- I

ECONOMIC IMPLICATIONS O F .k. r I 1NITEI) STATES SI'I RSONIC TRAN PORT

AIRCRAFT UPON AIRPORTS AND

-- T ENROIUTE SUPPORT SERVICES

- Volume I\1

Airport Pavement Requirements for

Large Commercial Aircraft

PFRC R-890

31 l)cember 1966- I-

II " I'Prcparcd for-

Offc e Of uperso,,ic "ran -port Ie,'opme, , .

.... Fe~1:~ dc.raI AIat i,,n A~,,y;

-PLANNING RESEARCH CORPORATIONLOS ANGELES, CALIFORNIA WASHINGTON, D.C.

low

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I~lJ

jO F e 1 t ric Pu r 0ra I

II

ECONOMIC IMPLICATIONS OF AUNITED STATES SUPERSONIC TRANSPORT

AIRCRAFT UPON AIRPORTS AND3 ENROUTE SUPPORT SERVICES

VOLUME IVAIRPORT PAVEMENT REQUIREMENTS FOR LARGE

COMMERCIAL AIRCRAFTII PRC R- 890

31 December 1966

This study has bee prepar by the Planning Research Corporation for the Office

of Supersonic Transport Development, Federal Aviation Agency, under ContractNo. FA-SS-66-15. Contents of this study reflect the views of the contractor whois responsible for the facts and the accuracy of the alta presented herein, and donot necessarily reflect the official views or policies of he FAA. This study doesnot constitute a standard, specification or regulation.

By

IRonald E, MorrisJohn B. Burcham Jr.George W.S. JohnsonKelly J. BlackRichard C. HannonKatherine L. Lehmann

PLANNING RESEARCH CORPORATION

LOS ANGELES. CALIF. WASHINGTON, D.C.

I

1IV~%,lk VbvJ--

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for any puriote othe ir th1V ill conec'iJ'Cui wih i d fin it cly rleat ue

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thereby incurs no responsibility uor any ebi. ig-,t ion wiatsocvcr;

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DIST. ,'A!.

This study has been prepared for the Office of Suprsonic Transport Development,

Federal Aviation Agency, by the Planning Research Corporation. It nay not bedistributed or in any way revealed outside of PRC, nor may any portion of it be

copied for any purpose without the written approval of:

Director of Supersonic Transport Development

Federal Aviation AgencyWashington, D. C. 20553

PRC R-890iii

ABSTRACT

Comp"lementing the three-volume analysis of the potential eco-nori impact of a United States SST upon airports and enr,,te sup-port services, Volume IV examines ai Dort pavement requirementsfor large commercial aircraft: Boeing models 707-320, 747, 2707;Lockheed models L-500 and L-2000; Douglas models DC-8-55 andDC-8-63: and the Anglo-French SST, Concorde.

PRC R-890V

TABLE OF CONTENTS

Page

ABSTRAC'1.................... .. ...... ...... .. .. . ...

A. Disparate Methods for Determining Pavemenz,Stress Capabilities......... ..... . .. . .. .. .. .....

1. Survey of Pavement Analysis Methodologies 1

a. Flexible Pavement Analysis.... .. .. .. ..... 2

(1) FAA Method of Calculating

Pavement Strt ss .. ..... .........

(2) Corps of Engneers Method. ... ..... 9

(3) U.S. Air Force SEIL Method ....... 15

b. Rigid Pavement Analysis. ............ 15

(1) The 'Westergaard Analysis. .. ....... 15

(2) Infiuence Chart .. ... ............ l

(3) FAA Method. .... ............ 18

(4) Portlard Cement Association

M~ethod .. ........ .......... 21

() Load Classification NumberMethou .. ........ ......... 23

2. The Problem of Nonuiniform, Pavement AnalysisTechniques to Aircraft Designers .. .. ....... 24

a. Aircraft Landing Gear Design as itFunction of Pavement St rength. .. ......... 4

b. Absence of Correlation AmiongIPavement Analysis Methods. .. .. ....... 24

ftIUO

PRC R-890

TABLE OF CONTESTS(Continued'

Pag

Compatibility oi Present Airport Pavc.-entsWith Large Commercial Aircraft .......... 28

a. Methodology Uscd in Computations ...... .. 28

(1. Rigid Pavement ...... ............. 28

(2) Flexible Pavement ................ ... 29

B. Aircraft Pavement Loading Effects ................ .... 30

I

I

~I

0 F111tPRC R-890

vii

LIST OF EXHIBITS

1. Classification of Soils for Airport PavementConstruction ............ ........................ 3

2. Airport Paving Subgrade ClassiiicatLun .... ..........

3. Development of Flexible Pavement Curves,Dual-Tandem Gear ....... ..................... . ... 6

4. Load Distribution and Tire Imprint Data .... ......... 7

5. Design Curves, Flexible Pavement, Dual-TandemGear .............. ............................ 8

6. Flexible Pavement Design Curve for Convair 880 ....... 10

7. D-velopnent 'f Design Curves for a ',-Kip Loadion 1B-29 Dual Wheels ......... .................... 11

8. Dual-in-Tandem Example Reanalysis ... ........... ... 11

9. Deflection Factor F For Uniform Load Radiusr at Pents fbeneath x Axis .... ............... ... 13

10. Flexible Pavement I)esign Cwrves for Taxiways ..... .. 14

11. Approximate Interrelationships of SoilClass ification Systems .......... ................... 17

12. ;;'. liienc e Chart for the Moment Mn I Cont r tePavement Due to a Load in the Interior of the Slab . . . .

13. Design Cu rves, Rigid Pavement, Critical Area .. ..... 20

14. Portland Cement Association Design Chart ........

is. Atte lpted Correlation of Subgrade Tests atFifteen Maior Airports ..... .................. ...

I t. I-,2000 Pavenient Loading Suinm ary ...........

