Method for obtaining interlayer shear modulus of asphalt pavement based on three-dimensional ground penetrating radar
By combining high-frequency three-dimensional ground-penetrating radar and the bisection iterative method with core drilling verification, a quantitative relationship between interlayer shear modulus and reflected wave amplitude was established, solving the problem of inaccurate detection in existing technologies. This enabled non-destructive and efficient acquisition of interlayer shear modulus, improving the scientific accuracy of pavement structure life prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY
- Filing Date
- 2026-01-30
- Publication Date
- 2026-04-24
AI Technical Summary
Existing technologies for detecting the interlayer contact state of asphalt pavement have problems such as destructive testing, limited testing points, and qualitative test results that are unrelated to mechanical parameters, leading to inaccurate prediction of pavement structure life.
High-frequency three-dimensional ground-penetrating radar was used in combination with the binary iterative method and core drilling verification. Interlayer reflected wave amplitude data were obtained through non-destructive testing to establish a quantitative relationship between interlayer shear modulus and reflected wave amplitude. Combined with indoor direct shear test, representative values of interlayer shear modulus were obtained.
It enables the non-destructive, efficient, and accurate acquisition of interlayer shear modulus, which can represent the interlayer contact state of a large range of pavements and can be used for pavement structural mechanical response analysis and life prediction, thus improving the scientific nature of the design.
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Figure CN121613517B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of road engineering technology, and in particular to a method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground penetrating radar. Background Technology
[0002] During long-term service, the interlayer contact state of asphalt pavement (especially the interface between the surface layer and the base layer) gradually deteriorates. This interface is a critical area for stress transfer, and its deterioration directly alters the mechanical response characteristics of the pavement structure, thereby significantly shortening the pavement's structural life. Therefore, it is crucial to scientifically consider the actual impact of the interlayer contact state when estimating the remaining structural life of in-service asphalt pavements and performing mechanical calculations for overlays.
[0003] The current Chinese standard "Specifications for Design of Asphalt Pavement" (JTG D50-2017) typically assumes complete continuity between structural layers during reconstruction. This idealized assumption fails to accurately reflect the partial continuity or sliding states that may occur between layers in service pavements, leading to discrepancies between mechanical analysis results and actual stress conditions. Furthermore, due to material inhomogeneity, construction variations, and differences in load history, the interlayer contact state in different sections of service asphalt pavements often exhibits significant spatial variability and is not uniform.
[0004] Traditional methods for detecting interlayer contact conditions in pavement include core drilling and two-dimensional ground-penetrating radar (GPR). However, traditional core drilling is a destructive method that not only damages the pavement structure but also limits the number of detection points, making it difficult to reflect the spatial distribution characteristics of interlayer conditions over long road sections. Conventional two-dimensional GPR can only qualitatively determine the existence of interlayer separation through reflected wave signals. In contrast, patent CN114384511B proposes a three-dimensional ground-penetrating radar-based method for evaluating the interlayer condition of asphalt pavement. This method uses three-dimensional GPR to collect interlayer reflected wave amplitude data, divides the tested road section into evaluation units, calculates the average amplitude of each unit, and combines this with amplitude frequency distribution curves, cumulative frequency, core drilling, and Pavement Damage Index (PCI) calibration to achieve a graded evaluation of the interlayer condition. However, although this scheme can obtain a graded evaluation, its grading method relies on amplitude statistical characteristics (frequency distribution, cumulative frequency) and apparent condition (core sample integrity, PCI). The grading results are used to quickly identify road sections with poor interlayer conditions. It is a qualitative evaluation and is unrelated to mechanical parameters. Its results cannot be used for the design of subsequent refined maintenance schemes such as overlay design. Summary of the Invention
[0005] The purpose of this application is to provide a method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground-penetrating radar, which is non-destructive, efficient and accurate. It can reasonably determine the representative value of the interlayer contact state that can represent a large range of pavements, and use it as the input value of the mechanical response analysis model of asphalt pavement structure. It is more scientific to take the interlayer contact state of in-service asphalt pavement into the estimation of the remaining service life of pavement structure and the service life extension design.
