Assessing artificial neural network performance for predicting interlayer conditions and layer modulus of multi-layered flexible pavement

Abstract

The objective of this study is to evaluate the performance of the artificial neural network (ANN) approach for predicting interlayer conditions and layer modulus of a multi-layered flexible pavement structure. To achieve this goal, two ANN based back-calculation models were proposed to predict the interlayer conditions and layer modulus of the pavement structure. The corresponding database built with ANSYS based finite element method computations for four types of a structure subjected to falling weight deflectometer load. In addition, two proposed ANN models were verified by comparing the results of ANN models with the results of PADAL and double multiple regression models. The measured pavement deflection basin data was used for the verifications. The comparing results concluded that there are no significant differences between the results estimated by ANN and double multiple regression models. PADAL modeling results were not accurate due to the inability to reflect the real pavement structure because pavement structure was not completely continuous. The prediction and verification results concluded that the proposed back-calculation model developed with ANN could be used to accurately predict layer modulus and interlayer conditions. In addition, the back-calculation model avoided the back-calculation errors by considering the interlayer condition, which was barely considered by former models reported in the published studies.

Keywords

asphalt pavement / interlayer conditions / finite element method / artificial neural network / back-calculation

Introduction

Asphalt pavement (flexible pavement) structure is a multi-layered composite system, so the performance of pavement depends on both individual material of each layer and interlayer condition [¹–⁷]. The interlayer conditions between the adjunct layers of pavement structure are usually determined by a large variety of parameters and are often considered the weak Achilles’ heel of a pavement structure where horizontal water propagation of unbonded and cracks could easily occur [⁸–¹¹]. In the application of pavement performance evaluation and pavement structural design, the layers are assumed to be completed bonded to the adjacent structural layers, however, complete and total bonding should be considered an overestimation as of pavement performance as many environmental and material conditions are likely to vary. There are various studies from all over the world evaluated the performance of the pavement interlayers, especially the interlayer bond strength between pavement layers [¹²–¹⁹]. In the laboratory, the interlayer conditions are commonly determined and investigated by applying coaxial shear test and a layer-parallel direct shear test [⁸,²⁰–²³]. For example, in Italy, Canestrari and Santagata [²⁴] used the Ancona Shear Testing Research and Analysis to determine the effects of different variables on the shear behavior of tack coat. Sholar et al. [²⁵] at the Florida Department of Transportation (located in the USA) developed a simple direct shear device that could be used in a universal testing machine or a Marshall press. The test evaluated the impact of temperature and loading rate on the performance of interlayer bonding. Raab and Partl [²⁶] investigated the influence of tack coats on the interlayer adhesion of gyratory specimens in the laboratory using a layer-parallel direct shear test. Mohammad et al. [²⁷] evaluated the influence of tack coat types, application rates, and test temperature on the interface shear strength using the Superpave Shear Tester. West et al. [²⁸] developed a new test method, National Center for Asphalt Technology Bond Strength Test (BST), the interlayer bond strengths could be measured at different temperatures and normal pressure levels. Although there are so many studies reporting the laboratory approaches for the investigations of interlayer conditions, the useful methods to define or evaluate the interlayer conditions of situ pavement structures are seriously insufficient [³,¹⁵,²⁹–³²]. Therefore, the approaches for investigating interlayer conditions of situ pavement structures need further developments.

