Threshold Strain for Loading Frequency and Rate Effect on Shear Modulus and Damping Ratio of Sand–Clay Mixtures

A series of undrained dynamic hollow cylinder torsional shear tests were performed on sand–clay mixtures with different loading frequencies from f=0.05 to 10 Hz. Two types of clay were used for preparing samples with different fine content levels (FC=0% to 100%). Test results covered a wide spectrum of soils from clean sand to pure clay, with plasticity index (PI) values ranging from 0 to 42.7. Experimental results in the shear strain range γ=0.01% to 1% indicated that the frequency of loading had no effect on dynamic shear modulus of the mixtures, even for the mixture with the highest PI (42.7). Regarding damping ratio, there was a threshold strain that controls the soil response to frequency variation. Below this threshold strain, damping ratio curves were identical for tests conducted under different frequencies but beyond this point, increasing loading frequency increased the damping ratio of soils with a more pronounced effect at larger strains. The threshold point is strongly correlated with PI and FC in a way that soils with higher PI exhibited smaller threshold strains. Besides PI, the determinant role of FC for judgment of the loading frequency effect should not be disregarded. For a given PI, the soil with higher FC exhibited a smaller threshold strain and a more pronounced effect of loading frequency on damping ratio values. Additionally, based on the test results at various strain rates, the rate-dependent dynamic behavior of tested mixtures can be divided into three regions: in small-strain rates, damping ratio is solely dependent on shear strain and independent from strain rate and frequency, but in the large strain rates, the scatter of experimental data points is small enough to exhibit a unique relationship between damping ratio and strain rate, irrespective of the magnitude of loading frequency and strain amplitude. A transition zone connects these two regions wherein soil behavior gradually changes from the former to the latter.