岩盐循环荷载下基于DS黏壶的非线性流变模型研究
|
摘要
地下储气库围岩常常处于循环荷载作用下,构建适合的流变模型是分析其长期稳定性的关键内容。基于应力耗散原理建立了非线性黏壶力学元件(DS黏壶)和DS黏壶元件的微分本构方程,将Poyhting-Thomson模型与DS黏壶串联,构建了一个非线性流变模型(PT-DS),推导出PT-DS模型的微分本构方程。根据盐岩试块循环加载试验过程,建立了初始匀速加载段和循环荷载段的动应力方程,根据PT-DS模型,解析得到初始匀速加载段和循环荷载段应变随时间变化的本构方程。对循环荷载段应变本构方程进行了简化分析,得到循环荷载段应变曲线的上限线、中间线和下限线方程。用PT-DS模型的上限线、中间线和下限线本构方程对岩盐循环加载试验结果进行拟合分析,得到了相应的拟合参数。结果表明,应变拟合曲线、模拟曲线与试验曲线非常接近,PT-DS模型能很好的描述循环荷载下应变的发展过程。
The surrounding rock of underground gas storage is always under the action of cyclic loading. Constructing a suitable rheological model is the key to analyzing its long-term stability. Based on the principle of stress dissipation, a nonlinear dashpot element(DS-dashpot) and the differential constitutive equation of the DS-dashpot are established. A nonlinear rheological model(PT-DS) is constructed with the connection of Poyhting-Thomson model and the DS-dashpot in series. Meanwhile, a differential constitutive equation of PT-DS model is derived; According to the cyclic loading test process of rock salt specimen, the dynamic stress equation is established, which is divided into the initial uniform loading section and the cyclic load section. According to the analysis of PT-DS model, the constitutive equations of the time-dependent strain at the initial uniform loading and cyclic loading are obtained. The constitutive equation of cyclic loading section is simplified and analyzed and the equations of upper limit line, middle line and lower limit line are obtained. The cyclic loading test process of rock salt specimen are carried out; the test result is fitted using the constitutive equations of the upper limit line, the middle line, and the lower limit line of the PT-DS model; and the corresponding fitting parameters are obtained. The results show that the fitted curve and the simulated curve are very close to the test curve; so the PT-DS model can be used to describe the strain development process under the cyclic loading perfectly.
The surrounding rock of underground gas storage is always under the action of cyclic loading. Constructing a suitable rheological model is the key to analyzing its long-term stability. Based on the principle of stress dissipation, a nonlinear dashpot element(DS-dashpot) and the differential constitutive equation of the DS-dashpot are established. A nonlinear rheological model(PT-DS) is constructed with the connection of Poyhting-Thomson model and the DS-dashpot in series. Meanwhile, a differential constitutive equation of PT-DS model is derived; According to the cyclic loading test process of rock salt specimen, the dynamic stress equation is established, which is divided into the initial uniform loading section and the cyclic load section. According to the analysis of PT-DS model, the constitutive equations of the time-dependent strain at the initial uniform loading and cyclic loading are obtained. The constitutive equation of cyclic loading section is simplified and analyzed and the equations of upper limit line, middle line and lower limit line are obtained. The cyclic loading test process of rock salt specimen are carried out; the test result is fitted using the constitutive equations of the upper limit line, the middle line, and the lower limit line of the PT-DS model; and the corresponding fitting parameters are obtained. The results show that the fitted curve and the simulated curve are very close to the test curve; so the PT-DS model can be used to describe the strain development process under the cyclic loading perfectly.
引文
[1]FOSSUM A F,Munson D E,Chan K S,et al.Constitutive basis of the MDCF model for rock salt[C]//4th Conference on the Mechanical Behavior of Salt.Canada:Ecole Polytechnique Montreal,1996:235-248.
[2]CHAN K S,DEVRIES K L,BODNER S R,et al.Adamage mechanics approach to life prediction for a salt structure[R].NM:Albuquerque,Sandia National Laboratories,1994.
[3]LUX K H,HOU Z M.New developments in mechanical safety analysis of repositories in rock salt[C]//Proceedings of International Conference On Radioactive Waste Disposal,Technologies&Concepts.Berlin:Springer Verlag,2000:281-286.
[4]韦立德,杨春和,徐卫亚,等.基于细观力学的盐岩蠕变损伤本构模型研究[J].岩石力学与工程学报,2005,24(23):4253-4258.WEI Li-de,YANG Chun-he,XU Wei-ya.Study on creep damage constitutive model of salt rock based on mesomechanics[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(23):4253-4258.
[5]刘江,杨春和,吴文,等.盐岩蠕变特性和本构关系研究[J].岩土力学,2006,27(8):1267-1271.LIU Jiang,YANG Chun-he,WU Wen,et al.Study on creep characteristics and constitutive relation of rock salt[J].Rock and Soil Mechanics,2006,3(8):5-8.
