- Email: [email protected]
Analysis of geocell reinforced-soil covers over large span conduits
Computers and Geotechnics, Vol. 22, No. 3/4, pp. 205±219, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain P I I : S 0 2 6 6 - 3 5 2 X ( 9 8 ) - 0 0 0 0 8 - 1 0266-352X/98/$Ðsee front matter
Analysis of Geocell Reinforced-soil Covers Over Large Span Conduits Richard J. Bathursta* & Mark A. Knightb a
Department of Civil Engineering, Royal Military College of Canada, Kingston, ON, Canada, K7K 7B4 b Department 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 soil cover layers over ¯exible long span soil-steel bridge conduits is proposed. The soil cover is reinforced by a composite layer of geocell-soil whose properties have greater strength and stiness than the aggregate soil in®ll in an unreinforced condition. The paper describes a series of numerical simulations using a large strain non-linear ®nite element model to investigate the load-deformation response of midspan and eccentrically loaded steel conduits with and without reinforced geocell-soil covers. The simulation results show that the performance of soil-conduit systems with a conventional 1 m thick cover soil may be signi®cantly improved by introducing a single layer of geocell-soil material. Alternatively, thinner depths of soil cover are possible using this reinforcement technique compared to conventional unreinforced methods. # 1998 Elsevier Science Ltd. All rights reserved
INTRODUCTION Soil-steel bridges are corrugated structural steel plate conduits that are assembled on site in circular, elliptical or arch shapes and back®lled with granular soils. They are typically used to support highway pavements and railway tracks. The soil-steel bridge carries load through interaction between the conduit shell and the con®ning soil. *To whom correspondence should be addressed. Fax: 00 613-545-8336; e-mail: [email protected] 205
206
R. J. Bathurst and M. A. Knight
The economic viability of using soil-steel structures for long span structures (i.e. spans in excess of 3 m) is often controlled by the depth of soil cover required over the conduit crest (Ontario Highway Bridge Design Code (OHBDC) [1]). Field experience has shown that shear or tension failure of the cover soil is the typical failure mechanism. Relatively large long span conduits up to 16.8 m have also been built in recent years [2]. However, some large long span soil-steel structures with shallow covers have failed due to shell buckling [3]. Current design codes such as the American Association of State and Highway Transportation Ocials (AASHTO) [4], and the OHBDC [1] restrict cover soil thickness to a minimum of about Dh/6 in order to prevent soil cover failure, where Dh is the horizontal conduit diameter. Thus, these design codes may require signi®cant soil cover thickness for large span conduits and in turn render the structures uneconomical or unable to satisfy project geometric constraints. This paper describes a series of numerical simulations that were carried out to investigate the load-deformation response of midspan and eccentrically loaded steel conduits constructed with composite geocell-soil reinforced covers. The term geocell is a generic term describing a class of geosynthetic products manufactured from thin strips of polymeric material (usually high density polyethylene) bonded or welded together to form a three-dimensional cellular network that can be ®lled with compacted soil (Fig. 1). The eect of cellular con®nement on the in®ll soil is to increase the stiness and
Fig. 1. Single layer of polymeric geocell material.
Analysis of geocell reinforced-soil covers over large span conduits
207
shear strength of the con®ned soil. The results of large triaxial compression tests taken to collapse have demonstrated that cellular con®nement imparts additional apparent cohesion to aggregate in®ll soils while leaving the peak friction angle of the aggregate essentially unchanged [5]. The composite geocell-soil layer in road base applications has been demonstrated to act as a stiened mat that provides greater load bearing capacity and stiness than the same granular base constructed without cellular con®nement [6]. Layers of geocell-soil reinforcement have also been stacked to create composite material 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 reinforced soil cover may allow a reduction in cover soil thickness over these structures [8]. Single layers of composite reinforcement (0.2 m thick) placed within the conduit cover depth are demonstrated to increase the strength and stiness of the cover soil compared to unreinforced sections. Alternatively, the results of simulations reported here can be interpreted to show that thinner reinforced cover soil layers may be used to give the same or better performance than the same soil placed in an unreinforced condition. PROGRAM GEOFEM The non-linear ®nite element program GEOFEM (Geotechnical Finite Element Modelling), developed by the Department of Civil Engineering at the Royal Military College of Canada, was used to carry out the numerical simulations in the current study. GEOFEM is a general purpose ®nite element program for the analysis of structural and geotechnical problems. The program was speci®cally developed to investigate soil-structure interaction problems and uses a linearized updated Lagrangian method to accommodate large deformation behaviour [9±11]. VERIFICATION In the current study the results of program GEOFEM were validated against closed-form arch solutions, reduced-scale physical model experiments reported in the literature and a full-scale ®eld test. Arch solution Two-noded linear elastic beam elements were used to simulate the conduit shell in the current study. To test the accuracy of shell behaviour, in-isolation,
208
R. J. Bathurst and M. A. Knight
closed-form solutions [12] for a two-hinged circular arch loaded at midspan were compared to predicted values using the GEOFEM code. A total of 80 beam 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 at the University of Windsor in Ontario, Canada [13, 14]. A ®nite element mesh used in the current investigation to represent one of these physical experiments is reproduced in Fig. 3. Eight-noded quadrilateral continuum elements were used for the soil region. The soil elements were connected to the beam elements representing the conduit shell by six-noded interface elements. The surface of the soil was centrally loaded by a rigid 100 mm wide footing. The depth of cover in this experiment was 127 mm with the 0.78 m diameter conduit constructed from 4.76 mm thick aluminium plate with the following properties: elastic modulus, E=70 GPa; Poisson's ratio, 0:33; and yield stress, fy=275 MPa. No independent laboratory testing was carried out to determine mechanical properties of the sand used in the experiment or aluminium-sand interface properties. Based on the limited data available, the sand was matched to a Monterey no. 0 (SP-17a) sand soil found in a data base 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: 2 n Rf n Ki Pa 1 Ks 1 ÿ ci n tan i Pa
Fig. 2. Comparison of closed-form and numerical solutions to two-hinged circular arch problem.
