Influence of Statistical Variation in Falling Weight Deflectometers on Pavement Analysis

Transcription

1 TRANSPORTATON RESEARCH RECORD nfluene of Statistial Variation in Falling Weight Defletometers on Pavement Analysis RAJ SDDHARTHAN, PETER E. SEBAALY, AND MOHAN }AVAREGOWDA A relatively simple approah that is based on a Monte Carlo simulation proedure is presented to statistially investigate the.influene of variation in falling weight defletometer (FWD) measurements on pavement analysis. The fators onsidered are pavement moduli and pavement performane or response strains that orrelate with pavement performane. From extensive FWD data obtained in Nevada, the variability of FWD defletions was statistially quantified at six sites for two seasons. The FWD tests were arried out at an interval of 5 ft within a uniform 1,-ft test pavement setion at every site. Using these data, as many as 9 FWD sensor defletions with normal distribution for eah sensor were randomly generated for eah of the 12 ases (six sites, two seasons) studied. The MODULUS program was used in the bakalulation of the pavement layer moduli. The FWD measurements show substantial variation within all of the uniform pavement setions investigated. Bakalulated pavement layer moduli using the generated defletion data show a large variation. The oeffiient of variation for layer moduli vary from 5 to as muh as 65 perent. Larger variations were omputed for AC and base. However, the oeffiient of variations for pavement performane strains are smaller, varying from 8 to 25 perent. Beause the number of loading yles to ause pavement distress is sensitive to pavement performane strains, the variation in pavement strain aused by the variation in FWD measurements has a signifiant influene on pavement life preditions. As a onsequene of the dereasing number of new highway onstrution projets, muh attention is devoted to upgrading and maintaining existing highways. n this regard, effetive and often ustomized overlay design proedures are being atively researhed by state transportation departments. The primary objetive of an overlay design analysis is whether a highway setion requires overlaying and, if it does, by how muh; f an overlay is needed, then the goal is to arrive at a pavement setion that an withstand the expeted traffi loads' throughout the design life without exessive pavement failures suh as raking, rutting, or loss of servieability. The stiffness of the existing pavement layers is an important input parameter in the overlay design proedures. Although both laboratory and nondestrutive testing (NDT) may be used o estimate the stiffness (modulus) of pavement layers, the NDT methods have beome widely aepted beause they are heaper and more pratial. Through the years, NDT methods have undergone hanges beause of the need to more realistially simulate wheel loading. The simulation of wheel loading has evolved from a stati load to a more representative Department of Civil Engineering (258), University of Nevada, Reno, Nev impulse loading using the falling weight defletometer (FWD). The FWD is one of the most widely used NDT devies and is being used extensively in the Long-Term Pavement Performane (L TPP) evaluation that is being undertaken by the Strategi Highway Researh Program (SHRP). The pavement layer moduli are omputed using a "bakalulation proedure" in whih the measured defletions on the pavement surfae under FWD loading serve as input. n a typial pavement improvement projet, a streth of highway is divided into a number of representative pavement setions with similar pavement and traffi loading harateristis. Among other fators, important parameters suh as age, onstrution data, layer thiknesses, and pavement ondition are often used to determine the extent of representative pavement setions. Within a representative pavement setion, FWD tests are arried out at an interval that typially varies from 5 to 1, ft. n Nevada, the interval is often 5 ft. The pavement layer properties near an FWD test loation are assumed to be uniform. A deviation from this assumption will affet bakalulated moduli and, thus, introdue error in the subsequent pavement analysis proedures that use FWD-based results. A