Performance of Flexible Pavements

Transcription

1 TRANSPORTATON RESEARCH RECORD Performane of Flexible Pavements JAMES MARK MATTHEWS AND B. B. PANDEY An investigation was onduted to determine the life period of full-depth granular pavements in ndia. Benkelman beam defletions, rutting, raking, and pathing were measured on different test setions to alulate the performane of the pavements. A repeated-load-test apparatus was fabriated in the laboratory for testing the subgrade soils and water-bound maadam base to determine the elasti moduli under repeated triaxial stress onditions. A finite element omputer program was developed to determine the stresses and strains in pavement layers and to orrelate the pavement performane and the ritial stress and strain values. The pavement surfae defletions measured by Benkelman beam are in lose agreement with the values predited by the omputer program. From the repeated-load-test results, relationships were found between (a) the resilient modulus and the lateral pressure and (b) the resilient modulus and the sum of prinipal stresses. The equation developed for prediting the rut depth from the Benkelman beam defletion data is in lose agreement with that developed in the AASHO road test. The rut depth was also related to the gravel surfaing depth and the umulative axles. Finally, a regression equation for finding the lives of flexible pavements was established using the rut depth and subgrade vertial strain values. Highway engineers have been onstantly working toward developing a rational method to estimate the life of a given pavement through full-sale road tests, model studies, laboratory experiments, and theoretial analysis. Unlike steel and onrete, whose strutural properties are well defined, the behavior of rushed rok, water-bound maadam (WBM), and other granular materials is extremely omplex and was little understood until about 3 years ago. Sine then slow progress has been made in the development of a rational method to find the relationship between the life period of pavements and the design of onstituent layers. Flexible pavement methods are still empirial or semiempirial, on the basis of past experiene with similar subgrades, pavement materials, and traffi loads. These methods are satisfatory as long as the materials, traffi loading onditions, and layer thiknesses do not differ from those for whih the methods were developed. Beause of onsiderable inrease in frequeny and intensity of axle loads and the use of new pavement materials, the semiempirial design methods are no longer adequate. The fous here is on the study of the performane of WBM pavements and the laboratory evaluation of properties of the James Mark Matthews, Rihmond Field Station, nstitute of Transportation Studies, University of California, Berkeley, Calif Current affiliation: Department of Civil Engineering, Temple University, 12th and Norris Streets, Philadelphia, Pa B. B. Pandey, ndian nstitute of Tehnology, Kharagpur, , WB, ndia. pavement materials to predit the servieable life of a granular pavement in ndia. DEVELOPMENT OF FNTE ELEMENT ANALYSS A omputer program known as RAOP A VE was developed by idealizing the flexible pavement into a finite element ontinuum. The analysis was arried out for a single wheel load of 4,131 (9, lb) distributed over a irular area of 152- mm radius with a tire pressure of.55 MPa (8 psi). dealization n this investigation a layered pavement system was idealized as an axisymmetri solid with finite boundaries in both radial and axial diretions, as shown in Figure 1. The axisymmetri body was then divided into a set of ring elements, retangular in setion and onneted along their nodal irles. The finite elements are atually omplete rings in the irumferential diretion, and the nodal points at whih they are onneted are irular lines in plan view. Beause of axisymmetry, the three-dimensional problem redues to a two-dimensional ase similar to a plane strain problem. Tensile stresses and strains were taken to be positive, and ompressive stresses and strains negative. For eah element the four nodal points were numbered in the lokwise diretion. Eah node has two degrees of freedom. Displaement Funtions The two displaement omponents in a solid ontinuum varied as ompliated funtions of position. A number of approahes, inluding power series and Fourier series expansions, have been proposed by several researhers (1,2) to represent the behavior of displaement omponents inside eah element. Beause of the assumptions made about these funtions, the auray of the answer inreases as the element size dereases. For this investigation, the displaement funtions inside eah element were approximated by the following: where for eah element the loal oordinate system r',z' wa:s used, whih has its origin at the enter of eah element. (1) (2)

