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Determination of complex modulus gradients of flexible pavements using falling weight deflectometer and artificial intelligence

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Abstract

The modulus gradient of asphalt concrete (AC) layers is an important feature of flexible pavements. The variation of the modulus with depth results from the synthetical effect of material properties, the service time of pavements, loading and environmental conditions. Since the modulus gradient directly affects critical responses and performance of pavements, the determination of the modulus gradient of AC layers is necessary for the evaluation, maintenance and rehabilitation of flexible pavements. This paper aims to propose a method to obtain layer moduli of flexible pavements at different loading frequencies, which include a power function describing the modulus gradient of AC layers. The method utilizes results from a typical nondestructive test in the field applying the falling weight deflectometer and techniques of the fast Fourier transform, finite element model updating, kriging model and artificial intelligence. The method is validated by comparing layer moduli obtained from the proposed method and other backcalculation softwares.

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Funding

This work was supported by Changsha University of Science & Technology via Open Fund of National Engineering Laboratory of Highway Maintenance Technology (Grant Number: KFJ180104).

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Authors and Affiliations

  1. Zachry Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX, 77843, USA

    Yong Deng & Robert L. Lytton

  2. College of Civil Engineering and Architecture, Zhejiang University, 866 Yuhangtang Road, An-Zhong Bldg., Hangzhou, 310058, China

    Xue Luo

  3. National Engineering Laboratory of Highway Maintenance Technology, Changsha University of Science & Technology, Changsha, 410114, Hunan, China

    Xue Luo

  4. CCCC Second Highway Consultants Co., Ltd, Wuhan, 430052, Hubei, China

    Yazhou Zhang

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  1. Yong Deng
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Correspondence to Xue Luo.

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Appendix

Appendix

1.1 Determinations of the mesh size and model radius of the pavement

In the sensitivity analysis, structural parameters and material properties are the same as Fig. 2 of the manuscript. A standard FWD load was applied, of which the pressure magnitude is 565 kPa, the load cycle is 0.03 s and the load radius is 0.15 m. Figure 10 illustrates the model radius which was adjusted in the sensitivity analysis. For simplicity, the surface layer, base layer and subgrade were treated as elastic materials, of which the modulus are 2000 MPa, 500 MPa and 250 MPa, respectively. Table 3 shows the corresponding maximum deflection at the loading center when the model radius is 3 m, 4 m and 5 m. It shows that the maximum deflection at the loading center converges as the model radius increases. Since the relative error drops below 1% when the model radius is 5 m, this value was used in all FE models of this paper. Similarly, the sensitivity analysis was conducted on different meshes and results are presented in Table 4. The mesh setting in the case “Finer” was applied in all FE models of this paper.

Table 3 Maximum deflection at the loading center with different model radii
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Fig. 10
figure 10

Illustration of the model radius

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Table 4 Maximum deflection at the loading center with different meshes
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1.2 Validation of the UMAT for the surface layer

Two comparisons were conducted in this section to validate the UMAT for the modulus gradient of the surface layer. The structural parameters, loading condition and material properties of the base layer and subgrade are the same as Sect. 4.1. In the first comparison, \(E_{b}\), \(E_{s}\) and \(n\) in the UMAT were set to 2000 MPa, 2000 MPa and 1, which represents no modulus change with the depth. It was compared with the case where the module “Elastic” in ABAQUS was set for the surface layer and the modulus value was set to 2000 MPa. In the second comparison, \(E_{b}\), \(E_{s}\) and \(n\) in the UMAT were set to 1000 MPa, 2000 MPa and 1, which represents a linear decrease in the modulus value with the depth. It was compared with the case where the surface layer was divided into 5 identical sublayers. From the top to bottom, the elastic modulus was set to 1900 MPa, 1700 MPa, 1500 MPa, 1300 MPa, 1100 MPa, respectively.

Figure 11 shows the results of two comparisons. The time histories of the deflection at the loading center were compared. From the graph, it can be seen that results of the cases using the UMAT are nearly the same as cases using the default module in ABAQUS, which proves the accuracy of the UMAT used in the manuscript.

Fig. 11
figure 11

Validation of the UMAT

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1.3 Sensitivity analysis of layer modulus on deflections at sensor locations

Table 5 is the supplement of Fig. 3 of the manuscript. The loading condition, structural parameters and material properties except the modulus of the pavement are the same as Sect. 4.1. Table 5 shows the modulus of each layer and deflection magnitudes at four sensor locations. In Case 1–Case 10, only one property is adjusted and the rest are the same as Case 0.

Table 5 Maximum deflection at the loading center with different model radii
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Deng, Y., Luo, X., Zhang, Y. et al. Determination of complex modulus gradients of flexible pavements using falling weight deflectometer and artificial intelligence. Mater Struct 53, 100 (2020). https://doi.org/10.1617/s11527-020-01528-2

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