[American Society of Civil Engineers Geo-Shanghai 2014 - Shanghai, China (May 26-28, 2014)] Ground Improvement and Geosynthetics - Study of Geogrid Reinforcement Using Two-Dimensional

Study of Geogrid Reinforcement Using Two Dimensional Discrete Element Method

Xinbao Yu1 and Asheesh Pradhan2

1Corresponding Author: Assistant Professor, Department of Civil Engineering, the University of Texas at Arlington , Arlington, TX 76019, Ph (817) 272 1243, email: [email protected] 2Graduate Assistant, Department of Civil Engineering, the University of Texas at Arlington , Arlington, TX 76019, Ph (817) 272 6310, email: [email protected] ABSTRACT: Geogrid reinforced granular soils have been widely used in pavement, railway, and retaining wall. Understanding the reinforcement mechanism is important to appropriately design those earth structures. 2D Numerical models of geogrid reinforced granular soil samples were created using discrete element method. Biaxial compression tests were performed on the numerical soil samples. The numerical study focused on the influence factors that affect the reinforcement effect such as loading rate, boundary conditions, confining pressure, particle shape, and particle friction. The results show that loading rate and particle shape are dominant factors for geogrid-soil particle interaction. Recommendations have been provided for simulation of geogrid reinforced soil using discrete element method. INTRODUCTION Geogrid provides reinforcement by interlocking soil particles and also due to its relative structural stiffness. Konietzky et al. (2004) mentions that interlocking is the key mechanism as investigated in their three dimensional (3D) DEM simulation of circular particles with rigid wall boundary whereas the geogrid stiffness was found to have significant effect on reinforcement as investigated by Abu-Farsakh and Nazzal (2009) in their laboratory testing and two dimensional finite element modeling. Improvement in soil strength due to geogrid reinforcement in 2D DEM simulations has also been reported in terms of peak strength in biaxial compression test (Vinod, Nagaraja, Sitharam, & Dinesh, 2011) with rigid boundary walls but the mechanism of geogrid reinforcement was not discussed. Also, the strike through of the reinforced soil particle is not possible in 2D as in 3D and hence primary reinforcement mechanism in 2D simulation might be different than in 3D. However, the effect of loading rate has not been studied. Biaxial sample in compression test simulation can have different response to different loading rates.

299Ground Improvement and Geosynthetics GSP 238 © ASCE 2014

Ground Improvement and Geosynthetics

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Most if not all of lab testing of soils in compression have flexible boundary (such as latex membrane or air) as in conventional triaxial test and unconfined compressive strength tests, for example. These tests are better simulated with membrane boundary (Cheung & O' Sullivan, 2008). In reality physical specimens bulge when they fail which often times is clearly visible. Tannant & Wang (2007) have expressed unsuitability of using single rigid walls to simulate boundary confinement as they inhibit the sample from bulging. Nevertheless, rigid walls have been used to simulate boundary confinement in numerical simulations by several authors as Konietzky & Kamp (2004), Lu & McDowell (2010), Lu & McDowell (2008). 2D DEM simulation of biaxial compression test can be a convenient numerical method of investigating behavior of granular assembly and the effect of boundary types (O’Sullivan (2011); Indraratna, Thakur, & Vinod, (2010)) although the use of rigid or flexible boundary condition does not have significant effect on the peak strength (Cheung & O' Sullivan, 2008). In this paper the effect of rigid and flexible boundary has been extended to geogrid reinforced sample for various confining pressures.

Particle rotations in 2D DEM simulations have also been studied by authors Cheung and O’ Sullivan (2008). Although, the rounded shape of circular DEM particles rarely match the physical shape of granular materials and exhibit excessive rotation and should be inhibited for realistic resemblance of a physical test, particle rotations can provide insight into geogrid reinforcement mechanism.

