Effect of Fracture Healing on Laboratoryto-Field

Transcription

1 TRANSPORTATION RESEARCH RECORD Effect of Fractre Healing on Laboratoryto-Field Shift Factor ADLI AL-BALBISSI AND DALLAS N. LITTLE Laboratory fatige testing of asphalt co~crete can be sed t.o predict field performance. The introdction of a shift factor 1s necessary to accont for the effects of res!dal stresses and healin.g that occr in the field bt do not occr m the laboratory. In this stdy the healing mechanism in asphalt concrete is investigated. A theoretical hypothesis for the shift factor and a new approach to characterizing the toghness of paving mi~tres ba~ed on the I-integral concept are also introdced. Th~ shift factor 1s assmed to consist of the combined effect of a stram recovery component and crack recovery component. The two components can be determined from simple laboratory tests, inclding stress relaxation, beam fatige, and the overlay tests. The fractre mechanics approach, the J*, is based on the path-independent J mtegral, which can be defined as the energy released per mt area of crack extension. The J* parameter is adopted to characterize material toghness. Loss of strctral or fnctional pavement serviceability becase of load-related fatige cracking has long been a major topic of concern to highway engineers. Sch failres often occr becase of improper prediction of pavement fatige life or prematre failre from crack propagation. It is important, therefore, to nderstand the mode of fractre initiation and propagation for carefl design of highway or airport pav~ments. Sch nderstanding may lead to a procedre for estimating a shift factor between laboratory and field reslts that will consider the actal mechanics of fractre. Althogh sch a factor may seem to be of little se to someone dealing with everyday pavement problems, it is of great significance for a more accrate prediction of pavement life and can be of great practical vale.. The primary goal of this stdy is to introdce a practical approach to estimating the shift factor and to investigating and evalating the effect of rest periods on healing fatigecased fractres in asphalt-treated mixtres. It is believed that the effect of healing and residal stresses that occr in the field bt not in the laboratory are the major factors that will contribte to more accrate prediction of fatige performance. In fact, prediction of field performance based on laboratory testing will normally reslt in miscomptation of the pavement life by a range of 3 to 2, percent. Identification of the healing mechanism and qantification of the effects of selected variables will, no dobt, lead to a mch improved ability to predict pavement life. It will provide the basis for procedres to increase the life of asphalt strctres by maximizing the healing process. A. H. Al-Balbissi, Civil Engineering Department, Jordan University of Science and Technology, Irbid, Jordan. D. N. Little, Texas A&M University, College Station, Tex Evidence for the existence of a healing mechanism has been provided by several laboratory stdies, in addition to that prodced by the AASHTO Road Test. The most detailed stdy has been reported by Rothly and Sterling (1,2), with additional evidence being provided by McElvaney and Pell (3), Borgin and Forier (4), and Van Dijik (5). These stdies have attempted to qantify the effect of rest periods and have expressed the reslt as a ratio of the nmber of cycles to failre with rest to the nmber of cycles to failre withot rest. The stdies mentioned above all indicate that the ratio is greater than one, that is, life measred dring cyclic loading that incldes rest periods is greater than life nder continos cyclic loading. These stdies spport the view that asphaltic materials have the capacity to recover from the effects of stress- that is, there is a healing mechanism. Previos stdies have also mentioned that the healing process is affected by the rate of loading, stress level, dration of rest periods, and the method sed to apply the loads. METHODOLOGY Althogh there is not mch literatre abot healing stdies for asphalt cement and asphalt concrete, there is literatre abot evalating the healing of polymers. The experimental concept for the evalation of healing has generally been to select a convenient dimensionless recovery ratio, sch as the ratio of fractre stress for the virgin material to fractre stress of the healed material. In many relevant stdies the healing process was described as taking place in several stages (6, 7). Woo and O'Conner (6) and Jd et al. (7) were able to develop relations for strength, elongation to break, impact energy, and fractre parameters as a fnction of time, moleclar weight, temperatre, pressre, and processing conditions. Many of their theoretical predictions were spported by experimental data. These stdies provided excellent indications that mechanical means (throgh the laws of fractre mechanics) can be sed to determine the strength change cased by healing. In this stdy the energy concept is selected as the indicator for material healing. This criterion is adopted becase of its engineering significance and its relative ease of measrement. In addition, the increase in dissipated energy reslting from rest time is adopted to otline a model for the estimation of a shift factor between laboratory and field reslts. The testing procedre sed in this stdy employed the overlay tester, which was developed at Texas A&M University, College Station. The overlay tester is a fatige testing machine designed to model displacements cased by thermal stresses in asphalt pavements reslting from cyclic changes in the