2 52 TRANSPORTATON RESEARCH RECORD RAD mm-j &.,,,,_,, 1:!., v FGURE 1 Finite element idealization..:= '* - A. A 1 V' "' l 1 l.? ), "' Global Stiffness The stiffnesses of all elements were assembled to obtain the total stiffness for the system. The required assembly was aomplished by using the element-node table and displaementode number array. Beause the system stiffness matrix omes out to be banded and symmetri, it is assembled in half-band form. A onsistent load vetor was formulated using the priniple of virtual work (3). Boundary Conditions Nodal points on the vertial boundary at a distane of 12 radii from the enter and on the enterline were onstrained from rndial movement; those on the bottom boundary were not allowed to move vertially or horizontally. The bottom boundary was fixed at a depth of 5 radii in aordane with the findings of Dunan et al. ( 4). Verifiation of Elasti Finite Element Analysis The validity of the finite element omputer program was established by omparing the results with those of Ahlvin and Ulery (5). The vertial and radial stresses along the enterline of the load, as shown in Figures 2 and 3, respetively, and at a radial distane of.752 radii (from the enterline of the load) obtained by the program, were ompared with those obtained by the elasti half-spae analysis after Ahlvin and Ulery. The defletions and stresses omputed by this program agree losely with those obtained from the elasti half-spae analysis. A detailed printout of the omputer program is provided by Tangella (6). Several other elasti multilayered omputer programs (e.g., ELSYM, BSAR, LLPAVE, and FEPAVE) are available for the strutural analysis of a pavement, and any of them also an be used. However, the finite element method using the priniple of stress transfer developed by Zienkiewiz et al. (2) is suitable for eliminating the tensile stresses in unbound granular layers. This work is beyond the sope of the present study and has been done elsewhere (7). EXPERMENTAL SETUP The shemati diagram of the experimental setup for repeated load triaxial tests is shown in Figure 4. The details of this setup and its mode of working are given by Tangella (6) and Tangella and Pandey (8).

3 Matthews and Pandey 53 1 BO " 6 CL ",,; 111 iii 4 u -e > " 2..!-.--r-rT,,.,.,,,.,,,.m,,-m.,,m;:;;;;:;;:;:;:""T"rm.,.,-, ) fh p.,. 111 rjelow fo<:e, rudii FGURE 2 Comparison between vertial stresses of RAOPAVE (open irles) and elasti half-spae analysis (at enterline of load) (losed irles) " u l; CL 5 "' iii u "' (J 2. 4 G. OeJ.dli Below Sudoe, Radii 8 ()fl 11)1 111 FGURE 3 Comparison between radial stresses of RAOPAVE (open irles) and elasti half-spae analysis (at enterline of load) (losed irles). Repeated-Load Experiments Speimens 1 mm in diameter and 2 mm in height were ast using the soil samples brought from the subgrades of the field test setions. The field bulk density was alulated for eah test setion at the maximum in-situ moisture ontent for eah of the four seasons. The samples were ast to the field density at the highest value of the in situ moisture ontent. Trials were made, varying the number of layers and the number of blows, using the standard Protor hammer (of N weight and 3-mm fall) to ompat the soil to the fixed volume. The variation in the moisture ontent of the speimen was kept within.2 perent. nitially, 1 load repetitions were applied to ondition the speimen. After 1, repetitions, for a given deviatori stress and for eah set of lateral pressures, the load ell and linear variable differential transformer (L VDT) pulses were reorded for about 3 load repetitions. The proess was ontinued until all sets of deviatori stresses were reorded. Strit ontrol was exerised in asting the speimens at the in situ moisture ontent and field density. Figure 5 shows the repeatability of two experiments. Deviatori stresses ranging

4 , l 7 s--- ':? -, [ "'l._, lo _l T l > i., _l "' Not to sale All dimension in FGURE 4 Experimental setup.!ll OU 1 OU ::; i in '- z ::; HO vi "S :::; 6 _'!' -;;;,, 1r 4 Confining Pressure J B KNSOM Material Subgrade 1 E. > r SECTON NO 1 lriol No l1ial No 2 ;>] u 1111 so uo 1 15 Deviolori Slress, KNSQ.M, 2 FGURE 5 Repeatability of two experiments.

