A method and system for detecting the protective performance of a highway concrete guardrail

Abstract

The application discloses a highway concrete guardrail protection performance detection method and system, relates to the technical field of concrete guardrail protection performance detection, and comprises the following steps: constructing a reference plane and obtaining a joint edge space form; combining vehicle and road parameters, calculating a vehicle incident small angle, a normal distance and a lateral gap; establishing a correlation between a vehicle running state and a guardrail local geometry; calculating an equivalent intrusion amount of surface contact and edge contact, and combining a side surface relative stiffness ratio obtained by a vibration measuring point to determine a critical switching state; obtaining a critical switching accessibility index based on vehicle running statistics, forming accessibility density and geometric contribution, and generating a protection performance detection result. The application can accurately identify a high-risk section of a concrete guardrail adjacent to a expansion joint, and improve the accuracy of protection capability evaluation.

Description

Technical Field

[0001] This invention relates to the field of concrete guardrail protective performance testing technology, and in particular to a method and system for testing the protective performance of highway concrete guardrails. Background Technology

[0002] With the continuous increase in highway traffic volume and vehicle speed, concrete guardrails installed at bridge and tunnel entrances and roadbed joints have become crucial collision prevention facilities for restraining out-of-control vehicles and reducing accidents involving vehicles veering off the road. Especially in the connection area near bridge expansion joints, geometric discontinuities such as local height differences, longitudinal misalignment, and irregular alignment can easily occur between the guardrail surface and the expansion joint edge due to structural temperature changes, concrete shrinkage and creep, support displacement, construction errors, and repeated long-term traffic loads. Furthermore, the internal reinforcement anchorage and structural details in this area differ from ordinary continuous guardrail surfaces, making the overall stiffness and stress transmission path more complex. When vehicles pass near expansion joints at high speeds, driving deviations, crosswind disturbances, and changes in road surface smoothness can cause a certain incident angle and lateral deviation relative to the road direction. Once contact occurs with local geometric discontinuities, it may induce a concentrated contact near the joint edge instead of a surface graze, increasing the risk of impact to the guardrail. Therefore, it is necessary to conduct specialized protective performance testing and evaluation of the concrete guardrail connection area near expansion joints.

[0003] Current methods for assessing the protective capabilities of highway concrete guardrails largely rely on crashworthiness calculations during the design phase or a limited number of actual vehicle crash tests. During the operational phase, the assessment of guardrail defects is primarily based on visual inspection, local geometric measurements, or simple static testing. These methods typically treat the area adjacent to expansion joints as having the same structure as ordinary straight guardrails, failing to systematically consider the relationship between joint edge geometry, guardrail connection stiffness variations, and operational parameters such as vehicle incident angle and lateral clearance. This makes it difficult to quantify the boundary conditions that cause vehicles to transition from contact with the guardrail surface to concentrated contact with the joint edge under different driving conditions. Furthermore, the lack of segmented risk distribution information along the arc length of the expansion joint hinders the timely identification of localized weak points and the provision of a basis for refined maintenance and reinforcement. Summary of the Invention

[0004] The purpose of this invention is to address the problem in the prior art of quantitatively evaluating the protective performance of concrete guardrails near bridge expansion joints and identifying local high-risk sections, taking into account the influence of guardrail spatial shape, vehicle operation status, and connection stiffness. Therefore, this invention proposes a method and system for testing the protective performance of highway concrete guardrails.

[0005] To address the problems existing in the prior art, the present invention adopts the following technical solution:

[0006] A method for testing the protective performance of highway concrete guardrails includes:

[0007] S1. Perform three-dimensional measurement on the concrete guardrail surface and expansion joints, establish a reference plane based on the three-dimensional measurement point set, and calculate the normal micro-misalignment and tangential step difference from the edge of the expansion joint to the reference plane.

[0008] S2. Based on the vehicle's heading angle, the geometric center of the front wheels, and the road direction, calculate the small incident angle of the vehicle relative to the road and the normal geometric distance from the vehicle's front wheels to the reference plane.

[0009] S3. Determine the equivalent intrusion amount of surface contact based on the normal geometric distance of the vehicle's front wheels, and determine the equivalent intrusion amount of edge contact by combining the normal micro-misalignment, tangential step difference and incident small deflection angle.

[0010] S4. Vibration measuring points are set up at the joint edge of the expansion joint and the concrete guardrail surface, and the relative stiffness ratio of the edge surface is obtained based on the vibration response.

[0011] S5. Generate critical switching accessibility index based on the relative stiffness ratio of edge and surface, the equivalent intrusion amount of edge contact, and the equivalent intrusion amount of surface contact;

[0012] S6. Generate the protection test results of the concrete guardrail based on the critical switching accessibility index.

