孔隙介质的时域BEM计算

丁伯阳; 蒋佳琪

doi:10.3879/j.issn.1000-0887.2015.01.003

孔隙介质的时域BEM计算

doi: 10.3879/j.issn.1000-0887.2015.01.003

浙江工业大学建筑工程学院, 杭州 310014

基金项目: 国家自然科学基金(11172268；51478435)

详细信息

作者简介:
丁伯阳(1949—),男, 浙江绍兴人,教授（E-mail: dingboyang@hzcnc.com）；蒋佳琪（1990—)，男，浙江湖州人,硕士生(通讯作者. E-mail: jiang-jiaqi@163.com;).

中图分类号: O357.3
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出版历程
- 收稿日期: 2014-04-03
- 修回日期: 2014-12-01
- 刊出日期: 2015-01-15

Time-Domain BEM Calculation for Porodynamics

College of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, P.R.China

Funds: The National Natural Science Foundation of China(11172268；51478435)

摘要

摘要: 根据Biot饱和孔隙介质动力方程，结合快、慢纵波解耦法得到时域Green函数U-P表达以及Somigliana表象积分，采用BEM分析了集中力作用下饱和孔隙介质时域动力响应.详细论述了孔隙介质时域边界积分方程的离散化方法与形式，它的Stokes状态解答和借用已有技术成果对计算奇异性的处理.在无量纲材料参数的数值分析计算中，以图表形式给出结果.由于孔隙介质的时域BEM计算在相关文献中较为罕见，因此文中结果会对两相饱和介质动力响应特性等相关研究提供一些新的途径.
- 时域BEM /
- 饱和孔隙介质 /
- 动力响应 /
- Green函数 /
- 奇异性处理方法
Abstract: The boundary element method (BEM) in time domain was employed for the dynamic analysis of saturated porous media subjected to external forces. Based on Biot’s porodynamic equations, the U-P formulation of Green’s function obtained through decoupling of the fast and slow dilational waves, the transformation of Stokes’state as well as Somigliana’s representation, the discretization forms of the boundary integration equations in time domain were discussed in detail. Specially, with the aid of achievement for a single-phase medium, the singularity in the integration of the BEM for a porous medium was successfully treated in numerical implementation. Finally, in several examples, the response results of the displacements and pore pressures from numerical calculation with dimensionless material parameters were presented. Since the time-domain BEM calculation is hardly found in porodynamics as yet, the proposed method makes a new way for the research of dynamic response of 2phase saturated porous media.
- BEM in time domain /
- saturated porous medium /
- dynamic response /
- Green’s function /
- singularity treatment

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参考文献(40)

