Quantification of bulk form and angularity of particle with correlation of shear strength and packing density in sands

Highlights

• Sphericity and roundness are independent with each other while round particles tend to be spherical in sands

• Computing sphericity is sufficient to establish correlation with soil properties rather than hardly quantifiable roundness

• Quantification of particle shape in 2D is rational to comprehend shape-dependent properties

Abstract

The study presents the quantification of shape parameters in sands. Natural sands, crushed sands, and glass beads are subjected to 2D microscopic and 3D X-ray computed tomographic imaging. Parameters of sphericity, elongation and slenderness are selected for analyzing the bulk forms and roundness is selected to quantify the angularity. Relationship among 2D shape parameters confirms that sphericity, elongation and slenderness are independent with roundness. Critical state friction angles are obtained by a direct shear test and void ratio ranges are measured as well. Both sphericity and roundness denote the strong linearity with void ratio range (e_max − e_min) bounded 0.15 and critical state friction angle (ϕ_cs) delineated by 20° at the unity, emphasizing that readily computable sphericity is sufficient to estimate properties of sands even without roundness. The multiple 2D projections of 3D images and their correlation for different orientation support that either bulk form or angularity in 2D images are acceptable enough to establish correlations between shape parameters and properties in sands. It implies that 2D quantification of particle shape is rational and can be used to approximate soil properties without conducting the laboratory experiments.

Introduction

The irregularity of particle shape is in general described by bulk form, angularity (e.g., particle-scale smoothness), and surface texture (sub-particle roughness) depending on observation scales (Barrett, 1980, Mitchell and Soga, 2005, Rodriguez et al., 2013). Quantification of particle shape can be achieved by introducing dimensionless shape parameters such as: sphericity to quantify the bulk form, and roundness and roughness to quantify the angularity and surface texture. However, due to the difficulties and complexities of measuring the surface roughness, most shape analysis focuses on bulk form and angularity (Cho et al., 2006, Zheng and Hryciw, 2015). It has been known that bulk form and angularity are independent shape parameters while both properties phenomenologically increase with decreasing irregularity although they are largely scattered and not proportional (Cho et al., 2006, Hayakawa and Oguchi, 2005). Therefore, it is desired to directly compare shape parameters at different observation scales (e.g., sphericity for bulk form and roundness for angularity). The origin, history of transportation, deposition, and production process naturally determine the particle shape in sand, which is in turn strongly correlated with index and geomechanical properties. Previous studies revealed that void ratio range (e.g., e_max − e_min) and compressibility increase with increasing irregularity of particles (Cavarretta et al., 2010, Cho et al., 2006, Jia and Williams, 2001, Shin and Santamarina, 2013). Round particles tend to have higher thermal conductivity than irregular particles under densification and loading because of the increase of inter-particle contact area and contact quality (Yun and Santamarina, 2008). Similarly, α-factor and β-exponent in shear velocity-stress relationship increase and decrease, respectively, with increasing particle angularity (Lee and Santamarina, 2005). Particle irregularity also affects the particle mobilization and resultant friction angles at large strain that are attributed to particle rotation, frustration and contact slippage (Cho et al., 2006, Kim et al., 2016, Shin and Santamarina, 2013, Yasin and Safiullah, 2003). These observations reside in three dimensional mechanisms while most efforts to quantify the particle shape and to correlate it with other properties of interests have been done either by semi-quantitative charts developed by Krumbein and Sloss (1963) and Powers (1953) or by two dimensional inspections including fractal approaches (Arasan et al., 2011, Cavarretta et al., 2010, Cho et al., 2006, Santamarina and Cho, 2004, Shin and Santamarina, 2013, Vallejo and Zhou, 1995, Vesga and Vallejo, 2010, Yang and Luo, 2015). Recent advances in 3D imaging technology and numerical simulation methods often allow the accurate quantification of 3D analysis for granular materials (Druckrey and Alshibli, 2016, Erdogan et al., 2006, Fonseca et al., 2012, Kim et al., 2016, Sun et al., 2014, Zeng et al., 2015, Zhao and Wang, 2016). Yet, the applicability of 3D shape parameters and correlation with geomechanical properties still need further investigation. We therefore investigate the validity and applicability of each shape parameters correlated with critical state friction angle and void ratio range in both 2D and 3D with the aid of microscopic and X-ray computed tomographic imagings.