Implementation of a New Flexible Pavement Design Procedure for U.S. Military Airports

Transcription

1 Fourth LACCEI Internatonal Latn Amercan and Carbbean Conference for Engneerng and Technology (LACCEI 006) Breakng Fronters and Barrers n Engneerng: Educaton, Research and Practce -3 June 006, Mayagüe, Puerto Rco. Implementaton of a New Flexble Pavement Desgn Procedure for U.S. Mltary Arports Carlos R. Gonale, PE Research Cvl Engneer Engneer Research and Development Center Vcksburg, Msssspp, USA Carlos.R.Gonale@erdc.usace.army.ml Dr. Walter R. Barker, PhD, PE Research Cvl Engneer Engneer Research and Development Center Vcksburg, Msssspp, USA Walter.R.Barker@erdc.usace.army.ml Abstract The U.S. Mltary (Army, Ar Force and Navy) thckness desgn procedures for flexble arport pavements are based the CBR (Calforna Bearng Rato) method. Ths method was orgnally developed n the 940 s for desgn of flexble pavements to support the then new heavy bombers. The orgnal arfeld desgn curves were an extrapolaton, based on shear stress, of the Calforna pavement desgn curves for hghway pavements. The extrapolated curves were modfed and verfed by extensve full scale feld testng. The classcal CBR equaton was then developed from these curves. Recent research conducted at the U.S. Army Engneer Research and Development Center revealed that the classc CBR equaton can be derved from a stress dstrbuton represented by Frohlch s stress concentraton factor equal to. Ths dscovery led to the reformulaton of the classcal CBR equaton nto a more general equaton n terms vertcal stresses as computed wth a stress concentraton factor. Ths paper presents the mplementaton of ths new formulaton nto a more comprehensve desgn procedure for arport pavements. The paper wll present a bref descrpton of the development of the new procedure, flowcharts descrbng ts mplementaton, and pavement thckness comparson between the old and the new procedures. The mportance and postve mpact to the U.S. Mltary by the adopton of ths new methodology wll also be presented and dscussed. Keywords CBR equaton, Vertcal Stress, Flexble Pavement Desgn, U.S. Mltary, Arfeld, Implementaton. Background The Calforna Bearng Rato (CBR) procedure has been the prncpal method used for desgn of flexble pavements for both mltary roads and arfelds snce ts development n the 940s. Ths procedure has been very successful n the mltary, and t has been currently used throughout the world. Its smplcty, practcablty, hstory, and feld experence has motvated the U.S. Army Corps of Engneers to contnue

2 promotng and mprovng ths technology. The crtera currently mplemented s represented by equaton t α ESWL A 8. CBR π () where: t desgn thckness; ESWL equvalent-sngle-wheel load; CBR represents the sol strength at the depth t A contact area for the ESWL whch s assumed be a constant and equal to the contact area of a tre n the gear assembly α thckness adjustment factor that s a functon of traffc volume and number of tres n the tre group Equaton can also be wrtten n the form as shown n Equaton, n whch β s defned by Equaton 3, and can be related to traffc volume n terms of coverages as shown n Fgure. ESWL A t () β CBR π σ π β (3) CBR 00 FAA TEST FACILITY 6-WHEEL FAA TEST FACILITY 4-WHEEL MWHGL 747 GEAR MWHGL C-5 GEAR COMPUTED BETA BASED ON n log C log β log C R 0.54 ALL SINGLE-WHEEL DATA FIT THROUGH DATA TRAFFIC LEVEL IN COVERAGES Fgure. Beta (β) as Functon of Traffc Volume n Terms of Coverages For a gven traffc level of an ESWL, the value of β can be determned from Fgure, whch may then be used n Equaton to compute the requred pavement thckness. It was shown by Barker and Gonale (006), that Equaton and thus Equaton represent a specal case of the general soluton as gven n Equaton 4 for the vertcal stress n a half-space. The general soluton for vertcal stress (σ ) n a half-

3 space due to a pont load (P ) at the surface s gven n Equaton 4. Fgure provdes the descrpton for the parameters of Equaton 4. σ wheels n P π R cos n θ (4) P θ R r Fgure. Parameter Defnton for Equaton 4. The factor n n Equaton 4 s Frohlch s concentraton factor whch modfes the dstrbuton of vertcal stress n the half-space system. When factor n s equal to 3, Equaton 4 represents Boussnesq stress dstrbuton; for values of n less than 3, Equaton 4 represents stress dsperson; for values of n greater than 3, Equaton 4 represents a stress concentraton. It has been shown (Barker and Gonale,006) that the current CBR crtera are based on a factor of n equal to. For the specal case of stress under the center of a unform crcular load, Equaton 4 can be rewrtten n the closed-form gven by Equaton 5, n whch r represents the radus of the loaded area and σ 0 s the surface pressure appled over the loaded area. σ σ (5) 0 n r + Although the current CBR desgn crtera are based on a Frohlch s concentraton factor of, t has been argued by Barker and Gonale (006) that the n should be a functon of the subgrade CBR. Barker and Gonale also proposed to defne n as a functon of CBR as shown n Equaton CBR n 6 (6) Equaton 4 s the bass for the general case soluton for computng the vertcal stress n a half-space due to mult-wheel tre groups. Computer software has been developed for computng, usng numercal ntegraton technques, the vertcal stress ( σ ) at the top of subgrade due to a mult-wheel tre group. For the specal case of a sngle wheel, the stress can be computed n a closed manner usng Equaton 5. For 3