7. 13.-2000 Flexible Pave men t Critical Thickness.FAA Method . . . . . . . . . . . . . . . . . . . . . . . . Q

PRC R-890viii

LIST OF EXHITMITS(Continued)

18. L-?000 Flexible Pavement Critical Thickness,CBR Method ......... ......................... ... 33

19. L-2000 Rigiu r-aveient Stress, Xo esirgaarci Metnod • • 34

20. B-2707 Pavement Loading Summary .... ............ ... 35

21. B-2707 Flexible Pavement Critical Thickness,FAA Method .......... ......................... 3,

22. i-Z707 Flexible Pavement Critical Thickness,C5R Method ......... ........................ ... 37

23. 1B-2707 Rigid Pavement Stress, Westergaard Method • . 38

24. Concorde Pavement Loading Summary ........... 30

25. Concorde Flexible Pavement Critical Ihickness,FAA Method .......... ......................... 4

ft,. Concorde Flexible Pavement Critical Thickness,CPR Method ............ ........................ 4

27. Concorde, Rigid Pavement Stress. WestergaardMethod ............. ........................... 42

28. "-747 Pavement Loading Surmmarv. ..... ............ 43

2"). 747 Fl'exible Pavement Crit ical 1 hit kt es,"AA Met hod ......... ........................ ... 44 I

10. !'-747 F'exible Pavement Critical Thikness.

CI R Met hod. . .......... ......................... Ii1. 1'.-747 Rigid Pavement Strcss., Westerpaard Methok! .... 4

j2. L-; 00 Pavement Loading Summary ................... 4-

13. 1.-',00 Fltxible Pavement Critical Thickness.FAA Method ......... .......................... 4I

rroolla AI

.0i

PRC R-890ix

LIST OF EXHIBITS(Continued)

Page

34. L-500 Flexible Pavement Critical Thickness,CBR Method ......................... 49

35. L-500 Rigid Palement Stress, WestergaardM-thod .......... ........................... .... 50

36. DC-8-63 Pavement Loading Summary ............. .... 51

37. DC-8-b3 Flexible Pavement Critical Thickness,FAA Method .......... .......................... Z

38. DC-8-63 Flexible Pavement Critical Thickness,CBR Method ......... ........................ ... 53

39. DC-8-63 Rigid Pavement Stress, WestergaardMethod .......... ........................... .... 54

40, B-707 Pavement Loading Summary ................ .... 55

41. 1-707 Flexible Pavement Critical Thickness,FAA Method ......... ......................... .

42. B-707 Flexible Pavement Critical Thickness,CBR Method ............ ........................ 57

43. 1-707 Rigid Pavement Stress, WestergaardM ethod . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

44. DC-F-SS Pavement Loading Summary ... ........... . ...

4 . DC-8-5S Flexible Pavement Critical Thickness,FAA Method ......... ......................... 0

4t,. DC-8-cS Flexible Pavement Critical Thickness,CBR Method ......... ......................... .

47. DC-8-;5 Rigid Pavement Stress. Wes:ergaardMet hoi .. .......... ............................ .

I

PPC R-H9O

A. Dibjarcate Methods for Determining Pavement Stress Capabilities

The rapid growth of commerciai aviation has brought about many

technological changes in transport aircraft. These changes have ir.-

cluded large increases in rangc, speed, and aircraft size. However,

since ranges have become adequate for most operations and speed ca-

pability has surpassed the speed of sound, the outlook lor f-ature tech-

nological changes to a Ireat extent concerns increases in aircraft size.

Even in the case of the super.,unic transpo-t in wvhich a three -fold

speed increase is planned, the increase in size is also very important.

The weights predicted for transport aircraft about lQ8O are in some

Case's as MtUch as thrce *.nes that of todiy ' 5 heaviest comne rcial air-

planes. The tu, hniological f ea-sibhty of such foreca sts ha s lI rought

'Ibout reali? ition of the need for studies concerning the stress cap.ahili-

ities of pavemi-el' s at m:Ijor airports in et.lation to the ex~ eptional

loads i.%hich inay be imiposed uI',On them. The necessity for extenisive

research cone e rnini Li !nding gear flotation chara, teristics has been

recogniized and! the maijority of airc raft mianilacture rs have alreAdy

pe rf.o rnited somev research in this area.

Investigation of thec methods used to compart- pavcment strength

and the potential load to be imposed by spec ific a irc raft re veals con -

side rac te un'fus ion. Therefore, before -A recommendation tor the uise

of Lt specific mtstliodjoigy can be made, it is necessary to SLummnarl.~e

and CoMpare the ts -. era I accepted inethods for per n orm lug these

c alIc ulat ionis.

1. Siir-vev of P avemeiCnt Anal~svt Met ,koqfojogi E

T k , iu sme-thodol og ics f or Laiculaiit g p& t'e rr, stress

and I hi ~ ness requiroe nts ,an he divided into tmwo areas, Accordin

o the tvo mai ?TUzlgroup'ngs of pa Diverent t vpe a. Thes e types a ire: flex

bi pav(ement, ',Ohi ch is defined asa a mi xtu re of bitunti n''li mater ial

and aggregate overlaid on one or more base And subbase cotirses Lk

PRC R- 90

high-quality granular mnateriail, and zigid pavement or concrete,

which nr-ay or may not iaclude an. undieriying subbase course, In the

discussion o; flexible pavemrgnt which folicw5, the nethod of determin-

ing stre5s and r* uired pavement thiceness which is endorsed by the

Federal Aviation Agency will be treated fnrst. in approach developed

by the U.S. Army Corps of Engineers ,"then be rnr-rized, ard

the U.S. Air Force (SEFL) nicthod which was used for flotation analv-

ses of the military C5A will be deocribcri. The pioneer work of

Dr. H. M. Westergaard :id Dr. Gerald Pickett on rigid pa,.-enent

analysi3 will be surmarized and an explianation vi the adaptation,: of

their work by the FAA and by the Portland Cernent As.-')iati-.,n will

be presented. The Load Clas: ficaton Nurnbe: (LGN} veth-d which

is used in the British Isles will be rnentio!.cd.

a. Flexible Patvei-ent AnaL :ii,

(1) FAA M.e"od of ,a-cu: a avericnt Stre e

The Fed. rai. Avi,im Ai[e',:-y advisory circular

AC150/5320-6 entitled Airport Paving; which was po;Aished in Jun-

1964, sets forth the basic concepts involved i,, 'he FAA method of

calculating pavement stress -.nd -:equired thickness. The de.ermination

of soil characteristics and thei:r evaluation arid claosifi:ation are cen-

tral to this method. Exhibit I prc'sents the clacsification of soiis

recommended by the FAA. It is noted that this classification not only

includes an indication of the relative coarseness of the samples, but

aso includes the liquidity and plasticity factors. The total of these

three, factors is represented by an E number which ranges from E-1

through E-13. When combined with factors for drainage and frost as

shown in Exhi' it 2, the E numbers can be translated into F numbers

(or R numbers for rigid pavement). It is evident that a sample of a

particular soil group may fall in one of several subgrade classes.

