引潮力作用下饱和地质岩体的力学响应
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摘要
本文应用孔隙弹性理论,探讨了引潮力作用下饱和地质岩体的力学响应。首先通过引潮力作用下饱和岩体的自由能表达式,得到岩体孔压与应力、应力与应变之间的关系;然后从引潮力作用下饱和岩体的平衡微分方程出发,结合流-固耦合理论,分析了饱水岩体应变与引潮位之间的关系;最后推导出饱和岩体的两大力学物理量——孔压和潮汐应力(平均应力)与引潮位之间的物理关系。模型表明:饱和岩体孔压与引潮位成反比,平均潮汐应力与引潮位成正比;比例系数不仅与岩体骨架的Lame系数有关,而且与Biot模量有关。将模型应用于会理川-18井水位变化分析,估计出水位响应系数D,并以此为基础,求得岩体孔压、潮汐应力与引潮位的相关系数(A和C)及Skempton系数B。最后对比分析了耦合条件下与不考虑耦合时得到的各参数之间的差异,分析表明:对饱和地质岩体而言,应力、孔压对引潮力的响应是流-固耦合作用的产物;研究其力学响应时必须充分考虑耦合效应。模型的建立,为研究引潮力作用下井-承压含水层系统力学、水动力学、与地震有关的断层力学以及引潮力触发机制的定量研究提供了基础。
It explores with poroelastic theory the mechanical response of saturated geological rock under the tidal force.First,we use the free energy formula of saturated rock under the tidal force to study the relationship of rock pore pressure responding to stress and stress to strain.And then we analyze the relationship between strain of rock and tide-generating potential by using the balance differential equations of saturated rock under the tidal force.Finally,we derive two physical parameters(pore pressure and tidal stress) of saturated rock mechanics: the physical relationship between the parameters and the tidal force.The relationship shows that pore pressure is in direct proportion with the tide-generating potential,and average tidal stress of saturated rock is inversely proportional with the tide-generating potential.The ratio coefficient is not only related to the Lame coefficients of the rock skeleton,but also to the Biot modulus.By using this model to analyze groundwater level observation changes of Sichuan-18 well which locates in Huili,Sichuan,to estimate the well level response coefficient(D) that response to earth tide.By this way,we have derived the Skempton coefficient(B) and the coefficient A and C which mean the rock pore pressure as well as tidal stress response to tide-generating potential.The final comparative analysis of the differences between each parameter of coupling and non-coupling shows that for saturated rocks,the response stress and pore pressure is a product of coupling.And,it is necessary to take into account the coupling when we study the mechanical response.The model will not only provides the basis for the study of well-confined aquifer system mechanics,hydrodynamics,and the mechanics of faulting under tidal force,but also quantitative research for trigger mechanism of tidal force.
It explores with poroelastic theory the mechanical response of saturated geological rock under the tidal force.First,we use the free energy formula of saturated rock under the tidal force to study the relationship of rock pore pressure responding to stress and stress to strain.And then we analyze the relationship between strain of rock and tide-generating potential by using the balance differential equations of saturated rock under the tidal force.Finally,we derive two physical parameters(pore pressure and tidal stress) of saturated rock mechanics: the physical relationship between the parameters and the tidal force.The relationship shows that pore pressure is in direct proportion with the tide-generating potential,and average tidal stress of saturated rock is inversely proportional with the tide-generating potential.The ratio coefficient is not only related to the Lame coefficients of the rock skeleton,but also to the Biot modulus.By using this model to analyze groundwater level observation changes of Sichuan-18 well which locates in Huili,Sichuan,to estimate the well level response coefficient(D) that response to earth tide.By this way,we have derived the Skempton coefficient(B) and the coefficient A and C which mean the rock pore pressure as well as tidal stress response to tide-generating potential.The final comparative analysis of the differences between each parameter of coupling and non-coupling shows that for saturated rocks,the response stress and pore pressure is a product of coupling.And,it is necessary to take into account the coupling when we study the mechanical response.The model will not only provides the basis for the study of well-confined aquifer system mechanics,hydrodynamics,and the mechanics of faulting under tidal force,but also quantitative research for trigger mechanism of tidal force.
