A Road Rutter Analysis Method for Lateral Distribution of Autonomous Driving Fleets

Abstract

The present invention discloses a method for analyzing pavement rutting for the lateral distribution of an autonomous driving fleet. First, typical asphalt pavement structure and material information are obtained to establish a model. Then, the tire contact shape is transformed from an approximate ellipse to a rectangle, the vehicle load action mode and parameters are calculated, and based on this, the load action area is divided on the model. Next, a half-sine load is used to characterize the single-vehicle load action, the interval period between the actions of the front and rear vehicles and the rest period between the actions of the front and rear fleets are calculated, and a periodic amplitude curve of the repeated load action of the fleet is obtained. Calculate the fleet load 1000 times, and obtain the initial rutting development curve of the lateral coordinate points from the time variation law of the vertical displacement at the top of the middle layer in the calculation results, and predict the later rutting depth based on this. Use a frequency curve to describe the lateral distribution and perform equivalent discretization, calculate the rutting lateral distribution curve for different traffic volumes after allocating the total traffic volume, and superimpose them after offsetting to obtain the pavement rutting under the lateral distribution of the fleet.

Description

Technical Field

[0001] The present invention belongs to the field of road engineering technology, and particularly relates to a pavement rut analysis method for the lateral distribution of autonomous driving vehicle fleets. Background Art

[0002] When autonomous driving vehicle fleets are put into large-scale use, it will lead to more channelized traffic loads, shorter following distances between vehicles, higher driving speeds, and more unified vehicle types. The change in the load form will further cause the existing pavement structure to exhibit different mechanical behaviors and responses under the action of the vehicle fleet load, ultimately affecting the long-term service performance of the road. Therefore, the research on the impact of autonomous driving vehicle fleets on pavement life has also become prominent in terms of importance and urgency. Summary of the Invention

[0003] In order to solve the technical problems mentioned in the above background art, the present invention proposes a pavement rut analysis method for the lateral distribution of autonomous driving vehicle fleets.

[0004] In order to achieve the above technical objectives, the technical solution of the present invention is as follows:

[0005] A pavement rut analysis method for the lateral distribution of autonomous driving vehicle fleets, comprising the following steps:

[0006] Step 1: Obtain asphalt pavement structure and material information based on actual engineering problems, and establish a lateral two-dimensional asphalt pavement finite element model;

[0007] Step 2: Convert the tire contact shape from an approximate ellipse to a rectangle, calculate the vehicle load action mode and parameters, and accordingly divide the load action area on the lateral two-dimensional asphalt pavement finite element model;

[0008] Step 3: Use a half-sine load to represent the single-vehicle load action, calculate the interval period between the actions of the front and rear vehicles and the rest period between the actions of the front and rear vehicle fleets, and realize the loading of the repeated vehicle fleet load through a load subroutine;

[0009] Step 4: Apply the vehicle fleet load 1000 times in the load action area, obtain the initial rut development curve of different lateral coordinate points on the road surface from the time history change of the vertical displacement at the top of the middle layer in the calculation results, and predict the later rut depth based on this;

[0010] Step 5: Use the frequency curve within a half lane to describe the lateral distribution, equivalently discretize the frequency curve within a half lane and distribute the traffic volume, calculate the rut lateral distribution curve under different traffic volumes through the initial rut development curve, and superpose them after offset to obtain the pavement rut under the lateral distribution of the vehicle fleet.

[0011] Preferably, the specific steps of Step 2 are as follows:

[0012] Step 2.1: According to the principle of stress equivalence, approximately elliptical load is simplified to rectangular load, and the acting length L of the rectangular load, the acting width B of the rectangular load, and the center distance D between two wheels are obtained;

[0013] Step 2.1.1: Calculate an approximate elliptical load composed of a rectangle of 0.4L * ×0.6L * and two semi - circles with a radius of 0.3L * according to the actual engineering situation. L * is the acting length of the elliptical load, the acting width of the elliptical load is 0.6L * , and the contact area is A, which is expressed by the formula:

[0014] A = 0.4L * ×0.6L * +(0.3L * ) 2 ×π

[0015] A = F / p

[0016]

[0017] Where: F is the single - wheel axle load, and p is the tire pressure;

[0018] Step 2.1.2: Further equivalently simplify the elliptical load obtained in Step 2.1.1 to a rectangular load, which is expressed by the formula:

[0019] L = 0.8712L * , B = 0.6L * , D = 1.5d

[0020] Where: d is the equivalent circle diameter of a single - wheel ground contact of the double - circle uniform load;

[0021] Step 2.2: Divide the load - acting width range of the two - dimensional asphalt pavement finite - element model according to the calculated rectangular load, and calculate the applied load magnitude p * for the two - dimensional plane problem according to the principle of static equivalence. The formula is expressed as:

[0022] p * = F / B.

[0023] Preferably, Step 3 specifically includes the following steps:

[0024] Step 3.1: Select a half - sine load to characterize the single - vehicle load action, that is, the load intensity changes with time t in a half - sine function. The single - vehicle load model p(t) is shown as follows:

[0025]

[0026] t 0 = 12L / v

[0027] Where: p * is the load magnitude for two-dimensional plane problems, t 0 is the acting time of a single vehicle load, L is the acting length of the rectangular load, v is the driving speed, and t is time;

[0028] Step 3.2: Calculate the interval period t 1 between the actions of the front and rear vehicles in the vehicle fleet and the rest period t 2 between the actions of the front and rear vehicle fleets. Then, a cycle T of a single action of the entire vehicle fleet is:

[0029] T = n × t 0 + (n - 1) × t 1 + t 2

[0030] Where: n is the number of vehicles in the vehicle fleet;

[0031] Step 3.3: In the Dload subroutine, achieve the repeated action of the vehicle fleet load by restricting the STEPTIME range and setting the MOD function.

[0032] Preferably, step 4 specifically includes the following steps:

[0033] Step 4.1: Determine the lateral influence range of the vehicle load on the road surface. Taking the wheel trace center point when the vehicle fleet travels along the road center line as the coordinate origin, equally spaced i lateral coordinate points are taken;

[0034] Step 4.2: Apply 1000 repeated loads of the vehicle fleet traveling along the road center line to the asphalt pavement, and output the vertical displacement time history curves at the top of the surface layer at i lateral coordinate points;

[0035] Step 4.3: Take the vertical displacement value at the end of a single cycle as the rut depth value at the end of this cycle, convert the initial vertical displacement time history curve into a relationship curve between rut depth and the number of loadings, and fit out the relationship formula to predict the later rut development.

[0036] Preferably, step 5 specifically includes the following steps:

[0037] Step 5.1: Use a mathematical method to describe the lateral distribution to obtain the frequency curve within the half lane. Divide the distribution range of the wheels into j intervals equally. The frequency value in the middle of each interval multiplied by the corresponding interval length is the distribution frequency of the vehicle fleet within each interval, thereby realizing the equivalent discretization of the lateral distribution frequency curve;

[0038] Step 5.2: Multiply the distribution frequency of the vehicle platoons in each interval by the total traffic volume to obtain the traffic volume exerted by the vehicle platoons on each interval, and calculate the rut transverse distribution curves under different traffic volumes based on the initial rut development curves of i horizontal coordinate points, that is, j rut transverse distribution curves;

[0039] Step 5.3: The offset distance is the coordinate difference between the midpoint of each interval and the center point of the wheel tracks when the vehicle platoon travels along the road center line. Superimpose the j rut transverse distribution curves after offsetting them according to the offset distance at i horizontal coordinate points, so as to obtain the pavement rut under transverse distribution.

