饱和土固结的轴对称边界元特殊积分法分析
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摘要
根据饱和土Biot固结理论,采用特殊积分法在柱坐标系下,建立了饱和土体固结的轴对称边界元积分方程。首先通过全局形函数及虚密度函数表示饱和土体Navier方程中的孔压与孔隙流量方程中的瞬态项,从而得到特殊的孔压、位移及流量积分,然后在柱坐标系下将特殊解沿环向积分,得到饱和土体固结问题的轴对称边界元积分方程,最后通过算例与文献结果进行比较,验证此方法的正确性。
Based on the Biot’s consolidation theory and according to the particular integrals method,the axisymmetric BEM formulation is developed for analyzing the consolidation of saturated soil in the cylindrical coordinates.By approximating the pore pressure loading term in the Navier equation and the transient terms in the pore fluid flow equation with known global shape functions and fictitious density functions,the particular integrals for displacement and pore pressure can be easily derived.In order to obtain the corresponding axisymmetric BEM formulation for analyzing the consolidation of the saturated soil,the particular integrals are rewritten in cylindrical coordinates by integrating along the circumferential direction.Numerical results for axisymmetric problems of soil consolidation are given and compared with the known results to demonstrate the validity and accuracy of the present formulation.
Based on the Biot’s consolidation theory and according to the particular integrals method,the axisymmetric BEM formulation is developed for analyzing the consolidation of saturated soil in the cylindrical coordinates.By approximating the pore pressure loading term in the Navier equation and the transient terms in the pore fluid flow equation with known global shape functions and fictitious density functions,the particular integrals for displacement and pore pressure can be easily derived.In order to obtain the corresponding axisymmetric BEM formulation for analyzing the consolidation of the saturated soil,the particular integrals are rewritten in cylindrical coordinates by integrating along the circumferential direction.Numerical results for axisymmetric problems of soil consolidation are given and compared with the known results to demonstrate the validity and accuracy of the present formulation.
引文
[1]BANERJEE P K,BUTTERFIELD R.Boundary elementmethods in engineering science[M].London:McGraw-Hill,1981.
[2]CHENG A H D,LIGGETT J A.Boundary integral equationmethod for linear porous elasticity with application to soilconsolidation[J].International Journal for NumericalMethods in Engineering,1984,20(2):255-278.
[3]CHEN J,DARGUSH G F.Boundary element method fordynamic poroelastic and thermoelastic analyses[J].International Journal of Solids and Structures,1995,32(15):2259-2278.
[4]DARGUSH G F,BANERJEE P K.A new boundary elementmethod for three-dimensional coupled problems ofconsolidation and thermoelasticity[J].Journal of AppliedMechanics,ASME,1991,58(1):28-36.
[5]DARGUSH G F.A boundary element method foraxisymmetric soil consolidation[J].International Journal ofSolids and Structures,1991,28(7):897-915.
[6]PARK K H,BANERJEE P K.Two-and three-dimensionaltransient thermoelastic analysis by BEM via particularintegral[J].International Journal of Solids and Structures,2002,39(10):2871-2892.
[7]PARK K H,BANERJEE P K.A simple BEM formulation forporoelasticity via particular integrals[J].International Journalof Solids and Structures,2006,43(11):3613-3625.
[8]张玉红,黄义,王忠建.层状饱水软土地基三维非轴对称动力响应分析方法[J].地震工程与工程振动,2002,22(4):47-52.(ZHANG Yu-hong,HUANG Yi,WANGZhong-jian.Analysis procedures of dynamic response of 3-Dnon-axisymmetric layered saturated soil[J].EarthquakeEngineering and Engineering Vibration,2002,22(4):47-52.(in Chinese))
[9]BANERJEE,P K.The boundary element methods inengineering[M].London:McGraw-Hill,1994.
[10]BIOT M A.General theory of three-dimensionalconsolidation[J].Journal of Applied Physics,1941,12(2):155-164.
[11]CRYER C W.A comparison of the three-dimensionalconsolidation theories of Biot and Terzaghi[J].The QuarterlyJournal of Mechanics and Applied Mathematics,1963,16(4):401-411.
[12]GIBSON R E,SCHIFFMAN R L,PU S L.Plane strain andaxially symmetric consolidation of a clay layer on a smoothimpervious base[J].The Quarterly Journal of Mechanics andApplied Mathematics,1970,23(4):505-520.
[2]CHENG A H D,LIGGETT J A.Boundary integral equationmethod for linear porous elasticity with application to soilconsolidation[J].International Journal for NumericalMethods in Engineering,1984,20(2):255-278.
[3]CHEN J,DARGUSH G F.Boundary element method fordynamic poroelastic and thermoelastic analyses[J].International Journal of Solids and Structures,1995,32(15):2259-2278.
[4]DARGUSH G F,BANERJEE P K.A new boundary elementmethod for three-dimensional coupled problems ofconsolidation and thermoelasticity[J].Journal of AppliedMechanics,ASME,1991,58(1):28-36.
[5]DARGUSH G F.A boundary element method foraxisymmetric soil consolidation[J].International Journal ofSolids and Structures,1991,28(7):897-915.
[6]PARK K H,BANERJEE P K.Two-and three-dimensionaltransient thermoelastic analysis by BEM via particularintegral[J].International Journal of Solids and Structures,2002,39(10):2871-2892.
[7]PARK K H,BANERJEE P K.A simple BEM formulation forporoelasticity via particular integrals[J].International Journalof Solids and Structures,2006,43(11):3613-3625.
[8]张玉红,黄义,王忠建.层状饱水软土地基三维非轴对称动力响应分析方法[J].地震工程与工程振动,2002,22(4):47-52.(ZHANG Yu-hong,HUANG Yi,WANGZhong-jian.Analysis procedures of dynamic response of 3-Dnon-axisymmetric layered saturated soil[J].EarthquakeEngineering and Engineering Vibration,2002,22(4):47-52.(in Chinese))
[9]BANERJEE,P K.The boundary element methods inengineering[M].London:McGraw-Hill,1994.
[10]BIOT M A.General theory of three-dimensionalconsolidation[J].Journal of Applied Physics,1941,12(2):155-164.
[11]CRYER C W.A comparison of the three-dimensionalconsolidation theories of Biot and Terzaghi[J].The QuarterlyJournal of Mechanics and Applied Mathematics,1963,16(4):401-411.
[12]GIBSON R E,SCHIFFMAN R L,PU S L.Plane strain andaxially symmetric consolidation of a clay layer on a smoothimpervious base[J].The Quarterly Journal of Mechanics andApplied Mathematics,1970,23(4):505-520.
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