Prediction of ational Airport Pavement Test Facility Pavement Layer Moduli from Heavy Weight Deflectometer Test Data Using Artificial eural etworks Kasthurirangan Gopalakrishnan Department of Civil, Construction and Environmental Engineering Iowa State University 192 Town Engineering Building Ames, IA 511 rangan@iastate.edu ABSTRACT The ational Airport Pavement Test Facility (APTF) was constructed to generate full-scale testing data to investigate the performance of airport pavements subjected to complex gear loading configurations of new generation aircraft. During the first test program, the APTF test sections were simultaneously subjected to Boeing 777 trafficking in one lane and Boeing 747 trafficking in another lane using the ational Airport Pavement Test Machine. To monitor the effect of time and traffic on pavement structural responses, heavy weight deflectometer (HWD) tests were conducted on the trafficked lanes and the untrafficked centerline of flexible test sections as trafficking progressed. The primary objective of this study was to develop a tool for backcalculating APTF non-linear flexible pavement layer moduli from HWD data using artificial neural networks (A). A multi-layer, feedforward network that uses an error-backpropagation algorithm was trained to approximate the HWD backcalculation function. The synthetic database generated using the non-linear pavement finite element program, ILLI-PAVE, was used to train the A. Using the A, the asphalt concrete moduli and subgrade moduli were successfully predicted. Further research is required to develop A models for predicting the granular layer moduli. These results could be used to compare the relative effect of Boeing 777 and Boeing 747 trafficking on the elastic moduli and characterize the seasonal variation in moduli values. The same concept could also be used for backcalculating non-linear pavement moduli of highway pavements for input into mechanistic-empirical analysis and design. Key words: artificial neural networks ILLI-PAVE ational Airport Pavement Test Facility pavement moduli Proceedings of the 25 Mid-Continent Transportation Research Symposium, Ames, Iowa, August 25. 25 by Iowa State University. The contents of this paper reflect the views of the author(s), who are responsible for the facts and accuracy of the information presented herein.
ITRODUCTIO The Federal Aviation Administration s (FAA) ational Airport Pavement Test Facility (APTF) is located at the Atlantic City International Airport, ew Jersey. It was constructed to generate full-scale test data needed to develop pavement design procedures for the new generation of large civil transport aircraft, including the Boeing 777 and Boeing 747. During the first series of tests, two gear configurations, a six-wheel tridem landing gear (Boeing 777) in one lane and a four-wheel dual-tandem landing gear (Boeing 747) in the other lane, were tested simultaneously. Heavy weight deflectometer (HWD) tests were conducted at regular time intervals as trafficking continued. The primary objective of this study was to develop a tool for backcalculating APTF non-linear pavement layer moduli from HWD test data using artificial neural networks (A). The elastic layer moduli backcalculated from non-destructive test results are good indicators of pavement layer condition (Xu, Ranjinathan, and Kim 21) as well as required inputs for the a priori mechanistic design of a flexible pavement. The backcalculation approach is particularly appealing for characterizing subgrade soils that display large variability in subgrade modulus (as large as 35% 5% over few miles of a pavement) (Thompson, Tutumluer, and Bejarano 1998). Conventional elastic layer program (ELP)-based backcalculation software assumes that pavement materials are linear-elastic, homogenous, and isotropic. The non-linearity or stress-dependency of resilient modulus for unbound granular materials and cohesive fine-grained subgrade soils is well documented in the literature (Hicks 197; Thompson and Robnett 1979). Previous studies have observed the nonlinearity of underlying layers at the APTF. Gomez-Ramirez and Thompson (Garg and Marsey 22) reported the presence of material non-linearity at