For t xample, soils of the E-5 group may be classed is F-I subgrade

f PRC R-8903

.~ 0 0

a a +

U ~4.JNJ(04' r- LI :DO 00 0

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a -I NJ N-e '

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_ _ _ _ _0u j

enk r-wCy-

PRC R-8904

for good drainage and no frost, F-2 for good drainage and severe

frost, F-3 for poor drainage and no frost, and F-4 for poor drainage

and severe frost.

After the subgrade classification has been determined, other fac-

tors such as the magnitude and character of the aircraft loads to be sup-

ported, the volume of traffic, the concentration of traffic in certain areas,

and the landing gear geometry and dimensions must be considered. De-

termination of pavement thickness requirements is not an exact science.

Solutions must be based on theory, analytical experiments, and perform-

ance of pavements under actual service. The FAA method has been de-

veloped from a correlation of the data obtained from all three sources.

The FAA assumes that 5 percent of the gross weight of the aircraft

is supported by the nose wheel and the remaining 95 percent is distributed

equally between two main undercarriage assemblies. These assemblies

may take the form of single-wheel, dual-wheel, and dual-tandem arrange-

ments. For each of these configurations, the FAA has developed design

curves, a sample of which (for the dual-tandem configuration) is shown

in Exhibit 3. The F curves on the chart are taken as given, a-d the

landing gear characteristics and load are superimposed over them. Ex-

hibit 4 indicates the two major measurements used in superimposing

these characteristics. They are d , defined as the distance between

the inner faces of two dual tires, and S (or SD in the case of dual-

tandem gear), which represents the distance between the center lines

of dual tires. (This is the diagonal distance between one front tire and

the opposite rear tire for dual-tandem gear. ) The depth d/2 and the

single-wheel load (gear loading divided by the number of tires) for three

representative aircraft of 50,000, 100,000, and 200,000 pounds are used

to establish line a in Exhibit 3 and the depth 2S D and total gear load

are used to establish line b . Exhibit 5 presents the result of the con-

version of data in Exhibit 3 from the single-wheel load concept to gross

aircraft weight in thousands of pounds, which is used on the vertical

axis. This is made possible by the gear dimension assumptions used

in preparing the design chart.

o~y'

PRC R-8905

EXHIBIT 2 - AIRPORT PAVING SUBGRADE CLASSIFICATION

Subgrade Class

Soil Group Good Drainage Poor Drainage

No Frost Severe Frost No Frost Severe Frost

E-1 Fa or Ra Fa or Ra Fa or Ra Fa or Ra

E-2 Fa or Ra Fa or Ra Fl or Ra FZ or Ra

E-3 Fl or Ra Fl or Ra F2 or Ra FZ or Ra

E-4 F1 or Ra Fl or Ra F2 or Rb F3 or Rb

E-5 Fl or Ra F2"or Rb F3 or Rb F4 or Rb

E-6 F2 or Rb F3 or Rb F4 or Rb F5 or Rc

E-7 F3 or Rb F4 or Rb F5 or Rb F6 or Rc

E-8 F4 or Rb F5 or Rc F6 or Rc F7 or Rd

E-9 F5 or Rc F6 or Rc F7 or Rc F8 or Rd

1,- 10 F5 or Rc F6 or Rc F7 or Rc F8 or Rd

E-11 F6 or Rd F7 or Rd F8 or Rd F9 or Re

E-12 F7 or Rd F8 or Re F9 or Re F10 or Re

E-13 Not suitable for subgrade

Source (a): Federal Aviation Agency, Advisory Circular AC 150/5320-6,Airport Paving, 10 June 1964, p. 15

As an example of the use of these charts, assume a soil classi-

fication of E-8, good drainage and severe frost. From the table above,

the subgrade classification would be F-5. The pavement thickness re-1

quirement in critical areas is determined by the following procedures.

Assume that the aircraft for which the pavement is being designed

has a maximum gross weight of 320,000 lbs. Entering Exnibit 3 from

the vertical axis, proceed horizontally to the intersection with the sub-

grade classification F-5, and then vertically to the critical pavement

thickness scale. The conclusion is that such an aircraft would require

approximately 30 inches of flexible pavement.

ICenter portions of runways on which aircraft are usually in varyingstages of liftoff are not considered critical.

0ONLY

PRC R-890

0 z

00 -

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0 ul a 1r) co 0 0 0 a a a 0 kr0 r- Lf) 1 0 , 00 r- t -r '- ^

NS U I C -t) -ILU I 11 -r ' w

PRC R-8907

DISTRIBUTION OF WHEEL LOADS THROUGH FLEXIBLE PAVEMENTS

ST IO6V

Kw

DUAL TANDEM GEAR TIME IMPRINT SINGLE TIRE IMPRINT

Sor :(a) F.>idcrj' A Aiatit Advisory Circular AC 15OI5 3Z0-6,Airpiurt Pav~ing, 1 U Iin- 1904, Appenix 1, p). 3

EXHIBIT 4 - LOAD DISITRIBUTION AND TIRE IMPRINT DATA

OFFtbl*.tLY

PRC R-890

8

Thickness - Bituminous Surface3" Critical Areas2" Noncritical Areas

Noncritical Areas -Total Pavement Thickness (inches)

812 16 20 24 28 32 36 40 44 4852

360C

320-

Vo 280C

00240-

0

cZOO

00

U

00

8 115 20 25 30 35 40 45 50 55 b0 6 5Critical Art-as -Total Pavement Thickness (inches)

Source- (a) Federal Aviation Agency Advisory Circular AC 150/5320-6,Airrt Pjin, 10 June 1964, p. 2 9

EXHIBIT 5 - DESIGN CURVES, FLEXIBLE PAVEMENT, DUAL-TANDEM GEAR

PRC R-8909

Going back to the intersection of F-5 and the 320,000-lb. line,

proceed downward and to the right, parallel with the dotted lines. It

is seen that this particular aircraft requires a base course thickness

of 11 inches for critical areas.

If the area being examined had been noncritical rather than crit-

ical, the total pavement thickness would have varied downward by a

factor of 20 percent. Total pavement thickness in noncritical areas

would have been 24 inches, 9 of which would be for the base course.

