Continuum approach to the theory of waves in fragmentary media

Details Continuum approach to the theory of waves in fragmentary media Continuum approach to the theory of waves in fragmentary media

Jan 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988pepi...50...32n&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 50, Issue 1, p. 32-38.

Physics

Scientific paper

Experiments with stress waves in marine sands of different wetness have shown the existence of some dominant frequencies. These frequencies are connected with redistribution of microstresses acting inside sand particles in contact. An adequate continuum mathematical theory is developed for the propagation of weak nonlinear waves in fragmentary media. The medium elements are interacting in a viscoelastic manner and can oscillate. The constitutive law includes the second and third order time derivatives of strains and takes geometrical nonlinearity into account. The `masses' of oscillators correspond practically to the internal linear scales of the fragments. The effects of physical nonlinearity are discussed. The slow changes of waves are studied using a perturbation method in a moving frame. It is known that in the first approximation the seismic fronts propagate in accordance with the traditional dynamic elasticity theory. However, the evolution equations include dissipation and dispersion terms. Practically, the evolution of P-waves is governed by the Burgers-Korteweg-de Vries equation with the addition of a fourth order spatial derivative. Some numerical calculations are shown. The evolution of S-waves is described by a similar, but linear, equation. Surface waves propagate with the Rayleigh velocity and the derivation of the proper evolution equation is discussed.

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