考虑耦合质量影响的饱和多孔介质动力响应分析的显式有限元法
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摘要
根据B iot饱和多孔介质动力方程,采用解耦技术,提出了考虑耦合质量aρ影响的饱和多孔介质中动力响应分析的显式有限元法。文中建立并推导了显式有限元的公式,编制了相应的计算程序并进行了实例计算。计算结果与解析解进行了对比,两者符合很好,表明本文方法是处理饱和多孔介质动力问题的一种有效方法。文中还分析了耦合质量aρ对固相和液相动位移的影响。
An explicit finite element method considering the effect of coupling mass for dynamic analysis of fluid saturated porous media is developed.In the paper,the formulas of the explicit finite element are deduced,and the computer program is developed.The results show that the differences between the results of the explicit finite element method and the results of the analytical methods are very small and the accuracy is satisfactory.Application showed that the explicit finite element method developed in the paper is a very efficient method for dynamic analysis of fluid saturated porous media.The effects of coupling mass on the dynamic displacements of solid and liquid phase is also analyzed.It revealed that the coupling mass of fluid saturated porous media has some considerable effects on the dynamic displacements of the liquid phase,but no obvious effects on the dynamic displacements of solid phase.
An explicit finite element method considering the effect of coupling mass for dynamic analysis of fluid saturated porous media is developed.In the paper,the formulas of the explicit finite element are deduced,and the computer program is developed.The results show that the differences between the results of the explicit finite element method and the results of the analytical methods are very small and the accuracy is satisfactory.Application showed that the explicit finite element method developed in the paper is a very efficient method for dynamic analysis of fluid saturated porous media.The effects of coupling mass on the dynamic displacements of solid and liquid phase is also analyzed.It revealed that the coupling mass of fluid saturated porous media has some considerable effects on the dynamic displacements of the liquid phase,but no obvious effects on the dynamic displacements of solid phase.
引文
[1]BO IT M A.T heory of propagation of e lastic w ave ina flu id-saturated porous so lid[J].T he J ourna l of theA coustica l S ociety of Am erica,1956,28(2):168-178.
[2]赵成刚,等.固体、流体多相孔隙介质中的波动理论及其数值模拟进展[J].力学进展,1998,28(1):83-92.(ZHAO Cheng-gang,et a l.R ev iew of w avepropagation theory in saturated and unsaturatedporous m ed ium and its num erica l nethods[J].A d-vances in M echan ics,1998,28(1):83-92.(inCh inese))
[3]赵成刚,高福平,等.波在饱和多孔介质与弹性固体介质交界面上的界面效应[J].地震工程与工程振动,1999,19(1):1-6.(ZHAO Cheng-gang,GAO Fu-p ing,et a l.Boundary effect of w ave propagatingfrom liqu id-filled porous m ed ium to so lid m ed ium[J].E arthquake E ng ineering and E ng ineering V i-bra tion,1999,19(1):1-6.(in Ch inese))
[4]李伟华,赵成刚.圆弧形凹陷饱和土场地对平面P波散射问题的解析解[J].地球物理学报,2003,46(4):539-546.(L IW e i-hua,ZHAO Cheng-geng.A n ana-lytica l so lu tion for the d iffraction of p lane P-w avesby c ircu lar cy lindrica l canyons in a flu id-saturatedporous m ed ia ha lf space[J].Ch inese J ourna l of G eo-phy sics,2003,46(4):539-546.(in Ch inese))
[5]李伟华,赵成刚.饱和土沉积谷场地对平面P波的散射[J].岩土工程学报,2003,25(3):346-351.(L IW e i-hua,ZHAO Cheng-gang.Scattering of p lane Pw aves in a lluv ia l va lleys w ith saturated so l depos its[J].Ch inese J ourna l of G eotechn ica l E ng ineering,2003,25(3):346-351.(in Ch inese))
[6]CHEN J.T im e dom a in fundam en ta l so lu tion to B iotcom p lete equations of dynam ic poro-e lastic ity Part I:tw o-d im ens iona l so lu tion[J].Int J S olid s S truc-tures,1994,31(10):1447-1490.
[7]Z IENK IEW ICZ O C,et a l.D ynam ic behav ior of sat-urated porous m ed ia,the genera lized B iot form u latinand its num erica l so lu tion[J].Int J N um er Ana lM ethod s G eom ech,1984(8):71-96.
[8]PREVO ST JH.W ave propagation in flu id-saturatedporous m ed ia:A n effic ien t fin ite e lem en t procedure[J].S oil Dynam ics and E arthquake E ng ineering,1985,4(4):183-201.
