Design of Corrugated Metal Box Culverts

Transportation Researh Reord 18 33 Design of Corrugated Metal Box Culverts J. M. DUNCAN, R. B. SEED, and R. H. DRA WSKY ABSTRACT Corrugated metal box ulverts provide large ross-setional areas for water onveyane vertial learane is limited. Beause they have nearly flat rowns and large widths ompared with their heights, they behave differently from onventional metal ulverts, and different methods are required for their design. The design proedure presented is based on field experiene, finiteelement analyses, and instrumented load tests on box ulverts. The proedure enompasses bending moments in the rown and haunh setions due to bakfill and traffi loads, design of portland ement onrete relieving slabs for onditions over depth is severely limited, reommended load fators for design, and defletions in servie for metal box ulverts with spans as large as 26 ft. Corrugated metal box ulverts were developed to meet a need for strutures with large ross-setional areas for water onveyane at sites with limited vertial learane. Beause of their great widths ompared with their heights, box ulverts are well suited to these onditions, as shown by the typial box ulvert shapes in Figure 1. Rise= 2 1-6 11 Span = 8' - 9" Rise = 6 1-2 11 Span= 25'-2" Rise = 1'-2" Span =25'-5" R' se : 7 ' 2 " Spon il' 4" FGURE 1 Aluminum box ulvert shapes. Beause they have distintly different shapes from onventional metal ulverts, it would be antiipated that traditional design proedures, based largely on experiene and appliable to ulverts that arry a major portion of their loads through arh ation, would not be appliable to strutures with large-radius rown setions and straight sides as shown in Figure 1. The first orrugated metal box ulverts, whih were produed by using ribbed aluminum strutural plate, were built in 1975. The design of these strutures was ompletely empirial, relying on field load tests to establish aeptable strutural plate thiknesses and rib spaings. Within 3 years a onsiderable number of box ulverts had been onstruted, and demand for additional sizes inreased to a point ompletely empirial design proedures were no longer appropriate. n 1978 a study was undertaken at the University of California to develop rational designs for aluminum box ulvert strutures. The first phase of these studies was a program of finite-element soil-struture interation analyses to evaluate the bending moments and axial fores in box ulvert strutures under loads imposed by bakfill and live loads. Experimental studies were also onduted to evaluate the stiffness and bending moment apaity of aluminum strutural plate with stiffener ribs bolted to one or both sides. n 198 additional finite-element analyses were performed to assess the behavior of box ulverts with spans up to 26 ft. n 1981 fullsale loading tests were performed on an instrumented box ulvert struture to provide a basis for detailed omparison of design alulations and measured behavior. n 1984 additional finite-element analyses were performed to develop bending moment oeffiients for box ulverts with portland ement onrete (PCC) relieving slabs over the top. The results of these various studies have been used to design a family of 87 aluminum box ulvert strutures with spans ranging from 8 ft 9 in. to 25 ft 5 in. and heights from 2 ft 6 in. to 1 ft 6 in. The design formulas and oeffiients an also be applied to steel box ulverts, if desired. As of August 1984, about 1, aluminum box ulvert strutures had been put into servie in the United States. All told, these strutures afford approximately 4, struture-years of experiene under field onditions. n all but three of these ases, the box ulverts have performed without problems. n all three ases problems have developed, the ause was the same--damage to the rown of the struture aused by operating heavy live loads over the ulvert with less over than the minimum speified. These experienes point out the importane of ensuring that minimum over depths are maintained over metal ulverts so that the design loading onditions will not be exeeded. The purpose of this paper is to draw together the results of the studies and experiene on whih the design of aluminum box ulvert strutures is based