2 174 TRA NSPORTA TION RESEA RCH RECORD 1286 FIGURE 2 Specimen monted on plates. FIGURE 1 Overlay testing device. ambient temperatre. A servohydralic mechanism controls the rate of loading as well as the crack opening displacement and allows a controlled strain condition to be maintained throghot the test. Beam samples 3 in. by 3 in. by 15 in. are prepared and then cred in an environmentally controlled room (77 F, 25 percent relative hmidity) for a minimm of 3 days. Each sample is gled to a pair of alminm base plates in an arrangement that simlates the constrction of an overlay over a cracked or jointed pavement. Figre 1 shows an illstration of the testing device. Figre 2 shows an illstration of specimen monting. The overlay tester is calibrated to ensre the desired maximm displacement of.4 in. or.2 in. A movement of.4 in. is approximately eqivalent to the displacement experienced by a Portland cement concrete pavement with 15-ft joint or crack spacings as it ndergoes a 6 F change in pavement temperatre. The actal testing procedre consists of sbjecting the overlay samples to an oscillating movement of opening and closing the btt joint of the two base plates. This type of movement cases a crack to form from the bottom of the sample pward throgh the sample. "Failre" is defined as the condition in which a continos reflection crack is visible p both sides of the sample and across the entire width of the top of the sample, as observed when the overlay tester is in the "open" position. Under this condition, the load reqired to open the gap between the sample base plates is cased by the frictional forces that mst be overcome to separate the two sample parts. A loading rate of one cycle per 1 seconds was sed throghot the test program. The cyclic motion was maintained except dring the rest periods, dring which the samples were left in the "closed" position. The load and displacement vales were monitored and recorded only dring selected cycles of each test. An X-Y recorder was sed to plot the applied load verss displacement relationship dring the selected cycles. Figre 3 shows an illstration of the X-Y plotter. Figre 4 illstrates the general shapes of typical load verss displacement graphs at varios stages dring the test. ANALYTICAL APPROACH To precisely evalate the energy associated with fractre fatige or, more generally, crack propagation, one mst select a theoretically sond analytical approach. The science of fractre mechanics offers sch an approach. Of corse, asphalt cement and, in trn, asphalt concrete is not a linear-elastic material. Conseqently, linear-elastic fractre mechanics is not valid. It is safe to assme that the behavior at the crack tip is nonlinear with a relatively large plastic zone preceding the crack tip. Possible methods of analysis inclde the crack tip opening displacement method (CTOD), R-crve analysis, or the ] integral method. Under conditions of plane strain in which the crack tip plastic zone is small, linear elastic analysis is appropriate. For materials and conditions nder which the plastic zone becomes larger, it is important that the effective crack length be sed to calclate an effective stress intensity factor. However, becase the plastic zone itself is a fnction of the stress intensity factor, an iterative process is necessary to calclate an effective stress intensity factor; as the size of the plastic zone adjstment becomes larger, relative to the crack size, the comptation becomes less accrate. Under sch conditions a method that permits extension of linear-elastic fractre mechanics into the elastic-plastic region mst be sed. The I-integral is best sited for the analysis of test data in this stdy. A major advantage of the I-integral method is that it does not reqire a stringent

