Geogrids are the geosynthetics of choice for soil reinforcement applications. To evaluate the efficiency of geogrid reinforcement, several methods are used including field tests, laboratory tests and numerical modeling. Field studies consume long period of time and conducting these investigations may become highly expensive because of the need for real-size structures. Laboratory studies present also significant difficulties: large-size testing machines are required to accommodate realistic geogrid designs. The discrete element method (DEM) may be used as a complementary tool to extend physical testing databases at lower cost. Discrete element models do not require complex constitutive formulations and may be fed with particle scale data (size, strength, shape) thus reducing the number offree calibration parameters. Discrete element models also are well suited to problems in which large displacements are present, such as geogrid pullout. This paper reviews the different approaches followed to model soil-geogrid interaction in DEM and presents preliminary results from pull-out conditions.Peer ReviewedPostprint (author's final draft

CJ Jones

GR McDowell

M Sugimoto

MS Khedkar

PA Cundall

RM Koerner

VDH Tran

English

Crossref

Discrete Element Models of Soil-Geogrid Interaction

Irsainova, Alina

Arroyo Alvarez de Toledo, Marcos

Kim, Jong-Ryeol

UPCommons. Portal del coneixement obert de la UPC

Discrete Element Models of Soil-GeogridInteractionAlina Irsainova1, Marcos Arroyo2, and Jong-Ryeol Kim1(&)1 Nazarbayev University, Astana 010000, Kazakhstanjong.kim@nu.edu.kz2 Universitat Politècnica de Catalunya, 08034 Barcelona, SpainAbstract. Geogrids are the geosynthetics of choice for soil reinforcementapplications. To evaluate the efficiency of geogrid reinforcement, several methodsare used including field tests, laboratory tests and numerical modeling. Fieldstudies consume long period of time and conducting these investigations maybecome highly expensive because of the need for real-size structures. Laboratorystudies present also significant difficulties: large-size testingmachines are requiredto accommodate realistic geogrid designs. The discrete element method (DEM)may be used as a complementary tool to extend physical testing databases at lowercost. Discrete element models do not require complex constitutive formulationsand may be fed with particle scale data (size, strength, shape) thus reducing thenumber offree calibration parameters. Discrete elementmodels also arewell suitedto problems inwhich large displacements are present, such as geogrid pullout. Thispaper reviews the different approaches followed to model soil-geogrid interactionin DEM and presents preliminary results from pull-out conditions.Keywords: Discrete element method (DEM)  Soil reinforcement  Geogrids1 Introduction1.1 GeogridsGeosynthetics are synthetically manufactured products used with soil, rock, and earthso overcome civil engineering problems. Geosynthetics can be used in a wide spectrumof fields such as transportation, geotechnical, environmental, hydraulics, and privatedevelopment [1].Geogrids are one of the types of geosynthetics that are quickly growing in usage. Itsstructure consists of plastic ribs forming big apertures. Due to its open-like structure, itcan be used for reinforcement and stabilization. Transverse and longitudinal ribs of thegeogrids are manufactured from high-modulus polymers; therefore, the strength ofgeogrid ribs is higher than the strength of geotextiles. Transverse members of thegeogrids serve as an abutment or anchor due to their location parallel to the face ofstructure. Therefore, the main function of longitudinal ribs is to keep the transverse ribsin position [2]. The opening size of geogrids is sufficient enough to allow soil contactand interlocking between particles. Geogrid reinforcement provides higher shearstrength of soil mass and higher load bearing capacity. Geogrids are also helpful in© Springer Nature Switzerland AG 2019W. Wu (Ed.): Desiderata Geotechnica, SSGG, pp. 67–74, 2019.https://doi.org/10.1007/978-3-030-14987-1_7preventing soil erosion. Moreover, use of geogrids in construction reflects otheradvantages such as ease of construction, high durability, resistance to environmentalissues, availability of the material, and low cost [3].1.2 Geogrid Modeling MethodsModeling of geogrids can be categorized as soil-inclusion problems. Applying finiteelement method (FEM) for such case is widely practiced [4, 5]. However, using FEMto model soil-inclusion problems faces difficulties in the definition of crucial param-eters that represent grid-soil interaction. Application of discrete element method(DEM) may be useful, particularly for cases involving large sized granular materials.There are several studies that describe conventional method of modeling representingsoil and soil inclusion as rigid spherical particles [6]. Some studies develop soil-inclusion model by using mix of methods: where soil was modeled by discrete element(DE) and geogrid was modeled by finite element (FE) [7]. A summary example ofgeogrid modeling methods is given in Table 1.2 Numerical Modeling2.1 Numerical Modeling MethodA method to model geogrid-soil interactions through representing geogrids asdeformable cylinders according to the concept by Minkowski sum has been recentlyproposed by Thoeni et al. [8]. Main components of Minkowski sum include rigidTable 1. Summary of geogrid modeling methods.