Since a surface course thickness of 3 inches is recommended,

and the base course thickness is determined by the chart, the required

thickness of the subbase is determined by subtraction.

(,') Corps of Engineers Method

The California Bearing Ratio (CBR) pavement

evaluation method was developed by the California Division of Highways

in 1928. The method was adopted in 1942 by the U.S. Ariny Corps of

Engineers for nilitarv airport use. It is now used by many civilian

engineers to determine soil characteristics and in the calculation of

the required thickness of flexible airport pavenents.

The CBR :est expresses an index of the shearing strength of soil.

Essentially the test consists of compacting and soaking a soil sample,

then penetrating the sample with a steel piston at a specified load. The

soil's resistance, expresseu as a percentage of the resistance for a

standard crushed stone, is the CBR level. An empirical relationship

was developed between the test value and adequate pavement thickness

under various loads. Load data for aircraft was at first extrapolated

from truck experience curves and later verified empirically. In this

method, aircraft load characteristics are usually expressed as a curve,

the axes of which are the CBR value and pavement thickness, as in

Exhibit 6.

Two methods of determining appropriate pavement thickness for

loads resting on mu-tiple wheels have been used b the Corps of Engineers.

PRC R-89010

Grs Wegh Lod hiknssfr BR(ichs

1558 94

55 1000 2000 05

, 35 ~ CLfora Teicns RafoC (nhs

EXHIBI 6r (kLXBLiAEENp EIG)UV FRCNVI8

Iniialy a tigh line sueimoe ove gie CB au re aused~~12 (mu0 lik 4h1rsn A ehdwt isFvlecr~swt

the ~ 4 plo pons.rtesrih iedtrie ytetikesa hceach~~15 tir st59e th4u6aea n needn ntaln hte~aload~~17 divde by th5u1ro ie ntegerasmladtetik

ness5 at000 whic 1h1 tot0 55bro ie tese h ug ea n

secod, 2 and4P (or daltondem Bear),g Rastin h A ehd

eac timpe itss n ine Exhbita 7. a needetui ln \-itega

€0

PRC R-89011

8015 109 8 7 6 5 4 3CBR70 it At It A.. ..

60 HY A Y I

50 30-kip singie-w wheel load a~ ] / [ I _; I i3- I0-in. L IA.-I Ihe60"kiP odsingle'

30hikns 7 5-in. thickne9s

30

19 20 30 40 0 60 70 h t

Thickness of Base and Pavement (inches)

EXHIBIT 7 - DEVELOPMENT OF DESIGN CURVES FOR AbC-KIP LOAD ON B-29 DUAL WHEELS

6.51 r

XTTB A 1

C-I

EXHIBIT 8 - DUAL-IN-TANDEM EXAMPLE REANALYSIS

r r

PRC R-89012

In 1954. the procedure for measuring pavement stress imposed

by multiple wheel assemblies was re-examined by the Corps of Engineers,

and a new system based on deflection factors in the pavement was adopted.

From an analysis of deflection at equal depths from single and multiple

wheels, it was found that a single-wheel load which yields the same max-

imum deflection as a multiple-wheel load would produce equal or more

severe strains on pavements in comparison with the multiple-wheel load.

Thus the problem became one of finding the location of an imagi-

nary single wheel, or the point and corresponding depth at which max-

imurn deflection takes place as illustrated in Exhibit 8. In determining

this point, tht unit of measurement for distance from the actual wheel

locations is the radius of the circle which is assumed to be the shape of

the equivalent single-wheel imprint. The area of this circle is equal to

the area of the actual imprint of a single tire.

After determination of the point and depth of maximum deflection,

its value is found from Exhibit 9 and compared to the deflection caused

by one wheel of the assembly. This ratio is then divided by the number

of wheels in the assembly and the result is the percentage of the total

gear load represented by the equivalent single-wheel load. The three

necessary parameterr are now known, and a chart showing equivalent

single-wheel load as a function of pavement :hickness and CBR can be

constructed, as shown in Exhibit 10. If iO.sir,.d, the curves can be

translated to gross aircraft weight for use with readily available data.

For noncritical areas, required thickness is reduced by 10 percent.

PRC R-89013

150

140

130 L12 0

c 110 Offset 0O.00r- _ _ _ _"Offset 0 2.-)r

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000 )t1 , vl , Off-e " O t. e -r~

Ooo* 040 0 t 310

0

010

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EXIB~IT -DEFLECTION FACTOR F FOR UNIVORMt LOAD OF'".\DIUS r AT POINTS BENEATH x AXIS

PRC R-89014

0Single wheel 1 1 1

£:1omU

~20 -0r

25 0-LRIK

~'40

> 45 0

55 0- J-: A ~ i3 4 5 67 8 910 1215 20 2530 -10 50670

California Bearing Ratio

200-psi tire pressure (1)

Note: (1) Thickness should be reduced 10 percent for centralportion of runways (area between 1,000-ft. sectionat each end.)

EXHIBIT 10 - FLEXIBLE PAVEMENT DESIGN CURVES FOR TAXIWAYS

PRC R-890

15

(3) U.S. Air Force SEFLMethod

In designing the landing gear for the giant C-5A

aircraft, the Air Force recommended that the design competitors

(Boeing, Douglas, and Lockheed) employ the Corps of Engineers method,

utilizing the California Bearing Ratio method. However, some modifi-

cations were suggested which are worthy of note.

Slight changes were made in the deflection factor - offset value

chart (Exhibit 9) through theoretical analysis. In the range of offset

values from 0 to 20 radii, a value equal to .0019 (radii of offset) is sub-

tracted from the theoretical value. Further, at offset distances greater

than 20 radii, the deflection factor is assumed to be zero.

Upward adjustments of indicated thicknesses in the high CBR value

range is made through a simplified curve extension method.

The CBR procedures as originally developed assumed a surface

designed to withstand a load repetition factor or coverage level of 5,000.

This would represent unlimited operation of the aircraft for a period of

approximately 10 years. Ln the case of the C-5A, it was considered de-

sirable to investigate lower coverage levels. This was accomplished by

adjusting the thickness requirement by a factor equal to (.15 + .231 log C)

where C is the coverage level desired.

b. Rigid Pavement Analysis

In contrast to the various methods used in flexible

pavement calculations, rigid pavement analysis is generally accom-

plished through the use of a uniform method. The method was developed

by Dr. H. M. Westergaard and utilizes a factor for soil strength called

the "modulus of subgrade reaction" or the "k" factor. Dr. Gerald

Pickett has performed further studies, and has developed a set of in-

fluence charts as a means of determining concrete thickness require-

ments without the exhaustive mathematics required by the Westergaard

method ;-lone.

