ARTICLE

Three-dimensional numerical analysis of geocell-reinforcedsoft clay beds by considering the actual geometry of geocellpocketsA.M. Hegde and T.G. Sitharam

Abstract: Due to its complex honeycomb structure, the numerical modeling of the geocell has always been a big challenge.Generally, the equivalent composite approach is used to model the geocells. In the equivalent composite approach, the geocell–soil composite is treated as the soil layer with improved strength and stiffness values. Though this approach is very simple, it isunrealistic to model the geocells as the soil layer. This paper presents a more realistic approach of modeling the geocells inthree-dimensional (3D) framework by considering the actual curvature of the geocell pocket. A square footing resting on geocellreinforced soft clay bed was modeled using the “fast Lagrangian analysis of continua in 3D” (FLAC3D) finite difference package.Three different material models, namely modified Cam-clay, Mohr–Coulomb, and linear elastic were used to simulate thebehaviour of foundation soil, infill soil and the geocell, respectively. It was found that the geocells distribute the load laterallyto the wider area below the footing as compared to the unreinforced case. More than 50% reduction in the stress was observedin the clay bed in the presence of geocells. In addition to geocells, two other cases, namely, only geogrid and geocell withadditional basal geogrid cases were also simulated. The numerical model was systematically validated with the results of thephysical model tests. Using the validated numerical model, parametric studies were conducted to evaluate the influence ofvarious geocell properties on the performance of reinforced clay beds.

Key words: geocells, geogrid, numerical modeling, fast Lagrangian analysis of continua in 3D (FLAC), soft clay, plate load test,bearing capacity, footing.

Résumé : En raison de la structure en nid d’abeille complexe des géocellules, la modélisation numérique de celles-ci a toujoursété un grand défi. Généralement, l’approche du composite équivalent est utilisée pour modéliser les géocellules. Dans le cas del’approche du composite équivalent, le composite géocellule–sol est traité comme la couche de sol ayant des valeurs amélioréesde force et de rigidité. Quoique cette approche soit très simple, il est peu réaliste de modéliser les géocellules comme étant lacouche de sol. Cet article présente une approche plus réaliste pour modéliser les géocellules dans le cadre tridimensionnel enconsidérant la courbure réelle de la poche de la géocellule. Une semelle carrée reposant sur un lit d’argile molle renforcé degéocellules a été modélisée au moyen du progiciel en différences finies « fast Lagrangian analysis of continua in 3D » (FLAC3D).Trois modèles de matériau différents, l’argile Cam modifié, le Mohr–Coulomb et l’élastique linéaire ont été utilisés pour simulerle comportement du sol de fondation, du sol de remplissage et de la géocellule, respectivement. On a trouvé que les géocellulesdistribuent la charge latéralement a la zone plus large au-dessous de la semelle par rapport au cas non renforcé. On a observé uneréduction de plus de 50 % de la contrainte dans le lit d’argile en présence de géocellules. En plus des géocellules, deux autres cas,a savoir la géogrille seule et les géocellules avec géogrille de fond supplémentaire ont aussi été simulés. Le modèle numérique aété systématiquement validé par les résultats des essais sur modèle physique. Le modèle numérique validé a servi a réaliser desétudes paramétriques afin d’évaluer l’influence des diverses propriétés des géocellules sur la performance des lits d’argilerenforcés. [Traduit par la Rédaction]

Mots-clés : géocellules, géogrille, modélisation numérique, « fast Lagrangian analysis of continua in 3D » (FLAC), argile molle, essaide charge avec plaque, capacité portante, semelle.

