Neural Networks Analysis of Airfield Pavement Heavy Weight Deflectometer Data

Transcription

1 The Open Civil Engineering Journal, 28, 2, Neural Networks Analysis of Airfiel Pavement Heavy Weight Deflectometer Data Kasthurirangan Gopalakrishnan* Department of Civil, Construction an Environmental Engineering, Iowa State University, Ames, Iowa, USA Abstract: The Heavy Weight Deflectometer (HWD) test is one of the most wiely use tests for assessing the structural integrity of airport pavements in a non-estructive manner. The elastic mouli of the iniviual pavement layers preicte from the HWD eflection measurements through inverse engineering analysis are effective inicators of pavement layer conition. The primary objective of this stuy was to evelop a tool for backcalculating non-linear pavement layer mouli from HWD ata using Artificial Neural Networks (ANN) for rapi structural evaluation of airfiel pavements. A multilayer, fee-forwar backpropagation ANN which uses an error-backpropagation algorithm was traine to approximate the HWD backcalculation function. The synthetic atabase generate using an axisymmetric pavement finite-element program was use to train the ANN. Using the ANN, the Asphalt Concrete (AC) mouli an subgrae mouli were successfully preicte. Apart from the mouli, an attempt was mae to preict the critical pavement structural responses using ANN moels. The final prouct was use in backcalculating pavement layer mouli an preicting subgrae eviator stresses from actual fiel ata acquire at the Feeral Aviation Aministration s National Airport Pavement Test Facility (NAPTF). INTRODUCTION The Falling Weight Deflectometer (FWD) test is one of the most wiely use tests for assessing the structural integrity of roas in a non-estructive manner. In the case of airfiels, a Heavy Weight Deflectometer (HWD) test, which is similar to a FWD test, but using higher loa levels, is use. In an FWD/HWD test, an impulse loa is applie to the pavement surface by ropping a weight onto a circular metal plate an the resultant pavement surface eflections are measure irectly beneath the plate an at several raial offsets. The eflection of a pavement represents an overall system response of the pavement layers to an applie loa. A conventional Asphalt Concrete (AC) pavement is typically mae up of three layers: a surface layer pave with AC mix, a base or/an subbase layer mae up of crushe stone, an a subgrae layer mae up of natural soil. When a wheel loa is applie on an AC pavement, the pavement layers eflect nearly vertically to form a basin. The FWD/HWD test tries to replicate the force history an eflection magnitues of a moving truck tire/aircraft tire. The eflecte shape of the basin is preominantly a function of the thickness of the pavement layers, the mouli of iniviual layers, an the magnitue of the loa. Backcalculation is the accepte term use to ientify a process whereby the elastic (Young s) mouli of iniviual pavement layers are estimate base upon measure FWD/HWD surface eflections. As there are no close-form solutions to accomplish this task, a mathematical moel of the pavement system (calle a forwar moel) is constructe an use to compute theoretical surface eflections with assume initial layer mouli values at the appropriate *Aress corresponence to this author at the Department of Civil, Construction, an Environmental Engineering, 354 Town Engineering Builing, Iowa State University, Ames, IA 511, USA; Tel: ; Fax: ; rangan@iastate.eu,rangan18@gmail.com FWD/HWD loas. Through a series of iterations, the layer mouli are change, an the calculate eflections are then compare to the measure eflections until a match is obtaine within tolerance limits. Most of the commercial backcalculation programs currently in use (e.g. WESDEF, BISDEF) utilize an Elastic Layer Program (ELP) as the forwar moel to compute the surface eflections. For example, WESDEF uses WESLEA an BISDEF uses BISAR. The ELPs consier the pavement as an elastic multilayere meia, an assume that pavement materials are linear-elastic, homogeneous an isotropic. However, in reality, it has been foun that certain pavement materials o not show linear stress-strain relation uner cyclic loaing. The non-linearity or stress-epenency of resilient moulus for unboun granular materials an cohesive fine-graine subgrae soils is well ocumente in literature [1,2]. Unboun granular materials use in the base/subbase layer of an AC pavement show stress-harening behavior (increase in resilient moulus with increasing hyrostatic stress) an cohesive subgrae soils show stress-softening behavior (reuction in resilient mouli with increase eviator stress). Therefore, the layer moulus is no longer a constant value, but a function of the stress state. Also, the ELPs o not account for the available shear strength of these unboun materials an frequently preict tensile stresses at the bottom of unboun granular layers which excees the available strength. Thus, the pavement layer mouli values preicte using ELP-base backcalculation programs are not very realistic. ILLI-PAVE is a two-imensional axi-symmetric pavement finite-element (FE) software evelope at the University of Illinois at Urbana-Champaign [3]. It incorporates stress-sensitive material moels an it provies a more realistic representation of the pavement structure an its response to loaing. The primary objective of this stuy was to evelop a tool for backcalculating non-linear pavement /828 Bentham Science Publishers Lt.