[0006] To achieve the above objectives, this application provides the following technical solution:
[0007] A method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground-penetrating radar includes the following steps:
[0008] S1. High-frequency three-dimensional ground-penetrating radar is used to perform non-destructive testing on the target asphalt pavement, tracing the surface layer-base layer line, and collecting the amplitude intensity value of the reflected wave at the surface layer-base layer interface at intervals of 10cm in the driving direction and 10cm in the perpendicular direction of driving, obtaining the in-phase axis reflected wave amplitude data of the surface layer-base layer interface; statistically analyzing these data, the range of reflected wave amplitude intensity of the target asphalt pavement is obtained as [A]. Min A Max ];
[0009] S2. The critical amplitude A1 for characterizing the "interlayer separation" between the surface layer and the base layer is determined by using the binary iterative method combined with core drilling verification, and the iteration continues until the accuracy of A1 reaches the expected level.
[0010] S3. Establish a quantitative relationship between the amplitude intensity of radar reflected waves and the interlaminar shear modulus K in the Goodman model; when the amplitude value is [A Min Within the range of A1], multiple points with different amplitude values were selected. For each amplitude value, three representative points were drilled and core samples were taken. The interlayer shear modulus K of the obtained core samples was determined by indoor direct shear test, and the average value was taken as the representative value of the interlayer shear modulus corresponding to that amplitude value. Then, regression analysis was used to establish the relationship between interlayer reflection amplitude A and representative value of interlayer shear modulus. The quantitative fitting relationship between them is called the AK relationship;
[0011] S4. Divide the long test section into several basic evaluation units of equal length. Select different quantiles as the amplitude representative values for each basic evaluation unit according to the highway grade, denoted as A. 单元 .
[0012] Furthermore, in step S2, firstly, the midpoint amplitude value A is taken. mid = (A Min +A Max ) / 2, for the amplitude value A at the midpoint midCore sampling is performed in the corresponding area. If the core sampling results show that interlayer separation and core sample fracture have occurred at the midpoint, it proves that the critical amplitude A1 is located in [A]. Min A mid If the core sample layers are continuous, then the critical amplitude A1 is located within the range [A]. mid A Max Within the new judgment interval, repeat the process of taking the midpoint amplitude value, core sampling, and verification until the critical amplitude A1 data accuracy reaches the expected level, such as 0.05mm, 0.1mm, 0.2mm, etc.
[0013] For example, the first time A is taken. mid = (A min +A max If core sampling is performed in region ) / 2 and the core sample results show interlayer separation and core sample fracture, then the new judgment interval is [A]. min A mid ]; The next core sampling will take the amplitude value A = (A min +A mid Core samples were taken from the area at ) / 2 to check for interlayer separation or core sample breakage; if these occurred, it indicates that the critical amplitude is located at [A]. min , (A min +A mid If the interval is continuous, it indicates that the critical amplitude is located in the interval [(A / 2]; if continuous, it means that the critical amplitude is located in the interval [(A / 2]]. min +A mid ) / 2, A mid [Range]. Continue core sampling until the critical amplitude A1 data accuracy reaches the expected level.
[0014] If A is chosen the first time... mid = (A min +A max After core sampling in region ) / 2, if the core sample is continuous, then the new judgment interval is [A]. mid A max ]; The next core sampling will take an amplitude A = (A mid +A max Core samples were taken from the area at ) / 2 to check for interlayer separation or core sample breakage; if these occurred, it indicates that the critical amplitude is located at [A]. mid , (A mid +A max If the interval is continuous, it indicates that the critical amplitude is located in the interval [(A / 2]; if continuous, it means that the critical amplitude is located in the interval [(A / 2]]. mid +A max ) / 2, A max [Range]. Continue core sampling until the critical amplitude A1 data accuracy reaches the expected level.
[0015] Furthermore, step S3 establishes the relationship between interlayer reflection amplitude A and representative value of interlayer shear modulus through regression analysis. The quantitative fitting relationship between them is:
[0016] ;
[0017] In the formula, The critical amplitude, The fitting coefficients are denoted as .