number of soures of error are assoiated with FWD measurements. The influene of all of the error soures annot be ompletely eliminated. For instane, human fators an influene FWD testing but annot be preditd. An additional fator to be onsidered is the pavement setion variability. Even though the asphalt onrete (AC) and base layers may have relatively onstant properties, the subgrade onditions often vary erratially even within a short distane. The University of Nevada, Reno, and the Nevada Department of Transportation (NDOT) have olleted an extensive FWD data base on a variety of pavements loated around the state during at least 4 years and for all four seasons. This data base, in whih the FWD measuremets were taken at 5-ft intervals within a representative uniform pavement setion, has been used to study statistially the variability in pavement defletions aused by various error soures. FWD data olleted at these muh finer intervals are onsidered to reflet the true variation of the material properties within a pavement setion that is assumed to be uniform. Under these irumstanes, the FWD defletion measurements olleted at finer intervals an be onsidered as random variables, and a probabilisti approah seems appropriate to interpret the results given by subsequent bakalulation analysis. This paper uses a Monte Carlo simulation proedure to quantify the

2 58 influene of error in FWD defletion measurements on pavement moduli. The data base of pavement moduli values generated by this approah an be used to study the orresponding layer moduli variation. One of the main purposes of estimating the pavement layer stiffnesses is to use them to mpute the stresses and trains in the pavement under the design wheel loads. These stresses and strains an then be used as input to pavement distress (performane) models (e.g., rutting and fatigue). The investigation of the influene of the variation in FWD sensor defletions on pavement strains is also presented in this paper. BACKGROUND The FWD auses the pavement to deflet by dropping a freefalling mass that strikes a spring buffered plate. By hanging the mass, the drop height, or both, the impulse fore on the pavement an be hanged. The defletions of the pavement surfae are measured at a number.of predetermined loations using veloity transduers. These defletion data, along with the thikness of pavement layers and other pavement properties, are used to predit the resilient modulus of the layers using a ertain bakalulation proedure. By far, the most widely used bakalulation proedures assume stati layered elasti onditions. The pavement materials are haraterized to be elasti, homogeneous, and isotropi, with full ontat at layer interfaes. The bottom boundary may be assumed to be loated at some depth below the top of the subgrade or at a very large depth (half-spae). A reent NCHRP researh program on the nondestrutive evaluation of pavement layer stiffnesses has assessed all types of NDT equipment for both projet-level and network-level pavement ondition evaluation (J). This extensive study learly outlines the appliability and limitations of FWD testing to obtain pavement layer stiffnesses. The researh onluded that FWD testing is the most suitable for both projet- and network-level pavement evaluation. The study also outlines a muh more effiient bakalulation proedure that is based on linear elasti theory in whih the best values of the layer moduli are estimated using interpolation between alulated defleetion basins. This bakalulation analysis method is inorporated into a program alled MODULUS. This paper uses the MODULUS program to bakalulate pavement layer moduli. Several state transportation agenies and private firms are urrently using MODULUS. Mehanisti or mehanisti-empirial design proedures haraterize the long-term performane of pavements in terms of basi performane or response parameters suh as stresses and strains that are indued in the pavement. n these methods, the failure is normally defined in terms of speifi mehanisms suh as fatigue raking, rutting, and low temperature raking. Mehanisti-empirial methods depend in part on empirial relationships between pavement stresses and strains and the number of load