A method and system for predicting the life of an environmentally friendly asphalt pavement

Abstract

The present invention discloses an environmentally friendly asphalt pavement life prediction method and system, belonging to the field of road engineering technology. The method comprises: S1, collecting raw radar signals from the asphalt pavement and obtaining pavement condition information based on the raw radar signals; S2, constructing a prediction model, and predicting the pavement condition information based on the prediction model to obtain a prediction result. The present invention uses a three-dimensional radar to obtain radar signals, and based on the radar signals, obtains the real-time pavement interlayer adhesion state. Based on the constructed prediction model, the pavement interlayer adhesion state is predicted to be a pavement condition grade, and the asphalt pavement life is predicted based on the pavement condition grade and a fatigue performance evaluation model. This provides certain reference data for scientific pavement maintenance and efficient operation.

Description

Technical Field

[0001] The present invention belongs to the technical field of road engineering, and in particular relates to a method and system for predicting the life of an environmentally friendly asphalt pavement. Background Art

[0002] Asphalt pavement performance prediction is the basis for making decisions on asphalt pavement maintenance and management, and is also the basis for transportation infrastructure planning, construction, and resource allocation. Accurate and reasonable prediction of asphalt pavement performance is of guiding significance for the scientific maintenance and efficient operation of highways.

[0003] Currently, pavement performance prediction models based on state degradation can be categorized into deterministic, statistical, and stochastic models. Deterministic models describe degradation paths as linear or nonlinear regression equations; statistical models treat degradation rates as random variables and estimate reliability by fitting data to probability distribution functions. However, due to the variability of factors such as materials, environment, traffic loads, and maintenance practices, road performance degradation is subject to significant uncertainty, making quantification of pavement degradation parameters difficult, statistical analysis time-consuming, and difficult to update later. Stochastic models consider data as a macroscopic manifestation of the combined effects of various influencing factors on road performance. By fully exploiting and mining data and extracting useful information, they can effectively describe the patterns of pavement performance degradation. This is also applicable to the current characteristics of asphalt pavements in China, which are characterized by small sample sizes, limited information, and uncertainty. The Markov process is a widely recognized stochastic model and has been extensively applied to asphalt pavement performance prediction. However, as a discrete stochastic process, the Markov process cannot describe the continuous characteristics of pavement degradation. Summary of the Invention

[0004] The present invention aims to address the deficiencies of the existing technology and proposes an environmentally friendly asphalt pavement life prediction method and system. By using a three-dimensional radar, radar signals are obtained, and based on the constructed prediction model, the radar signal is used to predict the pavement condition grade, and the asphalt pavement life is predicted based on the pavement condition grade and fatigue performance evaluation model.

[0005] To achieve the above object, the present invention provides the following solution: a method for predicting the life of an environmentally friendly asphalt pavement, comprising the following steps:

[0006] S1. Collecting original radar signals of an asphalt pavement and obtaining pavement condition information based on the original radar signals;

[0007] S2. Construct a prediction model, and predict the road surface condition information based on the prediction model to obtain a prediction result.

[0008] Further preferably, S1 includes:

[0009] S1.1. Collecting raw radar signals from an asphalt pavement using a three-dimensional radar, and preprocessing the raw radar signals to obtain processed signals;

[0010] S1.2. Obtain an asphalt pavement interlayer adhesion state image based on the processed signal, and obtain the pavement state information based on the interlayer adhesion state image.

[0011] Further preferably, the method for the prediction model to predict the road surface state information includes:

[0012] The road surface state information is input into the prediction model and passed through a 3×3 convolutional layer to obtain a preliminary feature matrix;

[0013] Afterwards, the preliminary feature matrix is ​​passed through the intermediate layer to obtain a weighted relationship between each channel of the preliminary feature matrix and each spatial position;

[0014] After that, it is outputted by the middle layer and connected to the 1×1 convolutional layer for feature extraction to obtain the second feature matrix;

[0015] The second feature matrix is ​​processed by global average pooling and then passes through two fully connected layers to obtain the final output, and the size of the final output is 1×1×6.

