基于应变能的岩石黏弹塑性损伤耦合蠕变本构模型及应用
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摘要
在Perzyna黏弹塑性理论的基础上,引入基于应变能理论的岩石细观单元强度损伤模型,同时考虑岩石蠕变过程中蠕变速率随时间变化的特性,构建了能描述岩石从初始蠕变、稳定蠕变到非线性加速蠕变整个蠕变过程的细观黏弹塑性损伤耦合蠕变本构模型,并将该模型嵌入到三维弹塑性细胞自动机模拟系统(EPCA3D)中,通过实验数据验证该模型的正确性。应用该模型进行不同轴向应力、不同围压和不同均质度系数条件下的单、三轴压缩蠕变过程数值实验,结果表明:(1)轴向应力提高增加了蠕变速率,因此减少了蠕变失效时间;(2)围压和均质度系数的增加降低了蠕变速率并增加了蠕变失效时间,较好的再现了典型的实验现象。将该模型用于解释煤矿中"蠕变型"冲击地压的力学机理,较好的反映了煤矿巷道开挖后弹性应变能累积,围岩经历稳定蠕变和加速蠕变的损伤破坏过程,可为岩体工程的长期稳定性研究提供分析工具。
On the basis of elasto-viscoplastic theory of Perzyna,a mesoscopic coupled elasto-viscoplastic damage model,describing the whole creep process of rock from initial creep,stable creep to nonlinear acceleration creep,is constructed by introducing a mesoscopic unit strength damage model based on the strain energy theory.The characteristics of the creep rate change with time in the creep process of rock can be taken into consideration,and can be integrated into the EPCA3D.The model was verified by the experimental data and then applied to the numerical experiments of single and triaxial compression creep process under different axial stresses,confining the pressures and homogeneity coefficients.The results showed that,on one hand,the increased axial stress can speed up the creep rate,which reducesthe creep failure time.On the other hand,the increased confining pressure and homogeneity coefficient can reduce the creep rate and lead to the increase of creep failure time.This study can better reproduce the typical experimental phenomena.It can be used to explain the mechanical mechanism of creep-induced rock burst in coal mines,and also better reflect the accumulation of elastic strain energy after the excavation of coal mine roadway and the damage process of surrounding rock undergoing stable creep and accelerating creep.This study can provide an analytical tool for the long-term stability of rock mass engineering.
On the basis of elasto-viscoplastic theory of Perzyna,a mesoscopic coupled elasto-viscoplastic damage model,describing the whole creep process of rock from initial creep,stable creep to nonlinear acceleration creep,is constructed by introducing a mesoscopic unit strength damage model based on the strain energy theory.The characteristics of the creep rate change with time in the creep process of rock can be taken into consideration,and can be integrated into the EPCA3D.The model was verified by the experimental data and then applied to the numerical experiments of single and triaxial compression creep process under different axial stresses,confining the pressures and homogeneity coefficients.The results showed that,on one hand,the increased axial stress can speed up the creep rate,which reducesthe creep failure time.On the other hand,the increased confining pressure and homogeneity coefficient can reduce the creep rate and lead to the increase of creep failure time.This study can better reproduce the typical experimental phenomena.It can be used to explain the mechanical mechanism of creep-induced rock burst in coal mines,and also better reflect the accumulation of elastic strain energy after the excavation of coal mine roadway and the damage process of surrounding rock undergoing stable creep and accelerating creep.This study can provide an analytical tool for the long-term stability of rock mass engineering.
引文
[1] ZHOU Hongwei,WANG Chunping,HAN B B,et al.A creep constitutive model for salt rock based on fractional derivatives[J].International Journal of Rock Mechanics and Mining Sciences,2011,48(1):116-121.
[2] XU Tao,TANG Chunan,ZHAO Jian,et al.Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks[J].Geophysical Journal International,2012,189(3):1781-1796.
[3] LI Xiang,CAO Wengui,SU Yonghua.A statistical damage constitutive model for softening behavior of rocks[J]. Engineering Geology,2012,143:1-17.
[4] CHEN Liang,WANG Chunping,LIU Jianfeng,et al. A damagemechanism-based creep model considering temperature effect ingranite[J].Mechanics Research Communications,2014,56:76-82.
[5] PING Cao,WEN Youdao,WANG Yixian,et al. Study on nonlinear damage creep constitutive model for high-stress soft rock[J].Environmental Earth Sciences,2016,75(10):900.