5 Mathews and Pandey 55 from 15 to 15 knm 2 were applied to samples of 15 test setions. Lateral pressures of 13.8 knm 2 (2 psi) and 2. 7 kn m 2 (3 psi) were applied, whih are very lose to the subgrade lateral pressures found by the omputer program. Beause there is no signifiant hange in results under the yli lateral pressure or the onstant lateral pressure (equivalent to the mean of the yli lateral pressure) (9), a onstant lateral pressure is used in the laboratory study even though yli lateral pressure ours under atual onditions. The duration of the loading pulse was.12 se (JO). Tests for Other Soil Properties The laboratory California bearing ratio (CBR) tests at field densities and in-situ moisture ontents, liquid limit, plasti limit, and Protor ompation tests were onduted on soil samples of the subgrades of all the test setions of national highways. Repeated-Load Tests on Granular Materials Two types of aggregate gradations were adopted for repeatedload triaxial tests. One gradation adopted is the same as that of Monismith et al. (11,12), and the other orresponds to that of the ndian Roads Congress (RC ). The maximum size of the aggregate is 2 mm. Hiks and Monismith (13) found that the influene of grading on the resilient modulus for rushed rok is negligible. Hene, the results of repeatedload tests on RC B-type sreenings were used to analyze all layers of the WBM portion of the test setions. Dolerite hips were rushed to the required gradations, and 1 kg of material was prepared for eah speimen. Speimens of 1-mm (4-in.) diameter and 2-mm (8-in.) height were ast using a split mold. With the help of a needle vibrator, dry densities of 2224 kgm 3 (139 lbft 3 ) for the gradation given by Monismith et al. (11,12) and 2127 kgm 3 (133 lbft 3 ) for the gradation given by RC for B-type sreenings were obtained. A 5-psi sution was applied during asting of the sample and was ontinued until the sample was fixed in the triaxial ell. The proedures used to fix the sample and ondut the test are the same as those followed for soil samples, exept for the following details. Three sets of deviatori stresses were applied for all samples. The values were knm 2, knm 2, and knm 2 For eah of the deviatori stresses, seven sets of lateral pressures were applied (14): 69 knm 2 (1 psi), 138 knm 2 (2 psi), 27 knm 2 (3 psi), 276 knm 2 (4 psi), 345 knm 2 (5 psi), 414 knm 2 (6 psi), and 483 knm 2 (7 psi). All of these stresses are found in the field pavement strutures ( 6, 1,11). Using the results, relationships were found between (a) the resilient modulus and the lateral pressure, as shown in Figures 6 and 7, and (b) the resilient modulus and the sum of prinipal stresses, as shown in Figures 8 and 9. The results of this investigation are lose to those of Monismith et al. (J). EXPERMENTS ON N-SERVCE PAVEMENTS Seletion of Test Setions Fifteen test setions were seleted in the eastern parts of ndia, overing about 25 km 2 between the latitudes 19 N and 27 N and the longitudes 83 E and 88 E. For uniformity and quality ontrol in the test setions, the following riteria were used: 1. The preferred length of the test setion is 3 m. 2. The setion should be a straight streth with uniform soil harateristis and pavement strutural omposition. Steep longitudinal gradients and urves must be avoided. The streth should be ontinuous with no major repairs and with no ulverts in between. 1. :i i (fl ' z :::;, 2 Note:ndividual data points are not available for Monismith's work (Referene 11) - 3 _ llatarial:wbk r oulld in this invesligotion Monismith el al. (Conzales l>ye- poss, base) ( ll) 3. Monlsmith el al. (Morro bye, sub -base) (11) 1 1 Confining Pressure, KNSQM, FGURE 6 Confining pressure versus resilient modulus (11).