(1) The Westergaard Analysis

Dr. H. M. Westergaard was dean of the Graduate

School of Engineering at Harvard for several years. His analysis is for

iIoa,

jPRC R-89016

computing critical stresses developed in a concrete slab in the in-

terior of the slab, and near the edge or near an unsupported joint.

The formula which is more common in usage is that for the interior

of the slab, which is as follows:

0275 (1+") log 0 Eh 4 + 0.239 (l- b)

where a = maximum tensile stress at the slab bottom under the

center of the load

P = load in pounds

a, b = semiaxes of an ellipse which represents the footprint

of tf.. tire

h = slab thickness in inches

E = modulus of concrete elasticity in psi per inch

k = modulus of subgrade reaction in psi per inch

1 = Poisson's ratio

The modulus of subgrade reaction is determined by a procedure

of applying loads to a steel plate 30 inches in diameter by means of

hydraulic jacking at representative areas of the foundation material.

By definition,

k = pressure in psi to cause a deformation of 0.05 inches0.05 inches

While other factors (such as moisture content) certainly affect

this test, it is noted that stress is also sensitive to k value. In theory,

k is related to other soil classifications through estimates of a soil

value as a foundation material, as seen in Exhibit 11.

(2) Influence Chart

The basic Westergaard equations can be used

for stress induced by gear configuration, but the procedure is tedious.

- Y

PRC R-89017

C)

* n n 0

0

C 0

Cd/

o -4 z

C)Lr Nu -- L~i.6C

- C 0 *:

-~ In CX

N ** 01

.Milli

A

PRC R-89018

To save time, Dr. Gerald Pickett developed influence charts from the

Westergaard equations. A sample chart is shown as Exhibit 12.

The essential data for using the influence charts are the gear load,

tire spacing, tire pressure, the modulus of elasticity of the concrete

(assumed at 4,000 pounds per square inch), Poisson's ratio (assumed

at 0.15), k or the modulus of subgrade reaction, and concrete thick-

ness. The value , , the radius of relative stiffness, is then computed

by the equation

Eh 3

The scale on the influence chart is then assigned the value of t and the

gear configuration, drawn tco the same scale, is superimposed over the

chart. The tire footprint area (wheel load divided by tire pressure) is

assumed to be equal to .5227 times the square of the imprint length. Im-

print width is .6 of Cie !ength so the footprint shape is that of a rectangle

with semicircular ends.

The number of influence chart blocks covered by the tire imprints

is then counted, and the superimposed gear tracing is moved until a

point is found at which a maximun number is covered. Using the for-

mula in Exhibit 12. moment is then computed. The flexural stress can

now be found by multiplying rnonient by the. section modulus of the slab.

(3) FAA Method

Utilizing the influence charts developed by

Pickett from Westergaard's formulae, the FAA has prepared standard

curves for estimating rigid pavement thickness. These three curves

are assumed to be representative of all aircraft using single, dual,

-ind dual-tandem wheel assemblies, respectively. They are based on

gross aircraft weight, as seen in Exhibit 13. It is necessary to find

the required thickness of subbase from the lower half of Exhibit 13.

No subbase is needed for Ra subgrades.

PRC R-89019

Note: ()Subgrade is as sumed to be a dense liquid. Poisson's rat io()r pavement is assumed to be 0. 1 S.

EXHIBIT 12 -INFLUENCE CHART FOR THE MOMENT My, IN ACONCRETE PAVEMENT DUE TO A WAD INTHE INTERIOR OF TH4E SLAB

PRC R-890 ES --9lO - -rw -

-0400

C300

250

I-e

I-O

4--0

7t 10 1 1i

CR~~~ d~A.AF

PRC R-89021

In order to form these general curves, special assumptions were

necessary. They are: k = 300 psi/i, 400 psi working stress, 150 psi

tire pressure, E = 4,000,000 psi, and p : 0.15.

The gear dimensions were assumed to be: for dual wheels, 20

inches center-to-center for the iower aircraft weights and 30 inches

for the heavier aircraft, and for dual-tandem gear, 20 x 45 inches

for the lower end of the weight scale and 30 x 55 inches for tile heavier

weights. i ive percent of the weight is assumed on the nose wheel in

all cases. Thicknesses are again reduced by 20 percent for noncritical

areas.

(4) Portland Cement Association Method

Exhibit 14 is an example of the type of graphi-

cal analysis performed by the Portland Cement Association. This chart

is taken directly from the influence charts previously discussed. The

assumptions regarding tire imprint, modulus of elasticity, and Poisson's

r,tio which wert used by West, rgaard arc retained. Th, formula for

loads in the interior of a slab is assumed to be applicable btecause ade-

quate load transter devices between slabs enable a paved area to act as

one large sltb.

Safety factors are established before using the dlesign chart (Ex-

hibit 14). 'hty are 1.7 to 2.0 (depending on the number of operations

by planes wth the design wheel load) for critical areas, and 1.25 to

1. 5 for central portions t runwrays. This factor is applied to the

n-odulus ot rupturc of the (uncrete to find allowable stress, which is on

the left vertical axis in Exhibit 14. Entering the chart at that point,

proceed horizontally to the appropriate k factor, then verticall." to the

applicable gear-load ,urve. Continuing horizon. illy and to the right,

read requir-d thickness ircim tht, right axis. The procedur, may be

reversvd to fieternine stress ?,'i- thickness is already known.

Al thoukzh the- m-thorloluo v (1o.s not preclude Ionsideration of un-

usual gear conhIo'irations (through development of special design charts

h\ using the influenct ch,,ir.s), onvlv single, dual, and dual-tandem gear

of specified dimensions Irc charted in the Association's booklet. Where

'1I -

PRC R-89022

860 SpeciA' Design Chart "AB"for

Concrete Airport Pavement(from Influence Chart No. 2) -10

Douglas DC-8Dual-Tandem Landing GearE 4.000,000 psi IA 0.15S

0"0

0- 0

bu() lb

N 1

CC

0~~ 14

CL

712

F;IIIM11TT 14 -POP T LA ND C EME N ASSOCIATION DE:SIG'N (IIART

PRC R-89023

thicknesses for aircraft with other dimensions are required, the follow-

ing suggestions make possible the use of the charts presented:

* For increases in center-to-center spacing up to 10 inches,

the required thickness should be reduced by 0.6 percent for

each inch.

