Civil, Construction and Environmental EngineeringPublications Civil, Construction and Environmental Engineering

5-2009

Neural Network-Based Approach for Analysis ofRigid Pavement Systems Using Deflection DataM. Birkan BayrakIowa State University

Halil CeylanIowa State University, hceylan@iastate.edu

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acterize the layer properties as inputs into available numerical oranalytical programs, backcalculation of pavement layer propertiesis a very useful tool. Most backcalculation procedures estimatepavement properties by matching measured and calculated pavementsurface deflection basins.

There are many advantages to using FWD tests in lieu of or to supplement traditional destructive tests for pavement structuralevaluation. Most important is the capability to gather data quicklyat several locations while keeping a runway, taxiway, or apronoperational during these 2- to 3-min tests, provided the testing isperformed in close coordination with air traffic control. WithoutFWD–HWD testing, structural data must be obtained from numerouscores, borings, and excavation pits on existing highway or airportpavements. This can be very disruptive to highway and airport oper-ations. FWD tests are economical to perform and data can be collectedat up to 250 locations per day. FWD–HWD equipment measurespavement surface deflections from an applied dynamic load thatsimulates a moving wheel (1).

The elastic modulus of the portland cement concrete (PCC)slab, EPCC, and the coefficient of subgrade reaction, ks, are the back-calculated layer moduli parameters for the jointed plain concretepavement (JPCP) systems. Over the years, researchers have devel-oped several different methodologies for backcalculation of con-crete pavement layer moduli from FWD measurements, includingthe AREA method for rigid pavements (2–4), ILLI-BACK (5),graphical solution by using ILLI-SLAB (6), use of regressionanalysis to solve the AREA method for rigid pavements (7, 8), useof a best-fit algorithm to find the radius of relative stiffness (� )(8, 9), and many others.

The primary focus of this study is the backcalculation of the rigidpavement parameters with high accuracy by using artificial neuralnetworks (ANNs), particularly the determination of the elastic mod-ulus of the slab and the coefficient of subgrade reaction of the pave-ment foundation that are used in the analysis and design of therigid pavements using FWD data. FWD deflections and the PCCthickness of the test section are the only information needed forbackcalculation of the rigid pavement parameters with developedANN-based models. There is no need for the provision of seed mod-uli in this approach. The use of the ANN models also results in adrastic reduction in computation time compared with other method-ologies. ANN-based analysis models can provide pavement engi-neers and designers with state-of-the-art solutions, without the needfor a high degree of expertise in the input and output of the problem,for rapid analysis of a large number of rigid pavement deflectionbasins needed for project-specific and network-level pavement test-ing and evaluation.

Neural Network-Based Approach for Analysis of Rigid Pavement SystemsUsing Deflection Data

M. Birkan Bayrak and Halil Ceylan

61

This paper focuses on the development of backcalculation modelsbased on artificial neural networks (ANNs) for predicting the layermoduli of the jointed plain concrete pavements, that is, the elasticmodulus of the portland cement concrete (PCC) layer and the coefficientof subgrade reaction for the pavement foundation. The ANN-basedmodels were trained to predict the layer moduli by using the falling-weight deflectometer (FWD) deflection basin data and the thicknessof the concrete pavement structure. The ISLAB2000 finite elementprogram, extensively tested and validated for more than 20 years, hasbeen employed as an advanced structural model for solving the responsesof the rigid pavement systems and generating a knowledge database.ANN-based backcalculation models trained with the results from theISLAB2000 solutions have been found to be viable alternatives forrapid assessment (capable of analyzing 100,000 FWD deflection profilesin a single second) of the rigid pavement systems. The trained ANN-basedmodels are capable of predicting the concrete pavement parameterswith very low (<0.4%) average absolute error values. The ANN modelpredictions and closed-form solutions were compared through the useof the FWD deflection data, and the results are summarized in thepaper. In addition, a sensitivity study was conducted to verify the sig-nificance of the layer thicknesses and the effect of bonding betweenthe PCC and the base layer in the backcalculation procedure. Theresults of this study demonstrated that the ANN-based models arecapable of successfully predicting the rigid pavement layer moduliwith high accuracy.