appliations that the pavement an support before failure. For example, the strain.at the bottom of the existing asphalt layer is normally orrelated to fatigue failure. n some instanes, the stress or strain at the top of the subgrade has been used to orrelate rutting failure. n general, mehanisti-empirial proedures have been widely TRANSPORTATON RESEARCH RECORD 1377 aepted by pratitioners and researhers in reent years beause they have been proven to be somewhat more reliable and beause the pavement performane parameters an be obtained easily. One of the major uses of the layer stiffnesses is to obtain the pavement performane parameters mentioned above. Stati multilayer linear elasti omputer programs, suh as ELSYM5 and CHEVRON, are often used to estimate these pavement performane parameters. t has been argued that, if both the pavement performane parameter evaluation and FWD bakalulation proedures are arried out under a onsistent set of onditions (i.e., stati layered elasti), the dynami effets and nonlinear soil properties may not be important. t will be- lear from the next setion that there are a number of soures of error in FWD defletion measurements that annot be totally eliminated. The paper investigates the influene of the variation in FWD measurements aused by suh errors on the bakalulated pavement layer moduli and also on the pavement performane parameters mentioned earlier. RESEARCH APPROACH Soures of Variability in FWD Testing t is important that the soures of variability assoiated with FWD testing be identified and redued to a minimum. n general, there are two kinds of errors: random and systemati. These error soures result in a variation in the FWD measurements even within a uniform pavement setion. Systemati errors an be identified and may be quantified, whereas random errors are a result of random variations in the measurements or in the pavement materials. Random errors are present in measurements reorded by the load ell and veloity transduers. Although they may be redued somewhat by repeated testing and averaging, random errors annot be totally eliminated. For example, Dynatest FWD defletion sensors have an auray of approximately ± 2 perent as provided by the manufaturer. Other soures of random error inlude spatial variation of the material properties, both with depth and along the pavement length, and distortion in the defletion aused by passing traffi in the adjaent lanes. On the other hand, systemati errors are introdued by bias; therefore, their effets may be eliminated by removing the soure of the bias. Lytton et al. (J) have doumented a number of systemati error soures. These soures inlude (a) erroneous assumptions made in the bakalulation proess (e.g., the appliability of the stati linear elasti approah), (b) a deviation of the ontat pressure from a uniform distribution, and () a temporal variation in material properties within one layer aused by signifiant thermal and sution gradients. Existing pavements are seldom perfetly flat; therefore, when the FWD falling mass strikes the base plate, uniform ontat pressure may not be present under the plate. Furthermore, to ahieve uniform ontat pressure, the plate should be substantially flexible enough to deform and math the pavement surfae. Reent studies by Touma et al. (2) and Uzan and Lytton (3) show that signifiant errors may result in the bakalulated layer moduli values if full ontat between the base plate and pavement is not present.

3 Siddharthan et al. Nevada FWD Data Base NDOT is sponsoring a researh projet at the University of Nevada, Reno, to develop a ustomized overlay design proedure that takes into aount the loalized onditions that exist throughout the state. The overlay design proedure that is being developed uses a mehanisti-empirial approah in whih pavement performane is predited on the basis of stresses and strains indued in the pavement. As a part of this projet, a total of 27 representative highway sites were seleted for monitoring on the basis of fators suh as limate, traffi age, and type of onstrution. At eah of the sites, the test setion onsists of a 1,-ft highly uniform setion on the outside traffi lane. The uniformity of the test setions was heked