岩石滞后非线性弹性响应的物理模型
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摘要
介绍了岩石滞后非线性弹性的几个物理模型。赫兹颗粒接触模型是具有多尺度和滞后特性的经典模型,它预测了岩石中强烈的非线性;软的粘结系统几乎决定了岩石的力学性质,粘结系统中的流体对非线性响应的贡献特别显著,但是目前还没有搞清楚粘结系统和孔隙流体究竟是如何影响非线性响应的;GL模型是一个基于金属位错的物理模型,这是滞后动力行为方面一个开拓性的微观模型;PM模型是一个基于岩石细观尺度的唯象模型,它对理解岩石滞后非线性的机制和尺度是很重要的。
Several physical models of hysteretic nonlinear elasticity of rock are introduced.The Hertz grain contact model is a typical model with multi-scale and hysteretic behavior,which predicts strong nonlinearity in rocks.The soft adhesion system almost determines the mechanical properties of rock,and the fluid in the system has great contribution to nonlinear response.However,how the adhesion system and the pore fluid affect the nonlinear response remains unclear.The GL model based on metal dislocation is a physical model,which is a pioneering microscope model in hysteretic dynamic behaviour.The PM model is a phenomenological model based on mesoscopic elastic units in rock,which is important in understanding the mechanism and extent of hysteretic nonlinearity in rocks.
Several physical models of hysteretic nonlinear elasticity of rock are introduced.The Hertz grain contact model is a typical model with multi-scale and hysteretic behavior,which predicts strong nonlinearity in rocks.The soft adhesion system almost determines the mechanical properties of rock,and the fluid in the system has great contribution to nonlinear response.However,how the adhesion system and the pore fluid affect the nonlinear response remains unclear.The GL model based on metal dislocation is a physical model,which is a pioneering microscope model in hysteretic dynamic behaviour.The PM model is a phenomenological model based on mesoscopic elastic units in rock,which is important in understanding the mechanism and extent of hysteretic nonlinearity in rocks.
引文
[1]Guyer R A,Johnson P A.Nonlinear mesoscopic elasticity:ev-idence for a new class of materials[J].Physics Today,1999,52:30-36.
[2]Guyer R A,TenCate J,Johnson P.Hysteresis and the dy-namic elasticity of consolidated granular materials[J].Physi-cal Review Letters,1999,82(16):3280-3283.
[3]Johnson P A,McCall K R.Observation and implications ofnonlinear elastic wave response in rock[J].Geophysical Re-search Letters,1994,97.
[4]许江,鲜学福,王鸿,等.循环加、卸载条件下岩石类材料变形特性的实验研究[J].岩石力学与工程学报,2006,25(S1):3040-3045.
[5]陈运平,刘干斌,姚海林.岩石滞后非线性弹性模拟的研究[J].岩土力学,2006,27(3):341-347.
[6]陈运平,席道瑛,薛彦伟.循环荷载下饱和岩石的滞后和衰减[J].地球物理学报,2004,47(4):672-679.
[7]陈运平,王思敬,王恩志.岩石应力-应变滞后现象的定量研究[J].岩石力学与工程学报,2007,26(S2):4066-4073.
[8]Tutuncu A N,Podio A L,Gregory A R,et al.Nonlinear vis-coelastic behavior of sedimentary rock,PartⅠ:Effect of fre-quency and strain amplitude[J].Geophysics,1998,63:184-194.
[9]Tutuncu A N,Podio A L,Gregory A R,et al.Nonlinear vis-coelastic behavior of sedimentary rock,part II:hysteresiseffects and influence of type of fluid on elastic moduli[J].Geo-physics,1998,63(1):195-203.
[10]TenCate J A,Smith D E,Guyer R A.Universal slow dy-namics in granular solids[J].Physical Review Letters,2000,85:1020.
[11]TenCate J A,Shankland T J.Slow dynamics in the nonlinearelastic response of Berea sandstone[J].Geophysical ResearchLetters,1996,23:3019.
[12]TenCate J A,Pasqualini D,Habib S.Nonlinear and Non-equilibrium Dynamics in Geomaterials[J].Physical ReviewLetters,2004,93(6):065501/1-4.
[13]Landau L D,Lifshitz E.Theay of elasticity,(3rd edition)[M].Oxford:Pergamon Press,1986.
[14]Walsh J B.Seismic wave attenuation in rock due to friction[J].Journal of Geophysical Research,1966,71:2591-2599.
[15]Mavko G M.Frictional attenuation:An inherent amplitudedependence[J].Journal of Geophysical Research,1979,84:4769-4775.
[16]Mason W P.Internal friction mechanism that produces an at-tenuation in the earth's crust proportional to the frequency[J].Journal of Geophysical Research,1979,84,4963-4966.
