基于应变软化指标的岩石非线性蠕变模型
|
摘要
研究并提出一种以应变软化指标为基础的岩石非线性蠕变模型。首先,基于岩石三轴压缩试验结果,分析提出一种峰后应变软化指标R_1来描述岩石峰后力学参数软化与塑性变形间的关系。接着,通过分析加速蠕变阶段与峰后段的联系,建立加速蠕变应变软化指标R_2,并以此为基础构建非线性黏塑性体。然后,将其与Hook体和Kelvin元件串联,组建非线性蠕变模型,并将模型嵌入ABAQUS有限元程序。最后,针对砂岩和泥岩三轴蠕变试验建立数值模型,模拟曲线与试验曲线吻合良好,说明所建模型适用于硬岩/软岩加速蠕变现象的模拟。其中,参数b对加速蠕变曲线形态起调节作用,显示模型模拟脆性-延性流变破坏的特点。另外,模型参数均可由常规压缩破坏试验以及蠕变试验确定,易于获取。
A nonlinear creep model is researched and proposed on the basis of a new proposed strain softening index. Firstly,according to the triaxial experimental data of rock, a strain softening index R_1 is presented to describe the relationship between the softening of the post-peak mechanical parameters and the plastic strain. Secondly, by analyzing the relationship between the tertiary creep and the general post-peak stage, a strain softening index R_2 in the tertiary creep is put forward to establish a non-linear viscoplastic element. Thirdly, by connecting the nonlinear viscoplastic element with the Hook and the Kelvin viscoelastic models, a nonlinear creep model is established inserting into the ABAQUS software. Finally, the proposed model is applied to simulate the triaxial creep experiments of sandstone and mudstone. The numerical results are in good agreement with the experiments indicating that the proposed model is capable of characterizing the accelerated creep behaviors of hard and soft rocks. The parameter β can adjust the curve form of the tertiary creep, showing the function to model the brittle-ductile failure. Furthermore, the parameters in the model can be readily identified by the conventional compression failure test and the creep test.
A nonlinear creep model is researched and proposed on the basis of a new proposed strain softening index. Firstly,according to the triaxial experimental data of rock, a strain softening index R_1 is presented to describe the relationship between the softening of the post-peak mechanical parameters and the plastic strain. Secondly, by analyzing the relationship between the tertiary creep and the general post-peak stage, a strain softening index R_2 in the tertiary creep is put forward to establish a non-linear viscoplastic element. Thirdly, by connecting the nonlinear viscoplastic element with the Hook and the Kelvin viscoelastic models, a nonlinear creep model is established inserting into the ABAQUS software. Finally, the proposed model is applied to simulate the triaxial creep experiments of sandstone and mudstone. The numerical results are in good agreement with the experiments indicating that the proposed model is capable of characterizing the accelerated creep behaviors of hard and soft rocks. The parameter β can adjust the curve form of the tertiary creep, showing the function to model the brittle-ductile failure. Furthermore, the parameters in the model can be readily identified by the conventional compression failure test and the creep test.
引文
[1]张治亮,徐卫亚,王伟.向家坝水电站坝基挤压带岩石三轴蠕变试验及非线性黏弹塑性蠕变模型研究[J].岩石力学与工程学报,2011,30(1):132-140.ZHANG Zhi-liang,XU Wei-ya,WANG Wei.Study of triaxial creep tests and its nonlinear visco-elastoplastic creep model of rock from compressive zone of dam foundation in Xiangjiaba hydropower station[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(1):132-140.
[2]STERPI D,GIODA G.Visco-plastic behaviour around advancing tunnels in squeezing rock[J].Rock Mechanics and Rock Engineering,2009,42(2):319-339.
[3]YANG W D,ZHANG Q Y,LI S C,et al.Time-dependent behavior of diabase and a nonlinear creep model[J].Rock Mechanics and Rock Engineering,2014,47(4):1211-1224.
