Shear modulus of cohesionless soil: variation with stress and strain level

The value of the secant shear modulus (G) of sand measured in cyclic tests reduces as the amplitude of cycling increases. As a first approximation, it is assumed that the curve joining the extreme points of stress-strain (tau-gamma) loops of different amplitudes (a so-called "backbone curve") is hyperbolic. The shear strength (tau(max)) of sand is directly proportional to the mean effective confining pressure (p'), whereas the maximum shear modulus (G(o)) is proportional to (p')n, with n being between 0.4 and 0.5. Based on these assumptions, it is shown that at the same shear strain level, different G/G(o) values should be expected at different p' values. One of the features of a hyperbolic tau-gamma-curve is that there is a unique linear relationship between G/G(o) and normalized shear stress level (defined as tau/tau(max)), independent of p'. Therefore, considering the normalized shear stress level rather than the shear strain level may be a more logical and unifying way of examining the variation in G/G(o).