孔隙固体超弹性本构模型与应用
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摘要
油气井封固、核废料填埋与浅层地热能利用等问题是能源岩土领域的研究热点。土体、岩石、混凝土材料的多场耦合本构模型理论是这些研究热点问题的核心所在。传统固体弹塑性力学、岩土力学与孔隙固体力学理论相比,由于其基本假设或构建手段的局限性,其关于岩石与混凝土材料的变形计算往往会产生较大误差,且理论扩展性不强。该文分别从饱和岩土力学理论、经典Biot孔隙弹性力学理论出发,阐述其在孔隙固体材料本构理论的相关研究工作,并进行梳理与对比;其后运用严格物理热力学理论框架,建立孔隙固体材料的超弹性本构模型;最后针对石灰石与水泥石的既有试验数据,验证孔隙固体超弹性本构模型的有效性。
The sealing of oil and gas wells, nuclear waste landfilling, and shallow geothermal energy utilization are hot research topics in the field of energy geotechnics, while the constitutive model theory of soil, rock, and concrete materials is the core area of these studies. However, errors arise from the calculation of deformation of rock and concrete materials due to the limitations of basic assumptions or construction methods in traditional soil mechanics and pore elasticity theory, the theoretical scalability of which is also weak. Based on the theory of saturated soil mechanics and pore elasticity theory, this paper analyzes and evaluates the related research work on the constitutive theory of porous solid materials. Furthermore, it uses thermodynamic means to establish the hyperelastic constitutive model of porous solid materials. The effectiveness of the proposed mechanical model is verified by the existing experimental datum on limestone and hardened cement paste.
The sealing of oil and gas wells, nuclear waste landfilling, and shallow geothermal energy utilization are hot research topics in the field of energy geotechnics, while the constitutive model theory of soil, rock, and concrete materials is the core area of these studies. However, errors arise from the calculation of deformation of rock and concrete materials due to the limitations of basic assumptions or construction methods in traditional soil mechanics and pore elasticity theory, the theoretical scalability of which is also weak. Based on the theory of saturated soil mechanics and pore elasticity theory, this paper analyzes and evaluates the related research work on the constitutive theory of porous solid materials. Furthermore, it uses thermodynamic means to establish the hyperelastic constitutive model of porous solid materials. The effectiveness of the proposed mechanical model is verified by the existing experimental datum on limestone and hardened cement paste.
引文
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[2]Ghabezloo S,Sulem J.Effect of the volume of the drainage system on the measurement of undrained thermos-poro-elastic parameters[J].International Journal of Rock Mechanics&Mining Sciences,2010,47(1):60―68.
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[5]李广信.高等土力学[M].第2版.北京:清华大学出版社,2016:336―346.Li Guangxin.Advanced Soil Mechanics[M].2nd ed.Beijing:Tsinghua University Press,2016:336―346.(in Chinese)
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[9]金浏,杜修力.孔隙率变化规律及其对混凝土变形过程的影响[J].工程力学,2013,30(6):183―190.Jin Liu,Du Xiuli.Variation of porosity and its effect on the deformation process of concrete[J].Engineering Mechanics,2013,30(6):183―190.(in Chinese)
[10]金浏,张仁波,杜修力.力学损伤混凝土热传导行为细观研究[J].工程力学,2018,35(2):84―91.Jin Liu,Zhang Renbo,Du Xiuli.Meso-scale investigation on thermal conduction behavior in concrete with mechanical damage[J]Engineering Mechanics,2018,35(2):84―91.(in Chinese)
[11]高彦芳,陈勉,林伯韬,等.多相非饱和多重孔隙介质的有效应力定律[J].工程力学,2019,36(1):32―43.Gao Yanfang,Chen Mian,Lin Botao,et al.Generalized effective stress law for multi-porosity media unsaturated with multiphase fluids[J].Engineering Mechanics,2019,36(1):32―43.(in Chinese)
[12]Ghabezloo S.A micromechanical model for the effective compressibility of sandstones[J].European Journal of Mechanics A/Solids,2015,51:140―153.
[13]David E C,Zimmerman R W.Elastic moduli of solids containing spheroidal pores[J].International Journal of Engineering Science,2011,49(7):544―560.
[14]Cheng A D.Material coefficients of anisotropic poroelasticity[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(2):199―205.
[15]阚晋,王建祥.一种孔隙介质力学模型及在水泥基材料的应用[J].力学学报,2012,44(6):1066―1070.Kan Jin,Wang Jianxiang.A mechanical model of porous media and it’s application in cement materials[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(6):1066―1070.(in Chinese)
[16]蔡新树,陈勉,金衍,等.各向异性多重孔隙介质有效应力定律[J].工程力学,2009,26(4):57―60.Cai Xinshu,Chen Mian,Jin Yan,et al.An effective stress law for anisotropic multi-porosity media[J].Engineering Mechanics,2009,26(4):57―60.(in Chinese)
[17]张宏.热弹塑性孔隙介质固结问题研究[J].岩石力学与工程学报,2000,19(增刊):845-848.Zhang Hong.Analysis on consolidation of poremedia of thermo-elasto-plasticity[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(Suppl):845―848.in Chinese)
[18]Jiang Yimin,Liu Mario.Granular solid hydrodynamics[J].Granular Matter,2009,11(3):139―156.
[19]Jiang Yimin,Itai Einav,Liu Mario.A thermodynamic treatment of partially saturated soils revealing the structure of effective stress[J].Journal of the Mechanics and Physics of Solids,2017,100:131―146.
[20]Zhang Z C,Cheng X H.Effective stress in saturated soil:a granular solid hydrodynamics approach[J].Granular Matter,2014,16(5),761―769.