34 Transportation Researh Reord 18 -, 1-1<: - 1 1 1 1 1 1 1 1!! L. - -- -H--U + ll-- - -. [ ' ' J f777'77'7' Beam ElemenlsJ ' 7 Soil Elements -' FGURE 2 Finite-element mesh for analysis of box ulvert. and to omment on the field behavior of this new type of flexible metal ulvert struture. BASS FOR DESGN OF ALUMNUM BOX CULVERTS Design of aluminum box ulverts is based on three prinipal steps: 1. Evaluation of bending moments and axial fores through finite-element soil-struture interation analysis, 2. Evaluation of moment apaity and flexural stiffness through laboratory flexural tests, and 3. Determination of suitable load fators to ensure safe behavior under servie load onditions. These aspets of the design and the orrespondene between the analytial studies and atual field behavior are disussed in the following setions. Finite-Element Analyses The finite-element proedures used for the soilstruture interation analyses are based on the tehniques for modeling soil stress-strain behavior developed by Dunan and Chang (1) and the methods for performing soil-struture iii""teration analyses developed by Dunan and Clough (2). A typial finite-element mesh for box ulvert -analysis is shown in Figure 2. Previous appliations of finite-element analyses to ulvert design have been desribed by Dunan (_!) and by Dunan and Drawsky (i_) The analyses are performed step by step, beginning with the struture resting on its foundation with no bakfill. Then plaement of the first layer of bakfill alongside the ulvert is modeled by adding the first layer of soil elements to the mesh. At the same time, loads are applied representing the weights of the added elements. Through their interation, the soil elements load the struture. Subsequent steps of the analyses are performed in the same way, adding one layer of elements at a time, whih simulates the proess of bakfilling around and over the ulvert. As soil elements are added above the rown of the ulvert, they load it downward, and the sides of the struture tend to flex outward against the adjaent bakfill. After the final layer of fill has been plaed over the top of the struture, loads are applied to the surfae of the fill to simulate vehiular traffi loads. The behavior of box ulverts is dependent to a large degree on their interation with the surrounding bakfill, whih restrains the tendeny of the sides of the struture to flex outward and greatly inreases the load-arrying apaity as ompared with that of a free-standing struture. t is this aspet of their behavior that makes the use of soilstruture interation analyses, with simulation of the behavior of both bakfill and ulvert, absolutely essential to provide a realisti basis for design. Beause box ulverts are relatively flat and beause they usually have small depths of over over them, bending moments are quite signifiant and must be onsidered arefully in design. Bending-moment diagrams for two box ulvert shapes are shown in Figure 3. t may be seen that the moment diagrams have two maxima, one in the rown beneath the applied load and another at the haunh. An extensive series of analyses was performed to evaluate rown and haunh bending moments in large and small box ulverts with a range of over depths and live loads of various magnitudes on the surfae. The results of these studies have been put in the form of a set of equations that an be used to alulate bending moments in box ulverts with spans up to 26 ft under a variety of onditions of over depth and live load. These equations and the limitations on their use for design are disussed in a subsequent setion. wyn 3.2 k/ft 3.2 k/ft!! 8.4 k fl/ft Span 15' -4" Rise = 6 1-2" Cover = 1' -6 11 Span 9'-5" Rise = 6'-o" over = 1 1 - o" 4. 2 k/ft FGURE 3 Calulated moment distributions. Experimental Loading Te s t s })J\l'Yfi Dring the summer of 1981 an experimental loading of a full-sale box ulvert was undertaken to obtain data for detailed omparison with the finite-element analysis proedures used for design. Figure 4 shows the ulvert during the field load test. The ulvert tested had a span of 17 ft 6 in. and a rise of 6 ft 2 in. t was a standard member of the family being produed at that time exept that the strutural plate in the haunh was.175 in. thik rather than the standard.2-in. thikness. (The partiular dimensions of this box ulvert are no

Dunan et al. 35 n the field the ulvert was loaded by a large fork lift parked with its heavily loaded front axle at midspan, as shown in Figures 4 and 5. Conrete bloks were loaded on a pallet supported on the forks, raising the front axle load from 11, to 37,8 lb, about 2 perent more than the design H-2 loading. To hek the behavior of the box ulvert under repeated loading, the onrete bloks were removed and replaed on the fork lift. Analysis of the measured defletions and strains in the ulvert showed that the finite-element analyses used for design were aurate with respet to the maximum bending moment at midspan and somewhat onservative with respet to the maximum bending moment in the haunh and the defletion of the box ulvert under load. Speifially, omparison of the analytial and experimental results showed the following: FGURE 4 Field loading, view from northeast orner of struture. longer produed.) A total of 96 strain gauges was attahed to the ulvert at two setions, one at the haunh and one at the rown. Half of the gauges were attahed to the strutural plat e at the