A method and system for calculating asphalt pavement deflection based on traffic speed deflectometer

Abstract

The present invention discloses a method and system for calculating the deflection of an asphalt pavement based on a traffic speed deflectometer, which relates to the field of road engineering and non-destructive testing technology, including: collecting test data through TSD, and establishing a mechanical model of a typical asphalt pavement structure under different working conditions; determining the theoretical deflection slope distribution characteristics of a typical asphalt pavement structure under TSD load under different working conditions, and performing curve fitting; determining the zero-point response position of the theoretical deflection slope; calculating the deflection value of each sensor position by integral calculation based on a curve fitting method, and correcting the measured deflection slope; and comparing and evaluating the results. The present invention can improve the accuracy of the calculation of the deflection value, and solves the problems of systematic error and computational complexity existing in the traditional TSD measurement method by optimizing the deflection slope fitting curve, clarifying the deflection slope characteristics of the typical pavement structure, and setting the theoretical deflection slope zero-point position, thereby achieving a more scientific and efficient evaluation of road structure performance.

Description

Technical Field

[0001] The invention relates to the technical field of road engineering and non-destructive testing, and more particularly to a method and system for calculating the deflection of an asphalt pavement based on a traffic speed deflectometer. Background Art

[0002] Deflection plays a vital role in evaluating the strength and structural bearing capacity of the road surface, and is an important reference for designing asphalt pavements and ensuring construction quality. In recent years, the traffic speed deflectometer (TSD), as an advanced non-destructive testing device, can continuously and in real time obtain pavement deformation data without affecting traffic. In view of these advantages, TSD has been used by more and more institutions to evaluate the structural bearing capacity of asphalt pavements. The principle of TSD detection is to use the center of the wheel gap of the right double wheel group of the rear axle load of the vehicle as the starting point, and arrange multiple laser vibrometer sensors along the driving direction. During high-speed driving, the road surface deformation speed and deflection slope (i.e., the ratio of deformation speed to driving speed) near the moving load are detected, and then the detected road surface deformation speed and deflection slope are converted into deflection values.

[0003] At present, there are two main methods for converting the test results into deflection values: elastic foundation beam theory and multi-layer viscoelastic analysis solution. The elastic foundation beam theory simplifies the road surface into an infinitely long beam on an elastic foundation and evaluates the road surface performance by calculating the deflection basin curve. This method is simple to calculate and easy to implement, but it ignores the viscoelasticity and nonlinear characteristics of the pavement material and cannot accurately reflect the actual situation. The multi-layer viscoelastic analysis solution comprehensively considers the viscoelasticity of the pavement material, the nonlinearity of the structural layer, and the dynamic influence of the load, providing a more accurate theoretical basis. However, the multi-layer viscoelastic analysis method faces problems such as complex calculations, numerous parameter inputs, and difficulty in achieving rapid road detection and real-time data processing.

[0004] In order to avoid the complexity of theoretical assumptions and viscoelastic calculation formulas, the curve area integration method was proposed and applied. This method mainly uses the PCHIP interpolation method to fit the measured deflection slope data, and integrates the deflection slope curve starting from the reference sensor (i.e., S3500) located 3.5m from the load center to obtain the deflection value. This method effectively solves the problem of unreliable calculation of deflection values ​​far from the load center, but it also has some disadvantages: First, the interpolation method depends heavily on the selected sensor readings. If the sensor readings cannot accurately reflect the actual changes in the deflection slope, for example, assuming that the readings of sensors S100 or S200 are the maximum deflection slope, and the theoretical maximum deflection slope position deviates from these positions, calculation errors will occur. Second, the deflection slope is affected by various complex factors such as pavement structure, material properties, and environmental conditions. Simple interpolation methods may not fully capture the impact of these factors. In addition, the current curve area integration method generally assumes that the deflection slope at the sensor S3500 is 0 mm / m. This assumption is relatively reasonable for flexible asphalt pavements, but there is insufficient research support for its applicability to semi-rigid pavements. Therefore, the existing TSD deflection calculation method cannot achieve effective measurement and still needs further research and improvement.

[0005] Therefore, how to propose a method and system for calculating the deflection of an asphalt pavement based on a traffic speed deflectometer to improve measurement accuracy and adapt to various working conditions, improve the accuracy of deflection value calculation, especially the accuracy of actual measurement of semi-rigid base asphalt pavement is a problem that technical personnel in this field urgently need to solve. Summary of the invention

[0006] In view of this, the present invention provides a method and system for calculating the deflection of an asphalt pavement based on a traffic speed deflectometer. By optimizing the deflection slope fitting curve, clarifying the deflection slope characteristics of a typical pavement structure, and setting the theoretical deflection slope zero point position, the system error and calculation complexity problems existing in the traditional TSD measurement method are solved, and a more scientific and efficient road structure performance evaluation is achieved. In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A method for calculating asphalt pavement deflection based on a traffic speed deflectometer, comprising:

[0008] The test data was collected through TSD, and the mechanical model of the typical asphalt pavement structure under different working conditions was established using the finite element method;

[0009] Determine the theoretical deflection slope distribution characteristics of typical asphalt pavement structures under TSD loads under different working conditions, and perform curve fitting on the theoretical deflection slope distribution characteristics;

[0010] Determine the zero-point response position of the theoretical deflection slope;

[0011] Based on the selected curve fitting method, the deflection value at each sensor position is calculated by integration, and the measured deflection slope is corrected to obtain the corrected deflection value by considering the characteristics of the pavement structure and the test conditions;

[0012] The corrected deflection values ​​are compared and evaluated with the actual measured values ​​and the values ​​calculated using the finite element method.

[0013] Optionally, the typical asphalt pavement structure includes a flexible pavement and a semi-rigid pavement, and a mechanical model of the typical asphalt pavement structure is established using the finite element method; the different working conditions include different driving speeds, temperatures, base moduli, roadbed moduli and structural layer thicknesses.

[0014] Optionally, the determination of theoretical deflection slope distribution characteristics of a typical asphalt pavement structure under TSD load under different working conditions includes:

[0015] The finite element method is used for calculation, and the pavement load is the deflection slope curves of two typical asphalt pavement structures under TSD moving load; the theoretical deflection slope distribution characteristics of the two typical asphalt pavement structures under TSD load are determined, and the deflection slope curves and extreme value characteristics of the two typical asphalt pavement structures under different working conditions are obtained.