Analysis of geocell reinforced-soil covers over large span conduits
209
where Ks is tangential stiness; Ki is the initial stiness, Rf is the ratio between failure shear stress and asymptotic shear stress, and n are shear and 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 stiness value (Kn ) was assumed to be constant except when the normal stress becomes tensile, at
Fig. 3. Comparison of experimental and predicted load-displacement response of reducedscale soil-conduit model test. TABLE 1 Hyperbolic parameters for soils Parameter
Young's modulus component, Ks Exponent for Young's modulus, n Bulk modulus, Kb Exponent for bulk modulus, m Minimum Poisson's ratio, Failure ratio, Rf Cohesion, c kPa Friction angle at 1 atm. pressure, o ( ) Change in friction due to 10-fold increase in con®ning pressure, ( ) Dilation angle, ( ) Unit weight, (kN mÿ3) Lateral earth pressure coecient, Ko a
Monterey Monterey no. 0 no. 0 (SP-17a) (SP-17c) sand [15] sand [15]
Dense silica sand a
Composite geocell dense silica sand a
920 0.79 465 0.32 0.30 0.96 0 33 0
3200 0.78 1400 0.45 0.25 0.92 1.0 45 3
507 0.76 570 0.5 0.25 0.64 1 45 0
1033 0.77 1755 0.41 0.25 0.85 190 45 0
0 20.3 0.47
0 19.0 0.35
0 15.7 0.35
0 15.7 0.35
Interpreted from data reported by Bathurst and Karpurapu [5].
210
R. J. Bathurst and M. A. Knight
which point a small residual value is assumed. Values for interface properties used in this veri®cation exercise are given in Table 2 and are the same values used 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 constitutive models selected. Full-scale ®eld test Bakht [16] reports the measured results of a full-scale ®eld trial of a soil-steel bridge (White Ash Creek) under live loading. Hafez [13] and Hafez and Abdel-Sayed [17] carried out ®nite element model (FEM) predictions of the system response. Program GEOFEM was also used to predict the response of the White Ash Creek ®eld trial. The conduit walls were modelled using two-noded beam elements with the linear elastic material properties reported by McVay and Selig [18] (Table 3). McVay and Selig note that bolted seams in a ¯exible steel conduit can cause the circumferential stiness of the conduit wall under compressive loads to be lower than that of a continuous corrugated-steel plate. Thus, to model the bolted corrugated-steel plate used for large span conduits a reduction in thrust stiness (EA) is required to maintain the same bending stiness (EI) of the shell. McVay and Selig also found that reducing the crosssectional area of beam elements by six times their original area provided a better model response. This same reduction factor has been used in this study. TABLE 2 Non-linear hyperbolic interface element properties [13] Parameter
Value
Initial tangent stiness, Ki Normal stiness, Kn (kN mÿ3) Exponent, n Failure ratio, Rf Interface cohesive strength, ci kPa Interface friction angle, i ( )
43,070 2.7108 0.6 0.834 1.0 23
TABLE 3 Corrugated plate properties [18] Parameter
Value 2
ÿ1
Unreduced area (m m ) Modulus of elasticity (MPa) Poisson's ratio Moment of inertia (m4 mÿ1) Plate thickness (m)
6.810ÿ3 2.0105 0.33 2.0810ÿ6 5.510ÿ3
Analysis of geocell reinforced-soil covers over large span conduits
211
The results of simulations using program GEOFEM and FEM predictions reported by Hafez and Abdel-Sayed [17] are presented in Fig. 4 together with measured values of axial thrust calculated from strain gauge measurements. Program GEOFEM gives reasonably accurate predictions of conduit wall axial thrust for this shallow cover large span circular ¯exible steel conduit. NUMERICAL SIMULATION OF GEOCELL-SOIL REINFORCED CONDUITS Geometry The plane strain geometry used to investigate the in¯uence of unreinforced and composite geocell-soil reinforcement on system load-deformation performance is illustrated in Fig. 5. A circular steel conduit of diameter (span) D located 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 at the soil surface. The contact between the bearing area B and the soil surface is 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.
212
R. J. Bathurst and M. A. Knight
. Sixty two-noded beam elements to represent the circular steel conduit constructed out of 5 gauge steel with 51152 mm corrugations. . A maximum of 392 eight-noded quadrilateral continuum elements to represent the composite geocell-soil reinforcement layer, back®ll and cover soil. The number of continuum elements varied with simulated depth of cover. . Thirty six-noded interface elements to connect the beam elements to the continuum elements. The ®nite element mesh was designed so that the continuum elements above the conduit are 0.2 m high matching the 0.2 m thick geocell thickness
Fig. 5. Problem geometry.
