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with 0.4 to 2.5 m (1.3 to 8.2 ft) of fillabove it with the span shown in Fig. 3would have had wall thicknesses inthe range of 600 to 900 mm (24 to 36in.). These large thicknesses would berequired to resist the bending momentsfrom soil pressures and highway traffic loadings, with relatively smalldeformations.The precast concrete arch used forthe railway overpass near Obed, Alberta, has wall thicknesses that are inthe range of 300 mm ( 11.8 in.) (seeFig. 3). To achieve these substantialsavings in materials, transportationcosts and erection costs, it was assumed that the arch would interactwith the surrounding soil to resistloads. The arch is relatively flexible sothat large bending moments do not develop as the structure displaces and interacts with the surrounding backfill.In the early 1980s, soil-structure interaction was considered in the designof precast concrete arches for the firsttime by Hebden.' Hebden designedthree thin-w a lled precast concretearches for the Coquihalla Highway inBritish Columbia, Canada . Thesearches have 20 m (65.6 ft) spans with250 mm (9.8 in .) thick wall sections,and carry the highway over creeks. Incontrast to the clay till at the Obedsite, the footings for the Coquihallaarches were founded on rock.Subsequent to the design of the Coquihalla culverts and the Obed culvertconsidered in this paper, the Reinforced Earth Company Ltd. '·' has introduced the trademarked TechSpanSystem to North America. The TechSpan System consists of 150 to 350mm (6 to 14 in .) thick precast concretesegments which are erected to form athree-point hinged arch. A ReinforcedEarth Company Ltd.' brochure illustrates a 12 m (39.4 ft) wide structureover a railway in Madrid, Spain.Computer ModelThe Obed arch considered herein,and the Coquihalla arches, were analyzed using the NLSSIP computer program developed by Byrne and Duncan. Thi s program uses the finiteelement method to account for thenonlinear response of the soil-archsystem. The soil was modeled by twoJanuary-February 1993dimensional isoparametric finite elements, assuming plane strain andisotropic behavior. The concrete archwas modeled by beam elements.Fig. 4 shows the finite elementmodel of the Obed arch and surrounding soil. The arch was loaded incrementally by assuming that the soil wasplaced sequentially in construction layers 1 through 9. Within each load increment, the structural response was assumed to be linear. To approximatenonlinear and stress-dependent soil behavior, the elastic properties of the soilwere adjusted in accordance with calculated stress levels after the placementof each construction layer. Althoughgeometric nonlinearities were accounted for, the arch beam elementswere assumed to have the same elasticproperties for all load increments.The soil response was representedby a tangent Young's modulus, ,, anda tangent bulk modulus, B using thefollowing expressions:E Kpa[ 1rx2l- R1 (1-sin ) )(0 1 -0 3 )][2c cos ) 20 3 sin ) (l)and(2)In Eq. (1), K is the modulus number,n is the modulus exponent, R1 is thefailure ratio, Pais atmospheric pressureexpressed in the same units as stresses,0 1 and 0 3 are the major and minorprincipal stresses, and c and ! are theMohr-Coulomb strength parametersof cohesion and angle of internal friction . The development of Eq. (l) is explained by Duncan and Chang.'Duncan et al. 6 indicate that the angleof internal friction to be used in Eq.