[0016] Optionally, performing curve fitting on the theoretical deflection slope distribution characteristics includes:

[0017] The finite element method is used to calculate the deflection basin data under different working conditions;

[0018] Using Table Curve software, various curve forms are fitted to the bending basin data;

[0019] The coefficient of determination R 2 The root mean square error (RMSE) index is used to comprehensively evaluate the fitting effects of various curve forms and select the optimal curve.

[0020] Optionally, the optimal curve uses a second-order composite polynomial 0 / 2 as the curve type for the deflection basin fitting, and the deflection y(x) and the deflection slope curve y′(x) are obtained according to the fitting curve in the following form:

[0021]

[0022] Where aj represents the coefficient in the fitting curve, which is determined by fitting the theoretical deflection data calculated by finite element method.

[0023] Optionally, determining the theoretical deflection slope zero-point response position includes:

[0024] The finite element analysis method is used to analyze the influence of the change of soil foundation modulus on the deflection slope at different horizontal positions;

[0025] The absolute change rate between adjacent intervals is used to characterize the change in deflection slope.

[0026] When using TSD to measure the deformation of semi-rigid base asphalt pavement structure, the length of TSD beam is extended according to the actual deflection basin range, so that the reference sensor is located outside the deflection basin;

[0027] Select a fixed soil base modulus and set multiple reference sensors in sequence according to the distance to the load center;

[0028] Taking the deflection slope at the standard distance from the load center as the reference, the absolute value of the change rate at the remaining offsets is calculated, and the distance of the reference sensor from the load center is obtained based on the stability of the deflection slope change rate.

[0029] Optionally, the calculating the deflection value at each sensor position by integration based on the selected curve fitting method comprises:

[0030] The distribution of deflection slope of semi-rigid pavement is simulated using finite element method;

[0031] Through the finite element simulation results, a new reference point with a theoretical deflection slope of 0 mm / m was found;

[0032] Analyze the difference between TSD measured data and finite element simulation values, determine the difference in deflection slope at different offset positions, and correct the deflection value;

[0033] The fitting deflection curve is obtained by using the area under curve integration method of the second-order composite polynomial CPM at the new reference point, and compared with the finite element calculated value and the corrected deflection value;

[0034] The correction results were verified by comparing the deflection values ​​calculated by finite element method to evaluate the accuracy of the correction.

[0035] Optionally, the step of correcting the measured deflection slope in consideration of the characteristics of the pavement structure and the test conditions to obtain a corrected deflection value includes:

[0036] For S i ≤X m, the fixed value of the finite element method at X m is selected as the correction amount; for S i >X m, select the finite element calculation value of the corresponding position as the correction value;

[0037] The calculation formula of the corrected deflection slope value is as follows:

[0038]

[0039] Where, DS correction value is the corrected deflection slope, mm / m; DS measured value is the deflection slope measured by TSD, mm / m; DS FE值at S3500 is the deflection slope calculated at the offset position of S3500 using the finite element method, mm / m; DS FE值at Si is the FE method in S i Calculated deflection slope at the offset position, mm / m.

[0040] Optionally, the comparing and evaluating the corrected deflection value with the actual measured value and the value calculated by the finite element method includes:

[0041] The Winkler foundation beam model, PCHIP interpolation method and optimal curve are used to fit the measured TSD deflection slope data;

[0042] By integrating the deflection slopes at different offset positions, the deflection values ​​under different methods are obtained;

[0043] The deflection values ​​calculated by each method were compared with the measured deflection values, and the error RMSE was analyzed;

[0044] The finite element calculated value is used as a benchmark to compare the deflection values ​​obtained by PCHIP interpolation method and area integration under the optimal curve fitting, and the error between the two and the theoretical deflection value calculated by finite element calculation is calculated.

[0045] Optionally, an asphalt pavement deflection calculation system based on a traffic speed deflectometer comprises:

[0046] Collection module: used to collect test data through TSD;

[0047] Finite element construction module: used to establish the mechanical model of typical asphalt pavement structure under different working conditions using finite element method;

[0048] Analysis module: used to determine the theoretical deflection slope distribution characteristics of typical asphalt pavement structures under TSD loads under different working conditions;

[0049] Curve fitting module: used to perform curve fitting on theoretical deflection slope data using Table Curve software;

[0050] Zero point response position determination module: used to determine the zero point response position of the theoretical deflection slope;

[0051] Integration module: used to calculate the deflection value at each sensor location by integration based on the selected curve fitting method;

[0052] Correction module: used to correct the measured deflection slope by taking into account the characteristics of the pavement structure and the test conditions to obtain the corrected deflection value;

[0053] Evaluation module: used to compare and evaluate the corrected deflection value with the actual measured value and the value calculated by the finite element method.

[0054] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method and system for calculating the deflection of an asphalt pavement based on a traffic speed deflectometer, which has the following beneficial effects:

[0055] The present invention proposes a method for calculating the deflection of an asphalt pavement based on a traffic speed deflectometer, comprising: collecting test data through TSD, and using the finite element method to establish a mechanical model of a typical asphalt pavement structure under different working conditions; determining the theoretical deflection slope distribution characteristics of a typical asphalt pavement structure under the action of TSD load under different working conditions, and curve fitting the theoretical deflection slope distribution characteristics; determining the zero-point response position of the theoretical deflection slope; based on the selected curve fitting method, calculating the deflection value of each sensor position by integration, and correcting the measured deflection slope by considering the characteristics of the pavement structure and the test conditions to obtain a corrected deflection value; and comparing and evaluating the corrected deflection value with the actual measured value and the finite element method calculated value. The present invention can improve the accuracy of the deflection value calculation, especially for the actual measurement of semi-rigid base asphalt pavement. By optimizing the deflection slope fitting curve, clarifying the deflection slope characteristics of the typical pavement structure, and setting the theoretical deflection slope zero point position (integral starting point), the system error and calculation complexity problems existing in the traditional TSD measurement method are solved, and a more scientific and efficient road structure performance evaluation is achieved. Furthermore, (1) the accuracy of deflection calculation is improved: by simulating multiple working conditions and accurately correcting the zero response position, the systematic error in the traditional TSD measurement method is significantly reduced, and the calculation accuracy of the deflection value is improved. (2) Wide range of applications: through simulation and verification under multiple working conditions, the universality of the method is ensured. Whether it is under different driving speeds, temperatures, material properties or structural thicknesses, this method can provide reliable deflection calculation results. (3) High computational efficiency: the improved curve area integration method simplifies the calculation process, reduces the dependence on complex theoretical models and a large number of parameter inputs, improves computational efficiency, and makes it suitable for rapid road detection and real-time data processing. (4) Scientific guidance for road maintenance and design: it provides a more accurate method for evaluating pavement structure performance, provides a scientific basis for road maintenance and design, and helps to extend the service life of roads and improve driving safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0057] Figure 1 A schematic flow chart of a method for calculating asphalt pavement deflection based on a traffic speed deflectometer provided by the present invention.

