Condition Assessment of Composite Pavement Systems Using Neural ...

TRB Paper 07-3356

Paper Submitted to the Transportation Research Board for Presentation and Publication at the 86th Annual meeting to be held on January 21-25, 2007 in Washington, D.C..

Condition Assessment of Composite Pavement Systems Using Neural Network-Based Rapid Backcalculation Algorithms by Alper Guclu Graduate Research Assistant 480 Town Engineering Building Department of Civil, Construction and Environmental Engineering Iowa State University, Ames, IA 50011-3232 Phone: 1-515-294-0223 Fax: 1-515-294-8216 E-mail: [email protected] and Halil Ceylan, Ph.D. (Corresponding Author) Assistant Professor 482B Town Engineering Building Department of Civil, Construction and Environmental Engineering Iowa State University, Ames, IA 50011-3232 Phone: 1-515-294-8051 Fax: 1-515-294-8216 E-mail: [email protected]

(Word Count: Abstract: 202, Text: 4,708, Tables: 1,500, Figures: 1,500, Total: 7,708)

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ABSTRACT The objective of this study was to develop artificial neural network (ANN)-based advanced backcalculation models as pavement structural analysis tools for the rapid and accurate prediction of asphalt concrete (AC) overlaid Portland cement concrete (PCC) composite pavement layer moduli under typical highway loadings. The DIPLOMAT program was used for solving deflection profiles of composite pavement systems. The DIPLOMAT solutions were compared with the solutions of ISLAB2000 and ILLI-PAVE pavement analysis programs. ANNbased backcalculation models trained with the results from the DIPLOMAT solutions have been found to be practical alternatives for routine pavement evaluation using the falling weight deflectometer (FWD) deflection data. The trained ANN models in this study were capable of predicting AC and PCC layer moduli, and the coefficient of subgrade reaction value with low average absolute errors. A dimensional analysis approach was also adopted by introducing the dimensional terms of AC modulus over PCC modulus ratio and PCC modulus over coefficient of subgrade reaction ratio value. Both methods were verified by synthetically generated DIPLOMAT deflection profiles. ANN-based backcalculation models developed in this study were also capable of successfully and rapidly (capable of analyzing 100,000 FWD deflection profiles in one second) predicting the pavement layer moduli from the FWD deflection basins in real time during field testing. The developed models were successfully validated by results from the Long-Term Pavement Performance (LTPP) FWD tests conducted on US29, Spartanburg County, South Carolina. Key Words: Artificial Neural Networks, Falling Weight Deflectometer, Composite Pavements, Pavement Layer Backcalculation, Nondestructive Testing and Evaluation, Finite Element Analysis

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INTRODUCTION Evaluation of pavement layer moduli using the falling weight deflectometer (FWD) has become the main non-destructive testing technique for the structural evaluation of pavement systems over the last decade. FWD testing involves measurement of vertical deflections due to dropping of a mass with known weight from various heights. Sensors located at specific radial distances monitor the deflection history. The deflections measured at radial distances away from load form the deflection basin. In order to calculate the pavement structural capacity accurately the deflection basins should be measured and analyzed accurately. Although there are numerous methods for evaluating the structural capacity of pavements from deflection basin data, there is no standard or universally accepted procedure that presently exists [1]. Several pavement layer moduli backcalculation programs have been proposed in the literature. The AREA method for flexible pavements [2], AREA method for rigid pavements [3-5], ILLISLAB [6], ILLI-BACK [7], best fit algorithm [8-9], ELMOD [10], WESDEF [11], DIPLOBACK [12], and MODCOMP [13-14] are examples of FWD interpretation programs and algorithms for rigid, flexible and composite pavements. Backcalculation programs based on multi-layer elastic layer theory are generally used for AC pavements. For rigid pavements, plate theory for a slab resting on a Winkler foundation or elastic solid foundation. There is no widely accepted methodology for AC overlaid PCC type of composite pavements on Winkler foundation. The backcalculation programs, WESDEF, BISDEF, and ELSDEF, are based on multi-layer elastic analysis programs, WESLEA, BISAR and ELSYM, respectively. These programs require the thickness, Poisson’s ratio and a seed modulus as inputs. The forward elastic layer program iterates the given seed modulus until the given deflections matches with calculated deflections. Thus, the modulus of pavement layer is highly affected by the seed modulus. Consequently, experienced engineers are required to use these backcalculation programs [15]. Moreover, elastic layer programs (ELPs) used in asphalt pavement analysis assume linear elasticity. Pavement geomaterials do not, however, follow a linear type stress-strain behavior under repeated traffic loading [16, 19]. The ILLI-PAVE [16-18] finite element program which is commonly used in structural analysis of flexible pavements takes into account nonlinear geomaterial characterization. Other finite element programs such as ABAQUS, ANSYS, and DYNA3D are very powerful programs since they can be used in three-dimensional nonlinear dynamic analysis. Several studies have focused on 3-D finite element modeling of pavements in last decade [20-22]. Drawbacks associated with these 3-D finite element programs are that considerable computational resources and time are required for developing a structural model for each problem. There are also several finite element based programs exist specifically designed for the analysis of rigid pavement systems such as ISLAB2000 [23-25]. ISLAB2000 contains many advanced features that distinguish it from other pavement programs that are based on plate theory. KENSLABS [26] and WESLIQID [27] are pavement analysis programs for multi-wheel loading of one- or two-layered medium thick plates resting on a Winkler foundation or elastic solid. DIPLOMAT [24, 28-29] provides the capability to model pavement layers as plates, springs and/or elastic layers. DIPLOMAT assumes infinite joints in the horizontal direction. An ANN based backcalculation procedure was developed for composite pavements by Khazanovich and Roesler [12] using DIPLOMAT solutions and implemented into program called DIPLOBACK. DIPLOBACK procedure solutions were agreed with WESDEF solutions [12].

