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1 TECHNICAL REPORT STANOARD TITLE PAGE 1. Report No. 2. Goyernment Aceession No. 3. Recipient" s Catalog No. FHWA/TX-86/ F 1-: TTi::itl.-: e =and7sy::;:b:;-:tit:;:le:-----"----..j..._ '5:-. -;:R;-"ep-o-rt-:::D-at-e Effeciiof Atomobile Tire Loads On Thin Flexible Pavements 7. Athort.) Freddy L. Roberts, Roberto rrela and Mikael P. J. nlc:n 9. Performing Organization Name and Address Texas Transportation Institte The Texas A&M niversity System College Station, Texas April Performing Organi zalion Cod;;- 8. Performing Organ. zation Report No. Research Report 345-2F 10. Work nit No. 11. C9nlr'll't or G,{al},t N,II. Stay IO.,-ti-ti3-345 :--::-- :-- --I13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address S t b 1982 Texas State Department of Highways and Pblic Final _ ep em er Transportation; Transportation Planning Division April 1987 P. O. Box 5051 Astin, Texas Spplementary Notes Research performed in cooperatio n with DOT, FHWA. Research Stdy Title: Performance Considerations Asphaltic Concrete 16. Abstract -----: Span sari ng Agency. Code and Specifications of Hot-Mix This report incldes the reslts of an analytical stdy of the effects of atomobile tire loads on thin asphalt pavements over flexible bases. Two different ways of calclating the tire contact pressre were sed and the strains indced in the pavement strctre were evalated. The niform pressre tire model assmes that the tire contact pressre is eqal to the tire inflation pressre. The Tielking tire model is a finite element compter program that models the tire as a shell of revoltion and calclates the contact pressre distribtion by sing the tire carcass properties and the tire load. The contact pressre distribtions were sed in ILLIPAVE to calclate the strains at varios locations in a pavement having a srface of thickness ranging fron 1 to 4 inches and m0dli ranging from 50 to qoo Ksi. A granlar base 8 inches thick with 2 different modli was over a sbgrade soil with a modls of 10 Ksi. The reslts were analyzed and the findings indicate that atomobile tire loads can lead to fatige failre and rtting problems for certain combinations of srface thickness - modl i over weak bases. The best performance occrred when stiff bases were sed. 17. Key Words Contact pressre, thin pavements, fatige cracking, rtting, ILLIPAVE, Tielking tire model, niform pressre model. 18. Distribtion Statement No restrictions. This docment is available to the pblic throgh the National Technical Information Service 5285 Port Royal Road Springfield, Virginia Secrity Classil. (of this report) 20. Secrity ClalSif. (of this page) 21. No. of Pages 22. P ri ce ncl ass ifi ed nclassified 65 Form DOT F (S-69)

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3 EFFECTS OF ATOMOBILE TIRE LOADS ON THIN FLEXIBLE PAVEMENTS by Freddy L. Roberts Roberto rrela and Mikael P. J. Olsen Research Report 345-2F Research Stdy Nmber Performance Considerations and Specifications of Hot-Mix Asphaltic Concrete Sponsored by Texas State Department of Highways and Pblic Transportation in cooperation with. S. Department of Transportation, Federal Highway Administration April 1987 TEXAS TRANSPORTATION INSTITTE The Texas A&M niversity System College Station, Texas

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5 -, _s, yd Mi.. '.. ' yd' filii o. '",.,. Tbq fi.. pi -, f'] y.'., A.,,,.i,,, ConVl"i... t. M.tric M... WII Y.. a._ "lilt;,.,.,.. fid Iftche. I,,ord. ",.1... htc:hel eqer. f.....:r...,mi...,... 1 eer.. o... ee. pond. short ton. IlOOO.b' c_ pih'l"..., poena bl.,poortl fivol..... nonl cbic t... cbic,..., Fehrefttteit,."". LENGTH 2.5 JO.., I.' AREA I.' ' 0. MASS (w.i,hl) 2. 0.'5 0.' VOLME, 15 JO O.tS J.' O.OJ 0.71 TEMPERATRE (lct' 51' C... bi,.cli"l ]1. c... t.,..'.' c...,... Me"".flamec.,. c.,.,..,., ,.... f il... hec... 9'-..ilogr... 10ft"" ",ill'i.,... ",illili"'. Miltili, Ii'... linf' Ii' Ii'... cillb,e me'f"f' c... ie..., Ce'sit..,..,...-. S,.hl cm C'"... k'".,.' ",' ",' km'... t., "'. "'. "'. ",'... ' c METRIC CONVERSION FACTORS.. I ;;;;.... ;: = :! =: = E E == E :.. - "--; =... =. =-- : r- I.. S,.h. c'"......,.,.. '... ' lie 9... I ",'... ' c A".ni c... i Ir M.tric MII.lr.. w Y a ,., " hfiti4 -. LENGTH tren'...,ord. ""I1.,.,.tf' centi,...,..,... e"...,...il... '., ;... c.ttt......,.. Met... CIO.- ",',.-,ogrems,_ k" mi.,i1... "M', I ii... cbic mel... cbic:..., Ce'", 0.04 J.J AREA MASS (.llllit] ' VOLME '.OJ " '.21 ]5 1.J TEMPERATRE (eet' , I....- _,.,...t... 1!hor'I'". _.Mi...,,'.... 1VhI _321,.- flvi4 no.. II... cbic _... c,ord. '--., '... _i' 0,,I.. liz -0: "" r o I '.', t,'o, I,'o z L i I I I iii iii -00 -'0 0 ZO C J1 C,,...,.. ;ft i. yd "'... ' ",,' o. lin pi 'II..,.. ' '.,

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7 DISCLAIMER The contents of this reoort reflect the views of the athors, who are responsible for the facts and the accracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Ferleral Highway Administration. This report does not constitte a standard, specification, or reqlation. ; ; ;

