Quantitative assessment of the influence of surface roughness on soil stiffness

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, G₀ = A (p′/p_r)^b, where A is a constant and p_r 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 small-strain shear modulus to surface roughness.