This paper presents the results from direct shear testing of gravel-rubber mixtures through laboratory experiments and numerical simulations using discrete element method (DEM). Mixtures with volumetric proportions of 0%, 10%, 25%, 40% and 100% granulated rubber were tested using a conventional, medium-sized direct shear apparatus under three normal confining stresses: 30, 60 and 100 kPa. Experimental results show a decrease in shear strength, greater strain at peak shear stress and less dilative behaviour with increasing rubber content. A selection of experimental results was used to calibrate the DEM model to examine the macro- and micro-responses of these mixtures. Good agreement was attained between the simulation and laboratory results under the considered confining stresses. This simulation exercise demonstrates the ability of DEM to describe the mechanical behaviour of mixtures consisting of hard-gravel and soft-rubber particles under direct shear loads without overly complex input parameters.
In 2015, less than a quarter of the four million waste tyres were recycled, with most ending up in landfills or dumped in stockpiles around the country (Minister of the Environment, 2015). This issue plagues several countries globally. Many are now mandating strict regulations on deposing waste tyres and implementing recycling/reuse schemes. In New Zealand, a new and innovative system, Eco-rubber geotechnical seismic-isolation (ERGSI) foundation systems, is proposed to help address this problem. This system uses gravel-recycled tyre rubber mixtures to improve the seismic performance of medium-density, low-rise residential buildings. The ERGSI provides an appreciable level of base isolation and energy dissipation during ground shaking. Thus, reducing the potential damage to the structure during major seismic events. This study is part of a multi-disciplinary research project undertaken by researchers at the University of Canterbury and the Institute of Environmental Science and Research (ESR) Ltd. (Chiaro et al. 2019; Banasiak et al. 2019; Hernandez et al. 2020).
The incorporation of rubber in granular soils has been increasingly common since the 1990s. Rubber’s low unit weight has seen its use as a lightweight backfill material for retaining walls and embankments (Lee et al. 1999; Humphrey & Manion 1992). The energy dissipative effects of rubber have been studied as a countermeasure against liquefaction (Hazarika et al. 2020; Anastasiadis et al. 2012) and as a geotechnical isolation system (Tsang 2008) for seismic applications.
Previous studies of soil-rubber mixtures have predominantly focused on sand-rubber mixtures, SRM (e.g. Mashiri et al. 2015; Valdes & Evans 2008; Hazarika et al. 2008; Lee et al. 2014). However, the use of gravel in place of sand in soil-rubber mixtures has been recommended (Hazarika & Abdullah 2016) as this avoids inherent segregation of binary (large/small) mixtures (Lee & Santamarina, 2008). Yet, studies on gravel-rubber mixtures are limited (e.g. Signes et al. 2013, Pasha et al. 2018).
With the advancement of computing power in the past few decades, many researchers have attempted to use numerical simulations to study the microscopic behaviours of soil mixtures. DEM has been widely used in recent years to study the behaviour of geomaterials such as SRM and railway ballast subjected to direct shear, compression and triaxial tests (e.g. Lopera-Perez et al. 2018; Asadi et al. 2018; Gong et al. 2019; Wang et al. 2018; Lim and McDowell 2005; Indraratna et al. 2014).
In this study, the behaviour of gravel-rubber mixtures under direct shear has been investigated considering different rubber contents and normal stresses using experimental and numerical methods. Emphasis is placed on developing a tool to complement laboratory experiments to better understand the fundamental behaviours of mixtures using insights from microscopic level responses.
Material and Testing Procedures
The direct shear apparatus used in this study consists of a 100 mm by 100 mm wide metal square box with a height of 53 mm divided into two halves (refer to Figure 4 for details). The tested materials consisted of a uniformly-graded granulated tyre rubber (specific gravity = 1.15; mean particle size = 4 mm) and a uniformly-graded rounded gravel (specific gravity = 2.71; mean particle size = 6 mm). The aspect ratio () of the mixtures was approximately 1.5. The particle size distribution of the gravel and rubber alongside a specimen of the geomaterial tested are shown in Figure 1.
The direct shear tests were conducted in accordance with ASTM D3080 under normal stresses of 30, 60 and 100 kPa. Mixtures with varying volumetric proportions of rubber crumbs (e.g. 10%, 25% and 40% rubber content) were prepared by mixing dry gravel and rubber particles. The test specimens were placed into the shear box in four roughly equal layers. A small compacting force was applied at each layer (refer to under-compaction method by Ladd, 1978) to ensure the specimens were properly packed inside the box while avoiding segregation. The relative density of all specimens before applying any vertical stress was 50%.
A displacement-controlled procedure was used to shear the specimen at a rate of 1 mm/min to a maximum shear displacement of 16 mm. Shear stress, vertical displacement, and horizontal displacement were recorded throughout the test. A summary of the direct shear tests carried out on various gravel-rubber mixtures is reported in Table 1.
