GEOTECHNIQUE, vol.63, no.1, pp.54-70, 2013 (SCI-Expanded)
Deformations of sandy soils around geotechnical structures generally involve strains in the range small (0.01%) to medium (0.5%). In this strain range the soil exhibits non-linear stress-strain behaviour, which should be incorporated in any deformation analysis. In order to capture the possible variability in the non-linear behaviour of various sands, a database was constructed including the secant shear modulus degradation curves of 454 tests from the literature. By obtaining a unique S-shaped curve of shear modulus degradation, a modified hyperbolic relationship was fitted. The three curve-fitting parameters are: an elastic threshold strain gamma(e), up to which the elastic shear modulus is effectively constant at G(0); a reference strain gamma(r), defined as the shear strain at which the secant modulus has reduced to 0.5G(0); and a curvature parameter a, which controls the rate of modulus reduction. The two characteristic strains gamma(e) and gamma(r) were found to vary with sand type (i.e. uniformity coefficient), soil state (i.e. void ratio, relative density) and mean effective stress. The new empirical expression for shear modulus reduction G/G(0) is shown to make predictions that are accurate within a factor of 1.13 for one standard deviation of random error, as determined from 3860 data points. The initial elastic shear modulus, G(0), should always be measured if possible, but a new empirical relation is shown to provide estimates within a factor of 1.6 for one standard deviation of random error, as determined from 379 tests. The new expressions for non-linear deformation are easy to apply in practice, and should be useful in the analysis of geotechnical structures under static loading.