Analysis of Geocell Reinforced-soil Covers Over Large Span Conduits

Analysis of Geocell Reinforced-soil Covers Over Large SpanConduits

Richard J. Bathursta* & Mark A. Knightb

aDepartment of Civil Engineering, Royal Military College of Canada, Kingston, ON, Canada, K7K 7B4bDepartment of Civil Engineering, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

(Received 16 January 1998; revised version received 21 May 1998; accepted 28 May 1998)

ABSTRACT

A novel technique to improve the load-deformation performance of thin soilcover layers over ¯exible long span soil-steel bridge conduits is proposed.The soil cover is reinforced by a composite layer of geocell-soil whoseproperties have greater strength and sti�ness than the aggregate soil in®llin an unreinforced condition. The paper describes a series of numericalsimulations using a large strain non-linear ®nite element model to investi-gate the load-deformation response of midspan and eccentrically loadedsteel conduits with and without reinforced geocell-soil covers. The simula-tion results show that the performance of soil-conduit systems with a con-ventional 1m thick cover soil may be signi®cantly improved by introducinga single layer of geocell-soil material. Alternatively, thinner depths of soilcover are possible using this reinforcement technique compared to conven-tional unreinforced methods. # 1998 Elsevier Science Ltd. All rightsreserved

INTRODUCTION

Soil-steel bridges are corrugated structural steel plate conduits that areassembled on site in circular, elliptical or arch shapes and back®lled withgranular soils. They are typically used to support highway pavements andrailway tracks. The soil-steel bridge carries load through interaction betweenthe conduit shell and the con®ning soil.

Computers and Geotechnics, Vol. 22, No. 3/4, pp. 205±219, 1998# 1998 Elsevier Science Ltd. All rights reserved

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205

*To whom correspondence should be addressed. Fax: 00 613-545-8336;

e-mail: [email protected]

The economic viability of using soil-steel structures for long span struc-tures (i.e. spans in excess of 3m) is often controlled by the depth of soil coverrequired over the conduit crest (Ontario Highway Bridge Design Code(OHBDC) [1]). Field experience has shown that shear or tension failure ofthe cover soil is the typical failure mechanism. Relatively large long spanconduits up to 16.8m have also been built in recent years [2]. However,some large long span soil-steel structures with shallow covers have failed dueto shell buckling [3].Current design codes such as the American Association of State and

Highway Transportation O�cials (AASHTO) [4], and the OHBDC [1]restrict cover soil thickness to a minimum of about Dh/6 in order to preventsoil cover failure, where Dh is the horizontal conduit diameter. Thus, thesedesign codes may require signi®cant soil cover thickness for large span con-duits and in turn render the structures uneconomical or unable to satisfyproject geometric constraints.This paper describes a series of numerical simulations that were carried out

to investigate the load-deformation response of midspan and eccentricallyloaded steel conduits constructed with composite geocell-soil reinforcedcovers.The term geocell is a generic term describing a class of geosynthetic pro-

ducts manufactured from thin strips of polymeric material (usually highdensity polyethylene) bonded or welded together to form a three-dimen-sional cellular network that can be ®lled with compacted soil (Fig. 1). Thee�ect of cellular con®nement on the in®ll soil is to increase the sti�ness and

Fig. 1. Single layer of polymeric geocell material.

206 R. J. Bathurst and M. A. Knight

shear strength of the con®ned soil. The results of large triaxial compressiontests taken to collapse have demonstrated that cellular con®nement impartsadditional apparent cohesion to aggregate in®ll soils while leaving the peakfriction angle of the aggregate essentially unchanged [5]. The compositegeocell-soil layer in road base applications has been demonstrated to act as asti�ened mat that provides greater load bearing capacity and sti�ness thanthe same granular base constructed without cellular con®nement [6]. Layersof geocell-soil reinforcement have also been stacked to create compositematerial zones for earth retaining wall structures [7].In this paper the use of geocell-soil composites is extended to soil covers

over ¯exible steel conduits. The improved mechanical properties of the rein-forced soil cover may allow a reduction in cover soil thickness over thesestructures [8]. Single layers of composite reinforcement (0.2m thick) placedwithin the conduit cover depth are demonstrated to increase the strength andsti�ness of the cover soil compared to unreinforced sections. Alternatively,the results of simulations reported here can be interpreted to show thatthinner reinforced cover soil layers may be used to give the same or betterperformance than the same soil placed in an unreinforced condition.

