[M]. Beijing:Tsinghua University Press,1997:78–92.(in Chinese))
[12] FENG X Q,QIN Q H,YU S W. Quasi-micromechanical damage model for brittle solids with interacting microcracks[J]. Mechanics of Materials,2004,36(3):261–273.
[13] 高蕴昕,郑泉水,余寿文. 各向同性弹性损伤的双标量描述[J]. 力学学报,1996,28(5):542–549.(GAO Yunxin,ZHENG Quanshui, YU Shouwen. Double-scalar formulation of isotropic elastic damage[J]. Chinese Journal of Theoretical and Applied Mechanics,1996,28(5):542–549.(in Chinese))
[14] ZHENG Q S,BELTEN J. On damage effective stress and equivalence hypothesis[J]. International Journal of Damage Mechanics,1996,5(3):219–240.
[15] 杨 强,陈 新,周维垣. 岩土材料弹塑性损伤模型及变形局部化分析[J]. 岩石力学与工程学报,2004,23(21):3 577–3 583.(YANG Qiang,CHEN Xin,ZHOU Weiyuan. Elasto-plastic damage model for geomaterials and strain localization analyses[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(21):3 577–3 583.(in Chinese))
[16] SHAO J F,HOXHA D,BART M. et al. Modelling of induced anisotropic damage in granites[J]. International Journal of Rock Mechanics and Mining Sciences,1999,36(8):1 001–1 012.
[17] WANG J. High-level radioactive waste disposal in China:update 2010[J]. Journal of Rock Mechanics and Geotechnical Engineering,2010,2(1):1–11.
[18] 刘月妙,王 驹,谭国焕,等. 高放废物处置北山预选区深部完整岩石基本物理力学性能及时温效应[J]. 岩石力学与工程学报,2007,26(10):2 034–2 042.(LIU Yuemiao,WANG Ju,THAM L G,et al. Basic physico-mechanical properties and time-temperature effect of deep intact rock from Beishan preselected area for high-level radioactive waste disposal[J]. Chinese Journal of Rock Mechanics and Engineering,2007,26(10):2 034–2 042.(in Chinese))
[19] 杨春和,王贵宾,王 驹,等. 甘肃北山预选区岩体力学与渗流特性研究[J]. 岩石力学与工程学报,2006,25(4):825–832.(YANG Chunhe,WANG Guibin,WANG Ju,et al. Study on rock mass mechanics and seepage characteristics of candidate site-Beishan,Gansu Province[J]. Chinese Journal of Rock Mechanics and Engineering,2006,25(4):825–832.(in Chinese))
[20] MAZARS J,PIJAUDIER-CABOT G. Continuum damage theory- application to concrete[J]. Journal of Engineering Mechanics,1989,115(2):345–365.
[21] RAMTANI S,BERTHAUD Y,MAZARS J. Orthotropic behavior of concrete with directional aspects:modeling and experiments[J]. Nuclear Engineering and Design,1992,133(1):97–111.
[22] 中华人民共和国国家标准编写组. GB/T50266—99 工程岩体试验方法标准[S]. 北京:中国计划出版社,1999.(The National Standards Compilation Group of People?s Republic of China. GB/T50266—99 Standard for tests method of engineering rock masses[S]. Beijing:China Planning Press,1999.(in Chinese))
[23] 中华人民共和国行业标准编写组. SL264—2001 水利水电工程岩石试验规程[S]. 北京:中国水利水电出版社,2001.(The Professional Standard Compilation Group of People?s Republic of China. SL264—2001 Specifications for rock tests in water conservancy and hydroelectric engineering[S]. Beijing:China Water Power Press,2001.(in Chinese))
[24] 谢和平. 岩石混凝土损伤力学[M]. 徐州:中国矿业大学出版社,1990:136–152.(XIE Heping. Damage mechanics of rock and concrete[M]. Xuzhou:China University of Mining and Technology Press,1990:136–152.(in Chinese))
[25] 谢和平,陈志达. 岩石的连续损伤力学模型探讨[J]. 煤炭学报,1998,23(2):32–42.(XIE Heping,CHEN Zhida. Study of a rock model with continuous damage mechanics[J]. Journal of China Coal Society,1998,23(2):32–42.(in Chinese))
[26] 彭瑞东,谢和平,鞠 杨. 砂岩拉伸过程中的能量耗散与损伤演化分析[J]. 岩石力学与工程学报,2007,26(12):2 526–2 531.(PENG Ruidong,XIE Heping,JU Yang. Analysis of energy dissipation and damage evolution of sandstone during tensile process[J]. Chinese Journal of Rock Mechanics and Engineering,2007,26(12):2 526–2 531.(in Chinese))
[27] LEMAITRE J. Evolution of dissipation and damage in metals submitted to dynamic loading[C]// Proceedings of ICM–1. Kyoto,Japan:[s. n.],1968:151–157.
[28] ZHU Q Z,KONDO D,SHAO J F. Micromechanical analysis of coupling between anisotropic damage and friction in quasi brittle material:Role of the homogenization scheme[J]. International Journal of Solids and Structures,2008,45(5):1 385–1 405.
[29] MATÉTREY P H,WILLAM K J. Triaxial failure criterion for concrete and its generalization[J]. ACI structural Journal,1995,92(3):311–318.
[30] PIETRUSZCZAK S,JIANG J,MIRZA F A. An elastoplastic constitutive model for concrete[J]. International Journal of Solids and Structures,1988,24(7):705–722.
[31] PIETRUSZCZAK S,LYDZBA D,SHAO J F. Modeling of inherent anisotropy in sedimentary rocks[J]. International Journal of Solids and Structures,2002,39(3):637–648.
[32] MAZARS J. Application de la mécanique de l?endommagement au comportement non linéaire du béton de structure[Ph. D. Thesis][D]. Paris:Université Paris 6,1984.