8 PRI:FACF This is the second and final report dealinq with the conditions of se, constrction, and specifications of hot mixed asphalt materials sed in thin, flexible oavements. This report is an extension of the first report with an emphasis on the effect. of atomohile tire loads on strains in thin asphalt concrete pavements over flexible bases. Jst as in the first report, the analysis in this report is concentrated on an evalation of strain in thin asphalt concrete pavements and in defininq the material property combinations that show strains too larqe to ensre adeqate performance. This report was completed with the assistance of many people. Special appreciation is extended to Drs. Robert L. Lytton and Thomas Tielkinq for their help with the compter modelinq and to Messrs. James L. Rrown and Robert L. Miklin of the Texas State Deoartment of Hiqhways and Phlic Transportation for their encoraqement and constrctive criticism. Appreciation is also extended to the secretarial staff of the Materials, Pavements, and Constrction Division of TTI who prepared the manscript materials. The spport of the Federal Hiqhway Administration, Department of Transportation, is qrateflly acknowledqed. Freddy L. Roberts Roberto tjrrela Mikael p.j. Olsen iv

9 SMMARY This report smmarizes the reslts from an analytical stdy to determine the material properties and thicknesses of asphalt srface layers needed to provide adeqate resistance to fatige cracking for thin flexible pavements being sbjected to atomobile tire loads. The analytical stdy incldes the effects of an important parameter not generally considered in these stdies: the tire contact pressre distribtion. Reslts indicate that the effects of tire inflation pressre on strain are very important. These reslts show that srface materials which served adeqately when atomobile loads are assmed to be applied at 26 psi contact pressre can fail when very high repetitions of atomobile tire loads are actally applied at a contact pressre of 65 psi. The contact pressre distribtions sed in the stdy were developed from a finite element compter program that models the tire sing its constitent elements. The contact pressre distribtions were for a typical radial atomobile tire that carried two different loads of 800 and 1320 ponds per tire. These contact pressre distribtions were then sed to evalate the effect of srface and base properties and thicknesses. The reslts indicate that (1) thick and stiff granlar bases provide the best protection for the sbgrade soil, especially for thin srfaces, (2) that crrent asphalt materials can serve adeqately if stiff bases are sed and if srface thicknesses arond 2-inches are avoided, and (3) on weak bases the thin, very flexible srfaces or the thick, very stiff srfaces provide the best opportnity for achieving a reasonable fatige life. v

10 IMPLEMENTATION TATEMENT Rased on the findinqs from this stdy it is apparent that thin layers of conventional asphalt concrete materials shold be sed with cation on granlar bases. Flexible pavements with srfaces arond -inches thick combined wit weak qranlar hases shold probably not he sed at all. Fvalations of the reslts from this stdy show that for flexible pavements over nbond, granlar bases the srface thickness and stiffness combinations affect the tensile strains siqnificantly and that bitminos srfaces of (1) 1-inch or less shold be very flexible and placed on very stiff bases, (2) 2 to 4-inches shold be stiff and stronq and placed on stiff bases, and (1) arond?-inches shold orobably not he nlaced on weak bases since the strains are very hiqh and early crackinq is expected. In considerinq the se of 1 to 3-inch bitminos srfaces, carefl consideration shold be qiven to the nmber of loads to be applied by trcks since a relatively small nmber of these loads can lead to nrematre failre even thogh the atomobile loads can be handled adeqately. Therefore, the reslts of this project indicate that intermediate srface thicknesses shold be sed only after a carefl analysis of each pavement strctre to ensre that overstressinq of the srface does not occr. vi

11 TABLE OF CONTENTS METRIC CONVERSION CHART DISCLAIMER PREFACE SMMARY IMPLEMENTATION STATEMENT TABLE OF CONTENTS... LIST OF TABLES.... LIST OF FIGRES CHAPTER I I NTRODCTI ON II LAYERED SYSTEM CONCEPTS III TIRE MODELS Tielkinq Tire Model niform Pressre Model IV STDY PARAMETERS AND RESLTS. Stdy Parameters. Stdy Reslts. Tire Pressre Effects Tire Load Effects Page ii iii iv v vi vii ix x Layer Modls and Thickness Effects. 20 Tensile Strain at Bottom of Srface 23 Vertical Sbgrade Compressive Strain. 28 Tensile Strain at the Top of the Srface Fatige Damaqe Effects. Rtting Effects Comparison of the Response of Stress Sensitive and Linear Elastic Granlar Materials vii

12 TABLE OF CONTENTS (contined) CHAPTER V SMMARY AND CONCLSIONS. Smmary. Conclsions REFERENCES. Page 5" viii

13 LIST OF TARLES Table Page 1 2 Vertical Sbgrade Compression Strain for a Base Modls of 30 Ksi, a Contact Pressre of 65 psi, and a Tire Load of 1320 lbs Cmlative Nmber of Vehicle Load Applications for 500 AOT and 10 Percent Trcks ix

14 LIST OF FIGRES Fi g re Page Cylindf!r pavement configration.... Rectanglar half space of an axisymmetric solid Stress-strain behavior of pavement materials 4 Finite elements positionen on the G78-14 tire carcass mid-srface Deflected shape and tire contact pressre distribtion reslts from finite element tire model for a G78-14 tire Effect of inflation pressre on footprint pressre di stri hti on of radi al passenqer car ti res Effect of inflation pressre on footdrint pressre distribtion of radial passenger car tires Effect of tire pressre on tensile strain at the bottom of a srface with a modls of 400 Ksi for a P20S/7SR passenqer ti re load of 1320 lbs q Fffect of ti re pressre on tensile strain at the bottom of the s rface with a modls of SO Ksi for a P?OSI75R passenqer tire load of 1320 lbs.. Effect of ti re load on tensile strains at the bottom of the srface with a modls of 400 Ksi and a base modls of 30 Ksi Effect of ti re load on tensile strains at the bottom of the s rface with a modls of 400 Ksi and a base modls of 60 Ksi Tensile mi c ro-strai n contors at the bottom of the s rface for a 60 Ksi base modls and a tire load of 13?0 1 bs Tensile micro-strain contors at the bottom of the srface for a 60 Ksi base modls and a tire load. of 800 lbs.... x