6 56 TRANSPORTATON RESEARCH RECORD :::i i Vl ' z :::; 3 Material:WBN Do l ll Deviatori Set Stress, KNSO A Confinin g Pressure, KNSOM FGURE 7 Confining pressure versus resilient modulus for granular materials (RC ). 1 :::i i ll ' z ::; J 2 1. ;;; "' Dolo Oeviotori Set Stress, KN SQ M J _ Material: WBN MR= 16.J(). 42 o Su m or Pr inipal Stresses, KNSQ M FGURE 8 Sum of prinipal stresses versus resilient modulus (11). 3. The maximum height of the embankment should be less than 6 m. 4. The setion should not be loated in areas likely to be flooded. 5. The setion should not be part of a newly onstruted road. 6. The oeffiient of variation of the Benkelman beam defletion data should be less than 33 perent to ensure the uniform strength of the test setion. Benkelman Beam Defletion Tests The Benkelman beam test was onduted using the Canadian Good Roads Assoiation's proedure (15) on the outer wheelpaths in both diretions at 1-m intervals. For a 3-m test setion, a total of 62 points were tested. Measurement of Rutting, Craking, and Pathing Rutting in wheelpaths was measured by a 3-m straightedge plaed transversely on the arriageway surfae. The observations were taken on both sides of the pavement. The maximum value of rutting in the wheel trak was measured at 1-m intervals. The perentage of raked and pathed areas of the pavement was measured for eah test setion. The strutural geometries, field densities, and moisture ontents were reorded.

7 Matthews and Pandey 57 1,J. 2 l ;;; " "' Data Devialori Set Stress, KNSQ M. l Material: WBH HR lb. *().412,. 1 t ,.-.,.---, , 1 1 Sum of Prinipal Stresses, KN SQ M. FGURE 9 Sum of prinipal stresses versus resilient modulus. Relationship Between CBR and Subgrade Modulus The relationship between the laboratory CBR (at field density and in situ moisture ontent) and the resilient modulus was developed for various deviatori stresses on the 15 test setions. The deviatori stress was varied from 15 to 15 knm 2. Figure 1 shows that the resilient modulus (MR) values are between the lines E (MNm 2 ) = 19.6 * CBR and E (MNm 2 ) = 7.55 * CBR with a mean line as follows: E = * CBR (3) Similar work was arried out on the subgrade of the Alonbury Hill experimental road (16). The relationship between the in situ CBR value and the modulus of elastiity determined from the Rayleigh wave veloity, shown in Figure 11, was as follows: E (MNm 2 ) = 13.3 * CBR PREDCTON OF BENKELMAN BEAM DEFLECTON AND VERTCAL SUBGRADE STRANS (4) Most roads in developing ountries (inluding large portions of the national highways) have WBM bases with a thin bituminous surfaing in the form of premix arpet or surfae dressing. Development of a suitable method for prediting surfae defletions and stresses and strains for these pavement strutures would be a valuable step in solving the problem of estimating the life period for a given thikness of WBM layer on a hosen subgrade soil. n this study the methodology adopted for stress analysis is similar to that used by Monismith et al. (11). The resilient modulus of the subgrade soil was estimated from Equation 3. Subbase and base ourses onsist of untreated granular materials. Beause these layers annot withstand tensile stresses, twie the value of subgrade modulus was assigned (17-19). The vertial and radial stresses were obtained at different points using the finite element omputer program. To these stresses the effet of self weight of the road struture was added. For eah layer a point is seleted at the enter of the layer on the axis of the wheel load. For these points the sum of the prinipal stresses was alulated in the WBM layers, and deviatori stresses were alulated in the