(1) decreases in proportion to minorprincipal stress in accordance with thefollowing expression:where l o is the value of the angle ofinternal friction at a minor principalstress equal to atmospheric pressureand .tl ) is the reduction in the angle ofinternal friction for a tenfold increasein the minor principal stress.In Eq. (2), is the bulk modulusnumber and m is the bulk modulus exponent. The development of Eq. (2) isexplained by Duncan et al. 6Table 2 presents the parameters recommended by the Geotechnical Services Section of Alberta Transportation and Utilities for the various typesof soil shown in the finite elementmodel in Fig. 4. The earth pressure coefficients given in the table were usedto evaluate the initial stresses in thefoundation and each newly placedlayer of soil during backfilling.To account for various degrees ofcompaction, three sets of soil parameters were considered for the pit rungravel backfill. A controlled pit rungravel backfill was specified for theproject, since it was necessary toachieve both adequate compaction anddrainage around the arch structure.Table 3 presents representative values of the tangent Young 's modulus,tangent bulk modulus and angle of internal friction for the so il materialsaround the arch. These values werecalculated for major and minor principal stresses equal to atmospheric pressure, which is equal to 10.33 t/m '(2. 12 ksf).The Young's and bulk moduli implied by the parameters given in Table2 for Material 2, native till, were about2 to 2.5 times greater than those justified by the laboratory and field test results referred to previously.Although the test results werejudged to be too low by the geotechnical specialist, the strength of the culvert was also checked assuming amodulus number of 400, a modulusexponent of 0, a failure ratio of 0.75, abulk modulus number of 200, a bulkmodulus exponent of 0 , a cohesion of3 t/m' (615 psf) , an angle of internalfriction of 22.5 degrees at a minorprincipal stress equal to atmosphericpressure, a reduction in angle of internal friction of 0, and an earth pressurecoefficient of 0.7 for the native till.For the concrete arch, an effectivemoment of inertia of 0.25 times thevalue calculated from the gross concrete section was used in the computer45

Table 2. Properties of soils, concrete and ytillSoilaroundfootingsCompactedclay tillConcretePit run gravelCrushedgravelStandard Proctor density (percent)IOO 9590Unit weight (tim' )2.142.142.242.242.42.322.242.162.16Unit weight (pcf)134134140140150145140135135Modulus 0.340.50.40.4Modulus exponentFailure ratio0.60.750.70.700.60.70.70.7Bulk modulus number2400450175175124,00072045017575Bulk modulusexponent0.2500.30.300.250.250.20.2Cohesion (tim')2.550002140000Cohesion (psf)52200043,8000000Angle of internalfriction (degrees)503732321551414235Reduction in angleof internal .50.75Earth pressurecoefficient* See Fig. 4 fo r location in computer model.Table 3. Representative values of moduli and angle of internal friction.Material*I2ParameterSandstoneNativeclay till4Compactedclay till6Pit run gravel(Density 95 percent)Tangent Young'smodulus (tim' )41 ,300847046508780Tangent Young' smodulus 250373241Tangent bulkmodulus (tim' )Tangent bulkmodulus (ksf)Angle of internalfriction (degrees)* See Fig. 4 for location in computer model.model for the beam elements (seeFig. 4). An effective moment of inertiawas used to account for increases inflexibility owing to cracking, creepand shrinkage effects.In the computer model, the footingswere allowed to deflect and rotate asthe surrounding soil elements deformed under load.For strength calculations, load factors of 1.3 and 0.98 were used for soil46placed in layers above the footingsand for the self-weight of the arch, respectively. Load Case 1 in Fig. 4 is forunbalanced fill on the arch. The truckloads shown for Load Cases 2, 3 and4 are for a MS300 (HS33.7) truck,assuming a load factor of 2.17 and a3.7 m (12ft) lane width. Although theroad crosses on a skew, for design itwas conservatively assumed thattrucks cross perpendicular to the Ion-gitudinal axis of the arch .To account for a total backfill depthof 2.5 m (8.2 ft) above the crown ofthe arch at certain locations along thelength of the structure, for some of theresults presented, an additional surcharge load of 3.36 t/m 2 (0.69 ksf) wasadded to the loads shown in Fig . 