15 LIST OF FIGRES (contined) Fiqre 14 Tensile micro-strain contors at the bottom of the srface for a 30 Ksi base modls and a tire load of 1320 lbs Tensile micro-strain contors at the bottom of the srface for a 30 Ksi base modls and a tire load of ROO lbs. Hi Compressive micro-strain contors at the top of the sbqrade for a 60 Ksi base modls and a tire load of 1320 lbs Compressive micro-strain contors at the top of the sbqrade for a O Ksi hase modls and a tire load of ROO lbs Compressive micro-strain contors at the top of the sbqrade for a 30 Ksi hase modls and a tire load of 1320 lbs.... lq Compressive micro-strain contors at the top of the sbgrarle for a 30 Ksi base modls and a tire load of 800 lbs Tensile micro-strain contors at the top of the srface for a no Ksi base modls and a tire load of 1320 lbs. 21 Tensile micro-strain contors at the top of the srface for a 30 Ksi base modls and a tire load of bs. 22 Tensile micro-strain contors at the top of the srface for a 60 Ksi base modls and a tire load of OO 1bs.. 23 Tensile micro-strain contors at the top of the srface for a 30 Ksi base modls and a tire load of ROO 1bs 24 Nf contors in millions as a fnction of the tensile strain at the ottom of the srface for a no Ksi base modls and a tire load of 1320 lbs.. Page xi

16 LIST OF FIGRES (contined) Fi gre Page 25 Nf contors in millions as a fnction of the tensil e strain at the bottom of the srface for a 30 Ksi base modls and a tire load of 1320 lbs Nf contors in millions as a fnction of the tensile strain at the hottom fo the srface for a 60 Ksi base modls and a tire load of 800 lbs Nf contors in millions as a fnction of the tensile. 40 strain at the bottom of the srface for a 30 Ksi base modls and a tire load of 800 lbs ?R Cmlative nmher of vehicle load applications Tensile micro-strain contors at the bottom of the srface for a hase modls and a tire load of l32() 1 bs xii

17 CHAPTER I I NTROOCTI ON Most stdies of the effect of wheel loads on thin flexible pavements have exclsively considered trck tire loads which sally make p less than 10 percent of the traffic. The atomobile tire load has been considered to case minor damage compared to the trck tire load, especially since the AASHO Road Test findings. The oroose of this stdy is to take a closer look at the resoonse of thin flexible asphalt pavements sb.iected to oassenqer car tire loads by modeling the tire sing two different models, the Tielkinq tire model and the niform pressre model. These tire models describe the intensity of the pressre distribtion and the area of the srface over which the load is apolied. With the niform pressre model, the tire load is represented s a niform pressre eqal to the inflation pressre which is spread over a circlar area with no lateral shear stresses prodced by the tire rollinq on the srface. Stdies condcted by the tire indstry have shown that the contact pressre is not niform ht rather has a niqe shape, dependinq on the type and strctre of the tire. The Tielking tire model reflects more accrately the effect of the tire carcass on the contact pressre distribtion at the roadway srface. The first part of this reoort describes the comoter programs sed in this stdy alonq with the two tire models sed to estimate the interaction between the tire and the road srface. The second part of the report consists of the stdy reslts which inclded tire pressre and tire load effects as well as thickness and modls effects on strain in thin flexible pavements. These strains are sed to estimate the fatiqe and rttinq life of a thin flexible pavement sbject to passenger car tire loads. 1

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19 CHAPTER II LAYERED SYSTEM CONCEPTS Pvement desiqners are makinq increased se of theoretical strctral analysis techniqes. A major reason is the ease of se and availability of compter proqrams. There are, however, a nmber of potential pitfalls involved in sing these technioes incldinq inpt data reliability, a tendency to se the analysis s an end in itself rather than as a tool, a tendency to hlindly se compter nroqrams as "black boxes" with complete trst in the reslts, and, perhaps, a lack of experience and appreciation of the sensitivity of the design factors and their effect on reslts. Fven thogh these programs are a qreat help in making pavement design more fndamental in natre, the pitfalls shold be clearly recogni zed. The theoretical layer methods allow the engineer to calclate stresses, strains and deflections at selected points in the pavement strctre. The stresses and strains most often considered are the vertial compressive stress at the top of the sbqrade and the horizontal tensile strain at the bottom of the asphalt layer. The following inpt information is reqired in order to condct an elastic layered strctral analysis of a flexible pavement: 1) wheel load and tire pressre?) modls of pach layer material, and of the shqrade 1) Poisson's ratio of each layer material (the ratio of lateral displa"cement to vertical displacement) Crrently, there are a nmber of compter models available to perform strctral analysis inclding ELSYM5, CRANLAY, PLANE, RISAR, ILLIPAVE, etc. 0). The ILLIPAVE (2,1) compter proqram was selected primarily for two reasons: 1) non-niform tire contact oressre distribtions had to be accepted as inpt in order to sccessflly model tire contact pressre distribtions, and 3

20 2) the modls of non-stahilized pavement layers had to be modeled as stress sensitive materials. In this compter program, the pavement is modeled as a three-dimensional pavement section by sing a two-dimensional half-space of a cylindrical finite solin as shown in Figre 1. This rectanqlar half-space is then divided into a set of rectanglar elements connected at their nodal points as shown in Figre 2. One of the siqnificant featres of the ILLIPAVE finite element model of pavement analysis is the ability to incorporate both nonlinear and linear stress-strain behavior of component pavement materials (Figre 3). Loadinq in ILLIPAVE is specified sing the srface contact pressre and the radis of the loaded area. The loading is of the "flexible olate" type, i.e., a niform circlar contact pressre. The ILLIPAVE inpt was modified to allow a non-niform pressre distribtion to be calclated and inpt directly as nodal forces (1). 4

21 - I N V) V) ->C < I N LOAD LOAD -- R-AXIS.. R-AXI S Figre 1 Cylindrical pavement configration Figre 2 Rectanglar half space of an axisymmetric solid 5

22 (NEAR) ( NON-LINEAR ) (STRAIN) Figre 3. Stress-strain behavior of pavement materials. 6