APTF by separately analyzing the individual layer compression from multi-depth deflectometer (MDD) readings. Garg and Marsey (22) have similarly observed the stress-dependent nature of the granular and subgrade layers in APTF flexible test sections. Therefore, it is more realistic to use non-linear layer moduli for conducting APTF pavement structural analysis and for studying the variation in moduli with trafficking. ILLI-PAVE is a two-dimensional axi-symmetric pavement finite-element software developed at the University of Illinois at Urbana-Champaign (UIUC) (Raad and Figueroa 198). It incorporates stresssensitive material models and provides a more realistic representation of the pavement structure and its response to loading (CHRP 199). Based on extensive repeated laboratory testing data at UIUC, Thompson and Robnett (1979) indicated that the breakpoint resilient modulus (E Ri ), typically associated with a repeated deviator stress of about six psi, is a good indicator of the subgrade soil s resilient modulus. The Asphalt Institute s Thickness Design Manual MS-1 (Asphalt Institute 1982) recommends E Ri (subgrade modulus at a deviator stress of six psi) as the subgrade modulus input for ELP analysis. The E Ri is also one of the subgrade material property inputs to ILLI-PAVE. However, there is no commercial ILLI-PAVE-based backcalculation program currently available. Previous research at UIUC showed that the asphalt concrete moduli and non-linear subgrade moduli (E Ri ) could be successfully predicted using an A trained with the ILLI-PAVE database (Gopalakrishnan and Thompson 24). Ceylan et al. (24) demonstrated the use of As trained with ILLI-PAVE results as pavement structural analysis tools for the rapid and accurate prediction of critical responses and deflection profiles of flexible pavements subjected to typical highway loadings. Ongoing research at Iowa State University on backcalculting pavement moduli using A is being performed under Dr. Halil Ceylan s supervision. However, the current research specifically focuses on developing a tool for backcalculating APTF pavement nonlinear moduli using A trained with ILLI-PAVE results. Gopalakrishnan 2
ATIOAL AIRPORT PAVEMET TEST FACILITY The APTF test pavement area is 9 feet (274.3 meters) long and 6 feet (18.3 meters) wide. The first test series installation included a total of nine test sections (six flexible and three rigid) built on three different subgrade materials: low-strength (target CBR of 4), medium-strength (target CBR of 8), and high-strength (target CBR of 2). Two different base sections are used in flexible test sections: conventional (granular) and stabilized (asphalt concrete). The low-strength and the medium-strength flexible test sections alone are considered in this study. The naturally occurring sandy soil material at the APTF site underlies each subgrade layer. Pavement Sections Each APTF test section is identified using a three-character code, where the first character indicates the subgrade strength (L for low, M for medium, and H for high), the second character indicates the test pavement type (F for flexible and R for rigid), and the third character signifies whether the base material is conventional-aggregate (C) or asphalt-stabilized (S). Thus, test section refers to a conventionalbase flexible pavement built over a medium strength subgrade, whereas test section refers to a stabilized-base flexible pavement built over a medium-strength subgrade. Cross-sectional views of the asbuilt APTF flexible test items considered in this study are shown in Figure 1. ote that P-41 asphalt concrete was used in the surface layer and in the stabilized base layer as well. AC Surface (P-41) 5 in. AC Surface (P-41) 5 in. AC Surface (P-41) 5.1 in. AC Surface (P-41) 5 in. Granular Base (P-29) 7. in. Asphalt Stab. Base (P-41) 4.9 in. Granular Base (P-29) 7.9 in. Asphalt Stab. Base (P-41) 4.9 in. Granular Subbase (P-4) 36.4 in. Granular Subbase (P-29) 29.6 in. Granular Subbase (P-4).1 in. Granular Subbase (P-29) 8.5 in. LOW Strength Subgrade LOW Strength Subgrade MEDIUM Strength Subgrade MEDIUM Strength Subgrade Subgrade=94.7 in. Subgrade=.5 in. Subgrade=94.8 in. Subgrade=11.6 in. Traffic Testing