4.This surcharge load accounts for 1.5 m(4.9 ft) more backfill than is represented by the model shown in Fig. 4.In the analysis , the displacementsand stresses in the soil and the displacements, forces and moments in thearch were recorded after each layer ofsoil (from Layers 1 through 9 inFig. 4) was added. This simulates theresponse of the soil-structure system asbackfill was placed. The correspondingdisplacements, stresses, forces and moments were also recorded after eachload case was considered.Results of Computer AnalysisFig. 5 presents the total factoredbending moments for the concretearch as the soil layers are added duringbackfilling. These moments were calculated using the Table 2 soil properPCI JOURNAL

8(0)020103040I0 /,7E"E(f)1-- 5I' -I 0,-15z''w 0w'' , I/III I'I·,"', /-2060"""·,,'-- .'',.1-90--03·105,,.- -30 '-' ·;.- -40- -50- -60\ r' ":L-30 --25-'.a.,---- -- -- ----07lI ---so-70 lLI 00- -20a:080/v,,1\ \'-X''V-,.-/ -70 /- 0//' I50-35-40CONSTRUCTION }LAYERFig . 5. Sample bending moments du ri ng backfilling .ties with pit run gravel backfill compacted to 95 percent of Standard Proctor density. T he angle 8 is measuredrelative to th e top of the left-h andfoo ting in Fig. 4. Moments are positive if they result in compression onthe outside fiber of the arch.Fig. 6 shows the increme ntal factored bending moments for the unbalanced soil and truck loadi ngs describedin Fig. 4. Although a non linear analysis was used, the incremental momentsof Fig. 6 can be added to the momentsfor Layer 9 in Fig. 5 to obtain an approximation of the combined moments8(0)0I0203040for the various loading conditions.One might anticipate that rock is required below the footi ngs of an arch tooffer enough restraint to sustain negative moments at the junction betweenthe bottom of the arch and the tops ofthe foot ings . It might be anticipatedthat the clay till founding material atObed is not stiff or strong enough toresist negative moments.Even though the Obed structure isnot founded in rock, the geometry andstiffness of the arch and surroundingso il are suc h that negative momentscan be sustained at the junction be-5060708090I 00I I0I 20tween the bottom of the arch and thetops of the footings (see Fig. 5).The factored axial forces in the archfollowing the placement of backfillLayer 9 were 58, 70 and 123 tim (39,47 and 83 kip/ft) at angles of 90, 40and 0 degrees, respectively. The incremental factored axial forces for LoadCase 4 (see Fig. 4) were 18, 25 and 19tim (12, 17 and 13 k.ip/ft) at the respective positions on the arch. Load Case 4resulted in larger incremental axialforces than did Load Cases 2 and 3.Fig. 7 show s the computed soilstresses at working load levels assuming that 2.5 m (8.2 ft) of backfill hasbeen placed over the crown of thearch. By way of comparison, assumingan earth pressure coefficient of 0.5 , byconventional calculations one wouldexpect horizontal soi l pressures varying from 0 at the ground surface to13.7 t/m ' (2.8 1 ksf) at the level ofPoint 139 in Fig. 7.An estimate of the soil pressuresund er the footings can be made bysumming the weight of the soil abovethe footings and arch, the weight of thearch and the weight of the footings , anddividing this total by the sum of thefooting areas . By these conventionalcalculations, the soi l pressure wou ld beapproximately 56.3 tim' ( 11 .5 ksf), assuming 2.5 m (8.2 ft) of soi l is abovethe arch crown. The vertical pressuresshown in Fig. 7 are approximately 20percent lower than the pressures obtained by conventional calculations.I 30I 40I 50I 60I 70I 8020L )AD CASE4-.0wa:OEOE/.u.- (·J ((f),--;- '\/101-'-.01-1-zz :,,, ., . ,r--ww woa: -100z//',,-- f.-'/--r-"·,.- ,----·" / /lL,/·\-- ---\.\ - 40-30:::-20 -"-1·0 \'\N.\.-0/ I·,"·v']' ':. : -"r--7'LOAD r.AsE 1 /LOA D CA E 2LpAD ASE 3,,,/- 20,/"'' - --1--, ;.L,0p-/-v'-- 10-- 20-30- 40Fig. 6. Sample bending moments from unbalanced soil and truck loading.January-February 199347

