Backcalculation of Airport Flexible Pavement Non-Linear Moduli Using Artificial Neural Networks

Transcription

1 Backcalculation of Airport Flexible Pavement Non-Linear Mouli Using Artificial Neural Networks Kasthurirangan Gopalakrishnan an Marshall R. Thompson Grauate Research Assistant an Professor Emeritus Department of Civil Engineering, University of Illinois at Urbana-Champaign, 25 N. Mathews Ave., Room 322, NCEL, Urbana, IL 6181 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 backcalculate from the HWD eflection measurements are effective inicators of layer conition. Most of the backcalculation programs that are currently in use o not account for the non-linearity of unboun granular materials an fine-graine cohesive soils an therefore o not prouce realistic results. 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). A multi-layer, fee-forwar network which uses an error-backpropagation algorithm was traine to approximate the HWD backcalculation function. The synthetic atabase generate using the nonlinear pavement finite-element program ILLI-PAVE was use to train the ANN. Using the ANN, we were successfully able to preict the AC mouli an subgrae mouli. The final prouct was use in backcalculating pavement layer mouli from actual fiel ata acquire at the National Airport Pavement Test Facility (NAPTF). test tries to replicate the force history an eflection magnitues of a moving truck tire/aircraft tire. Figure 1. Illustration of Deflection Surface Cause by Moving Wheel Loas Introuction 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 as illustrate in Figure 1. The FWD/HWD Figure 2. Schematic of FWD Loa-Geophone Configuration an Deflection Basin The eflecte shape of the basin (Figure 2) 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 FWD/HWD loas. Through a series of iterations, the layer mouli are change, an the calculate eflections are then compare

2 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 finegraine subgrae soils is well ocumente in literature (Hicks 197; Thompson an Robnett 1979). 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 (Raa an Figueroa 198). 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 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 traitionalbasin matching programs. ANNs have been successfully use in the past for the backcalculation of flexible pavement mouli from FWD ata (Meier an Rix 1993). 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 errorbackpropagation 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. Database Generation Using ILLI-PAVE 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-θ moel was use for the base an subbase layers: σ D n M R = = Kθ ε R Where M R is resilient moulus (psi), θ is bulk stress (psi) an K an n are statistical parameters. Base on extensive testing of granular materials, Raa an Witczak (1981) propose the following relationship between K an n (R 2 =.68, SEE =.22): Log 1 (K) = n The stress-softening bilinear moel was use for the subgrae layer: M M R R = M = M Ri Ri + K + K 1 2.( σ σ ) Where M R is resilient moulus (psi), σ 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. Deflection Basin Parameters (DBPs) erive from FWD/HWD eflection measurements are shown to be i.( σ σ ) i for σ for σ < σ > σ i i

3 goo inicators of selecte pavement properties an conitions (Hossain an Zaniewski 1991). Recently Xu et al (21) use DBPs in eveloping new relationships between selecte pavement layer conition inicators an FWD eflections by applying regression an ANN techniques. 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 ). Table 1. Deflection Basin Parameters (DBPs) Use in this Stuy Deflection Formula Basin Parameter (DBP) Area Uner AUPP = (5D 2D 12 2D 24 D 36 )/2 Pavement Profile Area Inex AI 4 = (D 36 + D 48 )/2D Base Curvature Inex Deflection Ratio BCI = D 24 D 36 DR = D 12 /D 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 range 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 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 2. Range of Layer Properties Use to Train the ANN Pavemen t Layer Thickness (inches) Elastic Layer Moulus (psi) Asphalt 5 1,58 1,999,884 Concrete Base 8 K b : 1,628 19,747 n b :.2.8 Subbase 12 K s : 1,628 19,75 n s :.2.8 Subgrae 95 1,63 19,743 San 12 45, Network Architecture A generalize n-layer feeforwar artificial neural network which uses an error-backpropogation algorithm (Haykin 1994) 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 fourlayer 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 [ j Y ( X j )] j= 1 N 2 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.