orrugation rowns and valleys, and half were attahed to the stiffener ribs. The strain gauges were alibrated by loading the struture in the laboratory before it was installed in the field. The laboratory loading, arranged so that the indued bending moments were similar to those resulting from the field loading, applied a total load of 5, lb to a setion of the ulvert 9 ft long. The additional 2 ft 3 in. was removed for the laboratory test so that the struture wou l d fit into the 9-ft 3-in. throat of the testing mahine at t he Uni versity o f California Rihmond Field Stat i on. Followi ng i t s l oading i n t he laboratory, the ins t r umented box ulver.t wa s assembled to its.full l ength (11 f t 3 in.) a nd i nstalled i n a.n e xava t i on t hat had been dug in t he layey g round a t t he Rihmond Fi eld S t a tion. The ulvert was bakfilled wi th a uniform fine sand to a depth of 1.75 ft above the rown, as shown i n F i gu r e 5. The s and bakfill was ompated by using a v i brating pl ate ompa tor t o 96 perent o f the standard AASHTO (ASTM 698) maximum. This orresponds t o a r elative density (ASTM 249) of 6 perent and r elati ve ompati on o f a bout 9 1 perent by the modified AASHTO t e s t (ASTM Dl 557) -.. """""".. Un i t6r Snd Bakfill FGURE 5 Field loading. Total Load 38, lb F: ont Whe es ::;,;::,Lif: 1. Atual defletions of aluminum box ulverts due to traffi loads are likely to be only about one-fourth as large as defletions alulated from design finite-element analyses. This differene is mainly beause the bakfill around the box ulvert exhibits inreased stiffness when it is unloaded and reloaded, whih is not refleted in the design finite-element analyses but is harateristi of the stress-strain behavior of all soils. 2. Atual bending moments in the rown setions of aluminum box ulverts are likely to be essentially the same as those alulated by design finiteelement analyses. The analyses appeared to represent quite aurately the onditions in the most severely loaded setion of the rown. 3. Atual bending moments in the haunh setions of aluminum box ulverts are likely to be appreiably smaller than those alulated from design finite-element analyses. The differene is beause there is onsiderable load spreading longitudinally within the struture, whih is not refleted in the finite-element analyses. Additional studies of the fators ontroling this longitudinal load spreading have been performed in the period sine the load tests were ompleted, and this aspet of the behavior of box ulverts has been inorporated in the design haunh moment equations disussed in subsequent setions. The experimental l oad testing program thus showed that the design finite-element a nalyses were valid in some respets and onservative in others and provided a basis for refi nemen t of box ulvert designs. BENDNG MOMENTS N METAL BOX CULVERTS Approximately 1 finite-element analyses were performed to study variations of bending moments and axial fores in metal box ulverts under various onditions of ulvert span, ulvert rise, over depth, reliev i ng-sl ab stiffness, relieving-slab length, vehile i oad, wheel onfigurat i on, l oad posi t i on, bakfill type, and degree of ompation. From these ana l yses, a number of important onlu s i ons we r e r e ahed t hat guided t he development of the design method. These are as follows: 1. For the onditions under whih box ulverts are usually employed, in whih over depths a re l ess than 5 ft, t he effets of axial fores a r e s mall in omparison wi th t he effets o f bending moments, and only bending moments need be onsidered for hoos ing design setions. 2. Culvert rise has only a small effet on moments due to live load. Bending moments determined for low-rise ulverts are slightly larger than those for high-rise ulverts.

36 Transportation Researh Reord 18 3. The effetiveness of relieving slabs in reduing live-load moments inreases as the distane that they projet beyond the edge of the ulvert inreases. 4. The riti al position for vehile loads is always at or near enter span. 5, Bakfill quality and density have some slight effets on ulvert bending moments ; better bakfill quality and higher degrees of ompation result in smaller moments. For purposes of design, however, bending moment oeffiients have been based on results of analyses that use the lowest quality aeptable bakfill, a lay of low plastiity ompated to 9 perent of standard AASHTO maximum dry density (CL9 bakfill) BENDNG MOMENTS DUE TO BACKFLL AND COVER LOADS Bending moments indued by bakfill up to the rown level of box ulverts vary quite signifiantly with the rise/span ratio of the ulvert. High-rise ulverts bend inward more at the sides and upward more at the rown during early stages of bakfilling than do low-r ise ulverts. As over is plaed over the rown and as live loads are applied to the