IntroductionGround improvement using the soil reinforcement technique has

grown substantially in the last three decades. The technique hasgrown from use of metal grids to use of geosynthetic products suchas geogrids and geocells to reinforce soft soil. Nowadays, geocells arebeing widely used in geotechnical engineering to strengthen softsoil. General applications of geocell include pavements, foundations,and embankments. By virtue of its three-dimensional (3D) box-likestructure, geocell provides additional confinement to the soil. Geo-cells offer faster, cheaper, sustainable, and environmentally friendlysolutions to many complex geotechnical problems. Many research-

ers have highlighted the beneficial effects of the geocells with thehelp of 1g model tests (Sitharam et al. 2005; Dash et al. 2007;Moghaddas Tafreshi and Dawson 2010; Dash and Bora 2013; Tanyuet al. 2013; Hegde and Sitharam 2014a; Hegde et al. 2014). Some re-searchers in the past also studied the efficacy of geocells using thefull scale field tests and the case studies (Cowland and Wong 1993;Han et al. 2011; Kief et al. 2011; Yang et al. 2012; Moghaddas Tafreshiet al. 2013, 2014; Sitharam and Hegde 2013). However, very few re-searchers have attempted the numerical modeling of the geocellsdue to difficulty in modeling its complex honeycomb structure. Be-cause geocell applications are growing at a rapid rate nowadays; it is

Received 6 September 2014. Accepted 10 February 2015.

A.M. Hegde and T.G. Sitharam. Department of Civil Engineering, Indian Institute of Science, Bangalore, India, 560012.Corresponding author: A.M. Hegde (e-mail: amarnathhegde@gmail.com).

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Can. Geotech. J. 52: 1–12 (2015) dx.doi.org/10.1139/cgj-2014-0387 Published at www.nrcresearchpress.com/cgj on 14 February 2015.

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high time to demonstrate the realistic approach of modeling thegeocells. The design computations often require quick calculationsto understand the effect of the various key parameters in the design.In such situations, one cannot always depend on the experimentaland field studies. Numerical modeling technique not only helps tocarry out quick calculations, but also provides the scientific repre-sentation of the results.

In the recent past, the geocells have been modeled using theequivalent composite approach and in which the geocell–soilcomposite is treated as the soil layer with improved strengthand stiffness values (Bathurst and Knight 1998; Madhavi Latha andRajagopal 2007; Madhavi Latha and Somwanshi 2009; Hegde andSitharam 2013; Mehdipour et al. 2013). Though this approach isvery simple, it is unrealistic to model geocells as the soil layer.Because geocells have a 3D structure, it is always appropriate tomodel them in a 3D framework. Han et al. (2008) carried out thenumerical simulation of a single cell geocell subjected to uniaxialcompression in FLAC3D. In their study, the cell was modeled as thesquare box due to the difficulty in modeling the actual shape. Forthe same reason, Hegde and Sitharam (2014b) adopted the circularshaped pocket geometry while modeling the problem of the sin-gle cell geocell subjected to uniaxial compression. In their study,the researchers observed the deviation in the experimental andnumerical pressure–settlement response at the higher settlement.The researchers had attributed this anomaly to the circular shapedgeometry used in the modeling process and emphasized the impor-tance of modeling the actual shape of the geocells. Saride et al. (2009)adopted the square shaped geometry of the cell pocket while mod-eling the multiple cell geocell in FLAC3D. A similar approach was alsoused by Leshchinsky and Ling (2013) while modeling a geocell rein-forced ballast system. However, the actual shape (i.e., 3D honeycombshape) of the single cell geocell was modeled by Yang et al. (2010) intheir study.

Contrary to the previous studies, an attempt has been made tomodel the real shape of the multiple cell geocells by consideringthe actual curvature of its pocket. The foundation soil, infill soil,and the geocell materials were assigned with three different ma-terial models to simulate the real case scenario. To validate thenumerical modeling, the laboratory plate load tests were con-ducted on soft clay bed reinforced with geocells. The validatednumerical model was further used to study the influence of thevarious geocell properties on the performance of the reinforcedclay beds. Though this manuscript mainly discusses the numeri-cal simulations of the geocells in detail, the essential details of theexperimental studies are also presented.

Experimental studiesFigure 1 shows the schematic representation of the test setup

used in the laboratory studies. A cast iron test tank of size 900 mmlength, 900 mm width, and 600 mm height was used. The tank wasconnected to the loading frame that was attached to a manuallyoperated hydraulic jack. A square shaped steel plate of 150 mm wideand 20 mm thick was used as the model footing. The bottom of thefooting was made rough by coating a thin layer of sand with epoxyglue.