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In this paper, the artificial neural networks (ANNs) methodology is applied to rapidly backcalculate the AC overlaid PCC type composite pavement layer moduli properties. The pavement structural properties that are of interest in this study are: (1) AC modulus (EAC), (2) PCC Modulus (EPCC), (3) ks – coefficient of subgrade reaction. To generate a deflection database, the DIPLOMAT structural analysis program was chosen. DIPLOMAT is chosen specifically for its capability to analyze pavement layers as plates, elastic, and springs. The results from DIPLOMAT were compared with those produced by ISLAB2000 and ILLIPAVE. DIPLOMAT deflection basins were then used to train ANN models for backcalculation of the pavement structural properties. When compared with the actual DIPLOMAT analysis, the trained ANN models successfully predicted the pavement layer moduli values, but with several added advantages. COMPARISON OF DIPLOMAT WITH OTHER PAVEMENT STRUCTURAL ANALYSIS PROGRAMS DIPLOMAT Model DIPLOMAT is a multi-layered linear elastic structural analysis program for computing pavement responses (stresses, strains and displacements) subjected to single- or multi-wheel traffic loads where each load applied over a circular area with a uniform pressure [24]. Each component of the multi-layered pavement system can be an isotropic, elastic layer, or a plate or a spring layer. The solution algorithm is based on a generalization of Burmister's layered elastic theory [30-31]. Tensile stresses and downward displacements are assumed to be positive [24]. DIPLOMAT can accommodate solutions for plate on elastic layer, or elastic layer on plate, or spring models. Since DIPLOMAT performs analysis using numerical integration methods, it is faster than finite element programs. DIPLOMAT vs. ISLAB2000 Comparison DIPLOMAT and ISLAB2000 solutions were compared to investigate the differences in pavement deflections. ISLAB2000 is a finite element model based program specifically designed for analyzing rigid pavement systems. In large part, it is an extension and improvement of the ILLI-SLAB [6] and ILSL2 [24] programs. ISLAB2000 is a significant improvement over other finite element programs for the analysis of rigid and composite pavements, enabling users to analyze a wide range of problems that are not possible with other programs. Deflection data for the analyzed test pavement section was extracted from both DIPLOMAT and ISLAB2000 solutions. The layout of a generic AC overlaid PCC test section considered in this study is given in Figure 1, and the material properties are summarized in Table 1. Primary consideration in this comparison was how well the DIPLOMAT solutions match with the ISLAB2000 solutions. Four different slab sizes were considered in ISLAB2000; (1) CP150 composite pavement with sizes 3.8 x3.8 m (150 x150 in.), (2) CP300 - composite pavement with slab sizes 7.6 x 7.6 m (300 × 300 in.), (3) CP600 - composite pavement with slab sizes 15 x 15 m (600 x 600 in.), and (4) CP900 - composite pavement with slab sizes 23 x 23 m (900 x 900 in.). All the slabs were loaded at the slab center, and the deflections were extracted at radial distances of 0, 20, 30, 45, 61, 91, 122, 152 cm (0, 8, 12, 18, 24, 36, 48, and 60 in.) away from the load. Both programs were analyzed by assuming plate theory for modeling the slab systems. Table 2

