Wave propagation in fluid-saturated porous media: An efficient finite element procedure

Abstract An efficient finite element procedure to analyze wave propagation phenomena in fluid-saturated porous media is presented. The saturated porous medium is modelled as a two-phase system consisting of a solid and a fluid phase. Time integration of the resulting semi-discrete finite element equations is performed by using an implicit-explicit algorithm. In order to remove the time step size restriction associated with the presence of the stiff fluid in the mixture, the fluid contribution to the equations of motion is always treated implicitly. The procedure allows an optimal selection of the time step size independently of the fluid. Depending upon the particular intended applications (e.g., seismic, blast loading,...) the fluid may be assumed incompressible or compressible. Numerical results which demonstrate the accuracy and versatility of the proposed procedure are presented.

[1]  Jamshid Ghaboussi,et al.  Variational Formulation of Dynamics of Fluid-Saturated Porous Elastic Solids , 1972 .

[2]  T. Belytschko,et al.  A Précis of Developments in Computational Methods for Transient Analysis , 1983 .

[3]  John D. Ingram,et al.  A Continuum theory of chemically reacting media—I , 1965 .

[4]  O. Zienkiewicz,et al.  Dynamic behaviour of saturated porous media; The generalized Biot formulation and its numerical solution , 1984 .

[5]  John Lysmer,et al.  Analytical Procedures in Soil Dynamics , 1978 .

[6]  COMPLETENESS THEOREMS FOR LINEARIZED THEORIES OF INTERACTING CONTINUA , 1968 .

[7]  Jean H. Prevost,et al.  PLASTICITY THEORY FOR SOIL STRESS-STRAIN BEHAVIOR , 1978 .

[8]  D. H. Brownell,et al.  Shock−wave propagation in fluid−saturated porous media , 1975 .

[9]  M. Biot.  Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range , 1956 .

[10]  Jean H. Prevost,et al.  A simple plasticity theory for frictional cohesionless soils , 1985 .

[11]  J. Prévost.  Nonlinear transient phenomena in saturated porous media , 1982 .

[12]  John D. Ingram,et al.  A continuum theory of chemically reacting media—II Constitutive equations of reacting fluid mixtures☆ , 1967 .

[13]  J. Z. Zhu,et al.  The finite element method , 1977 .

[14]  R. Hill.  A general theory of uniqueness and stability in elastic-plastic solids , 1958 .

[15]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[16]  Thomas J. R. Hughes,et al.  Implicit-explicit finite elements in nonlinear transient analysis , 1979 .

[17]  K. Terzaghi.  Theoretical Soil Mechanics , 1943 .

[18]  Sabodh K. Garg,et al.  Compressional waves in fluid‐saturated elastic porous media , 1974 .

[19]  Chyr Pyng Liou,et al.  Numerical Model for Liquefaction , 1977 .

[20]  J. Prévost.  Mechanics of continuous porous media , 1980 .

[21]  Thomas J. R. Hughes,et al.  Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory , 1978 .

[22]  Thomas J. R. Hughes,et al.  IMPLICIT-EXPLICIT FINITE ELEMENTS IN TRANSIENT ANALYSIS: IMPLEMENTATION AND NUMERICAL EXAMPLES. , 1978 .

[23]  A. Cemal Eringen,et al.  Mechanics of continua , 1967 .

[24]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[25]  P. M. Naghdi,et al.  A Dynamical theory of interacting continua , 1965 .

[26]  Jamshid Ghaboussi,et al.  Liquefaction Analysis of Horizontally Layered Sands , 1978 .

[27]  Chiang C. Mei,et al.  Wave-induced responses in a fluid-filled poro-elastic solid with a free surface : A boundary layer theory , 1981 .

[28]  R. M. Bowen,et al.  Plane Progressive Waves in a Binary Mixture of Linear Elastic Materials , 1978 .

[29]  Jean H. Prevost,et al.  Implicit-explicit schemes for nonlinear consolidation , 1983 .