[0058] Figure 2 Schematic diagram of the TSD11 deflection detection system provided by the present invention.

[0059] Figure 3 This is a schematic diagram of the test section division provided by the present invention.

[0060] Figure 4 The deflection slope distribution diagram of a typical pavement structure provided by the present invention.

[0061] Figure 5 A schematic diagram of the cumulative probability of root mean square errors of different fitting curves provided by the present invention.

[0062] Figure 6 A schematic diagram of the deflection slope of the semi-rigid asphalt pavement under different soil base moduli provided by the present invention.

[0063] FIG. 7( a ) is a schematic diagram showing a comparison of the deflection slopes before and after correction provided by the present invention.

[0064] FIG. 7( b ) is a schematic diagram showing the comparison of deflection before and after correction provided by the present invention.

[0065] FIG8( a ) is a schematic diagram showing the fitting results of the deflection slope / deflection value at Station 1 provided by the present invention and the measured value.

[0066] FIG8( b ) is a schematic diagram of the fitting results of the deflection slope / deflection value at Station 2 provided by the present invention and the measured value.

[0067] FIG8( c ) is a schematic diagram of the fitting results of the deflection slope / deflection value at Station 1 provided by the present invention and the measured value.

[0068] FIG8( d ) is a schematic diagram of the fitting results of the deflection slope / deflection value at Station 1 provided by the present invention and the measured value.

[0069] FIG9( a ) is a schematic diagram showing a comparison between the deflection slope curve provided by the present invention when Es=60 MPa and the theoretical value.

[0070] FIG9( b ) is a schematic diagram showing a comparison between the deflection slope curve provided by the present invention when Es=100 MPa and the theoretical value.

[0071] FIG9( c ) is a schematic diagram showing a comparison between the deflection slope curve provided by the present invention when Es=140 MPa and the theoretical value.

[0072] FIG9( d ) is a schematic diagram showing a comparison between the deflection slope curve provided by the present invention when Es=200 MPa and the theoretical value. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0074] The embodiment of the present invention discloses a method for calculating the deflection of an asphalt pavement based on a traffic speed deflectometer. Figure 1 As shown, it includes: collecting test data through TSD, and using the finite element method to establish a mechanical model of a typical asphalt pavement structure under different working conditions; determining the theoretical deflection slope distribution characteristics of a typical asphalt pavement structure under TSD load under different working conditions, and curve fitting the theoretical deflection slope distribution characteristics; determining the theoretical deflection slope zero-point response position; based on the selected curve fitting method, the deflection value of each sensor position is calculated by integration, and the measured deflection slope is corrected to obtain a corrected deflection value considering the characteristics of the pavement structure and the test conditions; the corrected deflection value is compared and evaluated with the actual measured value and the finite element method calculated value. The present invention can improve the accuracy of deflection value calculation, especially for the actual measurement of semi-rigid base asphalt pavement. By optimizing the deflection slope fitting curve, clarifying the deflection slope characteristics of the typical pavement structure and setting the theoretical deflection slope zero-point position (integral starting point), the system error and calculation complexity problems existing in the traditional TSD measurement method are solved, and a more scientific and efficient road structure performance evaluation is achieved.

[0075] In a specific implementation, a method for calculating asphalt pavement deflection based on a traffic speed deflectometer includes the following specific steps:

[0076] Step 1: TSD measured data collection and processing: Select a suitable test section, use TSD to detect the road surface deformation at different speeds in the test section, record the driving speed, road surface deformation speed, deflection slope and other data at different offset positions, and process abnormal values.

[0077] In a specific embodiment: the deflection detection device TSD is used, model TSD11, the total length of the carrier vehicle is 8.6m, the rear axle load of the vehicle is 100kN, and the tire inflation pressure is 0.7MPa. The offset positions of the Doppler sensors from the rear wheel center are 0.1, 0.2, 0.3, 0.6, 0.9, 1.5m and 3.5m respectively, and the corresponding sensor names are S100, S200, S300, S600, S900, S1500 and S3500 respectively, such as Figure 2 As shown, S3500 is a reference sensor used to correct the readings of the other six sensors.

[0078] (1) To ensure that the TSD test can provide reliable road structure performance evaluation data, the total length of the test section is 1500m (at least 1000m). The specific divisions are as follows:

[0079] 1) Vehicle acceleration area: The first 300m is used for vehicle acceleration to ensure that the vehicle can smoothly reach the specified test speed.

[0080] 2) Data collection area: The middle 500-1000m is used for data collection to ensure that the vehicle travels at a constant speed within the specified speed to obtain accurate deformation data.

[0081] 3) Vehicle deceleration area: The last 200m is used for vehicle deceleration to ensure that the vehicle can decelerate safely at the end of the test. Figure 3 shown.

[0082] (2) The calibration of the Doppler sensor should be completed before the test. At the beginning of the test, all systems of the equipment should be turned on and checked to ensure that the computer, software acquisition and calculation, and warning lights are all normal. On the test section, a clear measuring line is marked on the wheel track parallel to the lane line, and the detection position is marked with paint every 10m. The center of the right rear wheel of the TSD is positioned at the starting point of the test section. Before the vehicle starts, the data acquisition system is turned on; the acceleration is completed in the acceleration area, and the speed is maintained at a constant speed of 10, 20, 30, 40, and 50 km / h in the detection area, and the laser is aligned with the drawn measuring line as much as possible until the data acquisition is stopped after passing the end point. To ensure the accuracy and reliability of the test value, each test speed is repeated 3 times, and the average value is calculated as the measurement result. Finally, the abnormal values ​​in the TSD test data are eliminated based on mathematical statistics methods.

[0083] Step 2: Establish mechanical model: Use finite element method (FE) to establish mechanical model of typical asphalt pavement structure (flexible pavement and semi-rigid pavement). Consider the viscoelastic properties of the asphalt layer and simulate the pavement deformation under TSD rolling load. The simulated working conditions include different driving speeds (vv), temperatures (T), base modulus (E b ), roadbed modulus (Es ) and structural layer thickness (H). The potential impact of these conditions on TSD theoretical deflection and deflection slope is comprehensively evaluated.

