Silent boundary conditions for wave propagation in saturated porous media

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 20, Issue 4, 1996, Pages 253-273

  Gajo, A ^a   Saetta, A ^b   Vitaliani, R ^c  

^a UNIVERSITY OF TRENTO   (Italy)

^b UNIVERSITY IUAV OF VENICE   (Italy)

^c UNIVERSITY OF PADOVA   (Italy)

Author keywords

Elastic porous media; First order silent boundary technique; Wave propagation

Indexed keywords

BOUNDARY CONDITIONS; ELASTIC WAVES; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; POROUS MATERIALS; WAVE PROPAGATION;

FIRST ORDER SILENT BOUNDARY TECHNIQUE; SATURATED POROUS MEDIA;

SOIL MECHANICS;

BOUNDARY CONDITIONS; ELASTIC POROUS MEDIUM; FINITE ELEMENT MODEL; SILENT BOUNDARY; WAVE PROPAGATION;

EID: 0030114785     PISSN: 03639061     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1096-9853(199604)20:4<253::aid-nag820>3.0.co;2-n     Document Type: Article

References (47)

1. D. Givoli, 'Non-reflecting boundary conditons: a review', J. Comput. Phys. 94, 1-29 (1991)
2. O. C. Zienkiewicz, D. W. Kelly and P. Bettess, 'The coupling of the finite element method and boundary solution procedure', Int. j. numer. methods eng., 11, 355-375 (1977).
3. H. L. Wong, 'Effect of surface topology on the diffraction of P, SV and Rayleigh waves', Bull. Seism. Soc. Am., 72, 1167-1183 (1982).
4. F. J. Sanchez-Sesma, 'Diffraction of elastic waves by three-dimensional surface irregularities', Bull. Seism. Soc. Am., 73, 1621-1636 (1983).
5. K. R. Khair, S. K. Datta and A. H. Shah, 'Amplification of obliquely incident seismic waves by cylindrical alluvial valleys of arbitrary cross-sectional shapes, Part I: Incident P and SV waves', Bull. Seism. Soc. Am., 79, 610-630 (1989).
6. E. Kausel, 'Local transmitting boundaries', J. Eng. Mech. Div ASCE, 114, 1011-1027 (1988).
7. H. Kawase, 'Time-domain response of a semi-circular canyon for incident SV, P and Rayleigh waves calculated by the discrete wave number boundary element method', Bull. Seism. Soc. Am., 78, 1415-1437 (1988).
8. D. Givoli, 'A numerical solution procedure for exterior wave problems', Comput. Struct., 43, 77-85 (1992).
9. J. Lysmer and R. L. Kuhlemeyer, 'Finite dynamic model for infinite media', J. Eng. Mech. Div. ASCE, 95, 859-877 (1969).
10. W. White, S. Valliappan and I. K. Lee, 'Unified boundary for finite dynamic models', J. Eng. Mech. Div. ASCE, 103, 949-964 (1977).
11. A. Castellani, 'Boundary conditions to simulate an infinite space', Meccanica, 9, 199-205 (1974).
12. M. Cohen and P. C. Jennings, 'Silent boundary methods for transient analysis', in T. Belytschko and T. J. R. Huges (eds), Computational Methods for Transient Analysis, Elsevier, Amsterdam, 1983, pp. 302-360.
13. R. Clayton and B. Enquist, 'Absorbing boundary conditions for acoustic and elastic wave equations', Bull. Seism. Soc. Am., 67, 1529-1540 (1977).
14. B. Engquist and A. Majda, 'Absorbing boundary conditions for the numerical simulation of waves', Math. Comput. 31, 629-651 (1977).
15. T. J. R. Hughes, 'A simple scheme for developing upwind finite elements', Int. j. numer. methods eng., 12, 1359-1369 (1978).
16. K. D. Mahrer, 'An empirical study of instability and improvement of absorbing boundary conditions for the elastic wave equation', Geophys, 51, 1499-1501 (1986).
17. E. Kausel, 'Physical interpretation and stability of paraxial boundary conditions', Bull. Seism. Soc. Am., 82, 898-913 (1992).
18. R. L. Higdom, 'Radiation boundary conditions for elastic wave propagation', SI AM J. Numer. Anal, 27, 831-870 (1990).
19. R. L. Higdom, 'Absorbing boundary conditions for acoustic and elastic waves in stratified media', J. Comput. Phys., 101, 386-418 (1992).
20. Z. P. Liao and H. L. Wong, 'A transmitting boundary for the numerical simulation of elastic wave propagation', Soil Dyn. Earthquake Eng., 3, 133-144 (1984).
21. R. L. Higdom, 'Initial-boundary value problems for linear hyperbolic systems', SI AM Rev., 28, 177-217 (1986).
22. Z. P. Liao and J. B. Liu, 'Numerical instabilities of a local transmitting boundary', Earthquake Eng. Struct. Dyn., 21, 65-77 (1992).
