4. Conclusion

In this chapter, an inverse determination of porosity and tortuosity is given using experimental reflected acoustic waves at different incidence angles. The inverse problem is solved numerically by the least-square method. The obtained values of porosity and tortuosity are close to those given using classical (non-acoustical) methods. Generally, the tortuosity is inverted easily using transmitted waves, and this is not the case for porosity because of its weak sensitivity in transmitted mode. This method is very interesting from its simplicity and constitutes an alternative to the usual method involving the use of a porosimeter introduced by Beranek [3] and improved by Champoux et al. [10] or the other ultrasonic methods based on transmitted mode. [5] Allard JF, Champoux Y. New empirical equations for sound propagation in rigid frame

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This method is valuable for porous materials having a rigid frame as air-saturated media, in which the equivalent fluid model is used. However, for liquid-saturated materials as rock or cancellous bone, this method cannot be used and should be adapted using the general Biot model [17, 18]. We hope, in the future, to extend this method to porous media with an elastic frame saturated with viscous fluid, in order to estimate other parameters that play an important role in acoustic propagation.