" For each inch decrease in dual spacing up to 10 inches, the

rcquired thickness should be increased by 0.6 percent.

(5) Load Classification Number Method

A procedure known as the Load Classification

Number system for classifying airports and aircraft was developed by

the British Air Ministry. Briefly, the supporting capacity of a pave-

ment is expressed in terms of a number known as LCN. This number

is obtained by making plate bearing tests on the pavement. Likewise,

the equivalent single-wheel load in any aircraft can also be expressed

in terms of LCN. This latter number, of course, is dependent on the

configuration of the gear, tire pressure, and type and thickness of run-

way. In a simplified analysis, if the LCN of an airfield pavement is

larger tuan the LCN of an aircraft, that aircraft cAn be assumed to be

saf, tn utilizing that facility. The LCN of an aircraft is determined in

the following mianner: first, the equivalent single-'heel load is computed

with the use of any appropriate procedure, such as the Corp of Engineers

or FAA m(-thod. Next, the contact area for each equivalent single-

wheel load is 'omputed, un(!er the assumption that the contact pressure

is the same as that for the wheel assembly. With this data. a graph

with tire pressure as the vertical axis and equivalent single-wheel load

as the horizontal axib is constructed, in which LCN curves intersect

contact area curves to give the L.CN for a particular aircraft.

In order to determine the pavenent's capacity to withstand load*

and express it as a single LCN, the idea of a standard load classifica-

tion curve was introduced, which expresses empirica! relationships be-

tween equivalent single-wheel load and contact areas. Failure load is

II

PRC R-89024

then expressed as a function of loaded contact area for ,arious pave-

ments, and an average curve was introduced which has the form:

Wl Al 4i Wi- =AlT

2. The Problem of Nonuniform Pavement AnalysisTechniques to Aircraft Designers

a. Aircraft Landing Gear Design as a Functionof Pavement Strength

Because of the extreme weight projected for future

large aircraft, it has been necessary to design landing gear which have

highly unusual configurations in comparison with the standard dual and

dual-tandem gear arrangements of the present family of commercial

transports. Proposals have been made which include triple-tandem

and quadruple-tandem arrangements, as well as combinations of two

or more dual- or triple-tandem sets under each wing. As nany as 30

wheels have been proposed for a single aircraft.

It is obvious that determination of flotation requirements for these

advanced systems is mire complex than it has been in the past. In fact,

it is highly improbable that the d/Z and 2S measurements are appro-

priate for configurations other than the dual or dual-tandem. The

Westergaard mathematics and the determinationi of the point of maximum

deflection have betomt- more important in relation to other methodologies.

b. Absence of Correlation Among PavementAnalysis. M-:thods

It should be noted that in the consideration of flexible

pavemnt design, the required thickness of the flexible pavement may

he nfluenced substantialiy by the method of analysis in use. Exp.rience

suggests that use of the ,AA method will result in a thickness require-

ment son-,owhat liow that rt suiting from use of the Corps of Engineers

mnthc'd. The Air Fort'r SEFL method is, perhaps, the most conser-

vative of all. and miy result in a thickness requirement greater than

r

PRC R-89025

either the FAA or Corps of Engineers method. However, it Is possible

to use any one of the three methods if the results are tempered by ex-

periernce and comparison with existing pavements.

Perh,.-s the most important element in the derivation of thickness

requirements is the manner in which the subgrade is tested. An FAA

oubgrade rating can only be related to a CBR rating through gross ap-

proximation (see Exhibit 11). It is possible that the different tests,

conducted at different times and by separate individuals, may not be

able to be equated, and the results may indicate differences in thick-

ness out of proporti-' to the normal variance. As an example, tests

were recently mac ; at Los Angeles International Airport, resulting in

an FAA soil classification of Fa and a CBR rating of 10. This results

in pavement thickness requirements for the DC-8-55 of 11.5 inches by

the FAA method, and 32.5 inches by the Corps of Engineers method.

In contrast, soil tests taken at Miami International Airport present an

FAA rating of Fa and a C BR of 60. This results in a requirement for

the DC-8 of 11.5 inches by the FAA method, and 1 inches by the Corps

of Enipneers method.

As a furth, r example of the lac- k of correlation between the vari-

ous subirade testing methods, the test data fIr 15 major U.S. airports

wcre examined. An attempt was made to relate the k factor, F num-

',er, and CBR value wherever more than one of these tejts had been

taken at the same location. The lack of correlation is demonstrated by

Exhibit 15.

The FAA methodology for rigid pavement analysis further adds

to the possibility of error by using curves whit h are derived from as-

sumned landing gear d.merisions. In addition, the curves (or dvAl and

dual-tandem gear are compromises between larger spacings at the

heavier weights and smaller spacings at the lower end of the scale.

This results in a design curve which overstates the thickness require-

sent by I to 2 inches. Suggestions made by the Portland Cement

Association are also conducive to approximat-on, as the curves are

only designed tor single, ,1 1, and duai-tandem arrangements. As

PHC R-89026

00

'00

o 0

0 it, H00 -

114 U

0

[.a4

Ln U0

0 0

H F-4

olow

PRC R-89027

previously stated, the FAA method for determining flexible pavement

thickness must use d/2 and S or S D , because these measurements

are most applicable to dual or dual-tandem arrangements.

The influence charts developed by Pickett to simplify the mathe-

matics associated witl, the Westergaard method also praduce results

that vary slightly from an all-mathematical analysis. This variance is

attributable to the difficulty in counting squares, and especially in

determining the maximum count as the tracing of the gear is rotated on

the influence chart. This variance may result in a differerce of 2 to

3 percent. Another contribution to the variance is the shape of the

contact area: Westergaard used an ellipse while Pickett used a rec-

tangle with semi-circular ends.

For these and other reasons, the Westergaard equations (and

their direct use rather than their use through compromise curves or

influence charts) and the Corps of Engineers method of determining the

point and depth of maximum deflection become more important and

more applicable to determination of pavement thickness for future air-

craft.

In the inclusion of analyses of flexibie pavements by the FAA

method, it is recognized that a discrepancy will result in the case of

aircraft with six-wheel gear. That is, the Corps of Engineers method

will produce less favorable flotation characteristics for six-wheel gear

than will the FA.A method. It is impossible to state which is most

nearly correct at the present time, because experience with such gear

configurations nas not provided empirical data.