[1]	Biot M A. General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,12(2): 155-164.
[2]	Frenkel J. On the theory of seismic and seismoelectric phenomena in a moist soil[J]. Journal of Physics,1944,13(4): 230-241.
[3]	Biot M A. Theory of propagation of elastic waves in a fluid-saturated porous solid—1: low frequency range[J].J Acoust Soc Am,1956,28(2): 168-178.
[4]	Biot M A. Theory of propagation of elastic waves in a fluid-saturated porous solid—2: higher frequency range[J].J Acoust Soc Am,1956,28(2): 179-191.
[5]	Biot M A, Willis D G. The elastic coefficients of the theory of consolidation[J].J Appl Mech,1957,24: 594-601.
[6]	Biot M A. Generalized theory of acoustic propagation in porous dissipative media[J].J Acoust Soc Am,1962,34(5): 1254-1264.
[7]	Bowen R M. Incompressible porous media models by use of the theory of mixtures[J].Int J Engng Sci,1980,18(9): 1129-1148.
[8]	Bowen R M. Compressional porous media models by use of the theory of mixtures[J].Int J Engng Sci,1982,20(6): 697-735.
[9]	Plona T J. Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies[J].Appl Phys Lett,1980,36(4): 259-261.
[10]	丁伯阳. 含裂隙介质受压破裂前地震波特性的综合实验研究与理论分析[J]. 西北地震学报, 1983, 5(5): 21-33.（DING Bo-yang. Experimental study and theoretical analysis of seismic wave charactristics before the cracks and pore medium[J].Northwestern Seismological Journal,1983,5(5): 21-33.(in Chinese)）
[11]	Plona T J, Johnson D L. Acoustic properties of porous systems—I: phenomenological description[C]//Physics and Chemistry of Porous Media . New York: Johnson D L, Sen P N, 1984: 89-104.
[12]	Burridge R, Vargas C A. The fundamental solution in dynamic poroelasticity[J].Geophys J Roy Astron Soc,1979,58(1): 61-90.
[13]	Manolis G D, Beskos D E. Integral formulation and fundamental solutions of dynamic poroelasticity and thermoelasticity[J].Acta Mechanica,1989,76(1/2): 89-104.
[14]	Manolis G D, Beskos D E. Errata inintegral formulation and fundamental solutions of dynamic poroelasticity and thermoelasticity[J].Acta Mechanica,1990,83(3/4): 223-226.
[15]	Norris A N. Radiation from a point source and scattering theory in a fluid saturated porous solid[J].J Acoust Soc Am,1985,77(6): 2012-2023.
[16]	Nowacki W.Dynamics Problems of Thermoelasticity[M]. Noordhoff, 1975.
[17]	Senjuntichai T, Rajapakse R K N D. Dynamic Green’s functions of homogeneous poroelastic half-plane[J].Journal Engineering Mechanics, ASCE,1994,120(11): 2381-2464.
[18]	Halpern M R, Christiano P. Response of poroelastic half space to steady-state harmonic surface tractions[J].Int J Numer Anal Meth Geomech,1986,10(6): 609-632.
[19]	Kaynia A M, Banerjee P K. Fundamental solutions of Biot’s equation of dynamic poroelasticity[J].Int J Engng Sci,1993,31(5): 817-830.
[20]	Auriault J L, Borne L, Chambon R. Dynamics of porous saturated media, checking of the generalized law of Darcy[J].J Acoust Soc Am,1985,77(5): 1641-1650.
[21]	Auriault J L. Dynamic behaviour of a porous medium saturated by a Newtonian fluid[J].Int J Engng Sci,1980,18(6): 775-785.
[22]	Cleary M P. Fundamental solutions for a fluid-saturated porous solid[J].Int J Solid Struct,1977,13(9): 785-806.
[23]	Philippacopoulos A J. Waves in a partially saturated layered half-space analytic formulation[J].Bull Seism Soc Am,1987,77(5): 1838-1853.
[24]	Philippacopoulos A J. Lamb’s problem for fluid-saturated porous media[J].Bull Seism Soc Am ,1988,78(2): 908-923.
[25]	Bonnet G. Basic singular solutions for a poroelastic medium in the dynamic range[J].J Acoust Soc Am,1987,82(5): 1758-1762.
[26]	Cheng A H D, Badmus T, Beskos D E. Integral equation for dynamic poroelasticity in frequency domain with BEM solution[J].Journal Engineering Mechanics,1991,117(5): 1136-1157.
[27]	Cheng A H D, Detournay E. On Singular integral equations and fundamental solutions of poroelasticity[J].Int J Solids Struct,1998,35(34/35): 4521-4555.
[28]	Erigen A C, Suhubi E S.Elastodynamics—II: Linear Theory [M]. New York: Academic, 1975.
[29]	Cheng A H D, Detournay E. A direct boundary element method for plane strain poroelasticity[J].Int J Numer Anal Meth Geomech,1988,12(5): 551-572.
[30]	Manolis G D. A comparative study on three boundary element method approaches to problems in elastodynamics[J].Int J Numer Meth Engng,1983,19(1): 73-91.
[31]	Banerjee P K, Ahmad S, Manolis G D.Transient elastodynamic analysis of three-dimensional problems by boundary element method[J].Earthquake Engng Struct Dyn,1986,14(6): 933-949.
[32]	Dominguez J.Boundary Elements in Dynamics [M]. Southampton/London: Computational Mechanics Publications/Elsevier, 1993.
[33]	Dominguez J, Marrero M. Numerical behavior of time domain BEM for three-dimensional transient elastodynamic problems[J].Engng Analysis With Boundary Elements,2003,27(1): 39-48.
[34]	姚振汉, 王海涛. 边界元法[M]. 北京: 高等教育出版社, 2010.(YAO Zhen-han, WANG Hai-tao.Boundary Element Methods [M]. Beijing: Higher Education Press, 2010.(in Chinese))
[35]	Ariza M P, Saez A, Dominguez J. A singular element for three dimensional fracture mechanics analysis[J].Engng Anal Bound Elem,1997,20(4): 275-285.
[36]	Chen J. Time domain fundamental solutions to Biot’s complete equations of dynamic poroelasticity—part I：two-dimensional solution[J].Int J Solid Struct,1994,31(10): 1447-1490.
[37]	Chen J. Time domain fundamental solutions to Biot’s complete equations of dynamic poroelasticity—part II: three-dimensional solution[J].Int J Solid Struct,1994,31(2): 169-202.
[38]	DING Bo-yang, Alexander H D Cheng, CHEN Zhang-long. Fundamental solutions of poroelastodynamics in frequency domain based on wave decomposition[J].J Appl Mech,2013,80(5): 061021(1)-061021(12).
[39]	Ding B Y, Yuan J H. Dynamic Green’s functions of a two-phase saturated medium subjected to a concentrated force[J].Int J Solids Struct,2011,48(16/17): 2288-2303.
[40]	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): 1066-1074.(DING Bo-yang, DANG Gai-hong, YUAN jin-hua. Lamb’s integral formulas of two-phase saturated medium for soil dynamic with drainage[J].Appl Math Mech,2010,31(9): 1066-1074.(in Chinese))