Falling-weight deflectometer (FWD) and heavy-weight deflectometer(HWD) testing have become the main nondestructive testing (NDT)techniques to evaluate structurally in-service pavements over thelast 20 years. FWD testing is often preferred over destructive test-ing methods because FWD testing is faster than destructive testsand does not entail the removal of pavement materials. In addition,the testing apparatus is easily transportable. Pavement propertiesare backcalculated from the observed dynamic response of thepavement surface to an impulse load (the falling weight). To eval-uate the structural condition of in-service pavements and to char-

M. B. Bayrak, 353 Town Engineering Building, and H. Ceylan, 482B Town Engineer-ing Building, Department of Civil, Construction, and Environmental Engineering,Iowa State University, Ames, IA 50011-3232. Corresponding author: H. Ceylan,hceylan@iastate.edu.

Transportation Research Record: Journal of the Transportation Research Board,No. 2068, Transportation Research Board of the National Academies, Washington,D.C., 2008, pp. 61–70.DOI: 10.3141/2068-07

FINITE ELEMENT PROGRAMS FOR RIGID PAVEMENT SYSTEMS

Today, a variety of finite element (FE) programs are available for theanalysis and design of pavement systems. The two main categoriesof FE programs are (a) programs specifically designed for the analysisof pavement systems and (b) general-purpose programs. FE programssuch as ABAQUS, ANSYS, and DYNA3D are powerful general-purpose programs with three-dimensional (3-D) nonlinear dynamicanalysis capabilities. In several research studies, these programshave been used successfully for pavement analysis. A number of FEmodels built by means of these programs have been reported in theliterature (10–12). In contrast, considerable computational resourcesand time needed for analysis of a structural system are among thelimitations of the general-purpose FE programs.

FE-based programs developed specifically for analysis of concretepavement systems include ISLAB2000 (13–15), DIPLOMAT (16),KENSLABS (17 ), WESLIQID (18), J-SLAB (19), FEACONS-IV(20), KOLA (21), and EverFE (22). Most of these programs cananalyze multiwheel loading of one- or two-layered medium-thickplates resting on a Winkler foundation or elastic solid (ISLAB2000,KENSLABS, WESLIQID). EverFE can analyze multilayered pave-ment systems by means of a 3-D-continuum brick element for the PCCand base layers. ISLAB2000 contains many advanced features thatdistinguish it from other pavement programs based on plate theory.

In addition to the FE programs, Westergaard (23) solutions (platetheory) for PCC pavements are also used to analyze the rigid pave-ments. ANN trainings are also used for interpreting results from data-bases of deflection profiles to estimate pavement properties (24–26).Although there are different FE programs and other approaches to ana-lyze the rigid pavements, all methods do not produce exactly the sameresults. For better understanding of the results produced by differentprograms, a sensitivity analysis was performed as part of this study.

62 Transportation Research Record 2068

COMPARISON OF FE MODELS AND CLOSED-FORM SOLUTIONS

A sensitivity study was performed to analyze the differences in theslab-center deflections (D0, the maximum FWD deflection) obtainedfrom ISLAB2000, DIPLOMAT, KENSLABS, and Westergaard solu-tions. ISLAB2000 is a FE modeling program designed specificallyfor analyzing rigid pavements. In large part, it is an extension andimprovement of the ILLI-SLAB (6) and ILSL2 (14) programs.

ISLAB2000 allows the user to define an unlimited number of nodes,pavement layers, and wheel loads. It also includes an improvedvoid-analysis model. DIPLOMAT was developed by Khazanovichand Ioannides (16) and is an extension of elastic layer and platetheories. Several programs have been developed on the basis of theBurmister elastic layer solutions, but only DIPLOMAT can modelpavement layers as plates, springs, and elastic layers together. How-ever, one disadvantage of DIPLOMAT and other elastic layer pro-grams (ELPs) is that joints cannot be modeled because layers areassumed infinite in the horizontal direction. The KENSLABS com-puter program is based on the FE method, in which slabs are dividedinto rectangular FE with a large number of nodes.

In this study, plate theory was used in the analyses, and the pave-ment foundation is assumed to be a DL foundation (as in the Winkler-spring method). Different configurations of EPCC, thickness of PCClayer (hPCC,), and ks were defined, and the D0 deflections obtainedfrom ISLAB2000, DIPLOMAT, and KENSLABS FE programs andWestergaard solutions were compared with each other (Figure 1).The deflection profiles obtained from ISLAB2000, DIPLOMAT,and KENSLABS FE models for three pavement configurations arealso presented in Figure 1.