2 16 The Open Civil Engineering Journal, 28, Volume 2 Kasthurirangan Gopalakrishnan layer mouli from FWD/HWD ata using Artificial Neural Networks (ANN). The reason for using ANN to accomplish this task is that once traine, they offer mathematical solutions that can be easily calculate in real-time on even the basic personal computers, unlike conventional backcalculation programs. Also, ANN can learn a backcalculation function that is base on much more realistic moels of pavement response (e.g., ILLI-PAVE) than are use in traitional-basin matching programs. ANNs have been successfully use in the past for the backcalculation of flexible pavement mouli from FWD ata [4]. However, they i not account for realistic pavement layer properties as ELP-generate synthetic atabase was use to train the ANN. Therefore, ILLI-PAVE was use in this stuy to evelop the synthetic atabase which accounts for the nonlinearity in unboun material behavior. A multilayer, fee-forwar network which uses an error-backpropagation algorithm (LMS minimization) was traine to approximate the HWD backcalculation function. The final prouct was use in backcalculating pavement layer mouli from actual fiel ata acquire at the National Airport Pavement Test Facility (NAPTF). The NAPTF was constructe to generate full-scale testing ata to support the investigation of the performance of airport pavements subjecte to new generation aircrafts. The results from this stuy were compare with those obtaine using a traitional ELP-base backcalculation program. It is note that this is a preliminary stuy specifically targete towars the backcalculation of pavement layer mouli from HWD ata acquire at the NAPTF. Recent research stuies at the Iowa State University an University of Illinois have focuse on the evelopment of ANN base flexible pavement analysis moels to preict critical pavement responses an layer mouli [5]. Researchers have successfully emonstrate the use of ANNs traine with ILLI-PAVE results as pavement structural analysis tools for the rapi an accurate preiction of critical responses an eflection profiles of flexible pavements subjecte to typical highway loaings [5]. The current stuy escribe in this paper focuse on the evelopment of ANNbase moels for the rapi non-estructive evaluation of airport flexible pavements subjecte to new-generation, heavy aircrafts such as Boeing B-777. DATABASE GENERATION FOR ANN TRAINING AND TESTING A conventional airport flexible pavement section was moele as a five-layere (AC layer, base layer, subbase layer, subgrae layer an a san layer as constructe in conventional NAPTF test sections), two-imensional, axisymmetric FE structure. A typical HWD test is performe by ropping a 36,-lb loa on the top of circular plate with a raius of 6 inches resting on the surface of the pavement. The loaing uration is about 3 ms. Deflections are typically measure at offsets of -,12-,24-,36-,48- an 6- inches from the center of loaing plate. The effect of HWD loaing was simulate in ILLI-PAVE. The AC layer an the san layer were treate as linear elastic material. Stress-epenent elastic moels along with Mohr-Coulomb failure criteria were applie for the base, subbase an subgrae layers. The stress-harening K- moel was use for the base an subbase layers: M = = D n R K R (1) where M R is resilient moulus (psi), is bulk stress (psi) an K an n are statistical parameters. The following relationship exists between K an n (R 2 =.68, SEE =.22) [6]: Log ( K) = n (2) 1 The stress-softening bilinear moel was use for the subgrae layer: M M R R = M = M Ri Ri + K1.( i ) + K.