The works by the several authors on laboratory experiments and numerical modeling of geogrid reinforcement have increased the knowledge on geogrid reinforcement mechanisms. However, several other factors such as loading rates, boundary types, and particle shape can have significant influence on the simulation results besides the exclusive effect of presence of geogrid, number of layers of geogrid, and its structural stiffness. Furthermore, such various factors can have different influence on geogrid reinforced sample than on unreinforced sample and is the motivation for the study. BACKGROUND ON DEM AND PFC2D

Discrete Element Method (DEM) was proposed by Cundall and Strack (1979) for modeling granular soil particles with circular discs in two dimensions. A commercial software package PFC2D used here uses similar logic but with rigid, circular discs with soft contact model which allow complete detachments and formation of new contacts and have been classified as discrete element code (Itasca Consulting Group Inc, 2008). The particles move according to the Newton’s second law of motion due to the forces acting on them that result from force-displacement law applied to each contact. Elements of a PFC2D Model

In PFC2D circular particles can be treated as spheres or circular discs of unit length into the plane of viewing with coplanar centroids but the stresses in out-of-plane direction are not considered i.e., plane strain condition. Two or more circular particles can be combined to form complex shapes which can be bonded with breakable or



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unbreakable bonds, the latter being called clumps that act as one rigid particle. Walls can be used for simulating boundary conditions for providing confinement, applying load, and providing displacements. In PFC2D walls do not interact with each other.

Particles can be generated randomly or in specified geometry but for study of soils, the random generation is preferred as it can provide particle arrangement similar to that in the field soil samples. For a particular particle size distribution, presence of interparticle friction and or shear stiffness can significantly affect the initial porosity, stresses, and fabric of the DEM sample. For example, it is not possible to generate identical samples with different stresses. Stress and strains are usually defined in terms of continuum but DEM, as the name suggests, does not form continuous solid samples. Hence the stress and strain are calculated as average over surfaces and volumes. NUMERICAL STUDY Biaxial compression test models were created using PFC2D due to high computation efficiency of 2D model. A biaxial model with selected circular particles, boundary condition, sample preparation, and loading rate was created as a comparison basis for the study of different influence factors. Details of different numerical samples are discussed in the following sections. Numerical Model A standard biaxial sample with circular particles was generated in a rectangular area bounded by four walls, the two horizontal walls on top and bottom as loading platen in PFC2D. For the case of flexible boundary, the vertical walls were replaced by 50 vertical wall segments on each vertical boundary. The sample height was 30 cm and width 15 cm based on several studies (Abu-Farsakh & Nazzal, 2009). The average initial stress on the confining walls was 10 kPa to represent initial reference stress state and the sample behaved as loose soil with friction angle of 24 degrees and initial porosity of 0.185 with relative density of 0%. The following



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Table 1 presents the micro properties of the DEM particles and the properties of the boundary walls used in the simulation and FIG. 1 is the particle size distribution curve. The effect of shape was studied using clump particles that have relatively greater angularity, generated by replacing each circular particle in the biaxial sample with a two particle template as show in the FIG. 2. The clump particles were then scaled down or up as required to represent the exact volume of the original circular particle being replaced. The constituent particles for the creation of clumps were the same particles whose properties are presented in

Table 1.



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Table 1. Properties of DEM Particles and Boundary Walls

Property Value Normal stiffness, Kn 1e8 N/m Shear stiffness, Ks 8.5e7 N/m

Density of a particle 2600 kg/m3 Friction coefficient of particle surface 0.55

Initial porosity 0.185 Wall normal stiffness 1e7 N/m

Loading platen surface friction 1 Vertical wall surface friction 0

Reinforced sample was created by placing the geogrid at the mid-height of the sample. The walls of the reinforced sample were moved outwards expanding the sample to achieve the initial reference stresses state on the boundary walls with only 0.6 % increase in the sample height. Geogrid was modeled using strings of circular particles joined together with contact and parallel bond. Reinforced particles can occupy the apertures of geogrid in three dimensions and provide interlocking effect, and to achieve such phenomenon in PFC2D nodes were provided at junction locations as shown in FIG. 3. Table 2 provides the properties of the constituent particles of the geogrid simulation. The geogrid was calibrated to simulate the tensile strength of BX1100 from Tensar International Corporation, Inc. which has the tensile strength of 8.5 kN/m at 5 % strain and 25 mm aperture along machine direction. The interparticle friction between geogrid and soil particles in the simulations was 0.55.