Fig. 6. Finite element mesh (midspan load con®guration).
Analysis of geocell reinforced-soil covers over large span conduits
213
that is typical for a single layer of this material in the ®eld. For eccentrically loaded tests the mesh in Fig. 6 was doubled in size. Material properties Beam elements The conduit walls were modelled using linear elastic material properties reported by McVay and Selig [18] (Table 3). The axial thrust capacity of the conduit walls before buckling was assumed to be 436 kN mÿ1 in accordance with OHBDC [1] guidelines. Soil properties Bathurst and Karpurapu [5] report the results of large triaxial cell compression tests on unreinforced and geocell-reinforced specimens of dierent granular soils prepared at dierent densities. Test specimens were 200 mm in diameter by 200 mm high matching the single cell size typical of commercially available geocell products. The results of tests using a standard laboratory silica sand are illustrated in Fig. 7. The data shows that the eect of geocell con®nement is to increase both the stiness and shear capacity of the soil. The composite geocell-soil material and unreinforced soil behaviour can be approximated using the hyperbolic model proposed by Duncan et al. [15] as illustrated on the same ®gures. Hyperbolic model parameters for unreinforced and reinforced soil materials are summarized in Table 1. It must 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]).
214
R. J. Bathurst and M. A. Knight
not capture the eect of many cells. However, larger multi-cell specimens are not possible to test with conventional large-scale triaxial test devices. Nevertheless, the results of full-scale tests of geocell-reinforced granular bases over compressible foundations using the same geocell material showed signi®cant increases in the stiness and shear strength of the granular layers [6]. Soil-beam interface properties Non-linear (hyperbolic) soil-beam interface element material properties were obtained from Hafez [13] (Table 2). Mesh construction and loading For each test series the following construction procedure was adopted: . The ®nite element mesh was constructed in 12 increments to simulate a typical construction sequence and to allow conduit stresses during construction to develop. Prior to the application of the next construction increment the gravity force for each element was applied in 10 equal load steps. . Using a plane strain displacement controlled boundary, an equivalent rigid footing of width B=0.2 m was pushed into the cover soil in increments of 0.005 m until the total surface de¯ection was 0.5 m. Failure was de®ned by bearing capacity failure of the soil cover or when axial thrust values in the beam elements representing the conduit walls exceeded the ¯exural (buckling) capacity of the material. RESULTS Selected simulation results are presented in Figs 8±11. The reference case for the parametric analyses in this paper is the midspan load con®guration with an unreinforced cover height of 1 m. The collapse load for this system is 167 kN mÿ1 at approximately 0.19 m of surface de¯ection (e.g. Fig. 8). In this reference case the maximum applied load resulted in a conduit axial thrust that was well below yield strength of the conduit walls and hence the peak load capacity of the system was controlled by soil shear strength. The curves in Fig. 8 show that system stiness and load capacity are improved signi®cantly by placing a single reinforcement layer within a 1 m thick cover soil layer. For a cover thickness of 1 m, the optimum location of a 0.2 m thick reinforcement layer is at 0.2 m below the loading surface. Figure 8 also shows that the location of the reinforcement layer can in¯uence the failure mode as well as the collapse load of the system. For example, attenuation of stresses by the reinforcement layer above the conduit is more eective at z=0 and
Analysis of geocell reinforced-soil covers over large span conduits
215
0.2 m than at 0.4 m. At the shallower reinforcement depths the geocell-soil composite layer is better able to ``bridge over'' the conduit and thus prevent overstressing of the conduit shell. The greater collapse load due to soil failure for reinforcement at a depth of z=0.2 m compared to z=0 may be explained by the larger volume of the potential shear failure zone that passes through the 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. 8. Load-de¯ection response at soil surface for midspan loading case and variable reinforcement layer depth.
Fig. 9. In¯uence of reinforcement on load-de¯ection response at soil surface and conduit crown for midspan loaded conduit.
216
R. J. Bathurst and M. A. Knight
deformations at the crown are similar for reinforced and unreinforced systems up to shear failure of the unreinforced soil cover. The overall greater stiness of the reinforced system recorded at the point of load application is clearly due to the improved stiness and strength properties of the composite geocell-soil material. Figure 10 compares the reference unreinforced system response to reinforced systems with a single layer of reinforcement 0.2 m thick placed at the surface of variable thickness cover soils. The results show that improved performance with a reduced cover thickness is possible by using a single layer of geocell-soil reinforcement. The curves also illustrate that a 0.4 m thick
Fig. 10. In¯uence of cover thickness and single reinforcement layer on load-de¯ection response at soil surface for midspan loaded conduit.
Fig. 11. Load-de¯ection response at soil surface for eccentric surface load case.
