Phase and amplitude responses associated with the measurement of shear-wave velocity in sand by bender elements: Discussion

Abstract

Discussions 484 The paper has two distinct parts. The authors present f rst an interpretative model of bender element testing systems; then some results from tests on Levenseat sand. The basic model is linear and comprises three subsystems (shown in Fig. 1) namely the bender-transmitter, soil, and bender-receiver. It is argued that a Biot plane shear wave model provides a transfer function for the soil subsystem and that the signal generation and bender system can be represented by a forced hamonic (damped) oscillator (FHO). It would seem, however, that for any symmetric experimental arrangement where the source and receiver are identical, the transfer function of both subsystems should cancel out. This is a common assumption while testing with a single transducer in the echo mode (e.g., Fratta and Santamarina 1996). For the case of through transmission, the same reasoning applies if the mechanical properties of the opposite sample-transducer contact are similar. This is generally the case, especially for the identical mounting arrangements found when benders are installed in triaxial and oedometer cells. Should different mounting arrangements result in the bender elements having different transfer functions, the overall phase shift will be less than π but could be positive or negative. We disagree with the summary interpretation given by eq. [10]. A dispersive model necessarily implies a phase velocity varying with frequency, but not also a shear modulus varying with frequency. This is patent, for instance, in the Biot model, where the shear modulus is constant and dispersion is induced by the presence of a viscous pore fluid. As a generalization of eq. [1] we would suggest instead