As Figure 1 shows, a good match was obtained for results fromdifferent models. Finally, a solution database using the ISLAB2000FE model was created because ISLAB2000’s ease of modeling and

0

100

200

300

400

0 5 10 15 20 25 30 35 40

Different JPCP System Configurations

D0

(mic

rom

eter

) WestergaardISLAB2000DIPLOMATKENSLABS

FWD Sensors

ISLAB2000KENSLABSDIPLOMAT

D0 D12 D24 D36 D48 D60

FWD Sensors

ISLAB2000KENSLABSDIPLOMAT

D0 D12 D24 D36 D48 D60 0

100

200

300

FWD Sensors

Def

lect

ion

s (m

icro

met

er)0

100

200

300Def

lect

ion

s (m

icro

met

er)

0

100

200

300Def

lect

ion

s (m

icro

met

er)

ISLAB2000KENSLABSDIPLOMAT

D0 D12 D24 D36 D48 D60

FIGURE 1 Comparison of ISLAB2000, DIPLOMAT, and KENSLABS finite element model solutions with Westergaard theoretical solutions.

flexibility in analysis are convenient compared with other methods.In contrast, there might be various reasons for the observed differencesin the deflection profiles from different methods. These reasons areas follows:

• ISLAB2000 and KENSLABS use finite slabs in the analysis(slab sizes, joints, and load transfer efficiencies must be identifiedin the programs), but DIPLOMAT and Westergaard solutions do nottake into account the slab size, joints, and load transfer efficiencies.

• ISLAB2000 and KENSLABS use a rectangular or square load-ing area, while DIPLOMAT and Westergaard solutions consider acircular loading area.

GENERATING ISLAB2000 FE SOLUTION DATABASE

To train the ANN models, 51,714 ISLAB2000 runs were generatedby modeling slab-on-grade concrete pavement systems. A singleslab layer resting on a Winkler foundation was analyzed in all cases.Concrete pavements analyzed in this study were represented by a six-slab assembly, each slab having dimensions of 6.1 × 6.1 m(20 × 20 ft) (Figure 2).

To maintain the same level of accuracy in the results from allanalyses, a standard ISLAB2000 FE mesh was constructed for theslab. This mesh consisted of 10,004 elements with 10,209 nodes.The ISLAB2000 solution database was generated by varying the EPCC,ks, and hPCC over a range of values representative of realistic variationsin the field. The ranges used in the analyses are shown in Table 1.The Poisson ratio (µ), the slab width (W), the slab length (L), the PCCunit weight (γ), and the coefficient of thermal expansion (α) were setequal to 0.15, 6.1 m (20 ft), 6.1 m (20 ft), 2,408.15 kg/m3 (0.087 lb/in.3),and 9.9 × 10−6/°C (5.5 × 10−6/°F), respectively.

Bayrak and Ceylan 63

The total number of the ISLAB2000 runs conducted in thisstudy was 51,714. However, some of the deflections obtained fromISLAB2000 (especially D48, D60, and far outer deflections) had neg-ative values (upward) due to the very low EPCC, hPCC, and ks combina-tions. Therefore, the FE runs with negative deflections were excludedfrom the database used for the ANN trainings. The number of pat-terns included in the ANN trainings were 51,539 and 41,026 for ks

and EPCC predictions, respectively. For each training, the ISLAB2000solution database was first portioned to create a training (TRN) setof 49,539 (for ks) and 39,026 (for EPCC) and an independent testing(TST) set of 2,000 patterns to check the prediction performance ofthe trained ANN models. Backpropagation-type ANN architectureswith two hidden layers were used for the ANN models trained in thisstudy (25, 26 ).