Analysis of geocell reinforced-soil covers over large span conduits
217
cover with a 0.2 m thick reinforcement layer gives the largest load capacity of all con®gurations represented in the ®gure (approximately a four fold increase in load capacity). This is thought to be due to a reinforced slab eect that becomes pronounced for shallow reinforced soil cover depths (i.e. when the ratio of reinforced soil volume to unreinforced soil volume above the conduit increases). Figure 11 shows results for a single eccentric load applied to 1 m thick cover soils. As may expected, the load-deformation response (stiness) improves as the point of load application moves further from the centreline of the conduit. However, load capacity is controlled in many of the cases shown by the assumed conduit buckling strength. The failure load for reinforced systems is less under eccentric loading compared to midspan loading. Hafez and AbdelSayed [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 and eccentrically loaded circular ¯exible steel conduit with and without composite geocell-soil reinforcement in the soil cover layer were carried out. The ability of program GEOFEM to simulate the behaviour of conventional large span soil-conduit bridges was veri®ed against closed-form two hinge circular arch solutions and the results of experimental and full-scale ®eld tests. The results of reinforced and unreinforced cover soil simulations demonstrated that: (1) The introduction of one layer of composite geocell-soil reinforcement in a conventional 1 m depth of soil cover can increase the midspan load capacity of the system by up to a factor of four. (2) Alternatively, thinner layers of reinforced cover soil can be used to provide the same or enhanced load-de¯ection response (stiness) as a conventional 1 m thick unreinforced soil cover. (3) Based on the limited number of numerical simulations carried out, the optimum placement depth of a layer of composite geocell-soil reinforcement with thickness T=0.2 m is estimated to be z/B=1 to 2. (4) The improvement in load capacity using reinforcement improves with magnitude of surface de¯ection. (5) The load-deformation (stiness) and collapse load for reinforced and unreinforced systems is in¯uenced by surface load eccentricity. The signi®cant increase in system load capacity using geocell-soil composite reinforcement is attributed to the apparent cohesion and increased stiness
218
R. J. Bathurst and M. A. Knight
that is imparted to the granular cover soil due to soil con®nement [5]. The novel technique of improving the mechanical properties of a granular soil cover over large span steel-bridge conduits through the use of polymeric cellular con®nement (geocells) holds promise to reduce the cost and increase the range of soil-steel bridge applications. ACKNOWLEDGEMENTS Financial support for the work reported here was provided through an Academic Research Program (ARP) grant awarded to the senior writer by the Department of National Defence, Canada. REFERENCES 1. Ontario Ministry of Transportation Quality and Standards Division, Ontario Highway Bridge Design Code, 3rd edn. Ontario Government Bookstore, Toronto, ON, 1992. 2. Abdel-Sayed, G. and Bakht, B., Analysis of live-load eects in soil-steel structures. Transportation Research Record, 1982, 878, 49±55. 3. Mohammed, H. and Kennedy, J. B., Economical design for long-span soil-metal structures. Canadian Journal of Civil Engineering, 1996, 23, 838±849. 4. American Association of State Highway and Transport Ocials, Standard Speci®cations For Highway Bridges, 16th edn. Washington, DC, 1996. 5. Bathurst, R. J. and Karpurapu, R. G., Large-scale triaxial compression testing of geocell-reinforced granular soils. Geotechnical Testing Journal, 1993, 16(3), 296±303. 6. Bathurst, R. J. and Jarrett, P. M., Large-scale model tests of geocomposite mattresses over peat subgrades. Transportation Research Record, 1988, 1188, 28±36. 7. Bathurst, R. J. and Crowe, E. R., Recent case histories of ¯exible geocell retaining walls in North America. In Recent Case Histories of Permanent Geosynthetic-Reinforced Soil Retaining Walls, ed. F. Tatsuoka and D. Leshchinsky. A. A. Balkema, Rotterdam, 1992, pp. 3±20. 8. Knight, M. and Bathurst, R. J., Finite element analysis of reinforced geocell-soil covers over large span conduits. In 5th International Symposium on Numerical Models in Geomechanics NUMOG V. ed. S. Pietruszczak and G. Paude. A. A. Balkema, Rotterdam, 1997, pp. 269±274. 9. Karpurapu, R. G. and Bathurst, R. J., Numerical investigation of controlled yielding of soil-retaining wall structures. Geotextiles and Geomembranes, 1992, 11(2), 115±131. 10. Bathurst, R. J. and Karpurapu, R. G., Users Manual for Finite Element Modelling GEOFEM, Vols. 1±3. Royal Military College of Canada, Kingston, ON, 1993. 11. Karpurapu, R. G. and Bathurst, R. J., Behaviour of geosynthetic reinforced soil retaining walls using the ®nite element method. Computers and Geotechnics, 1995, 17(3), 279±299.
Analysis of geocell reinforced-soil covers over large span conduits
219
12. Spoord, C. M., Theory of Continuous Structures and Arches. McGraw±Hill, New York, 1937. 13. Hafez, H. H., Soil-steel structures under shallow cover. Ph.D. thesis, University of Windsor, Windsor, ON, 1981. 14. Hafez, H. and Abdel-Sayed, G., Soil failure in shallow covers above ¯exible conduits. Canadian Journal of Civil Engineering, 1983, 10, 654±661. 15. Duncan, J. M., Byrne, P., Wong, K. S. and Mabry, P., Strength, stress±strain and bulk modulus parameters for ®nite element analyses of stresses and movements in soil masses. Geotechnical Engineering Report UCB/GT/80-01, University of California, Berkeley, CA, 1980. 16. Bakht, B., Soil-steel structure response to live loads. Proceeding of the ASCE, 1981, 107(GT6), 779±798. 17. Hafez, H. and Abdel-Sayed, G., Finite element analysis of soil-steel structures. Canadian Journal of Civil Engineering, 1983, 10, 287±294. 18. McVay, M. C. and Selig, E. T., Performance and analysis of a long-span culvert. Transportation Research Record, 1982, 878, 23±29.