The nondestructive testing and back-calculation methods provided ideal means to evaluate the performance of pavement structure in a rapid and convenient manner [³³–³⁷]. Back-calculation is a mechanistic investigation of pavement surface deflection basins generated by various pavement deflection devices. Back-calculation takes a measured surface deflection and attempts to match it with a calculated surface deflection generated from an identical pavement structure using assumed layer stiffness, which is exactly the opposite of the forward calculation [³⁸]. In the last few decades, significant developments have been applied in the situ pavements. The back-calculation method could be considered to assess the interlayer condition in addition to the pavement layer stiffness, from falling weight deflectometer (FWD) test results, since the shear bond stiffness at the interlayer were considered as a variable affecting the FWD deflections and therefore back-calculated in a similar manner to a surface layer modulus [³⁹]. It should be noted that FWD is a pavement analysis technique that is now widely used in pavement engineering to test the structural performance of pavements nondestructively. The impulsive load is applied to the surface of the pavement structure, and sensors are set at a group of radical points to record the deflection response [⁴⁰]. The FWD method can back-calculate the layer modulus of asphalt pavement and predict the residual life of the pavement structure [⁴¹]. Bilodeau and Dore [⁴²,⁴³]. back-calculated the layers modulus and analyzed the mechanistic of pavement structure based on the data of the deflection basin and estimated the vertical strain at the top of the subgrade layer on the basis of the FWD basin results. Grenier et al. [⁴⁴,⁴⁵] used both back-calculation and forward calculation to analyze the dynamic response of flexible pavements under FWD loads based on the spectral element method. However, these studies rarely considered the effect of interlayer conditions on the pavement performance, most of which treated the interlayers as bonded. Therefore, it is necessary to further consider the different interlayer conditions in the back-calculation of pavement performance, and a reliable back-calculation model is also very important for this item.

Artificial neural network (ANN) method is a useful computation tool to analyze complex multi-layered structures, which include different evaluation parameters, and it has the ability to tolerate relatively imprecise tasks, approximate results, and even has less sensitivity to outliers [⁴⁶–⁴⁸]. ANN enable to tolerate relatively imprecise tasks, approximate results and even has less sensitivity to outliers [⁴⁶,⁴⁹]. Anitescu et al. [⁵⁰] reported one approach for solving partial differential equations using ANNs and an adaptive collocation strategy. The provided method increased the robustness of the neural network approximation and resulted in obvious computational savings. In the applications of ANN in civil engineering, Tarefder et al. [⁵¹] developed one four-layered ANN model to determine to map by associating the design and testing factors of asphalt mixtures with their performance in repetitive rutting tests and observed excellent agreement between simulations and the test data. They also used a developed ANN technique to estimate the optimum asphalt content of a Superpave mix. In addition, the fatigue life of asphalt mixtures, structure layer modulus and the interlayer bonding performance of pavement also can be predicted with ANN models [⁵²–⁵⁵]. Hadidi and Gucunski [⁵⁶] analyzed the response of pavement under FWD loads and assessed the in situ pavement layer modulus with the back-calculation of the FWD test, an optimal back-calculation method was proposed according to test results. Among these back-calculation methods, increasing interest was observed for the ANN method due to the advantages and disadvantages of coexistence characteristics. ANN method is capable of learning directly from examples and finding a relation between input and output variables, however, ANN has some limitation such as long training time, difficulty in selecting sets of input variables and a large amount of training data [⁵⁷–⁶⁰]. Considering above-mentioned features, the developed ANN techniques will be adopted into this study to predict the interlayer conditions and structure modulus for the multi-layered flexible pavements.

The objectives of this study are to assess the performance of the ANN based back-calculations for predicting the interlayer conditions and layer modulus of multi-layered flexible pavements. This study employed the ANN method to provide two models for predicting the interlayer conditions and surface layer modulus in the pavement with four types of structure. The application of ANN based on the database built with finite element method computations for four types of structures under FWD load. The ANN models were also verified by comparing with the multiple regression and PADAL models by using the measured deflection basin data.

Effect analysis for interlayer conditions of a pavement structure

Numerical computation model

Asphalt pavement is a multi-layer system composed of the asphalt concrete (AC) layer, base layer, and subgrade layer. The different interlayer conditions between layers have a great influence on the mechanical response of the pavement structure. Four types of pavement structures were investigated in this study to represent the influence of interlayer condition between the AC layer and base layer on the surface deflection basin. The basic technique indexes of proposed pavement structures are shown in Table 1. The commercial computing software ANSYS was applied to analyze the influence of interlayer conditions on the pavement structures.