( ) 2 i for < for > where M R is resilient moulus (psi), is applie eviator stress (psi), an K 1 an K 2 are statistically etermine coefficients from laboratory tests. The thickness of the AC, base, subbase, subgrae an san layers were hel at constant values of 5, 8, 12, 95, an 12 inches respectively. These layer thicknesses are for a conventional AC pavement section (referre to as MFC ) constructe at the NAPTF. The elastic moulus of the san layer was fixe at 45, psi. Pavement surface eflections were compute at spacings of (D ), 12 (D 12 ), 24 (D 24 ), 36 (D 36 ), 48 (D 48 ), an 6 (D 6 ) inches from the loa center. Apart from the eflection basins, the strains at the bottom of the AC layer ( AC ) an on top of the subgrae ( SG ), major an minor stresses ( 1 an 3 ) an eviatoric stress on top of subgrae ( D ) were also compute. The importance of these parameters in the context of airport flexible pavement esign is iscusse later. Deflection Basin Parameters (DBPs) erive from FWD/HWD eflection measurements are shown to be goo inicators of selecte pavement properties an conitions [7]. Recently, DBPs were use in eveloping new relationships between selecte pavement layer conition inicators an FWD eflections by applying regression an ANN techniques [8]. The DBPs consiere in this stuy are shown in Table 1. Each DBP supposely represents the conition of specific pavement layers. For example, AUPP is sensitive to the AC layer properties whereas BCI an AI 4 are expecte to reflect the conition of subgrae. Some of these DBPs were inclue as inputs for training the ANN apart from the 6 inepenent eflection measurements (D to D 6 ). A total of 5, ata sets were generate by varying the AC an subgrae layer mouli, the K b - n b an K s - n s values (note that K an n are relate) for the base an subbase layers respectively. Of the total number of ata sets, 3,75 ata vectors were use in training the ANN an the rest 1,25 ata vectors were utilize for the testing the network after the training was complete. The ranges of layer properties use in training the ANN are summarize in Table 2. In orer for the network weights to compare the features to one another more easily, it is generally esirable to reuce each feature in the ata set to zero mean an an approximately equal variance, usually unity. But, in this case, as i i (3)

3 Neural Networks Analysis of Airfiel Pavement Heavy Weight The Open Civil Engineering Journal, 28, Volume 2 17 the ata was well controlle, all the features were reuce to similar orers of magnitue. Also, it is crucial that the training an test ata both represent sampling from the same statistical istribution, which is also taken care of in this stuy. Table 1. Deflection Basin Parameters (DBPs) Use in this Stuy Deflection Basin Parameter (DBP) Formula AREA AREA = 6(D + 2D D 24 + D 36)/D Area Uner Pavement Profile (AUPP) AUPP = (5D 2D 12 2D 24 D 36)/2 Area Inex AI 4 = (D 36 + D 48)/2D Base Curvature Inex (BCI) BCI = D 24 D 36 BCI2 = D 6 D 48 Base Damage Inex (BDI) BDI = D 12 D 24 Deflection Ratio DR = D 12/D Shape Factors F 1 = (D D 24)/D 12 F 2 = (D 12 D 36)/D 24 NETWORK ARCHITECTURE A generalize n-layer feeforwar artificial neural network which uses an error-backpropogation algorithm [9] was implemente in the Visual Basic (VB 6.) programming language. The program can allow for a general number of inputs, hien layers, hien layer elements, an output layer elements. Two hien layers were foun to be sufficient in solving a problem of this size an therefore the architecture was reuce to a four-layer feeforwar network. A four-layer feeforwar network consists of a set of sensory units (source noes) that constitute the input layer, two hien layer of computation noes, an an output layer of computation noes. The following notation is generally use to refer to a particular type of architecture that has two hien layers: (# inputs)-(# hien neurons)-(# hien neurons)-(# outputs). For example, the notation refers to an ANN architecture that takes in 1 inputs (features), has 2 hien layers consisting of 4 neurons each, an prouces 3 outputs. An ANN-base backcalculation proceure was evelope to approximate the FWD/HWD backcalculation function. Using the ILLI-PAVE synthetic atabase, the ANN was traine to learn the relation