PROGRAM GEOFEM

The non-linear ®nite element program GEOFEM (Geotechnical Finite Ele-ment Modelling), developed by the Department of Civil Engineering at theRoyal Military College of Canada, was used to carry out the numericalsimulations in the current study. GEOFEM is a general purpose ®nite ele-ment program for the analysis of structural and geotechnical problems. Theprogram was speci®cally developed to investigate soil-structure interactionproblems and uses a linearized updated Lagrangian method to accommodatelarge deformation behaviour [9±11].

VERIFICATION

In the current study the results of program GEOFEM were validated againstclosed-form arch solutions, reduced-scale physical model experiments repor-ted in the literature and a full-scale ®eld test.

Arch solution

Two-noded linear elastic beam elements were used to simulate the conduitshell in the current study. To test the accuracy of shell behaviour, in-isolation,

Analysis of geocell reinforced-soil covers over large span conduits 207

closed-form solutions [12] for a two-hinged circular arch loaded at midspanwere compared to predicted values using the GEOFEM code. A total of 80beam elements were used and good agreement was shown for axial thrust,shear and moment in the arch as illustrated in Fig. 2.

Reduced-scale experimental test

Reduced-scale plane strain soil-conduit experiments have been carried out atthe University of Windsor in Ontario, Canada [13, 14]. A ®nite elementmesh used in the current investigation to represent one of these physicalexperiments is reproduced in Fig. 3. Eight-noded quadrilateral continuumelements were used for the soil region. The soil elements were connected tothe beam elements representing the conduit shell by six-noded interface ele-ments. The surface of the soil was centrally loaded by a rigid 100mm widefooting. The depth of cover in this experiment was 127mm with the 0.78mdiameter conduit constructed from 4.76mm thick aluminium plate with thefollowing properties: elastic modulus, E=70GPa; Poisson's ratio, � � 0:33;and yield stress, fy=275MPa. No independent laboratory testing was carriedout to determine mechanical properties of the sand used in the experiment oraluminium-sand interface properties. Based on the limited data available, thesand was matched to a Monterey no. 0 (SP-17a) sand soil found in a database for hyperbolic model parameter values [15] (Table 1).A non-linear hyperbolic model was used to model the aluminium-sand

interface [10] and is expressed as:

Ks � 1ÿ Rf�

ci � �n tan�i

� �2

KiPa�nPa

� �n

�1�

Fig. 2. Comparison of closed-form and numerical solutions to two-hinged circular arch problem.


where Ks is tangential sti�ness; Ki is the initial sti�ness, Rf is the ratiobetween failure shear stress and asymptotic shear stress, � and �n are shearand normal stresses acting at the interface, Pa is atmospheric pressure, ci and�i are interface cohesive strength and interface friction angle, respectively,and n is an exponent. In this model the normal sti�ness value (Kn) wasassumed to be constant except when the normal stress becomes tensile, at

TABLE 1Hyperbolic parameters for soils

Parameter Montereyno. 0

(SP-17a)sand [15]

Montereyno. 0

(SP-17c)sand [15]

Densesilicasand a

Compositegeocelldensesilicasand a

Young's modulus component, Ks 920 3200 507 1033Exponent for Young's modulus, n 0.79 0.78 0.76 0.77Bulk modulus, Kb 465 1400 570 1755Exponent for bulk modulus, m 0.32 0.45 0.5 0.41Minimum Poisson's ratio, � 0.30 0.25 0.25 0.25Failure ratio, Rf 0.96 0.92 0.64 0.85Cohesion, c kPa� � 0 1.0 1 190Friction angle at 1 atm. pressure, �o (

�) 33 45 45 45Change in friction due to 10-fold increase

in con®ning pressure, �� (�)0 3 0 0

Dilation angle, (�) 0 0 0 0Unit weight, (kNmÿ3) 20.3 19.0 15.7 15.7Lateral earth pressure coe�cient, Ko 0.47 0.35 0.35 0.35

aInterpreted from data reported by Bathurst and Karpurapu [5].