bakfill over the ulvert, the rowns of both high-rise and low-rise ulverts bend downward. The ritial design ondition is always one of downward bending in the rown due to over and live load, and it has been found to be onservative to neglet the early upward bending in high-rise box ulverts and to base designs of both high- and low-rise ulverts on the results of analyses of low-rise strutures. Suh an approximation appears justified in view of the simpliity it affords by eliminating rise as a fator and beause the bending moments due to bakfilling just up to the rown level are a small part (typially less than 1 perent) of the total design moment, Thus the bending moments disussed in the following paragraphs are those determined for low-rise strutures; they are slightly onservative when applied to high-rise strutures. Variations of bakfill moments with over depth are shown in Figure 6 for four diffe rent spans varying from 9.7 to 25.4 ft. The verti al axes in these figures are the sum of the absolute values of rown a nd haunh moments due to bakfill <Mee + MBal The hori zontal axes are (H - Hminl, H is the total over depth and Hmin is t he mi nimum allow- able over depth. For onditions soil and asphalt onrete pavement over the rown of the struture, the minimum over depth is 1.4 ft. For onditions a PCC relieving slab overs the rown, the minimum over depth is the slab thikness, usually slightly less than 1 ft. Beause 1.4 ft of soil and 1. ft of onrete impose approximately the same loading, the same minimum-over moments an be used for either ase. The moments for this ase are those shown on the left edge o f the plots in Figur e 6, wher e (H - Hm1nl = O. As t he over dept h i nreases above Hm i n the total bending moments inrease i n proportion. t may be s een that the rate of inrease is larger for larger spans. The proposed design lines shown in Figure 6 orrespond to the following equation: B sum of rown and haunh moments due to bakfill (kip-ft/ft);.53 -.24 (S - 12 ft) for 8 ft.s. s.s. 26 ft;.53; unit weight of bakfill (kips/ft'); span (ft); over depth (ft), H Hmin1 minimum over depth (ft), Hmin = 1.4 ft of soil, or required slab thikness for onrete. Equation 1 is valid for 8 ft.s. S.S. 26 ft. These design moments are represented graphially in Figure 7, whih shows bakfill moments as a fun- ( ) 15 15 = SPAN 9.7 ft SPAN= 15.5 ft 1 1 lo Proposed 1 5 desi9n line Proposed desl9n line 2 4 6 2 4 6 ( H-Hmin> - ft (H-Hminl- fl R/S.2 -.4 Cl R/ S = 4 -.6 25 25 SPAN 19.1 ft 2 2 15 m. 1 :::i: SPAN 25.4 ft Proposed des ign line o 2 4 6 o 2 4 6 (H-Hminl-ft (H Hmin>-ft FGURE 6 Variations of bakfill moments with span and over depth. FGURE 7 Bakfill moments. tion of span for y =.125 kip/ft' and over depths varying from Hmin to 5 ft. Values of rown moment and haunh moments an be derived from the total moments by using the following equations: M B=P Mni (2) (3)

Dunan et al. 37 Mes rown moment due to bakfill (kip-ft/ft), Mila haunh moment due to bakfill (kip-ft/ft), and P s rown moment oeffiient. Values of P, determined from the results of finiteelement analyses, are shown in the upper part of Figure 8. 1. o.e..6.4 u.2 o.e a:: u := o." u.2 s Appliable Ran2e 1 15 2 S =Span ft Appltable RonQe 3 H Cover Depth -ft FGURE 8 Coeffiients P and RHB BENDNG MOMENTS DUE TO LVE LOADS As a vehile moves aross a orrugated metal box ulvert, the bending moments around the struture vary in both magnitude and sign. Therefore, to determine bending moments for design, it is neessary to study a range of live-load positions from the enter of the span to the edge of the struture. For most aluminum box ulvert shapes the ritial load position for both rown and haunh moments is at or near enter span. The live-load bending moments disussed in the following paragraphs are the largest alulated for the rown and the haunh, even though these may not orrespond to exatly the same position of the load. The maximum moments are always downward bending in the rown (tension i n side) and outward bending in the haunh (tension outside), with the types of distributions shown in Figure 3. Bending moments due to live loads vary quite signifiantly with over depth: The deeper the over, the smaller are the moments indued by a given vehile load. This effet results from greater spreading of the load at greater over depth. The spreading that ours parallel to the span of a ulvert an be modeled by finite-element analyses, but t.he spreading that ours parallel to the ulvert axis annot. To aount for load spreading along the ulvert axis, equivalent line loads (LL in kips per foot) were used in the finite-element analyses. These equivalent line loads are seleted so that they produe the same peak vertial stress at the level of the rown of the struture as the atual disrete 4 25 3 5 wheel loads that they model, based on Boussinesq