Dynamic stress intensity factor of a rectangular crack in an infinite saturated porous medium: Mode I problem

A scattering problem of a harmonic plane compressional wave disturbed by a fluid filled rectangular crack, which is embedded in an infinite saturated poro-elastic solid, is investigated. With the aid of the two-dimensional Fourier integral transform technique, the original boundary value problem is formulated by a pair of dual integral equations in terms of the crack surface displacement. By expressing the crack surface displacement into a series of Jacobi polynomials, the solution of the dual integral equations is derived, where the coefficients involved are obtained with the aid of the Schmidt method. The stress intensity factors of the Mode I crack problem are obtained. Numerical results are performed to discuss the influence of the frequency of the incident compressional wave and the geometric parameter of the rectangular crack on the stress intensity factor and crack surface displacement in detail. The present analytical solutions may benefit future simplified and numerical studies.