Abstract
The evolution of compression waves propagating in a fluid-saturated granular solid is considered. The pore fluid is assumed to consist of a liquid with a small amount of free gas. The stiffness of such a solid increases with increasing pressure. This property leads to the transformation of continuous compression waves into shock fronts after a finite time of propagation. The aim of the study is to calculate the critical distance covered by a continuous wave before it loses continuity. Critical distances are calculated for weak discontinuities (acceleration waves) propagating into a quiescent region. In numerical examples, the pressure dependence of the stiffness is taken in a form typical of granular solids. Emphasis is placed on the influence of free gas in the pore fluid and the permeability of the skeleton. Comparison of locally undrained and drained behaviour reveals that the drained model with low permeability turns out to be misleading for the calculation of the critical distance of a compression wave.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Courant R., Friedrichs K.O.: Supersonic flow and shock waves. Springer, Berlin (1976)
Osinov V.A.: On the formation of discontinuities of wave fronts in a saturated granular body. Continuum Mech. Thermodyn. 10, 253–268 (1998)
Courant R., Hilbert D.: Methods of mathematical physics, vol. II, Partial differential equations. Interscience, New York (1965)
Whitham G.B.: Linear and Nonlinear Waves. Wiley, New York (1974)
Boillat G., Ruggeri T.: On the evolution law of weak discontinuities for hyperbolic quasi-linear systems. Wave Motion 1, 149–152 (1979)
Ruggeri T.: Stability and discontinuity waves for symmetric hyperbolic systems. In: Jeffrey, A. (eds) Nonlinear Wave Motion., pp. 148–161. Longman, London (1989)
Donato A.: Nonlinear waves. In: Ames, W.F., Rogers, C. (eds) Nonlinear Equations in the Applied Sciences., pp. 149–174. Academic Press, New York (1992)
Wilmanski K.: Thermomechanics of Continua. Springer, Berlin (1998)
Wilmanski K.: Critical time for acoustic waves in weakly nonlinear poroelastic materials. Continuum Mech. Thermodyn. 17, 171–181 (2005)
Zienkiewicz O.C., Chan A.H.C., Pastor M., Schrefler B.A., Shiomi T.: Computational geomechanics with special reference to earthquake engineering. Wiley, Chichester (1999)
Zienkiewicz O.C., Shiomi T.: Dynamic behaviour of saturated porous media: the generalized Biot formulation and its numerical solution. Int. J. Numer. Anal. Methods Geomech. 8, 71–96 (1984)
Biot M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. J. Acoust. Soc. Am. 28, 168–178 (1956)
Biot M.A.: Mechanics of deformation and acoustic propagation in porous media. J. Appl. Phys. 33, 1482–1498 (1962)
Simon B.R., Zienkiewicz O.C., Paul D.K.: An analytical solution for the transient response of saturated porous elastic solids. Int. J. Numer. Anal. Methods Geomech. 8, 381–398 (1984)
Hardin, B.O., Richart, F.E.: Elastic wave velocities in granular soils. J. Soil Mech. Found. Div., ASCE 89, SM 1, 33–65 (1963)
Lambe T.W., Whitman R.V.: Soil Mechanics. Wiley, New York (1969)
Santamarina J.C., Klein K.A., Fam M.A.: Soils and Waves. Wiley, Chichester (2001)
Osinov V.A.: Cyclic shearing and liquefaction of soil under irregular loading: an incremental model for the dynamic earthquake-induced deformation. Soil Dyn. Earthq. Eng. 23, 535–548 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Osinov, V.A. Transition from acceleration waves to strong discontinuities in fluid-saturated solids: drained versus undrained behaviour. Acta Mech 211, 181–193 (2010). https://doi.org/10.1007/s00707-009-0233-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-009-0233-9