[0018] Furthermore, in step S4, all interlayer reflection amplitudes within each basic evaluation unit are arranged in ascending order to obtain a data sequence; for highways, the 95th percentile of the data sequence is taken as A. 单元 The value of A is taken as follows: For Class I highways, the 90th percentile is taken as A. 单元 The value of A is taken as follows: For secondary highways, the 85th percentile is taken as A. 单元 The value of A is taken as follows: For Class III highways, the 80th percentile is taken as A. 单元 The value of A is taken as follows: For Class IV highways, the 70th percentile is taken as A. 单元 The value of .
[0019] Furthermore, the method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground-penetrating radar also includes step S4.1: for a long test section composed of several basic evaluation units, the representative value of the interlayer condition of the long test section is obtained by combining the spatial variation coefficient CV, denoted as A. 长 If the coefficient of variation CV < 10%, then take the representative value A of the interlayer reflected wave amplitude of the basic evaluation unit that makes up the long test section. 单元 The arithmetic mean of A 长 If CV ≥ 10%, cluster analysis is used to merge spatially continuous basic evaluation units with a coefficient of variation CV < 10% into several homogeneous design sub-segments, and the A value of all basic evaluation units within each sub-segment is taken. 单元 The arithmetic mean of A 长 .
[0020] For the 10km long test section, it was divided into 10 basic evaluation units of 1000m each, ordered by spatial location as X1, X2, X3, X4, X5, X6, X7, X8, X9, X 10 The representative value of the reflected wave amplitude between each layer is A. x1 A x2 A x3 A x4 A x5 A x6 A x7 A x8 A x9 A x10Calculate the arithmetic mean, standard deviation, and coefficient of variation of 10 basic evaluation units. If the obtained coefficient of variation CV ≥ 10%, it indicates that the long detection road segment is heterogeneous and cluster analysis is required to divide the long road segment into several sub-segments. Division process: (1) First, determine the initial number of divisions as 2, and determine the optimal division point by the minimum total sum of squares within the group. For example, assume the division point is 4-5 (divide the long detection road segment into a group of 4 units in the first group and a group of 6 units in the last group); calculate the arithmetic mean and sum of squares of these two groups of data respectively, and add the two sums of squares to obtain the total sum of squares within the group of the long detection road segment SS. 总 If the sum of squared deviations within groups for all other split points (including 1-2, 2-3, 3-4, ..., 9-10) is greater than the sum of squared deviations within groups for split point 4-5 (SS) 总 If the optimal segmentation point is 4-5, then the optimal segmentation point is 4-5. (2) Verify the homogeneity of the sub-segments. Calculate the arithmetic mean, standard deviation, and coefficient of variation of the two sets of data respectively; if the coefficient of variation of the two sets of data is less than 10%, then the long test segment can be divided into the first 4 units (X1-X4) and the last 6 units (X5-X6). 10 If there is a coefficient of variation greater than or equal to 10% for two sub-segments, increase the number of divisions and repeat the above steps until the coefficient of variation of each sub-segment is less than 10%. Output the optimal division point and each sub-segment that meets the requirements.
[0021] Furthermore, in step S1, the frequency of the high-frequency three-dimensional ground-penetrating radar is set to 300MHz to 3GHz, and the antenna spacing is 7.5cm.
[0022] The technical solution of this application has the following beneficial effects:
[0023] This application provides a method for obtaining the interlayer shear modulus of pavement related to the interlayer shear modulus. Different quantiles are adopted according to the highway grade to select the representative value of the interlayer reflected wave amplitude of the basic evaluation unit. Considering the spatial variability of the interlayer condition of the in-service pavement, the homogeneous sub-segments are divided by the coefficient of variation CV. Finally, the representative value of the interlayer shear modulus that can be used for calculation by various pavement mechanics calculation models is output.
[0024] This application utilizes three-dimensional ground-penetrating radar detection, a bisection iterative method, and core drilling verification to rapidly approximate and pinpoint the critical amplitude threshold characterizing interlayer separation between the surface layer and the base layer using a minimal number of core samples. Based on this critical amplitude determination, a representative value for the interlayer shear modulus is established through systematic core sampling and indoor direct shear tests. The fitting relationship with the interlayer reflected wave amplitude A converts the interlayer reflected wave amplitude intensity A obtained from nondestructive testing into the interlayer bonding coefficient (interlayer shear modulus) used in the Goodman model to represent the interlayer contact condition.