# Modeling approaches Applications Refs.1 Model by using FEM: whereboth soil and geogrid wasmodeled by finite elementPull-out behavior of the modelwas investigatedSugimoto andAlagiyawanna [4];Khedkar andMandal [5]2 DEM model representing soiland soil inclusion as rigidspherical particlesCyclic triaxial loadingsimulation with sphericalballast particlesMcDowell et al.[6]3 DEM-FEM models: where soilwas modeled by sphericaldiscrete element and geogridwas modeled by finite element(FE)Pull-out test was performed todefine relationships betweenpull-out force anddisplacementsTran et al. [7]4 DEM model by representinggeogrids as deformablecylinders according to theMinkowski sum concept andrepresenting soil as sphericalparticlesPull-out test was performed inorder to check effectiveness ofthe modelThoeni et al. [8]68 A. Irsainova et al.spheres (Fig. 1a) and cylinders represented by sphere and line (Fig. 1b). Each rib of thegrid can be modeled by one or more cylinders depending on geometry of grid.Contacts between each component are treated as sphere-sphere interconnectionallowing to use basic mathematical formulation for contact forces.2.2 Inter-particle Contact LawA linear contact stiffness law and Mohr-Coulomb friction were used in the software todescribe inter-particle interaction. This law implements the classical linear elastic-plastic law from Cundall Strack [9]. The normal force is (with the convention ofpositive tensile forces) Fn = min (knun, 0), where un is the normal distance between twospheres. The shear force is Fs = ksus, where us is the relative shear displacement. Theplasticity condition defines the maximum value of the shear force: Fs maxð Þ ¼ FntanðuÞ, with u the friction angle. The linear contact model stiffness is derived from thenormal and shear stiffness kn and ks assigned to the contacting objects. Linear contactmodel represents two contacting objects to be in series; hence, normal secant stiffnessof contact is defined by following equation:kn ¼ kn1kn2kn1þ kn2 ¼2E1R1E2R2E1R1þE2R2where, kn1, kn2 = normal stiffness of contacting objects. Whereas shear tangent stiff-ness of the contact is defined by:(a)                                              (b)Fig. 1. Minkowski sum components: (a) sphere and (b) cylinder [8](a) (b)FsFig. 2. Contact forces between components: (a) sphere-sphere and (b) sphere and virtual sphereof cylinder or pfacet [8]Discrete Element Models of Soil-Geogrid Interaction 69ks ¼ ks1ks2ks1þ ks2 ¼2E1R1m1E2R2m2E1R1m1þE2R2m2where, ks1, ks2 = shear stiffness of contacting objects, E1, E2 = Young’s modulus, R1,R2 = radii of the contacting spheres, and m1, m2 = Poisson’s ratio. When a soil particlecontacts a grid component the same formulas apply, but the grid is assigned the radiusof the virtual inscribed sphere (see Fig. 2(b)).3 Results and DiscussionOngoing work is directed to apply the discussed geogrid modeling technique in real-istic laboratory configurations. A pull-out test was initially modeled in order to observethe potential of the approach chosen. The contact properties of soil and geogridmaterial are assumed to be the same (Table 2). Note that, for simplicity, no rollingfriction was included in the contact model. Square grid mesh of 9.5 cm  9.5 cmdimensions with 1 cm openings was introduced to the model (Fig. 3a). Pull-out of thegrid for cubic soil matrix with sides of 10 cm was performed applying a constantvelocity of 0.06 m/s to the grid. All numerical simulation was performed using Yadesoftware [10].Table 2. Summary of material properties.Parameter ValueYoung’s modulus, E 5000 kPaDensity, q 2650 kg/m3Poisson’s ratio, t 0.3Friction angle, u 20°(a) (b)Fig. 3. Geogrid mesh: (a) rectangular and (b) triangular70 A. Irsainova et al.Figure 4 shows a pull-out test at several stages, with the grid at different positions.Figure 4(a) shows when the displacement of a grid at the initial stage (Dx = 0), whileFig. 4(b) and (c) present pull-out at the intermediate stage (Dx = 4.75 cm) and totalpullout (Dx = 9.5 cm) respectively. The entrapment of soil particles can be observed asgrey soil columns became mixed with green columns as geogrid is being pulled-out.This is indicative of the interlocking properties of the grid because soil particles arecaptured in the grid openings and while it is pulled out, the particles move along themovement direction.A parametric study was conducted, in which the grid pull-out was performed underdifferent conditions. The parameters explored included the vertical confining pressureat the top wall of the box, size of soil particles and the shape of the grid pulled out. Thecorresponding values of the parameters are presented in Table 3. It is noted that auniform sized particle distribution was used in all cases. The schematic view of10 cm  8.7 cm triangular geogrid can be seen in Fig. 3(a) and its geometry is morecomplex compared to the rectangular. Triangles of the grid are equilateral with thesides of 1.43 cm and vertical components at both sides of the grid are 1.24 cm.