(1. State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan,Hubei 430071,China;2. City College,Wuhan University of Science and Technology,
Wuhan,Hubei 430083,China)
Abstract:A stress path model with the subloading surface based on the Drucker-Prager yield criterion and the subloading surface theory was established to reflect accurately the response of rock under the action of earthquake. A dynamic constitutive model of rock material was proposed considering the rate effect of elastic modulus and strength. The proposed model was applied to the Xianglushan tunnel. The results show that the stress path model describes the Masing effect and the ratchet effect of basalt better than Drucker-Prager criterion under cyclic loading. When the rate effect is not taken into account,the slope of the stress-strain curve is smaller than that of test curve and the cumulative strain is larger than that of test curve. In the process of cyclic loading and unloading,the dynamic modulus obtained with the dynamic model is larger than that from the stress path model with subloading surface and the deformation obtained with the dynamic model is smaller than that from the stress path model with subloading surface. Therefore,the proposed model reflected well the dynamic mechanical properties and deformation properties of the rock. In comparison with the results from Drucker-Prager criterion, the instantaneous relative peak deformation between the left and right monitoring points of the tunnel from the dynamic model increased 0.67 cm,and the permanent relative deformation between the bottom and top monitoring points and between the left and right monitoring points are increased 0.19 cm and 0.77 cm respectively. This indicates that the dynamic model reflected better the large deformation of the surrounding rock. The dynamic model of rocks is more effective in filtering the high frequency than Drucker-Prager criterion and linear elastic constitutive.
[1] 宫凤强,陆道辉,李夕兵,等. 不同应变率下砂岩动态强度准则的试验研究[J]. 岩土力学,2013,34(9):2 433–2 441.(GONG Fengqiang,LU Daohui,LI Xibing,et al. Experimental research of sandstone dynamic strength criterion under different strain rates[J]. Rock and Soil Mechanics,2013,34(9):2 433–2 441.(in Chinese))
[2] 李海波,王建伟,李俊如,等. 单轴压缩下软岩的动态力学特性试验研究[J]. 岩土力学,2004,25(1):1–4.(LI Haibo,WANG Jianwei,LI Junru,et al. Mechanical properties of soft rock under dynamic uniaxial compression[J]. Rock and Soil Mechanics,2004,25(1):1–4.(in Chinese))
[3] 梁昌玉,李 晓,李守定,等. 岩石静态和准动态加载应变率的界限值研究[J]. 岩石力学与工程学报,2012,31(6):1 156–1 161. (LIANG Changyu,LI Xiao,LI Shouding,et al. Study of strain rates threshold value between static loading and quasi-dynamic loading of rock[J]. Chinese Journal of Rock Mechanics and Engineering,2012,31(6):1 156–1 161.(in Chinese))
[4] 钱七虎,戚承志. 岩石、岩体的动力强度与动力破坏准则[J]. 同济大学学报:自然科学版,2008,36(12):1 599–1 605.(QIAN Qihu,QI Chengzhi. Dynamic strength and dynamic fracture criteria of rock and rock mass[J]. Journal of Tongji University:Natural Science,2008,36(12):1 599–1 605.(in Chinese))
[5] LINDHOLM U S,YEAKLEY L M,NAGY A. The dynamic strength and fracture properties of dresser basalt[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1974,11(2):181–191.
[6] PERZYNA P. Fundamental problems in visco-plasticity[J]. Advances in Applied Mechanics,1966,(9):243–377.
[7] WANG Z L,LI Y C,WANG J G. A damage softening statistical constitutive model considering rock residual strength[J]. Computers and Geosciences,2007,33(1):1–9.
[8] 戴 俊. 岩石动力学特性与爆破理论[M]. 2版. 北京:冶金工业出版社,2014:56–60.(DAI Jun. Dynamic behaviors and blasting theory of rock[M]. 2nd ed. Beijing:Metallurgical Industry Press,2014:56–60.(in Chinese))
[9] 单仁亮,薛友松,张 倩. 岩石动态破坏的时效损伤本构模型[J]. 岩石力学与工程学报,2003,22(11):1 771–1 776.(SHAN Renliang,XUE Yousong,ZHANG Qian. Time dependent damage model of rock under dynamic loading[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(11):1 771–1 776.(in Chinese))
[10] 刘恩龙,张建海,何思明,等. 循环荷载作用下岩石的二元介质模型[J]. 重庆理工大学学报:自然科学,2013,27(9):6–11.(LIU Anlong,ZHANG Jianhai,HE Siming,et al. Binary medium model of rock subjected to cyclic loading[J]. Journal of Chongqing University of Technology:Natural Science,2013,27(9):6–11.(in Chinese))
[11] 莫海鸿. 岩石的循环试验及本构关系的研究[J]. 岩石力学与工程学报,1988,7(3):215–224.(MO Haihong. Investigation of cyclic loading tests and constitutive relation of rock[J]. Chinese Journal of Rock Mechanics and Engineering,1988,7(3):215–224.(in Chinese))
[12] HASHIGUCHI K. Generalized plastic flow rule[J]. International Journal of Plasticity,2005,21(2):321–351.