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summarizes the calculated deflections. The results of this study suggest that the DIPLOMAT solutions match quite well with ISLAB2000 solutions for large joint spacing which is mainly due to the infinite slab size assumption in horizontal direction in the DIPLOMAT model.

AC: υ, hAC, EAC

hAC

PCC: υ, hPCC, EPCC

hPCC

Subgrade: ks

FIGURE 1 Layout of an AC overlaid PCC composite pavement section.

TABLE 1 AC Overlaid PCC Type of Composite Pavement Material Properties AC Properties EAC = 6.9 GPa (1,000 ksi) hAC = 30 cm (12 in) Poisson’s ratio = 0.40

PCC Properties EPCC = 27.6 GPa (4,000 ksi) hPCC = 25 cm (10 in) Poisson’s ratio = 0.20

Subgrade Properties ks = 40.71 kPa/mm (150 psi/in)

TABLE 2 Comparison of ISLAB2000 and DIPLOMAT Solutions ISLAB2000 Deflections w (mm) FWD Sensor CP150 CP300 CP600 CP900 D0 133 92 85 85 D12 128 89 82 82 D18 125 87 79 79 D24 121 83 76 76 D36 113 76 69 68 D48 105 67 61 61 D60 96 59 53 53 D72 89 51 46 45

DIPLOMAT w (mm) 89 86 83 79 71 63 55 47

DIPLOMAT vs. ILLI-PAVE Comparison ILLI-PAVE was developed at the University of Illinois [19] based on the finite element code used by Duncan et. al. [32] for analyzing highway pavement systems. Since then, numerous research studies have demonstrated that the ILLI-PAVE model provides a realistic pavement structural response for highway and airfield pavement systems [16-18]. Recent research studies

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at the Federal Aviation Administration’s Center of Excellence established at the University of Illinois also supported the development of a new, updated version of the program known as the ILLI-PAVE 2000. Pavement test section layout and material properties (see Figure 1 and Table 1) used in ISLAB2000 comparison were used in ILLI-PAVE comparison except that the pavement layers were assumed to be linear-elastic in both DIPLOMAT and ILLI-PAVE and the layers were assumed fully bonded in both programs. Table 3 summarizes the results of comparison. ILLIPAVE solutions were approximately 15% higher than DIPLOMAT solutions. The deflection profiles showed the same trend in both cases. TABLE 3 Comparison of ILLI-PAVE and DIPLOMAT Solutions FWD Sensor D0 D12 D24 D36 D48 D60 D72

ILLI-PAVE w (mm) 121.4 97.7 92.2 87.5 80.9 73.0 65.8

DIPLOMAT w (mm) 106.9 83.1 75.9 68.3 60.4 52.4 44.8

ARTIFICIAL NEURAL NETWORKS (ANNs) Backpropagation type artificial neural network models were trained in this study with the results from the DIPLOMAT model and were used as rapid analysis design tools for predicting layer moduli in AC overlaid PCC composite pavements. Backpropagation ANNs are very powerful and versatile networks that can be taught a mapping from one data space to another using a representative set of patterns/examples to be learned. The term “backpropagation network” actually refers to a multi-layered; feed-forward neural network trained using an error backpropagation algorithm. The connection weights in the backpropagation ANNs are initially selected at random. Inputs from the mapping examples are propagated forward through each layer of the network to emerge as outputs [33]. The errors between those outputs and the correct answers are then propagated backwards through the network and the connection weights are individually adjusted to reduce the error. After many examples (training patterns) have been propagated through the network many times, the mapping function is learned with some specified error tolerance. This is called supervised learning because the network has to be shown the correct answers for it to learn. The learning process performed by this algorithm is called “backpropagation learning” which is mainly an “error minimization technique” [34]. NEURAL NETWORK DESIGN AND TRAINING ANN analyses were designed with 20,000 DIPLOMAT solutions. The AC overlaid PCC pavement layout shown in Figure 1 were used. The input ranges are shown in Table 5 below.