Analysis of Geocell Reinforced-soil Covers Over Large Span Conduits Richard J. Bathursta* & Mark A. Knightb a
Department of Civil Engineering, Royal Military College of Canada, Kingston, ON, Canada, K7K 7B4 b Department 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 soil cover layers over ¯exible long span soil-steel bridge conduits is proposed. The soil cover is reinforced by a composite layer of geocell-soil whose properties have greater strength and stiness than the aggregate soil in®ll in an unreinforced condition. The paper describes a series of numerical simulations using a large strain non-linear ®nite element model to investigate the load-deformation response of midspan and eccentrically loaded steel conduits with and without reinforced geocell-soil covers. The simulation results show that the performance of soil-conduit systems with a conventional 1 m thick cover soil may be signi®cantly improved by introducing a single layer of geocell-soil material. Alternatively, thinner depths of soil cover are possible using this reinforcement technique compared to conventional unreinforced methods. # 1998 Elsevier Science Ltd. All rights reserved
INTRODUCTION Soil-steel bridges are corrugated structural steel plate conduits that are assembled on site in circular, elliptical or arch shapes and back®lled with granular soils. They are typically used to support highway pavements and railway tracks. The soil-steel bridge carries load through interaction between the conduit shell and the con®ning soil. *To whom correspondence should be addressed. Fax: 00 613-545-8336; e-mail: [email protected] 205
206
R. J. Bathurst and M. A. Knight
The economic viability of using soil-steel structures for long span structures (i.e. spans in excess of 3 m) is often controlled by the depth of soil cover required over the conduit crest (Ontario Highway Bridge Design Code (OHBDC) [1]). Field experience has shown that shear or tension failure of the cover soil is the typical failure mechanism. Relatively large long span conduits up to 16.8 m have also been built in recent years [2]. However, some large long span soil-steel structures with shallow covers have failed due to shell buckling [3]. Current design codes such as the American Association of State and Highway Transportation Ocials (AASHTO) [4], and the OHBDC [1] restrict cover soil thickness to a minimum of about Dh/6 in order to prevent soil cover failure, where Dh is the horizontal conduit diameter. Thus, these design codes may require signi®cant soil cover thickness for large span conduits and in turn render the structures uneconomical or unable to satisfy project geometric constraints. This paper describes a series of numerical simulations that were carried out to investigate the load-deformation response of midspan and eccentrically loaded steel conduits constructed with composite geocell-soil reinforced covers. The term geocell is a generic term describing a class of geosynthetic products manufactured from thin strips of polymeric material (usually high density polyethylene) bonded or welded together to form a three-dimensional cellular network that can be ®lled with compacted soil (Fig. 1). The eect of cellular con®nement on the in®ll soil is to increase the stiness and
Fig. 1. Single layer of polymeric geocell material.
Analysis of geocell reinforced-soil covers over large span conduits
207
shear strength of the con®ned soil. The results of large triaxial compression tests taken to collapse have demonstrated that cellular con®nement imparts additional apparent cohesion to aggregate in®ll soils while leaving the peak friction angle of the aggregate essentially unchanged [5]. The composite geocell-soil layer in road base applications has been demonstrated to act as a stiened mat that provides greater load bearing capacity and stiness than the same granular base constructed without cellular con®nement [6]. Layers of geocell-soil reinforcement have also been stacked to create composite material 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 reinforced soil cover may allow a reduction in cover soil thickness over these structures [8]. Single layers of composite reinforcement (0.2 m thick) placed within the conduit cover depth are demonstrated to increase the strength and stiness of the cover soil compared to unreinforced sections. Alternatively, the results of simulations reported here can be interpreted to show that thinner reinforced cover soil layers may be used to give the same or better performance than the same soil placed in an unreinforced condition. PROGRAM GEOFEM The non-linear ®nite element program GEOFEM (Geotechnical Finite Element Modelling), developed by the Department of Civil Engineering at the Royal Military College of Canada, was used to carry out the numerical simulations in the current study. GEOFEM is a general purpose ®nite element program for the analysis of structural and geotechnical problems. The program was speci®cally developed to investigate soil-structure interaction problems and uses a linearized updated Lagrangian method to accommodate large deformation behaviour [9±11]. VERIFICATION In the current study the results of program GEOFEM were validated against closed-form arch solutions, reduced-scale physical model experiments reported in the literature and a full-scale ®eld test. Arch solution Two-noded linear elastic beam elements were used to simulate the conduit shell in the current study. To test the accuracy of shell behaviour, in-isolation,
208
R. J. Bathurst and M. A. Knight
closed-form solutions [12] for a two-hinged circular arch loaded at midspan were compared to predicted values using the GEOFEM code. A total of 80 beam 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 at the University of Windsor in Ontario, Canada [13, 14]. A ®nite element mesh used in the current investigation to represent one of these physical experiments is reproduced in Fig. 3. Eight-noded quadrilateral continuum elements were used for the soil region. The soil elements were connected to the beam elements representing the conduit shell by six-noded interface elements. The surface of the soil was centrally loaded by a rigid 100 mm wide footing. The depth of cover in this experiment was 127 mm with the 0.78 m diameter conduit constructed from 4.76 mm thick aluminium plate with the following properties: elastic modulus, E=70 GPa; Poisson's ratio, 0:33; and yield stress, fy=275 MPa. No independent laboratory testing was carried out to determine mechanical properties of the sand used in the experiment or aluminium-sand interface properties. Based on the limited data available, the sand was matched to a Monterey no. 0 (SP-17a) sand soil found in a data base 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: 2 n Rf n Ki Pa 1 Ks 1 ÿ ci n tan i Pa
Fig. 2. Comparison of closed-form and numerical solutions to two-hinged circular arch problem.