[17]Johnson K L,Kendall K,Roberts A D.Surface energy andthe contact of elastic solids[A]∥Proc.R.Soc.Ser.A[C].London:[s.n.],1971,324,301.
[18]Sharma M M,Tutuncu A N.Grain adhesion hysteresis:amechanism for attenuation of seismic waves[J].GeophysicalResearch Letters,1994,21(21):2323-2326.
[19]Wilmanski K.A few remarks on Biot's model and linear a-coustics of poroelastic saturated materials[J].Soil Dynamicsand earthquake engineering,2006,26:509-536.
[20]Khanzanehdari J,Sothcott J.Variation in dynamic elasticshear modulus of sandstone upon fluid saturation and substi-tution[J].Geophysics,2003,68(2):472-481.
[21]Zinszner B,Johnson P A,Rasolofosaon P N J.Influence ofchange in physical state on elastic nonlinear response on rock:Significance of effective pressure and water saturation[J].Journal of Geophysical Research,1997,102:8105-8120.
[22]Belyaeva I,Zaitsev V,Ostrovsky L.Nonlinear acoustoelasticproperties of granular media[J].Acoustical Physics.1993,39(1):11-14.
[23]Tutuncu A N,Sharma M M.The influence of fluids on graincontact stiffness and frame moduli in sedimentary rocks[J].Geophysics,1992,57(12):1571-1582.
[24]席道瑛,陈运平,陶月赞,等.岩石的非线性弹性滞后特征[J].岩石力学与工程学报,2006,25(6):1086-1093.
[25]Van Den Abeele K E A,Carmeliet J,Johnson P A,et al.In-fluence of water saturation on the nonlinear elastic mesoscopicresponse in earth materials and the implications to the mecha-nism of nonlinearity[J].Journal of Geophysical Research,2002,107(B6):4-11.
[26]席道瑛,杜赟,易良坤,等.液体对岩石非线性弹性行为的影响[J].岩石力学与工程学报,2009,28(4):687-696.
[27]杜赟,席道瑛,徐松林,等.岩石非线性细观响应中孔隙液体的影响[J].岩石力学与工程学报,2010,29(1):209-216.
[28]McCall K R,Guyer R A.Equation of state and wave propa-gation in hysteretic nonlinear elastic materials[J].Journal ofGeophysical Research,1994,99:23887-23897.
[29]Guyer R A,McCall K R,Boitnoitt G N,et al.Quantitativeimplementation of Preisach-Mayergoyz space to find staticand dynamic elastic moduli in rock[J].Journal of Geophysi-cal Research,1997,102:5281-5293.
[30]席道瑛,徐松林,李廷,等.岩石中微细观结构对外力和温度响应的概率研究[J].岩石力学与工程学报,2007,26(1):15-21.
[31]任隽,朱元清,秦浩文.上海地震台阵标定及结果分析[J].西北地震学报,2002,24(4):325-329.
[32]任隽,陈运平,潘纪顺,等.海南岛及其近海中强地震前加卸载响应比的变化特征[J].西北地震学报,2005,27(1):71-74.
[33]郭晓,张元生,何斌.兰州市及其附近地区介质衰减特征研究[J].西北地震学报,2010,32(3):244-247.
[34]唐益群,崔振东,王兴汉.密集高层建筑群的工程效应引起地面沉降的初步研究[J].西北地震学报,2007,29(2):105-108.
[35]杨庆华,姚令侃,邱燕玲,等.高烈度地震区岩土体边坡崩塌动力学特性研究[J].西北地震学报,2011,33(1):34-39.
[2]Guyer R A,TenCate J,Johnson P.Hysteresis and the dy-namic elasticity of consolidated granular materials[J].Physi-cal Review Letters,1999,82(16):3280-3283.
[3]Johnson P A,McCall K R.Observation and implications ofnonlinear elastic wave response in rock[J].Geophysical Re-search Letters,1994,97.
[4]许江,鲜学福,王鸿,等.循环加、卸载条件下岩石类材料变形特性的实验研究[J].岩石力学与工程学报,2006,25(S1):3040-3045.
[5]陈运平,刘干斌,姚海林.岩石滞后非线性弹性模拟的研究[J].岩土力学,2006,27(3):341-347.
[6]陈运平,席道瑛,薛彦伟.循环荷载下饱和岩石的滞后和衰减[J].地球物理学报,2004,47(4):672-679.
[7]陈运平,王思敬,王恩志.岩石应力-应变滞后现象的定量研究[J].岩石力学与工程学报,2007,26(S2):4066-4073.
[8]Tutuncu A N,Podio A L,Gregory A R,et al.Nonlinear vis-coelastic behavior of sedimentary rock,PartⅠ:Effect of fre-quency and strain amplitude[J].Geophysics,1998,63:184-194.
