Effect of local non-convexity on the critical shear strength of granular materials determined via the discrete element method

doi:10.1016/j.partic.2019.12.008

Particuology

Volume 52, October 2020, Pages 105-112

https://doi.org/10.1016/j.partic.2019.12.008 Get rights and content

Highlights

•
Effect of local nonconvexity on the residual shear strength of granular matter is studied.
•
Contributions of certain contact types to the residual shear strength are analyzed.
•
Effect of local nonconvexity on fabric anisotropy is evaluated.

Abstract

Multi-sphere clumps are commonly used to simulate non-spherical particles in discrete element method simulations. It is of interest whether the degree of local non-convexity λ affects the mechanical behaviour of granular materials with the same non-convexity η. A series of discrete-element-method biaxial shear tests are conducted on rough particle packings with η = 0.075 and different λ values (ranging from 0.134 to 0.770). The microscale results show that the contact type changes with an increase in λ. However, the critical strength is independent of λ. The evaluation of the contributions of different contact types to the critical shear strength and a detailed analysis of the anisotropies help clarify the microscopic mechanisms that result in the independence of the critical shear strength from λ.

Graphical abstract

Introduction

There are three important scales regarding the particle shape of granular materials: sphericity (eccentricity or plainness), roundness (angularity), and roughness (smoothness or non-convexity) (Cho, Dodds, & Santamarina, 2006). Various previous experimental and numerical studies have reported that sphericity and roundness affect the mechanical behaviours of granular materials (Azéma & Radjai, 2010; Azéma, Radjai, & Dubois, 2013; Brown et al., 2011; Feng, Zhao, Kato, & Zhou, 2017; Jensen, Bosscher, Plesha, & Edil, 1999; Meng, Li, Lu, Li, & Jin, 2012). However, only a few studies have focused on the effect of roughness, which also affects the properties of granular materials. In terms of experimental studies, Narayan and Hancock (2003) noted that the indentation hardness, elastic modulus, and brittle fracture index of particles gradually decrease with increasing roughness. Additionally, Santamarina and Cascante (1998) and Otsubo, O’sullivan, Sim, and Ibraim (2015)) reported that rough spheres have a smaller shear stiffness than smooth spheres. Furthermore, Anthony and Marone (2005) found that an increase in particle roughness increases the frictional strength and affects the distribution of stress within sheared layers. Alternatively, the discrete element method (DEM) can be adopted for the efficient numerical modelling of the effects of roughness on the macroscale and microscale properties of granular materials (Otsubo, O’Sullivan, Hanley, & Sim, 2017; Rémond, Gallias, & Mizrahi, 2008; de Graaf, van Roij, & Dijkstra, 2011; Yang, Cheng, & Sun, 2017). Using clumps composed of sub-spheres is the most common method of simulating non-spherical particles with the DEM. The effect of roughness can then be studied by changing the properties (e.g., radius and position) of the sub-spheres of the clumps. Taking this approach, Ludewig and Vandewalle (2012) found that when particles are modified to have a high roughness, particle interlocking and multiple contact points develop in the packing; nonconvex particle packings have a lower density and are more stable than spherical packings. Saint-Cyr et al. (Saint-Cyr, Delenne, Voivret, Radjai, & Sornay, 2011; Saint-Cyr, Radjai, Delenne, & Sornay, 2013) reported that both the internal angle of friction and the maximum cohesion increase linearly as the roughness increases, but the former approaches a certain value. Furthermore, Azéma, Radjai, Dubois et al. (2013) observed that the critical shear strength is an increasing function of roughness. In the above-mentioned DEM simulations, roughness was quantified as the concavity of the entire particle surface, which is composed of various local non-convexities. Note that non-convexity is of concern in practical engineering, particularly in the storage, handling, and recycling of crushed hollow industrial by-products and sintered powders (Azéma, Radjai, & Saussine, 2009; Rémond et al., 2008). For a given overall roughness, the form of local non-convexity may not be the same (see Fig. 1). Indeed, the variation in local non-convexity may be a noise factor when using clumps in DEM simulations. The critical shear strength reflects the intrinsic shear strength of the granular material and is independent of the initial state. Thus, it is of interest whether different local non-convexities affect the critical shear strength of granular materials with identical roughness. This issue is the motivation of the present work, wherein we conduct grain-scale modelling using the DEM, which has previously been demonstrated to reproduce certain key features of granular materials (Azéma, Radjai, Peyroux, & Saussine, 2007; Brown et al., 2011; Gong, Wang, Li, & Nie, 2019; Nie, Zhu, Wang, & Gong, 2019).

In this paper, the effect of local non-convexity on the shear behaviour of particle packings is explored through a series of drained biaxial compression tests using the DEM. The rest of the paper is organized as follows. First, a brief introduction of DEM modelling is given. Then, contact types and microscale simulation results of each contact type, including the coordination number and proportions related to the contact type, are studied. Next, the stress–strain characteristics and the contributions of certain contact types to the critical shear strength are analysed. Subsequently, the effect of the local non-convexity on fabric anisotropy is evaluated. Finally, main conclusions are presented.

Section snippets

DEM modelling

Biaxial compression tests were conducted using the well-recognized DEM program PFC^2D (Itasca, 2014), which was originally developed by Cundall and Strack (1979). Simulations were carried out using the linear elastic contact model, as used in several previous studies (Gong, Nie, Zhu, Liang, & Wang, 2019; Gu, Huang, & Qian, 2014; Minh & Cheng, 2013). The microscale parameters used in the present study were selected by referring to many previous experimental and numerical studies. Specifically,

Results and discussion

The present paper focuses on critical state behaviour. All samples were sheared to axial strain of ε₁ = 30%. Note that the characteristic critical conditions, such as a constant q $´$ /p´ and volume, are basically satisfied at deformation of ε₁ ≥ 10% for all samples. This paper defines axial strain ε₁ being in the range [10%, 30%] as the critical state, and the values of each parameter in the critical state are the average values within this interval.

Previous numerical studies investigated the

Conclusions

This study investigated the effects of local non-convexity on the critical shear strength of granular materials using the DEM. A series of drained biaxial tests were conducted on rough particle packings with a uniform non-convexity η of 0.075 and different values of local non-convexity λ ranging from 0.134 to 0.770. The results show that the contact type changes with an increase in λ but the critical shear strength is not affected by λ. Through analysis of the contact types and their

Declaration of interest statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The study is financially supported by the National Natural Science Foundation of China, China (No. 51809292, 51478481 and 51508141), Postdoctoral Fund of Central South University, China (No. 205455) and Beijing Municipal Science and Technology Project: Research and Application of Design and Construction Technology of Railway Engineering Traveling the Rift Valley, China (No. Z181100003918005). The authors express their appreciation for the financial assistance.

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Short communicationEffect of local non-convexity on the critical shear strength of granular materials determined via the discrete element method

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

DEM modelling

Results and discussion

Conclusions

Declaration of interest statement

Acknowledgments

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Short communication
Effect of local non-convexity on the critical shear strength of granular materials determined via the discrete element method