Figure 1. Cross-sectional views of as-built APTF flexible test sections A six-wheel dual-tridem gear configuration (Boeing 777) with 54-inch (1,372-mm) dual spacing and 57- inch (1,448-mm) tandem spacing was loaded on the north wheel track, while the south side was loaded with a four-wheel dual-tandem gear configuration (Boeing 747) having 44-inch (1,118-mm) dual spacing and 58-inch (1,473-mm) tandem spacing. The wheel loads were set to, lbs (2.4 tons) each and the tire pressure (cold) was 188 psi (1,295 Kpa). In the (a conventional aggregate-base pavement built over low-strength subgrade) and (an asphalt-stabilized base pavement built over low-strength subgrade) test sections, the wheel loads were increased from, lbs (2.4 tons) to, lbs (29.4 tons) after 2, initial load repetitions. Throughout the traffic test program, the traffic speed was 5 mph (8 kmh). Gopalakrishnan 3
APTF Flexible Pavement Failure Criterion The APTF failure criterion is based on the criterion utilized by the U.S. COE MWHGL Tests (Ahlvin et al. 1971). It is defined as 1-inch (25.4-mm) surface upheaval adjacent to the traffic lane. This is considered to reflect a structural or shearing failure in the subgrade. Data Availability All test data referenced in this paper are available for download on the FAA Airport Pavement Technology website: http://www.airporttech.tc.faa.gov/naptf/. HEAVY WEIGHT DEFLECTOMETER TESTS For HWD testing, the FAA HWD KUAB Model 24, configured with a -inch loading plate and a 27 3 msec pulse width, was used. The deflections were measured with seven seismometers at offsets of - inch (D ), -inch (35-mm) (D ), 24-inch (61-mm) (D 24 ), 36-inch (9-mm) (D 36 ), 48-inches (1,219- mm) (D 48 ), and 6-inch (1,524-mm) (D 6 ) intervals from the center of the load. The HWD tests were performed at nominal force amplitudes of, lbs or kip (53.4 k), 24, lbs or 24 kip (.8 k), and 36, lbs or 36 kip (.2 k). These tests were performed on the centerline, Boeing 777 traffic lane (Lane 2) and Boeing 747 traffic lane (Lane 5). The HWD test sequences were repeated at 1-foot (3.1-meter) intervals along the test lanes. The location and orientation of HWD test lanes are illustrated in Figure 2. -3 ft. - ft. B777 LAE 2 ft. C/L ft. B747 LAE 5 3 ft. Figure 2. APTF HWD test lanes Pavement Temperature The temperature of the asphalt concrete layer at the time of FWD testing has a significant influence on the surface deflections. During the APTF construction, static temperature sensors were installed at different depths along the test sections to record the pavement temperatures at different times of the day. The HWD Gopalakrishnan 4
tests were all conducted between January 11, 2 and June 6, 21. The asphalt concrete temperature varied between 4 F to F during the entire duration of traffic testing. DATABASE GEERATIO USIG ILLI-PAVE To generate the synthetic database for training the A, each APTF flexible test section was modeled in ILLI-PAVE. The as-constructed layer thicknesses (see Figure 1) were used for each test section. The individual pavement layers were characterized as follows. The asphalt concrete layer and the sand layer were treated as linear elastic material. Stress-dependent elastic models along with Mohr-Coulomb failure criteria were applied for the base, subbase, and subgrade layers. The stress-hardening K-θ model was used for the base and subbase layers: M R σ = ε = D n Kθ (1) R Where M R is resilient modulus (psi), θ is bulk stress (psi), and K and n are statistical parameters. The following relationship exists between K and n (R 2 =.68, SEE =.22) (Rada and Witczak 1981): Log 1 (K) =4.7 1.87n (2) The stress-softening bilinear model was used for the subgrade layer: M M R R = M = M Ri Ri + K.( σ σ ) + K.