between the synthetic eflection basins (inputs) an the pavement layer mouli (outputs). To track the performance of the network a Root Mean Square Error (RMSE) at the en of each epoch was calculate. An epoch is efine as one full presentation of all the training vectors to the network. The RMSE at the en of each epoch efine as: RMSE = N 2 [ j Y( X j) ] j= 1 N Where j is the esire response for the input training vector X j, an N is the total number of input vectors presente to the network for training. In orer for the network to learn the problem smoothly, a monotonic ecrease in the RMSE is expecte with increase in the number of epochs. Separate ANN moels were use for each esire output rather than using the same architecture to etermine all the outputs together. The most effective set of input features for each ANN moel were etermine base on both engineering jugment an the experience gaine through past research stuies conucte at the University of Illinois. Parametric analyses were performe by systematically varying the choice an number of inputs an number of hien neurons to ientify the best-performance networks. As it was foun that the preiction accuracy of the network remaine the same for hien layers greater than or equal to two, the number of hien layers was fixe at two for all runs. The learning curve (RMSE Vs number of epochs) an the testing RMSE were stuie in orer to arrive at the best networks. A range of (-.2, +.2) was use for ranom initialization of all synaptic weight vectors in the network. The presence of a nonlinear activation function, (.) in the hien layer(s) is important because, otherwise, the input-output relation of the network coul be reuce to that of a single-layer perceptron. The computation of the (local graient) for each neuron of the multilayer perceptron requires that the function (.) be continuous. For this problem, an asymmetric hyperbolic tangent function (tanh) was chosen as the nonlinear activation function at the output en of all hien neurons. Since, the final outputs (layer mouli) are real values rather than binary outputs, a linear combiner moel (4) Table 2. Ranges of Layer Properties Use to Train the ANN Pavement Layer Thickness (in.) Elastic Layer Moulus (ksi) Poisson s Ratio Asphalt Concrete 5 1 2,.35 Base 8 K b: n b: Subbase 12 K s: n s: Subgrae San

4 18 The Open Civil Engineering Journal, 28, Volume 2 Kasthurirangan Gopalakrishnan was use for neurons in the output layer, thus omitting the nonlinear activation function. A smooth learning curve was achieve with a learning-rate parameter of.1. A Summary of the sensitivity analyses performe to select the best-performance networks for preicting AC moulus (E AC ) an subgrae moulus (E Ri ) in MFC section are shown in Table 3. Similarly, the best-performance networks for preicting n b an n s in MFC section are highlighte in Table 4. The base an subbase layer mouli were the harest to preict. The ifficulty associate with Table 3. Summary of Sensitivity Analyses for Preicting AC an Subgrae Mouli Trial Input Output Network Architecture No. of Epochs E AC (ksi) Testing RMSE E Ri (ksi) 1 D ~ D 72 E AC, E Ri , D ~ D 72 E AC, E Ri , D ~ D 6 E AC, E Ri , D ~ D 6 E AC, E Ri , D ~ D 6 E AC , 86-6 D ~ D 6 E AC , 11-7 D ~ D 6 E AC , 69-8 D ~ D 6 E Ri , D ~ D 6 E Ri , D ~ D 6, BCI, AI 4 E Ri , D ~ D 6, BCI, AI 4 E Ri , D ~ D 6, BCI, AI 4 E Ri , D ~ D 6, BCI, AI 4 E Ri , -.8 Table 4. Summary of Sensitivity Analyses for Preicting Base/subbase Mouli Parameters Trial Input Output Network Architecture No. of Epochs Testing RMSE n b n s 1 D ~ D 72, BCI, BDI n b, n s , D ~ D 72, BCI, BDI n b, n s , D ~ D 72, BCI, BDI n b , D ~ D 6, BCI, SCI n b , BCI, BDI n b , D ~ D 6, AUPP n b , D ~ D 6, AUPP, E AC n b , D ~ D 6, AUPP, E AC, D 1/D n b ,.13-9 D ~ D 6, AUPP, E AC, D 1/D n b , D ~ D 6, BCI, BDI n s , D ~ D 6, BCI, BDI n s , D ~ D 6, BCI, BDI n s , D ~ D 6, BCI, F 1 n s , D ~ D 6, E AC, E Ri n b, n s , D ~ D 6, E AC, E Ri n s , -.136

