Influence of non-plastic fines content on maximum shear modulus of granular materials

Resonant column tests were conducted on clean Hostun sand and Hostun sand mixed with 5%, 10%, 20%, 30% and 40% fines (particle size smaller than 0.075 mm) to assess the influences of void ratio (e), effective confining stress (p′) and fines content (fc) on the maximum shear modulus, Gmax. A significant reduction of Gmax was observed with increasing fc. While the Hardin׳s empirical relation was adequate to capture the influence of e and p′ on Gmax, each sand with an fc has to be considered as separate soil. The micro-CT scans of these sand with fines mixture provided a qualitative observation of the initial skeleton structures of the "fines-in-sand" or "sand-in-fines" of equivalent granular void ratio, e*. Therefore, e was replaced by e* in Hardin׳s relation for clean Huston sand to overcome the effect of fc. The conversion of e to e* requires two parameters: b and m. Four different approaches, including the calibration of b and m, were used to obtain e* and to verify the performance of e* in capturing the effect of fc. The performances of the calibrations, in terms of the root-mean-square-deviation and R2, are discussed. The Gmax of Hostun sand with a range of fc can be predicted with good accuracy using Hardin׳s relation for clean Hostun sand when e is replaced by e*. Then, collected data sets from the literature were also analyzed to validate e* in capturing the effect of fc.