In ANSYS, the considered pavement structure was assumed to be 4.7 m in the horizontal direction and 5.0 m in the vertical direction. The geometry of ANSYS model was calculated using SOLID45, while the interlayer condition between the AC layer and the base layer was simulated by CONTA170 and TARGE173 [⁶¹–⁶³]. Rayleigh damping was adopted in the finite element model with a damping ratio of 0.05 [⁶⁴,⁶⁵]. FWD load was idealized as a half-sin dynamic load uniformly distributed over a circular region with a radius of 0.15m, the peak magnitude of 0.72 MPa and duration of 0.03 s. This FWD load was applied on the top surface of the pavement structure model, in the z-direction, and it can be illustrated as p(t)=0.72sin(πt/0.03). The details of the boundary conditions, circular loading, and element meshes of ANSYS model were depicted in Figs. 1(a)–1(b). It is worth noting that the friction between the two layers is expressed by friction coefficients, and the friction coefficient values include 0.05, 0.2, 0.4, 0.8, 1.0, 3.0, 5.0, 7.0, 9.0, and LX (referred as to fully bonded in this study) to demonstrate the different interlayer conditions [³²].

Verification of ANSYS model

The ANSYS model used in this study was verified with an existing exact analytical solution. To verify the results from half-space, the calculated results based on ANSYS model in this study are compared with those obtained by an analytical solution [⁶⁶]. The cited article provided an analytical solution for the mechanical behavior analyses of the multi-layered medium under FWD load. Here, an efficient computational tool of Fourier-Hankel transform was used in the solving process. The structural parameters of the cited article were inputted in the proposed ANSYS model. Then, the vertical displacements (r = 0.0 m) of pavement structure from ANSYS model and cited article were compared in Fig. 1(c). As shown in Fig. 1(c), the calculated results via the proposed ANSYS model are almost identical with the results mentioned in the cited article. Therefore, the proposed ANSYS model for the database building is effectively available.

Numerical results and discussion

The deflection (or vertical displacement) is an important technique index because it reflects the pavement strength and is the basis for back-calculating of pavement structures. Prior to the investigation of the relationship between distribution regularity of the pavement deflection and the interlayer condition, Fig. 2 illustrated the comparisons of pavement deflection at various friction coefficients and locations. The bigger interface friction coefficients between the AC and base layer corresponding to a better interlayer condition and LX represented a continuous interlayer state. The selected measuring points from load center were 0.0, 0.6, 1.2, and 1.5 for each type of the pavement structure, and the corresponding measuring points were referred as to d0.0, d0.6, d1.2, and d1.5 in this study, respectively.

It can be seen that the influence of friction coefficient on pavement deflections of each measuring points could be ignored when the interlayer condition was partially or completely smooth (f≤0.2), the deflection decreases gradually with the increase in friction coefficient when the friction coefficient was greater than 1.0 (close to the complete continuous state), and the deflection was stable when the friction coefficient increased to values higher than 7.0. Additionally, when the friction coefficient varied between 0.2 and 1.0, the change in the interlayer state had a great influence on pavement deflection. Therefore, the numerical results demonstrated in Fig. 2 concluded that the change in friction coefficient between AC and base layer did not obvious influence on the deflection values with the increase in distance between the load center and the measuring points. For the distance greater than 1.5 m away from the load center, the reflection will not change with the change in friction coefficient.

Back-calculation models of interlayer and layer modulus based on ANN

ANN model

ANN is a flexible mathematical structure capable of identifying complex nonlinear relationships between input and output data, the neural networks are composed of simple elements operating in parallel [⁶⁷,⁶⁸]. In the back-calculation application by using ANN, the neural network can be trained to perform a particular function by adjusting the values of the connections (weights) between these elements. ANN modeling consists of two steps: the first step is to train the network; the second step is to test the network with data, which are not used for training [⁶⁹]. However, it is well known that training of ANN is an optimization task since it is desired to find the optimal weight set of a neural network in the training process. Traditional training algorithms have some drawbacks, such as computational complexity, so it is necessary to find better training algorithms to replace it. The back-propagation (BP) algorithm is one type of training multilayer Feed-Forward ANNs, and the gradient of BP training algorithms descent with momentum is often too slow for practical problems because they require small learning rates for stable learning [⁷⁰–⁷²]. In addition, the success in algorithms depends on the user-dependent parameters of learning rate and momentum constant. There are some faster algorithms, for example, Yan and You [⁷⁰] applied standard numerical optimization techniques. Therefore, in order to improve the effectiveness of the proposed model, the network training in this study applies the specific algorithms to minimize the network output error through determination and updating of the connection weights and biases.