Analysis of geocell reinforced-soil covers over large span conduits
209
where Ks is tangential stiness; Ki is the initial stiness, Rf is the ratio between failure shear stress and asymptotic shear stress, and n are shear and 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 stiness value (Kn ) was assumed to be constant except when the normal stress becomes tensile, at
Fig. 3. Comparison of experimental and predicted load-displacement response of reducedscale soil-conduit model test. TABLE 1 Hyperbolic parameters for soils Parameter
Young's modulus component, Ks Exponent for Young's modulus, n Bulk modulus, Kb Exponent for bulk modulus, m Minimum Poisson's ratio, Failure ratio, Rf Cohesion, c kPa Friction angle at 1 atm. pressure, o ( ) Change in friction due to 10-fold increase in con®ning pressure, ( ) Dilation angle, ( ) Unit weight, (kN mÿ3) Lateral earth pressure coecient, Ko a
Monterey Monterey no. 0 no. 0 (SP-17a) (SP-17c) sand [15] sand [15]
Dense silica sand a
Composite geocell dense silica sand a
920 0.79 465 0.32 0.30 0.96 0 33 0
3200 0.78 1400 0.45 0.25 0.92 1.0 45 3
507 0.76 570 0.5 0.25 0.64 1 45 0
1033 0.77 1755 0.41 0.25 0.85 190 45 0
0 20.3 0.47
0 19.0 0.35
0 15.7 0.35
0 15.7 0.35
Interpreted from data reported by Bathurst and Karpurapu [5].
210
R. J. Bathurst and M. A. Knight
which point a small residual value is assumed. Values for interface properties used in this veri®cation exercise are given in Table 2 and are the same values used 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 constitutive models selected. Full-scale ®eld test Bakht [16] reports the measured results of a full-scale ®eld trial of a soil-steel bridge (White Ash Creek) under live loading. Hafez [13] and Hafez and Abdel-Sayed [17] carried out ®nite element model (FEM) predictions of the system response. Program GEOFEM was also used to predict the response of the White Ash Creek ®eld trial. The conduit walls were modelled using two-noded beam elements with the linear elastic material properties reported by McVay and Selig [18] (Table 3). McVay and Selig note that bolted seams in a ¯exible steel conduit can cause the circumferential stiness of the conduit wall under compressive loads to be lower than that of a continuous corrugated-steel plate. Thus, to model the bolted corrugated-steel plate used for large span conduits a reduction in thrust stiness (EA) is required to maintain the same bending stiness (EI) of the shell. McVay and Selig also found that reducing the crosssectional area of beam elements by six times their original area provided a better model response. This same reduction factor has been used in this study. TABLE 2 Non-linear hyperbolic interface element properties [13] Parameter
Value
Initial tangent stiness, Ki Normal stiness, Kn (kN mÿ3) Exponent, n Failure ratio, Rf Interface cohesive strength, ci kPa Interface friction angle, i ( )
43,070 2.7108 0.6 0.834 1.0 23
TABLE 3 Corrugated plate properties [18] Parameter
Value 2
ÿ1
Unreduced area (m m ) Modulus of elasticity (MPa) Poisson's ratio Moment of inertia (m4 mÿ1) Plate thickness (m)
6.810ÿ3 2.0105 0.33 2.0810ÿ6 5.510ÿ3
Analysis of geocell reinforced-soil covers over large span conduits
211
The results of simulations using program GEOFEM and FEM predictions reported by Hafez and Abdel-Sayed [17] are presented in Fig. 4 together with measured values of axial thrust calculated from strain gauge measurements. Program GEOFEM gives reasonably accurate predictions of conduit wall axial thrust for this shallow cover large span circular ¯exible steel conduit. NUMERICAL SIMULATION OF GEOCELL-SOIL REINFORCED CONDUITS Geometry The plane strain geometry used to investigate the in¯uence of unreinforced and composite geocell-soil reinforcement on system load-deformation performance is illustrated in Fig. 5. A circular steel conduit of diameter (span) D located 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 at the soil surface. The contact between the bearing area B and the soil surface is 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.
212
R. J. Bathurst and M. A. Knight
. Sixty two-noded beam elements to represent the circular steel conduit constructed out of 5 gauge steel with 51152 mm corrugations. . A maximum of 392 eight-noded quadrilateral continuum elements to represent the composite geocell-soil reinforcement layer, back®ll and cover soil. The number of continuum elements varied with simulated depth of cover. . Thirty six-noded interface elements to connect the beam elements to the continuum elements. The ®nite element mesh was designed so that the continuum elements above the conduit are 0.2 m high matching the 0.2 m thick geocell thickness
Fig. 5. Problem geometry.
Fig. 6. Finite element mesh (midspan load con®guration).