Natural clayey soil with specific gravity 2.66 was used to preparethe foundation bed. The liquid limit and the plastic limit of theclayey soil were 40% and 19%, respectively. According to the Uni-fied Soil Classification System (ASTM 2011), the soil was classifiedas clay with low compressibility (CL). The maximum dry densityand the optimum moisture content of the soil in the StandardProctor condition were found to be 18.2 kN/m3 and 13.2%, respec-tively. Dry sand with specific gravity of 2.64, effective particle size(D10) of 0.26 mm, coefficient of uniformity (Cu) of 3.08, coefficientof curvature (Cc) of 1.05, maximum void ratio (emax) of 0.81, mini-mum void ratio (emin) of 0.51, and angle of internal friction (�) of36° was used to fill the geocell pockets. As per the Unified Soil

Classification System, the sand was classified as poorly gradedsand with symbol SP. Figure 2 represents the grain-size distribu-tion curve of sand and clay. The geocell used in the study wasmade up of Neoloy (novel polymeric alloy). Figure 3 shows thephotograph of the geocell. A biaxial geogrid made of polypropyl-ene was used at the base of the geocell. The properties of thegeocells and geogrids are listed in Table 1. Tensile stress–strainbehaviour of the geocell and the geogrid is shown in Fig. 4.

The clayey soil was powdered and then mixed with a predeter-mined amount of water. The moist soil was placed in the airtightcontainer for 3–4 days for allowing uniform distribution of mois-ture within the sample before kneading again. Soil was uniformlycompacted in 25 mm thick layers to achieve the desired height ofthe foundation bed. A manually operated plate compactor was usedfor the purpose. The sides of the tank were coated with polyethylenesheets to avoid side friction. By carefully controlling the compactioneffort and the water content of the test bed, a uniform test conditionwas maintained in all the tests. The fall cone apparatus was used tomeasure the undrained cohesion of the bed. The test bed had a unitweight of 18.63 kN/m3, moisture content of 26%, degree of saturationof 91%, undrained shear strength of 5 kPa, and average dry density of14.81 kN/m3. Reinforcements of width equal to 5.8B were placed at

Fig. 1. Schematic view of test setup.

Fig. 2. Grain-size distribution curves for clay and sand.

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the depth of 0.1B (where B is the width of the footing). The cell pock-ets were filled up with the clean sand using pluviation technique tomaintain uniform density. A layer of geotextile was used as a sepa-rator between the soft clay bed and the sand overlaying it. Uponfilling the geocell with the sand, the footing was placed on top andthe load was applied. The footing was placed such that it rested onthe center of the geocell pocket.

Numerical analysis

Modeling detailsIn the present study, FLAC3D was chosen for the analysis consider-

ing its ability to model a wide range of geotechnical problems.FLAC3D uses an explicit finite difference solution scheme to solve theinitial and boundary value problems. It has several built-in materialmodels and structural elements to model the variety of geomaterialsand the reinforcements. It provides the option to use the interfaceelements to accurately model the joints and the interfaces betweentwo materials. FLAC3D also contains a powerful built-in program-ming language called FISH that enables the user to define new vari-ables and functions.

In the present study, the dimension of the model was kept thesame as that of the test bed used in the experiments. The modifiedCam-clay model was used to simulate the behaviour of the softclay bed and the Mohr–Coulomb model was used to simulate thebehaviour of the infill soil, i.e., sand. The geocell was modeled usingthe geogrid structural element. The geogrid structural elements canresist the membrane stresses, but cannot resist the bending stresses.The rigid nature of the geocell joint was simulated by fixing thenodes representing the joints. A linear elastic model was used tosimulate the behaviour of the geocell. The interfaces between thegeocell and the soil were linearly modeled with Mohr–Coulomb yieldcriterion as shown in Figs. 5a–5b. Only a quarter portion of the testbed was modeled using symmetry to reduce the computational ef-fort. The quarter symmetric model of size 0.45 m × 0.45 m × 0.6 mwas discretised into 9216 zones. Analyses were carried out undercontrolled velocity of a magnitude of 2.5 × 10−5 m/step. The displace-ment along the bottom boundary (which represents the tank bot-tom) was restrained in both horizontal as well as vertical directions.The side boundaries (which represent the tank sides) were restrainedonly in the horizontal direction, such that the displacements wereallowed to occur in the vertical direction. By providing the lateralresistance to the soil nodes representing the area of the footing,roughness of the footing was simulated. Similar to the laboratorystudies, the undrained test condition was maintained during themodeling process.