FIG. 1. Particle size distribution.

FIG. 2. Template for clump particle.

FIG. 3. PFC2D simulation of geogrid.

2 mm

6 mm



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Table 2. Properties of Geogrid Particles and Contacts

Property Value Density 2000 kg/m3

Friction coefficient of particle surface 0.55 Normal stiffness, Kn 5e8 N/m Shear stiffness, Ks 1e8 N/m

Normal contact bond strength, n_bond 1e6 N Shear contact bond strength, s_bond 1e6 N

Ball radius 0.5 mm Parallel bond radius, pb_rad 1 mm

Parallel bond normal strength, pb_n 1e6 N Parallel bond shear strength, pb_s 1e6 N

Parallel bond normal stiffness, pb_kn 1e8 N/m Parallel bond shear stiffness, pb_ks 1e8 N/m

Table 3: Summary of samples and test runs

Sample Shape Boundary Confinement

(kPa) Reinforcement Loading

rate (m/s)

C1 Circular Flexible 100 No 0.005 C2 Circular Flexible 100 No 0.05 C3 Circular Flexible 100 Yes 0.005 C4 Circular Flexible 100 Yes 0.05 C5 Circular Flexible 50 No 0.005 C6 Circular Flexible 400 No 0.005 C7 Circular Flexible 50 Yes 0.005 C8 Circular Flexible 400 Yes 0.005 C9 Circular Rigid 50 No 0.005 C10 Circular Rigid 100 No 0.005 C11 Circular Rigid 400 No 0.005 C12 Circular Rigid 50 Yes 0.005 C13 Circular Rigid 100 Yes 0.005 C14 Circular Rigid 400 Yes 0.005 CL1 Clump Flexible 100 No 0.005 CL2 Clump Flexible 100 No 0.05 CL3 Clump Flexible 100 Yes 0.005 CL4 Clump Flexible 100 Yes 0.05

All the simulations were performed with damping constant α set at 0.7. The fixed value of α assures that all the particles are equally damped.

Effect of Loading Rate Faster loading rate provides higher deviatoric stress reading in numerical simulations due to inertial effects (Chent, Nakata, & Bolton, 2003). The time step



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being calculated based on mass, moment of inertia, translational, and rotational stiffness in PFC2D, remained almost constant. Hence, higher loading rate caused greater overlaps which caused higher deviatoric readings and concentration of force chains near loading platens. By shearing the unreinforced sample at different loading rate, the optimum loading rate of 0.005 m/s was identified. Optimum loading rate is the threshold loading rate below which slower loading rate will not change the stress-strain behavior of the sample. The peak strength increased with faster loading rate as seen for reinforced sample in FIG. 6. The optimum loading rate was selected for the study of geogrid reinforcement to compare the reinforced and unreinforced sample behavior. Also volumetric dilation of reinforced samples were smaller than unreinforced sample. Higher loading rate produced smaller volumetric dilation in unreinforced sample but did not have significant effect on the reinforced sample.

The reinforced biaxial sample was also loaded at the optimum rate at confining pressures of 50 kPa, 100 kPa, and 400 kPa to 5 % axial strain as

shown in FIG. 7. The pressure terms in the legend denote the applied confinement. The single layer of geogrid reinforcement did not increase the peak strength of the sample significantly at the confinement pressures of 50 kPa, 100

kPa, and 400 kPa which is in agreement with the results obtained by Vinod et al. (2011). The initial tangent modulus of elasticity also did not change due to the reinforcement. There were 237 particles in contact with the geogrid and the number did not vary significantly. A factor called reinforcement factor was

calculated to assess the increase in peak strength due to geogrid reinforcement which is the ratio of peak strength of reinforced sample to unreinforced sample.