Fig. 3. Comparison of experimental and predicted load-displacement response of reduced-scale soil-conduit model test.


which point a small residual value is assumed. Values for interface propertiesused in this veri®cation exercise are given in Table 2 and are the same valuesused by Hafez [13].The curves in Fig. 3 show good agreement between experimental and

numerical results for de¯ection data using the material properties and con-stitutive models selected.

Full-scale ®eld test

Bakht [16] reports the measured results of a full-scale ®eld trial of a soil-steelbridge (White Ash Creek) under live loading. Hafez [13] and Hafez andAbdel-Sayed [17] carried out ®nite element model (FEM) predictions of thesystem response. Program GEOFEM was also used to predict the responseof the White Ash Creek ®eld trial. The conduit walls were modelled usingtwo-noded beam elements with the linear elastic material properties reportedby McVay and Selig [18] (Table 3).McVay and Selig note that bolted seams in a ¯exible steel conduit can

cause the circumferential sti�ness of the conduit wall under compressiveloads to be lower than that of a continuous corrugated-steel plate. Thus, tomodel the bolted corrugated-steel plate used for large span conduits areduction in thrust sti�ness (EA) is required to maintain the same bendingsti�ness (EI) of the shell. McVay and Selig also found that reducing the cross-sectional area of beam elements by six times their original area provided abetter model response. This same reduction factor has been used in this study.

TABLE 2Non-linear hyperbolic interface element properties [13]

Parameter Value

Initial tangent sti�ness, Ki 43,070Normal sti�ness, Kn (kN mÿ3) 2.7�108Exponent, n 0.6Failure ratio, Rf 0.834Interface cohesive strength, ci kPa� � 1.0Interface friction angle, �i (

�) 23

TABLE 3Corrugated plate properties [18]

Parameter Value

Unreduced area (m2 mÿ1) 6.8�10ÿ3Modulus of elasticity (MPa) 2.0�105Poisson's ratio 0.33Moment of inertia (m4 mÿ1) 2.08�10ÿ6Plate thickness (m) 5.5�10ÿ3


The results of simulations using program GEOFEM and FEM predictionsreported by Hafez and Abdel-Sayed [17] are presented in Fig. 4 togetherwith measured values of axial thrust calculated from strain gauge measure-ments. Program GEOFEM gives reasonably accurate predictions of conduitwall axial thrust for this shallow cover large span circular ¯exible steel con-duit.

NUMERICAL SIMULATION OF GEOCELL-SOIL REINFORCEDCONDUITS

Geometry

The plane strain geometry used to investigate the in¯uence of unreinforcedand composite geocell-soil reinforcement on system load-deformation per-formance is illustrated in Fig. 5. A circular steel conduit of diameter (span) Dlocated below a soil cover thickness H is loaded at midspan or eccentrically(distance e) by a line load P applied to a strip footing of width B placed atthe soil surface. The contact between the bearing area B and the soil surfaceis assumed to be perfectly rigid and fully bonded.

Finite element mesh

The ®nite element mesh that was used in the current study is shown in Fig. 6.For the FEM analysis the following element types were used:

Fig. 4. Comparison of measured and predicted axial thrust response from White Ash Creek

full-scale ®eld trial.


. Sixty two-noded beam elements to represent the circular steel conduitconstructed out of 5 gauge steel with 51�152mm corrugations.

. A maximum of 392 eight-noded quadrilateral continuum elements torepresent the composite geocell-soil reinforcement layer, back®ll andcover soil. The number of continuum elements varied with simulateddepth of cover.

