Evolution of surface roughness of single sand grains with normal loading

Abstract

The surfaces of soil grains are not perfectly smooth, especially examined at small scale. In geotechnical engineering, surface roughness has been found to be able to influence the inter-particle friction angle at micro scale and small-strain stiffness at macro scale. However, the quantity and quality of the studies on surface roughness of natural soils are still limited. In this study, the evolution of surface roughness of natural sand grains with increasing normal load was investigated by a single-particle compression apparatus. Thirty Leighton Buzzard sand (LBS) grains coarser than 2·36 mm were tested, and the surface roughness was measured before and after compression by an optical interferometer. The deformations of the asperities and of the bulk of the sand grains in the vicinity of the contact were mapped. Three stages were identified as the normal load increased: (a) plastic deformation of the asperities; (b) asperities and bulk plastic deformation; and (c) bulk only plastic deformation. At very small normal load, only the asperities were found to deform plastically, and the surface roughness of the sand grains decreases due to the flattening of the asperities. Within this regime, the load–displacement relationship of LBS grains under compression could be simulated by the modified Hertz model, which takes surface roughness into consideration. With increasing normal load, the bulk of the sand grains began to yield near the contact. The geometry of the surfaces of LBS grains in contact with the loading platen is the main factor that influences the plastic deformation of the bulk. Differently from the plastic deformation of the asperities, the plastic deformation of the bulk could both smoothen and roughen the surfaces. When plastic deformation of the bulk occurred, both Hertz and modified Hertz theory could not predict the load and displacement relationship of sand grains. Through analysing the cumulative distributions of surface roughness of 30 LBS grains at different normal loads by the Weibull function, the surface roughness was found to decrease dramatically with increasing normal load at first and then tended to be constant.