23 CHAPTER III TIRE MOOELS Historically, initial analysis of the stte of stress on solid bodies involved the se of a point load applied to a niform elastic material of semi-infinite extent: later analysis techniqes inclded striploads of finite width and infinite lenqth. As analysis of pavement systems became more sophisticated, the pavement was considered to have more than one layer and also beqan to inclde a model of the tire as a circle of niform vertical pressre with no srface shear forces. In more recent years, highway engineers have begn to se finite element models developed for tire carcass analvsis to define the stress conditions that occr at the tire-pavement interface. Tielkinq Tire Model The finite element tire model sed in this stdy was originally developed for the Federal Hiqhway Administration as part of an analytical and experimental investigation of tire-oavement interaction (). The proqram was developed to provide the capability for calclatinq the distribtions of sliding velocity and normal pressre at the tire-oavement contact interface. Tielkinq () chose a relatively qeneral, nonlinear, finite element shell of revoltion compter orogram to be the fondation for the finite element tire model. A Forier transform procedre was developed and incorporated into the finite element program, qivinq this tire model the niqe caoability of calclatinq the contact bondary and interface pressre distribtion for a specified tire deflection. The shell elements sed in the tire model are orthotropic. A material property sbrotine was developed to qenerate orthotropic modli from cord to rbber property data and qeometric data descrihinq the ply strctre in the tire crcass. Althoqh the shell elements are homogeneos orthotropic, they are sensitive to details of the carcass design inclding tire materials and qeometry. 7

24 The tire is modeled by an assemblaqe of axisymmetric crved shell elements. The elements are connected to form a meridian of arbitrary crvatre and are located at the carcass midsrface. Figre 4 shows the assembly of 22 elements along the midsrface of a G78-14 tire. A cylindrical coordinate system is sed, with r, w, and z indicating the radial, circmferential, and axial directions respectively. Each element forms a complete rinq which is initially axisymmetric with respect to z. The elements are connected at nodal circles (nmbered in Fi g re 4). The elements are homoqeneos orthotropic with a set of modli specified for each individal element. The orthotropic modli for each element are determined by the ply strctre srronding the element. The finite element is clamped at the edges (node 22 in Figre 4), oressrized, and rotated to indce centrifgal force loading. It is then broght into contact with a rigid, frictionless srface perpendiclar to the plane of symmetry (the specified loaded radis, R), measred from the z-axis. The internal pressre, the anglar velocity, and the loaded radis are the only operatinq variables soecified prior to calclating contact deformation and pressre in the contact region. Reference 4 describes the mathematical procedres sed to calclate the contact nressre distribtion and deformation of the tire deflected aqainst the pavement. The deflected shape of a nylon tire meridian passing throgh the center of the contact pressre is plotted in Figre 5 for a tire deflection of 0.9 inches. The calclated tire load is 850 lhs. for a deflection of O.g inches. This finite element tire model is believed to he the first to have the capability of calclating the contact pressre distribtion in the footprint of a deflected tire. Sch a capability is important becase contact pressre has a profond inflence on all aspects of tire performance. The finite element tire morlel permits analytical investigations of the effects of tire desiqn variables on contact pressre distribtion. 8

25 PLY 7 PLY PLY 2 PLY VI G78-14 I.r:. c VI..-." 0:: 8 a 7 T o Z (in.) Figre 4. Finite elements positioned on the G78-14 tire carcass mid-srface. 9

26 13 t a-0.81n en <1J.s: s::..- en ::s..- fo a:: G78-1. p. 32 pal L- L- -l o Z (in.) Figre 5. Deflected shape and tire contact pressre distribtion reslts from finite element tire model for a G78-14 tire. 10

27 The rolling tire reslts are calclated by sperimposin the anglar velocity of the rolling tire on the soltion for static contact against a frictionless srface. The sliding velocities of points in the contact reqion are calclated as otlined in Reference 4. The sliding velcity and the normal contact pressre determine the friction coefficient at each point in the footprint. The resltant braking, driving, and steering shear forces respond to tire operating variables sch as inflation pressre, tire load, and slid angle throgh the inflence of these operating variables on the distribtion of sliding velocity in the footprint. Tire side forces are- similarly obtained by smming the lateral shear forces in the contact reion. ti"iform Pressre Model Early models of tires as circles with niform vertical oressre did not inclde the effect of tire constrction and lateral shear forces were not inclded in the analysis: only the inflation pressre and the total tire load were considered important. The tire inflation pressre was assmed to be constant and the radis of the circlar tire print calclated as: R = V P /rrp R = rarlis of the circlar niform contact pressre, in inches. P = total tire load, in ponds. p = inflation pressre, psi. Notice that the tire contact pressre is assmed to be eqal to the inflation pressre. This assmption is tre only if the tire basically behaves as an inner tbe, i.e., if the tire itself has almost no strctral stiffness. Since Tielkin9 and others have shown that the tire does have a strctre and that this strctre siqnificantly affects the pressre transmitterl to the contact srface, a portion of this stdy incldes comparisons between comoter rns made sinq contact pressres from both the niform and Tielkinq tire models. 11

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29 CHAPTER IV STDY PARAMETERS AND RESLTS Stdy Parameters Severa 1 compter rns were made with ILL! PAVE by va ryi nq the srface characteristics sch as thickness and elastic modls and by varyinq the base modls. The srface thicknesses inclded were 1,2,3, and 4 inches. Taking into consideration the soil tyoes, temperatre ranges and moistre levels within the different regions of the state, a range of material properties was selected for typical srface, base, and sbgrades. The following set of material property combinations and layer thicknesses were inclded in the stdy. Srface: Thickness: 1,2,3, and 4 inches Elastic Modli: 50,200,400 and 800 Ksi. Poisson's Ratio: 0.3 Density 145 pcf. 8ase: Thickness: 8 inches Elastic Modli: 30 and 60 Ksi. Poisson's Ratio: 0.4 Density: 135 pcf Sbgrade: Thickness: infinite Elastic Modls: 5 Ksi Poisson's Ratio: 0.45 Density: 12() pcf. The tire selected for the stdy was a P205/75R14 radial passenqer vehicle tire with an inflation pressre of 26 psi. Two different magnitdes of tire load were sed: 1320 and 800 ponds. These two loads correspond to the maximm rated load and a fairly typical tire load on a lightly loaded vehicle. 13