23. C. Peng and M. N. Toksoz, 'An optimal absorbing boundary condition for finite difference modelling of acoustic and elastic wave propagation', J. Acoust. Soc. Am., 95, 733-745 (1994).
24. W. D. Smith, 'A non-reflecting plane boundary for wave propagation problems', J. Comput. Phys., 15, 492-503 (1974).
25. P. A. Cundall, 'Solution of infinite dynamic problems by finite modelling in time domain', Proc. 2nd Int. Conf. Appl. Math. Modeling, Madrid. 1978.
26. P. Bettess and O. C. Zienkiewicz, 'Diffusion and refraction of surface waves using finite and infinite elements', Int. j. numer. methods eng., 11, 1271-1290 (1977).
27. O. C. Zienkiewicz, K. Bando, P. Bettess, C. Emson and T. C. Chiam, 'Mapped infinite elements for exterior wave problems', Int. j. numer. methods eng., 21, 1229-1251 (1985).
28. Y. K. Chow and I. M. Smith, 'Static and periodic infinite elements', Int. j. numer. methods eng., 17, 503-526 (1981).
29. G. Degrande and G. De Roeck, 'An absorbing boundary condition for wave propagation in saturated poroelastic media. Part I: Formulation and efficiency evalution', Soil Dyn. Earthquake Eng., 12, 411-421 (1993).
30. G. Degrande and G. De Roeck, 'An absorbing boundary condition for wave propagation in saturated poroelastic media. Part II: Finite element formulation', Soil Dyn. Earthquake Eng., 12, 423-432 (1993).
31. M. A. Biot, 'General theory of three-dimensional consolidation', J. Appl. Phys., 12, 155-164 (1941).
32. M. A. Biot, Theory of propagation of elastic waves in a fluid saturated porous solid', J. Acoust. Soc. Am., 38, 168-191 (1956).
33. M. A. Biot, 'Mechanics of deformation and acoustic propagation in porous media', J. Appl. Phys., 33, 1482-1498 (1962).
34. M. A. Biot, 'Generalized theory of acoustic propagation in porous dissipation media', J. Acoust. Soc. Am., 34, 1254-1264 (1962).
35. A. H. D. Cheng, T. Badmus and D. E. Beskos, 'Integral equation for dynamic poroelasticity in frequency domain with BEM solution', J. Eng. Mech. Div. ASCE, 117, 1136-1157 (1991).
36. J. Chen, 'Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. Part I: two-dimensional solution', Int. J. Solids Struct., 31, 1447-1490 (1994).
37. O. C. Zienkiewicz and T. Shiomi, 'Dynamic behaviour of saturated porous media: the generalized Biot formulatlion and its numerical solution', Int. J. Numer. Anal. Methods Geomech., 8, 71-86 (1984).
38. B. R. Simon, J. S.-S. Wu, O. C. Zienkiewicz and D. K. Paul, 'Evaluation of u - w and u - π finite element methods for the dynamic response of saturated porous media using one-dimensional models', Int. J. numer. Anal. Methods Geomech., 10, 461-482 (1986).
39. A. Gajo, A. Saetta and R. Vitaliani, 'Evaluation of three and two field finite element methods for the dynamic response of saturated soil', Int. j. numer. methods eng., 37, 1231-1247 (1994).
40. S. K. Garg, H. Nayfeh and A. I. Good, 'Compressional waves in fluid-saturated elastic porous media', J. Appl. Phys., 45, 1968-1974 (1974).
41. A. Gajo, 'The influence of viscous coupling in the propagation of elastic waves in saturated soil', J. Geotech. Eng. ASCE, 121, (9), 636-644 (1995).
42. A. Gajo and L. Mongiovi, 'An analytical solution for the transient response of saturated porous elastic solids', Int. J. Numer. Anal. Methods Geomech., 19, 399-414 (1995).
43. J. D. Achenbach, Wave Propagation in Elastic Solids, North Holland Series in Applied Mathematics and Mechanics, Vol. 16, H. A. Lauwerier and W. T. Koiter (eds), 1991, Amsterdam, Holland.
44. H. Deresiewicz, 'The effect of boundaries on wave propagation in a liquid-filled porous solid: I. Reflection of plane waves at a free plane boundary (non-dispersive case)', Bull. Seism. Soc. Am., 50, 599-607 (1960).
45. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method., Vol. II, 4th edn., McGraw-Hill, New York, 1991.
46. N. M. Newmark, 'A method for computation for structural dynamics', Proc. ASCE, 85, EM1, 67-94 (1959).
47. O. C. Zienkiewicz, 'A further look at Newmark, Houbolt, and other time stepping schemes, A weighted residual approach', Earthquake Eng. Struct. Dyn., 5, 413-418 1977.