[9]赵成刚,等.流体饱和两相多孔介质动力反应分析的显式有限元法[J].岩土工程学报,2001,23(2):178-182.(ZHAO Cheng-gang,et a l.D ynam ic ana lys is ina flu id saturated porous so lid by us ing exp lic it fin itee lem en t m ethod[J].Ch inese J ourna l of G eotechn ica lE ng ineering,2001,23(2):178-182.(in Ch inese))
[10]赵成刚,李伟华,等.三种介质耦联系统动力分析的显式有限元法及其应用[J].地震学报,2003,25(3):262-271.(ZHAO Cheng-gang,L I W e i-hua,eta l.A n exp lic it fin ite e lem en t m ethod for dynam icana lys is in three-m ed ium coup ling system and itsapp lication[J].A cta S eism olog ica S in ica,2003,25(3):262-271.(in Ch inese))
[11]L IAO Z P,W ONG H L.A trans im itting boundaryfor num erica l s im u lation of e lastic w ave propagation[J].S oil dynam ics and E arthquake E ng ineering,1984,3(4):176-183.
[2]赵成刚,等.固体、流体多相孔隙介质中的波动理论及其数值模拟进展[J].力学进展,1998,28(1):83-92.(ZHAO Cheng-gang,et a l.R ev iew of w avepropagation theory in saturated and unsaturatedporous m ed ium and its num erica l nethods[J].A d-vances in M echan ics,1998,28(1):83-92.(inCh inese))
[3]赵成刚,高福平,等.波在饱和多孔介质与弹性固体介质交界面上的界面效应[J].地震工程与工程振动,1999,19(1):1-6.(ZHAO Cheng-gang,GAO Fu-p ing,et a l.Boundary effect of w ave propagatingfrom liqu id-filled porous m ed ium to so lid m ed ium[J].E arthquake E ng ineering and E ng ineering V i-bra tion,1999,19(1):1-6.(in Ch inese))
[4]李伟华,赵成刚.圆弧形凹陷饱和土场地对平面P波散射问题的解析解[J].地球物理学报,2003,46(4):539-546.(L IW e i-hua,ZHAO Cheng-geng.A n ana-lytica l so lu tion for the d iffraction of p lane P-w avesby c ircu lar cy lindrica l canyons in a flu id-saturatedporous m ed ia ha lf space[J].Ch inese J ourna l of G eo-phy sics,2003,46(4):539-546.(in Ch inese))
[5]李伟华,赵成刚.饱和土沉积谷场地对平面P波的散射[J].岩土工程学报,2003,25(3):346-351.(L IW e i-hua,ZHAO Cheng-gang.Scattering of p lane Pw aves in a lluv ia l va lleys w ith saturated so l depos its[J].Ch inese J ourna l of G eotechn ica l E ng ineering,2003,25(3):346-351.(in Ch inese))
[6]CHEN J.T im e dom a in fundam en ta l so lu tion to B iotcom p lete equations of dynam ic poro-e lastic ity Part I:tw o-d im ens iona l so lu tion[J].Int J S olid s S truc-tures,1994,31(10):1447-1490.
[7]Z IENK IEW ICZ O C,et a l.D ynam ic behav ior of sat-urated porous m ed ia,the genera lized B iot form u latinand its num erica l so lu tion[J].Int J N um er Ana lM ethod s G eom ech,1984(8):71-96.
[8]PREVO ST JH.W ave propagation in flu id-saturatedporous m ed ia:A n effic ien t fin ite e lem en t procedure[J].S oil Dynam ics and E arthquake E ng ineering,1985,4(4):183-201.
[9]赵成刚,等.流体饱和两相多孔介质动力反应分析的显式有限元法[J].岩土工程学报,2001,23(2):178-182.(ZHAO Cheng-gang,et a l.D ynam ic ana lys is ina flu id saturated porous so lid by us ing exp lic it fin itee lem en t m ethod[J].Ch inese J ourna l of G eotechn ica lE ng ineering,2001,23(2):178-182.(in Ch inese))
[10]赵成刚,李伟华,等.三种介质耦联系统动力分析的显式有限元法及其应用[J].地震学报,2003,25(3):262-271.(ZHAO Cheng-gang,L I W e i-hua,eta l.A n exp lic it fin ite e lem en t m ethod for dynam icana lys is in three-m ed ium coup ling system and itsapp lication[J].A cta S eism olog ica S in ica,2003,25(3):262-271.(in Ch inese))
[11]L IAO Z P,W ONG H L.A trans im itting boundaryfor num erica l s im u lation of e lastic w ave propagation[J].S oil dynam ics and E arthquake E ng ineering,1984,3(4):176-183.
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