30 Stdy Reslts In this stdy two tire models were sed, the Tielking tire model and the niform pressre model, to analyze the effect of radial passenger-car tires on thin asphalt pavements. The niform pressre model is sed to contrast the effect on the expected life of pavements of sing what has previosly been assmed in pavement design calclations with the more realistic reslts of the Tielking tire model. The contact pressre distribtions developed sing the Tielking tire model are shown in Figres 6 and 7. Figre 6 contains the contact pressre distribtion from front to back of the tire along the path of the vehicle. Figre 7 shows the transverse pressre distribtion across the middle of the tire. These plots show very strikingly the difference between the predictions from Tielking's model and the niform pressre model which assmes that the inflation pressre is the same as the contact pressre. To model the tire pressre distribtion for 26 psi inflation pressre, the tire load was divided by the loaded area from Tielking's analysis prodcing an average tire contact pressre of 65 psi. This average contact pressre was sed in all of the comparisons of reslts of the compter rns sing the 26 psi contact pressre. To assess the difference in the effect of the tire models on pavement strains, several types of comparisons have been made sing reslts from ILLIPAVE compter rns. These comparisons inclde plots to show the effects of tire pressre on horizontal tensile strains in the srface as well as the effects of layer modls and thickness on strains in the pavement. Additional analyses inclde the evalation of the effects of the tensile strains on predicted fatige damage and an assessment of the effects of the compressive strains on the permanent deformation in the pavement. Tire Pressre Effects A series of compter rns was made and the reslts were sed to analyze the effects of tire pressre on thin pavements sing both the Tielking and the niform tire models. To describe the effects of 14

31 I 315 -(J III g (,) I re cen er -3-2 _, 0, longitdinal Distance (in-i 2 3 Figre 6. Effect of inflation pressre on footprint pressre distribtion of radial passenger car tires. 15

32 P205/75 R lb load ':::0., Q ::I I l -(J «I -C I I I I I I I I I I I I I I I, f 'I I I I I I I I I I I,,, 10 I I Tllre ce,ter o, I ,5-1,0 -o Meridian Distance I In. I Figre 7. Effect of inflation pressre on footprint pressre distribtion of radial passenger car tires. 16

33 en QJ.c c -.. en en c c -.c to- QJ So. ::s en G),, 8 in. Base E, Ksi Ksi Ks1 p contact, psi o 26 t:l 65 o Tensile Strain. (x 10-6 in/in.) 200 Figre 8. Effect of tir.e pressre on tensile strain at the bottom of a srface with a modls of 400 Ksi for a P205/75R passenger tire load of 1320 Lbs. 17

34 4.0 en s:: 3.0 c -.. en en c :c 2.0 I- f '+ :::::II CJ') ,,, _ in. Base E. Ksi 60 Ksi Ksi P contact, psi 0 26 GJ 65 o 75 *c-- indicates that the srface is in compression Tensile Strain (x 10-6 in/in) Figre 9. Effect of tire pressre on tensile strain at the bottom of the srface with a modls of 50 Ksi for a P205175R passenger tire load of 1320 lbs. 18

35 atomobile tire pressre on tensile strains at the bottom of the srface, Figres 8 and 9 have been prepared. Figre 8 shows the change in tensile strain for a srface of varying thickness and with a modls of 400 Ksi There is an increase in tensile strain as the tire contact pressre increases for both the weak and stronq base as shown in Figre 9. Notice in Figre 8 that a 26 psi contact pressre on a 1 inch thick srface with a weak base cases a higher strain than the same pavement nder a 65 psi tire pressre bt with a stronger hase. This demonstrates the importance of providing an adeqate base. For the 60 Ksi base the strains are increased by approximately 100% as the tire pressre model is changed from the 26 psi niform to the 65 psi Tielking model reslts and a1most as mch for the 30 Ksi base, Figre 8. Notice that as the srface thickness decreases from 2 inches to 1 inch all the tensile strains at the bottom of the srface decrease and are moving toward compression. Comparisons between plots in Figres Rand 9 show the effect of redcing the srface modls on tensile strain. Notice that as the srface becomes thinner and the srface modls decreases, the differences in tensile strains between Figres 8 and 9 are qreater. Figre 9 also shows that the thin, low srface modli combinations experience compression at the bottom of the srface. If both the srface and base modls are low, these passenqer wheel loads will lead to rapid fatige failre becase the tensile strains are qite high. For the very low modls srface, Figre 9, the change in contact pressre shown by the 2 models prodces strains that are abot twice as high for the Tielking model as for the niform model for both base modli. Notice that for all cases, when the srface thickness is only 1 inch, the strain at the bottom of the srface is in compression. Tire Load Effects With the trend of the atomobile indstry to bild lighter and more efficient cars, two different magnitdes of tire loads were sed in this stdy. The highest load was that for the maximm rated tire load and the second was for a more typical vale for vehiclar loading. 19

36 To describe the effect of atomobile tire load on tensile strains at the bottom of the srface, Figres 10 and 11 have been prepared. Figre 10 shows the effect of tire load and pressre on different srface thicknesses having a srface modls of 400 Ksi over an 8 inch base with a modls of 30 Ksi. The figre shows that at 26 psi contact pressre the tensile strain increases by abot 20 to 25 micro-inches per inch when the tire load is increased from 800 lbs to 1320 lbs. However, for 65 psi contact pressre, increasing the load sbstantially increases the strain, with increases ranging from 30 to 50 micro-inches per inch. Figre 11 shows similar trends as those shown in Figre 10, the primary difference is that the change in strain de to increased load is lower becase the base modls is higher. As seen in Figre 11, there is little difference in the tensile strains for the 4 inch srface carrying a tire load of either 800 or 1320 at 26 psi contact pressre. Notice too that the strains are abot the same for a 1 inch srface sbjected to the two tire loads at both contact pressres. This means that the major effects on tensile strains de to tire loads increments occr for the pavement srface thicknesses between 1 and 4 inches. Layer Modls and Thickness Effects To show the effects of combinations of different srface modlis and thicknesses, base modli and inflation pressres on strains in the pavement strctre, a series of figres was prepared. This analysis is divided into three categories in order to evalate the effects of srface modls and thickness on: 1) tensile strains at the bottom of the srface, 2) compressive strains at the top of the sbgrade, and 3) tensile strains at the top of the srface. The two primary distresses considered in this part of the analysis are fatige and rtting. To evalate the occrrence of these distresses, the tensile strain in the bottom of the srface is sed to evalate fatige damage and the compressive strain at the top of the sbgrade is sed to evalate rtting. 20

