Fracture analysis on an infinite row of collinear permeable cracks in a porous medium

Abstract

The dynamic (frequency-dependent) mode-I stress intensity factor (SIF) is obtained for a porous medium containing an array of equally distributed collinear cracks. Unlike previous work in which the cracks are assumed to be dry and impermeable, this paper studies the case that the crack is fluid-saturated and permeable. The cracks are under the action of a normal incidence of a time-harmonic plane longitudinal (P) wave. The interaction between the collinear cracks and the mechanism of wave-induced fluid flow (scattered slow P wave) can significantly affect the magnitude and frequency-dependent trend of the SIF, in particular at low frequencies. At low frequencies, the magnitude of the SIF increases monotonously with the decreasing distance between the adjacent cracks and can be much larger than that of a single crack, implying that the material strength can be greatly lowered by the interaction of cracks. However, at higher frequencies, the impacts of interacting cracks are negligible. The comparison with the counterpart of dry impermeable cracks reveals that the magnitude of SIF is lower than that of dry impermeable cracks owing to effective normal stress effect. Moreover, unlike the SIF of dry impermeable cracks for which a peak value is observed around elastic wave resonance frequency, the corresponding SIF of fluid-saturated permeable cracks monotonously decreases with the increasing frequency. This frequency-dependent trend is attributed to the conversion of incident energy into the slow P wave. The obtained results reveal significant influences of the presence of pore fluid and interaction of collinear cracks upon the SIF, both magnitudes and frequency-dependent trends. Such information is useful in predicting the fracture strength of saturated porous materials subjected to oscillating loads.