Determination of model parametersTable 2 represents properties of different materials used in the

numerical simulations. An isotropic triaxial compression test wasconducted to determine the Cam-clay parameters: slope of thenormal consolidation line (�), slope of the swelling line (�), and

Fig. 3. Photograph of the geocell: (a) folded; (b) expanded.

Table 1. Properties of geocell and geogrid.

Parameter Value

GeocellCell size (mm × mm) 250 × 210Aspect ratio 0.6No. of cells/m2 40Cell depth (mm) 150Strip thickness (mm) 1.53Cell seam strength (N) 2150 (±5%)Density (g/cm3) 0.95 (±1.5%)Short term yield strength (kN/m) 20

GeogridPolymer PolypropyleneAperture size (mm × mm) 35 × 35Ultimate tensile strength (kN/m) 20Mass per unit area (g/m2) 220Shape of aperture opening Square

Fig. 4. Tensile stress–strain behaviour of geocell and geogrid.

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pre-consolidation pressure (pc′). Figure 6a shows the relationship

between specific volume (v) and natural logarithmic of mean ef-fective stress (ln p′). The isotropic triaxial compression test wascarried out in three cycles, i.e., loading, unloading, and reloading.During the loading cycle, the sample was consolidated underseven different confining pressures from 50 to 350 kPa with anincrement of 50 kPa in each step. At 100 kPa, a change in the slopeof the line was observed, indicating the particular value of thepressure is nothing but the pre-consolidation pressure. Duringunloading, the pressure was reduced from 350 to 50 kPa in sevensteps with the decrement of 50 kPa in each step. In the reloadingcycle, the confining pressure was increased to 450 kPa in eightsteps. The slope of the critical state line, parameter M, and elasticmodulus of the clay were determined from the consolidated un-drained triaxial compression test. The test was carried out at threedifferent confining pressures: 100, 200, and 300 kPa. Figure 6b

shows the critical state line determined from the consolidatedundrained triaxial test. Similarly, the elastic modulus of the sandwas also determined from the consolidated undrained triaxial test.The shear modulus values for both clay and sand were determinedfrom the elastic modulus value, assuming the Poison’s ratio of 0.5and 0.3, respectively, for clay and sand. The shear strength properties(cohesion C and �) of the sand were determined from the direct sheartest. The elastic modulus of the geocell and geogrid was determinedfrom tensile stress–strain behaviour shown in Fig. 4. The secant mod-ulus was determined corresponding to 2% axial strain in both thecases. The interface shear strength properties (interface cohesion, ci,and interface friction angle, �i) for both geocell and geogrids wereobtained from the modified direct shear test. The interface shear

Fig. 5. Interface shear behaviour between infill soil and geocell (Itasca 2008): (a) shear stress, �, versus shear displacement, u; (b) shear stress,�, versus normal stress, �.

Table 2. Properties of different materials used in nu-merical modeling.

Parameter Value

ClayShear modulus, G (MPa) 1.36Friction constant, M 0.68Slope of NCL, � 0.22Slope of swelling line, � 0.09Specific volume at reference pressure, v� 1.78Pre-consolidation pressure, pc

′ 100Unit weight, � (kN/m3) 20

SandShear modulus, G (MPa) 5.77Bulk modulus, K (MPa) 12.5Poisson’s ratio, � 0.3Cohesion, C (kPa) 0Friction angle, � (°) 36

GeocellsYoung’s modulus, E (MPa) 275Poisson’s ratio, � 0.45Interface shear modulus, ki (MPa/m) 2.36Interface cohesion, ci (kPa) 0Interface friction angle, �i (°) 30Thickness, ti (mm) 1.5

GeogridsYoung’s modulus, E (MPa) 210Poisson’s ratio, � 0.33Interface shear modulus, ki (MPa/m) 2.36Interface cohesion, ci (kPa) 0Interface friction angle, �i (°) 18Thickness, ti (mm) 1.5

Note: NCL, normal consolidation line.