elasti theory. Values of equivalent line load an be expressed in terms of the design axle load as follows: LL= AL/Ki equivalent line load (kips/ft), axle load (kips), and load spread fator (ft). Values of K4 depend on the wheel onfiguration and whether the ulvert has a relieving slab over the rown, as shown by the values listed in Table 1. Beause the vertial stress due to a line load is the same at every setion along the line, the use of equivalent line loads is inherently onservative. The ulvert is treated as if it were loaded uniformly all along its length at the same intensity as the most heavily loaded setion. Box Culverts Without Relieving Slabs Variations of live-load moments with over depth are shown in Figure 9. The vertial axes in these figures are t:m.rl the hange in total moment due to TABLE 1 Values for the Fator Ki for Calulating Equivalent Line Loads Values of K4 (ft) No Relieving Slab Cover Relieving Depth Two Wheels/ Four Wheels/ Eight Wheels/ Slab over (ft) Axle Axle Axle Crown 4.3 5. 8.5 12.8 2 5.3 6,4 9.2 3.4 3 7. 8.7 l.6 14. 5 12.3 12.5 13.5 14.6 7 14.4 14.5 14.6 15.3 1 16. 16. 16. 16. Note: LL= AL /. f.'or tandom axles spaed at less than one-third the span of the ulvert 1 AL ii h :sum of the londs arried on bo th axles. a The AASHTO HS(MS) truk has four wheels on one axle. i 1 '"2 5 ::i: 15---------. SPAN 9.7 ft _ 2-----6 _ 2---4----6.;. 1 -:, i" 5. H -ft 2.------,----.,-- SPAN 19, ft 15 O'----,,-- 2 4 6 H- ft 1 s 15 1 5 32k Vehile H - ft o,, ' ', o' ;. Proposed _/ 5design lines F. E.M. Analyses, e tandem axles, 2 wheels eoh O single axle, 4 wheels Proposed Design Lines, - tandem axles SPAN=254 fl --- single axle FGURE 9 Variations of live-load moments with span and over depth. (4)

38 Transportation Researh Reord 18 live load. These are the sum of the absolute values of hanges in rown and haunh moments due to live load at the most er i tial points on the rown and haunh. The proposed design lines shown in Figure 9 orrespond to the following equation: Over CrCWrfn K 3 O.OB/ (H/ S).2 for S.s_ 2 ft and K 3 = [O.OB -.2(S - 2 ft)]/(h/s).2 for 2 ft < S < 26 ft. rhese design moments are rep r esented g raphially in Figure 1, whih shows l ive-load moments as a funtion of span for the HS-2 vehile with 32 kips on four wheels on a single axle. 2.---r-.---,----r-.----,---r-.----. 'f g.9 G :J E 8 12 E "' :< Live Load Moments ore proportional to ox.le load Curves shown orrespnd to AL' 32 kips with four wheels on a single ixle (5) OXWA\ Soil Cover Over Relieving Slob,,,,,_- " hl!6'iaf "?? f::h.!ffl( Relieving Slob Over Soil Cover ''' F 77;eyrr FGURE 11 Metal box ulverts with PCC relieving slabs. E :---'--4. --;.s-'-12e-.--1-1s-'-2 J24---' S'Spon- ft FG URE O Live-load moments for box ulverts without relieving slabs. Values of live-load rown and haunh moments an be derived from the total live-load moments by using the following equations: Mi L = p ' b.mtl b.mtt L= (! -P) RH b.mn hange in rown moment due to live load (kip-ft/ft), hange in haunh moment due to live load (kip-ft/ft), and haunh moment redution fator. The fator RH represents an allowane for load spreading longitudinally along the ulvert with inreasing horizontal distane from the load. ts value, shown in Figure B, was determined from the results of a full-sale field load test. Box Culverts with PCC Relieving Slabs PCC relieving slabs an redue the bending moments in box ulverts signifiantly. As shown in Figure 11, relieving slabs may be used aross the rown with no soil over, aross tbe rown with soil over over the slab, or above the ulvert with soil over between the bottom of the slab and the top of the ulvert. n the design proedure desribed in the following paragraphs, the onditions with soil over the slab and soil under the slab would be onsidered the same for purposes of analysis. (6) (7 ) Live-load moments for box ulverts with relieving slabs are shown in Figure 12. t may be seen that these moments are onsiderably smaller than the live-load moments for 1 ft of soil over over the rown. (Note that 1 ft of soil over is less than Hminl this line is shown only for omparison purposes.) All of the differene between the two urves an be attributed to the greater ability of the PCC relieving slab to spread the liv,e loads longitudinally along the axis of the ulvert. For H = 1 ft, the value of LL for a single 32-kip axle with four wheels is 6.4 kips/ft for soil over, and 2.5 kips/ ft for a PCC relieving slab. Thus the value of LL for the ase with the relieving slab is 4 perent, 2 ::; R 16 Jf! 12 :E -:; :r " 8, E Live Load Moments ore proportional to axle load. Curves shown orrespond to AL 32 kips, with 4 wheels on a sin9le axle. / H ft of Soil Cover-,\/",,,,,," / / / "" / ",,,.,,,.,,"'' " 4 B 12 16 2 24 S Span f t FGURE 12 Live-load moments for box ulverts with PCC relieving slabs.