[13] 孔 亮,花丽坤,王燕昌. 次加载面理论及其在土体循环塑性模型中的应用[J]. 宁夏大学学报:自然科学版,2003,24(1):50–56.(KONG Liang,HUA Likun,WANG Yanchang. The subloading surface theory and its application to the cyclic plastic model for soil[J]. Journal of Ningxia University:Natural Science,2003,24(1):50–56.(in Chinese))
[14] 伍大鹏. 混凝土在循环荷载作用下的次加载面应力路径模型[硕士学位论文][D]. 北京交通大学,2012.(WU Dapeng. The sub-loading surface model of concrete under cyclic loading[M. S. Thesis][D]. Beijing:Beijing Jiaotong University,2012.(in Chinese))
[15] FU Y K,IWATA M K,DING W Q,et,al. An elastoplastic model for soft sedimentary rock considering inherent anisotropy and confining-stress dependency[J]. Soil and Foundations,2012,52(4):575–589.
[16] 周永强,盛 谦,冷先伦,等. 基于循环加卸载的次加载面模型在岩石中的初步应用[J]. 岩石力学与工程学报,2015,34(10):2 073–2 082.(ZHOU Yongqiang,SHENG Qian,LENG Xianlun,et al. Preliminary application of subloading surface to cyclic plastic model for rock under cyclic loading[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(10):2 073–2 082.(in Chinese))
[17] 郑颖人,沈珠江,龚晓南. 广义塑性力学——岩土塑性力学原理[M]. 北京:中国建筑工业出版社,2011:63–91.(ZHENG Yingren,SHEN Zhujiang,GONG Xiaonan. The generalized plastic mechanics- geotechnical plastic mechanics principle[M]. Beijing:China Building Industry Press,2011:63–91.(in Chinese))
[18] 白 冰,李小春,石 露,等. 基于虚强度参数的塑性硬化模式[J]. 长江科学院院报,2012,29(8):24–28.(BAI Bing,LI Xiaochun,SHI Lu,et al. A plastic hardening mode based on virtual strength parameters[J]. Journal of Yangtze River Scientific Research Institute,2012,29(8):24–28.(in Chinese))
[19] 张玉敏. 大型地下洞室群地震响应特征研究[博士学位论文][D]. 北京:中国科学院研究生院,2010.(ZHANG Yumin. Study on response characteristics of large underground cavern group under earthquake[Ph. D. Thesis][D]. Beijing:Graduate School of the Chinese Academy of Sciences,2010.(in Chinese))
[20] 赵 坚,李海波. 莫尔–库仑和霍克–布朗强度准则用于评估脆性岩石动态强度的适用性[J]. 岩石力学与工程学报,2003,22(2):171–176.(ZHAO Jian,LI Haibo. Estimating the dynamic strength of rock using Mohr-coulomb and Hoek-brown criteria[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(2):171–176.(in Chinese))
[21] 戚承志,钱七虎. 岩石等脆性材料动力强度依赖应变率的物理机制[J]. 岩石力学与工程学报,2003,22(2):177–181.(QI Chengzhi,QIAN Qihu. Physical mechanism of dependence of material strength on strain rate for rock-like material[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(2):177–181.(in Chinese))
[22] 宋玉普. 混凝土的动力本构关系和破坏准则[M]. 北京:科学出版社,2013:9–37.(SONG Yupu. Dynamic constitutive relation and failure criterion of concrete[M]. Beijing:Science Press,2013:9–37.(in Chinese))
[23] 李夕兵,左宇军,马春德. 中应变率下动静组合加载岩石的本构模型[J]. 岩石力学与工程学报,2006,25(5):865–874.(LI Xibing,ZUO Yujun,MA Chunde. Constitutive model of rock under coupled static-dynamic loading with intermediate strain rate[J]. Chinese Journal of Rock Mechanics and Engineering,2006,25(5):865–874.(in Chinese))
[24] JOHNSON G R,COOK W H. A constitutive model and data for metals subjected to large strain,high strain rates and high temperatures[C]// Proceedings of the 7th IntSymp Ballistics,Am Def Pre Org(ADPA). The Hague,Netherlands:[s.n.],1983:541–547.
[25] 崔 臻. 大型地下洞室群地震响应分析及动力稳定性问题研究[博士学位论文][D]. 北京:中国科学院大学,2013.(CUI Zhen. Seismic response and stability of underground cavern complex[Ph. D. Thesis][D]. Beijing:University of Chinese Academy of Sciences,2013.(in Chinese))