[0084] In the specific embodiment, two typical asphalt pavements are selected for evaluation: a typical flexible asphalt pavement and a typical semi-rigid asphalt pavement. The base of the flexible pavement is composed of graded crushed stone, while the base of the semi-rigid pavement is cement-stabilized crushed stone. The surface layers of both pavements are dense graded asphalt concrete AC-13, and the soil base is lime soil. The basic parameters of these two typical pavement structures are detailed in Table 1.

[0085] Table 1

[0086]

[0087] Finite element (FE) simulation was used to simulate all working conditions of two typical asphalt pavement structures, taking into full account the potential influence of different driving speeds, temperatures, surface layer thickness, base layer thickness, base layer modulus and soil subgrade modulus on the dynamic viscoelastic deflection value. The FE simulation conditions are shown in Table 2.

[0088] Table 2

[0089]

[0090]

[0091] Step 3: Clarify the theoretical deflection slope characteristics: Determine the theoretical deflection slope distribution characteristics of typical asphalt pavement structures under TSD loads. Analyze the deflection slope curves and extreme value characteristics of flexible pavements and semi-rigid pavements under different working conditions to lay the foundation for the subsequent curve fitting form and the determination of the theoretical deflection slope zero point.

[0092] In a specific embodiment, a finite element program is used for calculation, and the road surface load is a TSD moving load (taking 40 km / h as an example), and the road surface deflection slope curves of the two asphalt pavement structures are obtained as follows: Figure 4 shown.

[0093] 1) Curve characteristics: The deflection slope of the flexible asphalt pavement shows a trend of first decreasing, then increasing, and finally decreasing in the entire load application area. Figure 4 As shown on the right, the deflection slope shows a maximum value. Unlike the flexible pavement, the deflection slope of the semi-rigid asphalt pavement shows multiple extreme values, including the maximum and minimum values ​​in the front load area. In addition, under the same load conditions, the deflection slope of the semi-rigid pavement is usually lower than that of the flexible pavement, indicating a close relationship between the pavement stiffness and the deflection slope. The modulus distribution of the semi-rigid pavement is highest in the base layer, second in the surface layer, and lowest in the subgrade, so the deformation is smaller, but it is more complex and has multiple extreme values.

[0094] 2) Extreme value characteristics: After statistical analysis of the deformation results under different conditions, it was found that the maximum value position of the flexible pavement is consistent with the range of the TSD sensor, which is approximately S200-S450. For the semi-rigid pavement, the maximum value position corresponds to the range of S100-S200, and the minimum value position corresponds to the range of S300-S450. The low modulus and high elasticity of the flexible pavement will lead to more dispersed stress and deformation, resulting in a wider range of extreme value positions of the sensor. In contrast, the high modulus and low elasticity of the semi-rigid pavement will cause more concentrated stress and deformation, resulting in a narrower range of extreme value positions of the sensor.

[0095] 3) Influence of speed, temperature and base modulus: Speed, temperature and base modulus are the main factors affecting the extremum shift. Especially at high temperatures or when the structure thickness is insufficient, significant changes in the material's viscoelasticity can cause the deflection slope to change dramatically within a very short sensor range, resulting in a sudden shift in the deflection slope peak. These factors together affect the mechanical behavior of the pavement material, leading to the movement and change of the extremum.

[0096] Specifically, the deflection slope of the flexible asphalt pavement decreases significantly with the increase of horizontal distance, usually approaching 0 mm / m near the offset position of 3.5 m. In contrast, the deflection slope of the semi-rigid base asphalt pavement decreases more slowly, and the deflection slope has not yet dropped to 0 mm / m at the offset position of 3.5 m. This difference is mainly affected by the stiffness of the pavement material and the viscoelastic properties of the asphalt layer. The flexible pavement has a relatively low modulus and high elasticity, which can make the stress and deformation caused by the load more dispersed. Therefore, the deflection slope decreases rapidly to nearly zero at different offset positions away from the load center. However, for the semi-rigid pavement, the higher modulus and lower elasticity will cause the stress under the load to be more concentrated, and the deformation will not be transmitted as quickly as the flexible pavement. Therefore, even at a longer distance, the deflection slope of the semi-rigid pavement will remain at a certain level and will not drop to 0 mm / m quickly.

[0097] The analysis of theoretical values ​​shows that when TSD is used to evaluate semi-rigid pavement structures, it is particularly necessary to reselect the zero point position of the deflection slope. If the zero point position of the deflection slope (i.e., the reference sensor position) is not adjusted according to the actual pavement characteristics, it will lead to estimation errors in the conversion process from the deformation velocity measured by TSD to the deflection value, which may significantly affect the accuracy of road maintenance and design decisions.

[0098] Step 4: Fitting the theoretical deflection slope data: Taking into account the influence of different working conditions, the TableCurve software is used to fit the theoretical deflection slope data with different curves. The fitting effect is measured by the determination coefficient (R 2) and root mean square error (RMSE) to select an appropriate deflection slope curve to ensure that the selected fitting curve can accurately reflect the overall trend of the theoretical deflection slope.

[0099] In a specific embodiment, based on Table 1 and Table 2, a total of 38,400 sets of deflection basins under different working conditions were calculated using the finite element method (FE). Using Table Curve software, more than one hundred curve forms were fitted to these data, and the fitting effect was measured by the determination coefficient (R 2 ) and root mean square error (RMSE) for comprehensive evaluation.

[0100] (1) First, through R 2 >0.9, nine curve forms were initially screened out, such as Figure 5 As shown, the third-order composite polynomial: Second order composite polynomial: 2 / 2: Second order composite polynomial: 1 / 2: Second order composite polynomial: 0 / 2: Composite fraction curve: Cubic fraction curve: Quadratic fraction curve: Quintic polynomial: y = a + bx + cx 2 +dx 3 +ex 4 +fx 5 ; Quartic polynomial: y = a + bx + cx 2 +dx 3 +ex 4 , these curves show a high fitting quality. Secondly, these nine curve forms are used to fit the deflection data under all working conditions again.

[0101] In order to analyze the quality of fitting in depth, the RMSE indicator is used to further evaluate the fitting results. The calculation formula is as follows. The fitting results are divided into several categories according to the RMSE value of each function: 0-2%, 3-5%, 5-10%, 10-15%, 15-20%, 20-25%, and 25-100%, and the cumulative probability under different categories is calculated. The distribution results of the cumulative probability are shown in Figure 5 shown.