[6] WANG Rui,ZHUO Zhuang,ZHOU Hongwei,et al.A fractal derivative constitutive model for three stages in granite creep[J].Results in Physics,2017,7:2632-2638.
[7] TANG Hao,WANG Dongpo,HUANG Runqiu,et al. A new rock creep model based on variable-order fractional derivatives and continuum damage mechanics[J]. Bulletin of Engineering Geology and the Environment,2018,77(1):375-383.
[8] JIA Shanpo,ZHANG Liwei,WU Bisheng,et al.A coupled hydromechanical creep damage model for clayey rock and its application to nuclear waste repository[J]. Tunnelling and Underground Space Technology,2018,74:230-246.
[9] YANG Shengqi,HU Bo,RANJITH Pathegama G,et al.Multi-step loading creep behavior of red sandstone after thermal treatments and a creep damage model[J].Energies,2018,11(1):212.
[10] ZHAO Yanlin,ZHANG Lianyang,WANG Weijun,et al. Separation of elastoviscoplastic strains of rock and a nonlinear creep model[J]. International Journal of Geomechanics,2017,18(1):04017129.
[11]蔡美峰.岩石力学与工程[M].北京:科学出版社,2002.
[12]康永刚,张秀娥.一种改进的岩石蠕变本构模型[J].岩土力学,2014,35(4):1049-1055.KANG Yonggang,ZHANG Xiue.An improved constitutive model for rock creep[J]. Rock and Soil Mechanics,2014,35(4):1049-1055.
[13]沈才华,张兵,王文武.一种基于应变能理论的黏弹塑性蠕变本构模型[J].岩土力学,2014,35(12):3430-3436.SHEN Caihua,ZHANG Bing,WANG Wenwu. A new viscoelastoplastic creep constitutive model based on strain energy theory[J].Rock and Soil Mechanics,2014,35(12):3430-3436.
[14]王其虎,叶义成,刘艳章,等.考虑初始损伤和蠕变损伤的岩石蠕变全过程本构模型[J].岩土力学,2016,37(S1):57-62.WANG Qihu,YE Yicheng,LIU Yanzhang,et al. A creep constitutive model of rock considering initial damage and creep damage[J].Rock and Soil Mechanics,2016,37(S1):57-62.
[15]蒋昱州,王奔,王瑞红,等.基于应变屈服临界的岩石黏弹塑性蠕变模型研究[J].长江科学院院报,2017,34(11):89-95.JIANG Yuzhou,WANG Ben,WANG Ruihong,et al. Viscoelasticplastic creep model of rock based on strain yield critical criteria[J].Journal of Yangtze River Scientific Research Institute,2017,34(11):89-95.
[16] SIH George C. From monoscale to multiscale modeling of fatigue crack growth:Stress and energy density factor[J]. Science China Physics Mechanics and Astronomy,2014,57(1):39-50.
[17]王洪英,张凤翔.大安山矿房山采区冲击地压模拟试验研究[J].辽宁工程技术大学学报:自然科学版,1999,18(5):491-493.WANG Hongying,ZHANG Fengxiang.Simulating experiment investigation in Fangshan mining zone of Da Anshan Colliery[J]. Journal of Liaoning Technical University:Natural Science,1999,18(5):491-493.
[18]徐思朋,缪协兴.冲击地压的时间效应研究现状[J].矿业安全与环保,2001,28(2):27-29.XU Sipeng,MIU Xiexing. Research status of time effect of rock burst[J]. Mining Safety and Environmental Protection,2001,28(2):27-29.
[19] OWEN D R J,HINTON E.Finite elements in plasticity[M].Swansea:Pineridge press,1980.
[20]陈惠发,A F萨里普,萨里普,等.弹性与塑性力学[M].北京:中国建筑工业出版社,2005.
[21]孙钧.岩土材料流变及其工程应用[M].北京:中国建筑工业出版社,1999.
[22]潘鹏志,冯夏庭,申林方,等.裂隙花岗岩各向异性蠕变特性研究[J].岩石力学与工程学报,2011,30(1):36-44.PAN Pengzhi,FENG Xiating,SHEN Linfang,et al. Study of anisotropic creep behavior of fractured granite[J]. Chinese Journal of Rock Mechanics and Engineering,2011,30(1):36-44.
