Stress Regression Analysis of Asphalt Concrete Deck Pavement Based on Orthogonal Experimental Design and Interlayer Contact

A three-dimensional finite element box girder bridge and its asphalt concrete deck pavement were established by ANSYS software, and the interlayer bonding condition of asphalt concrete deck pavement was assumed to be contact bonding condition. Orthogonal experimental design is used to arrange the testing plans of material parameters, and an evaluation of the effect of different material parameters in the mechanical response of asphalt concrete surface layer was conducted by multiple linear regression model and using the results from the finite element analysis. Results indicated that stress regression equations can well predict the stress of the asphalt concrete surface layer, and elastic modulus of waterproof layer has a significant influence on stress values of asphalt concrete surface layer.


Introduction
The asphalt concrete deck pavement is multi-layered composite system, and it is usually composed of asphalt concrete surface layer, waterproof layer and cement concrete layer. Once the material parameters (such as thickness and elastic modulus) of these layers changed, mechanical response of asphalt concrete deck pavement would also change. On the other hand, the bonding condition between adjacent layers also plays an important part in structural response of asphalt concrete deck pavement, because it has influence on the stress transfer between the layers [1,2]. The poor bonding condition between adjacent layers reduce shear strength of asphalt concrete deck pavement, thereby result in several pavement distresses such as cracking, shoving and pothole [3][4][5]. Most former researches assumed two kinds of extreme interlayer bonding condition [2,6], which are the full-bond condition and the no-bond condition. In fact, it is not reasonable assumptions for the real asphalt concrete deck pavements. The real bonding condition between adjacent layers is thought to be neither the full-bond condition nor the no-bond condition [7], but lies somewhere in between.
A 3-dimensional elastic finite element model of a box girder bridge with asphalt concrete deck pavement was developed by ANSYS software in this research, and the interlayer bonding condition was assumed to be contact bonding condition. The model was used to analysis the influence of multiple material parameters on stress of asphalt concrete deck pavement under the contact bonding condition, and the material parameters of deck pavement will be arranged by orthogonal experimental design. Stress regression equations of asphalt concrete deck pavement will be established by multiple linear regression analysis, in addition, the important material parameters to asphalt concrete deck pavement will be found out.

Computing Model
The cross section size of the box girder bridge (with a span of 30m) and its pavement are shown in figure 1, and the direction of z-axis was the same with the driving direction. The loading position in the figure 1 is at the mid-span, and the pavement structure subjected to single-axis double-wheel load of 140KN [9], horizontal force F G λ = , λ is the braking coefficient and equals 0.5, and G is the wheel load. As previously mentioned, the interlayer bonding condition was assumed to be contact bonding condition, and the concept of contact bonding condition for interlayer modeling can be exhibited in figure 2. The adjacent layers were connected by translational spring elements, contact element and target element at the corresponding nodes. The shear stress transfer between the adjacent layers follows Coulomb friction model [10]: Where lim τ is ultimate shear stress, m is the sliding friction coefficient, it equals 0.5 in this paper, P is the contact compressive stress in normal direction, b is the cohesion between the adjacent layer,τ is the equivalent shear stress. In equation (1), if m equals 0 or P equals 0, the cohesion b still exist, if b equals 0, two adjacent layers appear cohesive failure. In inequation (2), when τ between two adjacent layers is less than or equal lim τ , the two layers keep sticking, or the two layers start to slide.

Regression Analysis and Significance Testing
The maximum transverse tensile stress max The test statistics F in F-test and the multiple correlation coefficient R will be calculated by Analysis of Variance for significance testing of stress regression equation, F and R are defined as follow: Where ij x is the i th value of the j th influencing factor in table 2. For a significance level 0.05 α = , the condition that the i th influencing factor is significant is

Results Analysis
Assumed that the interlayer bonding condition was contact bonding condition shown in figure 2 The   In conclusion, the elastic modulus of asphalt concrete surface layer and the waterproof layer have a significant influence on the tensile stress of asphalt concrete surface layer, and the thickness of asphalt concrete surface layer and the elastic modulus of waterproof layer have a significant influence on the longitudinal shear stress of asphalt concrete surface layer.

Conclusions
A summary of findings and conclusions in this study are presented as follows: (1) The three-dimensional elastic asphalt concrete deck pavement and box girder bridge model was developed, and the model adopted the concept of contact bonding condition between adjacent layers of deck pavement for more realistic and effective evaluating the stress of asphalt concrete deck pavement.
(2) By multiple linear regression analysis, the maximum tensile stress and the maximum longitudinal shear stress all have a significant linear correlation with the multiple material parameters, and the stress regression equations have an approximate trend as well as the magnitude compared with the calculated values, which can predict the stress values of asphalt concrete surface layer.
(3) The elastic modulus of waterproof layer has a significant influence on the stress of asphalt concrete surface layer. The elastic modulus of asphalt concrete surface layer affect the tensile stress of asphalt concrete surface layer, and the thickness of asphalt concrete surface layer affect the shear stress of asphalt concrete surface layer.