through oring and testing all of the layers in the pavement struture. Eah test setion was subdivided into 21 stations at 5-ft intervals, and FWD testing using Dynatest FWD model 8 was performed for eah of the four seasons for at least 2 years. Tests were arried out at four load levels varying from 6, lb to as muh as 2, lb. The data base that was generated by this projet is quite substantial. Variation in FWD Defletion Data The influene of the variation of the material properties an be somewhat redued by performing FWD testing at finer intervals within a test setion, but it annot be totally eliminated. n this paper no attempt is made to quantify the influene of the individual error soures identified earlier. The influenes of all of the error soures on the FWD measurements are lumped together, and the variability of the measurements within a uniform pavement setion is statistially quantified as desribed later. From the FWD data base desribed above, the defletion data olleted for six sites that have a thin to medium-thik AC layer were seleted for an in-depth study in this paper. The pavement setion thiknesses at these sites and the dates of the FWD measurements are shown in Table 1. Only measurements that were obtained for two seasons in 1988 and 1989 (summer and winter) were onsidered in this paper. Typial defletion results obtained below the enter of the plate (D-1) and at a point 55.1 in. from the plate (D-6) in August 1988 (summer) and February 1989 (winter) at Site 16 are shown in Figure 1. The defletions that orrespond to the FWD load that is losest to 9, lb were seleted and normalized to an FWD load of 9, lb. The defletions an be seen to vary substantially within a test setion. Among other reasons, one of the primary auses behind the variation in the defletion between the stations is the variability in the subgrade. This is beause the other fators, suh as the pavement ross setion, onstrution method, and material types used at the site are the same. The winter and summer defletions are similar in shape; however, the summer values at D-1 (Figure 1 (top)) are higher, whereas the winter values at D-6 (Figure 1 (bottom)) are higher. This differene is beause the defletion at D-1 is affeted by the material properties of all the pavement layers, whereas the defletion at D-6 is affeted by the properties of subgrade only. A histogram obtained for the defletion data at D-1 is presented in Figure 2. This histogram was obtained with an interval of.5 mils for August The histogram shows that the variation of defletion an, for pratial purposes, be onsidered to be normally distributed. The mean, standard deviation, and oeffiient of variation of the defletions of all the FWD sensors have been omputed, and the values assoiated with the first five transduers are presented for all the sites in Table 2. The mean defletion at Site 28 is substantially higher than that at other sites beause this site has the lowest AC and base thiknesses. The oeffiient of variation (COV) of defletions varies between 9. perent and as muh as 4.8 perent. Generally, higher COV values our for sensors loated farther away from the enter of the plate, where measured defletions are small. Proposed Monte Carlo Simulation Proedure t is lear from the previous disussion that the FWD defletions an vary substantially within a short distane and may be represented by a normal pistribution. t was deided to use the Monte Carlo simulation approah to investigate the influene of the variation in the FWD defletion ( 4,5). The variables investigated in the study are the bakalulated pavement layer moduli and pavement performane parameters. A random number generator routine that is available in a omputer library generates random numbers with a uniform density; therefore it was not used in the study. Random num- 59 TABLE 1 Details of Seleted Test Sites and Dates of FWD Measurement Site FWD A.C. Base No. Measured thikness thikness Dates (in) (in) and and and and and and

4 m 4 n Date: e- Date: Station Number 1.2 o 6 m.8 n.6 ;;::::.4.2 FGURE Station Number Variation of D-1 (top) and D-6 (bottom) aross Site 16. tj :; tj tj tj :J CT L: 2 Date: Defletion at D-1 (mils) FGURE 2 Histogram of D-1 aross Site 16.