5 Neural Networks Analysis of Airfiel Pavement Heavy Weight The Open Civil Engineering Journal, 28, Volume 2 19 backcalculating the base layer moulus, especially if a thin AC layer is use, is a well recognize problem [4]. For this problem, it is sufficient to preict either n or k for base an subbase layers as both these mouli parameters are relate to one another as iscusse before. Note that the bestperformance network for preicting n b contains ANNpreicte E AC as one of the inputs to the network. The most common inputs for mechanistic analysis of airport flexible pavement performance inclue: (1) AC, tensile strain at the bottom of the asphalt layer, (2) SG, vertical compressive strain on top of the subgrae, an (3) SSR, Subgrae Stress Ratio efine as follows: SSR = qu where is eviator stress on top of the subgrae an q u is the unconfine compressive strength of subgrae cohesive soils. Distress moes normally consiere in flexible pavement analysis an esign are fatigue cracking an rutting [1]. Classical flexible pavement esign proceures are base on limiting the vertical compressive strain on top of the subgrae (subgrae rutting failure criteria) an the tensile strain at the bottom of the lowest AC layer (AC fatigue failure criteria). (5) Using the results from ILLI-PAVE finite element analyses, researchers have showe that the SSR is a goo inicator of the subgrae conition [11]. The philosophy of the SSR criterion is to ensure that the pavement exhibits stable subgrae permanent eformation performance. The SSR criterion has been successfully utilize in the evelop-ment of ILLI-PAVE base flexible highway pave-ment esign proceures for the Illinois Department of Trans-portation [12]. The SSR-base subgrae criteria has been propose for airport flexible pavement esign [11]. Using the synthetic eflection basins generate by ILLI- PAVE an the erive DBPs, the possibility of eveloping ANN-base moels for preicting AC, SG, an was explore. Initial analyses showe that preicting these layer conition inicators were extremely ifficult. Of the three, AC was the most ifficult to preict. Table 5 summarizes the results of sensitivity analyses in selecting the best-performance networks for preicting AC, SG, an. Base on the magnitue of the testing RMSE for the selecte networks (highlighte in the Table), it can be sai that the preiction accuracy is reasonable, if not goo. DISCUSSION OF RESULTS Table 6 isplays the summary of all the best-performance ANN-base preiction moels ientifie by the parametric analyses in this stuy. The training progresses of the bestperformance networks are capture in Figs. 1 to 6. Table 5. Summary of Sensitivity Analyses for Preicting Pavement Critical Responses Trial Input Output Network Architecture No. of Epochs Testing RMSE (psi) SG (Microstrain) AC (Microstrain) 1 D ~ D , 9.79E-1 2 D ~ D , 9.68E-1 3 D ~ D , 9.47E-1 5 D ~ D 5 SG , D ~ D 5, BDI SG , D ~ D 6, BDI SG , 49 8 D ~ D 6, BDI SG , 26 4 D ~ D 6 SG , D ~ D 6, BDI, SCI AC , D ~ D 6, BDI, SCI AC , D ~ D 6, BDI, SCI AC , D ~ D 6, BDI, SCI AC , D ~ D 6, BDI, E AC AC , 12 1 D ~ D 6, AUPP, E AC AC , D ~ D 6, AUPP, E AC AC , D ~ D 6, AUPP, E AC AC , D ~ D 6, AUPP, E AC AC , 92

6 2 The Open Civil Engineering Journal, 28, Volume 2 Kasthurirangan Gopalakrishnan Table 6. Summary of Best-performance ANN Preiction Moels Output Inputs Network Architecture Testing RMSE E ac D ~ D ksi E ri D ~ D 6, BCI, AI ksi n b D ~ D 6, AUPP, E AC, D 12 /D n s D ~ D 6, E AC, E Ri D ~ D psi SG D ~ D millistrain AC D ~ D 6, AUPP, E AC microstrain Training RMSE (ksi) Training RMSE (psi) Fig. (1). Training curve for AC moulus. Fig. (4). Training curve for. Training RMSE nb ns Training RMSE (millistrain) Fig. (2). Training curves for n b an n s. Fig. (5). Training curve for SG. Training RMSE (ksi) Training RMSE (microstrain) Fig. (3). Training curve for subgrae moulus. Fig. (6). Training curve for AC.