( σ σ ) 1 d di d di (3) 2 d di for σ for σ d < σ > σ di Where M R is resilient modulus (psi), σ d is applied deviator stress (psi), and K 1 and K 2 are statistically determined coefficients from laboratory tests. A total of 5, input cases were generated for each test section by randomly varying the asphalt concrete and subgrade layer moduli and the K b - n b and K s - n s values (note that K and n are related) for the base and subbase layers, respectively. The effect of 36-kip HWD loading was simulated in ILLI-PAVE and the pavement surface deflections were computed. Initially, it was decided to use separate A models for each section. Of the total number of data sets for each test section, 3, data vectors were used in training the A and the remaining 1,25 data vectors were used to test the network after the training was completed. The range of layer properties used in training the A is summarized in Table 1. ARTIFICIAL EURAL ETWORK ARCHITECTURE A generalized n-layer feedforward A that uses an error-backpropogation algorithm (Haykin 1994) was implemented in the Visual Basic (VB 6.) programming language. The program can allow for a general number of inputs, hidden layers, hidden layer elements, and output layer elements. Two hidden layers were found to be sufficient for solving a problem of this size, and therefore the architecture was reduced to a four-layer feedforward network. A four-layer feedforward network consists of a set of sensory units (source nodes) that constitute the input layer, two hidden layers of computation nodes, and an output layer of computation nodes. The following notation is generally used to refer to a particular type of architecture that has two hidden layers: (# inputs)-(# hidden neurons)-(# hidden neurons)-(# outputs). For example, the notation 1-4-4-3 refers to an A architecture that takes in 1 inputs (features), has 2 hidden layers consisting of 4 neurons each, and produces 3 outputs. Gopalakrishnan 5
Table 1. Range of pavement layer properties used in generating the A training database Pavement layer Thickness (inches) Elastic layer modulus (ksi) Poisson s ratio Asphalt concrete Base Subbase Subgrade Sand 5 - & 1 - & 8 - & 8.5-29.5 - - 36.4-95 - & - & - Medium 4 - Low 1 2,5.35 K b : 1.6 2 n b :.2.8.35 K s : 1.6 2.35 n s :.2.8 1.6 2..4 An A-based backcalculation procedure was developed to approximate the HWD backcalculation function. Using the ILLI-PAVE synthetic database, the A was trained to learn the relationship between the synthetic deflection basins (inputs) and the pavement layer moduli (outputs). Initialization of Weights The first step in back-propogation learning is to initialize the network. It is recommended that the initialization of the synaptic weights of the network be uniformly distributed inside a small range. A range of -.2 to +.2 was used for random initialization of all synaptic weight vectors in the network. onlinear Activation Function The model of each neuron in the hidden layer(s) and output layer of the network includes a nonlinearity at the output end. The presence of a nonlinear activation function, ϕ(.), is important because otherwise the input-output relation of the network could be reduced to that of a single-layer perceptron. The computation of the local gradient for each neuron of the multilayer perceptron requires that the function ϕ(.) be continuous. In other words, differentiability is the only requirement that an activation function would need to satisfy. For this problem, an asymmetric hyperbolic tangent function (tanh) was chosen for which the output amplitude lies inside the range -1 y j +1. Since we require the final outputs to be real values instead of binary outputs, a linear combiner model was used for neurons in the output layer, thus omitting the nonlinear activation function. Performance Measure (RMSE) In order to track the performance of the network, the root mean squared error (RMSE) at the end of each epoch was calculated. An epoch is defined as one full presentation of all the training vectors to the network. The RMSE at the end of each epoch is defined as the following: RMSE = [ d j Y ( X j )] j= 1 2 Gopalakrishnan 6