[23]谭万鹏,郑颖人.岩质边坡弹黏塑性计算参数位移反分析研究[J].岩石力学与工程学报,2010,29(S1):2988-2993.TAN Wanpeng,ZHENG Yingren.Study of displacement back analysis of elasto-viscoplastic parameters of rock slope[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(S1):2988-2993.
[24] WEIBULL W.A statistical distribution function of wide applicability[J].Journal of Applied Mechanics,1951,18(3):293-297.
[25]潘鹏志.岩石破裂过程及其渗流-应力耦合特性研究的弹塑性细胞自动机模型[D].武汉:中国科学院武汉岩土力学研究所,2006.PAN Pengzhi. Research on rock fracturing process and coupled hydro-mechanical effect using an elasto-plastic celluar automaton[D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2006.
[26]沈才华,王浩越,王媛,等.基于COD理论的岩石蠕变加速判别法探究[J].岩石力学与工程学报,2017,36(S2):3752-3759.SHEN Caihua,WANG Haoyue,WANG Yuan,et al. Study on creep acceleration discrimination method based on COD theory[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(S2):3752-3759.
[27]姜福兴,冯宇,KOUAME,等.高地应力特厚煤层“蠕变型”冲击机理研究[J].岩土工程学报,2015,37(10):1762-1768.JIANG Fuxing,FENG Yu,KOUAME,et al.Mechanism of creep-induced rock burst in extrathick coal seam under high ground stress[J].Chinese Journal of Geotechnical Engineering,2015,37(10):1762-1768.
[28]苏国韶.高地应力下大型地下洞室群稳定性分析与智能优化研究[D].武汉:中国科学院武汉岩土力学研究所,2006.SU Guoshao. Study on stability analysis and intelligent optimiza-tion for large underground caverns under high geostress condition[D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2006.
[2] XU Tao,TANG Chunan,ZHAO Jian,et al.Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks[J].Geophysical Journal International,2012,189(3):1781-1796.
[3] LI Xiang,CAO Wengui,SU Yonghua.A statistical damage constitutive model for softening behavior of rocks[J]. Engineering Geology,2012,143:1-17.
[4] CHEN Liang,WANG Chunping,LIU Jianfeng,et al. A damagemechanism-based creep model considering temperature effect ingranite[J].Mechanics Research Communications,2014,56:76-82.
[5] PING Cao,WEN Youdao,WANG Yixian,et al. Study on nonlinear damage creep constitutive model for high-stress soft rock[J].Environmental Earth Sciences,2016,75(10):900.
[6] WANG Rui,ZHUO Zhuang,ZHOU Hongwei,et al.A fractal derivative constitutive model for three stages in granite creep[J].Results in Physics,2017,7:2632-2638.
[7] TANG Hao,WANG Dongpo,HUANG Runqiu,et al. A new rock creep model based on variable-order fractional derivatives and continuum damage mechanics[J]. Bulletin of Engineering Geology and the Environment,2018,77(1):375-383.
[8] JIA Shanpo,ZHANG Liwei,WU Bisheng,et al.A coupled hydromechanical creep damage model for clayey rock and its application to nuclear waste repository[J]. Tunnelling and Underground Space Technology,2018,74:230-246.
[9] YANG Shengqi,HU Bo,RANJITH Pathegama G,et al.Multi-step loading creep behavior of red sandstone after thermal treatments and a creep damage model[J].Energies,2018,11(1):212.
[10] ZHAO Yanlin,ZHANG Lianyang,WANG Weijun,et al. Separation of elastoviscoplastic strains of rock and a nonlinear creep model[J]. International Journal of Geomechanics,2017,18(1):04017129.
[11]蔡美峰.岩石力学与工程[M].北京:科学出版社,2002.
[12]康永刚,张秀娥.一种改进的岩石蠕变本构模型[J].岩土力学,2014,35(4):1049-1055.KANG Yonggang,ZHANG Xiue.An improved constitutive model for rock creep[J]. Rock and Soil Mechanics,2014,35(4):1049-1055.
[13]沈才华,张兵,王文武.一种基于应变能理论的黏弹塑性蠕变本构模型[J].岩土力学,2014,35(12):3430-3436.SHEN Caihua,ZHANG Bing,WANG Wenwu. A new viscoelastoplastic creep constitutive model based on strain energy theory[J].Rock and Soil Mechanics,2014,35(12):3430-3436.