7 Neural Networks Analysis of Airfiel Pavement Heavy Weight The Open Civil Engineering Journal, 28, Volume 2 21 In Figs. 7 to 11, the target an ANN-preicte values are compare for all the output variables using the 1,25 test ata vectors. Except for base an subbase mouli parameters, very goo agreement is foun between the target an ANN-preicte values for all output variables. Further research is require to ientify the appropriate input variables an the require network architecture to successfully preict the base an subbase mouli parameters. ANN Preicte SG (millistrain) R 2 =.89 ANN Preicte AC Moulus, E AC (ksi) R 2 = Target AC Moulus, E AC (Ksi) Fig. (7). Preiction of AC moulus. ANN Preicte Subgrae Moulus, E Ri (ksi) R 2 = Target Subgrae Moulus, E Ri (ksi) Fig. (8). Preiction of subgrae moulus, E Ri. ANN Preicte (psi) R 2 = Target (psi) Fig. (9). Preiction of subgrae eviator stress, Target SG Fig. (1). Preiction of vertical subgrae compressive strain, SG. ANN Preicte ac (microstrain) R 2 = Target ac (microstrain) Fig. (11). Preiction of horizontal tensile AC strain, AC. ANN APPLICATION TO FIELD DATA One of the major reasons for eveloping this backcalculation proceure is to reliably evaluate the structural integrity of the NAPTF pavement test sections as they were subjecte to traffic loaing. The NAPTF is locate at the Feeral Aviation Aministration (FAA) William J. Hughes Technical Center, Atlantic City International Airport, New Jersey. The NAPTF test pavement area is 9-foot long an 6-foot wie an it inclues six AC pavement sections. One of them is a conventional-base AC pavement built over a meium-strength subgrae which was moele in this stuy. This test section is referre to as the MFC. The test sections were subjecte to a six-wheel ual-triem aircraft laning gear (Boeing 777) in one lane an a four-wheel ualtanem laning gear (Boeing 747) in the other lane simultaneously. The wheel loas were set at 45, lbs an the spee was 5 mph uring trafficking. The test sections were trafficke to failure. Accoring to the NAPTF failure criterion, pavements were consiere to be faile when there is a 1-inch surface upheaval ajacent to the traffic lane. The MFC test section was the first one to fail at 12,952 loa repetitions exhibiting 3 to 3.5 inches of rutting an severe cracking. All NAPTF test ata referre in this research can be ownloae from the FAA Airport Technology website:

8 22 The Open Civil Engineering Journal, 28, Volume 2 Kasthurirangan Gopalakrishnan During the NAPTF traffic test program, HWD tests were conucte at various times to monitor the effect of time an traffic on the structural conition of the pavement. Tests were conucte on B777 traffic lane, B747 traffic lane an the untrafficke Centerline (C/L). Using the HWD test ata acquire at the NAPTF for the MFC test section, the AC mouli an subgrae mouli were backcalculate with the best-performance ANNs. The results were then compare with those obtaine using BAKFAA, an ELP-base backcalculation program. The BAKFAA program was evelope uner the sponsorship of the FAA Airport Technology Branch an is base on the LEAF layere elastic computation program. A stiff layer with a moulus of 1,, psi an a Poisson s ratio of.5 was use in backcalculation process. The plots comparing the results of ANN-base approach with those of BAKFAA are shown in Fig. 12 for AC moulus an in Fig. 13 for subgrae moulus. AC Resilient Moulus, E AC (ksi) B777-ANN B747-ANN C/L-ANN B777-FAABACKCAL B747-FAABACKCAL C/L-FAABACKCAL Number of Loa Repetitions (N) Fig. (12). Comparison of ANN-preicte AC mouli with BAKFAA AC mouli (Fiel Data). Subgrae Resilient Moulus, E Ri (ksi) Temperature Fig. (13). Comparison of ANN-preicte subgrae mouli with BAKFAA subgrae mouli (Fiel Data). In the Figures, B777- an B747- in the legen refer to B777 traffic lane an B747 traffic lane respectively. One of the objectives of the NAPTF traffic test program was to compare the amaging effect of B777 an B747 laning gears on airport pavements. In these Figures, the changes in layer mouli in B777 traffic lane an B747 traffic lane are Pavement Temperature (eg F) B777-ANN B777-FAABACKCAL B747-ANN B747-FAABACKCAL 19 C/L-ANN C/L-FAABACKCAL Number of Loa Repetitions (N) ue to both traffic loaing as well as variation in temperature an climate. The changes in pavement material properties in the pavement Centerline (C/L) are only