37 4.0 en 3.0 <..c c: -.. en en < c:..li: c t- <." '+ V') 1. a J,,,,,,,.,,,, ", " Es II: 400 Ksi Eb Co 30 Ksi t Tire Load, lbs Tbll: 8 in. P contact, psi a Figre 10. Tensile Strain (x 10-6 in/in) Effect of tire load on tensile strains at the bottom of the srface with a modls of 400 Ksi and a base modls of 30 Ksi. 21

38 a Tensile Strain. (x 10-6 in/in) Figre 11. Effect of tire load on tensile strains at the bottom of the srface with a modls of 400 Ksi and a base modls of 60 Ksi. 22

39 Tensile Strain at Bottom of Srface. To control the extent of fatige damage, the tensile strains at the bottom of the srface mst be kept fairly low, the exact level depending on the total traffic and the characteristics of the pavement strctre and especially the stiffness and thickness of the srface layer. A set of figres was prepared to show the different horizontal tensile strain as a fnction of srface thickness and modls for varios combinations of tire load and contact pressre. Figre 12 shows the changes in strain prodced by increasing the tire contact pressre from 26 to 65 psi for a constant tire load of 1320 ponds. In general, the tensile strains tend to increase as the contact pressre increases. The lowest strains occr in the pper right and lower left corners of the figres with the highest strains occring generally in the middle and pper left portions of the figres. Figre 13 shows the horizontal tensile strains for the same pavement strctre sbjected to a tire load of 800 ponds. Comparisons between Figre 12 and 13 show that increasing the load increases the horizontal tensile strains for both tire contact pressres. The difference in tensile strains is not so significant de to the high modli of the strong base layer. Figre 14 and 15 are similar to the previos plots except that the base layer has a low modls. Observe in Figre 14 the effect of increasing the tire contact pressre on the tensile strains is similar to that shown in Figre 12. The percentage increases in the strain are abot the same for increases in contact pressre in both Figres 12 and 14. Comparisons of data in Figres 14 and 15 indicate the effect of incrementing tire load on this particlar pavement strctre. Again, the lowest strains occr in the pper right and lower left corners of both figres and the highest strains occr in the middle and pper left at the low modli, thicker srface combinations. Vertical Sbgrade Compressive Strain. Vertical compressive strains have been sed as pavement design criteria to indicate whether the total pavement strctre above the sbgrade is thick enogh to protect the sbgrade from excessive vertical strain that leads to permanent deformation. A series of figres was prepared to show the effects of 23 --

40 Contact Pressre Distribtion: 26 psi 4.0 In QJ.s:: c: In In QJ c:..-.s:: t- QJ.., :l 1.0 en Compressive Strain a Srface Modls, Ksi Contact Pressre Distribtion: 65 psi In QJ 4.0.s:: c VI VI CI C s:: 2.0 t- CI :l 1.0 en 60 Strain 80 eo eo a Srface Modls, Ksi Figre 12. Tensile micro-strain contors at the bottom of the srface for a 60 Ksi base modls and a tire load of 1320 lbs. 24

41 Contact Pressre Distribtion: 26 psi '" cv 4.0.&:. C '" CV c: -.&: cv '- :::J 1.0 Con 40 o Srface Modls, Ksi Contact Pressre Distribtion: 65 psi en cv.&:. c: en en cv c:.c: c 10 '- :::J 1.0 Con Strain o Srface Modls, Ksi Figre 13. Tensile micro-strain contors at the bottom of the srface for a 60 Ksi base modls and a tire load of 800 lbs. 25

42 Contact Pressre Distribtion: 26 psi 4.0 VI <1J.&: C VI VI <1J C t- <1J '- 1.0 V) o Srface Modls, Ksi. Contact Pressre Distribtion: 65 psi 4.0 VI <1J C VI VI <1J C t- <1J '- 1.0 V) Strain o Srface Modls, Ksi Figre 14. Tensile micro-strain contors at the bottom of the srface for a 30 Ksi base modls and a tire load of 1320 lbs. 26

43 Contact Pressre Distribtion: 26 psi 4.0 '" QJ c: '" '" QJ c: -.s: I :l 1.0 V) Strain o Srface Modls, Ksi Contact Pressre Distribtion: 65 psi '" 4.1.s: c: 3.0 '" 4.1 c: :c I :l V) 'Compressive Strain Figre Srface Modls, Ks; Tensile micro-strain contors at the bottom of the srface for a 30 Ksi base modls and a tire load of bs '. 27

