Correlation of surface fractal dimension with frictional angle at critical state of sands

Abstract

INTRODUCTION The fractal approach is potentially a useful tool for studying the surface formation of sand particles (Anvir et al., 1985). A simple descriptor of surface texture is provided by the surface fractal dimension, which is assumed as an indicator to describe the surface roughness. The surface fractal dimensions of Ottawa sand and Madagascar quartz sand are 2.02 0.01 and 2.14 0.06 respectively, measured by sorption of gases and liquids (Anvir et al., 1985). Many researchers have estimated the surface fractal dimension of sand particles and have given it different significances (Moore & Donaldson, 1995; Vallejo, 1995; Vallejo & Zhou, 1995; Barak et al., 1996; Pardini & Gallart, 1998; Gori & Mari, 2001; Itabashi et al., 2001). Moore & Donaldson (1995) quantified soil microstructure as reflected by interconnectivity among the soil grains using fractal principles. A high fractal dimension implied a high space-filling potential. From the point of view of soil strength and compressibility, one would expect a soil with a high fractal dimension to be stronger and less compressible than one with a low fractal dimension (Moore & Donaldson, 1995). Vallejo (1995) and Vallejo & Zhou (1995) described the shape of granular materials using the surface fractal dimension. Pardini & Gallart (1998) applied laser technology to measure the effect of freezing and thawing on the surface roughness and surface fractal dimension of regolith. Gori & Mari (2001) measured the surface fractal dimension of sand particles using the imagery method, and tried to correlate surface fractal dimension with the internal friction angle of sand. It was thought that the surface fractal dimension of sand particles was able to describe all shape characteristics, such as particle shape, roundness, sphericity, and texture. Itabashi et al. (2001) evaluated the surface fractal dimension of sand particles through measuring the grain perimeter using a different ruler size on an enlarged photomicrograph. Itabashi et al. (2001) stated that the surface fractal dimension of sand particles represented the particle shape of microparticles and the surface roughness of microparticles. The values of the surface fractal dimension of sand particles were found in the range 2.01–2.14 from published data (Vallejo, 1995; Vallejo & Zhou, 1995; Barak et al., 1996; Pardini & Gallart, 1998; Gori & Mari, 2001; Itabashi et al., 2001). Quartz sand particles exhibit smoother surfaces, which result in surface fractal dimensions close to 2.0 (Barak et al., 1996). As regards the surface roughness and particle shape of sand particles, the fractal dimension has proved to be a good parameter for describing the particle microstructure, and it has some advantages over other methods used previously. In the work described in this paper, the surface fractal dimension was used to measure the surface roughness of sand particles, and the surface fractal dimension of 10 sand samples taken from different locations in Japan was measured using the imagery method. The relationship between the surface fractal dimension and the critical state angle of shearing resistance for sands was also studied.