[0016] Further preferably, the middle layer includes 16 MBConv modules, and the last 5 MBConv modules include a channel attention module and a position attention module;

[0017] The channel attention module is used to obtain feature dependencies between channels of the preliminary feature matrix;

[0018] The position attention module is used to obtain the spatial feature dependencies of the preliminary feature matrix.

[0019] The present invention also provides an environmentally friendly asphalt pavement life prediction system, comprising: a data acquisition system and a prediction system;

[0020] The data acquisition system is used to collect original radar signals of the asphalt pavement and obtain pavement status information based on the original radar signals;

[0021] The prediction system is used to construct a prediction model, and predict the road surface state information based on the prediction model to obtain a prediction result.

[0022] Further preferably, the data acquisition system includes: an acquisition module and a processing module;

[0023] The acquisition module collects the original radar signal from the asphalt road surface through a three-dimensional radar;

[0024] The processing module is used to preprocess the original radar signal to obtain a processed signal; obtain an asphalt pavement interlayer adhesion state image based on the processed signal, and obtain the pavement state information based on the interlayer adhesion state image.

[0025] Further preferably, in the prediction system, the method for the prediction model to predict the road surface state information includes:

[0026] The road surface state information is input into the prediction model and passed through a 3×3 convolutional layer to obtain a preliminary feature matrix;

[0027] Afterwards, the preliminary feature matrix is ​​passed through the intermediate layer to obtain a weighted relationship between each channel of the preliminary feature matrix and each spatial position;

[0028] After that, it is outputted by the middle layer and connected to the 1×1 convolutional layer for feature extraction to obtain the second feature matrix;

[0029] The second feature matrix is ​​processed by global average pooling and then passes through two fully connected layers to obtain the final output, and the size of the final output is 1×1×6.

[0030] Further preferably, the middle layer includes 16 MBConv modules, and the last 5 MBConv modules include a channel attention module and a position attention module;

[0031] The channel attention module is used to obtain feature dependencies between channels of the preliminary feature matrix;

[0032] The position attention module is used to obtain the spatial feature dependencies of the preliminary feature matrix.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] This invention uses three-dimensional radar to obtain radar signals. Based on these radar signals, it determines the real-time adhesion status of the pavement layers. Using a constructed prediction model, it predicts the pavement condition grade based on the interlayer adhesion status. Furthermore, it predicts the lifespan of asphalt pavements based on the pavement condition grade and fatigue performance assessment model. This provides reference data for scientific pavement maintenance and efficient operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1This is a flow chart of an environmentally friendly asphalt pavement life prediction method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0038] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] Example 1:

[0040] like Figure 1 As shown, this embodiment provides an environmentally friendly asphalt pavement life prediction method, including the following steps:

[0041] S1. Collecting original radar signals of an asphalt pavement and obtaining pavement status information based on the original radar signals.

[0042] Specifically, S1 includes:

[0043] S1.1. Collect original radar signals from an asphalt pavement using a three-dimensional radar, and pre-process the original radar signals to obtain processed signals.

[0044] The collected original radar signal may be subject to electromagnetic interference from various aspects. Therefore, this embodiment performs external signal source interference suppression and background noise removal processing on the original radar signal.

[0045] Among them, the method of suppressing interference from external signal sources includes:

[0046]

[0047] Where, D(f m ) represents the frequency f m The frequency domain signal, is the target signal, When the difference between the frequency of the interference signal and the frequency domain signal exceeds the threshold, the interference signal from the external signal source will be eliminated.

[0048] Methods for background noise removal include:

[0049]

[0050] Where x(i,j) is the original radar signal; N is the number of sampling points.

[0051] Afterwards, the preprocessed original radar signal is converted from a frequency domain signal to a time domain signal using discrete Fourier transform to obtain a processed signal.

[0052] S1.2. Based on the processed signal, an image of the interlayer adhesion state of the asphalt pavement is obtained, and pavement state information is obtained based on the interlayer adhesion state image.

[0053] Based on the processed signal, the event amplitude between the asphalt layer and the base layer is extracted to obtain the interlayer bonding state image of the asphalt pavement. The interlayer contact state is evaluated by the event amplitude strength of the asphalt pavement layer interface: the larger the event amplitude, the worse the interlayer contact state; the smaller the event amplitude, the better the interlayer contact state.

