饱和土中伴有排水问题爆炸场动力反应Green函数计算
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摘要
饱和土在动力作用下伴有排水的反应是工程中常见的现象,其计算也是一个非常复杂的数学力学问题。根据已经求得的集中力作用下两相饱和介质Green函数基本解,得到球坐标的扩张源固相位移时域Green函数的表达式。再以物理的方法推导出球坐标中心扩张源时域流相的压力Green函数;以及相对应的注入流相后,场点的时域固相位移Green函数和流相压力Green函数的表达式。再结合导出的两相饱和介质Lamb方程,进行动力排水问题的计算,解决饱和土爆炸场中伴有排水的动力反应计算问题。
It is a common phenomenon that vibration or shock of explosion field is accompanied with drainage under dynamic load in saturated soil.Based on the already derived 3-dimensional Green function of a two-phase saturated medium in time domain,the displacement Green function of solid-phase of a two-phase saturated medium with expansion source in spherical coordinate Grr(basic solution) was deduced.The corresponding pressure Green function of solid-phase G4r was also obtained with physical method.Likewise,the displacement and pressure Green functions Gr4 and G44 of fluid-phase were provided.Linking with Lamb integral formula(the representative theorem) for two-phase saturated medium,the dynamic responses of the explosive field with drainage in saturated soil were calculated.The nondimensional displacement,pore pressure and drainage flux were illustrated by figures in the paper.
It is a common phenomenon that vibration or shock of explosion field is accompanied with drainage under dynamic load in saturated soil.Based on the already derived 3-dimensional Green function of a two-phase saturated medium in time domain,the displacement Green function of solid-phase of a two-phase saturated medium with expansion source in spherical coordinate Grr(basic solution) was deduced.The corresponding pressure Green function of solid-phase G4r was also obtained with physical method.Likewise,the displacement and pressure Green functions Gr4 and G44 of fluid-phase were provided.Linking with Lamb integral formula(the representative theorem) for two-phase saturated medium,the dynamic responses of the explosive field with drainage in saturated soil were calculated.The nondimensional displacement,pore pressure and drainage flux were illustrated by figures in the paper.
引文
[1]Biot M A.Theory of propagation of elastic wave in a fluid-saturated soil[J].J Acoust Soc Am,1956,28:168-178.
[2]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].J Appl Phys,1962,33:1482-1498.
[3]刘银斌,李幼铭,吴如山.横向各向同性多孔介质中的地震波传播[J].地球物理学报,1994,37(4):499-514.
[4]丁伯阳,樊良本,吴建华.两相饱和介质中的集中力点源位移场解与应用[J].地球物理学报,1999,42(6):800-808.
[5]丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数[J].力学学报,2001,33(2):234-241.
[6]Chen J.Time domain function solution to biot’s complete equations of dynamic poroelasticity PartⅡ:two dimensional solution[J].Int.J.Solid Struct,1994,31(10):1447-1490.
[7]Chen J.Time domain function solution to biot’s complete equations of dynamic poroelasticity PartⅠ:three dimensional solution[J].Int.J.Solid Struct,1994,31(2):169-202.
[8]丁伯阳,宋新初,袁金华.关于两相饱和介质中流相Green函数的解析解[J].地球物理学报,2009,52(7):1858-1866.
[9]丁伯阳,党改红,袁金华,伴有排水的两相饱和介质动力问题的LAMB积分公式[J].应用数学和力学,2010,31(9):1131-1142.
[10]苗天德,朱久江,丁伯阳.对饱和多孔介质波动问题中本构关系的探讨[J].力学学报,1995,27(5):536-543.
[11]艾龙根,舒胡毕.弹性动力学[M].戈革,译.北京:石油工业出版社,1984.
[12]丁伯阳,袁金华,潘晓东.饱和土动力学问题Green函数计算的抽象集成与OPP实现[J].中国科学G辑,2009,39(2):284-292.
[13]丁伯阳,宋新初,袁金华.饱和土隧道内集中荷载作用下振动位移反应的Green函数解答[J].工程力学,2009,30(3):153-157.
[14]丁伯阳,党改红,袁金华.Green函数对饱和土隧道内集中荷载作用振动位移反应的计算[J].振动与冲击,2009,28(11):110-114.
[15]丁伯阳,丁翠红,陈禹,等.集中力作用下两相饱和介质二维位移场Green函数[J].应用数学和力学,2004,25(8):869-874.
[2]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].J Appl Phys,1962,33:1482-1498.
[3]刘银斌,李幼铭,吴如山.横向各向同性多孔介质中的地震波传播[J].地球物理学报,1994,37(4):499-514.
[4]丁伯阳,樊良本,吴建华.两相饱和介质中的集中力点源位移场解与应用[J].地球物理学报,1999,42(6):800-808.
[5]丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数[J].力学学报,2001,33(2):234-241.
[6]Chen J.Time domain function solution to biot’s complete equations of dynamic poroelasticity PartⅡ:two dimensional solution[J].Int.J.Solid Struct,1994,31(10):1447-1490.
[7]Chen J.Time domain function solution to biot’s complete equations of dynamic poroelasticity PartⅠ:three dimensional solution[J].Int.J.Solid Struct,1994,31(2):169-202.
[8]丁伯阳,宋新初,袁金华.关于两相饱和介质中流相Green函数的解析解[J].地球物理学报,2009,52(7):1858-1866.
[9]丁伯阳,党改红,袁金华,伴有排水的两相饱和介质动力问题的LAMB积分公式[J].应用数学和力学,2010,31(9):1131-1142.
[10]苗天德,朱久江,丁伯阳.对饱和多孔介质波动问题中本构关系的探讨[J].力学学报,1995,27(5):536-543.
[11]艾龙根,舒胡毕.弹性动力学[M].戈革,译.北京:石油工业出版社,1984.
[12]丁伯阳,袁金华,潘晓东.饱和土动力学问题Green函数计算的抽象集成与OPP实现[J].中国科学G辑,2009,39(2):284-292.
[13]丁伯阳,宋新初,袁金华.饱和土隧道内集中荷载作用下振动位移反应的Green函数解答[J].工程力学,2009,30(3):153-157.
[14]丁伯阳,党改红,袁金华.Green函数对饱和土隧道内集中荷载作用振动位移反应的计算[J].振动与冲击,2009,28(11):110-114.
[15]丁伯阳,丁翠红,陈禹,等.集中力作用下两相饱和介质二维位移场Green函数[J].应用数学和力学,2004,25(8):869-874.
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