5 Siddharthan et al. 61 TABLE 2 Summary of Mean and Standard Deviation of Measured Defletion for Seleted Sites Site Date Desaiption Dl Mean Std.Dev/C.O.V(%).67/ Mean Std.Dev/C.O.V{%) 1.8/18. Mean Std.Dev/C.O.V(%).97/W.2 u Mean Std.Dev/C.O.V(%) 1.41/32.7 Mean StdDev/C.O.V{%).99/ Mean Std.Dev/C.O.V(%).52/U.4 Mean Std.Dev/C.O.V(%) 1.24/9. 24 Mean Std.Dev/C.O.V(%).89/9.6 D2 D3 4 D / / /223.13/ / / / / /W.7.67/W.6.42/ / /3.6.85/27.1.5/ / / / /173.26/ / / / / / /9.7.73/11..54/ /9.8.78/1.1.62/ / Mean 8.12 Std.Dev/C.O.V(%) 1.27/15.6 Mean 1.82 Std.Dev/C.O.V(%) 1.58/ / / / / /U.9 1.4/ / / Mean 5.87 Std.Dev/C.O.V(%) 6.3/11.8 Mean Std.Dev /C.O.V(%) 6.21/ / / / / / / / /16.9 hers with a normal distribution an be obtained using the following equation (6, 7): X = V-2 log (U) os(21tv) (1) where U and V are two independent random variables with uniform densities on [,1]. U and V an be generated using the standard routines available in the omputers. The variation of X given by Equation 1 has a mean and a standard deviation of and 1, respetively. Now the random variable Z having a normal distribution with the mean of Z and a standard deviation of r an be obtained by using z = zx + (1 (2) This proedure was used to obtain all of the FWD sensor defletions independently for eah site and eah season using the means and standard deviations summarized in Table 2. n total, as many as 9 sets of defletion basins per ase were generated for all 12 ases identified in Table 2. n eah set, the sensor defletions were obtained independently of eah other using Equations 1 and 2. Only the randomly generated defletions that fell within the mean ± standard deviation were used in the omputations. Typial histograms obtained for Site 16 using the randomly generated defletions at D-1 and D-6 are shown in Figure 3. The variation indiated in Figure 3 (top) ompares favorably with the measured variation in Figure 2; in addition, the mean of the defletions math with those given in Table 2. Results of Bakalulation Proedure The defletion basins obtained using the Monte Carlo simulation proedure were used with the MODULUS program to bakalulate layer moduli (1). The input data for the MODULUS program inlude layer thiknesses, Poisson's ratio, v, for the layers, and estimated maximum and minimum resilient moduli values for the layers. These input parameters are shown in Figure 4. The sensor loations for D-1 through D-7 are loated at, 7.9, 11.8, 23.6, 36., 55.1, and 7.9 in. from the enter of the plate. The thikness of the subgrade layer is not required when using the MODULUS program beause it is treated as an additional unknown variable. The program omputes a series of defletion basins and tres to math the input defletion basin to arrive at the layer moduli

6 62 TRANSPORTATON RESEARCH RECORD Date: :::: O" u: ' Generated Defletion at D-1 (mils) :::J O" u: 1 5 o o.n5 o.825 o.875 o.925 Generated Defletion at D-6 (mils) FGURE 3 Variation of randomly generated defletion at D-1 (9 values) (top) and D-6 (9 values) (bottom). values and the thikness of the sub grade. This program is muh more effiient than other bakalulation programs and, in general, has been found to yield reasonable results. Table 3 summarizes the bakalulated moduli values for all the sites and seasons onsidered in the study. The table gives results in terms of the mean, standard deviation, and oeffiient of variation. Figure 5 shows the typial variation obtained for the AC resilient modulus at Site 16 (August 1988). These results learly show that a substantial differene in the bakalulated moduli exists for the randomly generated defletion basins. n the ase of AC and base, the oeffiients of variation vary from 12 to as muh as 65 pe'rent. The oeffiient of variation in the ase of subgrade is smaller, varying between 5 and 13 perent. On the average, the mean AC modulus of thin pavement setions (Sites 11 and 28) is not affeted by the seasonal variation. Site 16 showed the largest. variation. Pavement Performane Parameters Pavement performane riteria suh as AC fatigue and pavement rutting an be investigated for antiipated traffi loadings of existing pavements using layered linear elasti models, with layer moduli obtained from FWD data. A omprehensive review of AC fatigue failure studies indiated that rak initiation in AC is related to the maximum tensile strain, fa, in the AC layer (8,9). Some models suggest that the AC modulus and the fa are important fators that affet the AC fatigue life. However, the relative importane of the AC modulus is muh less than that of the fa. The maximum tensile strain in medium-thik pavements ours at the bottom of the AC layer. The other major fator that affets pavement performane is surfae rutting aused by permanent deformation in the pavement layers. Although the ontribution of all the pave-

