On the Biot–Gassmann equations for the elastic moduli of porous rocks (Critical comment on a paper by J. G. Berryman)

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Abstract
Equations for the Biot moduli H, C, and M by J. G. Berryman [J. Acoust. Soc. Am. 69, 416–424 (1981)] are shown to be wrong. A new first principles derivation of the generally accepted equations is given. It is obtained from relations which are tautological in the framework of elastostatics with one simplifying substitution which reflects the assumption that equal changes in pore pressure and confining pressure leave the porosity unchanged. An assumption equivalent to this was made by Biot. A porous rock with a matrix of homogeneous material would have this property. This was assumed by Gassmann.

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