0SURCHARGE 3 36 t1 m0102CONSTRUCTIONLAYER9rI82 83l/7v236v65v43vIO""x(t/m20\2l10 20 30 ""-""- ""-""-'-0\ .82010a;y 20(t/ m2 l 304050-X:I II8139""'II t/m2 0 .2049 ksf/Fig. 7. Soil pressures for backfill 2.5 m (8.2 ft) above c rown .Table 4. Calc ulated displacements at locations a ro und arch.IncrementalTotalPoint*Soil at crown (Layer 8)Xy(mm)(mm)Truck load at crown (Load Case 4)Soil 2.5 m above crownX(rnrn)yX(mm)(mm)y(rnrn)- 1.8829.2- 26.57.8- 43.1- I. I1394.5- 26.51.2- 43.1- 1.2- 1.823612.4- 8.89.7- 33.20.0- 5.82830.026.40.0- 6.01.3- 8.7* See Fig. 7 for locations of displacements.Note: I mm 0.03937 in .; I m 3.28 1 ftThe following are possible reasonswhy the vertical soil pressures underthe footings determined from the computer analy sis are smaller than thepressures obtained from conventionalcalculations:1. The footings are founded on claytill , which is more compressible than48the rock often present for arch structures. As the Obed structure was backfilled, the computer ana ly sis accounted for the settlement of thefootings relative to the adjacent soil.Some of the weight of the soil abovethe structure was transferred by arching action and shear stresses to theadjacent backfill material.2. The pressures from the computeranalysis are determined at the centersof the finite elements, rather than atlocations directly under the footings.lf a finer finite element mesh had beenused, higher vertical press ures mayhave been determi ned from the analyPCI JOURNAL

24402702701130(()(()w00t i li-12 - 50111 I.D. SHEATHS11-- ":.::::.::::.:::.:::.:""-!1-6 - 50111 I.D. SHEATHS(FOR#a8 -DYWIDAG THREADBARS)15M 9 -15M6 - 25MEXTRA6 6 -25M25M 15M 0 4509 -6 4 -4 -20M15M15M 50111 I. D. SHEATHS(FOR 119 DYWIDAGTHREADBARS)SIDE VIEWFig. 8. Typical precast concrete arch segments.DIMENSIONS IN mmI mm 0.03937 in.SEC] ON1980

sis directly below the footings .Working level displacements of theculvert during backfilling were alsocalculated by the computer program.Table 4 I ists displacements at locations around the arch and at the footing for various stages of construction.The points referenced in Table 4 areshown in Fig. 7. The same soil properties were used in the analysis undertaken to prepare Table 4 and Fig. 7.Upon backfilling to the level of thearch crown (Layer 8 in Fig . 7) , thetotal calculated footing settlement was26.5 mm ( 1.04 in.) and the upwardmovement at the crown was 26.4 mm(!.04 in.). With 2.5 m (8.2 ft) of backfill, the total calculated footing settlement increased to 43.1 mm (1.70 in.),but the crown moved 6.0 mm (0.24 in.)below its initial position prior to thestart of backfilling. As shown by LoadCase 4 in Table 4, the calculated incremental displacements for truck loadingwere relatively small.force interaction diagrams for the archwall at all sections . In general, thecomputed axial forces were well belowthe axial capacity of the arch sectionsat balanced load conditions, ensuringductile behavior near failure loads.Arch DesignFig. 8 shows the reinforcing steel arrangement used for a typical arch segment. Concrete with a minimum 35MPa (5080 psi) compressive strengthat 28 days and reinforcing steel with a400 MPa (58 ksi) yield strength wereused to construct the arch segments.The reinforcing steel was selected sothat the moments and axial forces calculated from a large number of computer analyses for various soil conditions were within the moment-axialFig. 9. Footing construction.Connections at theCrown and Footingsand Between SegmentsIn the initial design , the structurewas assumed to be a three-pointhinged arch . Computer calculations indicated that both wall bending moments and displacements would havebeen unacceptably large for the threepoint hinged system. To reduce moments and deflections for final design ,the adjacent arch segments were assumed to be continuous at the crownand rigidly connected to the footings .Figs. 3 and 8 show the thickening ofthe arch segments at the crown and the414 MPa (60 ksi) grade Dywidagthreadbars which were used in conjunction with a grouted longitudinaljoint to achieve continuity.The connection of the arch segmentsto the conventionally reinforced concrete strip footings is also illustrated inFigs. 