7 Siddharthan et al. 9 lbs 1, E max = 3, psi Asphalt Conrete E min 5, psi 'Y.35 E max 1, psi Base E min 1, psi 'Y.35 E max 6, psi Subgrade E min 5, psi (Unknown thikness) 'Y.4 Rigid Boundary /////////l//////ll//////ll///////ll/////l////////////// FGURE 4 nput data for MODULUS program. ment layers needs to be onsidered in rutting preditions, it is ustomary to pay the most attention to the ontribution from the subgrade. This is beause its ontribution is frequently dominant. A number of widely used pavement rutting models use the maximum vertial ompressive strain at the top of the subgrade, Es, as a measure of rutting in the sub grade (9-11). The design philosophy is that the pavement rutting an be redued by ontrolling Es. The bakalulated layer moduli values and the thikness of the subgrade given by the program MODULUS were input into the program NHELSYM5 to ompute the pavement strains, Ea and Es (12). This program, whih is based on the wellknown ELSYM5 program, is menu driven and user friendly. However, this program was further modified so that it an handle multiple data sets of layer properties. The single-axle dual-wheel onfiguration used with the modified NHELSYM5 program is shown in Figure 6. The tire pressures have substantially inreased from 6 to 7 lb/in. 2 in the 196s to as muh as 9 to 12 lb/in. 2 in reent years (11,13). A value of 11 lb/in. 2 for the tire pressure was used in the omputations. The strains Ea and Es (prinipal strains) at the bottom of the AC layer and at the top of the subgrade, respetively, were omputed at three vertial setions, as shown in Figure 6. These vertial setions are loated along the enter line of one tire midway between the enters of the tires and at the edge of a tire. Only the largest value out of these three values of Ea and Es was noted and is presented in Table 4. All 9 ases per site per season that were onsidered in the bakalulations were used in the omputations. Similar to earlier results, the variation in terms of the mean, standard deviation, and oeffiient of variation are presented for all of the sites. Figure 7 presents a typial variation of Ea and Es for Site 16 (August 1988). A number of observations an be made from Table 4 and Figure 7. First, it appears that, exept for Site 28, the strains strongly depend on the seasonal variation. This is mainly beause Site 28 does not experiene large environmental hanges between the seasons for whih the FWD measurements were made. Seond, even though a large variation in the bakalulated moduli values was obtained [oeffiient of variation (COV) as muh as 65 perent], the COVs of the omputed strain values are muh lower with a maximum of 25 perent. The range of COV for both strains is between 8 and 25 perent. This means that the pavement strain omputation is not very sensitive to variations in the pavement layer moduli. Third, the COV for the AC strain, Ea, is muh higher than the COV of the sub grade strain, Es. Finally, the strains developed for Site 28 are substantially larger than those obtained for the other sites. This an be traed to the substantially lower AC and base thiknesses at Site TABLE 3 Bakalulated Resilient Moduli for Pavement Layers Site Date Resilient Modulus of A.C (psi) Resilient Modulus of Base (psi) Resilient Mod. of Subgrade (psi) Mean Std. Dev.o.v (%) Mean Std. Dev.o.v (%) Mean Std. Dev.o.v (%) , , ,498 14, , ,56, , ,67 24, , , , ,74 13, , ,378, , ,484 15, , , , ,295 13, , ,719,57 33, ,335 19, , , , ,485 17, , , , ,615 3, , ,28, , , , ,48 283, ,773 29, , , , ,482 9, , , , ,975 6, ,

