Granular Matter (2011) 13:731–742 DOI 10.1007/s10035-011-0292-1 ORIGINAL PAPER Effect of particle size ratio and volume fraction on shear strength of binary granular mixture Takao Ueda · Takashi Matsushima · Yasuo Yamada Received: 22 September 2010 / Published online: 30 October 2011 © Springer-Verlag 2011 Abstract This paper deals with the mechanical properties of a binary granular mixture: a mixture of large and small frictional particles. The binary mixture is characterized by the particle size ratio (α = D L / D S ≥ 1), where D L and D S denote the diameter of large and small particles, and the volume fraction of the small particles W S . In order to eval- uate the shear strength of such a system, a transition range (W a S ≤ W S ≤ W b S ), where W a S and W b S are minimum and maximum W S values of the range, respectively, is defined as the range in which the interaction between the small and the large particles cannot be negligible. Then a simplified pack- ing structure model is proposed to estimate W a S and W b S with respect to α. A series of 2D Discrete Element simulation and physical experiment proved that the proposed method can successfully describe the shear strength transition of the densely packed granular material both in 2D and 3D. As a general trend, it also turns out that the contribution of the small particles cannot be negligible even in their small con- tent, and the contribution of large particles disappears when their average spacing with respect to the small particle size is around 2 both in the simulation and the experiment. Keywords Binary mixture · Discrete Element Method (DEM) · Direct shear test · Size effect 1 Introduction The mechanical behavior of granular materials is governed by their grain properties such as size, shape, hardness, crush- ability etc. and their packing structure. Among them, the T. Ueda (B ) · T. Matsushima · Y. Yamada Department of Engineering Mechanics and Energy, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan e-mail: t-ueda@edu.esys.tsukuba.ac.jp effect of grain size distribution has been extensively stud- ied mainly in the field of powder physics and technologies related to mixing and segregation phenomena in dynamic regime [1–3]. In the field of geotechnical engineering, on the other hand, the quasi-static behavior of well-graded granular materials is of great concern, but the studies from granular mechanics perspective are limited [4, 5]. This study deals with a densely packed binary sphere mix- ture (a mixture of poorly-graded large and small spheres) as a simplified version of a well-graded mixture. If the grain hardness is sufficiently large, the grain size distribution of the binary mixture is characterized by only two parameters, W S , the volume fraction of small grains, and α (= D L / D S ), the particle size ratio, where D L and D S denote the diame- ters of large and small grains, respectively. Although a binary mixture may be essentially different from a well-graded mix- ture in some aspects, Ueda et al. [6] proposed a method to determine W S and α of the binary mixture being mechani- cally equivalent to an arbitrary well-graded mixture. Previous research [7, 8] has examined the effect of W S and α on the static void ratio range under the Earth gravity; sev- eral models describing the void ratio as a function of W S have been proposed [9–11]. On the other hand, only a few studies are currently available on their mechanical behavior [4, 12]. Since the mechanical behavior of the mono-sized particles have been revealed from granular mechanics perspective to a considerable extent [13, 14], the authors calculated the contri- bution of each size component on the binary mixtures due to the composition when the mechanical characteristic of each type of components are given. The novelty of this method is to be applied to the binary mixtures composed of large and small different materials. On the basis of these background, a model which is able to predict the shear strength of binary mixture of various W S and α is presented, and its applicability on the binary mixture 123