Analysis of geocell reinforced-soil covers over large span conduits
213
that is typical for a single layer of this material in the ®eld. For eccentrically loaded tests the mesh in Fig. 6 was doubled in size. Material properties Beam elements The conduit walls were modelled using linear elastic material properties reported by McVay and Selig [18] (Table 3). The axial thrust capacity of the conduit walls before buckling was assumed to be 436 kN mÿ1 in accordance with OHBDC [1] guidelines. Soil properties Bathurst and Karpurapu [5] report the results of large triaxial cell compression tests on unreinforced and geocell-reinforced specimens of dierent granular soils prepared at dierent densities. Test specimens were 200 mm in diameter by 200 mm high matching the single cell size typical of commercially available geocell products. The results of tests using a standard laboratory silica sand are illustrated in Fig. 7. The data shows that the eect of geocell con®nement is to increase both the stiness and shear capacity of the soil. The composite geocell-soil material and unreinforced soil behaviour can be approximated using the hyperbolic model proposed by Duncan et al. [15] as illustrated on the same ®gures. Hyperbolic model parameters for unreinforced and reinforced soil materials are summarized in Table 1. It must 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]).
214
R. J. Bathurst and M. A. Knight
not capture the eect of many cells. However, larger multi-cell specimens are not possible to test with conventional large-scale triaxial test devices. Nevertheless, the results of full-scale tests of geocell-reinforced granular bases over compressible foundations using the same geocell material showed signi®cant increases in the stiness and shear strength of the granular layers [6]. Soil-beam interface properties Non-linear (hyperbolic) soil-beam interface element material properties were obtained from Hafez [13] (Table 2). Mesh construction and loading For each test series the following construction procedure was adopted: . The ®nite element mesh was constructed in 12 increments to simulate a typical construction sequence and to allow conduit stresses during construction to develop. Prior to the application of the next construction increment the gravity force for each element was applied in 10 equal load steps. . Using a plane strain displacement controlled boundary, an equivalent rigid footing of width B=0.2 m was pushed into the cover soil in increments of 0.005 m until the total surface de¯ection was 0.5 m. Failure was de®ned by bearing capacity failure of the soil cover or when axial thrust values in the beam elements representing the conduit walls exceeded the ¯exural (buckling) capacity of the material. RESULTS Selected simulation results are presented in Figs 8±11. The reference case for the parametric analyses in this paper is the midspan load con®guration with an unreinforced cover height of 1 m. The collapse load for this system is 167 kN mÿ1 at approximately 0.19 m of surface de¯ection (e.g. Fig. 8). In this reference case the maximum applied load resulted in a conduit axial thrust that was well below yield strength of the conduit walls and hence the peak load capacity of the system was controlled by soil shear strength. The curves in Fig. 8 show that system stiness and load capacity are improved signi®cantly by placing a single reinforcement layer within a 1 m thick cover soil layer. For a cover thickness of 1 m, the optimum location of a 0.2 m thick reinforcement layer is at 0.2 m below the loading surface. Figure 8 also shows that the location of the reinforcement layer can in¯uence the failure mode as well as the collapse load of the system. For example, attenuation of stresses by the reinforcement layer above the conduit is more eective at z=0 and
Analysis of geocell reinforced-soil covers over large span conduits
215
0.2 m than at 0.4 m. At the shallower reinforcement depths the geocell-soil composite layer is better able to ``bridge over'' the conduit and thus prevent overstressing of the conduit shell. The greater collapse load due to soil failure for reinforcement at a depth of z=0.2 m compared to z=0 may be explained by the larger volume of the potential shear failure zone that passes through the 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. 8. Load-de¯ection response at soil surface for midspan loading case and variable reinforcement layer depth.
Fig. 9. In¯uence of reinforcement on load-de¯ection response at soil surface and conduit crown for midspan loaded conduit.
216
R. J. Bathurst and M. A. Knight
deformations at the crown are similar for reinforced and unreinforced systems up to shear failure of the unreinforced soil cover. The overall greater stiness of the reinforced system recorded at the point of load application is clearly due to the improved stiness and strength properties of the composite geocell-soil material. Figure 10 compares the reference unreinforced system response to reinforced systems with a single layer of reinforcement 0.2 m thick placed at the surface of variable thickness cover soils. The results show that improved performance with a reduced cover thickness is possible by using a single layer of geocell-soil reinforcement. The curves also illustrate that a 0.4 m thick
Fig. 10. In¯uence of cover thickness and single reinforcement layer on load-de¯ection response at soil surface for midspan loaded conduit.
Fig. 11. Load-de¯ection response at soil surface for eccentric surface load case.