SUBGRADE SOIL CHARACTERIZATION

The dense-liquid (DL) model proposed by Winkler (27) was used tocharacterize the subgrade behavior in this study. Accurate modelingof subgrade support for pavement systems is not a simple task becausemany soil types exhibit nonlinear, stress-dependent elastoplasticbehavior, especially under moving heavy wheel loads. Nevertheless,

TABLE 1 Ranges of Input Parameters Used in ISLAB2000 Database Generation

Pavement System Input Min. Value Max. Value

EPCC, GPa (ksi) 6.90 (1,000) 103.50 (15,000)

ks, kPa/mm (psi/in.) 13.57 (50) 271.30 (1,000)

hPCC, cm (in.) 15.24 (6) 63.50 (25)

18.3 m (60ft)12.2 m (40ft)

SLAB 5 SLAB 3 SLAB 1

0

SLAB 6 SLAB 4 SLAB 2

Direction of Traffic

Direction of Traffic

9.15 m (30ft)

x-Coordinate, m (ft)

Vertical FWD Pressure (466.4 kPa)

6.1 m (20ft)

3.05

m (1

0ft)

6.1

m (2

0ft)

12.2

m (4

0ft)

y-C

oord

inat

e, m

(ft)

FIGURE 2 ISLAB2000 finite element model meshing for six-slab JPCP assembly.

experience in rigid pavements analysis and design has shown thatthe subgrade layer may be modeled as linear elastic because of thelower levels of vertical stresses acting on rigid pavement foundations.

A plate on a DL foundation is the most widely adopted mechanisticidealization for analysis of concrete pavements (28). A DL founda-tion is implemented in several FE models, including ISLAB2000,DIPLOMAT, KENSLABS, WESLIQID, J-SLAB, and FEACONS III(29). Consideration of the critical load-transfer phenomena, occurringat the PCC slab joints, and the concomitant development of majordistress types, such as faulting, pumping, and corner breaking, are thesignificant advantages of this approach. The DL foundation is thesimplest foundation model and requires only one parameter, the co-efficient of subgrade reaction, ks, which is the proportionality constantbetween the applied pressure and the load plate deflection. Subgradedeformations are local in character; that is, they develop only beneaththe load plate. Furthermore, their behavior is considered linear elastic,and deformations are recoverable upon removal of the load (28).

ANNs AS PAVEMENT ANALYSIS TOOLS

There are several different types of ANNs, such as backpropaga-tion neural networks (BPNN), radial basis function neural networks(RBFNN), probabilistic neural networks (PNN), and generalizedregression neural networks (GRNN), to name a few. Computingabilities of neural networks have been proven in the fields of predictionand estimation, pattern recognition, and optimization. The best-knownexample of a neural network training algorithm is backpropagation,which is based on a gradient descent optimization technique. Thebackpropagation neural networks are described in many sources(30–33). A comprehensive description of ANNs is beyond the scopeof this paper. The adoption and use of ANN modeling techniques inthe recently released Mechanistic–Empirical Pavement Design Guide(NCHRP Project 1-37A: Development of the 2002 Guide for theDesign of New and Rehabilitated Pavement Structures: Phase II)has especially placed the emphasis on the successful use of neuralnetworks in geomechanical and pavement systems.

ANN-BASED PAVEMENT LAYERBACKCALCULATION MODELS

Background

In this study, two groups of ANN-based backcalculation models(BCMs) were developed: BCM-ks models and BCM-EPCC models.FWD deflection readings [D0 (0 mm), D8 (203 mm), D12 (304 mm),

64 Transportation Research Record 2068

D18 (457 mm), D24 (610 mm), D36 (914 mm), D48 (1,219 mm), andD60 (1,524 mm)] and PCC layer thickness (hPCC) were used as inputparameters in the developed ANN backcalculation models. SeparateANN architectures were used for the backcalculation of elasticmodulus of the slab and the coefficient of subgrade reaction. Four-,six-, seven-, and eight-deflection ANN models were developed forbackcalculating the ks and EPCC values (Table 2).

Backcalculation Models

A network with two hidden layers was exclusively chosen for allmodels trained in this study. Satisfactory results were obtained in theprevious studies with these types of networks due to the networks’better ability to facilitate the nonlinear functional mapping (26, 34).ANN architectures, input parameters, output variables, and averageabsolute error (AAE) values of all developed models are tabulatedin Table 2. The comparison of the ISLAB2000 solutions and ANNpredictions for ks and EPCC are shown in Figures 3 and 4, respectively.Furthermore, Figure 5 shows the training and testing mean squarederror progress curves for the BCM-ks-(6) and BCM-EPCC-(4) models.