8 64 TRANSPORTATON RESEARCH RECORD Date: 8-88 Cl) (.J :; (.J (.J (.J Cl) :::: C' Cl) u: Computed AC Moduli (ksi) FGURE 5 Variation of bakalulated AC resilient moduli. 45 lbs p 1(11 A1 Asph t Conrete Base: 45 lbs p Tire 14.5 in ) j :'rsi al Subgrrade : : : Rigid A 1 R 1 r; 1 Boundary )// J'/J l"fj FGURE 6 Single-axle dual-wheel onfiguration used for pavement strain omputations. Consequene of the Variability in Pavement Strains A number of fatigue failure models are reported in the literature (14-16). One of the most widely used models is that of Monismith and Epps (16), whih an be written as log N 1 = log(ea) log (EA) (3) where N 1 is the number of yles to fatigue failure (given in miro strain) and EA is the asphalt onrete resilient modulus (in ksi). This equation an be rewritten as 1 (4) where a is a onstant that depends on EA and b = The equation an be used to ompare the relative inrease (or derease) in the number of load appliations for various strain values. Using a representative mean value of 1µ and a variation of ± 1 perent for Ea, the hanges in the number of yles to fatigue failure an be ompared using Equation 4. The alulations reveal that the ± 1 perent hange in Ea orresponds to hanges in the number of yles of - 27 and + 41 perent, respetively. Similar omputations an be arried out for rutting using the Chevron equation (1). The Chevron equation gives the number of yles, Nr, to ause a. 75-in. rut depth as The Es should be given in terms of miro strain. Using a representative mean value of 2µ and a variation of ± 1 perent for En the hanges in the number of yles to ause rutting failure an now be omputed using Equation 5. A ± 1 perent hange in Es orresponds to hanges in the number of loading yles of - 35 and + 6 perent, respetively. The hanges in the number of loading yles for both pavement failure models are substantial. This is beause these models are sensitive to strain values. SUMMARY AND CONCLUSONS The FWD testing, whih is a widely used NDT method, simulates traffi loading more losely than other NDT methods. The surfae defletions measured by FWD testing are used to estimate pavement layer moduli values using a "bakalulation proedure." The pavement moduli values are, in turn, often used with pavement performane models to predit the remaining life of pavement setions. There are a (5)

9 Siddharthan et al. 65 TABLE 4 Pavement Performane Strains Computed Using Modified NHELSYMS Max. Tensile Strain in Max. Comp. Strain in Site Date AC (mirons) Subgrade (mirons) Mean Std. Dev C.O.V(%) Mean Std. Dev C.O.V(%) ' : :; : :::J C" i.t Date: 8-88 : :; - : :::J C" i.t Date: Computed Max.Tensile Strain in AC (mirons) ==--_m_ _l-j--=...::m---j Computed Max.Compressive Strain in Subgrade (mirons) FGURE 7 Variation of maximum tensile strain in AC (left); variation of maximum ompressive strain in subgrade (right). number of soures of error relative to FWD testing. These errors an be broadly divided into two types: systemati and random. Systemati errors inlude errors aused by assumptions made in the bakalulation proess. Random errors are aused by, among other fators, deviations in sensor measurements, site variability, and passing traffi. Although they an be minimized by repeated testing and averaging, suh errors annot be totally eliminated. These error soures influene the FWD measurements taken even within a uniform pavement setion. The study reported here investigates the influene of the variation in FWD defletion measurements on pavement moduli and pavement performane strain preditions. As a part of the development of an overlay design proedure for Nevada, a total of 27 representative highway sites were seleted and FWD tests were performed for eah of the four seasons for at least 2 years. At eah site, the test setion onsists of a 1,-ft highly uniform pavement setion, and FWD tests were arried out at 5-ft intervals. By seleting suh fine testing intervals, the influene of the spatial variation in the material properties on the FWD measurements an be minimized. Defletion data from sites with thin to medium-: thik pavements were seleted to study the sensor defletion variability. The study reveals that the FWD measurements an be substantially influened by the various error soures for all of the sites onsidered.