ue to environmental effects as the C/L was not subjecte to trafficking. In Fig. 12, the variation in pavement temperature over the uration of trafficking program is inicate. Stuies have shown that the AC moulus is very sensitive to pavement temperature. Therefore, the pavement temperature is plotte as well in Fig. 12 on the seconary Y-axis. The AC moulus Vs N tren is similar for both ANN-preicte an FAABACKCAL results. The ANN-moel seems to be more sensitive to traffic loaing effects an temperature effects which is reflecte in the sharp ecrease in AC mouli with rise in temperature an number of loa repetitions. The B747 traffic lane is slightly more istresse in terms of reuction in elastic mouli compare to the B777 traffic lane. This is capture by the ANN-moel. This result was confirme by the NAPTF rutting stuy results [13]. The NAPTF trench stuy results showe that the subgrae layer contribute significantly to the total pavement rutting in the MFC test section. The ANN-moel shows an overall ecreasing tren in subgrae mouli with increasing number of loa repetitions, whereas the mouli values backcalculate using BAKFAA remain more or less the same throughout the trafficking program (see Fig. 13). During the NAPTF construction, 2-inch Pressure Cells (PCs) were installe on top of the subgrae to measure the vertical stresses inuce by the test gear uring trafficking. Using the 2-inch PC ata, vertical subgrae stresses were etermine for the B777 traffic lane an B747 traffic lane as a function of the number of loa repetitions (N). These values were converte to Subgrae Stress Ratios (SSRs) by iviing the vertical loa-inuce subgrae stresses by the unconfine compressive strength (Q u ) which was etermine to be 26.1 psi base on laboratory testing. The vertical loainuce subgrae stresses were assume to be approximately equal to the eviator stress on top of subgrae ( ) in calculating the SSRs. Subgrae eviator stresses ( ) were also compute from the HWD eflection basins using the ANN preiction moel an were converte to SSRs using the same proceure mentione above. The ANN results are compare with the actual PC results in Fig. 14. It is note that the orers of magnitues are ifferent for PC results an the ANN results although the trens are similar. This is because the ANN results are base on results from HWD tests which apply a 36,-lb (36-kip) loa on a 12-inch iameter plate on the pavement. Whereas, the PCs measure actual subgrae stresses inuce by moving wheel loas of B777 gear (6-wheel) an B747 gear (4-wheel) with 45,-lb (45-kip) on each wheel. Future research will focus on the feasibility of translating the 36-kip base ANN results to match the actual PC results. However, the ANN results capture the tren in the variation of subgrae stresse with N. The results also confirm that the B747 traffic lane was more istresse compare to the B777 traffic lane as a result of trafficking. SUMMARY AND CONCLUSIONS The Heavy Weight Deflectometer (HWD) test is one of the most wiely use tests for assessing the structural

9 Neural Networks Analysis of Airfiel Pavement Heavy Weight The Open Civil Engineering Journal, 28, Volume 2 23 integrity of airport pavements in a non-estructive manner. In this test, an impulse loa is applie to the pavement surface by ropping a weight onto a circular metal plate an the resultant pavement surface eflections are measure irectly beneath the plate an at several raial offsets. Backcalculation is the accepte term use to ientify a process whereby the elastic (Young s) mouli of iniviual pavement layers are estimate base upon measure HWD surface eflections. The elastic mouli of the iniviual pavement layers are effective inicators of layer conition. They are also necessary inputs to mechanistic-base analysis an esign of pavements. SSR ANN - B777 Lane PC - B777 Lane ANN - B747 Lane PC - B747 Lane Number of Loa Repetitions (N) Fig. (14). Comparison of ANN-preicte subgrae stresses with PC-measure subgrae stresses (fiel ata). The ELP-base backcalculation programs o not account for the stress-epenency of unboun granular materials (use in the base an subbase layers) an fine-graine cohesive soils (use in the subgrae layer) an therefore o not prouce realistic results. ILLI-PAVE is a pavement finite-element software that incorporates stress-sensitive material moels an it provies a more realistic representation of