SIGNIFICANCE OF THICKNESS AND LAYER BONDING IN PAVEMENT LAYER BACKCALCULATION

Two of the important issues in the backcalculation of the rigid pave-ment parameters are the degree of bonding between layers and thethickness of the PCC and base layers. To simplify the ANN-basedbackcalculation methodology developed in this study, only one thick-ness value (effective PCC thickness) was considered in the analysis.The effective thickness of the pavement structure is directly relatedto the bonding conditions between the PCC layer and the base layer.Because it is difficult to construct a long pavement section with auniform thickness value, it is assumed during the backcalculation ofthe pavement parameters that pavement thickness is uniform fora given section, and it is the value taken from the project files. Todetermine the effective thickness of a two-layer pavement sectionfor bonded, unbonded, and partially bonded cases, the equationsgiven below are considered (35).

Effective thickness for fully bonded PCC layers was computedwith the following equations:

h hE

Eh x

hh

E

Ehe b− = + + −⎛

⎝⎜⎞⎠⎟

+ −13 2

123 1

2

12

1112

2na xxh

hna +⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪2

2

22

1

13

( )

TABLE 2 ANN Architectures and Average Absolute Error (AAE) Values for ANN-Based Backcalculation Models

ANN Model Input Parameters ANN Architecture AAE (%)

BCM-ks-(4) D0, D12, D24, D36 4-60-60-1 0.28

BCM-ks-(6) D0, D12, D24, D36, D48, D60 6-60-60-1 0.20

BCM-ks-(7) D0, D8, D12, D18, D24, D36, D60 7-60-60-1 0.19

BCM-ks-(8) D0, D8, D12, D18, D24, D36, D48, D60 8-60-60-1 0.22

BCM-EPCC-(4) D0, D12, D24, D36 + hPCC 5-60-60-1 0.34

BCM-EPCC-(6) D0, D12, D24, D36, D48, D60 + hPCC 7-60-60-1 0.32

BCM-EPCC-(7) D0, D8, D12, D18, D24, D36, D60 + hPCC 8-60-60-1 0.29

BCM-EPCC-(8) D0, D8, D12, D18, D24, D36, D48, D60 + hPCC 9-60-60-1 0.30

Bayrak and Ceylan 65

Given kS (kPa/mm) 0 60 120 180 240 300

AN

N P

red

icti

on

s fo

r k S

(kP

a/m

m)

0

60

120

180

240

300

Given kS (kPa/mm) 0 60 120 180 240 300

AN

N P

red

icti

on

s fo

r k S

(kP

a/m

m)

0

60

120

180

240

300 AAE = 0.28 %

Line of Equality

Testing Set=2,000

BCM-kS-(4)

Inputs:D0,D12,D24,D36 Inputs:D0,D12,D24,D36 D48,D60

Line of Equality

Line of Equality Line of Equality

AAE = 0.20 % Testing Set=2,000

BCM-kS-(6)

Given kS (kPa/mm) 0 60 120 180 240 300

AN

N P

red

icti

on

s fo

r k S

(kP

a/m

m)

0

60

120

180

240

300

Inputs:D0,D8,D12,D18 D24,D36,D48,D60

AAE = 0.22 % Testing Set=2,000

BCM-kS-(8)

Given kS (kPa/mm) 0 60 120 180 240 300

AN

N P

red

icti

on

s fo

r k S

(kP

a/m

m)

0

60

120

180

240

300

Inputs:D0,D8,D12,D18 D24,D36,D60

AAE = 0.19 % Testing Set=2,000

BCM-kS-(7)

Line of Equality Line of Equality

Line of Equality Line of Equality

Given EPCC (GPa)0 20 40 60 80 120100

AN

N P

red

icti

on

s fo

r E

PC

C (

GP

a)

0

20

40

60

80

120

100

Inputs:D0,D8,D12,D18D24,D36,D60+hPCC

Inputs:D0,D8,D12,D18D24,D36,D48,D60+hPCC

AAE = 0.29 %Testing Set=2,000

BCM-EPCC-(7)

Given EPCC (GPa)0 20 40 60 80 120100

AN

N P

red

icti

on

s fo

r E

PC

C (

GP

a)