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TABLE 5 Input Ranges for DIPLOMAT Solutions AC Modulus

PCC Modulus

ks

hPCC

hAC

EPCC/ks EAC/EPCC

Min

689 GPa (100 ksi)

6,890 GPa (1,000 ksi)

13.5 kPa/mm (50psi/in)

152 mm (6 inch)

51 mm (2 inch)

1,023.9

0.008

Max

20,670 (3,000 ksi)

82,680 (12,000 ksi)

271 508 406 (1,000 psi/in) (20 inch) (16 inch)

230,674

2.92

Based on the theoretical data obtained from DIPLOMAT solutions two main groups of ANN runs were performed accounting for (1) composite pavement direct method analysis (CDR) runs, and (2) composite pavement dimensional analysis (CDM) runs. Both CDR and CDM runs had inputs of deflections at radial distances of 0, 20, 30, 45, 61, 91, 122, 152 cm (0, 8, 12, 18, 24, 36, 48, 60 in.) away from the load which are represented by D0, D8, D12, D18, D24, D36, D48, and D60, respectively, and pavement layer thickness information to predict the layer moduli of composite pavement systems. The thickness of AC and PCC were represented as hAC, and hPCC, respectively. The outputs were: (1) AC modulus (EAC), (2) PCC modulus (EPCC), and (3) ks – coefficient of subgrade reaction. A total of 12 ANN runs for CDR model were performed. These runs were categorized into 4 groups depending on the number of deflection data used as follows; (1) CDR-4 with inputs D0, D12, D24, D36, hAC, hPCC ; (2) CDR-6 with inputs D0, D12, D24, D36, D48, D60, hAC, hPCC; (3) CDR-7 with inputs D0, D8, D12, D18, D24, D36, D48, D60, hAC, hPCC (Deflections were according to the FWD Strategic Highway Research Program (SHRP) spacing for the analysis of LTPP database); (4) CDR-8 with inputs D0, D8, D12, D18, D24, D36, D60, hAC, hPCC. Three ANN runs were conducted per each group (CDR-4, CDR-6, CDR-7, and CDR-8) to predict three pavement layer properties; EAC, EPCC, and ks – coefficient of subgrade reaction i.e. CDR4 consists of CDR-4-EAC, CDR-4-EPCC, and CDR-4-ks. In the same way, CDM runs were prepared as CDM-4, CDM-6, CDM-7, and CDM-8. Similarly, each group had 3 runs to predict ks- the coefficient of subgrade, EAC/EPCC ratio, and EPCC/ks ratio. Other inputs were deflection and thicknesses, except EAC/EPCC runs in which EPCC/ks ratio was added to improve ANN learning. CDM models were developed to predict EAC and EPCC in stepwise. First the ks value should be predicted using CDM-ks prediction. Then using the predicted k value and CDM- EPCC/ks run, EPCC value is predicted. Finally, having known EPCC value, one can predict EAC with CDMEAC/EPCC ratio. ANN dataset consisted of 20,000 DIPLOMAT solutions. This dataset was separated into 18,500 training and 1,500 independent testing sets. ANNs learn the relationship between input parameters and output variables using the information provided in the training dataset. Then, the independent 1,500 test data set was used to test how well ANN models have “learned” the relationship between the input parameters and output variables. A network with two hidden layers and 60 neurons in each layer was exclusively chosen for the ANN models trained in this study. Satisfactory results were obtained in the previous studies with these types of networks due to their ability to better facilitate functional mapping [35-36]. Figure 2 depicts the calculated mean square error (MSE) at each epoch for training and testing of AC modulus for CDR-8. MSEs decreased as the networks grew in size with increasing number of epochs. The testing

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MSEs were, in general for all models, slightly lower than the training ones. The lowest training MSEs were in the order of 2.0×10-5 for EAC, 5.2×10-5 for EPCC, 3.6×10-6 for k, 6.0 ×10-5 for EAC/EPCC ratio, and for 1.3 ×10-4 EPCC/k ratio.