[0102]

[0103] In the formula, w cal represents the theoretical deflection value calculated by FE; w fit Represents the fitted deflection value.

[0104] according to Figure 5It can be seen that compared with other functions, the root mean square errors (RMSE) of the third-order composite polynomial, second-order composite polynomial and fifth-order polynomial are mainly concentrated in the range of 0-2%, indicating that these models provide better fitting effects. In contrast, the fitting effects of the remaining models are poor and therefore excluded from subsequent analysis.

[0105] In addition, although the third-order composite polynomial and quintic fraction curves show high accuracy in fitting the theoretical deflection values, the highest order of the derivative functions of these models reaches 6. Given that there are only 7 TSD laser sensors, high-order or complex function structures are prone to overfitting, especially when calculating the integral of the actual measured deflection slope data. Therefore, in order to avoid overfitting and simplify the computational complexity of the model, models with derivative functions exceeding 5 and models with complex derivative function structures are excluded. Finally, the second-order composite polynomial 0 / 2 was selected as the preferred curve type for deflection basin fitting and recorded as CPM. The specific deflection y(x) and deflection slope curves y′(x) are as follows:

[0106]

[0107] Taking into account the complexity of the pavement structure, the present invention selects a variety of curve forms for data fitting based on the FE calculation results of typical pavement structures under different working conditions, and calculates the coefficient of determination (R 2 ) and root mean square error (RMSE), and identified the fitting curve that best reflects the theoretical deflection slope. This method not only overcomes the limitations of the traditional interpolation method based on simplified assumptions, but also provides a more realistic deflection slope prediction method, significantly improving the prediction accuracy and adaptability of the model when dealing with complex road conditions.

[0108] Step 5: Determine the zero-point response position of the theoretical deflection slope: Considering that the existing TSD equipment generally sets the sensor S3500 as the reference sensor during detection (i.e., assuming that the deflection slope at 3.5m away from the load center is 0mm / m), whether this assumption is applicable to semi-rigid asphalt pavement structures remains to be verified. Therefore, the actual range of load propagation is determined through the theoretical deflection slope results calculated by finite element under tens of thousands of working conditions. Identify the position where the deflection slope is close to zero and establish a more scientific integral reference baseline for asphalt pavement structures.

[0109] In the specific embodiment, it can be seen from step 3 that the deflection slope of the semi-rigid base asphalt pavement at 3.5m is not 0mm / m, which indicates that the reference sensor S3500 of the TSD during detection is still located in the theoretical deflection basin. Therefore, when the TSD is used to actually measure the semi-rigid pavement, the deflection value calculated by the deflection slope must have errors. In order to accurately determine the reference position where the deflection slope is 0mm / m, it is necessary to clarify the actual range of load propagation on the semi-rigid base pavement, so as to reset a more scientific reference baseline.

[0110] Considering that the deformation of the far end of the semi-rigid base asphalt pavement is mainly affected by the soil modulus E s The influence of the soil base rebound modulus E s The values ​​are 60, 80, 100, 120, 140, 160, 180 and 200 MPa respectively. Finite element analysis was used to analyze the effect of soil modulus change on the deflection slope at different horizontal positions. The specific results are shown in Figure 6 shown.

[0111] (1) The absolute rate of change between adjacent intervals is used to characterize the change in deflection slope, as shown in the following formula:

[0112]

[0113] Where R is the absolute rate of change of the deflection slope (in mm / m 2 );D Si Indicates that in S i The deflection slope value at the position (in mm / m); S i It represents the distance (m) between the i-th sensor and the TSD load center; i represents the sensor index.

[0114] (2) Figure 6 The theoretical deflection slope curves of semi-rigid pavement structures under different soil base modulus conditions are shown. It can be found that at 3.5m from the offset position of the load center, the deflection slopes under various soil base modulus conditions did not drop to 0mm / m. For example, when the soil base modulus was set to 60, 100, 140, and 200MPa, the corresponding deflection slopes at S3500 were 0.0240mm / m, 0.0145mm / m, 0.0097mm / m, and 0.0067mm / m, respectively. These results show that as the soil base modulus decreases, the deflection slope of the semi-rigid pavement increases, the pavement deformation is more significant, and thus a larger impact range is shown in the TSD test. Therefore, when using TSD to measure the deformation of a semi-rigid base asphalt pavement structure, it is necessary to extend the length of the TSD beam according to the actual deflection basin range so that the reference sensor is located outside the deflection basin.

[0115] (3) In order to determine the exact position where the theoretical deflection slope is 0 mm / m, the soil modulus is selected as 60 MPa, and the reference sensors are set at 3.5 m, 4 m, 5 m, 6 m, 7 m, 8 m and 9 m from the load center. Based on the deflection slope at 3.5 m, the absolute values ​​of the change rates at the remaining offsets are calculated, which are 0.0172 mm / m 2 、0.0070mm / m 2 、0.0046mm / m 2 、0.0031mm / m 2 、0.0029mm / m 2 and 0.0020mm / m 2 .

[0116] The results show that as the offset increases, the rate of change of the deflection slope gradually decreases and basically stabilizes when the offset position reaches 9m. This trend shows that at the offset position of 9m, the rate of change of the deflection slope has stabilized, and the deflection response is no longer affected by the load outside this distance range and reaches a steady state. Therefore, the reference sensor needs to be set at least 9m away from the load center to ensure the accuracy of the TSD deflection calculation and the reliability of the test data.

[0117] Step 6: Deflection correction: Use the selected curve fitting method to calculate the deflection value at each sensor position by integration. In addition, for pavement structures where the deflection slope at S3500 is not 0 mm / m, the measured deflection slope needs to be corrected considering the characteristics of the pavement structure and the test conditions, and the corrected deflection value is calculated.

[0118] In a specific embodiment, according to step five, when using TSD to measure the road surface deformation of a semi-rigid pavement structure, the reference sensor needs to be set at least 9m away from the load center. However, it is currently difficult to directly change the position of the TSD vehicle reference sensor, that is, the deflection slope measured on the test road is still based on the calibrated value of the reference sensor S3500. If the currently configured vehicle continues to be used for actual measurement of the semi-rigid pavement, the measured values ​​at the 7 sensors need to be corrected. Therefore, the correction is combined with the FE theoretical value, and the specific steps are as follows:

[0119] 1) Finite element simulation: Finite element simulation is used to simulate the distribution of the deflection slope of the semi-rigid pavement. The simulation should take into account factors such as the actual pavement structure, material properties, loading speed, temperature, load size and its distribution.