Analysis of geocell reinforced-soil covers over large span conduits
217
cover with a 0.2 m thick reinforcement layer gives the largest load capacity of all con®gurations represented in the ®gure (approximately a four fold increase in load capacity). This is thought to be due to a reinforced slab eect that becomes pronounced for shallow reinforced soil cover depths (i.e. when the ratio of reinforced soil volume to unreinforced soil volume above the conduit increases). Figure 11 shows results for a single eccentric load applied to 1 m thick cover soils. As may expected, the load-deformation response (stiness) improves as the point of load application moves further from the centreline of the conduit. However, load capacity is controlled in many of the cases shown by the assumed conduit buckling strength. The failure load for reinforced systems is less under eccentric loading compared to midspan loading. Hafez and AbdelSayed [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 and eccentrically loaded circular ¯exible steel conduit with and without composite geocell-soil reinforcement in the soil cover layer were carried out. The ability of program GEOFEM to simulate the behaviour of conventional large span soil-conduit bridges was veri®ed against closed-form two hinge circular arch solutions and the results of experimental and full-scale ®eld tests. The results of reinforced and unreinforced cover soil simulations demonstrated that: (1) The introduction of one layer of composite geocell-soil reinforcement in a conventional 1 m depth of soil cover can increase the midspan load capacity of the system by up to a factor of four. (2) Alternatively, thinner layers of reinforced cover soil can be used to provide the same or enhanced load-de¯ection response (stiness) as a conventional 1 m thick unreinforced soil cover. (3) Based on the limited number of numerical simulations carried out, the optimum placement depth of a layer of composite geocell-soil reinforcement with thickness T=0.2 m is estimated to be z/B=1 to 2. (4) The improvement in load capacity using reinforcement improves with magnitude of surface de¯ection. (5) The load-deformation (stiness) and collapse load for reinforced and unreinforced systems is in¯uenced by surface load eccentricity. The signi®cant increase in system load capacity using geocell-soil composite reinforcement is attributed to the apparent cohesion and increased stiness
218
R. J. Bathurst and M. A. Knight
that is imparted to the granular cover soil due to soil con®nement [5]. The novel technique of improving the mechanical properties of a granular soil cover over large span steel-bridge conduits through the use of polymeric cellular con®nement (geocells) holds promise to reduce the cost and increase the range of soil-steel bridge applications. ACKNOWLEDGEMENTS Financial support for the work reported here was provided through an Academic Research Program (ARP) grant awarded to the senior writer by the Department of National Defence, Canada. REFERENCES 1. Ontario Ministry of Transportation Quality and Standards Division, Ontario Highway Bridge Design Code, 3rd edn. Ontario Government Bookstore, Toronto, ON, 1992. 2. Abdel-Sayed, G. and Bakht, B., Analysis of live-load eects in soil-steel structures. Transportation Research Record, 1982, 878, 49±55. 3. Mohammed, H. and Kennedy, J. B., Economical design for long-span soil-metal structures. Canadian Journal of Civil Engineering, 1996, 23, 838±849. 4. American Association of State Highway and Transport Ocials, Standard Speci®cations For Highway Bridges, 16th edn. Washington, DC, 1996. 5. Bathurst, R. J. and Karpurapu, R. G., Large-scale triaxial compression testing of geocell-reinforced granular soils. Geotechnical Testing Journal, 1993, 16(3), 296±303. 6. Bathurst, R. J. and Jarrett, P. M., Large-scale model tests of geocomposite mattresses over peat subgrades. Transportation Research Record, 1988, 1188, 28±36. 7. Bathurst, R. J. and Crowe, E. R., Recent case histories of ¯exible geocell retaining walls in North America. In Recent Case Histories of Permanent Geosynthetic-Reinforced Soil Retaining Walls, ed. F. Tatsuoka and D. Leshchinsky. A. A. Balkema, Rotterdam, 1992, pp. 3±20. 8. Knight, M. and Bathurst, R. J., Finite element analysis of reinforced geocell-soil covers over large span conduits. In 5th International Symposium on Numerical Models in Geomechanics NUMOG V. ed. S. Pietruszczak and G. Paude. A. A. Balkema, Rotterdam, 1997, pp. 269±274. 9. Karpurapu, R. G. and Bathurst, R. J., Numerical investigation of controlled yielding of soil-retaining wall structures. Geotextiles and Geomembranes, 1992, 11(2), 115±131. 10. Bathurst, R. J. and Karpurapu, R. G., Users Manual for Finite Element Modelling GEOFEM, Vols. 1±3. Royal Military College of Canada, Kingston, ON, 1993. 11. Karpurapu, R. G. and Bathurst, R. J., Behaviour of geosynthetic reinforced soil retaining walls using the ®nite element method. Computers and Geotechnics, 1995, 17(3), 279±299.
Analysis of geocell reinforced-soil covers over large span conduits
219
12. Spoord, C. M., Theory of Continuous Structures and Arches. McGraw±Hill, New York, 1937. 13. Hafez, H. H., Soil-steel structures under shallow cover. Ph.D. thesis, University of Windsor, Windsor, ON, 1981. 14. Hafez, H. and Abdel-Sayed, G., Soil failure in shallow covers above ¯exible conduits. Canadian Journal of Civil Engineering, 1983, 10, 654±661. 15. Duncan, J. M., Byrne, P., Wong, K. S. and Mabry, P., Strength, stress±strain and bulk modulus parameters for ®nite element analyses of stresses and movements in soil masses. Geotechnical Engineering Report UCB/GT/80-01, University of California, Berkeley, CA, 1980. 16. Bakht, B., Soil-steel structure response to live loads. Proceeding of the ASCE, 1981, 107(GT6), 779±798. 17. Hafez, H. and Abdel-Sayed, G., Finite element analysis of soil-steel structures. Canadian Journal of Civil Engineering, 1983, 10, 287±294. 18. McVay, M. C. and Selig, E. T., Performance and analysis of a long-span culvert. Transportation Research Record, 1982, 878, 23±29.