[6]王者超.盐岩非线性蠕变损伤本构模型研究[D].北京:中国科学院研究生院;武汉:中国科学院武汉岩土力学研究所,2006.Study on constitutive model of nonlinear creep damage of salt rock[D].Beijing:Graduate University of Chinese Academy of Sciences;Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Science.2006.
[7]胡其志,冯夏庭,周辉.考虑温度损伤的盐岩蠕变本构关系研究[J].岩土力学,2009,30(8):2245-2248.HU Qi-zhi,FENG Xia-ting,ZHOU Hui.Study of creep model of rock salt with thermal damage considered[J].Rock and Soil Mechanics,2009,30(8):2245-2248.
[8]王军保,刘新荣,郭建强,等.盐岩蠕变特性及其非线性本构模型[J].煤炭学报,2014,39(3):445-451.WANG Jun-bao,LIU Xin-rong,GUO Jian-qiang,et al.Creep properties of salt rock and its nonlinear constitutive model[J].Journal of China Coal Society,2014,39(39):445-451.
[9]刘迪,周宏伟,赵阳,等.基于声发射特征的盐岩蠕变本构模型研究[J].岩土力学,2017,38(7):1951-1958.LIU Di,ZHOU Hong-wei,ZHAO Yang,et al.Study of creep constitutive model of rock salt based on acoustic emission characteristics[J].Rock and Soil Mechanics,2017,38(7):1951-1958.
[10]杨春和,马洪岭,刘建锋.循环加、卸载下盐岩变形特性试验研究[J].岩土力学,2009,30(12):3562-3568.YANG Chun-he,MA Hong-ling,LIU Jian-feng.Study of deformation of rock salt under cycling loading and unloading[J].Rock and Soil Mechanics,2009,30(12):3562-3568.
[11]FUENKAJORN K,PHUEAKPHUM D.Effects of cyclic loading on mechanical properties of Maha Sarakham salt[J].Engineering Geology,2010,112:43-52.
[12]任松,白月明,姜德义,等.温度对盐岩疲劳特性影响的试验研究[J].岩石力学与工程学报,2012,31(9):1839-1845.REN Song,BAI Yue-ming,JIANG De-yi,et al.Experimental study of temperature effect on fatigue property of salt rock[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(9):1839-1845.
[13]黄明,刘新荣,祝云华,等.低频周期荷载下广义Kelvin-Voigt模型特性研究[J].岩土力学,2009,30(8):2300-2304.HUANG Ming,LIU Xin-rong,ZHU Yun-hua,et al.Astudy of behaviors of generalized Kelvin-Voigt model under low frequency cyclic load[J].Rock and Soil Mechanics,2009,30(8):2300-2304.
[14]王者超,赵建纲,李术才,等.循环荷载作用下花岗岩疲劳力学性质及其本构模型[J].岩石力学与工程学报,2012,31(9):1888-1900.WANG Zhe-chao,ZHAO Jian-gang,LI Shu-cai,et al.Fatigue mechanical behavior of granite subjected to cyclic load and its constitutive model[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(9):1888-1900.
[15]许宏发,王武,方秦,等.循环荷载下岩石塑性应变演化模型[J].解放军理工大学学报(自然科学版),2012,13(3):282-286.XU Hong-fa,WANG Wu,FANG Qin,et al.Evolution model of rock plastic strain under cyclic loading[J].Journal of PLA University of Science and Technology(Natural Science Edition),2012,13(3):282-286.
[16]王军保,刘新荣,黄明,等.低频循环荷载下盐岩轴向蠕变的Burgers模型分析[J].岩土力学,2014,35(4):933-942.WANG Jun-bao,LIU Xin-rong,HUANG Ming,et al.Analysis of axial creep properties of salt rock under low frequency cyclic loading using Burgers model[J].Rock and Soil Mechanics,2014,35(4):933-942.
[17]郭建强,黄质宏.循环荷载作用下岩石疲劳本构模型初探[J].岩土工程学报,2015,37(9):1698-1704.GUO Jian-qiang,HUANG Zhi-hong.Constitutive model for fatigue of rock under cyclic loading[J].Chinese Journal of Geotechnical Engineering,2015,37(9):1698-1704.
[2]CHAN K S,DEVRIES K L,BODNER S R,et al.Adamage mechanics approach to life prediction for a salt structure[R].NM:Albuquerque,Sandia National Laboratories,1994.
[3]LUX K H,HOU Z M.New developments in mechanical safety analysis of repositories in rock salt[C]//Proceedings of International Conference On Radioactive Waste Disposal,Technologies&Concepts.Berlin:Springer Verlag,2000:281-286.