subgrade soil. Using these values from the repeatedload experimental graphs (e.g., Figures 5 and 9), the moduli of the different layers were found. These modified stiffness values were then proessed by the omputer program. The iteration proess was ontinued until the moduli obtained from the omputer program oinided with those from the experimental data. Thus, the nonlinearity in the stiffness harateristis of the pavement materials is aounted for in the finite element omputer program. Table 1 presents a omparison of the predited surfae defletions obtained from the omputer program and the measured defletions obtained by the Benkelman beam method for the test setions. The average differene in the results of the two methods is 5 perent, with a range of 1.5 to 13.1 perent. Most of the test setions had granular base topped with a thin bituminous surfaing in the form of premix arpet or surfae dressing. The ontribution of thin, open-graded, bituminous surfaings to the strutural strength is negligible, and these highways were onsidered as full-depth granular highways. Although the bituminous surfaings of the five test setions (Setions 1, 9, 11, 12, and 14) had onsiderable thiknesses, severe grid pattern raking leading to the breakout of the bituminous surfaings was found on the wheel traks (beause of the large volume of truk traffi). Beause of this grid pattern raking, the load-spreading apaity of the bituminous surfaing redues onsiderably. Hene, for eah of the five test setions the bituminous surfaing was onsidered part of the granular layer. The total thikness of WBM and surfaing (equivalent WBM) is presented in Table 1. The defletions an also be measured using a suitable measuring

8 58 TRANSPORTATON RESEARCH RECORD l O - N ll - z 2: 2 -.!.. ;; ". E,!a.. is: n - FGURE 1. ' C.B.J\., 'Vo CBR versus resilient modulus. 9 zoo ;:; O z!,. '; :s " l o '"' t:j '.' : ':'!'.,. "'1 #' :: "' ',.,; A:,:: : -, o: '-r i"'l ; l' OXFORD CLAY AND SUPERMPOSED BOULDER CLAY PARTCULARLY STONY AREAS OF BOULDER CLAY ;;- "!""" -t- "'"' i' '!! tl"'! ; n situ CBR, ptr 1nt FGURE 11 n situ CBR versus modulus of elastiity for subgrode of Alonbury Hill Experiment rood (16). devie (e.g., the Benkelman beam). However, field measurements are ostly and time-onsuming, requiring interruption of the traffi (whih may be inonvenient, espeially on a busy freeway). Therefore, prediting the defletion would likely be useful to the field engineer in evaluating the strutural ondition of the pavement (2). On average, the test truk stands on a test point for 2 se during the Benkelman beam defletion test. From the test results given by Tangella (6), it an be observed that the effet of loading on resilient modulus is negligible (for a time range of.12 to 2 se). Figure 12 shows the results of a typial subgrade soil of a test setion. Hene, moduli values pertaining to.12-se loading time were used to analyze the pavement struture. The loading time due to traffi is about.12 se for a speed of 3 kmhr (JO) for the test setions under onsideration. The use of resilient moduli pertaining to.12- se loading duration is suitable to predit the subgrade vertial strains for developing relationships among rut depth, subgrade vertial strain, and umulative traffi in terms of equivalent single-axle loads (ESALs), as shown in the following setion. RESULTS AND CONCLUSONS Relationships were developed for 15 test setions on the national highways by arrying out regression analysis between (a) the laboratory CBR and the resilient modulus, (b) the average rut depth and the Benkelman beam defletion, () the average rut depth and the raking and pathing area, (d) the average rut depth and the