3 Al-Balbissi and Little 175 FIGURE 3 X-Y plotter. specimen size to ensre an acceptable small plastic zone size. The method allows the determination of energy release rate (1 1 ) sing a small specimen. Althogh pavement materials can be assmed to behave elastically in fractre becase of their large size, size limitations of laboratory specimens prevent similar behavior. The large size of pavement constittes a constraint to the development of a large plastic zone; ths, elastic behavior can be assmed. Conversely, the development of a large plastic zone in laboratory specimens is expected. The seflness of the I-integral analysis is that one can infer information abot the behavior of the elastic pavement based on laboratory specimens that may have experienced elastic deformation. The rationale is that the amont of energy released by a specific material per nit area of crack extension will be the same regardless of the size of the specimen. The I-integral procedre provides a way to calclate this energy release rate for an elastic material from small specimens that may have some plastic deformation. The path-independent I-integral proposed by Rice (8) is a method of characterizing the stress-strain field at the tip of a crack by an integration path taken sfficiently far from the crack tip to be sbstitted for a path close to the crack tip region. Ths, even thogh considerable yielding occrs in the vicinity of the crack tip, if the region away from the crack tip can be analyzed, behavior of the crack-tip region can be inferred. The I-integral is defined as the energy released per nit area of crack extension. It may be interpreted as the potential energy difference between two identically loaded bodies having neighboring crack size, or J = - (l/b) (dv/da) (1) I (+I 1 friction of Tt Appm1ts lncrting Displ11cement ~' ==~========================================== NO TEST SPECIMEN - Ttn sion A~.,, 3 Comprts.sion Area (-J Loa + din Cycle x Cy cle x +1 Tension Ar (+I Compression Area ( - I INTERMEDIATE STAliES OF TEST Tension De to Adhesion of Asphalt Cement to Broken rf aces Compression of Broken Specimen LATTER STAGES OF TEST (at or near failre) FIGURE 4 Typical recordings of load verss displacement at varios stages dring an overlay test.

4 176 TRANSPORTATION RESEARCH RECORD 1286 where V = potential energy, B = thickness, and a = crack depth. This definition is shown schematically in Figre 5. A more detailed discssion of the!-integral is provided elsewhere (8). Path independence of the!-integral has been shown ths far by sing only the deformation theory of plasticity, which does not allow for nloading. Therefore, the!-integral fractre criteria mst presently be restricted to conditions nder which nloading does not occr. In the overlay test, cyclic loading and nloading of the specimen occr, which sggests that the!-integral cannot be sed, becase the basic definition of the!-integral is the energy released per nit area of crack extension. The difference then in the released energy between the case with nloading and the case withot nloading is manifested in the area nder the load-displacement crve, i.e., when nloading is considered, the V* incldes all the area enclosed by the load-displacement loop, as illstrated in Figre 4. Therefore, the parameter J* = (l/b) (dv*/da) (2) where V* is the energy released, inclding the nloading area, was adopted for analysis. The total area (V*) reflects the energy released by the material and incldes the effect of nloading. Therefore, the J* parameter is deemed to be appropriate to characterize material toghness (the name J* was adopted becase it is analogos to the!-integral definition). p STUDY OF EFFECT OF REST PERIODS ON HEALING The fatige characteristics of pavement mixes are determined in continos loading tests. These conditions do not resemble actal loading conditions in the field. Under traffic, the pavement is loaded discontinosly becase the passage is interrpted by rest periods. Preliminary tests of this stdy indicated that a single rest period had no significant effect on pavement life or fractre characteristics. To obtain a more complete insight into the effect of rest periods on the fatige life, more tests were performed. A smmary of these tests is given in Table 1. The reslts of varios dration of rest indicate that very long rest periods did not indce significantly greater strain recovery than did shorter rest periods. Several drations were attempted on the same specimen. Test reslts show that the recovery rate decreased as the test progressed. Generally, test reslts showed that within a rest period of between 15 and 4 mintes, a considerable proportion of the recovery can be achieved, and longer rest periods of 1 or 2 days do not sbstantially increase recovery. However, a 4-minte period was not mch better (in terms of added energy) to a 15-minte rest period. In addition, a gap of 4 mintes between traffic vehicles in a real application occrs only on highways with very low traffic volme. Fatige is more a problem in highways with moderate to heavy traffic. Therefore, for these practical prposes, a rest period of 15 mintes was implemented in the remainder of the tests. Tests with a variable nmber of rest periods showed a very high correlation between the nmber of rest periods and fatige life. The reslts showed an increase in fatige life of the specimen by a factor of 2 to 5 when rest periods were introdced. These reslts were consistent at the two displacement magnitdes examined. SHIFT FACTOR HYPOTHESIS p -1 d1 I--- FIGURE 5 Interpretation of ]-integral. The shift factors sed to transform the laboratory phenomenological fatige model into a field "eqivalent" have, in the past, been determined empirically. Perhaps the best known version was developed by Finn et al. (9) from AASHTO Road Test data. Yandell and Lytton (1,11) condcted a detailed stdy of the residal stresses in a pavement. They indicated that, becase of residal compressive strain, the tensile strain reslting from a wheel load application is eqivalent to 8 percent of the strain that reslted from the preceding wheel load application. Frthermore, the athors presented some enlightening hypotheses on how the fatige shift factor is affected by rest periods and residal stresses. The athors examined these hypotheses throgh the stdy of the effect of rest periods on the fatige life of plasticized slfr binders sed in asphaltlike mixtres. These stdies have sbstantiated their hypotheses. Dring a rest period, two recovery processes may take place. In one process the material relaxes and loses some of its residal strain. In the other process the material is given time to heal from its distressed state, dring which the size of the plastic zone ahead of a formed crack is redced. Dring this time a portion of the crack can be closed becase of the