Figure 1: (a) Particle size distribution for the sourced gravel (G) and granulated rubber (R1); (b) photograph of a specimen of test materials used in this study.
Table 1: Properties of the gravel-rubber mixtures.
|Mixture ID||Volumetric rubber content, VRC (%)||Specific Gravity, Gs||(Initial) Void ratio, e|
Discrete Element method
The use of discrete elements methods (DEM) to model distinct particles was initially proposed by Cundall and Strack (1979) and is now widely used to study particulate systems. It has applications across several engineering fields, such as studies on jointed rock masses, rockfall modelling and behaviour of bulk materials under industrial processes.
Figure 2: Description of a calculation cycle in PFC3D (Itasca Consulting Group, 2019).
In this study, a commercially available software by Itasca Consulting Group – Particle Flow Code 3-dimensional (PFC3D) is used. PFC3D is based on the discrete numerical model originally proposed by Cundall and Strack (1979), which uses an explicit numerical scheme to monitor the interaction of particles individually and their corresponding contacts with neighbouring particles. This DEM framework utilises brief states of equilibrium to describe a dynamic behaviour numerically. It assumes that the velocities and accelerations are constant within each time step, and time steps are infinitesimal such that disturbances on a particle assembly does not propagate beyond its immediate neighbours (Cundall & Strack 1979). The calculation cycle in PFC3D is illustrated in Figure 2 and is fundamentally based on Newton’s second law and a user-defined force-displacement law.
In this context, rigid-hard gravels and soft granulated rubber are modelled in DEM as individual and unbonded particles where the physical properties of each particle are defined. Input parameters for each particle include shape, size, stiffness, surface friction and an interaction relationship (e.g. contact law) to describe the behaviour of particles within the system. Spring and dashpot forces as a function of the particle overlap are typically used to describe the interaction between model components at their contacts (Figure 3). When in motion, particle slip occurs when the tangential forces exceed the Coulomb limit defined by the friction coefficient, µ (Itasca, 2019).
Figure 3: Model component definitions and interactions for a linear contact model, where m and r denote mass and radius of ball respectively (Itasca, 2019).
Model Parameters and Setup
Figure 4 shows how the corresponding components of a direct shear apparatus are represented in the DEM model. The model consists of walls akin to boundaries and spherical particles grouped to form clumps. The box is sheared by moving the bottom half of the box at a constant deformation rate. To reduce computation time, the samples were sheared at a rate of 0.01 m/s found by limiting the inertia number, to satisfy quasi-static conditions (Lopera‑Perez at al., 2016).
Figure 4: (a) Schematic illustration of direct shear apparatus (Powrie 2014); (b) DEM model of the direct shear test in this study.
The inertia number is defined as I , where is the strain rate, is the average particle size, is the particle density, and is the mean effective stress assumed to be the normal confining stress applied. The average computational time was 2 hours per test using a 48 CPU (central processing unit) cluster and a time step in the order of 10-6 seconds.
The shear force is measured by taking the increments in the sum of forces in the shearing direction applied by the particles onto the walls of the top half of the box during shearing (Indraratna et al. 2014; Zhang & Thornton 2007).
As shown in Figure 5, simple shapes were used to represent the gravel and rubber particles. Conglomerates of balls (clumps) were used to represent the rounded gravels and rubber crumbs respectively. The gravel and rubber particles were generated based on the particle size distribution in Figure 1(a) and placed randomly with particle-to-particle overlaps in the shear box to achieve a target mass corresponding to 50% relative density.
Figure 5: Simple shapes used in this study to approximate gravel (G) and rubber (R) particle geometry.
A combination of parameters calibrated from test results and adopted from literature have been used in this study. The Hertz-Mindlin (Mindlin & Deresiewicz, 1953) contact law was found to be the most appropriate to reproduce the experimental results at different normal stresses. These numerical parameters are summarised in Table 2.
Table 2: Numerical parameters for gravel, rubber and shear box.
|Particle Density, ρ (kg/m3)||2710(1)||1150(1)||–|
|Shear modulus, G (MPa)||90 (2)||6 (3)||80,000 (4)|
|Poisson’s Ratio, υ||0.25 (2)||0.49||0.30 (4)|
|Coefficient of Friction *||0.80||0.30||0.70 for wall-gravel
0.20 for wall-rubber
|(1) Tasalloti et al., 2020; (2) determined from bender element test of G100-R0; (3) Lopera-Perez at al., 2018; (4) Beer et al., 2015.
* derived from calibration process
Results and discussions
Pure Gravel and Pure Rubber
The shear stress versus vertical displacement and horizontal displacement versus vertical displacement plots, experimentally and numerically obtained for pure gravel and rubber at 30, 60 and 100 kPa normal stresses, are shown in Figure 6. Key observations from this study are discussed below.