[0054] The obtained asphalt pavement interlayer adhesion state image was scored using a manual labeling method. The scored asphalt pavement interlayer adhesion state image was used as the pavement state information. The pavement state information was preprocessed by cropping and other preprocessing to obtain an image of size 224 pixels × 224 pixels.

[0055] The scoring is divided into: 100-road condition is level 6, 90-100-road condition is level 5, 80-90-road condition is level 4, 70-80-road condition is level 3, 60-70-road condition is level 2, and 0-60-road condition is level 1.

[0056] S2. Construct a prediction model, predict the road surface condition information based on the prediction model, and obtain a prediction result.

[0057] Specifically, the prediction model primarily consists of a 3×3 convolutional layer, an intermediate layer, and an output layer. A 224×224×3 image is input into the prediction model and, after passing through the 3×3 convolutional layer, a preliminary feature matrix of size 112×112×32 is obtained. The preliminary feature matrix is ​​then passed through the intermediate layer to obtain a weighted relationship between each channel and each spatial position in the preliminary feature matrix. In this embodiment, the intermediate layer includes 16 MBConv modules, the last five of which include a channel attention module and a position attention module. The channel attention module is used to obtain the feature dependencies between the channels of the preliminary feature matrix, while the position attention module is used to obtain the spatial feature dependencies of the preliminary feature matrix. The MBConv module includes a 1×1 convolutional layer connected to a batch normalization layer and a SiLU activation function. It generates a new feature matrix by calculating the linear combination function of each channel of the input feature matrix. It also includes a depthwise separable convolution operation, followed by a batch normalization layer and a SiLU activation function. The model then splits into two paths, one of which sequentially undergoes global average pooling, two fully connected layers, and a sigmoid activation function. The other branch does not perform any operation, but multiplies the principal elements of the results of the two branches. The multiplied result is output after passing through a 1×1 convolution layer. In the channel attention module, the input matrix first undergoes two parallel pooling operations to extract features and analyze weight relationships. It then passes through two fully connected layers, SiLU and Sigmoid activation functions to generate two new feature matrices. The two generated feature matrices are added together by element-by-element summation, and the channel attention matrix is ​​obtained after passing through the Sigmoid activation function. The channel attention matrix and the input matrix are element-by-element multiplied to obtain a fusion matrix. The fusion matrix is ​​input into the position attention module, and after two parallel pooling operations, the two results are concatenated to obtain the concatenated features. The concatenated features then pass through a 7×7 convolution kernel, a BN layer, and a Sigmoid activation function to obtain the position attention matrix.

[0058] After that, the output of the intermediate layer is connected to the 1×1 convolutional layer for feature extraction to obtain the second feature matrix; the second feature matrix is ​​processed by global average pooling and then passes through two fully connected layers to obtain the final output, and the final output size is 1×1×6.

[0059] The pavement condition grade is obtained through the above prediction model, and then an estimation model between the pavement condition grade and life is constructed. The estimation model includes:

[0060] Y=0.001e 0.0056Es ×1367.8e -0.004Eb ×(9×10 -6 μ+6×10 -5 )×802.55P -1.459 ,

[0061] Where Es is the modulus of the asphalt layer; Eb is the modulus of the base layer; μ is the friction coefficient between the surface layer and the base layer; and P is the load.

[0062] Among them, the friction coefficient between the surface layer and the base layer is related to the pavement condition level; when the pavement condition is level 6, the friction coefficient is 1; when the pavement condition is level 5, the friction coefficient is 0.9; when the pavement condition is level 4, the friction coefficient is 0.7; when the pavement condition is level 3, the friction coefficient is 0.4; when the pavement condition is level 2, the friction coefficient is 0.2; when the pavement condition is level 1, the friction coefficient is 0.1.

[0063] Example 2:

[0064] This embodiment provides an environmentally friendly asphalt pavement life prediction system, including: a data acquisition system and a prediction system.

[0065] The data acquisition system is used to collect the original radar signals of the asphalt pavement and obtain the pavement status information based on the original radar signals.