[4]CONG L,HU X L.Triaxial rheological property of sandstone under low confining pressure[J].Engineering Geology,2017,231:45-55.
[5]JIANG Q H,QI Y J,WANG Z J,et al.An extended Nishihara model for the description of three stages of sandstone creep[J].Geophysical Journal International,2013,193(2):841-854.
[6]ZHANG Q Z,SHEN M R,DING W Q.The shear creep characteristics of a green schist weak structural marble surface[J].Mechanics of Advanced Materials and Structures,2015,22(9):697-704.
[7]康永刚,张秀娥.岩石蠕变的非定常分数伯格斯模型[J].岩土力学,2011,32(11):3237-3241.KANG Yong-gang,ZHANG Xiu-e.Nonstationary parameter fractional Burgers model of rock creep[J].Rock and Soil Mechanics,2011,32(11):3237-3241.
[8]何志磊,朱珍德,朱明礼,等.基于分数阶导数的非定常蠕变本构模型研究[J].岩土力学,2016,37(3):737-744.HE Zhi-lei,ZHU Zhen-de,ZHU Ming-li,et al.An unsteady creep constitutive model based on fractional order derivatives[J].Rock and Soil Mechanics,2016,37(3):737-744.
[9]韩阳,谭跃虎,李二兵,等.岩石非定常Burgers蠕变模型及其参数识别[J].工程力学,2018,35(3):210-217.HAN Yang,TAN Yue-hu,LI Er-bing,et al.Non-stationary burgers creep model of rock and its parameter identification[J].Engineering Mechanics,2018,35(3):210-217.
[10]赵延林,唐劲舟,付成成,等.岩石黏弹塑性应变分离的流变试验与蠕变损伤模型[J].岩石力学与工程学报,2016,35(7):1297-1308.ZHAO Yan-lin,TANG Jin-zhou,FU Cheng-cheng,et al.Rheological test of separation between viscoelastic-plastic strains and creep damage model[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(7):1297-1308.
[11]LIU H Z,XIE H Q,HE J D,et al.Nonlinear creep damage constitutive model for soft rocks[J].Mechanics of Time-Dependent Materials,2017,21(1):73-96.
[12]LIU C,ZHOU F B,KANG J H,et al.Application of a non-linear viscoelastic-plastic rheological model of soft coal on borehole stability[J].Journal of Natural Gas Science and Engineering,2016,36(Part B):1303-1311.
[13]佘成学.岩石非线性黏弹塑性蠕变模型研究[J].岩石力学与工程学报,2009,28(10):2006-2011.SHE Cheng-xue.Research on nonlinear viscoelastoplastic creep model of rock[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(10):2006-2011.
[14]丁靖洋,周宏伟,陈琼,等.盐岩流变损伤特性及本构模型研究[J].岩土力学,2015,36(3):769-776.DING Jing-yang,ZHOU Hong-wei,CHEN Qiong,et al.Characters of rheological damage and constitutive model of salt rock[J].Rock and Soil Mechanics,2015,36(3):769-776.
[15]张凯,周辉,冯夏庭,等.大理岩弹塑性耦合特性试验研究[J].岩土力学,2010,31(8):2425-2434.ZHANG Kai,ZHOU Hui,FENG Xia-ting,et al.Experimental research on elastoplastic coupling character of marble[J].Rock and Soil Mechanics,2010,31(8):2425-2434.
[16]ZHANG K,ZHOU H,SHAO J F.An experimental investigation and an elastoplastic constitutive model for a porous rock[J].Rock Mechanics and Rock Engineering,2013,46(6):1499-1511.
[17]李鹏飞,赵星光,郭政,等.北山花岗岩在三轴压缩条件下的强度参数演化[J].岩石力学与工程学报,2017,36(7):1599-1610.LI Peng-fei,ZHAO Xing-guang,GUO Zheng,et al.Variation of strength parameters of Beishan granite under triaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(7):1599-1610.