. Thirty six-noded interface elements to connect the beam elements to thecontinuum elements.

The ®nite element mesh was designed so that the continuum elementsabove the conduit are 0.2m high matching the 0.2m thick geocell thickness

Fig. 6. Finite element mesh (midspan load con®guration).

Fig. 5. Problem geometry.


that is typical for a single layer of this material in the ®eld. For eccentricallyloaded tests the mesh in Fig. 6 was doubled in size.

Material properties

Beam elementsThe conduit walls were modelled using linear elastic material propertiesreported by McVay and Selig [18] (Table 3). The axial thrust capacity of theconduit walls before buckling was assumed to be 436 kN mÿ1 in accordancewith OHBDC [1] guidelines.

Soil propertiesBathurst and Karpurapu [5] report the results of large triaxial cell com-pression tests on unreinforced and geocell-reinforced specimens of di�erentgranular soils prepared at di�erent densities. Test specimens were 200mm indiameter by 200mm high matching the single cell size typical of commer-cially available geocell products. The results of tests using a standardlaboratory silica sand are illustrated in Fig. 7. The data shows that the e�ectof geocell con®nement is to increase both the sti�ness and shear capacity ofthe soil. The composite geocell-soil material and unreinforced soil behaviourcan be approximated using the hyperbolic model proposed by Duncan et al.[15] as illustrated on the same ®gures. Hyperbolic model parameters forunreinforced and reinforced soil materials are summarized in Table 1. Itmust be recognized that the triaxial test results for single geocell units may

Fig. 7. Triaxial test data for reinforced and unreinforced specimens of dense no. 40 silica sand(interpreted from Ref. [5]).


not capture the e�ect of many cells. However, larger multi-cell specimens arenot possible to test with conventional large-scale triaxial test devices. Never-theless, the results of full-scale tests of geocell-reinforced granular bases overcompressible foundations using the same geocell material showed signi®cantincreases in the sti�ness and shear strength of the granular layers [6].

Soil-beam interface propertiesNon-linear (hyperbolic) soil-beam interface element material properties wereobtained from Hafez [13] (Table 2).

Mesh construction and loadingFor each test series the following construction procedure was adopted:

. The ®nite element mesh was constructed in 12 increments to simulate atypical construction sequence and to allow conduit stresses during con-struction to develop. Prior to the application of the next constructionincrement the gravity force for each element was applied in 10 equalload steps.

. Using a plane strain displacement controlled boundary, an equivalentrigid footing of width B=0.2m was pushed into the cover soil in incre-ments of 0.005m until the total surface de¯ection was 0.5m.

Failure was de®ned by bearing capacity failure of the soil cover or whenaxial thrust values in the beam elements representing the conduit wallsexceeded the ¯exural (buckling) capacity of the material.

RESULTS

Selected simulation results are presented in Figs 8±11. The reference case forthe parametric analyses in this paper is the midspan load con®guration withan unreinforced cover height of 1m. The collapse load for this system is167 kN mÿ1 at approximately 0.19m of surface de¯ection (e.g. Fig. 8). In thisreference case the maximum applied load resulted in a conduit axial thrustthat was well below yield strength of the conduit walls and hence the peakload capacity of the system was controlled by soil shear strength. The curvesin Fig. 8 show that system sti�ness and load capacity are improved sig-ni®cantly by placing a single reinforcement layer within a 1m thick cover soillayer. For a cover thickness of 1m, the optimum location of a 0.2m thickreinforcement layer is at 0.2m below the loading surface. Figure 8 also showsthat the location of the reinforcement layer can in¯uence the failure mode aswell as the collapse load of the system. For example, attenuation of stressesby the reinforcement layer above the conduit is more e�ective at z=0 and


0.2m than at 0.4m. At the shallower reinforcement depths the geocell-soilcomposite layer is better able to ``bridge over'' the conduit and thus preventoverstressing of the conduit shell. The greater collapse load due to soil failurefor reinforcement at a depth of z=0.2m compared to z=0 may be explainedby the larger volume of the potential shear failure zone that passes throughthe improved geocell-soil composite zone.Figure 9 compares the deformations recorded at the conduit crown and

soil surface for reinforced and unreinforced cover systems. Vertical

Fig. 9. In¯uence of reinforcement on load-de¯ection response at soil surface and conduitcrown for midspan loaded conduit.