[0066] Specifically, the data acquisition system includes an acquisition module and a processing module. The acquisition module uses a 3D radar to collect raw radar signals from an asphalt pavement. The processing module pre-processes the raw radar signals to generate processed signals. Based on the processed signals, an image of the interlayer adhesion of the asphalt pavement is generated, and pavement condition information is derived from the interlayer adhesion image.

[0067] The collected original radar signal may be subject to electromagnetic interference from various aspects. Therefore, in this embodiment, the processing module first performs external signal source interference suppression and background noise removal processing on the original radar signal.

[0068] Among them, the method of suppressing interference from external signal sources includes:

[0069]

[0070] Where, D(f m ) represents the frequency f m The frequency domain signal, is the target signal, When the difference between the frequency of the interference signal and the frequency domain signal exceeds the threshold, the interference signal from the external signal source will be eliminated.

[0071] Methods for background noise removal include:

[0072]

[0073] Where x(i,j) is the original radar signal; N is the number of sampling points.

[0074] Afterwards, the preprocessed original radar signal is converted from a frequency domain signal to a time domain signal using discrete Fourier transform to obtain a processed signal.

[0075] Finally, based on the processed signal, the event amplitude between the asphalt layer and the base layer is extracted to obtain the interlayer bonding state image of the asphalt pavement. The interlayer contact state is evaluated by the event amplitude strength of the asphalt pavement layer interface: the larger the event amplitude, the worse the interlayer contact state; the smaller the event amplitude, the better the interlayer contact state.

[0076] The obtained asphalt pavement interlayer adhesion state image was scored using a manual labeling method. The scored asphalt pavement interlayer adhesion state image was used as the pavement state information. The pavement state information was preprocessed by cropping and other preprocessing to obtain an image of size 224 pixels × 224 pixels.

[0077] The scoring is divided into: 100-road condition is level 6, 90-100-road condition is level 5, 80-90-road condition is level 4, 70-80-road condition is level 3, 60-70-road condition is level 2, and 0-60-road condition is level 1.

[0078] The prediction system is used to build a prediction model, predict the road surface status information based on the prediction model, and obtain the prediction results.

[0079] In this embodiment, the constructed prediction model mainly consists of a 3×3 convolutional layer, an intermediate layer, and an output layer. A 224×224×3 image is input into the prediction model and passed through a 3×3 convolutional layer to obtain a preliminary feature matrix of size 112×112×32. The preliminary feature matrix is ​​then passed through the intermediate layer to obtain a weighted relationship between each channel and each spatial position of the preliminary feature matrix. In this embodiment, the intermediate layer includes 16 MBConv modules, and the last 5 MBConv modules include a channel attention module and a position attention module. The channel attention module is used to obtain the feature dependencies between the channels of the preliminary feature matrix; the position attention module is used to obtain the spatial feature dependencies of the preliminary feature matrix. The MBConv module includes a 1×1 convolutional layer connected to a batch normalization layer and a SiLU activation function. It generates a new feature matrix by calculating the linear combination function of each channel of the input feature matrix. It also includes a depthwise separable convolution operation, followed by a batch normalization layer and a SiLU activation function. It then splits into two branches, one of which sequentially undergoes global average pooling, two fully connected layers, and a sigmoid activation function. The other branch does not perform any operation, but multiplies the principal elements of the results of the two branches. The multiplied result is output after passing through a 1×1 convolution layer. In the channel attention module, the input matrix first undergoes two parallel pooling operations to extract features and analyze weight relationships. It then passes through two fully connected layers, SiLU and Sigmoid activation functions to generate two new feature matrices. The two generated feature matrices are added together by element-by-element summation, and the channel attention matrix is ​​obtained after passing through the Sigmoid activation function. The channel attention matrix and the input matrix are element-by-element multiplied to obtain a fusion matrix. The fusion matrix is ​​input into the position attention module, and after two parallel pooling operations, the two results are concatenated to obtain the concatenated features. The concatenated features then pass through a 7×7 convolution kernel, a BN layer, and a Sigmoid activation function to obtain the position attention matrix.