The reinforcement factors for several simulations are presented in Table 4. Effect of Boundary Type Two types of boundary confinements were used in the simulation – (a) a single rigid vertical wall on each side of the particle assembly and (b) 50 segments of rigid vertical wall on each side to simulate flexible boundary. Each of these single vertical walls for rigid boundary and segments of rigid walls for flexible boundary were then controlled by independent numerical servo mechanism to maintain constant confining stress during compression of samples. The samples were loaded at optimum loading rate to 5 % axial strain. FIG. 4 shows the deformed shape of geogrid reinforced circular particle assembly with flexible boundary at 5% axial strain and 100 kPa confining pressure that was loaded at 0.005 m/s. The FIG. 5 on the right shows the individually servo controlled vertical wall segments simulating flexible boundary interacting with the circular particles. The sample was created using predefined interparticle friction and tangent stiffness and hence did not have homogeneous distribution of porosity throughout. Such heterogeneity might have contributed to non-symmetric bulging. Such type of bulging failures of reinforced samples can be seen in the lab experiment performed by Abu-Farsakh et al. (2009).



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FIG. 4. Deformed shape of reinforced circular particle assembly due to

loading.

FIG. 5. Zoomed in view of the sample and the wall segments.

FIG. 6. Stress vs. strain behavior for different loading rates for unreinforced

and reinforced circular particles with flexible boundary and confining pressure of 100 kPa (UR = unreinforced, RE = reinforced).

FIG. 7. Stress vs. strain behavior of reinforced circular particles at optimum

loading rate and various confining pressures (UR = unreinforced, RE = reinforced).



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FIG. 8. Stress-strain behavior of reinforced circular particle assembly for

different boundary types at different confining pressures (RB = rigid boundary, FB = flexible boundary).

FIG. 8 compares the stress-strain behavior of reinforced circular particle assemblies with rigid and flexible boundary. The pressure terms in kPa in the legend denote the confinement maintained during compression. The overall behavior of the sample with both types of boundaries can be seen fairly similar. Significant differences in volumetric dilation were observed for reinforced samples between rigid and flexible boundary at lower confining stresses of 50 kPa and 100 kPa. Rigid boundary samples displayed higher volumetric dilation than flexible boundary samples. When compared with the unreinforced circular particle assembly, the reinforced assembly exhibited smaller volumetric dilation with flexible. As for unreinforced circular particles, neither the stress-strain behavior nor the volumetric dilation varied between rigid and flexible boundary. Effect of Particle Shape The circular particles were replaced by clump particles as previously described in the numerical model and loaded at optimum rate. It is important to note that the optimum loading rate for the circular particle assembly is not necessarily the optimum for clump as the boundary stresses and porosity of the sample change significantly when the circular particles are replaced by clump particles. Nonetheless, the methodology is useful for comparison. The improvement in strength due to geogrid reinforcement was observed to be more pronounced in clump particle assembly as can be seen in FIG. 9 with increased peak strength and higher initial tangent modulus of elasticity. With faster loading rate of 0.05 m/s the difference in peak strength was more pronounced. The initial tangent modulus also seemed to have increased due to faster loading rate when geogrid was present than at the slower rate. The reinforcement factor for the geogrid reinforced clump for loading rate of 0.005 m/s was calculated to be 1.33 at about 2.5 % axial strain showing greater effect of geogrid reinforcement in clumps than in circular particles. The reinforcement factor was 1.55 for the reinforced clump particle loaded at the faster rate of 0.05 m/s. Volumetric dilation greatly reduced due to the geogrid reinforcement and also with faster loading.



