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Analytic solutions are derived for the problem of scattering of obliquely incident plane waves from a rectangular crack in a fluid-saturated porous solid. The propagation direction and polarization direction of the incident waves can be arbitrary. The solutions are based on expanding the crack opening displacements in terms of Chebyshev functions. Explicit expressions for the frequency-dependent stress intensity factors and scattering far fields are obtained. The poroelastic effects play a key role in determining the crack opening mode by changing the effective normal stress applied on the crack surfaces. Consequently, the dynamic responses of the crack can be quite different from those of conventional dry crack in an elastic solid. The effects of scattered slow-P waves as well as wave-induced crack fluid pressure on the dynamic stress intensity factors are clarified, and a corner effect is observed in the scattering patterns for moderately high frequencies. The comparisons of synthetic seismograms with the elastic model show the slow-P waves can cause significant energy loss and waveform change. This study can be used for fracture analysis of porous media and nondestructive testing for individual hydraulic fractures in reservoirs. [ABSTRACT FROM AUTHOR]

A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a permeable penny-shaped crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow on the dynamic stress intensity factor is analyzed. The Hankel integral transform technique in conjunction with Helmholtz potential theory is used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. Using appropriate transforms, the dual integral equations can be reduced to a Fredholm integral equation of the second kind. The phenomenon of fluid flow along the crack surface has significant influences upon the frequency-dependent behavior of the dynamic stress intensity factor. The stress intensity factor monotonically decreases with increasing frequency, declining the fastest when the crack radius and the slow wave wavelength are of the same order. Such near-field information is of particular importance in predicting the crack strength subjected to oscillating loads. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack radius decreases. [ABSTRACT FROM AUTHOR]

• Analytic solutions of the stress intensity factors (SIFs) of a fluid-saturated permeable crack in a poroelastic material subjected to a time-harmonic elastic wave have been derived. • Insights of effects of incident wave types, material permeability, incident angle and crack surficial permeability on the frequency-dependent behaviors of the SIFs have been obtained through numerical examples. • Because of the wave-induced fluid flow, the crack fluid can significantly change the effective normal stress so that the magnitude of mode-I SIF can be lower than that of a dry impermeable crack. In many practices, cracks are filled with fluid and their background materials can be modelled within the framework of poroelasticity. Understanding the crack-tip mechanical behaviors of such a cracked medium subjected to dynamic loads is of importance for prediction of fracture failure. In this paper, based on Biot's theory of poroelastodynamics, solutions of mode-I and mode-II dynamic stress intensity factors (SIFs) of a Griffith crack are derived for the scattering problem of oblique incidence of in-plane time-harmonic P-SV waves. The crack surfaces are assumed to be permeable, and the crack is saturated by fluid. With the aid of Fourier integral transforms, the problem is reduced to a system of coupled Fredholm integral equations with special emphasis placed on finding the near-field solution. Impacts of incident wave type, material permeability and incident angle on the frequency-dependent behaviors of the SIFs have been shown graphically. It is found that the induced fluid pressure inside the crack can significantly change the effective normal stress so that the magnitude of mode-I SIF is much lower than that of a dry impermeable crack. Furthermore, the diffusion-type fluid flow (scattered slow P wave) can greatly lower the magnitude of mode-I SIF at low frequencies (much smaller than the resonance frequency). The characteristic frequency at which the curves of SIFs decline strongest occurs when the characteristic diffusion length is of the same order of the crack size. The fluid flow can also lower mode-II SIF at low frequencies and the effects are strong in the low permeability case. Specifically, in the case of scattering of SV waves, it is shown that the maximum drop of mode-II SIF in peak with respect to that of the corresponding dry crack in an elastic medium is about 10%. The obtained results reveal significant influences of the presence of pore fluid upon the SIFs, both magnitudes and frequency-dependent trends. Such information is useful in predicting the fracture strength of saturated porous materials subjected to oscillating loads. [ABSTRACT FROM AUTHOR]