4 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 bestperformance 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. 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 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. Discussion of Results The training progresses of the best-performance networks are capture in Figures 3-5. Table 3 summarizes the bestperformance network architectures efine by the input features, the esire output an their preiction performance. The base an the subbase layer mouli were the harest to preict. The ifficulty associate with backcalculating the base/subbase layer moulus, especially if a thin AC layer is use, is a well recognize problem. It is sufficient to preict either n or K as there is a relation between the two. Note that the AC moulus (E AC ) preicte using the best ANN moel is one of the inputs for preicting n b. The RMSEs are significantly higher for both n b an n s. Therefore, the accuracy of preicting base an subbase layer mouli from HWD ata using ANN is consiere poor in this stuy. Figures 6 an 7 compare the target an ANN-preicte mouli of the AC an subgrae layers, respectively for the 1,25 test ata vectors. The results are not shown for n b an n s as the R 2 values were poor. Excellent agreement is foun between the target an ANN-preicte layer mouli for AC an subgrae layers. These two ANN moels have successfully learne the backcalculation function over the entire range of pavement properties inclue in the training ataset. Training RMSE (ksi) Training Curve for AC Moulus (E AC ) Number of Epochs Figure 3. Training Curve for AC Moulus Training RMSE Training Curves for n b an n s Number of Epochs Figure 4. Training Curves for n b an n s Training RMSE (ksi) Figure 5. Training Curve for Subgrae Moulus Figure 6. Preiction of AC Moulus Figure 7. Preiction of Subgrae Moulus nb ns Training Curve for Subgrae Moulus (E Ri ) Number of Epochs ANN Preicte AC Moulus, E AC (ksi) ANN Preicte Subgrae Moulus, E Ri (ksi) R 2 = Target AC Moulus, E AC (Ksi) R 2 = Target Subgrae Moulus, E Ri (ksi)

5 Table 3. Summary of Best-Performance ANNs Output Inputs Network Testing Architecture RMSE E ac D - D ksi E ri D - D 6, BCI, AI 4 n b D - D 6, AUPP, E ac, D 12 /D n s D - D 6, E ac, E ri ksi ANN Application to Fiel 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 meiumstrength subgrae which was moele in this stuy. This test section is referre to as the MFC. All the pavement sections were subjecte to a six-wheel triem aircraft laning gear (Boeing 777) in one lane an a four-wheel tanem 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. 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 on the no-traffic 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 FAABACKCAL, an ELP-base backcalculation program. FAABACKCAL 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 FAABACKCAL are shown in Figure 8 for AC moulus an in Figure 9 for subgrae moulus. AC Resilient Moulus, E AC (ksi) B777-FAABACKCAL B747-FAABACKCAL C/L-FAABACKCAL Number of Loa Repetitions (N) Figure 8. Comparison of ANN-preicte AC Mouli with FAABACKCAL AC Mouli (Fiel Data) Subgrae Resilient Moulus, E Ri (ksi) B777-ANN B747-ANN C/L-ANN Temperature B777-ANN B747-ANN C/L-ANN Figure 9. Comparison of ANN-preicte Subgrae Mouli with FAABACKCAL 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 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 Figure 8, 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 Figure 8 on the seconary Y-axis. The AC moulus Vs N tren is similar for both ANN-preicte an FAABACKCAL results. The ANNmoel 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 B777-FAABACKCAL B747-FAABACKCAL C/L-FAABACKCAL Pavement Temperature (eg F) Number of Loa Repetitions (N)

6 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 (Gopalakrishnan an Thompson 23). 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 FAABACKCAL remain more or less the same throughout the trafficking program (see Figure 9). Summary 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. 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. 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 finiteelement 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. The final prouct was use in backcalculating pavement layer mouli 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. Acknowlegements/Disclaimer We woul like to thank Dr. Franco Gomez-Ramirez for generating the ILLI-PAVE synthetic atabase an for his valuable insights into the evelopment of the ANN-base backcalculation proceure. This paper was prepare from a stuy conucte in the Center of Excellence for Airport Technology at the University of Illinois at Urbana- Champaign. Funing for the Center of Excellence is provie in part by the Feeral Aviation Aministration uner Research Grant Number 95-C-1. References Gopalakrishnan, K., an Thompson, M. R. 23. Rutting Stuy of NAPTF Flexible Pavement Test Sections. In Proceeings of the 23 ASCE Airfiel Specialty Conference (in preparation). Las Vegas, Nevaa. Haykin, S Neural Networks: A Comprehensive Founation. Macmillan College Publishing Company, Inc., New York. Hicks, R. G Factors Influencing the Resilient Properties of Granular Materials. Ph. D. iss., University of California, Berkeley. Hossain, S. M. an Zaniewski, J. P Characterization of Falling Weight Deflectometer Deflection Basin. Transportation Research Recor 1293:1-11. Meier, R. W., an Rix, G. J Backcalculation of Flexible Pavement Mouli Using Artificial Neural Networks. In Proceeings of the 73 r Annual Meeting of the Transportation Research Boar, Washington, D.C. Raa L., an Figueroa, J. L Loa Response of Transportation Support Systems. Transportation Engineering Journal 16(TE1). Raa, G., an Witczak, M. W Comprehensive Evaluation of Laboratory Resilient Mouli Results for Granular Material. Transportation Research Recor 81. Thompson, M. R., an Robnett, Q. L Resilient Properties of Subgrae Soils. Transportation Engineering Journal 15(1). Xu, B.; Ranjithan, S. R.; an Kim, R. Y. 21. Development of Relationships between FWD Deflections an Asphalt Pavement Layer Conition Inicators. In Proceeings of the 81 st Annual Meeting of the Transportation Research Boar, Washington, D.C.