基于Normal分布的岩石统计热损伤本构模型研究
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摘要
基于Lemaitre应变等价性理论的岩石损伤模型,假定受热损伤的岩石微元强度服从Normal分布,考虑温度对岩石力学参数的影响,引入热损伤变量,在微元破坏符合Mohr-Coulomb准则条件下,建立高温作用后岩石统计热损伤本构模型。依据岩石屈服的概念,利用极值法确定模型参数,并与不同温度下花岗岩的压缩试验结果进行对比分析。研究结果表明:本模型所得曲线与三轴压缩试验曲线较吻合,并能很好地反映高温作用后岩石软化特征;本模型不包含非常规岩石力学参数,便于工程应用;研究成果能够为高温岩体工程的开发和防护提供参考。
Based on rock damage model founded by Lemaitre's strain equivalent theory and hypothesis that rock particles intensity obeys normal random distribution after the thermal treatment, a statistical thermal damage constitutive model for rocks was established by adopting Mohr-Coulomb criterion with the thermal damage variable being introduced. The parameters of the model parameters were determined by the extreme value method according to the conception of yielding. The rationality of the model was verified by the comparison of the calculated results with those of the uniaxial experiments and conventional triaxial experiments of granite after different high temperature treatments. The results show that the constitutive model can reflect the characteristics of rock strain softening rock at different temperatures. The model does not contain any unconventional rock mechanics parameters, and can be used easily in engineering. The researches can provide reference for the development and protection of high-temperature rock projects.
Based on rock damage model founded by Lemaitre's strain equivalent theory and hypothesis that rock particles intensity obeys normal random distribution after the thermal treatment, a statistical thermal damage constitutive model for rocks was established by adopting Mohr-Coulomb criterion with the thermal damage variable being introduced. The parameters of the model parameters were determined by the extreme value method according to the conception of yielding. The rationality of the model was verified by the comparison of the calculated results with those of the uniaxial experiments and conventional triaxial experiments of granite after different high temperature treatments. The results show that the constitutive model can reflect the characteristics of rock strain softening rock at different temperatures. The model does not contain any unconventional rock mechanics parameters, and can be used easily in engineering. The researches can provide reference for the development and protection of high-temperature rock projects.
引文
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[8]苏承东,韦四江,秦本东,等.高温对细砂岩力学性质影响机制的试验研究[J].岩土力学,2017,38(3):623-630.SU Chengdong,WEI Sijiang,QIN Bendong,et al.Experimental study of influence mechanism of high temperature on mechanical properties of sandstone[J].Rock and Soil Mechanics,2017,38(3):623-630.
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[10]TIAN Hong,ZIEGLER M,KEMPKA T.Physical and mechanical behavior of claystone exposed to temperatures up to1 000°C[J].International Journal of Rock Mechanics&Mining Sciences,2014(70):144-153.
[11]PENG Jun,RONG Guan,CAI Ming,et al.Physical and mechanical behaviors of a thermal-damaged coarse marble under uniaxial compression[J].Engineering Geology,2016,200(12):88-93.
[12]YANG Shengqi,XU Peng,LI Yanbao,et al.Experimental investigation on triaxial mechanical and permeability behavior of sandstone after exposure to different high temperature treatments[J].Geothermics,2017(69):93-109.
[13]吴刚,翟松韬,李玉寿,等.高温下大理岩受压破坏的细观结构分析[J].岩石力学与工程学报,2012,31(增2):3579-3585.WU Gang,ZHAI Songtao,LI Yushou,et al.Mesostructure investigation on marbles under uniaxial compression at high temperatures[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(Suppl 2):3579-3585.
[14]HUECKEL T,PEANO A,PELLEGRINI R.A thermo-plastic constitutive law for brittle-plastic behavior of rocks at high temperatures[J].Pure&Applied Geophysics,1994,143(1/2/3):483-510.
[15]朱元广,刘泉声,张程远,等.岩石非线性黏弹性蠕变特性的时温等效效应[J].岩土力学,2012,33(8):2303-2309.ZHU Yuanguang,LIU Quansheng,ZHANG Chengyuan,et al.Nonlinear viscoelastic creep property of rock with timetemperature equivalence effect[J].Rock and Soil Mechanics,2012,33(8):2303-2309.