[0025] The main purpose of this application is to obtain a representative value that can represent the interlayer contact state of the entire road section, thereby providing design parameters for the establishment of an analysis model of the mechanical response of asphalt pavement structure considering the interlayer contact state, and then obtaining the remaining life of the pavement structure considering the interlayer contact state, and selecting an appropriate life extension design scheme based on the remaining life, so as to make the prediction of the remaining life of the pavement structure and the corresponding life extension design more scientific. Attached Figure Description
[0026] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. Wherein:
[0027] Figure 1 Fitting curves of the AK relationship constructed for embodiments of this application. Detailed Implementation
[0028] The following will use examples to illustrate this application in detail.
[0029] The target asphalt pavement is a Class I highway with a total length of 10km, a design speed of 80km / h, four lanes in both directions, a roadbed width of 25.5m, and a pavement structure from top to bottom consisting of 4cm SMA-13, 6cm AC-20, 8cm AC-25, 40cm cement-stabilized crushed stone base course, and 15cm graded crushed stone subbase course. It has been in operation for 12 years.
[0030] A method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground-penetrating radar includes the following steps:
[0031] S1, 3D ground-penetrating radar detection and data processing;
[0032] High-frequency three-dimensional ground-penetrating radar (GPR) was used for non-destructive testing of the target asphalt pavement. The surface layer-base layer line was traced, and radar data was collected at intervals of 10cm in the driving direction and 10cm perpendicular to the driving direction (i.e., the smallest detection unit was 10cm × 10cm). After acquiring the 3D GPR data, interference suppression, Fourier transform, and background filtering were performed to remove electromagnetic interference and the influence of shallow signal waves from the original signal. Then, based on the processed 3D GPR data, the amplitude data of the reflected wave at the surface layer-base layer interface of the in-service asphalt pavement was obtained by identifying and tracing the continuous peaks or troughs (phase axes) at the surface layer-base layer interface. Statistically, the amplitude intensity range of the reflected wave across the entire pavement was [0.18mm, 5.03mm].
[0033] S2. The critical amplitude value for separation between the surface layer and the base layer is determined by the bisection iteration method;
[0034] Using the reflected wave amplitude range [0.18 mm, 5.03 mm] as the initial range, the critical amplitude value for interlayer separation was determined by combining the bisection iteration method with core drilling verification.
[0035] First: Core sampling was performed on the area corresponding to the midpoint amplitude value of A = (0.18 + 5.03) / 2 = 2.6 mm (rounded to one decimal place). The core sampling results showed that the core sample had delamination and fracture, indicating that the critical amplitude value of the surface layer-base layer delamination was ≤ 2.6 mm. The new interval is [0.18 mm, 2.6 mm].
[0036] Second: Take the area corresponding to the midpoint amplitude value A = (0.18 + 2.6) / 2 = 1.4 mm in the new interval for core sampling. The core sampling results show that the core sample is continuous, which means that the critical amplitude value of the separation between the surface layer and the base layer is ≥ 1.4 mm. The new interval is [1.4 mm, 2.6 mm].
[0037] Third time: Core sampling was carried out in the area corresponding to the midpoint amplitude value A = (1.4 + 2.6) / 2 = 2.0 mm in the new interval. The core sample was in the interlayer separation state, indicating that the critical amplitude is ≤ 2.0 mm. The new interval is [1.4 mm, 2.0 mm].
[0038] Fourth time: Take the area corresponding to the midpoint amplitude value A = (1.4 + 2.0) / 2 = 1.7 mm in the new interval and perform core sampling. The core sample is continuous, indicating that the critical amplitude is ≥ 1.7 mm. The new interval is [1.7 mm, 2.0 mm].
[0039] Fifth time: Take the area corresponding to the midpoint amplitude value A = (1.7 + 2.0) / 2 = 1.9 mm in the new interval and perform core sampling. The results show that the core sample is in a continuous state between layers, which means that the critical amplitude is located in [1.9 mm, 2.0 mm].