Fig. 8. Load-de¯ection response at soil surface for midspan loading case and variable rein-forcement layer depth.


deformations at the crown are similar for reinforced and unreinforced sys-tems up to shear failure of the unreinforced soil cover. The overall greatersti�ness of the reinforced system recorded at the point of load application isclearly due to the improved sti�ness and strength properties of the compositegeocell-soil material.Figure 10 compares the reference unreinforced system response to rein-

forced systems with a single layer of reinforcement 0.2m thick placed at thesurface of variable thickness cover soils. The results show that improvedperformance with a reduced cover thickness is possible by using a single layerof geocell-soil reinforcement. The curves also illustrate that a 0.4m thick

Fig. 11. Load-de¯ection response at soil surface for eccentric surface load case.

Fig. 10. In¯uence of cover thickness and single reinforcement layer on load-de¯ection

response at soil surface for midspan loaded conduit.


cover with a 0.2m thick reinforcement layer gives the largest load capacity ofall con®gurations represented in the ®gure (approximately a four foldincrease in load capacity). This is thought to be due to a reinforced slab e�ectthat becomes pronounced for shallow reinforced soil cover depths (i.e. whenthe ratio of reinforced soil volume to unreinforced soil volume above theconduit increases).Figure 11 shows results for a single eccentric load applied to 1m thick cover

soils. As may expected, the load-deformation response (sti�ness) improves asthe point of load application moves further from the centreline of the con-duit. However, load capacity is controlled in many of the cases shown by theassumed conduit buckling strength. The failure load for reinforced systems isless under eccentric loading compared to midspan loading. Hafez and Abdel-Sayed [14] have reported a similar result for unreinforced cover soils (i.e.minimum bearing capacity for a footing occurs between e=0 and e=R).

CONCLUSIONS

Plane strain non-linear ®nite element model simulations of midspan andeccentrically loaded circular ¯exible steel conduit with and without compo-site geocell-soil reinforcement in the soil cover layer were carried out. Theability of program GEOFEM to simulate the behaviour of conventionallarge span soil-conduit bridges was veri®ed against closed-form two hingecircular arch solutions and the results of experimental and full-scale ®eldtests. The results of reinforced and unreinforced cover soil simulationsdemonstrated that:

(1) The introduction of one layer of composite geocell-soil reinforcementin a conventional 1m depth of soil cover can increase the midspan loadcapacity of the system by up to a factor of four.

(2) Alternatively, thinner layers of reinforced cover soil can be used toprovide the same or enhanced load-de¯ection response (sti�ness) as aconventional 1m thick unreinforced soil cover.

(3) Based on the limited number of numerical simulations carried out, theoptimum placement depth of a layer of composite geocell-soil reinfor-cement with thickness T=0.2m is estimated to be z/B=1 to 2.

(4) The improvement in load capacity using reinforcement improves withmagnitude of surface de¯ection.

(5) The load-deformation (sti�ness) and collapse load for reinforced andunreinforced systems is in¯uenced by surface load eccentricity.

The signi®cant increase in system load capacity using geocell-soil compositereinforcement is attributed to the apparent cohesion and increased sti�ness


that is imparted to the granular cover soil due to soil con®nement [5]. Thenovel technique of improving the mechanical properties of a granular soilcover over large span steel-bridge conduits through the use of polymericcellular con®nement (geocells) holds promise to reduce the cost and increasethe range of soil-steel bridge applications.

ACKNOWLEDGEMENTS

Financial support for the work reported here was provided through anAcademic Research Program (ARP) grant awarded to the senior writer bythe Department of National Defence, Canada.

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Documents

Analysis of Geocell Reinforced-soil Covers Over Large Span Conduits