Where d j is the desired response for the input training vector X j, and is the total number of input vectors presented to the network for training. For the network to learn the problem smoothly, a monotonic decrease in the RMSE is expected with an increase in the number of epochs. A smooth learning curve was achieved with a learning-rate parameter (η) of.1. A IPUTS AD OUTPUTS Deflection basin parameters (DBPs) derived from falling weight deflectometer (FWD) and/or HWD deflection measurements are shown to be good indicators of selected pavement properties and conditions (Hossain and Zanniewski 1991). Recently, Xu et al. (21) used DBPs in developing new relationships between selected pavement layer condition indicators and FWD deflections by applying regression and A techniques. Apart from the six independent deflection measurements (D to D 6 ), some of the commonly used DBPs were included as inputs for training the A. The DBPs considered in this study are shown in Table 2. Each DBP supposedly represents the condition of specific pavement layers. For example, AUPP is sensitive to the asphalt concrete layer properties, whereas BCI and AI4 are expected to reflect the condition of subgrade. The desired outputs from the A are asphalt concrete modulus (E AC ), subgrade modulus (E Ri ), base modulus parameter (K b or n b ), and subbase modulus parameter (K s or n s ). ote that by predicting either K or n, the other parameter can be determined using the relation proposed by Rada and Witzcak (1981). Table 2. DBPs considered in this study Deflection basin parameter (DBP) Formula AREA AREA = 6(D + 2D + 2D 24 + D 36 )/D Area under pavement profile AUPP = (5D 2D 2D 24 D 36 )/2 (AUPP) Area index AI 4 = (D 36 + D 48 )/2D Base curvature index (BCI) BCI = D 24 D 36 BCI2 = D 6 D 48 Base damage index (BDI) BDI = D D 24 Deflection ratio DR = D /D Shape factors F 1 = (D D 24 )/D F 2 = (D D 36 )/D 24 SELECTIO OF BEST-PERFORMACE ETWORKS Separate A models were used for each desired output rather than using the same architecture to determine all the outputs together. The most effective set of input features for each A model were determined based on both engineering judgment and the experience gained through past research studies conducted at UIUC. Parametric analyses were performed by systematically varying the choice and number of inputs and number of hidden neurons to identify the best-performance networks. As it was found that the prediction accuracy of the network remained the same for hidden layers greater than or equal to two, the number of hidden layers was fixed at two for all runs. The learning curve (RMSE vs number of epochs) and the testing RMSE were studied in order to arrive at the best networks. A previous Gopalakrishnan 7
study that focused on the section alone showed that the base and subbase moduli parameters were the hardest to predict (Gopalakrishnan and Thompson 24). During the course of this study, the same conclusion was reached for other test sections. It was concluded that further research is needed to develop robust A models for predicting the base and subbase moduli parameters. RESEARCH RESULTS A summary of the sensitivity analyses performed to select the best-performance networks for predicting asphalt concrete modulus (E AC ) and subgrade modulus (E Ri ) in APTF test sections are shown in Table 3. ote that the A inputs are similar for all four test sections. In Figure 3, the A-predicted moduli values and the target values are compared using the 1,25 test data vectors for each APTF section. Excellent agreement is found between the predicted and target values for both E AC and subgrade modulus E Ri in all four test sections, except for E Ri in section, where an R 2 value of.81 was obtained. Table 3. Summary of best-performance A pavement moduli prediction models APTF etwork Training Testing Output Inputs section architecture RMSE RMSE E AC D ~ D 6 6-4-4-1 71 ksi 69 ksi E Ri D ~ D 6, BCI, AI 4 8-4-4-1.86 ksi.82 ksi E AC D ~ D 6 6-4-4-1 1 ksi 97 ksi E Ri D ~ D 6, BCI, AI 4 8-4-4-1 1.29 ksi 1.18 ksi E AC D ~ D 6 6-4-4-1 69 ksi 67 ksi E Ri D ~ D 6, BCI, AI 4 8-4-4-1.81 ksi.78 ksi E AC D ~ D 6 6-4-4-1 9 ksi 9 ksi E Ri D ~ D 6, BCI, AI 4 8-4-4-1 2.36 ksi 2. ksi One of the major reasons for developing this A-based backcalculation procedure is to evaluate the structural integrity of the APTF pavement test sections reliably as they were subjected to traffic loading. The APTF test sections were subjected to trafficking until they exhibited failure. The test section was the first one to fail at,952 load repetitions exhibiting 3 to 3.5 inches of rutting and severe cracking. In the section, localized failure occurred in the Boeing 777 traffic lane toward the west end. At 19,9 passes, 3.5 inches of