Dunan et al. 39 of that for the ase with only soil over. This differene in the values of LL aounts for the entire differene between the two urves in Figure 12. The proposed design line for the ase with the PCC relieving slab in Figure 12 was alulated by using Equation 5 together with a value of LL = 2. 5 kips/ft. Thus the same design equation and the same values of the oeffiient KJ an be used for ulverts with and without relieving slabs; only the value of LL (or K4) needs to be hanged to reflet the effet of the slab as shown in Table 1. This somewhat surprising result is due to the transmission by the relieving slab of the live load diretly to the rown of the ulvert essentially as a onentrated line load. Although this effet was onsistent in the analyses, it is the authors' belief that these analytial results may somewhat underestimate the benefiial effets of a relieving slab. t would be desirable to perform field tests to explore this question and perhaps establish a basis for refining the design of box ulverts with relieving slabs. n ases the slab projetion beyond the edge of the box ulvert is greater than l ft, the slab is more effetive in relieving live-load moments. This effet is shown in Figure 13. By extending the slab 5 ft beyond eah edge of the box ulvert, the live-load moments an be redued to 75 perent of the values for l ft of projetion. t m required slab thikness, tb basi slab thikness (for a slab on soi l with no underlying ulvert) (see Table 2), RAL axle load orretion fator (see Table 3), Re = onrete strength orretion fator (see Rf Table 3), and 1.2 (for box ulverts with spans less than 26 ft), TABLE 2 Basi Slab Thiknesses Slab Thikness (in.) by Relative Compation a Unified Classifiation of Subgrade Beneath 1 95 Slab Perent Perent GW, GP, SW, SP, or SM 7,5 8, SM-SC or SC 8. 8.5 ML or CL 8.5 9. 3 Perent of standard AASHTO maximum dry density. TABLE 3 Axle Load and Conrete Strength Corretion Fators 9 Perent 8.5 9. 9.5 Axle Load Fator Single Axle Load (kips) Conrete Strength Fator Conrete Compressive Strength, f (psi) O 2 3 32 4 45 5.6.8.97.OD 1.5 D 1.15 3, 3,5 4, 4,5 5, 5,5 6, 1.19 1.15 1.1 1.5.OJ.97.94 P 5 =Slob Projetion - t FGURE 13 Effet of slab projetion on live-load moments. The rown and haunh live-load moments with PCC relieving slabs an be alulated by using these equations: 6ML =P Rp 6MTL 6MHL =(! -P) Rp 6Mn Rp is the moment redution fator for slab projetion and the othe r terms are as defined previously. The fator RH does not appear in Equation 9 beause the live load, at a value of 2.5 kips/ft for a 32-kip axle, is already spread uniformly aross the traffi lane. Thus no further horizontal spreading is possible, SMPLFED DESGN OF PCC RELEVNG SLABS PCC relieving slabs over metal box ulverts (see Figure 11) may be designed by using the simplified proedures desribed in the following paragraphs or by using other proedures that have proven effetive for loal onditions. The required thikness of the PCC slab may be determined by using the following equation: (8) (9) (1) f another slab design proedure is used, the slab thikness should first be determined based on onsideration of the underlying soils only (ignoring the presene of the ulvert), and the resulting pavement thikness should then be inreased 2 perent by multiplying this onventional free-field slab thikness by the fator Rf = l,2 to allow for the fat that the pavement is being plaed over a flexible ulvert. Use of the thikness adjustment fator (Rf) is based on finite-element analyses omparing stresses in slabs on soil without underlying ulverts with stresses in slabs overlying ulverts, and the reonunended value Rf = 1. 2 is appliable to metal box ulverts with spans of less than 26 ft, The length of the PCC slab should be at least 2 ft greater than the span of the ulvert over whih it is plaed, so that it projets l ft beyond the haunh on eah side of the ulvert. As disussed previously, slab projetions in exess of this 1-ft minimum result in a redution in ulvert moments due to live loads (see F i gure 13). The PCC slab should be wide enough to extend ompletely aross the area traffi is permitted, inluding traffiable shoulders, beause the live-load moments disussed previously assume the presene of the PCC slab in all areas subjet to traffi loads. Temperature reinforement is not used in slabs designed by this proedure. nstead, joints are formed or ut as shown in Figure 14 in order to ontrol temperature raking. Alternative requirements for joint spaings, joint details, reinforement, subbase quality and thikness, and base ourse may