[0080] After that, the output of the intermediate layer is connected to the 1×1 convolutional layer for feature extraction to obtain the second feature matrix; the second feature matrix is ​​processed by global average pooling and then passes through two fully connected layers to obtain the final output, and the final output size is 1×1×6.

[0081] The pavement condition grade is obtained through the above prediction model, and then an estimation model between the pavement condition grade and life is constructed. The estimation model includes:

[0082] Y=0.001e 0.0056Es ×1367.8e -0.004Eb ×(9×10 -6 μ+6×10 -5 )×802.55P -1.459 ,

[0083] Where Es is the modulus of the asphalt layer; Eb is the modulus of the base layer; μ is the friction coefficient between the surface layer and the base layer; and P is the load.

[0084] Among them, the friction coefficient between the surface layer and the base layer is related to the pavement condition level; when the pavement condition is level 6, the friction coefficient is 1; when the pavement condition is level 5, the friction coefficient is 0.9; when the pavement condition is level 4, the friction coefficient is 0.7; when the pavement condition is level 3, the friction coefficient is 0.4; when the pavement condition is level 2, the friction coefficient is 0.2; when the pavement condition is level 1, the friction coefficient is 0.1.

[0085] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for predicting the life of an environmentally friendly asphalt pavement, characterized in that: The following steps are involved: S1. Collecting original radar signals of an asphalt pavement and obtaining pavement condition information based on the original radar signals; S2. Build a prediction model, and predict the road surface condition information based on the prediction model to obtain a prediction result; S1 includes: S1.

1. Collecting raw radar signals from an asphalt pavement using a three-dimensional radar, and preprocessing the raw radar signals to obtain processed signals; S1.

2. Obtaining an asphalt pavement interlayer adhesion state image based on the processed signal, and obtaining the pavement state information based on the interlayer adhesion state image; Based on the processed signal, the amplitude of the event axis between the asphalt layer and the base layer is extracted to obtain the asphalt pavement interlayer adhesion state image; using the manual labeling method, the obtained asphalt pavement interlayer adhesion state image is scored, and the asphalt pavement interlayer adhesion state image with the assigned score is used as the pavement state information; The method for predicting the road surface condition information using the prediction model includes: The road surface state information is input into the prediction model and passed through a 3×3 convolutional layer to obtain a preliminary feature matrix; Afterwards, the preliminary feature matrix is ​​passed through the intermediate layer to obtain a weighted relationship between each channel of the preliminary feature matrix and each spatial position; After that, it is outputted by the middle layer and connected to the 1×1 convolutional layer for feature extraction to obtain the second feature matrix; The second feature matrix is ​​processed by global average pooling and then passes through two fully connected layers to obtain the final output, the size of which is 1×1×6; The middle layer includes 16 MBConv modules, and the last 5 MBConv modules include a channel attention module and a position attention module; The channel attention module is used to obtain feature dependencies between channels of the preliminary feature matrix; The position attention module is used to obtain the spatial feature dependency of the preliminary feature matrix; The MBConv module includes a 1×1 convolution layer, connected to the BN layer and the SiLU activation function, and generates a new feature matrix by calculating the linear combination function of each channel of the input feature matrix; it also includes a depth-separable convolution operation, followed by a BN layer and a SiLU activation function; it is then divided into two branches, one of which is sequentially subjected to global average pooling, two fully connected layers, and a Sigmoid activation function; the other branch does not perform any operation, multiplies the main elements of the results of the two branches, and the result of the multiplication is output after passing through a 1×1 convolution layer; in the channel attention module, the input matrix first undergoes two parallel pooling operations to extract The features are analyzed and the weight relationship is analyzed. After that, two fully connected layers, SiLU and Sigmoid activation functions are applied to generate two new feature matrices. The two feature matrices are added together by element-by-element summation and the channel attention matrix is ​​obtained after the Sigmoid activation function. The channel attention matrix and the input matrix are element-by-element multiplied to obtain a fusion matrix. The fusion matrix is ​​input into the position attention module and sequentially passes through two parallel pooling operations. The two results are spliced ​​to obtain the spliced ​​features. After that, the spliced ​​features are sequentially passed through a 7×7 convolution kernel, a BN layer and a Sigmoid activation function to obtain the position attention matrix. The pavement condition grade is obtained through the prediction model, and then an estimation model between the pavement condition grade and life is constructed. The estimation model includes: Y=0.001e 0.0056Es ×1367.8e -0.004Eb ×(9×10 -6 μ+6×10 -5 )×802.55P -1.459 , Where Es is the modulus of the asphalt layer; Eb is the modulus of the base layer; μ is the friction coefficient between the surface layer and the base layer; and P is the load.