rut depth was observed on the Boeing 777 traffic lane, with upheaval outside the traffic path. Trafficking was terminated on the Boeing 777 traffic lane, but it continued on the Boeing 747 traffic lane. The Boeing 747 lane failed at 3, passes. HWD tests were not conducted on the section beyond 19,9 passes. The low-strength test sections ( and ) showed few signs of genuine distress, even after 2, passes, and therefore the wheel loading was increased from, lbs to, lbs. The trafficking was terminated in the low-strength test sections after 28, passes of, lbs. While the and sections failed at the subgrade level, the and sections failed in the surface layers, signifying tire pressure or other upper layer failure effects, but not subgrade level failure (Gervais, Hayhoe, and Garg 23). Gopalakrishnan 8
A Predicted AC Modulus, E AC (ksi) 25 2 1 5 R 2 =.98 5 1 2 25 A Predicted Subgrade Modulus, E Ri (ksi) 25 2 1 5 R 2 =.97 5 1 2 25 Target AC Modulus, E AC (Ksi) Target Subgrade Modulus, E Ri (ksi) A Predicted AC Modulus, E AC (ksi) 3 25 2 1 5 R 2 =.98 5 1 2 25 3 Target AC Modulus, E AC (Ksi) A Predicted Subgrade Modulus, E Ri (ksi) 25 2 1 5 R 2 =.95 5 1 2 25 Target Subgrade Modulus, E Ri (ksi) A Predicted AC Modulus, E AC (ksi) 3 25 2 1 5 R 2 =.99 5 1 2 25 3 A Predicted Subgrade Modulus, E Ri (ksi) 25 2 1 5 R 2 =.98 5 1 2 25 Target AC Modulus, E AC (Ksi) Target Subgrade Modulus, E Ri (ksi) A Predicted AC Modulus, E AC (ksi) 3 25 2 1 5 R 2 =.98 5 1 2 25 3 A Predicted Subgrade Modulus, E Ri (ksi) 25 2 1 5 R 2 =.81 5 1 2 25 Target AC Modulus, E AC (Ksi) Target Subgrade Modulus, E Ri (ksi) Figure 3. A prediction of APTF asphalt concrete moduli (left) and subgrade moduli (right) Gopalakrishnan 9
A vs FAABACKCAL Using the 36-kip HWD test data acquired at the APTF, the asphalt concrete moduli and subgrade moduli were backcalculated with the best-performance As for all four sections. The results were then compared with those obtained using FAABACKCAL, an ELP-based backcalculation program. FAABACKCAL was developed under the sponsorship of the FAA Airport Technology Branch and is based on the LEAF layered elastic computation program. In this program, the pavement layer moduli and subgrade moduli are adjusted to minimize the root mean square (rms) of the differences between FWD/HWD sensor measurements and the LEAF-computed deflection basin for a specified pavement structure. A standard multidimensional simplex optimization routine is then used to adjust the moduli values (McQueen, Marsey, and Arze 21). A stiff layer with a modulus of 1,, psi and a Poisson s ratio of.5 was used in backcalculation. Based on the as-constructed conditions, the stiff layer was set at 1 feet for the medium-strength test sections and at feet for the low-strength sections. The most recent version of the FAA backcalculation software is called BAKFAA. The detailed backcalculation results for APTF sections using FAABACKCAL are reported elsewhere (Gopalakrishnan and Thompson 24). The plots comparing the results of A-based backcalculation with those obtained using FAABACKCAL are shown in Figure 4 for asphalt concrete moduli and in Figure 5 for subgrade moduli. The gray arrow in the plots for the and sections indicate where (after 2, load repetitions) the wheel load was increased from, lbs to, lbs. In Figure 4, the variation in asphalt concrete temperature as a function of the number of load repetitions () in each test section is also included and is indicated by a gray line. In these plots, the changes in layer moduli in the Boeing 777 traffic lane and the Boeing 747 traffic lane are due to both traffic loading as well as variation in temperature and climate. The changes in pavement material properties in the untrafficked pavement centerline are only due to environmental effects. The trends for asphalt concrete moduli are very similar using both approaches. The asphalt concrete moduli values are significantly influenced by asphalt concrete temperature. In the and sections, the A approach seem to be more sensitive to trafficking and temperature, indicated by a sharp decrease in the moduli values towards the end of trafficking. In the and sections, the structural degradation resulting from increasing the