[9]Tutuncu A N,Podio A L,Gregory A R,et al.Nonlinear vis-coelastic behavior of sedimentary rock,part II:hysteresiseffects and influence of type of fluid on elastic moduli[J].Geo-physics,1998,63(1):195-203.
[10]TenCate J A,Smith D E,Guyer R A.Universal slow dy-namics in granular solids[J].Physical Review Letters,2000,85:1020.
[11]TenCate J A,Shankland T J.Slow dynamics in the nonlinearelastic response of Berea sandstone[J].Geophysical ResearchLetters,1996,23:3019.
[12]TenCate J A,Pasqualini D,Habib S.Nonlinear and Non-equilibrium Dynamics in Geomaterials[J].Physical ReviewLetters,2004,93(6):065501/1-4.
[13]Landau L D,Lifshitz E.Theay of elasticity,(3rd edition)[M].Oxford:Pergamon Press,1986.
[14]Walsh J B.Seismic wave attenuation in rock due to friction[J].Journal of Geophysical Research,1966,71:2591-2599.
[15]Mavko G M.Frictional attenuation:An inherent amplitudedependence[J].Journal of Geophysical Research,1979,84:4769-4775.
[16]Mason W P.Internal friction mechanism that produces an at-tenuation in the earth's crust proportional to the frequency[J].Journal of Geophysical Research,1979,84,4963-4966.
[17]Johnson K L,Kendall K,Roberts A D.Surface energy andthe contact of elastic solids[A]∥Proc.R.Soc.Ser.A[C].London:[s.n.],1971,324,301.
[18]Sharma M M,Tutuncu A N.Grain adhesion hysteresis:amechanism for attenuation of seismic waves[J].GeophysicalResearch Letters,1994,21(21):2323-2326.
[19]Wilmanski K.A few remarks on Biot's model and linear a-coustics of poroelastic saturated materials[J].Soil Dynamicsand earthquake engineering,2006,26:509-536.
[20]Khanzanehdari J,Sothcott J.Variation in dynamic elasticshear modulus of sandstone upon fluid saturation and substi-tution[J].Geophysics,2003,68(2):472-481.
[21]Zinszner B,Johnson P A,Rasolofosaon P N J.Influence ofchange in physical state on elastic nonlinear response on rock:Significance of effective pressure and water saturation[J].Journal of Geophysical Research,1997,102:8105-8120.
[22]Belyaeva I,Zaitsev V,Ostrovsky L.Nonlinear acoustoelasticproperties of granular media[J].Acoustical Physics.1993,39(1):11-14.
[23]Tutuncu A N,Sharma M M.The influence of fluids on graincontact stiffness and frame moduli in sedimentary rocks[J].Geophysics,1992,57(12):1571-1582.
[24]席道瑛,陈运平,陶月赞,等.岩石的非线性弹性滞后特征[J].岩石力学与工程学报,2006,25(6):1086-1093.
[25]Van Den Abeele K E A,Carmeliet J,Johnson P A,et al.In-fluence of water saturation on the nonlinear elastic mesoscopicresponse in earth materials and the implications to the mecha-nism of nonlinearity[J].Journal of Geophysical Research,2002,107(B6):4-11.
[26]席道瑛,杜赟,易良坤,等.液体对岩石非线性弹性行为的影响[J].岩石力学与工程学报,2009,28(4):687-696.
[27]杜赟,席道瑛,徐松林,等.岩石非线性细观响应中孔隙液体的影响[J].岩石力学与工程学报,2010,29(1):209-216.
[28]McCall K R,Guyer R A.Equation of state and wave propa-gation in hysteretic nonlinear elastic materials[J].Journal ofGeophysical Research,1994,99:23887-23897.
[29]Guyer R A,McCall K R,Boitnoitt G N,et al.Quantitativeimplementation of Preisach-Mayergoyz space to find staticand dynamic elastic moduli in rock[J].Journal of Geophysi-cal Research,1997,102:5281-5293.
[30]席道瑛,徐松林,李廷,等.岩石中微细观结构对外力和温度响应的概率研究[J].岩石力学与工程学报,2007,26(1):15-21.
[31]任隽,朱元清,秦浩文.上海地震台阵标定及结果分析[J].西北地震学报,2002,24(4):325-329.
[32]任隽,陈运平,潘纪顺,等.海南岛及其近海中强地震前加卸载响应比的变化特征[J].西北地震学报,2005,27(1):71-74.
[33]郭晓,张元生,何斌.兰州市及其附近地区介质衰减特征研究[J].西北地震学报,2010,32(3):244-247.
[34]唐益群,崔振东,王兴汉.密集高层建筑群的工程效应引起地面沉降的初步研究[J].西北地震学报,2007,29(2):105-108.
[35]杨庆华,姚令侃,邱燕玲,等.高烈度地震区岩土体边坡崩塌动力学特性研究[J].西北地震学报,2011,33(1):34-39.
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