Fig. 6. Cam-clay: (a) v versus lnp′; (b) critical state line.

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modulus value (ki) of 2.36 MPa/m was considered in the analysis forgeocells and geogrids (Itasca 2008).

The Cam-clay model in FLAC3D is only applicable to material inwhich the stress state corresponds to a compressive mean effectivestress. Hence, a minimum value of compressive mean effective stresswas initialized at the beginning. Given an initial mean effective pres-sure, po

′ , the initial specific volume, vo, must be consistent with thechoice of parameters �, �, p1

′, and pc′. The initial value vo was calcu-

lated corresponding to po′ on the swelling line using eq. (1) and the

same value was used in the analysis (refer Fig. 6a).

(1) vo v� � ln�pc′

p1′� � ln�pm

′

pc′ � � � ln�pm

′

po′ �

where, v� is the specific volume corresponding to the referencepressure; pc

′ is the pre-consolidation pressure; p1′ is the reference

pressure equal to 1 kPa; pm′ is the maximum mean effective stress

applied during the loading cycle of the isotropic compression test;and po

′ is the initial mean effective stress. Similarly, the initialvalue of the bulk modulus (K) was calculated using eq. (2) and thesame was used in the analysis.

(2) K vo po

′

�

Preliminary analyses carried out revealed that the boundary dis-tances did not influence the results as deformations and stresses

Fig. 7. FLAC3D model for different cases: (a) unreinforced; (b) geogrid reinforced; (c) geocell reinforced; (d) geocell and geogrid reinforced.

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were contained within the boundaries. It is understood that the geo-cell is made of multiple interconnected cells and the shape of all thecells is similar from one to another. Hence, a photograph of thesingle cell was taken and it was digitized to obtain the actual curva-ture of the cell. The coordinates were deduced from the curvatureand the same were used in the FLAC3D to model the actual shape ofthe geocell. Figure 7a–7d shows the FLAC3D models of the differentcases considered in the study. In addition to geocells, the geocell withadditional basal geogrid case and only geogrid cases were also mod-eled. The numerical results were compared with the results of theexperimental studies described in the earlier part of the manuscript.Using the validated model, the distributions of the stresses and dis-placements below the footing for different cases were obtained.

Results and discussionsFigure 8 shows the comparison of bearing pressure–settlement

curves obtained from experimental and numerical studies for dif-ferent type of reinforcements. A fairly good agreement was ob-served between the experimental and numerical results. In thecase of the unreinforced soft clay bed, ultimate bearing capacityin the range of 30 kPa was observed. Steep reduction in the slopeof the pressure–settlement curve indicates the punching shearbearing capacity failure of the test bed. In the case of the rein-forced clay beds, there was no clear cut failure, even at very largesettlements. Geocells take up the foundation load even after thefailure of the foundation bed. Out of all tested cases, maximumbearing capacity was observed in the case of the foundation bedreinforced with the combination of geocell and geogrid. Provisionof the basal geogrid not only imparts the additional strength tothe soil, but also resists the downward movement of soil due tothe footing penetration. Overall, good agreement was observedbetween the experimental and numerical results.

Figure 9 shows the normalized vertical stress measured at thedifferent depths of the test bed for different test cases. These valueswere obtained from numerical studies and correspond to the pointsexactly below the center of the footing at different depths. The ver-tical stress measured at a point (Pu) was normalized by the appliedfooting pressure (qu) on top of the clay bed. Similarly, the depth (Z)was normalized by footing width (B) for convenience. In Fig. 9 onlystress values from depth 1B to 2B are compared, because the height ofthe geocells mattress (H) is the same as that of footing width (B), thegeocell occupies the depth from 0 to 1B below the footing. In thepresent case, only those stress values measured below the geocellsare compared. A substantial reduction in the measured stress valuewas observed in the presence of different reinforcements as com-pared to unreinforced bed. When the clay bed was reinforced withgeocells, more than 50% reduction in the stress value was observed atthe top portion of the bed, just below the geocells. Maximum stressreduction of about 70% was observed when additional geogrid wasprovided below the geocells. It is always beneficial to use a combina-tion of geocell and geogrid reinforcement rather than using geocellalone.