wheel load from, lbs to, lbs after 2, repetitions is clearly reflected in the moduli values. Compared to the centerline moduli values, the traffic lane moduli values decrease further after 2, repetitions. In Figure 5, the Y-axis is magnified in the individual plots as the subgrade moduli values varied over a narrow range compared to the asphalt concrete moduli. ote that the subgrade modulus predicted by A is the stress-dependent breakpoint subgrade modulus (at a deviator stress of about 6 psi) and is indicated as E Ri. The subgrade modulus backcalculated by FAABACKCAL is indicated as E. The initial magnitudes of subgrade modulus obtained using both the approaches are similar for the and sections. For the and sections, the initial subgrade moduli obtained using the A are about 5 psi higher than the those obtained using FAABACKCAL. The sharp decrease in the subgrade modulus in the Boeing 777 traffic lane of the section towards the end of the trafficking, as captured by the A results, could be due to the localized failure, as mentioned earlier. The APTF rutting study results showed that the eest end of the Boeing 777 traffic lane in the section exhibited a rapid increase in surface rutting after, load repetitions (Gopalakrishnan and Thompson 23). Gopalakrishnan 1
AC Modulus, E AC (ksi) 3 25 2 1 5 A B777-A B747-A C/L-A 4 5 6 7 1 1 1 1 1 ACTemperature ( F) AC Modulus, E AC (ksi) 3 25 2 1 5 B777-FAABACKCAL B747-FAABACKCAL C/L-FAABACKCAL 4 5 6 FAABACKCAL 7 1 1 1 1 1 AC Temperature ( F) 35 4 35 4 AC Modulus, E AC (ksi) 3 25 2 1 5 5 6 7 AC Temperature ( F) AC Modulus, E AC (ksi) 3 25 2 1 5 5 6 7 AC Temperature ( F) 1 1 1 1 1 1 1 1 1 1 1 1 3 4 3 4 AC Modulus, E AC (ksi) 25 2 1 5 5 6 7 AC Temperature ( F) AC Modulus, E AC (ksi) 25 2 1 5 5 6 7 AC Temperature ( F) 1 1 1 1 1 1 1 1 1 1 1 1 35 4 35 4 AC Modulus, E AC (ksi) 3 25 2 1 5 5 6 7 AC Temperature ( F) AC Modulus, E AC (ksi) 3 25 2 1 5 5 6 7 AC Temperature ( F) 1 1 1 1 1 1 1 1 1 1 1 1 Figure 4. Comparison of A-predicted asphalt concrete moduli (left) with FAABACKCAL asphalt concrete moduli (right) for APTF test sections Gopalakrishnan 11
Subgrade Modulus, E Ri (ksi) 2 19 18 17 13 11 1 A B777-A B747-A C/L-A 1 1 1 1 1 Subgrade Modulus, E (ksi) 2 19 18 17 13 11 1 FAABACKCAL B777-FAABACKCAL B747-FAABACKCAL C/L-FAABACKCAL 1 1 1 1 1 Subgrade Modulus, E Ri (ksi) 2 19 18 17 13 11 1 1 1 1 1 1 1 Subgrade Modulus, E (ksi) 2 19 18 17 13 11 1 1 1 1 1 1 1 Subgrade Modulus, E Ri (ksi) Subgrade Modulus, E Ri (ksi) 1 8 6 4 1 8 6 4 1 1 1 1 1 1 1 1 1 1 1 1 Subgrade Modulus, E (ksi) Subgrade Modulus, E (ksi) 1 8 6 4 1 8 6 4 1 1 1 1 1 1 1 1 1 1 1 1 Figure 5. Comparison of A-predicted subgrade moduli (left) with FAABACKCAL subgrade moduli (right) for APTF test sections Gopalakrishnan
SUMMARY AD COCLUSIOS The primary objective of this study was to develop a tool for backcalculating APTF non-linear pavement layer moduli from HWD data using A. The APTF sections were modeled in ILLI-PAVE and a synthetic database was generated for a range of moduli values. A multi-layer feedforward network that uses an error-backpropagation algorithm was successfully trained to approximate the HWD backcalculation function using the ILLI-PAVE database. A models were successfully developed for predicting asphalt concrete and non-linear subgrade moduli. However, the base/subbase moduli could not be predicted using A. The best-performance A models were used to predict asphalt concrete and subgrade moduli from APTF HWD deflection basins collected at regular intervals during trafficking. The results were compared with results obtained using FAABACKCAL, a conventional ELP-based backcalculation software. The results definitely indicate that the non-linear pavement layer moduli could be successfully backcalculated from FWD/HWD deflection basins using an A trained with ILLI-PAVE results. The backcalculated results could be used to establish realistic a priori moduli inputs to mechanistic pavement structural analysis. Although regression models could also be developed for predicting layer moduli using ILLI-PAVE results, a significant advantage of using the A-based approach over the regression approach is that the functional forms of the relationships are not needed