0

20

40

60

80

120

100AAE = 0.30 %Testing Set=2,000

BCM-EPCC-(8)

Inputs:D0,D12,D24,D36,D48,D60+hPCC

Given EPCC (GPa)0 20 40 60 80 120100

AN

N P

red

icti

on

s fo

r E

PC

C (

GP

a)

0

20

40

60

80

120

100AAE = 0.32 %Testing Set=2,000

BCM-EPCC-(6)

Inputs:D0,D12,D24,D36,+hPCC

Given EPCC (GPa)0 20 40 60 80 120100

AN

N P

red

icti

on

s fo

r E

PC

C (

GP

a)

0

20

40

60

80

120

100AAE = 0.34 %Testing Set=2,000

BCM-EPCC-(4)

FIGURE 3 Prediction performances of ANN-based models for backcalculatingcoefficient of subgrade reaction, ks.

FIGURE 4 Prediction performances of ANN-based models for backcalculating PCClayer modulus, EPCC.

Effective thickness for unbonded PCC layers was computed withthe following equation:

h hE

Ehe u− = +⎛

⎝⎜⎞⎠⎟1

3 2

123

13

3( )

xE h

hE h h

h

E h E hna =+ +⎛

⎝⎜⎞⎠⎟

+

1 11

2 2 12

1 1 2 2

2 22( )

66 Transportation Research Record 2068

Effective thickness for partially bonded PCC layers was computedwith the following equations:

where

he−b = effective thickness of the fully bonded PCC layers,he−u = effective thickness of the unbonded PCC layers,he−p = effective thickness of the partially bonded PCC layers,

E1 or E2 = elastic modulus for Layer 1 or 2,h1 or h2 = thickness for Layer 1 or 2,

xna = neutral axis distance from top of layer, andx = degree of bonding (ranges between 0 and 1).

Effect of Layer Thickness in EPCC Predictions

The predicted layer moduli are very sensitive to the pavement layerthickness. Even a small change in the assumed PCC layer thicknesscauses considerable differences in the backcalculated elastic moduliof the PCC layer. To demonstrate the effect of the PCC thicknesson the backcalculated EPCC values, FWD data collected from theFAA’s National Airport Pavement Test Facility (NAPTF) were used(Figure 6a).

Effect of Pavement Layer Bonding in EPCC Predictions

The LRS (rigid pavement with stabilized base over low-strengthsubgrade) data were used to investigate the sensitivity of the thicknessand the degree of the bonding between the layers. The thickness andelastic modulus values for the LRS test section were assumed asfollows: EPCC = 34.5 GPa (5 × 106 psi), Ebase = 6.9 GPa (1 × 106 psi),hPCC = 28 cm (11 in.), and hbase = 15.6 cm (61⁄8 in.). The effectivethickness values were calculated as 28.2 cm (11.1 in.), 29.7 cm(11.7 in.), 31.0 cm (12.2 in.), 32.3 cm (12.7 in.), and 33.8 cm (13.3 in.)for the unbonded, 25% bonded, 50% bonded, 75% bonded, and fullybonded cases by means of the equations given above. The variationof the backcalculated EPCC values for the LRS section is presentedin Figure 6b.

xh h

h he p e u

e b e u

=−−

− −

− −

( )5

h x h x he p e u e b− − −= −( ) + ( )1 4( )

Learning Cycles (Epochs)0 4x1032x103 6x103 8x103 10x103 12x103

Mea

n S

qu

ared

Err

or

(MS

E)

0.000

0.005

0.010

0.015

0.020

Learning Cycles (Epochs)

(a)

(b)

0 4x1032x103 6x103 8x103 10x103 12x103

Mea

n S

qu

ared

Err

or

(MS

E)

0.000

0.005

0.010

0.015

0.020

Training MSETesting MSE

6 - 60 - 60 -1 NetworkInputs: D0, D12, D24, D36, D48, D60

Output: ks

ANN Model : BCM-ks-(6)

Training MSETesting MSE

5 - 60 - 60 -1 Network Inputs: D0, D12, D24, D36 +hPCC

Output: EPCC

ANN Model : BCM-EPCC-(4)

FIGURE 5 Training progress curves for (a) BCM-ks-(6) and (b) BCM-EPCC-(4) models.