5 Al-Balbissi and Little 177 TABLE 1 SUMMARY OF OVERLAY TESTS Di splacement magnitde (inl Witb rest periods Withot rest periods No. of Specimens Rest period dration (hr. l l i 24 No, of e.pecimena 2 1 l 2 l 1 t!ll!lll2~[ llt l-1!! ll-2q ~1-~Q t!lllll.!m 2~ PU ill~~ ;-~Q -~q ~H-f!Q till [&it 81;!~~im~J;UI compression reslting from bond forces between the particles of the material after the removal of the applied load. These two effects will reslt in increasing the expected fatige life of a specimen. Considering the fact that a field loading pattern is similar to laboratory loading with rest periods, an analytical approach can be postlated to estimate a shift factor between laboratory and field reslts. In this approach the shift factor is assmed to consist of two components as follows: SF, = { 11[ 1 - (1 - Po)t-"Jr (6) where k 2 is the slope of the beam fatige laboratory relationship between the nmber of cycles to failre (N 1 ) and initial strain. The shift factor component related to crack healing is estimated on the basis of rest period analysis. These analyses revealed a relationship between added energy and the logarithm of rest dration of the form (3) d = eh log I (7) where SF, = the shift cased by residal stresses, and SFh = the shift cased by crack healing and plastic zone redction. The behavior of the material dring the residal strain component (SF,) is very mch analogos to relaxation characteristics and strain recovery characteristics. This behavior permits the assmption of similar decay and recovery patterns. The stress relaxation relationship can be presented in the form where d = the added energy, t = time, and h = constant. The analysis also revealed a direct relationship between the amont of added energy and the increment in specimen life of the form d n 1 = a + m (d) (8) E(t)IE = 1-n (4) Combining the last two eqations gives where E(t) Eo n= the elastic modls at time t, the initial elastic modls, and the slope of the relaxation crve. The ratio of the strain at a given time to the initial strain [ P(t)/(P )] can be fitted to a relationship of the following form : P(t) = 1 - (1 - P )t-n (5) To reflect this characteristic pattern on the expected fatige life, the following relationship is assmed: d n 1 = a + m (eh log ') (9) Using the above eqation with coefficients developed experimentally, dn 1, and conseqently n 1, were compted for varios time periods. Frthermore, a relationship between cycles to failre and nmber of rest periods was developed (Figre 6) from the analysis of rest periods. Using this relationship, the corresponding nmber of rest periods (n,) for the compted N 1 was determined. The variable (n/n - 1)/ n,, where n is the fatige life withot rest, was then compted for the varios time periods. A relationship of the following form was then fitted to the compted variables:

6 178 TRANSPORTATION RESEARCH RECORD HO z: " L. ::i ~... "' 14 ~ 72 E- 6.. "'" 41 3 z NO.of Cyd to f1ilre YI No. of Rt Ptri1ds X X ~C Cl s.-iy' -- x AC- 1 Sm of Added Energy VS No. of Rt Periods.t AC-1 o---o CR I c: 15;:. w_..... >-, c. 75 -: < " ':; e ::I 1,5 VI Nmber of Rest Periods, N so FIGURE 6 Relationships between (a) nmber of cycles to failre and nmber of rest periods and (b) sm of added energy and nmber of rest periods. (N/No - l)!n, = x 1-3 e 1.9s6(1og rj (1) which can be redced to (N/N ) = x 1-3 e i.9s6(1og 1J (11) Combining the two shift factor proportions yields SF = { 1/ [ 1 - (1 - Po) t-n Jr X [ x 1-3 el.956(1og 'ln,] (12) Using a K 2 = (a typical slope coefficient developed for plasticized slfr binders in beam fatige tests) and typical slope vales of stress relaxation crves (n) for the same materials, with varios nmbers of rest periods (n,), several combinations of SF, and SFh were compted and are presented in chart form in Figre 7. The chart can be sed to select the two components of the shift factor that correspond to a certain rest time. The total shift factor will be the prodct of the two components. Asphalt cement (AC-1) is expected to have a higher shift factor becase it showed better healing characteristics. Test reslts indicate a K 2 vale of for asphalt cement (AC-1). This will reslt in higher vales for SF, and, conseqently, a higher overall shift factor.... ;t: ~ Rest Time, Min. FIGURE 7 Shift factor chart. 4