[0120] 2) Determine a new reference point: Through the finite element simulation results, find a new reference point with a theoretical bending slope of 0. In this embodiment, the reference point is determined to be 9 meters away from the center of the rear axle wheel gap.

[0121] 3) Correction of existing data: Analyze the difference between TSD measured data and finite element simulation values, and determine the difference in deflection slope at different offset positions within the distance from 0m to 9m. i ≤3.5m), the fixed value of FE at 3.5m is selected as the correction value; for the position after 3.5m (S i >3.5m), select the FE calculated value of the corresponding position as the correction value. The calculation formula for the corrected deflection slope value is as follows:

[0122]

[0123] Where, DS correction value is the corrected deflection slope (in mm / m); DS measured value is the deflection slope measured by TSD (in mm / m); DSFE value at S3500 is the deflection slope calculated at the offset position of S3500 using the FE method (in mm / m); DSFE value at S i is the calculated deflection slope at the Si offset position by the FE method (in mm / m).

[0124] 4) Recalculate the deflection value: Set the zero point of the deflection slope at 9m from the load center. Then, use the area integral method under the curve of the second-order composite polynomial CPM (the area integral is expressed as AUTC, and the area integral under the curve based on CPM is expressed as AUTC-CPM) to obtain the fitted deflection curve and compare it with the finite element (FE) value and the corrected deflection value.

[0125] 5) Verify the correction results: Verify the correction results by comparing the deflection values ​​calculated by finite element (FE) to evaluate the accuracy of the correction.

[0126] As shown in Figure 7(a), the measured deflection slope of the modified semi-rigid pavement structure can accurately reflect the actual situation, thereby ensuring the accuracy and practicality of the TSD data. The specific method is as follows: When Si≤3.5m, the theoretical value (e.g., 31.273) calculated by the finite element (FE) method at S3500 is uniformly added. When Si>3.5m, the FE value at each offset is directly added.

[0127] In order to evaluate the accuracy of the corrected deflection values, the deflection values ​​obtained by the AUTC-CPM method, the deflection values ​​measured by the original TSD, and the deflection values ​​calculated using the FE method were compared as shown in Figure 7(b). The comparison results show that:

[0128] 1) There is a significant deviation between the deflection value measured by the original TSD and the theoretical deflection value predicted by the FE model, indicating that there is a large measurement error.

[0129] 2) The corrected deflection values ​​calculated using the AUTC-CPM method are highly consistent with the theoretical deflection values ​​of the FE method over the entire offset range. This close agreement between the corrected deflection values ​​and the FE model values ​​verifies the accuracy of the correction method. By effectively reducing the differences in the original TSD measurements, the AUTC-CPM method ensures that the deflection data accurately reflects the actual road conditions. Therefore, this method improves the reliability and practicality of TSD data for semi-rigid pavement structures and provides a solid foundation for the accurate integration and calculation of deflection values ​​in road engineering applications.

[0130] Step 7: Verify the calculation method: Compare the deflection values ​​obtained by the improved method with the actual measured values ​​and the values ​​calculated by the traditional FE method to evaluate the effectiveness and accuracy of the new method. Through comparative verification under various conditions, the universality and reliability of the proposed method are ensured.

[0131] In a specific embodiment, the verification method includes:

[0132] (1) Verification method 1: measured value

[0133] The Winkler foundation beam model (WBM), PCHIP interpolation method and CPM curve proposed in this invention are used to fit the measured TSD deflection slope data. Then, the deflection values ​​under different methods are obtained by integrating the deflection slopes at different offset positions (the area integral is expressed by AUTC). Finally, the deflection values ​​calculated by each method are compared with the measured deflection values ​​(output by the TSD post-processing system), and the error RMSE is analyzed. The relevant results are shown in Figure 2. Figure 8(a)-Figure 8(d) Table 3 shows the RMSE of the deflection calculated by different methods and the measured deflection value.

[0134] Table 3

[0135]

[0136] Figure 8(a)-Figure 8(d) The errors between the deflection values ​​calculated by three different methods and the actual measured values ​​are shown. It can be seen that AUTC-PCHIP and composite polynomial AUTC-CPM are closer to the TSD measured deflection values, indicating that these two methods can better reflect the measured conditions. On the contrary, there is a large deviation between the AUTC-WBM method and the measured data.

[0137] As shown in Table 3, although in certain cases, such as shown in Figure 8(c), the performance of the AUTC-CPM method is not as good as that of the AUTC-PCHIP method, in most cases, the RMSE value of the AUTC-CPM method is lower than that of the AUTC-PCHIP method. This shows that the AUTC-CPM method can more accurately capture the changes in the actual deflection slope and provide deflection predictions that are closer to the measured data.

[0138] When selecting a deflection slope model, not only the accuracy of curve fitting should be considered, but also the applicability and flexibility of the model. The CPM curve provides a high degree of adaptability to nonlinear data and its characteristics, enabling the AUTC-CPM method to cope with a variety of practical scenarios and maintain a high prediction accuracy under different foundation conditions and load characteristics.

[0139] Therefore, the AUTC-CPM method has significant advantages over the AUTC-PCHIP method in terms of adaptability and flexibility. However, since the measured TSD deflection slope is a value based on the correction of the sensor S3500, the comparison between the model proposed in this invention and the measured value only partially reflects the nonlinear characteristics and fitting quality of the fitting model, and cannot fully prove the accuracy of the measured value obtained by the vehicle's own algorithm. Therefore, it is necessary to use other methods to further verify the accuracy of the fitting model.

[0140] (2) Verification method 2: finite element theoretical value

[0141] In order to further verify the accuracy of the improved deflection calculation method, the finite element calculation value is used as a benchmark to compare the deflection values ​​obtained by AUTC-PCHIP and the modified deflection calculation method proposed in the present invention, and the error between the two and the theoretical deflection value calculated by FE is calculated.

[0142] 1) The deflection slope of the semi-rigid pavement structure obtained by finite element (FE) calculation was used to read the readings at S100, S200, S300, S600, S900, S1500 and S3500. The reading at S3500 was taken as the benchmark, and the readings at these positions were subtracted from the reading at S3500 to simulate the test value of the TSD vehicle. The fitting deflection curve was obtained using the AUTC-PCHIP method.