Figure 10 shows the vertical stress contours for the different testcases. The reported stress contours correspond to the applied verticalstress equal to the ultimate bearing capacity of the unreinforced softclay bed. The distribution of the stress contours indicates that thetank boundaries have no bearing on the results. Uniform distribu-tion of the stresses up to the large depth was observed in the case ofthe unreinforced bed. In the geogrid reinforced case, the influencedepth of the stress was found to be reduced as compared to theunreinforced bed. In the case of geocells, the stresses are transferredrelatively to a shallow depth as compared to the previous two casesand are transferred laterally to the wider areas. Similar types of ob-servations were also made by Saride et al. (2009). The interconnectedcells form a panel that acts like a large mat that transfers the im-posed load to the larger area, leading to better performance of the

foundation beds. This mechanism is known as beam mechanism.When the basal geogrid was provided below the geocells, furtherreduction in the transferred stress to the soil subgrade was observed.

Figure 11 shows the pressure bulb corresponding to 0.1qu for theunreinforced and geocell with additional basal geogrid reinforcedcases. Due to the symmetry, only a half section of the pressurebulb has been shown in the figure. In the case of the unreinforcedbed, a uniform pressure bulb of circular shape was observed. Thepressure bulb was found to disperse up to the depth of 1.6B. In thegeocell and the geogrid reinforced case, the pressure bulb was notuniform as observed in the case of the unreinforced bed; instead apressure bulb of irregular shape was observed. However, the bulbwas confined within the depth of 1B, up to where the geocell layeris present. The bulb was found spreading in the lateral directionindicating the fact that the geocells distribute the load into thewider areas below the footing as compared to the unreinforcedbed.

Figure 12 shows the vertical displacement contours for differentcases. The reported contours correspond to the fill settlement of30% of the footing width (S/B = 30%). Uniform distribution of thecontours in a narrow band indicates the punching shear failure ofthe unreinforced soft clay bed (see Fig. 12a). In addition, the heav-ing of the soil surrounding the footing was also observed. Whengeogrid was used as the reinforcement, the settlement of the foot-ing and also the heaving surrounding the footing were foundreduced as compared to the unreinforced clay bed. In both unre-inforced and geogrid reinforced cases, the displacement contourswere confined within the footing size. However, in the case ofgeocells, due to the beam mechanism, the displacements werefound to spread outside the footing width. In addition, the surfaceheaving was not observed in the presence of geocells. In the ex-perimental results reported by the Hegde and Sitharam (2013), the

Fig. 8. Bearing pressure–settlement behaviour.

Fig. 9. Normalized vertical stress measured in the test bed fordifferent test cases.

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Fig. 10. Vertical stress distribution: (a) unreinforced; (b) geogrid only; (c) geocell only; (d) geocell and geogrid.

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tilting of the footing was observed at very high loads. However,numerical studies did not reveal any such findings. According tothe authors, this particular anomaly is due to the assigning of thesame material properties to the entire test bed. Uniform settle-ments are expected as long as the foundation material propertiesare homogeneous and the rate of application of the footing pres-sure is constant. However, in experiments, it is very difficult toprepare the entire test bed of homogeneous material properties.At very high loads, even a small change in the density of the testbed is sufficient to cause the tilting of the footing. Because of thislimitation, the model predicted only a small amount of heaving inthe geocell and geogrid reinforced case. A similar observation wasalso made by Hegde and Sitharam (2015) while carrying out the 3Dnumerical simulation of geocell reinforced sand beds. With theincrease in loading, the surface heaving was found to increase inthe model. To induce the settlement of S/B = 30%, the geocell andgeogrid reinforced clay bed was subjected to larger loading ascompared to the geocell reinforced clay bed.