10 66 By varying the sensor defletions within its range, 9 sets of independent defletion basins using a random number generator with a normal distribution were obtained for the six seleted sites and for two seasons. Bakalulation on these defletion basins was performed using the program MODULUS. The data base of bakalulated moduli given by MODULUS for the generated defletion basins showed a substantial variation. n the ase of AC and base, the oeffiients of variation vary from 12 to as muh as 65 perent. The oeffiient of variation for subgrade is smaller, varying between 5 and 13 perent. The pavement performane strains, suh as the maximum tensile strain in the AC and the maximum ompressive strain in the subgrade, were omputed using a modified version of the omputer program NHELSYM5. The bakalulated moduli and the subgrade thikness given by the program MODULUS were used as input. Even though the oeffiient of variation was large for bakalulated moduli, the oeffiients of variation of the omputed strain were lower, with a maximum of 25 perent. The pavement performane strains were used to estimate the number of loading yles required to ause pavement distress utilizing widely used pavement performane equations. This exerise suggests that the number of loading yles to ause pavement distress is sensitive to pavement performane strains. This means that the variation in pavement strains aused by the variation in FWD measurements an have a substantial influene on the pavement life preditions. Finally, the influene of other important fators suh as the variation in the thikness of the AC and base have not been investigated in this paper. n the study, these thikness values, whih were obtained from onstrution data and oring, were uniform aross a test setion. Studies investigating the influene of the hanges in the thikness of the top layers may also be arried out using the proposed Monte Carlo approah. ACKNOWLEDGMENT The researh reported here was funded by a grant from the Nevada Department of Transportation, whose support is gratefully aknowledged. REFERENCES TRANSPORTATON RESEARCH RECORD R. L. Lytton, F. P. Germann, Y. J. Chou, and S. M. Stoffels. NCHRP Report 327: Determining Asphalti Conrete Pavement Strutural Properties by Nondestrutive Testing. TRB, National Researh Counil, Washington, D.C., June B. E. Touma, J. A. Crovetti, and M. Y. Shahin. The Effets of Various Load Distributions on the Bakalulated Moduli Values in Flexible Pavements. Presented at 7th Annual Meeting of the Transportation Researh Board, Washington, D.C., Jan J. Uzan and R. L. Lytton. Analysis of Pressure Distribution Under Falling Weight Defletometer Loading. Journal of Transportation Engineering, ASCE, Vol. 116, No. 2, 199, pp A. Shreider. The Monte-Carlo Method: The Method of Statistial Trials. Pergamon Press, New York, J.M. Hammerslay and D. C. Handsomb. Monte-Carlo Methods. John Wiley Publiations, New York, L. J. Snell. ntrodution to Probability. Random House/Birkhouser Mathematis Series, New York, M. Dwass. Probability: Theory and Appliations. W. A. Benjamin n., New York, M: Gome.z and M. R. Thompson. Mehanisti Design Conepts for Full Depth Asphalt Conrete Pavements. Transportation Engineering Series, No. 41. University of llinois, Urbana Champaign, Aug Researh and Development of the Asphalt nstitute's Thikness Design Manual (MS-1), 9th ed. Researh Report The Asphalt nstitute, Aug L. E. Santuii. Thikness Design Proedure for Asphalt and Emulsified Asphalt Mixture. Pro., 4th nternational Conferene on the Strutural Design of Asphalt Pavement, University of Mihigan, Ann Arbor, 1977, pp K. Kim, C. A. Bell, and J. E. Wilson. Effet of nreased Truk Tire Pressure on Asphalt Conrete Pavement. Journal of Transportation Engineering, ASCE, Vol. 115, No. 4, July 1989, pp R. Henry and C. Goodspeed. NHELSYM5: Program for Pavement Analysis. Department of Civil Engineering, University of New Hampshire, Ot D. R. Middleton, F. L. Roberts, and T. Chira-Chavala. Measurements and Analysis of Truk Tire Pressures in Texas Highways. n Transportation Researh Reord 17, TRB, National Researh Counil, Washington, D.C., 1986, pp A. A. Bu-Bushsait. Development of a Flexible Pavement Fatigue Model for Washington State. Ph.D. dissertation, University of Washington, Seattle, P. S. Pell. Speial Report 14: Charaterization of Fatigue Behavior: Strutural Design of AC Pavements to Pavement Fatigue Craking. HRB, National Researh Counil, Washington, D.C., Jan C. C. Monismith and J. A. Epps. Asphalt Mixture Behavior in Repeated Flexure. Report TE nstitute of Transportation and Traffi Engineering, Berkeley, Calif., 1969.