vertial subgrade strain and umulative ESALs, and (e) the average rut depth and WBM thikness and umulative ESALs. Goodness of fit of the models, represented by the equations presented previously, to the observed data was evaluated by studying the orrelation oeffiients (R), the signifiane of eah independent variable, the standard error of estimate, and the residuals. For this purpose, t-tests and f-tests were done. A summary of the harateristis of the test setions is presented in Table 2. From the traffi data, inluding the axle equivaleny fators and the traffi growth rate (21), the umulative ESALs that

9 Matthews and Pandey 59 TABLE 1 COMPARSON OF PREDCTED AND MEASURED (BENKELMAN BEAM) DEFLECTONS OF TEST SECTONS Test Loation Equivalent Defletions seti on thikness Computed Measured Differ- WBM no. ene 1. Km to , NH6 2. Km to 14. O, NH32 3. Km 2S6.7 to 2S7., NHS 4. Km to 334.9, NHS s S.96S S OS3.999 S.1 s. Km 83.6 to 83.9, NHS Km 274.S to 274.8, NHS 7. Km 1. to 1.2, NHS 8. Km 137.S6 to , NH32 9. Km to 13S.O, NH33 1. Km 371. to 371.3, NHS 11. Km S9S.7S to S9S.37S, Nff Km 67. to 67.3, NH2 13. Km to 81. 7' NHS 14. Km 6S7.47S to 6S7.72S, NH2 15. Km to 13S.3, NH oos S S 1. s 26S 1. 6S S S S S.9 lso passed on eah test setion were found. The regression equation is expressed as follows: RD = *SYS * ESAL (5) U LOADNG TME, Se G"3. 1).f l(o1t1z Material Subgrade where RD average rut depth (mm), SYS subgrade vertial strain ( x 1-3 ) obtained from the omputer output (RAOPA VE), and ESAL = umulative equivalent single-axle loads ( x 17).,, N E % _, a; %. "! a; A;---- Equation 5 has a squared multiple regression oeffiient of. 951, a alulated F value of 116., and a ritial F value of at.1 signifiane level. Beause the alulated F value is greater than the ritial F value, the null hypothesis is rejeted, leaving the linear terms in the model. t would be useful, and seems a natural extension, to relate rut depth to gravel surfaing depth and umulative axles. This relationship is shown by the following equation: RD = * ESAL * TWBM (6) 2' where TWBM equals the thikness of WBM, in millimeters. Equation 6 has a squared multiple regression oeffiient of. 727, a alulated F value of 32., and a ritial F value of 6.93 at.1 signifiane level. --,;o--'1--',.o,oo Devi tori stron, Oj - Ci 3 (KN m 2) FGURE 12 Resilient modulus versus deviatori stress for subgrade soil of Test Setion 1. Comparison of Rutting Model For granular pavements, the loss of servieability is aused mostly by exessive permanent deformation along the wheel-

10 6 TRANSPORTATON RESEARCH RECORD 137 TABLE 2 SUMMARY OF CHARACTERSTCS OF TEST SECTONS Test Rut depth Total area umulative Sub<Jrade Lab. setion (mm) of raking no. of std. vertial CBR no. and pathing axles strain (\) (xlo millions) (x 1-3 ) (\) l , ) , path. Hene, in this study rutting was adopted as the index for judging pavement performane, whih is in agreement with British pratie (16,2,22). An average rut depth of 15 mm is onsidered adequate for an overlay done at the optimal time (2). Putting this value of rut depth in Equation 5, the following rutting model was developed for the traffi range overed in this study: SYS = 4.93 * 1 5 * ESAL (7) where SYS equals the subgrade vertial strain in.1 mm mm. Equation 7 was ompared with that of Shell (23), as shown in Figure 13: SYS = ESAL - 25 (8) The differene in the oeffiients of these equations is aused hy the differene in the material harateristis. Although the E ' [ E i z <( n::,. ll J <( (.) i= Lt'. l.j > w <( n:: Cl <D :::i () 1 ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' Shell Present Study. 1 ESAL s ( 1 millions) 1 FGURE 13 Comparison of rutting models.

