Effect of coefficient of friction on arch network in shearing process under low confinement
Graphical abstract
Arch network in shearing process, the collapse of which is attributed to contract sliding in the granular assembly.
Introduction
The micro-mechanical response of granular materials during interface shearing is of interest to geotechnical and mechanical applications, including the behavior of subsea pipelines, trenching picks and ploughing blades. Jamming and fluctuations during the slow drag of particles has been extensively studied, from which a stick-slip mechanism was found during the shearing process of an assembly of glass beads with intruding cylindrical rod [[1], [2], [3], [4]]. The stress distribution on the intruder surfaces was also discovered, in which the effect of the shape and size of the intruding object has been carefully studied. This has led to the formation of a force model that considers the reaction from the assembly on the surface of the intruding plate at a shallow depth, with angle of inclination and size of the mobilized area [[5], [6], [7]].
Arches represent collective structures in the granular assembly, whose existence and temporal variations dictate the overall properties of the system [8]. Previous studies on arches revealed that the formation of arches is crucial in the jamming and size segregation phenomena [9,10]. An arch identification algorithm has been proposed and verified in a bed of granular disks generated by a molecular dynamic-type simulation [8,11]. The study on granular deposit confirms that arches carry most of the weight in the deposit, and the connection between arches and force chains has attracted recent interest [11,12]. Arches are also encountered during the interface shearing process. Take subsea pipelines for an instance, an insightful study on the arch network helps us understand the surface movement above the pipelines and the mobilized area during the installation process, which can be taken into consideration for the pipeline design.
The inter-granular friction (μ) is an important physical parameter that affects the performance of soils and other granular materials in both dry and submerged situations, as revealed by a study of hopper flows [13]. For the packing of spherical particles, the variation of μ can generate spherical packings between the random loose packing (RLP) and random close packing (RCP) limits [14]. Since μ can control the behaviors of granular flow, the current study focuses on the effect of μ on the arch network as a parametric study. Due to the difficulty in controlling and accurately measuring μ of particles in experiments, particle-based numerical approaches, such as the discrete element method (DEM), represent a convenient tool for exploring the role of inter-granular friction. In this project, a DEM model has been established to simulate the behavior of a granular assembly sheared by an individual triangular interface element in order to identify how the shear deformation develops micromechanically. The DEM model has been verified qualitatively against a physical model. The interface elements and grains were scaled up to a size where direct measurements and observations of the shearing process could be made. The effect of μ on various micromechanical behaviors in granular shear with low confinement is described and quantified.
A brief description of the DEM model and the verifying physical model is contained in Section 2 with an account of the quasi-static checking. Section 3 presents verification of the DEM model against the physical model in terms of particle rearrangement, turbulent behavior in velocity vector field, and arch network. Section 4 presents the arch identification algorithm adopted in this study, together with simulation results and discussions on coordination number, packing fraction, arch size distribution and arch duration. Section 4 also justifies the correlation between arches and force chains, and reveals the relationship between particle rearrangement and arch network. Finally, Section 5 provides a summary of the key conclusions.
Section snippets
DEM and physical models
This study uses the commercial two-dimensional DEM software Particle Flow Code (PFC2D, Version 4) [15]. A DEM model [16] was created by randomly generating, depositing from the same height and settling particles under gravity layer by layer, as shown in Fig. 1(a). Following pouring, the entire array of discs was permitted to settle until static equilibrium was achieved. The shearing process was carried out by moving the wedge from left to right with a constant shearing velocity () of
Particle rearrangement
As there is a significantly large amount of information present in each simulated run, the global behavior of the shearing grains needed to be adequately reduced into controllable portions for analysis purposes. It was decided that specific vertical chains of grains would be “targeted” for analysis and for comparison throughout each shear run.
Fig. 3(a) shows an example of the positions of particles at different times for the case of μ = 0.5, as indicated by decreasing color tone. Before the
Identification of arches
The definition of arch is a mechanically stable structure of mutually stabilizing bodies [8]. To find supporting particles of each particle in dynamic simulations, the arch identification algorithm developed by Arévalo et al. [8] was adopted in this study. In Fig. 6(a), particle j and k supports particle i because the contact chord lies below the center of mass of particle i. Similarly, particle i and l supports particle k. Therefore, particle i and k supports each other, forming a mutually
Conclusions
In summary, 2D DEM simulations of a wedge shearing a granular assembly were conducted to investigate the effect of μ, focusing on the response of the sample in terms of particle rearrangement, sliding and rotation, the arch network, and contact forces. The model was verified qualitatively with data from corresponding physical model. Conclusions could be summarized into several points:
- (1)
A steady state was developed during the shearing process despite the existence of the boundary walls. The
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