[21]Zhang Z C,Cheng X H.A fully coupled THM model based on a non-equilibrium thermodynamic approach and its application[J].International Journal for Numerical and Analytical Methods in Geomechanics,2017,41(4):527―554.
[22]Einav,Itai,Liu Mario.Hydrodynamic derivation of the work input to fully and partially saturated soils[J].Journal of the Mechanics and Physics of Solids,2018,110:205―217.
[23]Boutéca M,Sarda J P.Experimental measurements of thermoporoelastic coefficients[J].Mechanics of Porous Media,1995:31―41.
[2]Ghabezloo S,Sulem J.Effect of the volume of the drainage system on the measurement of undrained thermos-poro-elastic parameters[J].International Journal of Rock Mechanics&Mining Sciences,2010,47(1):60―68.
[3]郑黎明,刘静,蒲春生,等.油藏渗流过程中孔隙弹性模型的分析与修正[J].中国石油大学学报(自然科学版),2017,41(3):114―121.Zheng Liming,Liu Jing,Pu Chunsheng,et al.Analysis and modification of Biot poro-elastic theory for application in flow modeling of oil reservoirs[J].Journal of China University of Petroleum,2017,41(3):114―121.(in Chinese)
[4]Biot M A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,12(10):155―164.
[5]李广信.高等土力学[M].第2版.北京:清华大学出版社,2016:336―346.Li Guangxin.Advanced Soil Mechanics[M].2nd ed.Beijing:Tsinghua University Press,2016:336―346.(in Chinese)
[6]Ghabezloo S,Sulem J,Guédon S,et al.Poromechanical behaviour of hardened cement paste under isotropic loading[J].Cement and Concrete Research,2008,38(12):1424―1437.
[7]Ghabezloo S.Association of macroscopic laboratory testing and micromechanics modelling for the evaluation of the poroelastic parameters of a hardened cement paste[J].Cement and Concrete Research,2010,40(8):1197―1210.
[8]张守伟,孙建孟,苏俊磊,等.砂砾岩弹性试验研究[J].中国石油大学学报(自然科学版),2010,34(5):63―76.Zhang Shouwei,Sun Jianmeng,Su Junlei,et al.Experimental investigation on elasticity of glutenite[J].Journal of China University of Petroleum,2010,40(8):1197―1210.(in Chinese)
[9]金浏,杜修力.孔隙率变化规律及其对混凝土变形过程的影响[J].工程力学,2013,30(6):183―190.Jin Liu,Du Xiuli.Variation of porosity and its effect on the deformation process of concrete[J].Engineering Mechanics,2013,30(6):183―190.(in Chinese)
[10]金浏,张仁波,杜修力.力学损伤混凝土热传导行为细观研究[J].工程力学,2018,35(2):84―91.Jin Liu,Zhang Renbo,Du Xiuli.Meso-scale investigation on thermal conduction behavior in concrete with mechanical damage[J]Engineering Mechanics,2018,35(2):84―91.(in Chinese)
[11]高彦芳,陈勉,林伯韬,等.多相非饱和多重孔隙介质的有效应力定律[J].工程力学,2019,36(1):32―43.Gao Yanfang,Chen Mian,Lin Botao,et al.Generalized effective stress law for multi-porosity media unsaturated with multiphase fluids[J].Engineering Mechanics,2019,36(1):32―43.(in Chinese)
[12]Ghabezloo S.A micromechanical model for the effective compressibility of sandstones[J].European Journal of Mechanics A/Solids,2015,51:140―153.
[13]David E C,Zimmerman R W.Elastic moduli of solids containing spheroidal pores[J].International Journal of Engineering Science,2011,49(7):544―560.
[14]Cheng A D.Material coefficients of anisotropic poroelasticity[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(2):199―205.
[15]阚晋,王建祥.一种孔隙介质力学模型及在水泥基材料的应用[J].力学学报,2012,44(6):1066―1070.Kan Jin,Wang Jianxiang.A mechanical model of porous media and it’s application in cement materials[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(6):1066―1070.(in Chinese)
[16]蔡新树,陈勉,金衍,等.各向异性多重孔隙介质有效应力定律[J].工程力学,2009,26(4):57―60.Cai Xinshu,Chen Mian,Jin Yan,et al.An effective stress law for anisotropic multi-porosity media[J].Engineering Mechanics,2009,26(4):57―60.(in Chinese)
[17]张宏.热弹塑性孔隙介质固结问题研究[J].岩石力学与工程学报,2000,19(增刊):845-848.Zhang Hong.Analysis on consolidation of poremedia of thermo-elasto-plasticity[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(Suppl):845―848.in Chinese)
[18]Jiang Yimin,Liu Mario.Granular solid hydrodynamics[J].Granular Matter,2009,11(3):139―156.
[19]Jiang Yimin,Itai Einav,Liu Mario.A thermodynamic treatment of partially saturated soils revealing the structure of effective stress[J].Journal of the Mechanics and Physics of Solids,2017,100:131―146.
[20]Zhang Z C,Cheng X H.Effective stress in saturated soil:a granular solid hydrodynamics approach[J].Granular Matter,2014,16(5),761―769.
[21]Zhang Z C,Cheng X H.A fully coupled THM model based on a non-equilibrium thermodynamic approach and its application[J].International Journal for Numerical and Analytical Methods in Geomechanics,2017,41(4):527―554.
[22]Einav,Itai,Liu Mario.Hydrodynamic derivation of the work input to fully and partially saturated soils[J].Journal of the Mechanics and Physics of Solids,2018,110:205―217.
[23]Boutéca M,Sarda J P.Experimental measurements of thermoporoelastic coefficients[J].Mechanics of Porous Media,1995:31―41.