[0040] Based on the accuracy requirement (0.1mm) of this embodiment, an amplitude of A = 2.0mm is taken as the critical amplitude value for the separation between the surface layer and the base layer. If more precision is required, the bisection method of core sampling can be continued.
[0041] S3. Establish representative values for interlayer shear modulus. Relationship with the amplitude A of the interlayer reflected wave;
[0042] Within the amplitude range [0.18mm, 2mm] of this road section, representative points corresponding to amplitude values of 0.2mm, 0.4mm, 0.6mm, 0.8mm, 1.0mm, 1.2mm, 1.4mm, 1, 6mm, 1.8mm, and 2.0mm were selected for core sampling (3 core sampling points for each amplitude value). Core samples with a diameter of 100mm were drilled and cut into shear specimens with a thickness of 100mm. The thickness of each of the upper and lower pavement structures in the shear specimen was 50mm. A direct shear test device was used to conduct shear tests under the conditions of test temperature 25℃, vertical pressure 0.7MPa, and shear rate 10mm / min. The interlayer shear modulus K of the core samples corresponding to different amplitudes was measured and multiplied by the shear rate correction factor 2.2 to obtain the interlayer shear modulus corresponding to a shear rate of 390mm / min (rounded to the nearest integer). The average value was taken as the representative value of the interlayer shear modulus corresponding to this amplitude value. The following experimental results were obtained;
[0043] Table 1. Core sample shear test results of the examples
[0044]
[0045] Then, the relationship between the interlayer reflection amplitude A and the representative value of the interlayer shear modulus was established through regression analysis (nonlinear explicit function fitting). The quantitative fitting relationship between them, namely the AK relationship; the AK relationship is shown in [link to AK formula]. Figure 1 And the following formula:
[0046] ;
[0047] The above fitting uses an allometric growth model. It is 0.94585, after adjustment It is 0.93908.
[0048] S4. Comprehensive evaluation of the interlayer condition of long-test road sections;
[0049] The long test section is divided into several basic evaluation units of equal length. Different quantiles are selected according to the highway grade as the representative amplitude values of each basic evaluation unit, denoted as A. 单元 ;
[0050] Using 1km as a basic evaluation unit, the 10km test section was divided into 10 basic evaluation units. The data sequence of all interlayer reflection amplitudes within each basic evaluation unit was obtained by arranging them in ascending order. The 90th percentile of this sequence was taken as the representative value A of the interlayer state for that basic evaluation unit. 单元 The inter-layer state representative value A of these 10 basic evaluation units 单元As shown in Table 2:
[0051] Table 2. Representative values A of 10 interlayer states in the embodiment. 单元 (Unit: mm)
[0052]
[0053] The arithmetic mean of the inter-layer state representative values of these 10 basic evaluation units, represented by unit A. The standard deviation is 1.32. The coefficient of variation is 0.11. The coefficient of variation was 8.33%. A value less than 10% indicates good homogeneity of the interlayer condition in this long test section. Therefore, the arithmetic mean of the representative values of the interlayer reflected wave amplitude of all basic evaluation units, 1.32 mm, is taken as the representative value A of the interlayer condition of this long test section. 长 The representative value A of the interlayer condition of the long-tested road section. 长 Substitute the numerical values into the representative values of inter-story shear modulus The fitting relationship (AK relationship) between the interlayer reflected wave amplitude A and the interlayer shear modulus is used to obtain the corresponding representative value. Length is 2558MN / m 3 .
[0054] Application examples
[0055] Based on the interlaminar shear modulus obtained in this application To estimate the remaining service life of in-service asphalt pavements and design for life extension.
[0056] The surface layer, base layer, and subgrade moduli of the in-service asphalt pavement were obtained by inversion using a falling weight deflectometer (FWD). The thickness of each structural layer of the in-service asphalt pavement was obtained using three-dimensional ground-penetrating radar (GPR), along with representative values of the interlayer shear moduli obtained from the above steps. A Goodman model considering the interlayer contact state of in-service asphalt pavement was established (except for the interlayer bond coefficient, which is used to represent the interlayer contact state between the surface layer and base layer of the in-service asphalt pavement, other structural layers were set to be completely continuous), and the remaining structural life N of the long test section was then estimated. f Make an estimate and design a life extension that takes into account interlayer contact conditions based on the remaining life.