It is believed that with careful soil classification, the Corps of

Engineers method for flexible pavement and the Westergaard analysis

for rigid pavement will result in satisfactory determination of pavement

thickness for the future heavy aircraft and for uncommon gear config-

urations. However, it seems advisable to apply the SEFL correction

regarding low thickness and high CBR values to the Corps of Engineers

methodology.

PRC R-89028

3. Compatibility of Present Airport Pavements with Largem mejrc i al Aircraft

a. Methodology Used in Computations

The U.S. supersonic transport airframe competitors,

Lockheed and Boeing, are proposing designs which incorporate maxi-

mum gross weights of 595,000 and 675,000 pounds respectively. In

addition to these aircraft, the Lockheed L-500 (the commercial version

of the C-5A), the Boeing 747, the DC-8-63, and the supersonic Con-

corde will be considered and their compatibility with airport pave-

ments analyzed. For comparative purposes, the Boeing 707 which

weighs 336,000 pounds and the DC-8-55 with 328,000 pounds are added

to the list.

Each of these aircraft is assumed to operate with a center of grav-

ity at maximum gross weight such that the nose wheels carry 5 percent

of the weight. Although this assumption is in accordance with FAA

procedures, it is not accurate. It is believed to be close to reality,

however, and is necessary to render the load per tire on the main gear

comparable for each airplane.

(1) Rigid Pavement

The induced stress in rigid pavements was

determined for various thicknesses and k values by means of the Wester-

gaard formula. The results for each airplane were plotted on charts in

which concrete thickness was plotted against stresses at various k

values. (See charts in subsection B.) For evaluation of an airport, the

pavement thickness and k value give concrete stress, which is then

compared to the allowable stress at the airport being asidered.

The required overlay was determined by the reverse procedure,

i.e., the charts were entered with the allowable stress and given k

value, which determined the needed thickness. The allowable stress

was based on the flexural strength of concrete that was at least 90 days

o'd.

PRC R-89029

The induced streFss is directly related to the wheel load, but is

rather insensitive to small changes in the wheel spacing and contact

area.

(2) Flexible Pavement

In the analysis of flexible pavements, the FAA

method is used wherever F numbers are available. Determination of

d and SD havc not been standardized for new gear configurations. It

was assumed in the case of aircraft using four dual-tandem bogies that

one dual tandem was representative, that all tires were equally loaded,

and that SD is a diagonal center-line distance on one bogie regardless

of the effects of an adjacent set of wheels. For the triple-tandem

arrangement, SD was measured from the center line of one front tire

to the center line of the opposite rearmost tire without regard to the

effects of the dual wheels in the middle, except for wheel-load deter-

mination. The same is true independently for the L-500, which uses

triple tandems fore and aft.

The Corps of Engineers method is used wherever CBR data is

available. Deflection factors are summed for all wheels in the triple-

tandem cases, but for the aircraft which use four dual-tandem main

gear, the bogies are treated as independent units. This assumption

was derived through calculation of the distance between centers of the

nearest tires of two adjacent bcgies. The result was approximately

16 and 14 radii for the B-2707 and the B-747, respectively. Using the

information in Exhibit 9, an offset value of 14 (if it were shown),

would give deflection factors of .05 or lower at all depths. This is

considered negligible in relation to actual deflection factors of 1.00

or more at relevant depths.

The Corps of Engineers analysis was accomplished by deternmin-

ing the maximum deflection factor at spacing intervals of 3 inches

throughout the relevant area covered by the landing gear. This was

repeated for a total of 10 depths from 5 to 80 inches.

*w~a 01u &-1 IlsybO

PRC R-89030

4Using the formula:

ESWLt SWL 1

1 CBR r-A 8.1p

where t = thickness or depth

ESWL = equivalent single wheel load

SWL = actual load on one wheel

A = tire imprint area

p = tire inflation pressure

CBR = California Bearing Ratio

the required CBR at each depth for a given aircraft weight and gear con-

figuration was computed and plotted. Ln evaluating airports, this CBR/

depth chart is used by entering with the actual CBR and determining re-

quired depth to support a given airplane in unlimited operation. As pre-

viously stated, the SEFL modification for shallow depths is incorporated

in the computations.

B. Aircraft Pavement Loading Effects

Exhibits 16 through 46 summarize the computations involved in

flexible and rigid pavement thickness determination. Gear configuration,

aircraft data, FAA chart, CBR chart, and concrete stress chart are

shown for each aircraft in turn.

V,

PRC R-89031

Gross % of Load Tire Im- TireRamp Weight on per Tire Tire print Area Pressure d/2 2 SDWeight Main Gear (lbs.) Size (sq in.) (psi) (in.) (in.)

595,000 95 47,100 50 x 18 255 185 11.9 239.7

±9

1,224"

146"1

00f

57"1

EXHIBIT 16 - L-2000 PAVEMENT LOADING SUMMARY

k1l V

PRC R-890

32

00

OD0_ _ _ _ - _ _ _ i_ _

%%b_ _ _

_ _ _ _ _

'44b E0

%Ak_ _ _

%w___ _ _ _ b

%b - - - - __ _

-ipto -osuoloi)PP' .- M W M

r PRG R-89033

z

NI

X'-

- -- -- - -

k '-

PRC R-89034

I ,000

900

$00\

10

21 00- ___ _

1000

IIL

EXHIBIT 19 - -'OG(O RIGID PAVEMIENT STRESS, WFSTERGAARr)METHOD

V

PRC R-89035

GCross '0 of Load Tire Ira- ireRamp Wt-iht on per Tire Tire prnt Ar. Pressure d/2-- 2SDWeight Main Guar (lbs.) Size (sq. in.) (psi) (in .) (in.)

6,75,000 9 40,100 45 x 19.2 217 185 1214 1 13.0

I I

1,478"

-14 8'

/>w w

l-l n] 9 I _ _ _ _ _ _ - _ _ _I I I __ i

EXHIBIT 20 - B-2707 PAVEMENT LOADING SUS' NIARY

*1r

I

PRC R-890

36

- -r_ 'If 0

____ o0-'I

- ___ 2'

- U__ _ 0

~M3' ~-. - - - - - - ______ - H-~ ~- - - -. ____ ______ ____ 2

~M *% ~ r-~ -~f

-~ U.0 -, h..4La.