7 Al-Balbissi and Li/e 179 TABLE 2 LABORATORY-TO-FIELD SHIFT FACTORS USED FOR ASPHALT CONCRETE AND SULPHLEX Shift Factors N1ab T 36 F T 68" F T = 11 F All parameters on the righthand side of the shift factor relationship can easily be determined from laboratory tests. Coefficients of the crack healing portion can be determined from overlay tests with rest periods. The n parameter can be determined from a relaxation test and the K 2 -parameter can be determined from a simple beam fatige test. This relationship presents a simple, practical, and convenient means to estimate a shift factor between laboratory and field reslts. ANALYSIS OF TEMPERATURE EFFECT To illstrate the effect of temperatre on the shift factor and to demonstrate the field conditions for comparative analysis it was necessary to represent field conditions. The shift factors sggested by Pickett et al. (12) (Table 2) were selected for both asphalt concrete and Slphlex for the following reasons: 1. Utilization of identical shift factors for asphalt and Slphlex is considered an acceptable approach ntil field verification indicates that different factors shold be sed, 2. The rest period analysis points ot a similar healing response for Slphlex CR5 and AC-1 specimens, and 3. Shifting AC-1 laboratory beam fatige data by means of the Pickett factors yields a realistic failre criterion, which is comparable to that of Finn et al. (13) (Figre 8). The time-temperatre shift factors (ar) for Slphlex and asphalt mixtres with varios aggregates and gradations were then compared and are shown in Figres 9 throgh 11. The following are apparent from these figres : 1. Shift factors for asphalt concrete and Slphlex for each mixtre evalated were similar. In fact, the effect of binder on ar was not statistically significant. fi1ld Crihrion AC- 1 L1bor1tory Crve Shilt by pik 111 shift factors ~ ' '".. ;:----"_,._,--'2...P.;::-:::::..-..::-,,,,,c_ , t Si. U! c: ;; L -V1.. ;;;.. i!!. fi1u CritloP Finn 1h 113 I Fro A SHTO Rd Tt Anlrsis Lib. Crihritn AC-11 Llbtr1hry." cr l TAHU I =-?k:-'"'"'.-----I Ulff1 1-_ tt' _.._~....L..,-~-..._._.. '-7--_. ~~. ~'""-;-_._-....'-:--'---'--'-~.,,.. 11,,, tt',,. FIGURE 8 Illstration of laboratory-to-field shifts. Ln~ Rtpttitiens

8 +2 " Is i IL i VI "'..3-2 ' ' ' ~ ~ :"-... CR S '< AC L-~~~-'-~~~---'~~~~_._~~~~~~~~~ Temperatre, ~ FIGURE 9 Time-temperatre shift factor for mixtres with crshed limestone aggregates ".. IL " i VI "'..3-2 ~ CR S AC Temperatre,~ FIGURE 1 Time-temperatre shift factor for mixtres with basalt aggregate.