[18]WONG T F.Effects of temperature and pressure on failure and post-failure behavior of westerly granite[J].Mechanics of Materials,1982,1(1):3-17.
[19]LIN Q X,LIU Y M,THAM L G,et al.Time-dependent strength degradation of granite[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(7):1103-1114.
[20]陈亮,刘建锋,王春萍,等.不同温度及应力状态下北山花岗岩蠕变特征研究[J].岩石力学与工程学报,2015,34(6):1228-1235.CHEN Liang,LIU Jian-feng,WANG Chun-ping,et al.Creep behavior of the Beishan granite under different temperature and stress conditions[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(6):1228-1235.
[21]CHEN L,WANG C P,LIU J F,et al.Effects of temperature and stress on the time-dependent behavior of Beishan granite[J].International Journal of Rock Mechanics and Mining Sciences,2017,93:316-323.
[22]TAKEMURA T,ODA M,KIRAI H,et al.Microstructural based time-dependent failure mechanism and its relation to geological background[J].International Journal of Rock Mechanics and Mining Sciences,2012,53:76-85.
[23]杨峰.高应力软岩巷道变形破坏特征及让压支护机理研究[D].徐州:中国矿业大学,2009.YANG Feng.Research on deformation and failure character and yielding support mechanism of high stress soft rock tunnel[D].Xuzhou:China University of Mining&Technology,2009.
[24]WANG W,LI L,XU W,et al.Creep failure mode and criterion of Xiangjiaba sandstone[J].Journal of Central South University,2012,19(12):3572-3581.ZHAO L Y,ZHU Q Z,XU W Y,et al.A unified micromechanics-based damage model for instantaneous and time-dependent behaviors of brittle rocks[J].International Journal of Rock Mechanics and Mining Sciences,2016,84:187-196
[2]STERPI D,GIODA G.Visco-plastic behaviour around advancing tunnels in squeezing rock[J].Rock Mechanics and Rock Engineering,2009,42(2):319-339.
[3]YANG W D,ZHANG Q Y,LI S C,et al.Time-dependent behavior of diabase and a nonlinear creep model[J].Rock Mechanics and Rock Engineering,2014,47(4):1211-1224.
[4]CONG L,HU X L.Triaxial rheological property of sandstone under low confining pressure[J].Engineering Geology,2017,231:45-55.
[5]JIANG Q H,QI Y J,WANG Z J,et al.An extended Nishihara model for the description of three stages of sandstone creep[J].Geophysical Journal International,2013,193(2):841-854.
[6]ZHANG Q Z,SHEN M R,DING W Q.The shear creep characteristics of a green schist weak structural marble surface[J].Mechanics of Advanced Materials and Structures,2015,22(9):697-704.
[7]康永刚,张秀娥.岩石蠕变的非定常分数伯格斯模型[J].岩土力学,2011,32(11):3237-3241.KANG Yong-gang,ZHANG Xiu-e.Nonstationary parameter fractional Burgers model of rock creep[J].Rock and Soil Mechanics,2011,32(11):3237-3241.
[8]何志磊,朱珍德,朱明礼,等.基于分数阶导数的非定常蠕变本构模型研究[J].岩土力学,2016,37(3):737-744.HE Zhi-lei,ZHU Zhen-de,ZHU Ming-li,et al.An unsteady creep constitutive model based on fractional order derivatives[J].Rock and Soil Mechanics,2016,37(3):737-744.
[9]韩阳,谭跃虎,李二兵,等.岩石非定常Burgers蠕变模型及其参数识别[J].工程力学,2018,35(3):210-217.HAN Yang,TAN Yue-hu,LI Er-bing,et al.Non-stationary burgers creep model of rock and its parameter identification[J].Engineering Mechanics,2018,35(3):210-217.
[10]赵延林,唐劲舟,付成成,等.岩石黏弹塑性应变分离的流变试验与蠕变损伤模型[J].岩石力学与工程学报,2016,35(7):1297-1308.ZHAO Yan-lin,TANG Jin-zhou,FU Cheng-cheng,et al.Rheological test of separation between viscoelastic-plastic strains and creep damage model[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(7):1297-1308.