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FIG. 9. Stress-strain behavior of geogrid reinforced clump particle assembly at

different loading rates with flexible boundary and confining pressure of 100 kPa (UC = unreinforced clump, RC = reinforced clump).

Particle Rotation The rotation of the circular and clump particles were also monitored during the simulations. The angular rotations presented are the difference in cumulative rotation of particles at 5 % axial strain and beginning of loading the samples in degrees. Clockwise rotations are taken positive and counter clockwise as negative. The vertical axis represents the location of the particles in the sample along the sample height. FIG. 10 and FIG. 11 show the difference in particle rotation in unreinforced and reinforced circular particles loaded at optimum loading rate with flexible boundary and at 100 kPa confinements. The rotation of particles at the height of 0.15 cm which is the location of geogrid in the sample, have been reduced significantly. This signifies the interlocking mechanism of geogrid which reduces particle rotations. Due to greater bulging at the top as seen in FIG. 4 the particles movement was greater and hence displayed greater particle rotations than at other locations in the sample. Similar trend was observed for the confining pressures of 50 kPa and 400 kPa. Particles rotations were reduced also with respect to increasing loading rates for both reinforced and unreinforced samples. In the case of unreinforced circular particle assembly with rigid boundary, particle rotations were found to be relatively uniform throughout the sample height as shown in FIG. 12 whereas for the flexible boundary, particles at the mid-height displayed more rotations than at the top and bottom as shown in FIG. 10. It can be noted from FIG. 13 that clump particles underwent significantly reduced rotations compared to circular particles.



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FIG. 10. Rotation of unreinforced circular particles for loading rate of 0.005 m/s with flexible boundary at 100 kPa confinement.

FIG. 11. Rotation of reinforced circular

particles for loading rate of 0.005 m/s with flexible boundary at 100 kPa confinement.

Table 4: Summary of Peak Strengths

Sample Particle

type Reinforcement Loading

rate (m/s) Peak

Strength (kPa)

Reinforcement factor

C2 Circular None 0.05 140 1.3 C4 Circular 1 layer geogrid 0.05 184 C1 Circular None 0.005 108 1.09 C3 Circular 1 layer geogrid 0.005 118

CL2 Clump None 0.05 180 1.55 CL4 Clump 1 layer geogrid 0.05 280 CL1 Clump None 0.005 143 1.33 CL3 Clump 1 layer geogrid 0.005 190

Reinforcement Factor

Reinforcement factor defined as the ratio of the peak strength for reinforced sample to the peak strength of unreinforced sample was calculated for several

simulations and have been presented in Table 4. The reinforcement factors have been calculated only for flexible boundary as peak strengths did not vary significantly between flexible and rigid boundary. The reinforcement factors derived from the work of Abu-Farsakh & Nazzal (2009) were also found to be 1.17 and 1.11 for “crushed limestone I” and “crushed limestone II” reinforced with single geogrid layer at mid-height of the sample with “geogrid type I” and “geogrid type II”. Although the samples were crushed lime limestone with D50 of approximately 2.5 mm and the simulation was a two dimensional finite element modeling, the results seem to agree on the level of reinforcement provided by single geogrid layer.



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FIG. 12. Rotation of unreinforced circular particles with rigid boundary at confining

pressure of 100 kPa and loading rate of 0.005 m/s.

FIG. 13. Rotation of unreinforced clump

particles with rigid boundary at confining pressure of 100 kPa and loading rate of

