On the Fundamental Solution of Dynamic Poroelastic Boundary Integral Equations in the Time Domain

REFERENCES

• Biot , M. A. 1956 . Theory of propagation of elastic waves in a fluid-saturated porous solid: I. Low-frequency range. II. Higher frequency range . J. Acoust. Soc. Am. , 28 : 168 – 191 .
   Web of Science ®Google Scholar
• Zienkiewicz , O. C. and Shiomi , T. 1984 . Dynamic behavior of saturated porous media; the generalized Biot formulation and its numerical solution . Int. J. Numer. Anal. Methods Geomech. , 8 : 71 – 96 .
   Web of Science ®Google Scholar
• Prevost , J. H. 1987 . Dynamics of porous media . Geotechnical Modeling and Applications , : 76 – 146 .
   Google Scholar
• Gatmiri , B. 1989 . A simplified finite element analysis of wave-induced effective stresses and pore pressures in permeable sea beds . Geotechnique , 40 : 15 – 30 .
   Google Scholar
• Manolis , G. D. and Beskos , D. E. 1989 . Integral formulation and fundamental solution of dynamic poroelasticity and thermoelasticity . Acta Mech. , 76 : 89 – 104 .
   Web of Science ®Google Scholar
• Noriss , A. N. 1985 . Radiation from a point source and scattering theory in a fluid-saturated porous solid . J. Acoust. Soc. Am. , 77 : 2012 – 2023 .
   Google Scholar
• Cheng , A. H.D. and Liggett , J. A. 1984 . Boundary integral equation method for linear porous elasticity with application to soil consolidation . Int. J. Numer. Methods Eng. , 20 : 255 – 278 .
   Web of Science ®Google Scholar
• Dominguez , J. 1991 . An integral formulation for dynamic poroelasticity . J. Appl. Mech. ASME , 58 : 588 – 591 .
   Google Scholar
• Dominguez , J. 1992 . Boundary element approach for dynamic poroelastic problems . Int. J. Numer. Methods Eng. , 35 : 307 – 324 .
   Google Scholar
• Kupradze , V. D. 1979 . Three Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity , Amsterdam : North-Holland .
   Google Scholar
• Bonnet , G. 1987 . Basic singular solutions for a poroelastic medium in the dynamic range . J. Acoust. Soc. Am. , 82 : 1758 – 1762 .
   Google Scholar
• Chang , A. H.D. , Badmus , T. and Beskos , D. E. 1991 . Integral equation for dynamic poroelasticity in frequency domain with boundary element solution' . J. Eng. Mech. ASCE , 117 : 1136 – 1157 .
   Google Scholar
• Nishimura , N. 1981 . “ A BIE formulation for consolidation problems ” . In Boundary element methods edited by Brebbia , 325 – 334 . Berlin : Springer .
   Google Scholar
• Dargush , G. F. and Banerjee , P. K. 1989 . A time domain boundary element method for poroelasticity . Int. J. Numer. Methods In Eng. , 28 : 2434 – 2449 .
   Google Scholar
• Mansur , W. J. 1983 . A time stepping technique to solve wave propagation problems using the boundary element method , Southampton University . Ph.D. Thesis
   Google Scholar
• Antes , H. 1985 . A boundary element procedure for transient wave propagation in two-dimensional isotropic elastic media . Finite Element Anal. Des. , 1 : 313 – 322 .
   Google Scholar
• Wiebe , Th. and Antes , H. 1991 . A time domain integral formulation of dynamic poroelasticity . Acta Mech. , 90 : 125 – 137 .
   Google Scholar
• Kaynia , A. M. 1992 . Transient greens functions of fluid-saturated porous media . Computers & Structures , 44 : 19 – 27 .
   Google Scholar
• Chen , J. 1994 . Time domain fundamental solution to Biot's equations of dynamic poroelasticity, Part I: Two-dimensional solution . Int. J. Solids Structures , 32 ( 15 ) : 2257 – 2278 .
   Google Scholar
• Gatmiri , B. and Kamalian , M. 1999 . “ Transient BIE and fundamental solutions of dynamic poroelasticity ” . In Numerical Models in Geomechanics , Graz : NUMOG VII .
   Google Scholar
• Ditkine , V. and Proudnikov , A. 1978 . Transformations integrales et calcul operationels , Editions Mir Moscau, Traduction francaise Editions Mir .
   Google Scholar
• Yew , C. H. and Jogi , P. N. 1978 . The determination of Biot's parameters for sandstones . Exp. Mech. , 18 : 167 – 172 .
   Web of Science ®Google Scholar
• Burridge , R. and Vargas , C. A. 1979 . The fundamental solution in dynamic poroelasticity . Geophys. J. R. Astr. Soc. , 58 : 61 – 90 .
   Web of Science ®Google Scholar