[0143] 2) Directly read the readings at the above positions, set the deflection slope zero point at 9m from the load center, and then use the AUTC-CPM method to obtain the fitted deflection curve. Finally, calculate the root mean square error RMSE between the fitting results of each method and the theoretical deflection value calculated by FE. The relevant results are as follows Figure 9(a)-Figure 9(d) As shown in Figure 4 and Table 4 are the RMSE of the fitting errors of different fitting curves based on the finite element calculation of deflection values.

[0144] Table 4

[0145]

[0146] Depend on Figure 9(a)-Figure 9(d) It can be seen that the selection of the reference sensor position (i.e., the point where the theoretical deflection slope is 0 mm / m) and the curve form of the deflection slope are crucial to accurately determine the deflection of the semi-rigid base pavement structure.

[0147] 1) Integration starting point: The position where the deflection slope of the semi-rigid asphalt pavement is set to zero determines the integration starting point, which has a decisive influence on the shape of the road surface deflection basin. Selecting the starting point in S3500 or S9000 will produce different deflection basin shapes due to the movement of the measurement baseline. An improperly selected starting point may lead to an inaccurate description of the pavement response, especially near the load center.

[0148] 2) Curve form: The form of the deflection slope curve obtained by PCHIP interpolation or CPM curve determines the smoothness of the curve transition and the consistency with the actual road behavior. PCHIP interpolation can ensure a smooth transition of the overall trend of the data, but its applicability in reflecting the actual deflection slope profile of the road surface is uncertain. On the other hand, the CPM curve provides a more realistic expression of the nonlinear characteristics of the road deflection slope.

[0149] In addition, it can be seen from Table 4 that the AUTC-CPM method shows lower RMSE values ​​for the deflection values ​​calculated with finite element (FE) under different test scenarios compared with the AUTC-PCHIP method. This indicates that the AUTC-CPM method has higher accuracy and can better capture the complex behavior of semi-rigid pavements under load. This superiority stems from the AUTC-CPM method's ability to adapt to a wider range of deflection shapes and its high sensitivity to different pavement conditions.

[0150] Therefore, the reasonable selection of the integral starting point and curve form has a far-reaching impact on the accurate prediction of road deflection. The improved deflection calculation method can effectively improve the accuracy and scientificity of TSD measured values, thereby providing stronger technical support for the design, maintenance and management of road projects.

[0151] The present invention proposes a deflection calculation method based on a traffic speed deflectometer (TSD). The method can improve the accuracy of deflection value calculation, especially for actual measurement of semi-rigid base asphalt pavement. By optimizing the deflection slope fitting curve, clarifying the deflection slope characteristics of typical pavement structures and setting the theoretical deflection slope zero point position (integral starting point), the system error and calculation complexity problems existing in the traditional TSD measurement method are solved, and a more scientific and efficient road structure performance evaluation is achieved. (1) Through systematic finite element simulation, the influence of various conditions such as driving speed, temperature, surface layer thickness, base layer thickness, base layer modulus and roadbed modulus on deflection and deflection slope is studied, and a large amount of simulation data of different working conditions is generated. These data are used to fit the deflection slope curve and are verified by actual measurement and traditional calculation methods. (2) Through finite element method (FE) simulation of various working conditions, the zero response position (i.e., the position where the deflection slope is 0 mm / m) of the semi-rigid base asphalt pavement under various conditions is identified and determined. This method ensures the accuracy of the zero response position under different measurement conditions and establishes a more scientific integral reference baseline. By correcting the measurement values ​​of semi-rigid pavement, it solves the systematic error problem in the traditional TSD measurement method and improves the calculation accuracy of the deflection value.

[0152] In a specific embodiment, a system for calculating the deflection of an asphalt pavement based on a traffic speed deflectometer includes:

[0153] Collection module: used to collect test data through TSD;

[0154] Finite element construction module: used to establish the mechanical model of typical asphalt pavement structure under different working conditions using finite element method;

[0155] Analysis module: used to determine the theoretical deflection slope distribution characteristics of typical asphalt pavement structures under TSD loads under different working conditions;

[0156] Curve fitting module: used to perform curve fitting on theoretical deflection slope data using Table Curve software;

[0157] Zero point response position determination module: used to determine the zero point response position of the theoretical deflection slope;

[0158] Integration module: used to calculate the deflection value at each sensor location by integration based on the selected curve fitting method;

[0159] Correction module: used to correct the measured deflection slope by taking into account the characteristics of the pavement structure and the test conditions to obtain the corrected deflection value;

[0160] Evaluation module: used to compare and evaluate the corrected deflection value with the actual measured value and the value calculated by the finite element method.

[0161] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0162] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating asphalt pavement deflection based on a traffic speed deflectometer, characterized in that: include: The test data was collected by using the traffic speed deflectometer TSD, and the mechanical model of the typical asphalt pavement structure under different working conditions was established using the finite element method; The typical asphalt pavement structure includes a flexible pavement and a semi-rigid pavement, and a mechanical model of a typical asphalt pavement structure is established using the finite element method; the different working conditions include different driving speeds, temperatures, base moduli, roadbed moduli and structural layer thicknesses; Determine the theoretical deflection slope distribution characteristics of typical asphalt pavement structures under different working conditions under the action of traffic speed deflectometer TSD load, and perform curve fitting on the theoretical deflection slope distribution characteristics; The curve fitting of the theoretical deflection slope distribution characteristics comprises: The finite element method is used to calculate the deflection basin data under different working conditions; Using Table Curve software, various curve forms are fitted to the bending basin data; The coefficient of determination R 2 The root mean square error (RMSE) index is used to comprehensively evaluate the fitting effects of various curve forms and select the optimal curve; The optimal curve uses the second-order composite polynomial 0 / 2 as the curve type for the deflection basin fitting. The deflection y(x) and the deflection slope curve y′(x) are obtained according to the fitting curve in the following form: Among them, the parameters aj represent the coefficients in the fitting curve, which are determined by fitting the theoretical deflection data calculated by finite element calculation; Determine the zero-point response position of the theoretical deflection slope; Determining the theoretical deflection slope zero-point response position includes: The finite element analysis method is used to analyze the influence of the change of soil foundation modulus on the deflection slope at different horizontal positions; The absolute change rate between adjacent intervals is used to characterize the change in deflection slope. When using the traffic speed deflectometer TSD to measure the deformation of the semi-rigid base asphalt pavement structure, the length of the traffic speed deflectometer TSD beam is extended according to the actual deflection basin range, so that the reference sensor is located outside the deflection basin; Select a fixed soil base modulus and set multiple reference sensors in sequence according to the distance to the load center; Taking the deflection slope at the standard distance from the load center as a reference, calculate the absolute value of the change rate at the remaining offsets, and obtain the distance of the reference sensor from the load center based on the stability of the deflection slope change rate; Based on the selected curve fitting method, the deflection value at each sensor position is calculated by integration, and the measured deflection slope is corrected to obtain the corrected deflection value by considering the characteristics of the pavement structure and the test conditions; The corrected deflection values ​​are compared and evaluated with the actual measured values ​​and the values ​​calculated using the finite element method.