[0040] Beneficial effects brought by adopting the above technical solution:

[0041] In the present invention, by adopting the finite element method for the conventional study of the influence of vehicle loads on the pavement, considering the interval period between the front and rear vehicles in the vehicle platoon load action, the idea of "replacing dynamic with static" in the conventional rut calculation is rejected, and the semi-sine load is used to realize the loading of the vehicle platoon load in Abaqus. However, if relying solely on this idea, the memory of the ODB result file in Abaqus will be limited by the number of load application times. Under this background, it is proposed to obtain the initial vertical displacement time history curve by loading a fixed number of times, further fit to obtain the relationship between the initial permanent deformation and the number of load applications, and predict the later ruts based on this. On the premise of a large-size model, the study of transverse distribution is realized by discretizing the transverse distribution frequency curve, translating the rut transverse distribution of the vehicle platoon acting on the road center line to different discrete points and superimposing the same horizontal coordinate points. The present invention uses the idea transformation to solve the two problems of reflecting the driving characteristics of the vehicle platoon and realizing the transverse distribution, and can effectively improve the calculation efficiency. Description of the Drawings

[0042] Figure 1 is a flowchart of a pavement rut analysis method for transverse distribution of an autonomous driving vehicle platoon according to the present invention;

[0043] Figure 2 is a calculation process diagram of the vehicle load action mode in the present invention;

[0044] Figure 3 is the load action range after the double-rectangle uniform load pattern and the two-dimensional model division in the present invention;

[0045] Figure 4 is a discrete process diagram of the transverse distribution frequency curve in the present invention;

[0046] Figure 5 is a pavement rut transverse distribution curve diagram under uniform distribution in the present invention. Detailed Embodiment

[0047] The technical solution of the present invention will be described in detail below in conjunction with the drawings.

[0048] The present invention simulates the rutting development process of an asphalt pavement under the repeated loads of an autonomous driving vehicle fleet on the premise that the vehicle fleet loads obey a certain lateral distribution. By changing the conventional thinking, the defects of the existing technology are avoided. The following further details a method for analyzing pavement rutting for the lateral distribution of an autonomous driving vehicle fleet according to the present invention through a specific example. The process is as Figure 1 shown.

[0049] Step 1: Establish a large-scale lateral two-dimensional finite element model of the asphalt pavement in the Part module to reduce the influence of the model size on the pavement mechanical response, divide each layer of the pavement, and assign corresponding material properties to each structural layer in the Property module;

[0050] Step 2: Simplify the load grounding model according to the driving characteristics of the vehicle fleet, divide the load acting zone, and calculate the magnitude of the load applied to the two-dimensional model;

[0051] Step 2.1: As Figure 2 shown, first calculate an approximately elliptical load that is more consistent with the actual situation to obtain the load acting length L * and the load acting width 0.6L * , and then for the convenience of calculation, further equivalently simplify the actual acting area into a rectangular equivalent area based on the principles of area and stress equivalence. The length of the rectangle L = 0.8712L * , and the width of the rectangle B = 0.6L * . The distance between the centers of the double wheels remains unchanged. Taking the standard axle load of 0.7 MPa as an example, the double-rectangular uniform load and the divided load acting range obtained are as Figure 3 shown;

[0052] Step 2.2: For the two-dimensional model, the applied load is transformed according to the principle of static equivalence, that is, p * = F / B = 25×10 3 N / 0.156 m = 160256 Pa;

[0053] Step 3: Use a half-sine load to characterize the action of a single vehicle load, and use the Dload subroutine to achieve the repeated action of the vehicle fleet load;

[0054] Step 3.1: When the speed v = 60 km / h, the action time t 0 of a single vehicle load = L / v = 12×0.226 m / 90 km / h = 0.10848 s ≈ 0.11 s, then the half-sine load model of a single vehicle action is p(t) = 160256sin(πt / 0.11) Pa;

[0055] Step 3.2: When the number of vehicles is 3, the vehicle spacing is 6 m, and the vehicle fleet spacing is 60 m, the interval period t between the actions of the front and rear vehicles in the vehicle fleet1 = 0.24 s, the rest period t when interacting with the front and rear vehicle fleets 2 = 2.4 s, and the period of a single action of the entire vehicle fleet is T = 3 × t 0 + 2 × t 1 + t 2 = 3.21 s;