4 sngle wheel desgns, Equaton 5 can be rearranged such that the requred thckness may be determned drectly (Equaton 7). t r n β CBR π p (7) For a mult-wheel gear the stress must be computed for dfferent postons wthn the gear to nsure the maxmum stress under the tre group s determned..0 New Performance Crtera The desgn crtera, to be referred to heren as the β -crtera, are to be defned as a relatonshp between traffc volume n terms of coverages to falure and the β parameter as defned by Equaton 8. The β parameter was prevously defned by Equaton Traffc Volume.778 log( β ) log( C ) (8) log( β ) Traffc volume s defned n terms of coverages as descrbed by the methodology developed by Brown and Thompson; and descrbed n an nstructonal report by Taboa Perera (97x). The methodology as presented by Barker-Gonale (006) s defned by Equatons 9 and 0. Usng Equatons 9 and 0 the traffc n terms of coverage (C x ) at partcular pont, defned by an offset dstance (x o ) from the center-lne of the traffc lane, can be computed for each tre group. C P x n o w xo + w xo m P σ x x σ e π dx (9) (0) The other varables n Equatons 9 and 0 are defned as: P s the probablty that a tre () wll traverse a pont; x s the dstance from the centerlne of the arcraft to the tre; w s the wdth of a tre; σ s the standard devaton of the traffc dstrbuton, and n o s the number of operatons of the partcular arcraft. The traffc dstrbuton s represented by the wander-wdth defned as the wdth of pavement n whch 75% of the traffc s appled. The standard devaton wll be one-half of the wander-wdth dvded by.5. For the arfeld runways and taxways, wander-wdths of 70 and 40 nches respectvely are used for the traffc dstrbutons. When desgnng a pavement for traffc of a sngle vehcle or arcraft, the desgn coverage level s found by computng the coverage levels at varous ponts across the pavement and selectng the maxmum coverage level for desgn. 4

5 3. Mxed Traffc For desgn of pavements consderng a mxture of vehcles or arcraft types, t s necessary to combne the effects of the dfferent loadngs and traffc volumes. Ths s to be accomplshed through the use of the cumulatve damage concept (Mner s hypothess). In the cumulatve damage concept, the damage caused by a sngle operaton of a vehcle or arcraft s the nverse of the allowable number of operatons, and can be summed to obtan the damage for all operatons and all vehcles/arcraft. The cumulatve damage concept s represented by Equaton. D total vehcles n C () In Equaton, D total s the total cumulatve damage for all vehcles; n s the appled coverage level for the th th vehcle, and C s the allowable coverage level of the vehcle. The pavement thckness s to be selected such that the total cumulatve damage shall not exceed one. Snce computng a value of requres a value of thckness, the desgn process requres an teratve procedure of successve approxmaton untl a value of D s obtaned that s suffcently close to one. total C 4.0 Desgn Procedure The general procedure for desgn of flexble pavements based on the CBR s descrbed by the flow dagram gven n Fgures 3 and 4. The basc CBR desgn procedure shall reman unchanged except for the methodology for computng allowable coverage levels and handlng mxed traffc. Procedures for selectng parameters, such as materal propertes, compacton requrements, desgn CBR, loads, tre pressures, and vehcles operatons, shall be the same as n the current CBR procedure. The desgn procedure can be descrbed for four loadng cases: () One sngle-wheel gear () Mxed traffc composed of sngle-wheel gears (3) One mult-wheel gear (4) Mxed traffc composed of mult-wheel and/or sngle-wheel gears Each of these loadng cases s dscussed n detal below. 5

