The nature of soil stiffness at small strains remains poorly understood. The relationship between soil
stiffness (e.g. shear stiffness, G0) and isotropic confining pressure ( p′) can be described using a power
function with exponent (b), that is, G0¼A ( p′=pr)
b
, where A is a constant and pr is an arbitrary reference
pressure. Experimentally determined values of b are usually around 0·5 and these are higher than the
value of 0·33 that can be analytically determined using Hertzian theory. Hertzian theory considers
contact between two smooth, elastic spheres; however, in reality, inter-particle contacts in soil are
complex with particle shape and surface roughness affecting the interaction. Thus Hertzian theory is
not directly applicable to predict real soil stiffness. It has, however, provided a useful basis to develop an
analytical framework to consider the influence of particle surface roughness on small-strain soil
stiffness. Here, earlier contributions using this framework are extended and improved by paying
particular attention to roughness and the tangential contact stiffness. Stiffness values calculated using
the newly derived analytical expressions were compared with the results of bender element tests on
samples of borosilicate glass beads (ballotini) whose surface roughness was quantified using an optical
interferometer. The analytical expression captures the experimentally observed sensitivity of the smallstrain
shear modulus to surface roughness