[11]LIU H Z,XIE H Q,HE J D,et al.Nonlinear creep damage constitutive model for soft rocks[J].Mechanics of Time-Dependent Materials,2017,21(1):73-96.
[12]LIU C,ZHOU F B,KANG J H,et al.Application of a non-linear viscoelastic-plastic rheological model of soft coal on borehole stability[J].Journal of Natural Gas Science and Engineering,2016,36(Part B):1303-1311.
[13]佘成学.岩石非线性黏弹塑性蠕变模型研究[J].岩石力学与工程学报,2009,28(10):2006-2011.SHE Cheng-xue.Research on nonlinear viscoelastoplastic creep model of rock[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(10):2006-2011.
[14]丁靖洋,周宏伟,陈琼,等.盐岩流变损伤特性及本构模型研究[J].岩土力学,2015,36(3):769-776.DING Jing-yang,ZHOU Hong-wei,CHEN Qiong,et al.Characters of rheological damage and constitutive model of salt rock[J].Rock and Soil Mechanics,2015,36(3):769-776.
[15]张凯,周辉,冯夏庭,等.大理岩弹塑性耦合特性试验研究[J].岩土力学,2010,31(8):2425-2434.ZHANG Kai,ZHOU Hui,FENG Xia-ting,et al.Experimental research on elastoplastic coupling character of marble[J].Rock and Soil Mechanics,2010,31(8):2425-2434.
[16]ZHANG K,ZHOU H,SHAO J F.An experimental investigation and an elastoplastic constitutive model for a porous rock[J].Rock Mechanics and Rock Engineering,2013,46(6):1499-1511.
[17]李鹏飞,赵星光,郭政,等.北山花岗岩在三轴压缩条件下的强度参数演化[J].岩石力学与工程学报,2017,36(7):1599-1610.LI Peng-fei,ZHAO Xing-guang,GUO Zheng,et al.Variation of strength parameters of Beishan granite under triaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(7):1599-1610.
[18]WONG T F.Effects of temperature and pressure on failure and post-failure behavior of westerly granite[J].Mechanics of Materials,1982,1(1):3-17.
[19]LIN Q X,LIU Y M,THAM L G,et al.Time-dependent strength degradation of granite[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(7):1103-1114.
[20]陈亮,刘建锋,王春萍,等.不同温度及应力状态下北山花岗岩蠕变特征研究[J].岩石力学与工程学报,2015,34(6):1228-1235.CHEN Liang,LIU Jian-feng,WANG Chun-ping,et al.Creep behavior of the Beishan granite under different temperature and stress conditions[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(6):1228-1235.
[21]CHEN L,WANG C P,LIU J F,et al.Effects of temperature and stress on the time-dependent behavior of Beishan granite[J].International Journal of Rock Mechanics and Mining Sciences,2017,93:316-323.
[22]TAKEMURA T,ODA M,KIRAI H,et al.Microstructural based time-dependent failure mechanism and its relation to geological background[J].International Journal of Rock Mechanics and Mining Sciences,2012,53:76-85.
[23]杨峰.高应力软岩巷道变形破坏特征及让压支护机理研究[D].徐州:中国矿业大学,2009.YANG Feng.Research on deformation and failure character and yielding support mechanism of high stress soft rock tunnel[D].Xuzhou:China University of Mining&Technology,2009.
[24]WANG W,LI L,XU W,et al.Creep failure mode and criterion of Xiangjiaba sandstone[J].Journal of Central South University,2012,19(12):3572-3581.ZHAO L Y,ZHU Q Z,XU W Y,et al.A unified micromechanics-based damage model for instantaneous and time-dependent behaviors of brittle rocks[J].International Journal of Rock Mechanics and Mining Sciences,2016,84:187-196