[16]张岩,李宁,于海鸣,等.温度应力对裂隙岩体强度的影响研究[J].岩石力学与工程学报,2013,32(S1):2660-2668.ZHANG Yan,LI Ning,YU Haiming,et al.Research on influence of thermal stress on fractured rock mass strength[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(S1):2660-2668.
[17]郤保平,赵阳升,万志军,等.热力耦合作用下花岗岩流变模型的本构关系研究[J].岩石力学与工程学报,2009,28(5):956-967.XI Baoping,ZHAO Yangsheng,WAN Zhijun,et al.Study of constitutive equation of granite rheological model with thermo-mechanical coupling effects[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(5):956-967.
[18]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 Yanlin,TANG Jinzhou,FU Chengcheng,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.
[19]徐银花,徐小丽.高温下岩石损伤本构模型研究[J].广西大学学报(自然科学版),2017,42(1):226-235.XU Yinhua,XU Xiaoli.Study on damage constitutive model of rock under high temperature[J].Journal of Guangxi University(Natural Science Edition),2017,42(1):226-235.
[20]李天斌,高美奔,陈国庆,等.应脆性岩石热-力-损伤本构模型及其初步运用[J].岩土工程学报,2017,39(8):1477-1484.LI Tianbin,GAO Meiben,CHEN Guoqing,et al.Athermal-mechanical-damage constitutive model for hard brittle rocks and its preliminary application[J].Chinese Journal of Geotechnical Engineering,2017,39(8):1477-1484.
[21]唐春安.岩石破裂过程中的灾变[M].北京:煤炭工业出版社,1993:13-31.TANG Chunan.Catastrophe in rock unstable failure[M].Beijing:China Coal Industry Publishing House,1993:13-31.
[22]曹文贵,方祖烈,唐学军.岩石损伤软化统计本构模型之研究[J].岩石力学与工程学报,1998,17(6):628-633.CAO Wengui,FANG Zulie,TANG Xuejun.A study of statistical constitutive model for soft and damage rocks[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(6):628-633.
[23]曹文贵,张超,贺敏,等.考虑空隙压密阶段特征的岩石应变软化统计损伤模拟方法[J].岩土工程学报,2016,38(10):1754-1761.CAO Wengui,ZHANG Chao,HE Min,et al.Statistical damage simulation method of strain softening deformation process for rocks considering characteristics of void compaction stage[J].Chinese Journal of Geotechnical Engineering,2016,38(10):1754-1761.
[24]CAO Wengui,LI Xiang,ZHAO Heng.Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination[J].Journal of Central South University of Technology,2007,14(5):719-724.
[25]LI Xiang,CAO Wengui,SU Yonghua.A statistical damage constitutive model for softening behavior of rocks[J].Engineering Geology,2012(143/144):1-17.
[26]ZHANG Hongwei,WAN Zhijun,WANG Chaoyi,et al.AStatistical damage constitutive model for geomaterials under plane-strain biaxial stress state[J].Advances in Mathematical Physics,2017(8):1-10.
[27]LEMAITRE J.How to use damage mechanics[J].Nuclear Engineering and Design,1984,80(2):233-245.
[28]TIAN Hong.Development of a thermo-mechanical model for rocks exposed to high temperatures during underground coal gasification[D].Aachen,Germany:RWTH Aachen University.Department of Geotechnical Engineering,2013:61-81.
[29]皮萨林科F C,列别捷夫A A.复杂应力状态下的材料变形与强度[M].江明行,译.北京:科学出版社,1983:129-140.ПИСАРЕНКОFС,ЛЕБЕДЕВA A.Deformation and strength of materials under complex stress state[M].JIANG Mingxing,trans.Beijing:Science Press,1983:129-140.
[30]KRAJCINOVIC D,SILVA M A G.Statistical aspects of the continuous damage theory[J].International Journal of Solids&Structures,1982,18(7):551-562.
[31]秦严.高温后花岗岩物理力学性质试验研究[D].北京:中国地质大学(北京)工程技术学院,2017:33-52.QIN Yan.High-temperature influence on physical and mechanical properties of diorite[D].Beijing:China University of Geosciences(Beijing).School of Engineering and Technology,2017:33-52.
