Ultrasonic Characterization of Water Saturated Double Porosity Media

Wave propagation through a multilayered structure consisting of a water saturated double porosity medium in an aluminum rectangular box immersed in water is studied. By assuming a plane incident wave from water onto the structure, the reflection and transmission coefficients are derived by application of the boundary conditions at each interface. Numerical computations are done for two particular double porosity media, ROBU® and Tobermorite 11 Å, that are assumed to obey Berryman's extension of Biot's theory [Berryman 1995, 2000]. The influence of the thickness of double porosity medium is investigated. To compare experiments to computations, two comparison coefficients Cnum and Cexp are introduced. The theoretical one Cnum is defined as the ratio of the transmission coefficient of the structure to the transmission coefficient of the box filled exclusively with water. The experimental comparison coefficient Cexp is defined as the ratio of the Fourier transforms of the transmitted signals by the box filled with the double porous medium to that of the transmitted signals by the box filled with water. A method of minimization based on a gradient descent algorithm is used to optimize some of the parameters of the double porosity media such as the bulk moduli.