0.025

Mean Square Error (MSE)

Training MSE Testing MSE 0.02

0.015

0.01

0.005

0 0

1,000

2,000

3,000

4,000

5,000

6,000

Learning Cycles

FIGURE 2 ANN training progress curve for predicting the AC layer moduli. Average absolute errors for each ANN training are summarized in Table 6 for EAC, EPCC, k, EAC/EPCC ratio, and EPCC/k ratio predictions. Figure 3 shows the EAC and k prediction performances for CDR-8 ANN model. Also EAC/EPCC and EPCC/k predictions for CDM-8 are shown in Figure 4. The outliers at figure 3 and 4 are corresponding to the very thin PCC layers with very low moduli values. TABLE 6 Prediction Performance of ANN-Based Backcalculation Models Developed in this Study Average Absolute Error (%) ANN Models EAC EPCC ks EAC/EPCC EPCC/k CDR-8 0.60 1.10 0.29 CDR-7 0.63 1.11 0.26 CDR-6 0.67 1.00 0.28 CDR-4 0.47 1.16 0.62 CDM-8 0.29 2.37 4.41 CDM-7 0.26 2.59 3.89 CDM-6 0.28 4.05 3.76 CDM-4 0.62 4.1 4.31

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ANN ks Prediction (kPa/mm)

ANN EAC Prediction (GPa)

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25

AAE = 0.6 % Training data: 18,500 20 Testing data: 1,500 15

Line of Equality

10 5

Inputs: 8 Def, hAC, hPCC Output: EAC

300

AAE = 0.3 % 250 Training data: 18,500 Testing data: 1,500 200

Line of Equality

150 100

0

Inputs: 8 Def, hAC, hPCC Output: ks

50 0

0

5

10

15

20

0

25

Given EAC (GPa) (a)

50

100

150

200

250

300

Given ks (kPa/mm) (b )

-3

ANN EPCC / ks Prediction (x10 )

ANN EAC / E PCC Prediction

FIGURE 3 Accuracy of prediction performance for CDR-8 ANN model: (a) EAC, and (b) ks.

2.5 2.0

AAE = 2.4 % Training data: 18,500 Testing data: 1,500

1.5 1.0

Line of Equality

0.5

Inputs: 8 Def, hAC, hPCC, Output: EAC / EPCC

0.0

0.0

0.5

1.0

1.5

Given EAC/EPCC (a)

2.0

2.5

250 200 AAE = 4.4 %

Training data: 18,500 150 Test data: 1,500 100

Line of Equality

50 0

Inputs: 8 Def, hAC, hPCC Output: EPCC / ks 0

50

100

150

200

250

Given EPCC/ks (x 10-3) ( b)

FIGURE 4 Accuracy of prediction performance for CDM-8 ANN model for: (a) EAC/EPCC, and (b) EPCC/ks ratio.

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VALIDATION

50

EAC

'89

ANN'89 AVG 3.5 ANN'92 STDEV 2.2 ANN'95 Mean Value =3.2 GPa

40

‘92

‘95

2.4

3.7

1.7

1.9

30 20 10 0

50

LTPP MODCOMP EAC Predictions (GPa)

ANN EAC Predictions (GPa)

To validate how well the trained ANN models perform using the field FWD data, the LTPP data site 45-7019 was selected. The FWD data was obtained from the pavement test sections on US29, Spartanburg County, South Carolina. Original construction date for this site was 1946. It is an AC overlaid PCC type composite pavement system. FWD deflections were taken from the “MON_DEFL_DROP_DATA_MT_TN” MS-Access file of LTPP standard data release 20 [36]. LTPP database contains data for the same section for years 1989, 1992, and 1995. The middle path pavement deflections were chosen for this analysis. LTPP MODCOMP v4.2 backcalculated values are presented for comparison in Figures 5 and 6. MODCOMP uses elastic layer theory, embodied in the CHEVRON computer code, as the method of forward calculation within an iterative approach [1]. Figures 5a and 5b show the ANN CDR-7-AC moduli and LTPP MODCOMP AC moduli predictions, respectively. Similarly, Figures 6a and 6b show the PCC moduli predictions for both CDR-7-PCC model and LTPP data set, respectively. As seen in Figures 5 and 6, EAC predictions are more consistent than the EPCC predictions. Both MODCOMP and ANN-based EAC values lie within ± 1,378 GPa (200 ksi) range. This range goes up to ± 6,890 GPa (1,000 ksi) in the case of EPCC. As seen from both AC and PCC prediction plots, the ANN and MODCOMP predictions, in general, are in good agreement. ANN and MODCOMP average moduli predictions are given in Figures 5 and 6. The former predictions for EAC average is 3.2 GPa, and EPCC average is 23.2 GPa, the latter prediction for EAC average is 4.1 GPa, and EPCC average is 25.4 GPa. Few spikes observed in the plots are due to faulty deflection basins. The scatter for ANN predictions is lower than MODCOMP predictions (see the standard deviation values presented in Figures 5 and 6) which demonstrates the power of the ANN-based approach. In addition, ANN moduli predictions for years 1989, 1992, and 1995 are more consistent compared to the MODCOMP predictions listed in the LTPP database. EAC