0.005 m/s. CONCLUSIONS The presence of single layer of geogrid did not have significant effect on the stress versus strain behavior of circular particle assembly which was shown by the reinforcement factor of 1.09 but there was significant increase in the peak strength of clump particle assembly shown by the reinforcement factor of 1.33. The presence of geogrid reinforcement was amplified by faster loading rate of 0.05 m/s with the reinforcement factor of 1.3 for circular particles and 1.55 for clump particles and increased the initial tangent modulus of elasticity. The presence of geogrid reduced volumetric dilation with reduced particle rotations in the vicinity of geogrid conforming that the geogrid model was able to provide interlocking even without strike through. The analysis shows that using higher loading rate unreinforced circular particle assembly can achieve peak strength of reinforced circular particle assembly or unreinforced clump particle assembly. Also, unreinforced clump particle assembly can exhibit peak strength of reinforced clump particle assembly with faster rate of loading. In general, it was observed that slower loading rates produced higher volumetric dilation than faster loading rates. Hence it is important to identify the optimum loading rate of an assembly to perform parametric study in micro and macro level.

The type of boundary, rigid or flexible, did not have significant effect on the stress-strain behavior of circular particle assembly whether it was unreinforced or geogrid reinforced. In terms of particle rotation, particles in flexible boundary showed greater amount of rotations around the mid-height of the sample whereas the particle rotations were relatively more uniform throughout the sample in rigid boundary. The volumetric dilation behavior of unreinforced circular particle assembly with flexible boundary was similar to that with rigid boundary but reinforced circular particle assembly with rigid boundary showed higher volumetric dilation than with



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the flexible boundary. In addition, the flexible boundary was able to produce the bulging of the particle assembly when it was loaded. Therefore, it might be important to consider the type of boundary to be used while performing micro level investigations than for macro level investigations.

The study helped in understanding the effect of geogrid reinforcement and its mechanism coupled with factors such as loading rate, boundary types, and particle shape. Future works can include studying the sole effect of geogrid stiffness and multiple geogrid layers and extending the analysis to three dimensional DEM.

REFERENCES

Abu-Farsakh, M. Y. and Nazzal, M. (2009). Evaluation of the base/subgrade soil under repeated loading: phase I – laboratory testing and numerical modeling of geogrid reinforced bases in flexible pavement, Louisiana Transportation Research Center, Baton Rouge, LA 70808.

Cheng, Y. P., Nakata, Y., and Bolton, M. D. (2003). "Discrete element simulation of crushable soil." Géotechnique,53(7), 633-641

Cheung, G., and O’Sullivan, C. (2008). “Effective simulation of flexible lateral boundaries in two- and three-dimensional DEM simulations.” Particuology, 6(6), 483-500.

Cundall, P. A. and Strack, O. D. (1979). “A discrete numerical model for granular assemblies.” Geotechnique., 29(1), 47-65.

Indraratna, B., Thakur, P. K., and Vinod, J. S. (2010). “Experimental study of railway ballast behavior under cyclic loading.” International Journal of Geomechanics, 10(4), 136-144

Itasca. (2008). “Particle flow code in two dimensions.” Itasca Consulting Group Inc., Minnesota.

Konietzky, H., te Kamp, L., and Groeger, T. (2004). “Use of DEM to model the interlocking effect of geogrids under static and cyclic loading.” Numerical Modeling in Micromechanics via Particle Methods, Taylor and Francis Group, London.

Lu, M., and McDowell, G. R. (2008). “Discrete element modeling of railway ballast under triaxial conditions.” Geomechanics and Geoengineering: An International Journal, 3(4), 257-270.

Lu, M., and McDowell, G. R. (2010). “Discrete element modeling of railway ballast under monotonic and cyclic triaxial loading.” Geotechnique, 60(6), 459-467.

O’Sullivan, C. (2011). “Particle-based discrete element modeling: geomechanics perspective.” International Journal of Geomechanics, 11(6), 449-464.

Vinod, J. S., Nagaraja, S., Sitharam, T. G., and Dinesh S. V. (2011). “Numerical Simulation of reinforced granular soils using DEM.” Geo-Frontiers, ASCE, 4242-4251.



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Documents

[American Society of Civil Engineers Geo-Shanghai 2014 - Shanghai, China (May 26-28, 2014)] Ground Improvement and Geosynthetics - Study of Geogrid Reinforcement Using Two-Dimensional