ANN-BCM-Epcc-(4) ANN-BCM-Epcc-(6) ClosedFormEq.(4Defl) ClosedFormEq.(6Defl)

25.4 cm

10"

27.9 cm

11"

30.5 cm

12"

33.0 cm

13"

35.6 cm

14"

PCC Thickness

0

40

80

120

160

200 ANN-BCM-Epcc-(4) ANN-BCM-Epcc-(6) Closed-Form Eq.(4Defl) Closed-Form Eq.(6Defl)

0 % 25 % 50 % 75 % 100 %

Bac

kcal

cula

ted

EP

CC, G

Pa

0

40

80

120

160

200

Bac

kcal

cula

ted

EP

CC, G

Pa

Unbonded

(a) (b)

Fully Bonded

FIGURE 6 Effect of (a) layer thickness on EPCC backcalculation and (b) degree of layer bonding on EPCC backcalculation.

As Figure 6b shows, the degree of layer bonding resulting in a2.5 cm (1 in.) change in the effective thickness of the pavement systemmay change the backcalculated EPCC value 17 GPa (2.5 × 106 psi) withthe assumed PCC and base layer moduli values. Therefore, resultsfrom this sensitivity analysis show the significance of the degree ofbonding and effective pavement thickness in the EPCC backcalculationprocedure. The closed-form equations used in this sensitivity analysiswere obtained from a statistical study with the ISLAB2000 solutiondatabase used in this paper. There is a unique relationship betweenAREA and radius of relative stiffness; � can be calculated from theAREA–� equations. AREA value was calculated from four deflec-tions (D0, D12, D24, and D36) and six deflections (D0, D12, D24, D36,D48, and D60) as shown in Equations 6 and 7 below. Load (P), radiusof load plate (a), and Poisson ratio (µ) were set to 40 kN (9 kips),150 mm (5.9 in.), and 0.15, respectively. The equations used inthe numerical backcalculation of the rigid pavement parametersare summarized below:

VALIDATION OF ANN-BASED MODELS:COMPARISON OF ANN-BASED MODELS WITH CLOSED-FORM EQUATIONS

To validate the ANN-based backcalculation models, ANN model pre-dictions were compared with the closed-form equation results by usingthe FWD–HWD test data collected from NAPTF. The FWD–HWDdeflection profiles obtained from the NAPTF’s LRS test sections aredepicted in Figure 7.

Ek

hi S

PCCPCC

=−( )⎛

⎝⎜⎞

⎠⎟12 1

114 2

3

� μ( )

kP

D

aS

i i

= ⎛⎝⎜

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Bayrak and Ceylan 67

All FWD–HWD test results were normalized to 40 kN (9 kips)to compare the results. The ANN BCM-ks-(6) model predictions andclosed-form equation solutions (Equations 7, 9, and 10) are presentedin Figure 8a for backcalculation of ks by use of the NAPTF–LRSFWD data. In addition, ANN BCM-EPCC-(4) model predictions andclosed-form equation solutions (Equations 6, 8, 10, and 11) werecompared and results are presented in Figure 8b for backcalculatingthe EPCC value by use of the same FWD data. The layers were assumedfully bonded in this analysis. As one can see from the comparisonof ANN models and closed-form equation predictions, the standarddeviations for the ANN-based predictions are lower than the ones forclosed-form equations. In addition, one can conclude that the scatterof the predictions is strongly dependent on the dates due to the repeatedtrafficking that the FWD–HWD deflection tests were conducted(Figure 7). Higher scattering in EPCC predictions can be explained byEPCC being dependent on the PCC layer thickness and the degree ofbonding between the PCC and the Econocrete base layers.