'89

LTPP'89 AVG 2.5 LTPP'92 STDEV 1.9 LTPP'95 Mean Value =4.1 GPa

40

‘92

‘95

3.1

6.9

5.7

5.7

30 20 10 0

0

50

100

150

200

Location (km) (a)

250

300

0

50

100

150

200

250

300

Location (km) ( b)

FIGURE 5 AC layer moduli predictions using: (a) ANN-based models, and (b) MODCOMP model.

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100

EPCC

'89

ANN'89 AVG 25.6 ANN'92 STDEV 10.4 ANN'95 Mean Value =23.2 GPa

80

‘92

‘95

22.4

21.6

9.4

8.3

60 40 20

100

LTPP MODCOMP EPCC Predictions (GPa)

ANN EPCC Predictions (GPa)

Guclu and Ceylan

EPCC

'89

LTPP'89 AVG 29 LTPP'92 STDEV 13.9 LTPP'95 Mean Value =25.4 GPa

80 60

‘92

‘95

25.6

21.4

13.7

9.6

40 20 0

0 0

50

100

150

200

250

Location (km) (a)

300

0

50

100

150

200

250

300

Location (km) (b )

FIGURE 6 PCC layer moduli predictions using: (a) ANN-based models, and (b) MODCOMP model.

SUMMARY AND CONCLUSIONS The use of artificial neural networks (ANNs) as pavement analysis tool was demonstrated in this paper by analyzing asphalt concrete (AC) overlaid Portland cement concrete (PCC) type composite pavement systems. A total of 12 ANN-based backcalculation models were developed for predicting each pavement layer moduli using some 20,000 DIPLOMAT model solutions. The ANN-based models successfully predicted pavement layer moduli values of EAC, EPCC, and k (modulus of subgrade reaction) with an overall average absolute error (AAE) value of less than 1.5 %. Similarly, ANN-based backcalculation models predicted the EAC/EPCC ratio and EPCC/k with an AAE of 3.0 % for models in which dimensional analysis was used. It was demonstrated that ANNs are capable of successfully predicting the pavement layer moduli values using the LTPP FWD field deflection measurements. Field moduli values were successfully predicted for the given deflection basins and comparison of the ANN-based predictions with the ones listed in the LTPP database showed the strength of the ANN-based backcalculation approach. Such ANN models are invaluable tools for pavement engineers for evaluating the structural condition of composite pavement systems. The adoption of ANN-based approach also resulted in both a drastic reduction in computation time and a simplification of the complicated traditional layer backcalculation approaches. Rapid prediction ability of the ANN models - capable of analyzing 100,000 FWD deflection profiles in one second - provide a tremendous advantage to the pavement engineers by allowing them to nondestructively assess the condition of the transportation infrastructure systems in real time while the FWD testing takes place in the field. Elimination of selecting seed layer moduli with the integration of ANN-based direct backcalculation approach can be invaluable for the state and federal agencies for rapidly analyzing large number of composite pavement deflection basins needed for routine pavement evaluation for both project specific and network level FWD testing.