3 and 8. By connecting the archsegments to the footings with groutedlongitudinal joints, negative momentscould be developed at the bottom ofthe arch as the weight of soil and lateral earth pressures caused the footings to rotate relative to the arch during backfilling.Note that the Dywidag threadbarstransfer the tensile forces at the inter-( 4.2 in.lCONTINUOUS GROUT KEY20M CONT. IN JOINTOUTSIDE w.,"'".,,. .:::.::: E0l{)r--(j)II-."'N!'()",;"'INSIDE0:::Ll· "'. b' 1ETHAFOAM FILLERFig. 10. Typical arch circumferential joint.50PCI JOURNAL

faces between the precast concrete segments and footing pedestals to anchorplates near the tops of the "knobs"at the bottoms of the segments (seeFig. 8). These tensile forces weretransferred to the outer layers of the reinforcing steel in the arch segmentwalls by concrete truss action.Fig. 9 shows the corrugated pipesthat were cast into the footings to accept the Dywidag threadbars from thearch segments.Adjacent arch segments were alsoconnected together circumferentiallyby grouted joints, as shown in Fig. 10.Although not relied upon to carryloads, the complete arch was tied together at the crown by four 4Kl5 longitudinal post-tensioning cables (seeFig. 3). These cables help to preventcircumferential shrinkage cracks fromforming in the arch and assist in transferring vehicular loads between adjacent segments.Fig. 11. Form for arch segments.PLANT MANUFACTURINGThe 140 segments for the arch weremanufactured in Edmonton by ConForce Structures Limited over a periodof seven months, starting in the summer of 1988 . In peak manufacturingperiods, one segment was cast eachday. The segments had a width of 2440mm (96 in.) and a mass of slightly lessthan 35 t (77.2 kip weight).The reinforcing steel for a givenarch segment was tied on a wood jigthe day before casting. It took approximately 12 man-hours to tie the steelfor one segment.The next day , the reinforcing steelwas lifted by crane into the steel formshown in Fig. II. The reinforcing steelwas adjusted, final reinforcing bars wereadded, and the segment was cast by expending approximately 40 man-hours.The segment was cured overnight.The next day, the segment was removedfrom the form by means of a four-pointcrane lift, and placed on the plant floorin the same position as it was cast. Toreduce stresses, the ends of the segmentswere connected together by using reinforcing bars to form a tied arch. Thesereinforcing bar ties also maintained theshape of the arch segments from thetime the segments were removed fromthe form until they were erected.January-February 1993Fig. 12. Trucking of arch segment.The segment was then moved to theplant yard for storage. Near winter'send, the segments were shipped to theproject site.SITE ERECTIONIn February of 1989, the arch segments were trucked a distance of 240km ( 150 miles) from Edmonton to theObed site. Fig. 12 shows the truckingof one of the segments. The reinforcing bars used to connect the ends ofthe segment together to form a tiedarch are apparent in the photograph.As shown in Fig. 13, the segmentswere erected in pairs without falseworkusing two conventional 81.6 t (90 Imperial ton) cranes. Canadian National Railsite representatives cooperated with theprecast concrete contractor during theerection of the arch segments, allowingat least one window of two hours eachda

3. Precast concrete arch 3,721,000 4. Bridge structure with Reinforced Earth 3,516,000 abutments 5. Conventional bridge structure 3,758,000 3. Precast concrete arch - Shown by Figs. 1 and 3, this alternative would consist of two precast concrete arcs of a circle that are connected together at the top to form an arch. The arch