Because the exact thickness of the PCC layer and the degree ofbonding between the PCC and the Econocrete layers are not exactlyknown, more scatter is expected in EPCC predictions. In addition,the time of the FWD–HWD testing is also crucial in the EPCC back-calculation due to curling and warping problems in rigid pavements.The results of previous studies indicate that the variations in tem-perature and moisture between two separate FWD tests affect pri-marily the elastic modulus of the slab (2). Because of slab curling andwarping, temperature and moisture differences across the depth ofthe concrete pavement in the NAPTF–LRS section are another majorreason for the scatter in EPCC predictions (36). Therefore, the mainreasons for the scatter in EPCC predictions are the curling and warpingof the plates, the degree of bonding between the PCC and Econocretelayers, and the thickness of the PCC layer. To improve further theEPCC backcalculation accuracy, NDT techniques, such as groundpenetrating radar (GPR) readings, or cores (destructive technique) canbe used along the pavement sections to determine the exact thicknessof the layers at the FWD–HWD test points. In addition, the testingtime of the FWD tests due to diurnal changes (curling and warping ofthe slabs due to temperature and moisture fluctuations) and the initialshape of the PCC slab (built-in curling and warping due to dryingshrinkage, etc.) should be taken into account in the interpretation ofthe deflection data analysis.

CONCLUSIONS

The primary goal of this study was to show that ANN models couldbe developed to perform rapid and accurate predictions of PCC layerelastic modulus (EPCC) and coefficient of subgrade reaction (ks)values from FWD–HWD deflection data. ANN-based backcalculationmodels developed in this study successfully predicted the PCC layerelastic modulus and coefficient of subgrade reaction values fromFWD–HWD deflection basins. In addition, a sensitivity study wasconducted to show the effect of the PCC layer thickness and bond-ing degree on the backcalculation of the concrete pavement layermodulus. The results showed that the backcalculated concrete pave-ment layer modulus was very sensitive to the PCC layer thickness andbonding degree, whereas the coefficient of subgrade reaction wasindependent of these values. The results of this study make clear thatthe developed ANN models can be used to predict the PCC layermodulus and the coefficient of subgrade reaction with very low AAEvalues (<0.4% for the theoretical deflection basins). The use of theANN-based models also resulted in a drastic reduction in computation

68 Transportation Research Record 2068

FWD Sensors

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FIGURE 7 FWD–HWD deflection basins normalized to 40-kN load level for NAPTF–LRS section.

time. The rapid prediction ability of the ANN models (capable ofanalyzing 100,000 FWD deflection profiles in 1 s) provides a tremen-dous advantage to pavement engineers by allowing them to non-destructively assess the condition of the transportation infrastructurein real time while the FWD–HWD testing takes place in the field.Finally, it can be concluded that ANN-based analysis models canprovide pavement engineers and designers with state-of-the-art solu-tions, without the need for a high degree of expertise in the input andoutput of the problem, to analyze rapidly a large number of rigid pave-ment deflection basins needed for project-specific and network-levelpavement testing and evaluation.

ACKNOWLEDGMENT

The authors gratefully acknowledge the Iowa Department ofTransportation for sponsoring this study.

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0

30

60

90

120

150

180

0 200100 300 400

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0 200100 300 400

FWD Data Points0 200100 300 400

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0 200100 300 400

FWD Data Points

k S (

AN

N P

red

icte

d),

kP

a/m

m

0

30

60

90

120

150

180

k S (

Eq

uat

ion

s), k

Pa/

mm

10/22/1999

11/19/1999

02/11/2000

03/20/2000

04/07/2000

04/20/2000

AVERAGE = 36.08 kPa/mm

STDEV = 12.50 kPa/mm

0

40

80

120

160

200

EP

CC (

AN

N P

red

icte

d),

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a0

40

80

120

160

200

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CC (

Eq

uat

ion

s), G

Pa

10/22/1999

11/19/1999

02/11/2000

03/20/2000

04/07/2000

04/20/2000

AVERAGE = 55.60 GPa

STDEV = 21.51 GPa

10/22/1999

11/19/1999

02/11/2000

03/20/2000

04/07/2000

04/20/2000

AVERAGE = 36.53 kPa/mm

STDEV = 13.24 kPa/mm

10/22/1999

11/19/1999

02/11/2000

03/20/2000

04/07/2000

04/20/2000

AVERAGE = 50.49 GPa

STDEV = 27.24 GPa

FIGURE 8 Comparison of (a) coefficient of subgrade reaction predictions and (b) PCC layer elasticmodulus predictions.

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The contents of this paper reflect the views of the authors, who are responsiblefor the facts and accuracy of the data. The contents do not necessarily reflect theofficial views and policies of Iowa DOT. This paper does not constitute a stan-dard, specification, or regulation.

The Strength and Deformation Characteristics of Pavement Sections Committeesponsored publication of this paper.