[2]徐小丽,高峰,张志镇.高温作用后花岗岩三轴压缩试验研究[J].岩土力学,2014,35(11):3177-3183.XU Xiaoli,GAO Feng,ZHANG Zhizhen.Research on triaxial compression test of granite after high temperatures[J].Rock and Soil Mechanics,2014,35(11):3177-3183.
[3]李二兵,王永超,陈亮,等.北山花岗岩热损伤力学特性试验研究[J].中国矿业大学学报,2018,47(4):735-741.LI Erbing,WANG Yongchao,CHEN Liang,et al.Experimental study of mechanical properties of Beishan granite’s thermal damage[J].Journal of China University of Mining&Technology,2018,47(4):735-741.
[4]郭清露,荣冠,姚孟迪,等.大理岩热损伤声发射力学特性试验研究[J].岩石力学与工程学报,2015,34(12):2388-2400.GUO Qinglu,RONG Guan,YAO Mengdi,et al.Experimental study on acoustic emission behaviors and mechanical properties of thermal damaged marbles[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(12):2388-2400.
[5]陈国飞,杨圣奇.高温后大理岩力学性质及其破坏规律研究[J].工程力学,2014,31(8):189-196.CHEN Guofei,YANG Shengqi.Study on failure mechanical behavior of marble after high temperature[J].Engineering Mechanics,2014,31(8):189-196.
[6]SU Naijing,JING Hongwen,YIN Qian,et al.Strength and deformation behaviors of veined marble specimens after vacuum heat treatment under conventional triaxial compression[J].Acta Mechanica Sinica,2017,33(5):886-898.
[7]吴刚,王德咏,翟松韬.单轴压缩下高温后砂岩的声发射特征[J].岩土力学,2012,33(11):3237-3242.WU Gang,WANG Deyong,ZHAI Songtao.Acoustic emission characteristics of sandstone after high temperature under uniaxial compression[J].Rock and Soil Mechanics,2012,33(11):3237-3242.
[8]苏承东,韦四江,秦本东,等.高温对细砂岩力学性质影响机制的试验研究[J].岩土力学,2017,38(3):623-630.SU Chengdong,WEI Sijiang,QIN Bendong,et al.Experimental study of influence mechanism of high temperature on mechanical properties of sandstone[J].Rock and Soil Mechanics,2017,38(3):623-630.
[9]尹土兵,李夕兵,殷志强,等.高温后砂岩静、动态力学特性研究与比较[J].岩石力学与工程学报,2012,31(2):273-279.YIN Tubing,LI Xibing,YIN Zhiqiang,et al.Study and comparison of mechanical properties of sandstone under static and dynamic loadings after high temperature[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(2):273-279.
[10]TIAN Hong,ZIEGLER M,KEMPKA T.Physical and mechanical behavior of claystone exposed to temperatures up to1 000°C[J].International Journal of Rock Mechanics&Mining Sciences,2014(70):144-153.
[11]PENG Jun,RONG Guan,CAI Ming,et al.Physical and mechanical behaviors of a thermal-damaged coarse marble under uniaxial compression[J].Engineering Geology,2016,200(12):88-93.
[12]YANG Shengqi,XU Peng,LI Yanbao,et al.Experimental investigation on triaxial mechanical and permeability behavior of sandstone after exposure to different high temperature treatments[J].Geothermics,2017(69):93-109.
[13]吴刚,翟松韬,李玉寿,等.高温下大理岩受压破坏的细观结构分析[J].岩石力学与工程学报,2012,31(增2):3579-3585.WU Gang,ZHAI Songtao,LI Yushou,et al.Mesostructure investigation on marbles under uniaxial compression at high temperatures[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(Suppl 2):3579-3585.
[14]HUECKEL T,PEANO A,PELLEGRINI R.A thermo-plastic constitutive law for brittle-plastic behavior of rocks at high temperatures[J].Pure&Applied Geophysics,1994,143(1/2/3):483-510.
[15]朱元广,刘泉声,张程远,等.岩石非线性黏弹性蠕变特性的时温等效效应[J].岩土力学,2012,33(8):2303-2309.ZHU Yuanguang,LIU Quansheng,ZHANG Chengyuan,et al.Nonlinear viscoelastic creep property of rock with timetemperature equivalence effect[J].Rock and Soil Mechanics,2012,33(8):2303-2309.
