Critique of the Biot Theory of Propagation in Fluid-Saturated Porous Solids

Biot's theory of porous media is discussed critically, with emphasis on the first 1956 JASA paper that purports to apply for low frequencies. It is pointed out that the use of two and only two displacement fields has a certain arbitrariness, and that models with additional displacement fields are possible. Biot's expression for the strain-energy per unit volume is justified in part, but it is pointed out that additional terms might be included. The theory in the low-frequency limit is discussed in detail, and the partitioning of the disturbance into three distinct types of fields is discussed. It is shown that there is sufficient latitude in the choice of coefficients in the Biot low-frequency model that the coefficients can be adjusted to fit all the major parameters associated with the three types of disturbances at low frequencies, but it is conjectured that the model will lead to inconsistencies for prediction of minor parameters. Unless measurements of such minor parameters are known from independent experiments, the model cannot be tested quantitatively. The use of the low-frequency Biot model at higher frequencies is discussed, and it is shown that in the high-frequency limit there are always two propagating modes where the displacement fields have zero curl. It is also shown that the model predicts the attenuation at high frequencies to be independent of frequency. The validity of such high-frequency predictions is questioned, and it is argued that the Biot low-frequency model has substantial wide-spread validity at low frequencies.

Automated summary

The critique of Biot's theory of porous media highlights potential arbitrariness and the possibility of additional displacement fields in the model. The discussion focuses on the theoretical aspects at low frequencies and the flexibility in coefficients selection within the Biot low-frequency model.