a priori. Also, the robustness of the A can be improved by including the field data sets in the training process, as they implicitly incorporate noise and errors typically seen in field measurements. Further research is needed to develop robust A models for predicting base/subbase moduli parameters. It is proposed that by including the A-predicted E AC and E Ri values as inputs to the A and by training the A with the ILLI-PAVE results for the -kip and 24-kip HWD loads, the chances of accurately predicting base/subbase moduli will increase. It is also noted that the A moduli backcalculation concept developed in this study could be used to backcalculate highway pavement non-linear moduli successfully. Gopalakrishnan 13
ACKOWLEDGMETS This paper was prepared from a study conducted in the Center of Excellence for Airport Technology. Funding for the Center is provided in part by the Federal Aviation Administration under research grant 95-C-1. The Center is maintained at the University of Illinois at Urbana-Champaign, which works in partnership with orthwestern University and the Federal Aviation Administration. The author gratefully acknowledges the financial assistance and support by Professor Marshall R. Thompson for conducting this research. The author is also grateful to Dr. Franco Gomez-Ramirez for his valuable help and suggestions in developing the training database. REFERECES Ahlvin, R. G., H. H. Ulery, R. L. Hutchinson, and J. L. Rice. 1971. Multiple-Wheel Heavy Gear Load Pavement Tests, Vol. 1: Basic Report. Technical Report o. AFWL-TR-7-113. Vicksburg, MS: U.S. Army Engineer Waterways Experiment Station. Asphalt Institute. 1982. Research and Development of The Asphalt Institute s Thickness Design Manual (MS-1) inth Edition. Research Report o. 82-2. College Park, MD: The Asphalt Institute. Ceylan, H., Tutumluer, E., Thompson, M. R., and F. Gomez-Ramirez. 24. eural etwork-based Structural Models for Rapid Analysis of Flexible Pavements with Unbound Aggregate Layers. Proceedings of the Sixth International Symposium on Pavements Unbound, ottingham, England, UK. Garg,. and W. H. Marsey. 22. Comparison Between Falling Weight Deflectometer and Static Deflection Measurements on Flexible Pavement at the ational Airport Pavement Facility (APTF). Paper presented at the 22 Federal Aviation Administration Airport Technology Conference, Chicago, IL. Gervais, E. L., G. F. Hayhoe, and. Garg. 23. Towards a Permanent Solution for 6-Wheel Landing Gear Aircraft. Proceedings of the 23 ASCE Airfield Specialty Conference, Las Vegas, V. Gopalakrishnan, K. and M. R. Thompson. 23. Rutting Study of APTF Flexible Pavement Test Sections. In Proceedings of the 23 ASCE Airfield Specialty Conference, Las Vegas, V. Gopalakrishnan, K. and M. R. Thompson. 24. Backcalculation of Airport Flexible Pavement on- Linear Moduli Using Artificial eural etworks. Proceedings of the 17 th International Florida Artificial Intelligence Research Symposium Conference, FLAIRS-24, Miami Beach, FL. Gopalakrishnan, K. and M. R. Thompson. 24. Comparative Effect of B777 and B747 Trafficking on Elastic Layer Moduli of APTF Flexible Pavements. In Proceedings of the 24 FAA Worldwide Airport Technology Transfer Conference, Atlantic City, J. Gomez-Ramirez, F. M., and M. R. Thompson. 22. Characterizing Aircraft Multiple Wheel Load Interaction for Airport Flexible Pavement Design. Civil Engineering Studies, COE Report. University of Illinois at Urbana-Champaign. Haykin, S. 1994. eural etworks: A Comprehensive Foundation. ew York: Macmillan College Publishing Company, Inc. Hossain, S. M. and J. P. Zaniewski. 1991. Characterization of Falling Weight Deflectometer Deflection Basin. Transportation Research Record 93. Washington, D.C.: TRB, ational Research Council, pp. 1 11. Hicks, R. G. 197. Factors Influencing the Resilient Properties of Granular Materials. Ph.D. dissertation, University of California, Berkeley. McQueen, R. D., W. Marsey, and J. M. Arze. 21. Analysis of ondestructive Data on Flexible Pavement Acquired at the ational Airport Pavement Test Facility. In Proceedings of the 21 ASCE Airfield Pavement Specialty Conference, Chicago, IL. Gopalakrishnan
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