Back-calculation of interlayer conditions

Creating a reasonable sample database is the first and the most important and crucial step in ANN based back-calculation. In the present study, the pavement structures of each group were divided into six forms, which correspond to the friction coefficients of 0.2, 0.6, 0.8, 1.0, 5.0, and 7.0. The sample data of AC layer modulus were in the range of 1000 to 21000 MPa, those of the base layer were from 500 to 4000 MPa, and in the range of 50 to 300 MPa for the subgrade. In addition, the computational deflection database was established by using ANSYS. According to the mentioned steps, the summary of the pavement parameters used in back-calculation as shown in Table 2. There are 1800 groups of computation samples achieved from ANSYS. The prepared sample database was divided into two parts, which include 1500 groups for model training (83.3% of total data) and 300 groups for the verification of model (16.7% of total data). The group of training was used to build the relationship between the inputs and outputs, while the verification group was applied to prevent over-fitting in ANN. It is noteworthy that the proposed division was according to the requirement of the training and verification groups that had almost similar distributions [⁶⁸]. The numerical discussion in section depicted that the pavement deflection did not obvious change with the change in friction coefficient when measuring point away from the load center greater than 1.5 m. Therefore, in order to make the back-calculation model more sensitive for the predictions, the measuring point whose distance from the load center is less than 1.5 m was selected as input parameters in the model.

ANN model applied in this paper was taken as computational deflection, AC layer thickness and base layer thickness as the model input parameters (set as input matrix), and the friction coefficient was taken as the output vector (evaluation parameters). It is worth noting that two groups of deflection data corresponding to different measurement points were employed in the ANN model. The group one includes seven points (distances from the load center are 0.0, 0.3, 0.6, 0.9, 1.2, 1.5, and 2.1 m), while the group two includes five points (distances from the load center are 0.0, 0.3, 0.6, 0.9, 1.2, and 1.5 m).

Furthermore, the factors were inputted into a MATLAB-based application program (i.e., ANN). To ensure the reliability of the back-calculation results, three models were selected for training and back-calculation comparison. Model-1 and Model-2 used the deflection data from group one and Model-3 used the deflection data from group two for back-calculate calculation. The specific parameters were set as shown in Table 3. The training functions in Model-1 and Model-2 correspond to Levenberg-Marquardt backpropagation, gradient descent with momentum, and one-step-secant algorithms, respectively. Trainoss is a network training function that updates weight and bias values according to the one-step-secant method. Levenberg-Marquardt backpropagation algorithm is an iterative technique that works in such a way that performance function will always be reduced in each iteration of the algorithm, which makes trainlm as the fastest training algorithm for networks of moderate size. Gradient Descent with Momentum algorithm performs like a low pass filter, which means that the network ignores small features in error surface with momentum. The network could get stuck into a shallow local minimum but with the momentum it slides via such local minimum [⁷³,⁷⁴]. In addition, learngdm and tansig were selected as adaption learning and transfer functions in the model training, respectively. Learngdm is the gradient descent with momentum weight and bias learning function, while tansig is the hyperbolic tangent sigmoid transfer function [⁷⁵].

Model evaluation is the utilization of the test data in a trained network to determine the prediction capability to compare the predicted and measured results [⁷⁰]. The good-fit statistics for ANN model prediction in the logarithmic scale were performed using statistical parameters, which include the coefficient of determination (R²) and the standard error of predicted data divided by the standard error of measured data (S_e/S_y). R² depicts the correlation between the predicted and measured values, while S_e/S_y indicates relative improvements in accuracy [⁷⁶]. Higher R² and lower S_e/S_y values are desired for the better performance of a model, and the equations for R² and S_e/S_y are shown in Eqs. (1) and (2), respectively. The set of criteria presented in Table 4, originally developed by Pellinen [⁷⁷], was also used in the evaluation.

