Advances in Civil Engineering

Volume 2019, Article ID 5732656, 12 pages

https://doi.org/10.1155/2019/5732656

## Effects of Particle Shapes and Sizes on the Minimum Void Ratios of Sand

Institute of Geotechnical Engineering, Yangzhou University, Yangzhou 225127, China

Correspondence should be addressed to Zhaoyang Xu; moc.qq@0863703401

Received 17 December 2018; Revised 28 February 2019; Accepted 6 March 2019; Published 14 April 2019

Academic Editor: Arnaud Perrot

Copyright © 2019 Zhaoyang Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The minimum void ratio is an important parameter for evaluating soil properties. It is closely related to the compressive properties, permeability, and shear strength of soil, and it is affected by particle size distributions and particle shapes. However, existing research generally focuses on modeling the minimum void ratio with the effect of particle size distributions, ignoring the influences of particle shapes on the minimum void ratio. This paper analyzes the influences of particle size distributions and particle shapes on the minimum void ratio using four types of sand and alternative materials. The experiments showed that the minimum void ratio first decreased and then increased with the increase of the fines content. The minimum void ratio reached a minimum value when the proportion of fines content was approximately 40%. The more irregular the particle shapes, the more complicated the contact between particles, the more the void existed between the particles, and the larger the minimum void ratio. Based on the experimental data, a relational model between the minimum value of the minimum void ratio and the particle sizes ratio was derived with binary mixtures of different particle sizes and shapes. This proposed model required only one parameter *T*, which was closely related to the sphericity of the particles, to predict the minimum value of the minimum void ratio with various fines contents. The experiment results showed that the predicted value was very close to the actual measured value.

#### 1. Introduction

The granular soil is a mixture of particles with different sizes, and the particle size distribution controls the structural form of the soil, which affects the mechanical properties of the soil (e.g., [1–5]). Particle size distributions are widely used in industrial productions such as concrete mixes [6], ceramics processing [7], and powder metallurgy [8]. As an important parameter reflecting the particle size distribution of soil in geotechnical engineering, the minimum void ratio (*e*_{min}) is closely related to the compressive properties, permeability, and shear strength of soil.

It is generally accepted that the fines content is the main factor affecting *e*_{min} [9–14]. Kezdi [15] proposed an analytical method for estimating *e*_{min} of a mixture of two particle sizes, but this method is only suitable for fillers with very small particles.

Cubrinovski and Ishihara [16] proposed a set of empirical equations for the effect of fines content on *e*_{min} by analyzing a large amount of test data for silt. Chang et al. [17–19] established a model with only two parameters to predict *e*_{min} of sand-silt mixtures with a dominant particle structure network concept. This model reflected a close correlation between particle size and *e*_{min}. The Furnas model [20] is only suitable for estimating the packing density of binary powder compacts, and it has not yet been examined for use with the packing density of sand-silt mixtures with different particle sizes.

It is generally accepted that another important factor is particles shapes, which affect *e*_{min} factor and thus affect the shear resistance of granular soils. Using a triaxial compression test of atomized stainless steel powder, Shinohara et al. [21] found that the internal friction angle increased with the increase of the grain edge angle and the initial compactness. Ashmawy et al. [22] analyzed the effect of particle shapes on liquefaction with a reciprocating loading undrained test. Sallam and Ashmawy [23] used the discrete element method to simulate the stress-strain relationship of flat and narrow element assemblies with different shapes, and they pointed out that the dilatancy angle was also largely restricted by the particle shapes. Different particle shapes can significantly change the integrity and shear resistance of granular soils [24–28]. Cho et al. [10] and Cherif Taiba et al. [29] already proposed that increasing particle irregularity caused a decrease in the stiffness but a heightened sensitivity to the state of stress.

Scholars have mainly studied the effect of particle size distributions on *e*_{min} of soils and proposed corresponding analytical methods to predict *e*_{min} for soil mixtures. However, very few studies on the effect of particle shapes on *e*_{min} have been carried out. In order to better study the distribution law of *e*_{min}, four types of sand from different origins were selected, and steel balls [11] and steel cylinder particles were introduced as alternative materials to further analyze the influence of particle shapes and particle size distributions on *e*_{min}.

#### 2. Experimental Method and Conditions

##### 2.1. Sand Used for Experimental Testing

The sand used in the experiment was from four different origins: Nanjing River Sand (abbreviated as NS), Dongting Lake Sand (DS), Yizheng Mountain Sand (YS), and Fujian Standard Sand (FS). The properties of these types of sand are presented in Table 1. The gradation curves of the four types of source sand before and after the compaction test are shown in Figure 1. The grain sizes ranged from 0.075 mm to 5 mm.