[0056] Step 3.3: Input T and t into the Dload subroutine 1 and t 2 , use the MOD function to find the remainder of the STEP TIME with respect to the period T to obtain the time t of the current period, thereby realizing the cyclic loading of the vehicle fleet load, and imposing constraints on t to achieve the spaced action of 3 vehicles within the vehicle fleet;

[0057] Step 4: Load a fixed number of times to fit the initial rut development curve, obtain the relationship between rut depth and the number of actions at different lateral coordinate points, and predict the later rut depth;

[0058] Step 4.1: Take the center point of the wheel track when the vehicle fleet travels along the center line of the road as the coordinate origin, determine the lateral influence range of the vehicle load on the road surface as [-0.648 m, 0.648 m], equally spacedly take 77 lateral coordinate points, and the distance between adjacent coordinate points is 0.018 m;

[0059] Step 4.2: Fix the vehicle fleet to travel along the center line of the road, apply 1000 times of repeated vehicle fleet loads to the road surface structure, and output the time history curve of the vertical displacement of the road surface at 77 lateral coordinate points within the range;

[0060] Step 4.3: Take the vertical displacement at the end moment of a cycle of the vehicle fleet action as the final rut depth of each action, obtain the scatter plot of the relationship between rut depth and the number of vehicle fleet loadings, perform power exponential function fitting in Origin to obtain the initial rut development relationship. Taking the coordinate point X = 0.126 m as an example, the relationship between rut depth and the number of actions is RD = 0.0543N 0.34716 (mm);

[0061] Step 5: Divide the wheel action area to discretize the lateral distribution frequency curve, calculate the rut lateral distribution under different traffic volumes, and superimpose after offset to obtain the rut on the road surface under the lateral distribution;

[0062] Step 5.1: Taking the uniform distribution as an example, the frequency distribution curve within the half lane is equivalently discretized. Given that the distribution range of the wheels is [-0.432 m, 0.432 m], this large interval is discretized into 24 small intervals, each with a range of 0.036 m. Multiplying the frequency value at the midpoint of the small interval by the interval length gives the distribution frequency of the vehicle fleet within that interval. Given that the frequency value at each coordinate point of the uniform distribution is 0.01157 (per 10 mm), the frequency value of each interval is 0.01157×3.6 = 0.041652. The discretization process is as Figure 4 shown;

[0063] Step 5.2: Allocate the total traffic volume according to the vehicle fleet distribution frequency within each interval. When the total traffic volume is 6000000 and the number of times of vehicle fleet load action is 2000000, the number of times of action in each interval is 83304. The rut transverse distribution under this traffic volume is obtained according to the rut development relationship of 77 transverse coordinate points;

[0064] Step 5.3: Taking the center point of the wheel track as the axis, shift the j rut transverse distribution curves to the corresponding interval midpoints respectively, calculate and superimpose the rut depth values of i transverse coordinate points to obtain the rut of the road surface under this transverse distribution mode. The rut transverse distribution curve of the road surface under uniform distribution is as Figure 5 shown, with the uplift displacement being 2.596 mm, the depression displacement being 7.066 mm, and the rut depth being 9.662 mm.

[0065] The embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the present invention.