2. The asphalt pavement deflection calculation method based on traffic speed deflectometer according to claim 1 is characterized in that: The determination of the theoretical deflection slope distribution characteristics of a typical asphalt pavement structure under different working conditions under the action of the traffic speed deflectometer TSD load includes: The finite element method is used for calculation, and the pavement load is the deflection slope curves of two typical asphalt pavement structures under the moving load of the traffic speed deflectometer TSD; the theoretical deflection slope distribution characteristics of the two typical asphalt pavement structures under the action of the traffic speed deflectometer TSD load are determined, and the deflection slope curves and extreme value characteristics of the two typical asphalt pavement structures under different working conditions are obtained.

3. The asphalt pavement deflection calculation method based on traffic speed deflectometer according to claim 1 is characterized in that: The method of calculating the deflection value at each sensor position by integration based on the selected curve fitting method includes: The distribution of deflection slope of semi-rigid pavement is simulated using finite element method; Through the finite element simulation results, a new reference point with a theoretical deflection slope of 0 mm / m was found; Analyze the difference between the measured data of the traffic speed deflectometer TSD and the finite element simulation value, determine the difference in the deflection slope at different offset positions, and correct the deflection value; The fitting deflection curve is obtained by using the area under curve integration method of the second-order composite polynomial CPM at the new reference point, and compared with the finite element calculated value and the corrected deflection value; The correction results were verified by comparing the deflection values ​​calculated by finite element method to evaluate the accuracy of the correction.

4. The asphalt pavement deflection calculation method based on traffic speed deflectometer according to claim 3 is characterized in that: The method of correcting the measured deflection slope by taking into account the characteristics of the pavement structure and the test conditions to obtain the corrected deflection value includes: For S i ≤X, the fixed value of the finite element method at X is selected as the correction amount; for S i >X position, select the finite element calculation value of the corresponding position as the correction value; The calculation formula of the corrected deflection slope value is as follows: Where, DS 修正值 is the corrected deflection slope, mm / m; DS 实测值 is the deflection slope measured by the traffic speed deflectometer TSD, mm / m; DS FE值atS3500 is the deflection slope calculated at the S3500 offset position using the finite element method, mm / m; is the FE method in S i Calculated deflection slope at the offset position, mm / m.

5. The asphalt pavement deflection calculation method based on traffic speed deflectometer according to claim 1 is characterized in that: The comparison and evaluation of the modified deflection value with the actual measured value and the finite element method calculated value respectively includes: The Winkler foundation beam model, PCHIP interpolation method and optimal curve are used to fit the measured traffic speed deflectometer TSD deflection slope data. The deflection values ​​obtained by different methods are obtained by integrating the deflection slopes at different offset positions. The deflection values ​​calculated by each method are compared with the measured deflection values, and the error RMSE is analyzed. The finite element calculated value is used as a benchmark to compare the deflection values ​​obtained by PCHIP interpolation method and area integration under the optimal curve fitting, and the error between the two and the theoretical deflection value calculated by finite element calculation is calculated.

6. An asphalt pavement deflection calculation system based on a traffic speed deflectometer, characterized in that: include: Acquisition module: used to collect test data through traffic speed deflectometer TSD; Finite element construction module: used to establish a mechanical model of a typical asphalt pavement structure under different working conditions using the finite element method; the typical asphalt pavement structure includes a flexible pavement and a semi-rigid pavement, and the mechanical model of the typical asphalt pavement structure is established using the finite element method; the different working conditions include different driving speeds, temperatures, base moduli, roadbed moduli and structural layer thickness; Analysis module: used to determine the theoretical deflection slope distribution characteristics of typical asphalt pavement structures under different working conditions under the action of traffic speed deflectometer TSD load; Curve fitting module: used to perform curve fitting on theoretical deflection slope data using Table Curve software; The curve fitting of the theoretical deflection slope distribution characteristics includes: The finite element method is used to calculate the deflection basin data under different working conditions; Using Table Curve software, various curve forms are fitted to the bending basin data; The coefficient of determination R 2 The root mean square error (RMSE) index is used to comprehensively evaluate the fitting effects of various curve forms and select the optimal curve; The optimal curve uses the second-order composite polynomial 0 / 2 as the curve type for the deflection basin fitting. The deflection y(x) and the deflection slope curve y′(x) are obtained according to the fitting curve in the following form: Among them, the parameters aj represent the coefficients in the fitting curve, which are determined by fitting the theoretical deflection data calculated by finite element calculation; The zero-point response position determination module is used to determine the theoretical deflection slope zero-point response position; the determination of the theoretical deflection slope zero-point response position includes: The finite element analysis method is used to analyze the influence of the change of soil foundation modulus on the deflection slope at different horizontal positions; The absolute change rate between adjacent intervals is used to characterize the change in deflection slope. When using the traffic speed deflectometer TSD to measure the deformation of the semi-rigid base asphalt pavement structure, the length of the traffic speed deflectometer TSD beam is extended according to the actual deflection basin range, so that the reference sensor is located outside the deflection basin; Select a fixed soil base modulus and set multiple reference sensors in sequence according to the distance to the load center; Taking the deflection slope at the standard distance from the load center as a reference, calculate the absolute value of the change rate at the remaining offsets, and obtain the distance of the reference sensor from the load center based on the stability of the deflection slope change rate; Integration module: used to calculate the deflection value at each sensor location by integration based on the selected curve fitting method; Correction module: used to correct the measured deflection slope by taking into account the characteristics of the pavement structure and the test conditions to obtain the corrected deflection value; Evaluation module: used to compare and evaluate the corrected deflection value with the actual measured value and the value calculated by the finite element method.

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