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ACKNOWLEDGEMENTS The authors gratefully acknowledge the Iowa Department of Transportation (IA-DOT) for sponsoring this study. The contents of this paper reflect the views of the authors who are responsible for the facts and accuracy of the data presented within. The contents do not necessarily reflect the official views and policies of the IA-DOT. This paper does not constitute a standard, specification, or regulation. REFERENCES (1) PCS/Law Engineering, SHRP's Layer Moduli Back-Calculation Procedure: Software Selection, SHRP-P651, Washington, DC: Strategic Highway Research Program, National Academy of Science, 1993. (2) Hoffman, M. S., and M. R. Thompson. Backcalculating Nonlinear Resilient Moduli from Deflection Data. Transportation Research Record 852, TRB, National Research Council, Washington, D.C., 1982, pp. 42-51. (3) Ioannides, A. M., E. J. Barenberg, and J. A. Lary. Interpretation of Falling Weight Deflectometer Results Using Principals of Dimensional Analysis. Proceedings, 4th International Conference on Concrete Pavement Design and Rehabilitation, Purdue University, 1989, pp.231-247. (4) Ioannides, A. M. Dimensional Analysis in NDT Rigid Pavement Evaluation. Journal of Transportation Engineering, Vol.116, No. 1, 1990, pp.23-36. (5) Barenberg, E. J., and K. A. Petros. Evaluation of Concrete Pavements Using NDT Results. Project IHR-512, University of Illinois at Urbana-Champaign and Illinois Department of Transportation, Report No. UILU-ENG-91-2006, 1991. (6) Foxworthy, P. T., and M. I. Darter. ILLI-SLAB and FWD Deflection Basins for Characterization of Rigid Pavements. Nondestructive Testing of Pavements and Backcalculation of Moduli. American Society for Testing and Materials, 1989, pp. 368-386. (7) Ioannides, A.M.. Concrete Pavement Backcalculation Using ILLI-BACK 3.0, Nondestructive Testing of Pavements and Backcalculation of Moduli. American Society for Testing and Materials, Vol. 2, 1994, pp.103-124. (8) Hall, K. T., M. I. Darter, T. Hoerner, and L. Khazanovich. LTPP Data Analysis – Phase I: Validation of Guidelines for K Value Selection and Concrete Pavement Performance Prediction. Interim Report prepared for FHWA, ERES Consultants, Champaign, IL, 1996. (9) Smith, K. D., M. J. Wade, D. G. Peshkin, L. Khazanovich, H. T. Yu, and M. I. Dater. Performance of Concrete Pavements, Volume II – Evaluation of In-Service Concrete Pavements. Report No. FHWA-RD-95-110, ERES Consultants, Champaign, IL, 1996.

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(10) Ullidtz, P., “ELCON: Evaluation of Layer Moduli and Overlay Design (ELMOD for Concrete)”, Dynatest Engineering A/S, Denmark, 1987. (11) Van Cauwelaert, F. J., Alexander, D. R., White, T. D., and W. R. Barker. Multilayer elastic program for elastic program for backcalculating layer moduli in pavement evaluation. Nondestructive Testing of Pavements and Backcalculation of Moduli, ASTM STP 1026, Philadelphia, USA, 1989. (12) Khazanovich, L. and Roesler, J.. DIPLOBACK: Neural Network based Backcalculation Program for Composite Pavements, Transportation Research Record No. 1570, TRB, National Research Council, Washington, D.C., 1997, pp. 143-150. (13) Irwin, L. H., Szenbenyi, T. User’s Guide to MODCOMP3 Version 3.2, CLRP Report Number 91-4, Cornell University, Local Roads Program, Ithaca, NY,1991. (14) Irwin, L. H., Instructional Guide for Back-Calculation and the Use of MODCOMP, CLRP Publication No. 94-10, Cornell University, Local Roads Program, Ithaca, NY, 1994. (15) Lytton, R.L. “Backcalculation of Pavement Layer Properties” Nondestructive Testing of Pavements and Backcalculation of Moduli” ASTM Testing and Materials, Philadelphia, pp. 7-38., 1989. (16) Brown, S.F. and Pappin, J.W. Analysis of Pavements with Granular Bases. Transportation Research Record 810, TRB, National Research Council, Washington, D.C., pp. 17-23. 1981. (17) Thompson, M. R. and R. P. Elliot ILLI-PAVE Based Response Algorithms for Design of Conventional Flexible Pavements. Transportation Research Record 1043, TRB, National Research Council, Washington, D.C. 1985. (18) Garg, N. E., Tutumluer, E., and M. R. Thompson. Structural Modelling Concepts for the Design of Airport Pavements for Heavy Aircraft. Proceedings of the Fifth International Conference on the Bearing Capacity of Roads and Airfields, Trondheim, Norway, 1998. (19) Raad, L. and J. L. Figueroa Load Response of Transportation Support Systems. Transportation Engineering Journal, ASCE, Vol 16, No. TE1., 1980. (20) Mallela, J., and K.P. George. Three-Dimensional Dynamic Response Model for Rigid Pavements. In Transportation Research Record: Journal of the Transportation Research Board, No. 1448, TRB, Washington, D.C., 1994. (21) Darter, M.I., K.T. Hall, and C. Kuo. Support Under Portland Cement Concrete Pavements. NCHRP Report 372. Washington, DC: National Cooperative Highway Research Program, 1995.