6 Select Pavement Offset Postons X j ; j, k Compute Appled Coverages, n j for Arcraft at poston Traffc Data for Arcraft, P p ; w ; x ; m N o ;, l Pavement Geometrcs Identfy Secton (Runway, Taxway, Assume thckness, t of Pavement to Start Iteraton Process m Compute Damage n, j at d j Poston, C Compute Allowable Coverages, C for Arcraft, m Adjust Thckness Select Poston wth Maxmum Damage, d Is max? No Performance Yes END Fgure 3. General Flow Dagram for Flexble Pavement Desgn Arcraft Pavement Thckness Tre Load Contact Area Tre Coordnates Compute Stress Concentraton Factor CBR n Compute Vertcal Stress on Top of Subgrade wheels n P n σ cos θ π R Subgrade CBR Compute β σ π β CBR Compute Allowable Coverages.778 log( β ) log( C ) log( β ) Allowable Coverages, Fgure 4. Performance Model for the CBR Desgn Procedure 4. Desgn Procedure for One Sngle-Wheel Gear When a flexble pavement s desgned based on a sngle-wheel gear, the thckness can be determned drectly by Equaton 7. In ths case, the traffc volume used to compute the value of β can be determned from publshed pass-to-coverage ratos, or by Equaton whch s a smplfed verson of Equaton 0. 6

7 w C σ n o () In ths equaton, σ takes the value of and for taxways and runways, respectvely; w s the wdth of the contact area of a tre, and n o s the number of operatons of the arcraft. 4. Desgn Procedure for Mxed Traffc Composed of Sngle-Wheel Gears The desgn procedure for mxed sngle-wheel gears s slghtly more nvolved than desgnng for one sngle-wheel gear. In ths procedure, the cumulatve damage concept must be employed and varous locatons across the pavement must be chosen to determne the locaton of the maxmum damage. The frst step n the recommended procedure s to determne the requred thckness for each vehcle usng the procedure outlned for a sngle-wheel gear. The maxmum thckness obtaned can be used as the startng thckness for the teratve process for determnng the requred thckness. In most cases, the fnal thckness s not lkely to be much thcker than the maxmum thckness obtaned for the ndvdual arcraft. For the startng thckness the cumulatve factor s computed for varous locatons (to locate the poston of the maxmum damage) across the pavement traffc lane. It should be noted that the poston of maxmum damage wll normally occur under the center of the traffc dstrbuton of the tre requrng the maxmum thckness of pavement. In computng the cumulatve damage, the value of β for a gven thckness s frst computed for each vehcle. Equaton 7 can be rearranged n the form of Equaton 3 below, such that, gven the thckness, β can be computed drectly for each vehcle. n r π p β + t (3) CBR Wth the value of β computed, the allowable traffc n terms of coverages s computed based on the performance crtera gven by Equaton 8. It should be noted that the allowable coverages for a partcular vehcle wll reman constant across the traffc lane, thus t wll only be necessary to compute the appled traffc for the dfferent postons. The traffc appled by each vehcle and for each poston s computed based on the general equaton for coverages. Havng determned the appled traffc ( n ) and the allowable traffc ( C ), the damage factor can be computed by Equaton. By selectng the ntal thckness n ths manner, the damage factor for the ntal thckness wll be less than one, thus the second teraton wll nvolve ncreasng the thckness and re-computng allowable traffc ( C ) for the new thckness. It should be noted that for a sngle-wheel gear, the locaton for the maxmum damage wll not change from teraton to teraton and the appled traffc wll reman at the same locaton for all teratons. 4.3 Desgn Procedure for One Mult-Wheel Gear The desgn case for one mult-wheel gear s smlar to the desgn procedure for one sngle-wheel gear n that t s not necessary to consder dfferent postons across the traffc lane (other than to determne the pass-to-coverage rato), nor s the cumulatve damage computaton necessary. The dfference between the two cases s that the thckness can not be drectly computed but must be determned by an teratve procedure. The basc procedure s that the desgn traffc volume n terms of coverages s frst determned. From the desgn traffc and desgn CBR, the value of β s determned from the β -crtera. Usng Equaton 4 below, the allowable vertcal stress (σ ) allow at the top of the subgrade s computed. 7