4 Transportation Researh Reord 18 4 in. 1/2 Sealant Reservoir, per monulalurers raommendollon. Sawed, 1/8 in. to l/4 in. width, or premolded insert. <f. l'zzzz!z!l7zli!l1zi$z2z?zlllllll>-o- Oowel 1. Needed if!ruk traffi volume exeeds 3 per day. > Sub9rade Crok. Aqqre9ate interlok provides sulliionl toad transfer ii truk tralli volume is less!hon 3 per day. FG URE 14 Contration joints for PCC relieving slabs. be employed instead of those given in Figure 14 and Tables 2 and 3 if loal pratie and experiene indiate that the alternative requirements are aeptable and desirable. To prevent exessive urling stresses, whih develop when the top of the slab is ooled or heated in relation to the bottom, joints are needed at spaings equal to or less than those shown in Figure 14 and Table 4. TABLE 4 Dowel Sizes Slab Dowel Dowel Minimum Joint Thikness Dia meter Length 3 Spaing (L) (t) (in.) (in.) (in.} (ft) 6 3/4 14 12 7 7/8 14 14 8 1 14 16 9 1 1/8 16 18 JO l l /4 18 2 11 1 3/8 18 2 12 1 /2 2 2 Note: Smooth round steej bars equiva]ent to ASTM A61S or CSA GJ.12 are used. 8 Spaed at 12 in. enter to enter. Half plaed o n eah side of joint. One-half painted with lead or tar paint to prevent bonding with onrete. Joints should onsist of a slot extending onefourth of the way through the slab, with a sealant reservoir at the top, as shown in Figure 14. The joint an be sawed or preformed. The size and shape of the sealant reservoir should onform to the sealant manufaturer's reommendations. Dowels should be used to failitate load transfer aross joints if the volume of truk traffi exeeds 3 vehiles per day. Dowels are smooth round steel bars 14 to 2 in. long that are installed at mid-depth of the slab. Half of eah dowel is painted with tar or lead paint to inhibit bonding on one side of the joint. Reommended dowel diameters and lengths are shown in Table 4. f the subgrade material is a gravel or sand that is free of fines and has high permeability (Unified Classifiations GW, GP, SW, or SP), no speial 1rnhh<1se materiiil is needed. f the subgrade ontains appreiable fines (Unified Classifiations SM, SM-SC, SC, ML, or CL), a layer 4 in. thik of gravel or sand without fines or a layer 4 in. thik of ement-stabilized material should be used as subbase, To provide a good onstrution platform and to prevent pumping of material from beneath the pavement in wet weather, the top 4 in. of material beneath the slab should be ompated to 1 perent of the standard AASHTO maximum dry density. Stabilized materials, if used, should have minimum unonfined ompressive strengths of 7 psi. RECOMMENDED LOAD FACTORS Load Fators for Design To provide a margin of extra load apaity in box ulverts, the bending moments determined from the studies disussed previously are inreased by load fators to establish the required moment apaities for the rown and haunh setions. The purpose of these load fators is to provide extra load-arrying apaity in order to make box ulverts apable of arrying inadvertent overloads arising from unantiipated departures from the design onditions of over depth, bakfill quality, and vehile load. The magnitudes of these load fators are as follows: 1. For dead load (the loads imposed by fill over the top of ulvert), load fator = 1.5 and 2. For live load (the loads imposed by vehiles on the ulvert), load fator s 2 Although no method of design an ensure the safety of a ulvert under all unforeseeable irumstanes, inluding disregard of speifi over depth and vehile load restritions, these load fators have proven to be large enough to aommodate the normal unertainties in site onditions and a degree of inadvertent deviation from speified over and load onditions. The strutural plate thiknesses, the rib sizes, and the rib spaings in the haunh and rown set ions should be seleted to provide plasti moment apaities at least equal to the design moments multiplied by the load fators given earlier. The plasti moment apaities used for design should be on irmed by laboratory testing using speimen lengths that result in bolt shears omparable with those antiipated in the most severe field loading onditions. The equations and figures disussed previously an be used to estimate onservative values of bending moments in the rown and haunh setions of box ulverts. To provide a margin of safety for design, these moments should be inreased by applying the load fators disussed earlier. The omponents of M and MH due to dead load.are multip l i ed by 2. to determine the design moment s Meo and MHD as shown by the following equations: Me o : 1.5 Mee + 2. 6 M L MH o : J5 MH e + 2D 6MH L (11) (12) Meo is the rown design moment and MHo is the haunh design moment. These design moments are used in seleting strutural plate thiknesses, rib sizes, and rib spaings for the rown and haunh setions. The strutural setion seleted should have a plasti moment apaity (Mpl at l east as large as the design moment. For exeptional loading onditi ons it may be appropriate to use other load fators. For example, if a box ulvert is to be subjeted to a small number of appliations of an exeptionally heavy vehile, it might be onsidered aeptable to use a load fator smaller than 2. for this loading. The load fators used in box ulvert design an be related to the AASHTO load and material fators as follows: LF: -r rm (13) LF y load fator as defined in the preeding paragraphs, AASHTO load fator,