9 Al-Balbissi and Little " s ".._ " i VI... ~ - 2 AC ) m T1111per1tr1,, FIGURE 11 Time-temperatre shift factor for mixtre with river gravel aggregate. 2. Ranges of shift factors between 1 F and 4 F are typical of those fond in the literatre for asphalt concrete (12) and slfr extended asphalt mixtres. 3. The effect on the shift factor of aggregate type was as great as that of binder type. Althogh for practical engineering prposes both Slphlex and asphalt concrete can be considered linearly viscoelastic, the application of a horizontal shift factor along the log time abscissa to prodce a master crve is sbjective. The vale becomes even more sbjective when the shift factor is described in terms of beta. The term beta is defined as the ratio of the change in log 1 at over a change in temperatre or a temperatre interval. Beta = Delta(log 1 at)/delta T (13) This vale assmes a linear relationship between log 1 at and temperatre. As can be seen from Figres 9 throgh 11, this relationship is not the case. The vales of beta are presented in Table 3. CONCLUSIONS In this stdy a new approach to characterizing the fractre behavior of paving mixtres has been introdced. A modified form of the!-integral was implemented. The modified form is based on the total area nder the load displacement crve that incldes the nloading portion instead of jst the loading area in the conventional!-integral approach. A major advantage to this approach is the ability to extend the analysis into the elastic-plastic region, ths eliminating the reqirements for a stringent specimen size to ensre plane strain conditions. The analysis of rest periods indicated a direct relationship between the nmber of rest periods and fatige life. The analysis showed that an increase in fatige life reslts from an increase in the nmber of rest periods. Additionally, the rate of incremental benefit from rest periods diminishes as the dration of the rest period increases (Figre 12). The rate of added energy decreases sbstantially for rest periods longer than 3 mintes. The recovery trend as a fnction of time can be described by an exponential fnction. Material recovery patterns as a fnction of crack length resemble energy release patterns. The theoretical basis for a shift factor is presented based on Lytton's hypothesis. The shift factor is assmed to consist of the combined effect of a strain recovery component and crack recovery component. The two components can be determined from simple laboratory tests consisting of stress relaxation, beam fatige, and overlay tests. Limited rest period testing on AC-1 specimens and CRS specimens at room temperatre reveal that althogh the fractre propagation life (N 1 ) is sperior for AC-1 specimens compared with that for CRS specimens, healing properties at 73 F are similar.

10 TABLE 3 SUMMARY OF BETA VALUES Binder Aggregate Air Voids Content,\ BETA AC-1 CLS RG Basalt CR5 CLS Basalt RG H l.o 2.7 {I. 2.4 Ltttn~ : I x. E 2.1 x CR AC 5-1 ~ ~ "a 1.5 t 1.2 x O.l Rest Period Dr1tion, Mintes FIGURE 12 Effects of dration of rest period on energy reqired for crack propagation (specimens were CRS and crshed limestone).

11 Al-Balbissi and Lillie REFERENCES 1. K. D. Rothly and A. B. Sterling. The Effect of Rest Periods on the Fatige Performance of a Hot-Rolled Asphalt Under Reversed Axial Loading. Proc., Association of Asphalt Pavmg Technologists, Vol. 39, K. D. Rothly and A. B. Sterling. Some Effects of Loadmg History on the Fatige Performance of Rolled Asphalt. Report LR496. Transport and Road Research Laboratory, Crowthorne, Berkshire, England, J. McElvaney and P. S. Pell. Fatige Damage of Asphalt: Effect of Rest Periods. Highways and Road Constrction, Vol. 41, No. 1766, October P. Borgin and J. B. Forier. Performability, Fatige, and Healing Properties of Asphalt Mixes. Proc., 2nd International Confer~nce on the Strctral Design of Asphalt Pavements, Ann Arbor, Mich., W. Van Dijik. Practical Fatige Characteristics of Bit.minos Mixes. Proc., Association of Asphalt Paving Technologists, Vol. 44, R. P. Woo and K. M. O'Conner. A Theory of Crack Healing in Polymers. Jornal of Applied Physics, Vol. 52, No. 1, 1981._ 7. K. Jd, H. H. Kasch, and J. G. Williams. Fractre Mechanics Stdies of Crack Healing and Welding of Polymers. Jornal of Materials Science, Vol. 16, No. 1, J. R. Rice. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Jornal of Applied Mechanics, Transactions, ASME, Vo.I. 35, Jne Use of Distress Prediction Sbsystems for Design of Pavement Strctres. Proc., 4th International Conference on the Strctral Design of Asphalt Pavements, University of Michigan, Ann Arbor, W. Yandell and R. L. Lytton. Residal Stresses De to Travelling Loads and Reflection Cracking. Report Texas Transportation In tittc, Co llege S1a 1ion. 11. W. Yandell and R. L. Lytton. The Effect of Residal Stress and Strain Bild-Up in a Flexible Pavement by Repeated Rolling of A Tire. Report RF487-l. Texas Transportation Institte, College Station. 12. Extension and Replacement of Asphalt Cement by Slfr. Re~ort FHWA-RD FHWA, U.S. DepartmentofTransportatmn, March F. Finn, C. L. Saraf, R. Klkarni, K. Nair, W. Smith, and A. Abdllah. NCHRP Report 291: Development of Pavement Strctral Sbsystems. TRB, National Research Concil, Washington, D.C., Pblication of this paper sponsored by Committee on Flexible Pavement Design. 183