(1)R^2=1-\mathrm{\sum }_{i=1}^n{(y_i^{\mathrm{t}}-y_i^{\mathrm{p}})}^2\sqrt{\mathrm{\sum }_{i=1}^n{(y_i^{\mathrm{t}}-\overline{y_i^{\mathrm{t}}})}^2},

(2)S_{\mathrm{e}}/S_{\mathrm{y}}=\sqrt{\left[\mathrm{\sum }_{i=1}^n{(y_i^{\mathrm{t}}-y_i^{\mathrm{p}})}^2\right]\times \left[\sqrt{\mathrm{\sum }_{i=1}^n{(y_i^{\mathrm{t}}-\overline{y_i^{\mathrm{t}}})}^2}\right]\times (n-P)},

where y_i^{\mathrm{t}} is the measured value (input data), y_i^{\mathrm{P}} is the predicted value (output data), n is the number of samples, and P is the number of independent variables in the model.

The training performance of the friction coefficient back-calculation model was shown in Fig. 3, and the back-calculation results of the interlayer friction coefficient (include training and verification group) were presented in Figs. 4 and 5. The comparative analysis of correlation coefficients and error ratios between the training and verification groups of the three models were demonstrated in Table 5.

As seen in Table 5, the developed ANN back-calculation model was satisfactory for predicting the interlayer friction coefficient (f). In the training group and verification group, the back-calculation correlation coefficients R² and the error ratios S_e/S_y of the two methods (using two different groups of deflection data), R² was greater than 0.85, and S_e/S_y was less than 0.55, which indicates that the data discretization can meet the engineering requirements on accuracy. In addition, although the back-calculation precision of using seven-point deflection values as input parameters was better than that of using five-point, the back-calculation accuracy of using five deflection values as input parameters was also satisfied the requirements of calculation.

Back-calculation of surface layer modulus

The input matrix of the back-calculation model was same as those of Section 3.2, except that the output vector was set to the AC layer modulus, and there are three types of models were employed for training and back-calculation. Figures 6, 7, and 8 depicted the back-calculation results, while Tables 6 and 7 illustrated ANN model calculation parameters and the evaluation results, respectively.

It can be seen from Table 7 that the accuracy of the back-calculation of AC layer modulus was obviously higher than that of the back-calculation of the interlayer friction coefficient. In addition, in the training and verification groups, the back-calculation results obtained by the two methods were close. The correlation coefficients R² were close to 1.0, and the error ratios S_e/S_y are less than 0.35. The Neural Network training function, hidden layers, the number of neural in each layer and the type of transfer function parameters significantly impact on training accuracy and back-calculation results in the training process of the ANN model. Therefore, the continuously debug and repeatedly verify the results is necessary to determine a reasonable back-calculation ANN model.

Verification by using the deflection data from field tests

In summary, the proposed ANN models can be applied to estimate the pavement structure modulus and interlayer condition. However, the computational deflection basin was adopted in the former part, instead of deflection data from a field test to conduct back-calculation. It is difficult to keep the computational deflection basin and the measured deflection basin consistent, due to the influence of various parameters. Therefore, this section was used to validate the feasibility of ANN back-calculation methods by using the measured deflection basin.

The field data from a test section were used as the measured data, which included the field deflection basin data and pavement modulus [³⁹]. Five sections with two different pavement structures were measured, and the measured sections were named as A, B, C, D, and E. The structures A, B, and C have the same pavement structure design with the structural thickness of 10, 14, and 50 cm for the surface layer, base layer, and subgrade layer, respectively. Moreover, the surface and base layers were treated as the whole layer in back-calculation analysis, which referred as to surface layer in structures D and E. The thickness of surface and subgrade layers are 21 and 50 cm, respectively, in the structures D and E. In both of these five sections, the Poisson’s ratios are 0.25, 0.25, and 0.35 for the surface, base, and subgrade layers, respectively. The measuring sensors were set at 0, 0.3, 0.6, 0.9, 1.2, 1.5, 2.1 m from the loading center. The load type is FWD with the peak of 700 kPa.