11 Mallhews and Pandey differene of the orresponding oeffiients in the two equations is onsiderable, the urves are lose to one another when plotted. For an ESAL value of 3 million (a typial valuethe ESAL range in this study is 8 to 45 million), both equations yielded a subgrade vertial strain of.38 mmmm, as shown in Figure 13. An average rut depth of 2 mm is onsidered adequate for the omplete failure of a pavement struture (6,19,2). For this rut depth, both equations gave the same subgrade vertial strain (.348 mmmm), for an ESAL value of 42 million. Determination of Pavement Lives The umulative ESALs were found using the value of 2 mm for rut depth (onsidering a omplete failure of pavement) and the subgrade vertial strain (obtained from the omputer program) of eah pavement setion in Equation 5. The life period of the pavement struture was alulated from the urrent traffi data. The present age was subtrated from the life period of the pavement struture to obtain the remaining life (in years). The results are presented in Table 3. This table shows that, for five test setions (Setions 7, 11, 12, 14, and 15), the pavement life was exhausted beause of the high magnitude of subgrade vertial strain and the large number of standard axles passed. For four test setions (Setions 1, 3, 6, and 9), the remaining life period is almost exhausted (less than 3.5 years). For the rest of the six test setions, the remaining life is longer (4.7 through 15 years) beause of the low magnitude of subgrade vertial strain and the smaller number of standard axles passed. Other Relationships Regression analysis was also arried out between the average surfae defletion (d) and the average rut depth (RD), both in millimeters. The equation developed is as follows: d = * RD (9) For Equation 9, the squared oeffiient of orrelation is.717, the alulated t value is 5.74, and the ritial t value is 3.1 (for a signifiane level of.1). This equation was ompared with that developed in the AASHO road test (24), whih is given as follows: d = * RD (1) where d and RD are in inhes. For Equation 1, the squared oeffiient of orrelation is.6. The trend and the magnitude of variables are similar in Equations 9 and 1. From the equation developed in this investigation, the surfae defletion found is 1.34 mm, whereas in the AASHO road test equation the surfae defletion is 1.48 mm, for the rut depth of 2 mm. The following equation was developed between the total raking and pathing area (CPA), in perent, and the average rut depth (RD), in millimeters: CPA = * RD (11) For Equation 11, the squared oeffiient of orrelation is.678, the alulated t value is 5.23, and the ritial t value is 61 TABLE 3 CALCULATED LVES OF PAVEMENT STRUCTURES Test Av. no. of Present Total no. of Remaining Remainset- ommerial age std. axles no. of ing ion vehiles (years) for full std. axles life no. per day life period (XlO mill- (years) (xlo millions) ions) NL NL NL NL NL NL NL NL NL NL

12 62 TRANSPORTATON RESEARCH RECORD (for a signifiane level of.1). Equation 11 yields a CPA value of 12 perent when ompared with the total pavement area, or 33 perent when ompared with the wheelpath area, for a rut depth of 2 mm. For thin asphalt pavements, Craus et al. (25) suggest 3 perent raking under the wheelpaths when limiting onditions are approahed. Limitations and Conlusion The equations developed here are valid only for the range of onditions evaluated in the study (e.g., traffi is 8 to 45 million ESALs, CBR of soil is 3 to 8 perent, and surfae defletion is.8 to 1.9 mm). The purpose of Equations 9 and 11 is to ompare the results with those of the AASHO road test and of Crause et al. (25). For designing the overlays and to ensure longer servieability, Equation 5 an be used to