Shear stiffness of granular material at small strains: does it depend on grain size?

The shear stiffness of granular material at small strain levels is a subject of both theoretical and practical interest. This paper poses two fundamental questions that appear to be interrelated: (a) whether this stiffness property is dependent on particle size; and (b) whether the effect of testing method exists in terms of laboratory measurements using resonant column (RC) and bender element (BE) tests. For three uniformly graded types of glass beads of different mean sizes (0.195 mm, 0.920 mm and 1.750 mm), laboratory tests were conducted at a range of confining stresses and void ratios, using an apparatus that incorporates both RC and BE functions and thus allows reliable and insightful comparisons. It is shown that the small-strain stiffness, determined by either the RC or BE tests, does not vary appreciably with particle size, and it may be practically assumed to be size independent. The laboratory experiments also indicate that the BE measurements of small-strain stiffness are comparable to the corresponding RC measurements, with differences of less than 10%. Furthermore, the BE measurements for fine glass beads are found to be consistently higher than the RC measurements, especially at large stress levels, whereas this feature becomes less evident for medium-coarse glass beads, and eventually diminishes for coarse glass beads. The study indicates that the characteristics of output signals in BE tests can be largely affected by the frequency of the input signal, the mean particle size of the material and the confining stress level, and that these factors are interrelated. Improper interpretation of wave signals may lead to shear stiffness measurements that are unreasonably low, either showing a substantial increase with particle size or showing the opposite. A micromechanics-based analysis assuming the Hertz-Mindlin contact law is presented to offer an understanding of the size effect from the grain scale.