44 srface modli and thicknesses, and tire loads and contact pressres on strains at the top of the sbgrade. The effect of tire contact pressre on vertical sbgrade strain is not significant for the thicker, stiffer srfaces, in fact, the differences in strains in Figre 16 are abot 20 micro-inches per inch for srfaces with greater than 2 inches having modli of 400 Ksi or greater. However, when both srface thickness and modls decrease, the strain differences are mch larger for tire contact pressres between 26 and 65 psi. In comparing the reslts between Figre 16 and 18, a decrease in the base modls slightly increases the strains for the thick, high modls srfaces bt sbstantially increases the strains for thin, low modls srfaces. Figres 17 and 19 contain plots of the vertical sbgrade compressive strain for a tire load of 800 ponds, base modli of 60 and 30 Ksi, and contact pressres of 26 and 05 psi. The effect of change in tire load on the sbgrade strain can best be evalated by comparing the reslts in Figre 16 with Figre 17 and the reslts in Figre 18 with Figre 19. These comparisons show that increasing the tire load has little effect on sbgrade strain for the thick, stiff srfaces bt has a sbstantial effect for the thin, flexible srfaces. This trend is tre for both the 60 and 30 Ksi bases bt the effect is mch more prononced for the 65 than for the 26 psi contact pressre. Tensile Strain at the Top of the Srface. Tensile strains at the top of the srface are generally lower than those at the bottom. A previos report on this project (1) showed that when the srface modls is less that 100 psi and the srface thickness is less than 1.5 inches, the maximm strains at the top of the srface are often larger than those at the bottom. Notice in Figre 21 that increasing the tire contact pressre from 26 to 65 psi prodces an increase in the tensile strains for the thin low modls srfaces. The higher modls combinations show no sbstantial change in strains with increase in contact pressre. 28

45 Contact Pressre Distribtion: 26 psi c or o Srface Modls, Ksi Contact Pressre Distribtion: 65 psi c or- 4.0r r-r c 2.0 r--r------; o Srface Modls, Ksi Figre 16. Compressive micro-strain contors at the top of the sbgrade for a 60 Ksi base modls and a tire load of 1320 lbs. 29

46 4.0 en GJ c: VI en GJ - c: 2.0 t- GJ fg s.. :::l V') 1.0 "22 Contact Pressre Distribtion: 26 psi '" '" ' _ "----'00_ _ a Srface Modls, Ksi Contact Pressre Distribtion: 65 psi 4.0 en GJ 120 c: en en 140 GJ c: t- GJ fg 180 s.. :::l V') 1.0 o Srface Modls, Ksi Figre 17. Compressive micro-strain contors at the top of the sbgrade for a 60 Ksi base modls and a tire load of 800 lbs. 30

47 Contact Pressre Distribtion: 26 psi V1 QJ.s:: c: V1 V1 QJ c: s:: I- IV 11:1 s.. :::s V') o Srface Modls, Ksi Contact Pressre Distribtion: 65 psi V1 IV.s:: c: ==== V1 '" IV c: :c 2.0 I- IV s.. :::s V') 1.0 o Srface Modls, Ks; Figre 18. Compressive micro-strain contors at the top of the sbgrade for a 30 Ks; base modls and a tire load of bs. 31

48 Contact Pressre Distribtion: 26 psi '1 QJ.&: c:: '1 11'1 QJ c:: &: I- QJ IG s.. =s V') a Srface Modls, Ksi. Contact Pressre Distribtion: 65 psi en en QI c:: :c 2.0 I- QI IG s.. ::l V') 1.0 a 50 Figre Srface Modls, Ksi Compressive micro-strain contors at the top of the sbgrade for a 30 Ksi base modls and a tire load of 800 lbs. 32

49 Figre 21 contains the same type of data as that in Figre 20 bt for the 30 Ksi base. However, nlike the data in Figre 20, there is a sbstantial increase in the strain at the top of the srface for the higher contact pressre case. This indicates that for srfaces between I and 2 inches thick, that also have low modli; the magnitde of the base modls very significantly affects the strain. For the low contact pressre case, the base modli prodce no sbstantial differences in the strain at the top of the srface. Figres 22 and 23 show the tensile strain at the top of the srface for the 800 pond tire load. It is interesting to notice that in Figre 22, increasing the tire pressre for the 60 Ksi base modls does not sbstantially alter the tensile strain at the top of the srface for any of the srface modls and thickness combinations; sch is not the case for the 30 Ksi base, as shown in Figre 23. Increasing the tire contact pressre prodces a significant increase in strain for the low modli and thickness srfaces indicating again the need to provide strong bases to protect these pavement strctres. Fatige Damage Effects The calclated tensile strains at the top and bottom of the asphalt concrete srface are sed to estimate the nmber of 18-Kip eqivalent single axle loads (ESAL) applications ntil class 2 cracking occrs. Class 2 cracking is defined as fatige cracking that has progressed to the point where cracks have interconnected to form a grid-type pattern (1). A pavement srface that has a class 2 cracking is assmed to have failed in fatige. "The cracks that exist still maintain some aggregate interlock and are so spaced that the srface layer is considered to retain some ability to spport the load. At the AASHO Road Test observations were made of srface condition and the nmber of load applications to failre for a variety of axle loads and pavement material combinations. These test sections covered a wide range of pavement thicknesses and the nmber of weighted 18-Kip single axle load applications reqired to prodce class 2 cracking were measred. Material property data has been combined with field 33

50 Contact Pressre Distribtion: 26 psi 4.0r-.----rr-----r VI.&; c 3.0 VI VI C -.s:: I-,., Its.. V) o ' Srface Modls, Ksi Contact Pressre Distribtion: 65 psi VI.s:: c -.. VI VI c -.s:: I-,., Its.. V) o Srface Modls, Ksi Figre 20. Tensile micro-strain contors at the top of the srface for a 60 Ksi base modls and a tire load of 1320 lbs. 34

51 Contact Pressre Distribtion: 26 psi 4.0 lit QJ.s:: c: 3.0 -lit lit QJ c: -.s:: t QJ 10 ;:, '" '" 1.0 o Srface Modls, Ksi Contact Pressre Distribtion: 65 psi 4.Q lit QJ -.s:: c:.. lit lit QJ c: -.s:: t QJ 10 '" ;:, '" o Srface Modls, Ksi Figre 21. Tensile micro-strain contors at the top of the srface for a 30 Ksi base modls and a tire load of 1320 lbs. 35

52 Contact Pressre Distribtion: 26 psi III QJ.s:; C 4.0., III III QJ C.s:; t- QJ fa '+- c.i) o Srface Modls, Ksi Contact Pressre Distribtion: 65 psi III QJ.s:; C en en 41 c -.s:; 2.0 t- 41 fa '+- c.i) o Srface Modls, Ksi Figre 22. Tensile micro-strain contors at the top of the srface for a 60 Ksi base modls and a tire load of 800 lbs. 36