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(22) Kennedy J.C. Material Nonlinear and Time-Dependent Effects on Pavement Design for Heavyweight, Multi-Wheel Vehicles. Proceedings of the First International symposium on 3D Finite Element for Pavement Analysis and Design, 1998. (23) Tabatabaie, A.M., and E.J. Barenberg. Finite Element Analysis of Jointed or Cracked Concrete Pavements. In Transportation Research Record: No. 671, TRB, 1978, pp. 11-18. (24) Khazanovich, L. Structural Analysis of Multi-Layered Concrete Pavement Systems, Ph.D. dissertation, University of Illinois, Illinois, USA, 1994. (25) Khazanovich, L., Yu, H.T., Rao, S., Galasova, K., Shats, E., and Jones, R. ISLAB2000 Finite Element Analysis Program for Rigid and Composite Pavements, User’s Guide, ERES Consultants, A Division of Applied Research Associates, Champaign, Illinois, 2000. (26) Huang, Y.H. A Computer Package for Structural Analysis of Concrete Pavements. Proceedings, 3rd International Conference on Concrete Pavement Design and Rehabilitation, Purdue University, 1985, pp.295-307. (27) Chou, Y. T. Structural Analysis Computer Programs for Rigid Multicomponent Pavement Structures with Discontinuities - WESLIQID and WESLAYER. Technical Report GL-81-6, U.S. Army Engineer Waterways Experiment Station, May 1981. (28) Ioannides, A.M. and Khazanovich, L., “Analytical and Numerical Methods for MultiLayered Concrete Pavements” Proceedings, Third International Workshop on the Design and Rehabilitation of Concrete Pavements, Krumbach, Austria, October, 1994. (29) Khazanovich, L., and Ioannides, A.M. DIPLOMAT: Analysis Program for Bituminous and Concrete Pavements. In Transportation Research Records: Journal of the Transportation Research Board, No. 1482, 1995, pp. 52-60. (30) Burmister, D.M. “The Theory of Stresses and Displacements in Layered Systems and Application to the Design of Airport Runways “Proceedings, Highway Research Board, Vol. 23, National Research Council, Washington D.C, 1943, pp. 126-144. (31) Burmister, D.M. “The General Theory of Stresses and Displacements in Layered Systems, “Journal of Applied Physics, 1945, Vol. 16, No. 2, pp. 89-96; No.3 pp. 126-127; No.5, pp. 296-302. (32) Duncan, J.M., Monismith, C.L., and Wilson, E.L. “Finite element analyses of pavements.” In Highway Research Record No. 228, HRB, National Research Council, Washington D.C., 1968. (33) Meier, R. W. and Rix, G. J., "Backcalculation of Flexible Pavement Moduli from Dynamic Deflection Basins Using Artificial Neural Networks," Transportation Research Record 1473, TRB, National Research Council, Washington, D. C., 1995

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(34) Haykin, S. Neural networks: A comprehensive foundation. Prentice-Hall, Inc., NJ, USA. 1999. (35) Ceylan, H. Analysis and Design of Concrete Pavement Systems Using Artificial Neural Networks, Ph.D. Dissertation, University of Illinois, Urbana-Champaign, IL, December, 2002. (36) Ceylan, H., Guclu, A., Tutumluer, E., and Thompson, M.R. Backcalculation of FullDepth Asphalt Pavement Layer Moduli Considering Nonlinear Stress-Dependent Subgrade Behavior. The International Journal of Pavement Engineering, Vol. 6, No 3, 2005, pp. 171– 182. (37) LTPP Standard Data Release 20, Long-Term Pavement Performance (LTPP) program, Federal Highway Administration, Washington DC, 2005.

TRB 2007 Annual Meeting CD-ROM

Paper revised from original submittal.