[4]韦立德,杨春和,徐卫亚,等.基于细观力学的盐岩蠕变损伤本构模型研究[J].岩石力学与工程学报,2005,24(23):4253-4258.WEI Li-de,YANG Chun-he,XU Wei-ya.Study on creep damage constitutive model of salt rock based on mesomechanics[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(23):4253-4258.
[5]刘江,杨春和,吴文,等.盐岩蠕变特性和本构关系研究[J].岩土力学,2006,27(8):1267-1271.LIU Jiang,YANG Chun-he,WU Wen,et al.Study on creep characteristics and constitutive relation of rock salt[J].Rock and Soil Mechanics,2006,3(8):5-8.
[6]王者超.盐岩非线性蠕变损伤本构模型研究[D].北京:中国科学院研究生院;武汉:中国科学院武汉岩土力学研究所,2006.Study on constitutive model of nonlinear creep damage of salt rock[D].Beijing:Graduate University of Chinese Academy of Sciences;Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Science.2006.
[7]胡其志,冯夏庭,周辉.考虑温度损伤的盐岩蠕变本构关系研究[J].岩土力学,2009,30(8):2245-2248.HU Qi-zhi,FENG Xia-ting,ZHOU Hui.Study of creep model of rock salt with thermal damage considered[J].Rock and Soil Mechanics,2009,30(8):2245-2248.
[8]王军保,刘新荣,郭建强,等.盐岩蠕变特性及其非线性本构模型[J].煤炭学报,2014,39(3):445-451.WANG Jun-bao,LIU Xin-rong,GUO Jian-qiang,et al.Creep properties of salt rock and its nonlinear constitutive model[J].Journal of China Coal Society,2014,39(39):445-451.
[9]刘迪,周宏伟,赵阳,等.基于声发射特征的盐岩蠕变本构模型研究[J].岩土力学,2017,38(7):1951-1958.LIU Di,ZHOU Hong-wei,ZHAO Yang,et al.Study of creep constitutive model of rock salt based on acoustic emission characteristics[J].Rock and Soil Mechanics,2017,38(7):1951-1958.
[10]杨春和,马洪岭,刘建锋.循环加、卸载下盐岩变形特性试验研究[J].岩土力学,2009,30(12):3562-3568.YANG Chun-he,MA Hong-ling,LIU Jian-feng.Study of deformation of rock salt under cycling loading and unloading[J].Rock and Soil Mechanics,2009,30(12):3562-3568.
[11]FUENKAJORN K,PHUEAKPHUM D.Effects of cyclic loading on mechanical properties of Maha Sarakham salt[J].Engineering Geology,2010,112:43-52.
[12]任松,白月明,姜德义,等.温度对盐岩疲劳特性影响的试验研究[J].岩石力学与工程学报,2012,31(9):1839-1845.REN Song,BAI Yue-ming,JIANG De-yi,et al.Experimental study of temperature effect on fatigue property of salt rock[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(9):1839-1845.
[13]黄明,刘新荣,祝云华,等.低频周期荷载下广义Kelvin-Voigt模型特性研究[J].岩土力学,2009,30(8):2300-2304.HUANG Ming,LIU Xin-rong,ZHU Yun-hua,et al.Astudy of behaviors of generalized Kelvin-Voigt model under low frequency cyclic load[J].Rock and Soil Mechanics,2009,30(8):2300-2304.
[14]王者超,赵建纲,李术才,等.循环荷载作用下花岗岩疲劳力学性质及其本构模型[J].岩石力学与工程学报,2012,31(9):1888-1900.WANG Zhe-chao,ZHAO Jian-gang,LI Shu-cai,et al.Fatigue mechanical behavior of granite subjected to cyclic load and its constitutive model[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(9):1888-1900.
[15]许宏发,王武,方秦,等.循环荷载下岩石塑性应变演化模型[J].解放军理工大学学报(自然科学版),2012,13(3):282-286.XU Hong-fa,WANG Wu,FANG Qin,et al.Evolution model of rock plastic strain under cyclic loading[J].Journal of PLA University of Science and Technology(Natural Science Edition),2012,13(3):282-286.
[16]王军保,刘新荣,黄明,等.低频循环荷载下盐岩轴向蠕变的Burgers模型分析[J].岩土力学,2014,35(4):933-942.WANG Jun-bao,LIU Xin-rong,HUANG Ming,et al.Analysis of axial creep properties of salt rock under low frequency cyclic loading using Burgers model[J].Rock and Soil Mechanics,2014,35(4):933-942.
[17]郭建强,黄质宏.循环荷载作用下岩石疲劳本构模型初探[J].岩土工程学报,2015,37(9):1698-1704.GUO Jian-qiang,HUANG Zhi-hong.Constitutive model for fatigue of rock under cyclic loading[J].Chinese Journal of Geotechnical Engineering,2015,37(9):1698-1704.