2. An environmentally friendly asphalt pavement life prediction system, the system is used to implement the method of claim 1, characterized in that: include: Data collection system and prediction system; The data acquisition system is used to collect original radar signals of the asphalt pavement and obtain pavement status information based on the original radar signals; The prediction system is used to construct a prediction model, and predict the road surface state information based on the prediction model to obtain a prediction result; The data acquisition system includes: an acquisition module and a processing module; The acquisition module collects the original radar signal from the asphalt road surface through a three-dimensional radar; The processing module is used to pre-process the original radar signal to obtain a processed signal; obtain an asphalt pavement interlayer adhesion state image based on the processed signal, and obtain the pavement state information based on the interlayer adhesion state image; Based on the processed signal, the amplitude of the event axis between the asphalt layer and the base layer is extracted to obtain the asphalt pavement interlayer adhesion state image; using the manual labeling method, the obtained asphalt pavement interlayer adhesion state image is scored, and the asphalt pavement interlayer adhesion state image with the assigned score is used as the pavement state information; In the prediction system, the method for the prediction model to predict the road surface state information includes: The road surface state information is input into the prediction model and passed through a 3×3 convolutional layer to obtain a preliminary feature matrix; Afterwards, the preliminary feature matrix is ​​passed through the intermediate layer to obtain a weighted relationship between each channel of the preliminary feature matrix and each spatial position; After that, it is outputted by the middle layer and connected to the 1×1 convolutional layer for feature extraction to obtain the second feature matrix; The second feature matrix is ​​processed by global average pooling and then passes through two fully connected layers to obtain the final output, the size of which is 1×1×6; The middle layer includes 16 MBConv modules, and the last 5 MBConv modules include a channel attention module and a position attention module; The channel attention module is used to obtain feature dependencies between channels of the preliminary feature matrix; The position attention module is used to obtain the spatial feature dependency of the preliminary feature matrix; The MBConv module includes a 1×1 convolution layer, connected to the BN layer and the SiLU activation function, and generates a new feature matrix by calculating the linear combination function of each channel of the input feature matrix; it also includes a depth-separable convolution operation, followed by a BN layer and a SiLU activation function; it is then divided into two branches, one of which is sequentially subjected to global average pooling, two fully connected layers, and a Sigmoid activation function; the other branch does not perform any operation, multiplies the main elements of the results of the two branches, and the result of the multiplication is output after passing through a 1×1 convolution layer; in the channel attention module, the input matrix first undergoes two parallel pooling operations to extract The features are analyzed and the weight relationship is analyzed. After that, two fully connected layers, SiLU and Sigmoid activation functions are applied to generate two new feature matrices. The two feature matrices are added together by element-by-element summation and the channel attention matrix is ​​obtained after the Sigmoid activation function. The channel attention matrix and the input matrix are element-by-element multiplied to obtain a fusion matrix. The fusion matrix is ​​input into the position attention module and sequentially passes through two parallel pooling operations. The two results are spliced ​​to obtain the spliced ​​features. After that, the spliced ​​features are sequentially passed through a 7×7 convolution kernel, a BN layer and a Sigmoid activation function to obtain the position attention matrix. The pavement condition grade is obtained through the prediction model, and then an estimation model between the pavement condition grade and life is constructed. The estimation model includes: Y=0.001e 0.0056Es ×1367.8e -0.004Eb ×(9×10 -6 μ+6×10 -5 )×802.55P -1.459 , Where Es is the modulus of the asphalt layer; Eb is the modulus of the base layer; μ is the friction coefficient between the surface layer and the base layer; and P is the load.

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