(a)                                                    (b)(c)Fig. 4. Pull-out of a grid: (a) Dx = 0, (b) Dx = 4.75 cm and (c) Dx = 9.5 cmDiscrete Element Models of Soil-Geogrid Interaction 71The resultant graph of pull-out force versus displacement is given in Fig. 5 forvarious confining pressure conditions. This case considers rectangular geogrid withmiddle (0.0015 m) soil particle dimension. The figure shows that pull-out responseslightly increases with increasing vertical confining stress of 75 kPa, 150 kPa and300 kPa. Average values of pull-out force are 20.11 N, 28.05 N and 31.20 Nrespectively. Interestingly there seems to be very little effect on the pullout force of thereduction of inserted grid length in the specimen; as long as there is one transversal ribin the box the pull-out force average is closely maintained.Another figure was built to illustrate variance of response of geogrid pull-outaccording to different shapes of geogrid. Figure 6 represents the case with verticalconfining stress of 150 kPa and with soil grain radius of 0.0025 m. The figure showsthat pull-out response for the rectangular grid is higher than triangular grid case, at leastuntil a large displacement has been achieved. Average pull-out forces for rectangularand triangular grid shapes are 36.66 N and 28.05 N respectively.Table 3. Range of parameters considered in the study.Parameter ValueConfining pressure, P (kPa) 75, 150 and 300Radius of soil grains, r (m) 0.001, 0.0015 and 0.0025Shape of geogrid Rectangular and triangular0 1 2 3 4 5 6 7 8 9 100102030405060708090100110Displacement (cm)Pull-out force (N)75 kPa150 kPa300 kPaFig. 5. Pull-out response of square geogrid: r = 0.0015 m72 A. Irsainova et al.Average pull-out force values for each case in the study are shown in Table 4. Asexpected, for all sizes of soil grains the pull-out response of the grid is higher forincreased vertical confinement. In order to quantify variation of the pull-out responseresults, coefficient of variation values were estimated. Table 5 includes coefficient ofvariation for different particles sizes and for varied vertical confining stress. As a result,variation coefficient decreases with the decreasing particle size for each confinementscenario. This indicates that variation of the pull-out response is smaller for smallergrain size which leads to more precise results. As the model becomes more continuousthe variance of the results related to the average value diminishes.01020304050607080901001100 1 2 3 4 5 6 7 8 9 10Pull-out force (N)Displacement (cm)RectangularTriangularFig. 6. Pull-out of geogrids: P = 150 kPa and r = 0.0025 mTable 4. Average pull-out force values with different parameters.Confiningpressure (kPa)Radius of soil particles (m) Triangular shape(r = 0.0025 m)0.0025 0.0015 0.001075 26.29 20.11 41.32 20.11150 36.66 28.05 42.41 28.05300 43.56 31.20 44.51 39.23Table 5. Coefficient of variation of pull-out force with different parameters.Confining pressure (kPa) Radius of soil particles (m)0.0025 0.0015 0.001075 0.543 0.445 0.242150 0.434 0.381 0.234300 0.413 0.406 0.230Discrete Element Models of Soil-Geogrid Interaction 73

Discrete element models of soil-geogrid interaction

Geogrids are the geosynthetics of choice for soil reinforcement applications. To evaluate the efficiency of geogrid reinforcement, several methods are used including field tests, laboratory tests and numerical modeling. Field studies consume long period of time and conducting these investigations may become highly expensive because of the need for real-size structures. Laboratory studies present also significant difficulties: large-size testing machines are required to accommodate realistic geogrid designs. The discrete element method (DEM) may be used as a complementary tool to extend physical testing databases at lower cost. Discrete element models do not require complex constitutive formulations and may be fed with particle scale data (size, strength, shape) thus reducing the number offree calibration parameters. Discrete element models also are well suited to problems in which large displacements are present, such as geogrid pullout. This paper reviews the different approaches followed to model soil-geogrid interaction in DEM and presents preliminary results from pull-out conditions.Peer Reviewe

UPCommons

Discrete element models of soil-geogrid interaction

Abstract

Similar works

Full text

Available Versions

Crossref

UPCommons. Portal del coneixement obert de la UPC

UPCommons