8 β CBR ( σ ) allow (4) π The desgn problem s then a problem of fndng the thckness for whch the stress at the top of the subgrade, due to the desgn arcraft, s approxmately equal to the allowable stress. For mult-wheel gears, the thckness can not be determned drectly but must be determned usng an teratve procedure. For a startng thckness, t s suggested that the thckness be computed usng Equaton 7 for a sngle wheel of the gear. Ths thckness wll be somewhat less that the fnal thckness, but, as was the case for the mxed sngle-wheel gears, the fnal thckness wll be somewhat greater than the thckness requred for a sngle tre. The vertcal stress at the top of the subgrade for the ntal thckness wll be compared wth the allowable stress. If requred, the thckness should be ncreased and the process repeated. Wth a few teratons the data from the computaton could be used to estmate the thckness for whch the computed stress would be approxmately equal to the allowable stress. 4.4 Desgn Procedure for a Mxed Traffc Composed of Mult-Wheel Gears The desgn procedure for mxed traffc composed of mult-wheel gears represents the general case as shown n Fgure 3. In general, the thckness desgn for mxed mult-wheel gears nvolves computng the traffc volume, n terms of coverages ( n ), for each vehcle at offsets across the traffc lane. Usng an assumed thckness, the allowable traffc volume ( C ) for each vehcle s computed as has been dscussed prevously. For a gven vehcle, the allowable traffc ( C ) wll be constant across the traffc lane. The cumulatve damage factor can then be computed usng Equaton for varous offsets across the traffc lane. The ntal thckness for the teratve process can be determned drectly usng Equaton 7 and the data for the tre havng the heavest loadng. The teratve process s contnued, as descrbed for the specal cases, untl the thckness correspondng to a maxmum cumulatve damage factor s approxmately equal to one. 4.5 Software for the Desgn Procedure The algorthms and equatons for the new CBR desgn procedure have already been developed and are avalable from the Arfeld and Pavements Branch, ERDC Vcksburg, MS. The new desgn procedure wll be ncorporated nto the PCASE software for the desgn of arfeld flexble pavements. 8

9 4.6 Comparson Between Current and Proposed Desgn Procedure Fgure 5 llustrates a thckness desgn comparson between the current desgn procedure and the new proposed CBR procedure based on vertcal stress. Ths comparson was done for a range of subgrade CBR values and 0,000 coverages of the C-7 arcraft. It can be observed that for low subgrade CBR values, the new desgn procedure wll yeld thnner pavement sectons than the current procedure. However, at hgher CBR values (.e. CBR>0 for ths partcular arcraft), the pavement thckness resultng form the new procedure s approxmately equal to or slghtly hgher than the current procedure. Ths typcal result shows that for low CBR values, the current mplementaton of the CBR procedure tends to overestmate the pavement thckness. 70 Desgn Total Thckness Above Subgrade, Inches C-7 Proposed Procedre Current Procedure Subgrade CBR, % Fgure 5. Comparson Between the Current Desgn Procedure and the New Proposed Procedure 5.0 Conclusons A new procedure for the desgn of flexble arfeld pavements has been presented. Ths procedure uses a stress-based approach that s consdered to be more robust than the current mplementaton. Ths new CBR mplementaton brngs ths methodology to par wth exstng state-of-the art desgn procedures based on layered elastc systems. It has been proven that the new renovated CBR procedure has a mechanstc bass whle stll keepng ts smplcty of use and mplementaton. References ASCE (950). Development of CBR Flexble Pavement Desgn Method for Arfelds, A Symposun. Paper No. 406, Transactons, Vol. 5, 950, p.453. Barker, W. R., and Brabston, W. N. (975). Development of a Structural Desgn Procedure for Flexble Arport Pavements, Techncal Report S-75-7, U.S. Army Engneer Waterways Experment Staton, Vcksburg, Msssspp Barker, W.R., and Gonale, C.R. (006). Independent Evaluaton of 6-Wheel Alpha Factor Report, Letter Report to the Federal Avaton Admnstraton, U.S. Army Engneer Research and Development Center, Vcksburg, Msssspp. 9

10 Barker, W.R., and Gonale, C.R. (006). Renovaton of the CBR Procedure, Under Preparaton, U.S. Army Engneer Research and Development Center, Vcksburg, Msssspp. Jumks, A. R. (964). Mechancs of Sols. D. Van Nostrad Company, Inc, Prnceton, New Jersey, Chapters 4 and 5. Jumks, Alfred R. (969). Stress Dstrbuton Tables for Sols Under Concentrated Loads. Engneerng Research Publcaton No. 48, Rutgers Unversty, Lbrary of Congress Catalog No Fne, L., and Remngton J. A. (97). The Corps of Engneers: Constructon n the Unted States, Unted States Army n World War II, Techncal Servces, Chapter XIX, Lbrary of Congress Card Number: , Offce of the Chef of Mltary Hstory, Washngton, D.C. Porter, O. J. and Company (948). Accelerated Traffc Test of Stockton Arfeld, Stockton, Calforna, Department of the Army, Corps of Engneers, Sacramento Dstrct, Stockton Test No., Appendx D. Ulldt, Per (998). Modelng Flexble Pavement Response and Performance, Copyrght 998, Polyteknsh Forlag Waterways Experment Staton, Corps of Engneers, U. S. Army, Vcksburg, Msssspp (956). Mathematcal Expresson of the CBR Relatons, Techncal Report No Authoraton and Dsclamer Authors authore LACCEI to publsh the papers n the conference proceedngs. Nether LACCEI nor the edtors are responsble ether for the content or for the mplcatons of what s expressed n the paper. 0