Dunan et al. 41 S AASHTO load oeffiient, and AASHTO apaity modifiation fator. The values of LF = 2. for live load and LF = 1.5 for dead load orrespond to values of SL = 1. 67, SE = 1.25, y = 1.2, and = 1. in the AASHTO system. These are ompared with the values speified by AASHTO for various types of strutures in Table 5. TABLE 5 Comparison of AASHTO and Reommended Design Fators Fator Live-load oeffiient (JL) Dead-load oeffiient (f3d Load fator (')') Capaity modifiation fator( ) mpat fator ()(%) AASHTO 1.-2.2 1.-1.5 L-1.3.67-3 Reommended 1.67 1.25 1.2 LOO The values of the oeffiients that are used in the reommended design proedures have been seleted onsidering that aluminum box ulverts reeive onsiderable engineering attention and are more arefully onstruted than small onventional metal ulverts. The value of = 1. was seleted onsidering that the aluminum strutural properties are minimum property values rather than typial values as used in onnetion with AASHTO designs. The impat fator of perent is believed justified by the strong influene of soil-struture interation in box ulverts: Under rapid loadings well-ompated soils reat with inreased stiffnes s and a great deal of inertia, resulting in greater rather than smaller margins of safety under loads that are applied for brief periods of time. The experiene with box ulverts to date and the omplete absene of problems attributable to design defiienies provide onsiderable support for ontinued use of the reommended fators for box ulverts. DEFLECTONS N SERVCE Defletions of aluminum box ulverts, like defletions of other flexible metal ulverts, are dependent on many fators, inluding the type of bakfill, bakfill ompation, water ontent of bakfill, type of pavement, vehile weight, and number of load repetitions. nformation on defletions of box ulverts omes from three soures--finiteelement soil-struture interation analyses, field loading experiments and measurements, and observations of box ulverts in servie. These studies and observations indiate the following: 1. The better the quality of the bakfill, the more densely it is ompated; and the lower its water ontent, the smaller are ulvert defletions during plaement of fill over the rown and during vehile loading. 2. Stiff pavements, mostly notably PCC pavement slabs, redue defletions as ompared with thin flexible pavements or no pavement over the top of the ulvert. 3. Live-load defletions inrease in proportion to the vehile axle load. 4. Defletions are larger under the first appliation of a partiular live load than under subsequent appliations of the same load. After many load appliations defletions are likely to be about onefourth as large as under the first appliation of the same load. The defletions shown in Figure 15 are intended to provide an estimate of the possible defletions of aluminum box ulverts in servie. They orrespond to onditions of minimum-quality bakfill, no pavement, and H-2 loading. Under most servie onditions defletions will be less than those shown in Figure 15. 3 3 _ J "' Li_ "' u -"" 21 Eslimaled Range for - "' "' "" u 2 a 2 _ Cover Depths f rem - =-=-.9 _J u= Q)i.::: u Q). "' "'"' u ;;:: -' fl. 'C "' "' ; -; O '"' o "' o- 1.- - 1 2 3 1 2 3 s Span- ft FGURE 15 Estimated defletions in servie. SUMMARY AND CONCLUSONS Corrugated metal box ulvert strutures were developed for onditions hydrauli requiremp.nts neessitate large areas for water onveyane and vertial learane is limited. The methods used for design of these strutures have evolved through finite-element soil- struture interation analyses, laboratory and field experimental studies, and field experiene. As of August 1984 about 1, aluminum box ulverts were in servie. A key element in box ulvert design is bendingmoment apaity. Design bending moments for different spans, over depths, and vehile loads have been established by finite-element soil-struture interation analyses and onfirmed by field loading tests. These are inreased by load fators to determine moment apaities for the rown and haunh setions of box ulverts. Field experiene of approximately 4, struture-years indiates that box ulverts designed by these proedures have performed well. REFERENCES 1. J.M. Dunan and C. -Y. Chang. Nonlinear Analyses of Stress and Strain in Soils. Journal of the Soil Mehanis and Foundations Division, ASCE, Vol. 96, No. SM5, Sept. 197. 2. J.M. Dunan and G.W. Clough. Finite Element Analyses of Port Allen Lok. Journal of the Soil Mehanis and Foundations Division, ASCE, Vol. 97, No. SM8, Aug. 1971. 3. J.M. Dunan. Behavior and Design of Long-Span Metal Culverts. Journal of the Geotehnial Engineering Division, ASCE, Vol. 15, No. GT3, Marh, 1979, pp. 399-418. 4. J.M. Dunan and R.H. Drawsky. Design Proedures for Flexible Metal Culvert Strutures. Geotehnial Engineering Researh Report UCB/GT/83-2. University of California, Berkeley, Feb. 1983. Publiation of this paper sponsored by Committee on Subsurfae Soil-Struture nteration.