Factors affecting performance of reinforced claybeds

In this section, the effects of various geocell properties, whichcould affect the performance of the reinforced clay bed are dis-cussed with the help of the validated numerical model. The keyparameters studied are the (i) elastic modulus of the geocell,(ii) elastic modulus of the basal geogrid, (iii) height of the geocell,(iv) pocket size of the geocell, and (v) interface friction angle. How-ever, the effects of the foundation bed parameters are not consid-ered in the present study.

Effect of geocell modulusBased on the baseline case illustrated in Fig. 7d and Table 2, the

modulus of the geocell was changed to one-fifth of its originalmodulus (i.e., 55 MPa) and five times its original modulus (i.e.,1375 MPa). The pressure–settlement behaviours of three differentcases are compared in Fig. 13a. The bearing capacity of the reinforcedbed increased with the increase in the modulus of the geocell. As thegeocell modulus increases, the higher confining pressure will be

exerted on the infill soil under same lateral deformation. The addi-tional confining pressure leads to the increase in the bearing capac-ity of the foundation bed.

Effect of basal geogrid modulusBased on the baseline case illustrated in Fig. 7d and Table 2, the

modulus of the basal geogrid was changed to one-fifth of its orig-inal modulus (i.e., 42 MPa) and five times its original modulus (i.e.,1050 MPa). The pressure–settlement behaviours of three differentcases are compared in the Fig. 13b. The bearing capacity of thereinforced bed increased with the increase in the modulus of thebasal geogrid. A similar observation was made by Sitharam andHegde (2013) with the help of analytical studies. As the tensilestrength of the basal geogrid increases, the resistance offered by thegeogrid to the downward movement of the soil also increases. How-ever, the effect of basal geogrid modulus is not as prominent as thegeocell modulus.

Height of geocell mattressThe height of the geocell used in the baseline case illustrated in

Fig. 7d and Table 2 is 0.15 m. The height of the geocell was reducedto two-thirds (0.1 m) and one-third (0.05 m) of its original height tomatch the height of commercial geocells available in the market.The pressure–settlement behaviours of three different cases arecompared in the Fig. 13c. The bearing capacity of the geocell rein-forced foundation bed increased with an increase in the height ofthe geocell. Similar types of observations were also made by Dashet al. (2001) using experimental investigations. As the height of thegeocell increases, the footing load will be dispersed to larger ar-eas. As a result of this, the pressure transmitted to the soil re-duces, which leads to improvement in the overall performance ofthe foundation bed.

Pocket size of geocellThe equivalent pocket diameter of the geocell used in the pres-

ent study is 0.22 m. The other pocket sizes of the geocells consid-ered in the analysis are 0.2, 0.25, and 0.3 m. The pocket sizes areselected to match the pocket sizes of the commercial geocells

Fig. 11. Pressure bulb of 0.1qu: (a) unreinforced; (b) geocell and geogrid reinforced.

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Fig. 12. Vertical displacement contours at S/B = 30%: (a) unreinforced; (b) only geogrid; (c) only geocell; (d) geocell and geogrid. S, fill settlement.

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available on the market. Figure 13d represents pressure–settlementbehaviour of the foundation bed reinforced with geocells withdifferent pocket sizes. The bearing capacity of the foundation bedincreased with a decrease in the pocket size of the geocell. As thecell size decreases the confinement offered per unit volume in-creases, which leads to increase in the load carrying capacity ofthe foundation bed.

Interface friction angleThe geocell used in the present study had a rough texture on its

surface. The interface friction angle obtained from the modified di-

rect shear test was 30° and the same was used in the baseline model.Most of the other types of geocells available on the market have asmooth surface. Hence, the corresponding interface friction anglewill be lesser in those cases than the present case. Hence, in thepresent study, different values of the friction angles lower thanthe present value are considered. The other values considered inthe present analysis are 12°, 18°, and 24°. The bearing capacityof the reinforced foundation bed marginally increased with anincrease in the interface friction angle as shown in Fig. 13e. As theinterface friction angle increases, the friction force will develop

Fig. 13. Bearing pressure–settlement curves: (a) different modulus of geocell; (b) different modulus of basal geogrid; (c) different height ofgeocell; (d) different pocket sizes of geocell; (e) different interface friction angles.