Claims

1. A pavement rut analysis method for the lateral distribution of an autonomous driving fleet, characterized in that, it includes the following steps: Step 1: Obtain asphalt pavement structure and material information based on actual engineering problems, and establish a lateral two-dimensional asphalt pavement finite element model; Step 2: Convert the tire contact shape from an approximate ellipse to a rectangle, calculate the vehicle load action mode and parameters, and accordingly divide the load action area on the lateral two-dimensional asphalt pavement finite element model; Step 3: Use a half-sine load to characterize the single-vehicle load action, calculate the interval period between the actions of the front and rear vehicles and the rest period between the actions of the front and rear fleets, and realize the loading of the fleet repeated load through a load subroutine; Step 4: Apply the fleet load 1000 times in the load action area, obtain the initial rut development curve of different lateral coordinate points on the road surface from the time history change of the vertical displacement at the top of the middle layer in the calculation results, and predict the later rut depth based on this; Step 5: Use the frequency curve within a half-lane to describe the lateral distribution, equivalently discretize the frequency curve within a half-lane and distribute the traffic volume, calculate the rut lateral distribution curve under different traffic volumes through the initial rut development curve, and superimpose them after offset to obtain the pavement rut under the lateral distribution of the fleet; The specific steps of Step 2 include the following steps: Step 2.1: According to the principle of stress equivalence, simplify the approximate elliptical load into a rectangular load, and obtain the rectangular load action length L, the rectangular load action width B, and the distance D between the centers of the two wheels; Step 2.1.1: Calculate an approximate elliptical load composed of a rectangle of 0.4L * ×0.6L * and two semi - circles with a radius of 0.3L * according to the actual engineering situation. L * is the acting length of the elliptical load, and the acting width of the elliptical load is 0.6L * , and the contact area is A, which is expressed by the formula: A = F / p In the formula: F is the single-wheel axle load, and p is the tire air pressure; Step 2.1.2: Further equivalently simplify the elliptical load obtained in Step 2.1.1 into a rectangular load, and the formula is expressed as: L = 0.8712L * , B = 0.6L * , D = 1.5d In the formula: d is the equivalent circle diameter of a single-wheel contact of the double-circle uniform load; Step 2.2: Divide the load acting width range of the two-dimensional asphalt pavement finite element model according to the calculated rectangular load, and calculate the magnitude p of the applied load according to the principle of static equivalence for two-dimensional plane problems. * The formula is expressed as: p * = F / B; The specific steps of Step 3 include the following steps: Step 3.1: Select a half-sine load to characterize the single-vehicle load action, that is, the load intensity changes with time t as a half-sine function, and the single-vehicle load model p(t) is as shown in the following formula: t 0 = 12L / v where: p * is the load magnitude for two-dimensional plane problems, t 0 is the acting time of a single vehicle load, L is the acting length of the rectangular load, v is the traveling speed, and t is the time; Step 3.2: Calculate the interval period t between the front and rear vehicles within the convoy 1 and the rest period t for the interaction between the front and rear convoys 2 , then a cycle T of a single interaction of the entire convoy is as follows: T = n×t 0 +(n - 1)×t 1 +t 2 In the formula: n is the number of vehicles in the fleet; Step 3.3: In the Dload subroutine, realize the repeated action of the fleet load by restricting the STEPTIME range and setting the MOD function; The specific steps of Step 4 include the following steps: Step 4.1: Determine the lateral influence range of the vehicle load on the road surface, take the center point of the wheel track when the fleet travels along the road center line as the coordinate origin, and equally spaced take i lateral coordinate points; Step 4.2: Apply 1000 times of the fleet repeated load to the asphalt pavement traveling along the road center line, and output the time history curve of the vertical displacement at the top of the middle layer at i lateral coordinate points; Step 4.3: Take the vertical displacement value at the end of a single cycle as the rut depth value at the end of this cycle, convert the initial vertical displacement time history curve into a relationship curve between rut depth and number of loading times, and fit out the relationship formula to predict the later rut development; The specific steps of Step 5 include the following steps: Step 5.1: Use a mathematical method to describe the lateral distribution to obtain the frequency curve within a half-lane, evenly divide the distribution range of the wheels into j intervals, and multiply the frequency value in the middle of each interval by the corresponding interval length to obtain the distribution frequency of the fleet in each interval, thereby realizing the equivalent discretization of the lateral distribution frequency curve; Step 5.2: Multiply the distribution frequency of the vehicle platoons in each interval by the total traffic volume to obtain the traffic volume exerted by the vehicle platoons on each interval. Calculate the rut transverse distribution curves under different traffic volumes, namely j rut transverse distribution curves, according to the initial rut development curves at i horizontal coordinate points. Step 5.3: The offset distance is the coordinate difference between the midpoint of each interval and the center point of the wheel tracks when the vehicle platoon travels along the road center line. Superimpose the j rut transverse distribution curves at i horizontal coordinate points after offsetting them by the offset distance, so as to obtain the pavement rut under transverse distribution.

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