monitor the performane at any stage during the life period of a pavement. REFERENCES 1. J. S. Przemienieki. Theory of Matrix Strutural Analysis. MGraw Hill, New York, C. Zienkiewiz and G. S. Hollister (eds.). Stress Analysis. Wiley, New York, C. Zienkiewiz. The Finite Element Method. Tata MGraw Hill, New Delhi, J. M. Dunan, C. L. Monismith, and E. L. Wilson. Finite Element Analysis of Pavements. n Highway Researh Reord 288, HRB, National Researh Counil, Washington, D.C., 1968, pp R. G. Ahlvin and H. H. Ulery. Tabulated Values for Determining the Complete Pattern of Stresses, Strains and Defletions Beneath Uniform Cirular Load on a Homogeneous Half Spae. Bulletin 342, HRB, National Researh Counil, Washington, D.C., 1962, pp C. R. Tangella. Performane Study of Flexible Pavements. Ph.D. thesis. ndian nstitute of Tehnology, Kharagpur, S. R. Doddihal and B. B. Pandey. Stresses in Full Depth Granular Pavements. n Transportation Researh Reord 954, TRB, National Researh Counil, Washington, D.C., 1984, pp C. R. Tangeila and B. B. Pandey. Repeated Load Test etup for Determining l'lasti Deformation Charateristis of Subgrade Soils. ndian Geotelmial Journal, Vol. 13, No. 2, 1983, pp S. F. Brown and A. F. L. Hyde. The Signifiane of Cyli Confining Stress in Repeated Load Triaxial Testing of Granular Material. n Transportation Researh Reord 537, TRB, National Researh Counil, Washington, D.C., 1975, pp R. D. Barksdale. Compressive Stress Pulse Times in Flexible Pavements for Use in Dynami Testing. n Highway Researh Reord 345, HRB, National Researh Counil, Washington, D.C., C. L. Monismith, H.B. Seed, F. G. Mitry, and C. K. Chan. Predition of Pavement Defletions from Laboratory Tests. Pro., 2nd nternational Conferene on the Strutural Design of Asphalt Pavements, University of Mihigan, Ann Arbor, 1967, pp. 19-1' Standard Speifiations. California Department of Transportation, Saramento, R. G. Hiks and C. L. Monismith. Fators nfluening the Resilient Response of Granular Materials. n Highway Researh Reord 345, HRB, National Researh Counil, Washington, D.C., 1971, pp C. R. Tangella and B. B. Pandey. Resilient Modulus Charateristis of Granular Materials. n Highway Researh Bulletin 29, Highway Researh Board, ndian Roads Congress, New Delhi, Canadian Good Roads Assoiation. Pavement Evaluation Studies in Canada. Pro., nternational Conferene on Lhe Strutural Design of Asphalt Pavements, Mihigan, 1962, pp A. R. Lee and D. Croney. British Full-Sale Pavement Experiments. Pro., nternational Conferene on the Stmtural Design of Asphalt Pavements, Mihigan, 1962, pp C. L. Monismith. Course Notes of CE 265: Pavement Design. University of California, Berkeley, E. J. Yoder and M. W. Witzak. Priniples of Pavement Design. Wiley, New York, 1975, pp C. R. Tangella. Development of Asphall Aggregate Mixlure Analysis System. Dotoral thesis. University of California, Berkeley, D. Croney. The Design and Performane of Road Pavements. Her Majesty's Stationery Offie, England, P. G. Bhattaharya and B. B. Pandey. Flexural Fatigue Strength of Lime-Laterite Soil Mixtures. n Transportation Researh Reord 189, TRB, National Researh Counil, Washington, D.C., 1986, pp D. Croney and J. Allister. Full Sale Pavement Design Experiment on A.1 Alonbury Hill, Huntingdonshire. Pro., nstitute of Civil Engineers, Vol. 3, Paper 6848, 1965, pp Shell Pavement Design Manual. Shell nternational, London, England, Speial Report 61A: The AASHO Road Test. HRB, National Researh Counil, Washington, D.C., J. Craus, R. Yue, and C. L. Monismith. Fatigue Behavior of Thin Asphalt Conrete Layers in Flexible Pavement Strutures. Pro., Assoiation of Asphalt Paving Tehnologists, Vol. 53, 1984, pp Publiation of this paper sponsored by Committee on Flexible Pavement Design.