the pavement structure an its response to loaing. The primary objective of this stuy was to evelop a tool for backcalculating non-linear pavement layer mouli from FWD/HWD ata using Artificial Neural Networks (ANN). A multi-layer, fee-forwar network which uses an errorbackpropagation algorithm was traine to approximate the HWD backcalculation function. The ILLI-PAVE generate synthetic atabase was use to train the ANN. Using the ANN, we were successfully able to preict the AC mouli an subgrae mouli. Apart from the mouli, the critical pavement responses such as subgrae eviator stress an horizontal AC tensile strain were also successfully preicte using the ANNs. The final prouct was use in backcalculating pavement layer mouli an in preicting SSRs from actual fiel ata acquire at the National Airport Pavement Test Facility (NAPTF).Although this is a preliminary stuy with a narrow scope, the results are very encouraging. Future stuies woul incorporate a wie range of pavement layer properties in the training ataset which woul improve the generalization capabilities of the ANN. They woul consier all four (two conventional-base an two asphalt-stabilize base) flexible test sections constructe at the NAPTF. The results woul be use in stuying the comparative effect of B777 an B747 gears on the mouli values. Further research is require to ientify the appropriate input variables an the require network architecture to successfully preict the base an subbase mouli parameters. ACKNOWLEDGEMENT The author gratefully acknowleges Prof. Marshall R. Thompson in guiing the stuy an Dr. Franco Gomez- Ramirez for generating the ILLI-PAVE synthetic atabase. Special thanks to Dr. Davi Brill an Dr. Goron Hayhoe of FAA Airport Technology Branch for their help in conucting this stuy. The ata reference in this paper was ownloae from the FAA Airport Technology Branch (NAPTF) Website. The contents of this paper reflect the views of the author who is responsible for the facts an accuracy of the ata presente within. The contents o not necessarily reflect the official views an policies of the Feeral Aviation Aministration. This paper oes not constitute a stanar, specification, or regulation. REFERENCES [1] G. R. Hicks, Factors influencing the resilient properties of granular materials, Ph.D. issertation, University of California, Berkeley, 197. [2] M. R. Thompson an Q. L. Robnett, Resilient properties of subgrae soils, J. Trans. Eng., vol. 15, pp , January [3] L. Raa an J. L. Figueroa, Loa response of transportation support systems, J. Trans. Eng., vol. 16, pp , Janueary 198. [4] R. W. Meier an G. J. Rix, Backcalculation of Flexible Pavement Mouli Using Artificial Neural Networks, in the 73r Annual Meeting of the Transportation Research Boar, [5] H. Ceylan, E. Tutumluer, M. Thompson an F. Gomez-Ramirez, Neural network-base structural moels for rapi analysis of flexible pavements with unboun aggregate layers, in 6th International Symposium on Pavements Unboun (UNBAR6), 24. [6] G. R. Raa an M.. W. Witczak, Comprehensive evaluation of laboratory resilient mouli results for granular material, Trans. Res. Rec., vol. 81, pp , [7] M. Hossain an J. P. Zaniewski, Characterization of falling weight eflectometer eflection basin, Trans. Res. Rec., vol. 1293, pp. 1-11, [8] B. Xu, R. S. Ranjithan, an R. Y. Kim, Development of Relationships between FWD Deflections an Asphalt Pavement Layer Conition Inicators, in the 81st Annual Meeting of the Transportation Research Boar, 21. [9] S. Haykin, Neural Networks: A Comprehensive Founation. New York: Macmillan College Publishing Company, [1] M. R. Thompson an D. Nauman, Rutting rate analysis of the AASHO roa test flexible pavements, Trans. Res. Rec., vol. 1384, pp , [11] M. Bejarano an M. R. Thompson, Subgrae soil evaluation for the esign of airport Flexible Pavements, FAA-COE Report No. 8, Department of Civil Engineering, University of Illinois at Urbana- Champaign, Urbana, Illinois, [12] M. R. Thompson an R. P. Elliot, ILLI-PAVE base response algorithms for esign of conventional flexible pavements, Trans. Res. Rec., vol. 143, pp. 5-57, [13] K. Gopalakrishnan an M. R. Thompson, Severity effects of ualtanem an ual-triem repeate heavier aircraft gear loaing on pavement rutting performance, Int. J. Pavement Eng., vol. 7, pp , September 26. Receive: January 1, 28 Revise: March 11, 28 Accepte: March 17, 28