[14]王其虎,叶义成,刘艳章,等.考虑初始损伤和蠕变损伤的岩石蠕变全过程本构模型[J].岩土力学,2016,37(S1):57-62.WANG Qihu,YE Yicheng,LIU Yanzhang,et al. A creep constitutive model of rock considering initial damage and creep damage[J].Rock and Soil Mechanics,2016,37(S1):57-62.
[15]蒋昱州,王奔,王瑞红,等.基于应变屈服临界的岩石黏弹塑性蠕变模型研究[J].长江科学院院报,2017,34(11):89-95.JIANG Yuzhou,WANG Ben,WANG Ruihong,et al. Viscoelasticplastic creep model of rock based on strain yield critical criteria[J].Journal of Yangtze River Scientific Research Institute,2017,34(11):89-95.
[16] SIH George C. From monoscale to multiscale modeling of fatigue crack growth:Stress and energy density factor[J]. Science China Physics Mechanics and Astronomy,2014,57(1):39-50.
[17]王洪英,张凤翔.大安山矿房山采区冲击地压模拟试验研究[J].辽宁工程技术大学学报:自然科学版,1999,18(5):491-493.WANG Hongying,ZHANG Fengxiang.Simulating experiment investigation in Fangshan mining zone of Da Anshan Colliery[J]. Journal of Liaoning Technical University:Natural Science,1999,18(5):491-493.
[18]徐思朋,缪协兴.冲击地压的时间效应研究现状[J].矿业安全与环保,2001,28(2):27-29.XU Sipeng,MIU Xiexing. Research status of time effect of rock burst[J]. Mining Safety and Environmental Protection,2001,28(2):27-29.
[19] OWEN D R J,HINTON E.Finite elements in plasticity[M].Swansea:Pineridge press,1980.
[20]陈惠发,A F萨里普,萨里普,等.弹性与塑性力学[M].北京:中国建筑工业出版社,2005.
[21]孙钧.岩土材料流变及其工程应用[M].北京:中国建筑工业出版社,1999.
[22]潘鹏志,冯夏庭,申林方,等.裂隙花岗岩各向异性蠕变特性研究[J].岩石力学与工程学报,2011,30(1):36-44.PAN Pengzhi,FENG Xiating,SHEN Linfang,et al. Study of anisotropic creep behavior of fractured granite[J]. Chinese Journal of Rock Mechanics and Engineering,2011,30(1):36-44.
[23]谭万鹏,郑颖人.岩质边坡弹黏塑性计算参数位移反分析研究[J].岩石力学与工程学报,2010,29(S1):2988-2993.TAN Wanpeng,ZHENG Yingren.Study of displacement back analysis of elasto-viscoplastic parameters of rock slope[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(S1):2988-2993.
[24] WEIBULL W.A statistical distribution function of wide applicability[J].Journal of Applied Mechanics,1951,18(3):293-297.
[25]潘鹏志.岩石破裂过程及其渗流-应力耦合特性研究的弹塑性细胞自动机模型[D].武汉:中国科学院武汉岩土力学研究所,2006.PAN Pengzhi. Research on rock fracturing process and coupled hydro-mechanical effect using an elasto-plastic celluar automaton[D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2006.
[26]沈才华,王浩越,王媛,等.基于COD理论的岩石蠕变加速判别法探究[J].岩石力学与工程学报,2017,36(S2):3752-3759.SHEN Caihua,WANG Haoyue,WANG Yuan,et al. Study on creep acceleration discrimination method based on COD theory[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(S2):3752-3759.
[27]姜福兴,冯宇,KOUAME,等.高地应力特厚煤层“蠕变型”冲击机理研究[J].岩土工程学报,2015,37(10):1762-1768.JIANG Fuxing,FENG Yu,KOUAME,et al.Mechanism of creep-induced rock burst in extrathick coal seam under high ground stress[J].Chinese Journal of Geotechnical Engineering,2015,37(10):1762-1768.
[28]苏国韶.高地应力下大型地下洞室群稳定性分析与智能优化研究[D].武汉:中国科学院武汉岩土力学研究所,2006.SU Guoshao. Study on stability analysis and intelligent optimiza-tion for large underground caverns under high geostress condition[D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2006.