[0057] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.
Claims
1. A method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground-penetrating radar, characterized in that: Includes the following steps: S1. Use high-frequency three-dimensional ground-penetrating radar to perform non-destructive testing on the target asphalt pavement, track the surface layer-base layer line, and collect the amplitude intensity value of the reflected wave at the surface layer-base interface at intervals of 10cm in the driving direction and 10cm in the perpendicular direction of driving to obtain the amplitude data of the in-phase axis reflected wave at the surface layer-base interface. Statistical analysis of these data yields the range of reflected wave amplitude intensity for the target asphalt pavement [A]. Min A Max ]; S2. The critical amplitude A1 for characterizing "interlayer separation" between the surface layer and the base layer is determined by a binary iterative method combined with core drilling verification. The iteration continues until the accuracy of A1 reaches the expected level. First, the midpoint amplitude value A is taken. mid = (A Min +A Max ) / 2, for the amplitude value A at the midpoint mid Core sampling is performed in the corresponding area. If the core sampling results show that interlayer separation and core sample fracture have occurred at the midpoint, it proves that the critical amplitude A1 is located in [A]. Min A mid If the core sample layers are continuous, then the critical amplitude A1 is located within the range [A]. mid A Max Within the new judgment interval, repeat the process of taking the midpoint amplitude value, core sampling, and verification until the critical amplitude A1 data accuracy reaches the expected level. S3. Establish a quantitative relationship between the amplitude intensity of radar reflected waves and the interlaminar shear modulus K in the Goodman model; when the amplitude value is [A Min Within the range of A1], multiple points with different amplitude values were selected. For each amplitude value, three representative points were drilled and core samples were taken. The interlayer shear modulus K of the obtained core samples was determined by indoor direct shear test, and the average value was taken as the representative value of the interlayer shear modulus corresponding to that amplitude value. Then, regression analysis was used to establish the relationship between interlayer reflection amplitude A and representative value of interlayer shear modulus. The quantitative fitting relationship between them is called the AK relationship; S4. Divide the long test section into several basic evaluation units of equal length. Select different quantiles as the amplitude representative values for each basic evaluation unit according to the highway grade, denoted as A. 单元 .
2. The method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground-penetrating radar according to claim 1, characterized in that: Step S3 establishes the relationship between inter-layer reflection amplitude A and representative value of inter-layer shear modulus through regression analysis. The quantitative fitting relationship between them is: ; In the formula, The critical amplitude, represents the fitting coefficient.
3. The method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground-penetrating radar according to claim 1, characterized in that: In step S4, all interlayer reflection amplitudes within each basic evaluation unit are arranged in ascending order to obtain a data sequence; for highways, the 95th percentile of the data sequence is taken as A. 单元 The value of A is taken as follows: For Class I highways, the 90th percentile is taken as A. 单元 The value of A is taken as follows: For secondary highways, the 85th percentile is taken as A. 单元 The value of A is taken as follows: For Class III highways, the 80th percentile is taken as A. 单元 The value of A is taken as follows: For Class IV highways, the 70th percentile is taken as A. 单元 The value of .
4. The method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground-penetrating radar according to claim 1, characterized in that: The method also includes step S4.1, which involves obtaining a representative value of the inter-layer condition of a long test road segment composed of several basic evaluation units, using the spatial variation coefficient CV, and denoted as A. 长 If the coefficient of variation CV < 10%, then take the representative value A of the interlayer reflected wave amplitude of the basic evaluation unit that makes up the long test section. 单元 The arithmetic mean of A 长 If CV ≥ 10%, cluster analysis is used to merge spatially continuous basic evaluation units with a coefficient of variation CV < 10% into several homogeneous design sub-segments, and the A value of all basic evaluation units within each sub-segment is taken. 单元 The arithmetic mean of A 长 .
5. The method for obtaining the interlayer shear modulus of asphalt pavement based on three-dimensional ground-penetrating radar according to claim 1, characterized in that: In step S1, the frequency of the high-frequency three-dimensional ground-penetrating radar is set to 300MHz to 3GHz, and the antenna spacing is 7.5cm.
Citation Information
Patent Citations
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