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between the inner surface of the geocell and the infill soil. Thedeveloped friction force will act in the upward direction and helpsto resist the imposed load, leading to improved performance ofthe foundation bed. This mechanism is known as lateral resis-tance mechanism offered by the geocells. Due to this mechanism,the textured geocell always yields better performance than thegeocell with smooth surface.

Scaling issuesThe results of the 1g model tests are prone to scale effects. As

suggested by Fakher and Jones (1996), the results of the small scalemodel tests can be extrapolated to prototype cases by carefullyapplying the scaling laws. If “N” is the scaling factor, then thetensile strength of the geocell and geogrid to be used in the pro-totype application is N2 times the tensile strength of the geocelland geogrid used in model tests (Viswanadham and König 2004;Sireesh et al. 2009). In model studies, commercial geocells andgeogrids with tensile strength of 20 kN/m were used. Hence, theextrapolated results are applicable to limited prototype applica-tions. The present results can be extrapolated to a prototype casewith scaling factor (N) maximum up to 2. In that case, the tensilestrength of the prototype geocell material falls in the range of80 kN/m. Generally, bamboo has the tensile strength in that range.The 3D cells and planar grids prepared from bamboo known as“bamboo cells” and “bamboo grids” could be used in the place ofgeocells and geogrids respectively, in prototype applications. It isadvised to carry out the chemical treatment of the bamboo usingimpregnation techniques to increase the durability. The further de-tails of bamboo cells – bamboo grids and their application in softsoils have been explained elsewhere Hegde and Sitharam (2014c).

In spite of the limitations, the 1g model tests and numericalsimulations carried out in the present study are successful enoughto highlight the efficacy of the geocells. The presented results arehelpful to understand the basic mechanism and overall trends inthe results. These results could be used in providing guidelines fordesign and construction of geocell-reinforced foundations, con-ducting large-scale model tests, and developing the analyticalmodels.

ConclusionsA realistic approach of modeling the geocells in a 3D framework

has been demonstrated in the paper. The actual curvature of thegeocell pocket was considered in the modeling process. The infillsoil, foundation soil, and the geocells were assigned with threedifferent material models to simulate the real case scenario. Themodel was validated with the experimental studies and it wasfound that the results were in good agreement with each other.When the clay bed was reinforced with geocells, more than 50%reduction in the stress was observed at the top portion of the bed,just below the geocells. About 70% reduction in the stress wasobserved when the additional geogrid was provided below thegeocells. The beam mechanism of the geocell was vindicated bythe shape of the stress and displacement contours. By virtue of thebeam mechanism, geocells distribute the load in the lateral direc-tion to wider areas and hence, lower the stress intensity on thesubgrade below. The parametric studies conducted revealed thatthe tensile strength of the geocell is responsible to a major extentfor imparting the strength to the foundation beds as compared toother properties. However, other properties such as height andpocket sizes of the geocells also have a direct influence on thebearing capacity of the foundation bed. It was also found that thegeocell with a textured surface yields better performance thanthe geocell with a smooth surface. The provision of the additionalgeogrid below the geocell, further improves the performance ofreinforced clay beds by virtue of the membrane mechanism. Thepresent model is elegant and accurate as compared to the equiv-alent composite approach of modeling the geocells. However, the

model has certain limitations. The model fails to capture the tilt-ing failure of the footing.

AcknowledgementsThe authors are thankful to Xiaoming Yang, Oklahoma State

University, USA, and Jie Han, University of Kansas, USA, for theirvaluable suggestions through email correspondence during theinitial stage of the work.

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This article has been cited by:

1. A.M. Hegde, T.G. Sitharam. 2015. Experimental and numerical studies on protection of buried pipelines and underground utilitiesusing geocells. Geotextiles and Geomembranes 43, 372-381. [CrossRef]

2. S.N. Moghaddas Tafreshi, T. Shaghaghi, Gh. Tavakoli Mehrjardi, A.R. Dawson, M. Ghadrdan. 2015. A simplified method forpredicting the settlement of circular footings on multi-layered geocell-reinforced non-cohesive soils. Geotextiles and Geomembranes43, 332-344. [CrossRef]

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