53 Contact Pressre Distribtion: 26 psi 4.0 VI C1J.s::: c: VI VI C1J c:....s:::.- C1J 10 ::::l V) o Srface Modls, Ks;. Contact Pressre Distribtion: 65 psi VI C1J.s:::... c:.. VI VI C1J c: -.s:::.- C1J 10 ::::l VI ) 10/ 20 I V o Srface Modls. Ks; Figre 23. Tensile micro-strain contors at the top of the srface for a 30 Ksi base modls and a tire load of 800 lbs 37

54 observations and theoretical stdies to develop a fatige relationship for the AASHO Road Test asphalt concrete pavements,6). Roberts and Rosson (1) recalclated the tensile strains at all AASHO test sections sing ILLIPAVE and an estimate of the contact pressre distribtion for a trck tire inflated to 75 psi. The revised fatige eqation is: W = E-13 (1/et) where W = nmber of axle loads prior to class 2 cracking and et = transverse tensile strain. The vale of K1, E-13g in the fatige eqation is an average vale that reflects the temperatre condition dring the AASHO Road Test since the applications to failre data were secred from those experiments. However, seasonal effects for different environments can be evalated by varying K1 with temperatre as shown by Roberts, von Qints, Finn, and Hdson (2). Since the objective of this portion of the analysis is to demonstrate the magnitde of the effect of tire pressre, the athors decided that sing a constant vale of K1 was sfficient. It shold be noted, however, that K1 varies over several orders of magnitde for temperatre ranges experienced in most locations. Figres 24 throgh 27 show the nmber of loads to failre, Nf, calclated by converting the strains from Figres to Nf for the varios combinations of srface thicknesses and modli. These data also show that the highest nmber of applications to failre occr in the pper right and lower left corners where the lowest strains occrred. Srface modls and thickness have a very significant effect on the nmber of applications to failre. To keep the fatige life of the pavement high, the srfaces shold be either weak and thin or strong and thick. To translate these data into years of life, consider that a low volme road experiences approximately 500 average daily traffic. For this type of road, the normal traffic in 5 years wold apply 1,905,000 axle loads. Figre 28 shows the cmmlative nmber of vehicle load applications for sch a road in a period of p to 20 years. Figre 24 indicates that thick, low modli srfaces will not provide adeqate life 38

55 Contact Pressre Distribtion: 26 psi 11'1 ell..t= c:... 11'1 11'1 ell c: -..t= t- ell IG 't- :::7 V) o Srface Modls, Ksi. Contact Pressre Distribtion: 65 psi 11'1 ell..t= c: '1 11'1 ell c: -.c t- ell <0 't- :::7 V) 4.0r o Srface Modls, Ksi Figre 24. N contors in millions as a fnction of the tensile strain f at the bottom of the srface for a 60 Ksi base modls and a tire loads of 1320 lbs. 39

56 Contact Pressre Distribtion: 26 psi ====== c or o Srface Modls, Ksi Contact Pressre Distribtion: 65 psi c or-. c or- 4.0 r p a Srface Modls, Ks; Figre 25. N contors in millions as a fnction of the tensile strain f at the bottom of the srface for a 30 Ksi base modls and a tire load of 1320 lbs. 40

57 Contact Pressre Distribtion: 26 psi 4.0r-1l1l---r ' c r----r c 2.0 r-1=====$=;;==----:: r------r o Srface Modls, Ksi Contact Pressre Distribtion: 65 psi c or- - c or o Srface Modls, Ksi Figre 26. N contors in millions as a fnction of the tensile strain f at the bottom of the srface for a 60 Ksi base modls and a tire load of 800 lbs. 41

58 Contact Pressre Distribtion: 26 psi I) QJ.s: c: -I) I) QJ c: -.s: t- QJ ;:, c.n '"' o Srface Modls. Ksi Contact Pressre Distribtion: 65 psi I) QJ.s: c: -.. I) I) QJ c: -.s: t- QJ :;, c.n '"' o Srface Modls, Ksi Figre 27. N f contors in millions as a fnction of the tensile strain at the bottom of the srface for a 30 Ksi base modls and a tire load of 800 lbs. 42

59 12-.. CD 9-. -«S -., Q. Q. c «S_ o -c:= 6- E -.s d z YEARS Figre 28. Cmlative nmber of vehicle load applications. 43

60 for this road. Observe that these thick, low modli srfaces provide less than 1,000,000 axle load applications. The nmber of axle load applications is considerably redced as the base modls decreases as shown in Figre 25. Notice again that thick, high modls srfaces or thin, low modls srfaces can provide adeqate service. Rtting Effects The calclation of cmlative permanent deformations in pavement strctres is a complex problem and research is still being condcted. Rtting can be the reslt of permanent strains that occr in any or all of the layers of a pavement strctre. Previos stdies ) have shown that protection of the sbgrade from rtting can occr if the vertical compressive strains are kept below a critical level. The compressive strains at the top of the sbgrade have been calclated sing ILLIPAVE and these strains were sed to estimate the nmber of axle load applications ntil excessive wheel path rtting develops. The model sed for these estimates was developed by Shell Development Corporation. Shell engineers (Z) sed reslts from the AASHO Road Test to develop a compressive strain criteria eqation: W = 6.15E17 (l/ec) 4.0 where W = No. of loads reqired to prodce a rtting failre. ec = vertical sbgrade compressive strain. Since the tensile strain criterion was developed sing data from the AASHO Road Test, the Shell compressive strain eqation was selected for se in this analysis for compatibility with the fatige model inclded in the previos section. Table 1 shows the vertical sbgrade compressive strain for different combinations of srface modli and thicknesses for the weak base layer, 65 psi contact pressre, and the 1320 ponds tire load. For the highest compressive strain, 1226 micro-inches for the 1 inch, 50 Ksi srface, the Shell eqation prodces an Nf of 240,000 load applications. In a similar stdy condcted on trck tires (1), the ESAL for a 1 inch, 50 Ksi srface on a weak base layer was only 13,900 wheel load applications. However, 44