[16]张岩,李宁,于海鸣,等.温度应力对裂隙岩体强度的影响研究[J].岩石力学与工程学报,2013,32(S1):2660-2668.ZHANG Yan,LI Ning,YU Haiming,et al.Research on influence of thermal stress on fractured rock mass strength[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(S1):2660-2668.
[17]郤保平,赵阳升,万志军,等.热力耦合作用下花岗岩流变模型的本构关系研究[J].岩石力学与工程学报,2009,28(5):956-967.XI Baoping,ZHAO Yangsheng,WAN Zhijun,et al.Study of constitutive equation of granite rheological model with thermo-mechanical coupling effects[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(5):956-967.
[18]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 Yanlin,TANG Jinzhou,FU Chengcheng,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.
[19]徐银花,徐小丽.高温下岩石损伤本构模型研究[J].广西大学学报(自然科学版),2017,42(1):226-235.XU Yinhua,XU Xiaoli.Study on damage constitutive model of rock under high temperature[J].Journal of Guangxi University(Natural Science Edition),2017,42(1):226-235.
[20]李天斌,高美奔,陈国庆,等.应脆性岩石热-力-损伤本构模型及其初步运用[J].岩土工程学报,2017,39(8):1477-1484.LI Tianbin,GAO Meiben,CHEN Guoqing,et al.Athermal-mechanical-damage constitutive model for hard brittle rocks and its preliminary application[J].Chinese Journal of Geotechnical Engineering,2017,39(8):1477-1484.
[21]唐春安.岩石破裂过程中的灾变[M].北京:煤炭工业出版社,1993:13-31.TANG Chunan.Catastrophe in rock unstable failure[M].Beijing:China Coal Industry Publishing House,1993:13-31.
[22]曹文贵,方祖烈,唐学军.岩石损伤软化统计本构模型之研究[J].岩石力学与工程学报,1998,17(6):628-633.CAO Wengui,FANG Zulie,TANG Xuejun.A study of statistical constitutive model for soft and damage rocks[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(6):628-633.
[23]曹文贵,张超,贺敏,等.考虑空隙压密阶段特征的岩石应变软化统计损伤模拟方法[J].岩土工程学报,2016,38(10):1754-1761.CAO Wengui,ZHANG Chao,HE Min,et al.Statistical damage simulation method of strain softening deformation process for rocks considering characteristics of void compaction stage[J].Chinese Journal of Geotechnical Engineering,2016,38(10):1754-1761.
[24]CAO Wengui,LI Xiang,ZHAO Heng.Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination[J].Journal of Central South University of Technology,2007,14(5):719-724.
[25]LI Xiang,CAO Wengui,SU Yonghua.A statistical damage constitutive model for softening behavior of rocks[J].Engineering Geology,2012(143/144):1-17.
[26]ZHANG Hongwei,WAN Zhijun,WANG Chaoyi,et al.AStatistical damage constitutive model for geomaterials under plane-strain biaxial stress state[J].Advances in Mathematical Physics,2017(8):1-10.
[27]LEMAITRE J.How to use damage mechanics[J].Nuclear Engineering and Design,1984,80(2):233-245.
[28]TIAN Hong.Development of a thermo-mechanical model for rocks exposed to high temperatures during underground coal gasification[D].Aachen,Germany:RWTH Aachen University.Department of Geotechnical Engineering,2013:61-81.
[29]皮萨林科F C,列别捷夫A A.复杂应力状态下的材料变形与强度[M].江明行,译.北京:科学出版社,1983:129-140.ПИСАРЕНКОFС,ЛЕБЕДЕВA A.Deformation and strength of materials under complex stress state[M].JIANG Mingxing,trans.Beijing:Science Press,1983:129-140.
[30]KRAJCINOVIC D,SILVA M A G.Statistical aspects of the continuous damage theory[J].International Journal of Solids&Structures,1982,18(7):551-562.
[31]秦严.高温后花岗岩物理力学性质试验研究[D].北京:中国地质大学(北京)工程技术学院,2017:33-52.QIN Yan.High-temperature influence on physical and mechanical properties of diorite[D].Beijing:China University of Geosciences(Beijing).School of Engineering and Technology,2017:33-52.