引文
方俊,1984,固体潮,241,北京:科学出版社。
刘元生、张昭栋、崔桂梅等,2000,由起潮力反演含油(水)层的应力变化,西北地震学报,22(3),329~332。
卢应发、郑俊杰、柴华友,2005,典型岩石和土的Skempton系数特征,岩石力学与工程学报,24(11),1847~1851。
王仁、丁中一,1979,轴对称情况下地球自转速率变化及引潮力引起的全球应力场,天文地球动力学论文集,8~21,上海:上海天文台出版。
王仁、丁中一,1982,轴对称情况下地球速率变化及引潮力引起全球应力场,地质力学论丛,第6号,北京:科学出版社。
汪成民、车用太、万迪垫等,1988,地下水微动态研究,北京:地震出版社。
晏锐、陈湧、高福旺等,2008,从昌平井体应变、水位对地震波的响应特征求算含水层的Skempton常数,地震学报,30(2),144~151。
张昭栋、郑金涵、冯初刚,1986,体膨胀固体潮对水井水位观测的影响,地震研究,9(4),465~472。
张昭栋、郑金涵、耿杰等,2002,地下水潮汐现象的物理机制和统一数学方程,地震地质,24(2),208~214。
Biot M.A.,1941,General theory of three-dimensional consolidation,J.Appl.Phys.,12(2),155~164.
Biot M.A.,1956,General solutions of the equations of elasticity and consolidation for a porous material,J.Appl.Mech.78:91~98.
Bredehoeft J.D.,1967,Response of well-aquifer systems to earth tides,J.Geophys.Res.,72(12),3075~3087.
Coussy.O,1995,Mechanics of Porous Continua,Chichester:Wiley,455.
Hamiel Y.,Lyakhovsky V.and Agnon A.,2004,Coupled Evolution of Damage and Porosity in Poroelastic Media:Theory and Applicationsto Deformation of Porous Rocks,Geophys.J.Int.,156:701~713.
Hamiel Y.,Lyakhovsky V.and Agnon A.,2005,Rock dilation,Nonlinear deformation,and pore pressure change under shear,Earthplanet.Sci.Lett.,237:577~589.
Malvern L.E.,1969,Introduction to the Mechanics of a Continuum Medium,Englewood Cliffs:Prentice-Hall Inc.,713.
Neuzil C.E.,2003,Hydromechanical coupling in geologic processes,Hydrogeology Journal,(11):41~83.
刘元生、张昭栋、崔桂梅等,2000,由起潮力反演含油(水)层的应力变化,西北地震学报,22(3),329~332。
卢应发、郑俊杰、柴华友,2005,典型岩石和土的Skempton系数特征,岩石力学与工程学报,24(11),1847~1851。
王仁、丁中一,1979,轴对称情况下地球自转速率变化及引潮力引起的全球应力场,天文地球动力学论文集,8~21,上海:上海天文台出版。
王仁、丁中一,1982,轴对称情况下地球速率变化及引潮力引起全球应力场,地质力学论丛,第6号,北京:科学出版社。
汪成民、车用太、万迪垫等,1988,地下水微动态研究,北京:地震出版社。
晏锐、陈湧、高福旺等,2008,从昌平井体应变、水位对地震波的响应特征求算含水层的Skempton常数,地震学报,30(2),144~151。
张昭栋、郑金涵、冯初刚,1986,体膨胀固体潮对水井水位观测的影响,地震研究,9(4),465~472。
张昭栋、郑金涵、耿杰等,2002,地下水潮汐现象的物理机制和统一数学方程,地震地质,24(2),208~214。
Biot M.A.,1941,General theory of three-dimensional consolidation,J.Appl.Phys.,12(2),155~164.
Biot M.A.,1956,General solutions of the equations of elasticity and consolidation for a porous material,J.Appl.Mech.78:91~98.
Bredehoeft J.D.,1967,Response of well-aquifer systems to earth tides,J.Geophys.Res.,72(12),3075~3087.
Coussy.O,1995,Mechanics of Porous Continua,Chichester:Wiley,455.
Hamiel Y.,Lyakhovsky V.and Agnon A.,2004,Coupled Evolution of Damage and Porosity in Poroelastic Media:Theory and Applicationsto Deformation of Porous Rocks,Geophys.J.Int.,156:701~713.
Hamiel Y.,Lyakhovsky V.and Agnon A.,2005,Rock dilation,Nonlinear deformation,and pore pressure change under shear,Earthplanet.Sci.Lett.,237:577~589.
Malvern L.E.,1969,Introduction to the Mechanics of a Continuum Medium,Englewood Cliffs:Prentice-Hall Inc.,713.
Neuzil C.E.,2003,Hydromechanical coupling in geologic processes,Hydrogeology Journal,(11):41~83.
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