Two surveys were conducted on the five sections of the pavement structures. The first survey was conducted when the pavement structure was just finished, while the second survey was conducted when the pavements were opened after six months. The detailed test deflection basin data were displayed in Tables 8 and 9.

Al Hakim et al. [³⁹] tried two methods to evaluate the performance of pavements. The first one is a pavement deflection analysis method (PADAL), which is a computer program for the back analysis of elastic layer stiffness of pavement structures according to the deflections measured by FWD [⁷⁸]. The interlayer condition was not considered in PADAL model, and the interlayer was assumed completely continuous. The other one is the double multiple regression method, in which the interlayer condition was considered, and the layer modulus was back-calculated. The interlayer shear stiffness was back-calculated so as to characterize the interlayer condition of a pavement. To validate the feasibility of the proposed ANN back-calculation models in the evaluation of field pavement structures, two ANN models were adopted to predict the actual performance of the pavement structure, where the deflection basin data of sensor seven (distance to the loading center 2.1 m). The predicted values were compared with the findings reported by Al Hakim et al. [³⁹], and the comparisons as shown in Tables 10 and 11, where the interlayer shear stiffness was represented by K. It is noteworthy that the interlayer condition is poor when K<10, the bond condition is intermediate when 10<K<10⁵, and the bond condition is good when K>10⁵.

The back-calculated modulus was underestimated for models without considering the interlayer conditions, and the evaluation results of the pavement structure were obviously lower. The main reason was that the measured deflection value was larger with bad interlayer conditions so that the back-calculated modulus was smaller. PADAL modeling results were not accurate due to the inability to reflect the real pavement structure since the actual situation was that the pavement structure was not completely continuous. The multiple regression method and two ANN models can better reflect the real pavement structure condition with the consideration of interlayer.

The multiple regression method used the shear stiffness K to represent an interlayer condition. K<10 means that the interlayer was close to the smooth state, K>10⁵ means that the interlayer was close to the continuous state, 10<K<10⁵ means that the interlayer was in the middle state, and the change of K in this range has great influence on the response of pavement mechanics. ANN models used a friction coefficient to represent interlayer conditions. As mentioned in Section 2.3, the smooth state of the interlayer is an unfavorable bonding situation when the friction coefficient is no more than 0.2, the normal interlayer condition had a friction coefficient varying between 0.2 and 1, and the interlayer condition was good when the friction coefficient was greater than 1.0. The pavement structure can be treated as continuous when the friction coefficient is greater than 7.0. The qualitative evaluation of the pavement interlayer condition obtained by those three back-calculation models (double multiple regression, ANN Model-1 and Model-2) are basically the same. This phenomenon means that it is feasible to evaluate the pavement interlayer conditions by using the proposed ANN back-calculation model. Using the friction coefficient to evaluate the interlayer condition is also proved as a simple and direct method.

The predicted layer modulus of the two ANN back-calculation models was also very close when the interlayer condition was considered. There were no significant differences between results estimated by ANN models and the double multiple regression method. The pavement modulus estimated by ANN was acceptable, however, if possible, the prediction accuracy can be further improved by increasing the training samples.

Summary and conclusions

The finite element method (ANSYS) was adopted to compare the influence of pavement structure type and interlayer friction coefficient on the surface deflection at different mearing points. ANN model was applied to back-calculate the surface layer modulus and interlayer condition of the pavement structures. The main findings are displayed as follows according to the finite element method analysis and ANN prediction results.

1)‚The influence of the interlayer condition on surface layer deflection highly depended on the position of the measuring point. The impact was greater when the position of the measuring point was closer to the loading center, while the influence can be neglected when the distance between loading center and the measuring point was greater than 1.5 m.

2)‚The proposed back-calculation model developed with ANN can be used to accurately predict the pavement modulus and the interlayer condition using finite element method test results. The back-calculation model avoided the back-calculation errors by considering the interlayer condition, which was barely considered by former models reported in the published studies.

3)‚The layer modulus and interlayer conditions estimated by ANN models were acceptable, while the accuracy and back-calculation results highly depended on the parameter setting of models. The limitation of the method is that the model needs to be adjusted and verified repeatedly to acquire suitable back-calculation models.

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