-% - ---- ~ ____ ___ H~ 4 -

%

H

z

.a. 4

I -

NCI N

x-, - - 2 2 2 2

- -a - IA.- -~

I U JfI e;'uw t~n~1) r.' ~ ~ ~

I

VP,

PRC R-89037

\ 177

IH

-V 4. z

- - - -

- .- - -4-= - -

MIN-

% ,A .

J 1 =

K~. -i- ~-- ~ -

I ,II -l) t ~ l l ".

i i ii ir0

PRC R-89038

1,000 ,I11

800-t

;000

11avI I1"rt I il i (11), ho

EXHIBIT 23 -B-2707 RIGID PAVEMENT STRESS, WESTERGAARDMETHOD

PRC R-89039

Gross % of Load Tire Im- TireRamp Weight on per Tire Tire print Area Pressure d/2 2 SDWeight Main Gear (lbs.) Sizt (sq. in.) (psi) (in.) (in.)

140,000 95 40,400 45 x 15.7, 205 197 7.e 136.2

,oil

EXHIBIT 24 - CONCORDE PAVEMENT LOADING SUMMARY

OFFI IY

PRC R-89040

12I LI0

____ ~ __

____ I K 4V - ~ __________0

__ :4 4 jr-

PRC R-89041

--

u

z

IH

N u0m

fl))

1-1-A-I-I-----I -- I I2

I N H

D H

\ oz

in-I t0 -x 2 X

4. -

4ft

I b..4fr

- - 0 ]t U

PRC R-89042

1,000r

900

7100

600 -

4003

100 -_____

1000

EXHIBIT 27 -CONCORDE RIGID PAVEMENT STRESS, WESTERGAARDMETHOD

PRC R-89043

Gross 01" of Load Tire Ir- TireRamp Weight on per Tire j Tire print Area Pressure d/Z 2 SDWeight Main Gear (lbs.) Size (sq. in.) (psi) (in.) (in.)

683,000 95 40,600 46 x 16 j 194 1 209 17.2 157.6

990'

,---21~ "5"

O0~ 1 -- - ,

A,

6 4"

I I Iy 6 4 1in

a8 A

EX14IBIT 28 -B-747 PAVEMENT LOADING SUMMARY

OFF p1

PRC R-890

00

- U)

0' %.T- T

_ _)U io jo _ _ _ _ ynti)Ii~

0 F tft "jtL

OFFI ftJww S VfL

PRG R-890

45

- - - - -Q

00

o nL

z

>

00-J :

(s~iq m!

AP L

PRC R-89046

1,000

900 - - _ _ _ _ _

700

00

'4 _____ ________________

Jos

EXHIBIT 31 -B-747 RIGID PAVEMFNT STRESS, WFSTERGAARDMETHOD

PRC R-89047

Gross Percent of Tire iI- TireRamp Weight on Load per Tire print Area Pressure d/2 2SDWeight Main Gear Tire (lbs.) Size (sq. in.) (psi) (in. ) (in.

728,000 95 28,900 44 x 13 179 162 17.6 213.2

946.

770.

r\III Q- ,00 PATiNTLA INGSNM

• - -+- 124

EXHIIBIT 2 - I.- 00 PAVE.MENTI LOADING SUMMARY

PRC R-89048

hL4

PRC R-89049

I

f.L

z

41

u

- ----------

L Y

PRC R-890

50

9oGu _ _ _ _____ ___

700 ~ - - _____

t L -I _ _ __ _ _ _ _ __Io-_ __ _ _ _ _ _

100U

PA% V l.ll I'l 1,1,ll

EXHIBIT 35 -L-500 RIGID PAV1EMENT STRESS, WESTERGAARDMETHOD

PRC R-89051

C ros s pe r, ent of n- TrRonp (,i;hr Load pe'r lire pr';t Atr P r. -or' 2SD

Wcight NM icn Gf.ar "Lir. .(Ibs (sq. Ii. I i ) (1:1.) (in.

353,00)0 9 41,900 46 It, 21-' 1 Q 126.6

T_ . .'

t!th

EXHIBIT 36 - 8-63 PAVEMENT LOADING SUMMARY

PRG R-890

0

crN

_ _ _ __ K__ _ __>

-. ~- -t -____ _______ - - nr~>

of4~

___ ~00u

___ ~ ~ C,~~

rn

(rputiod jo sputjejkLu4) pro IM~I"

~IONLY

OFFiPRC R-890

53

0

- --. H

0u

- - 0

u

(.12

- I H

PRC R-890

54

1,000

900

u

t 0 0

L '00 0

I )

l l m t 'hIL, ki{'ss (III, hf ,,)

EXHIBIT 39 - DC-8-63 RIGID PAVEMENT STRESS, WFSTERGAARDMETHOD

1F1 k E1 NLYUI

PRC R-89055

Gross Percent of Tire in- TireR. n, . Weight on Load per Tire print A rea Pressure d/2 2SDWteight Main Gear Tire (lbs. Si7e (sq i n.) (psi) (in. (in.

336,000 95 40.000 46 x 16 222 180 11.4 131.0

7(JM"

B44'

EXHTIBIT 40- B-707 PAVEMENT LOADING SUMMARY

OFNL

PRC R-89056

-'11

_ _ _ _ _ _ _'I

Fl ~I-1----- ____ cc

0 C, c cH

PRC R-8no57

Ic

PRC R-89058

4

800 ----------- t-- --

*~ ~ S--- . .. i GA A.

Gr.-s -) iIn- Il

P a nip W i.L n e rp,,- r, 'I

(1;)i) .. ) S4 z 214l r.) ( il) o

oi, 441 214

F;NimiT-.4 PC~-~PAVFAII." V O-AtIDIN SCMNiARY

PRG R-89060

C0

I I

10

13-4

IN]n

o, C) C' oL r-

(punod jo spu vsnotp) pt.'i ) 4M dI u

.. i rr I~~q'c w~.VL T

PRC R-89061

I~Ij I0

1 { - - '-

I I I I-~ ~ - ~fi,

LAI 0

K 7V1K

PRG R-89062

,'PC 1R-S90

1,000 1v -

0 0

00 L___

200

Pdx ernt Thic kness (ink he(s)

EXHIBIT 47 -DC-8-55 RIGID PAVEMENT STRESS,WESTERGAD O

Or USE O LY