On the theory of Brutsaert about elastic wave speeds in unsaturated soils

• We revisit Brutsaert's model on elastic wave speed in unsaturated soils.
• There is an inconsistency in the bulk modulus of fluid mixture in a porous aggregate.
• Brutsaert also assumed a saturation-independent Poisson's ratio fixed at 0.20.
• Use of Brutsaert's model by others is not conclusive in the inverse problem.
• We comment on the feasibility of deducing the water content from wave measurement.

Recently a theoretical model for elastic wave speeds in partially-saturated soils proposed by Brutsaert (and Luthin) in 1964 has been used to investigate the relationship between the elastic wave speeds and the moisture content in soils. It has been suggested that there was a ‘typing error’ in the formula for the composite fluid bulk modulus of the partially-saturated medium which has been modified accordingly. However we argue that the problem appears to be more of an inconsistency in the definition of the composite bulk modulus than a typing error: we have not been able to reproduce some numerical figures reported by Brutsaert and Luthin with the formulae therein. Moreover we point out that an assumption in the original theory of a saturation-independent Poisson's ratio has bigger implications for the more recent works as result (a) of not being realised and (b) of not being supported by experimental evidence. We comment also on the use of effective stress in unsaturated soils and the difficulty in deducing the moisture content from measurements of elastic wave speeds, due probably to the predominance of water potential rather than water content on the wave speed of shallow soils.