Figure 6: Experimental and numerical results of direct shear test on pure gravel and rubber.
There are several key differences between the behaviour of pure gravel and pure rubber samples under direct shear: (1) a clear peak is followed by strain softening as evident in the shear stress curve for pure gravel, which is absent in pure rubber; (2) pure gravel exhibits predominantly dilative behaviour during shearing while that of pure rubber is predominantly contractive; and (3) the maximum shear stress measured during shearing in gravel is significantly greater than rubber under the same normal stress.
Figure 6(a) compares the experimental results with the DEM numerical simulations for 100% rounded gravel under three different normal stresses at 50% relative density. The DEM results show good agreement with the experimental data in terms of trend, rate of dilation and total vertical displacement. At large deformation levels, the simulated shear stress is ±5 kPa to that measured in laboratory experiments. At the same time, the total vertical displacement predicted is slightly overestimated, differing by less than 1 mm.
For pure rubber, a good agreement is attained between the shear stress–shear displacement relationships experimentally obtained and the corresponding DEM simulations. As shown in Figure 6(b), the model prediction for the vertical-horizontal displacement plots is able to capture the overall qualitative trends. For example, contractive response followed by dilative behaviour after the maximum compression with the measured vertical displacement differing by less than 0.4 mm. Some small quantitative differences can also be observed. For instance, the rate of contraction is greater in the experimental results, and the numerical model achieves the maximum contraction at a larger displacement compared to the experiment.
Figure 7: Comparison of friction angle and shear stress results at failure/peak.
Lastly, the DEM model performed well when predicting the strength characteristics of gravel and rubber (e.g. peak shear stress and peak friction angle) as shown in Figure 7.
Figure 8 illustrates the rotation of the major principal stress in the DEM sample during shearing, which is characteristic of direct shear testing but not easily observable in laboratory experiments.
By measuring the average normal force component at each contact in the system, a distribution of average normal forces can be obtained as shown in Figure 8. Before shearing, the sample is inherently anisotropic with the direction of maximum average normal force,, orientated 90 degrees to the horizontal due to the non-isotropic conditions of the direct shear apparatus. During shearing, reduces to approximately 30 degrees at peak stress (4 mm displacement) and increases to 35-45 degrees at post-peak (>10 mm displacement). Note that may not necessarily be in line with the major principal stress direction but is a reliable proxy (Rothenburg & Bathurst 1989).
Figure 8: Polar histogram of average normal forces in the DEM sample at different deformation level for G100 under 60 kPa normal stress.
Figure 9: Friction angle at failure under different VRC.
The effects of different volumetric rubber content on the shear stress and vertical displacement under 30, 60 and 100 kPa normal confining stresses were also examined in this study. Experimental results show that the peak shear stress decreases with increasing rubber content, while the vertical displacement decreases with increasing rubber content (Tasalloti et al., 2020). The experimental results summarised in Figure 9 show that the inclusion of rubber causes a reduction in the friction angle (at peak or large displacements) for all normal stress levels.
It is evident that the inclusion of rubber causes a reduction in strength of the soil mixture. However, the peak friction angle measured for volumetric rubber content (VRC) of 40% or less were typically 35 degrees or greater, which is in the order of what it typically recommended for structural fills in practice (Chiaro et al., 2015).
Although specific simulation results are not reported in this paper, initial numerical results indicate that the gravel-rubber DEM model is able to capture the key characteristics and strength of the tested specimens under direct shear. In this context, the calibrated gravel and rubber models have been combined to study the prediction capabilities for gravel-rubber mixtures using DEM. Numerical results from mixtures of different volumetric rubber content will be published elsewhere in due course.
In this paper, the results of laboratory and numerical simulations of direct shear tests carried out on gravel-rubber mixtures, with volumetric rubber content VRC = 0, 10, 25, 40 and 100%, is presented. The experimental results show a decrease in shear strength, greater strain at peak shear stress and less dilative behaviour with increasing rubber content. The numerical investigation was conducted by developing a direct shear test model for hard-grain gravel and soft-particle rubber materials using a DEM software – PFC3D. With simple particle shapes, inputs from measured physical properties of gravel and rubber, and a rigorous calibration process, the DEM model results attained good agreement with the experimental study. Key characteristics of the mechanical behaviour of both gravel and rubber under direct shear load (e.g. peak shear stress, peak friction angle and dilative/contractive behaviours) were reproduced. This model will be further advanced to examine the complex behaviour of gravel-rubber mixtures made of hard and soft particles from a microscopic and granular mechanics points of view, which are not easily measurable in physical laboratory experiments.
This study was funded by the Ministry of Business, Innovation and Employment of New Zealand (MBIE Smart Ideas Research Grant No. 56289). A special thank you goes to the University of Canterbury IT staff (Paul Strange) for setting up the computation engine.
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