[0013] Preferably, three-dimensional measurements are performed on the concrete guardrail surface and expansion joints. A reference plane is established based on the set of three-dimensional measurement points, and the normal micro-misalignment and tangential step difference of the expansion joint edge to the reference plane are calculated, including:

[0014] Establish a three-dimensional rectangular coordinate system in the concrete guardrail connection area adjacent to the expansion joint, and define the arc length coordinate on the center line of the expansion joint;

[0015] Temperature sensors were installed in the concrete guardrail connection area near the expansion joint to obtain temperature data.

[0016] At each temperature, the concrete guardrail surface and the edge of the expansion joint are scanned using a three-dimensional measurement device to obtain a set of three-dimensional measurement points for the guardrail surface area and a set of three-dimensional measurement points for the edge area.

[0017] Based on the spatial orientation of the expansion joint, a correspondence is established between the three-dimensional measurement points of the joint edge and the arc length coordinates to obtain the spatial position data of the joint edge;

[0018] Plane fitting is performed on the three-dimensional measurement point set of the railing area to obtain the reference plane of the concrete railing surface;

[0019] Determine the normal direction perpendicular to the concrete guardrail surface in the reference plane;

[0020] Determine the tangential direction within the reference plane of the concrete guardrail surface that extends longitudinally along the road.

[0021] By orthogonally projecting the spatial position of the seam edge onto the reference plane, the spatial offset of the seam edge relative to the reference plane is obtained.

[0022] The component of the spatial offset in the normal direction is defined as the normal micro-misalignment of the seam edge relative to the railing surface;

[0023] The component of spatial offset in the tangential direction is defined as the tangential step difference of the seam edge relative to the railing surface.

[0024] Preferably, based on the vehicle's heading angle, the geometric center of the front wheels, and the road direction, the small incident angle of the vehicle relative to the road and the normal geometric distance from the vehicle's front wheels to the reference plane are calculated, including:

[0025] Acquire the vehicle's heading angle and the spatial position data of the geometric center of the vehicle's front wheels in a three-dimensional Cartesian coordinate system;

[0026] The spatial position data of the highway centerline in a three-dimensional rectangular coordinate system is obtained, and the centerline is parameterized according to the arc length coordinate to obtain the spatial coordinate data of the centerline at different arc length positions and the corresponding road direction angle data.

[0027] The road arc length coordinates of the vehicle are determined based on the minimum distance between the spatial position data of the geometric center of the vehicle's front wheels and the spatial position data of the road centerline.

[0028] Obtain the road direction angle data corresponding to the road arc length coordinates of the vehicle, and use the difference between the vehicle's heading angle data and the road direction angle data as the small incident deflection angle of the vehicle relative to the road direction.

[0029] Based on the spatial relationship between the reference plane of the concrete guardrail surface and the geometric center of the vehicle's front wheels, calculate the normal geometric distance of the geometric center of the vehicle's front wheels relative to the reference plane of the concrete guardrail surface.

[0030] Based on the spatial position data of the road centerline and the spatial position data of the geometric center of the vehicle's front wheels, the lateral geometric offset distance of the vehicle relative to the road centerline is calculated in the lateral direction of the road.

[0031] The lateral geometric offset distance is used as the lateral clearance between the vehicle and the guardrail.

[0032] Preferably, the equivalent intrusion amount of surface contact is determined based on the normal geometric distance of the vehicle's front wheels, and the equivalent intrusion amount of edge contact is determined by combining the normal micro-misalignment, tangential step difference, and incident small deflection angle, including:

[0033] If the normal geometric distance of the front wheel of the vehicle is negative, the absolute value of the normal geometric distance is taken as the equivalent intrusion amount of the surface contact; otherwise, the equivalent intrusion amount of the surface contact is zero.

[0034] The geometric correction amount of the normal micro-misalignment along the incident direction is obtained by multiplying the normal micro-misalignment step by the cosine of the incident small deflection angle.

[0035] The geometric correction of the tangential step along the incident direction is obtained by multiplying the tangential step by the sine of the incident small deflection angle.

[0036] The equivalent intrusion amount of surface contact is obtained by adding the geometric correction amount of the normal micro-misalignment along the incident direction and the geometric correction amount of the tangential step along the incident direction.

[0037] Preferably, vibration measuring points are installed at the edges of the expansion joint and the concrete guardrail surface. The relative stiffness ratio of the edges is obtained based on the vibration response, including:

[0038] A first vibration measuring point is set at the edge of the expansion joint, and a second vibration measuring point is set at the surface of the concrete guardrail.

[0039] Vibration response data of the first and second vibration measuring points at different frequencies were collected to construct the edge frequency response function at the seam edge and the fence surface frequency response function at the fence surface.

[0040] A common resonant frequency is determined in the amplitude spectra of the edge frequency response function and the rail surface frequency response function. The ratio of the amplitude of the edge frequency response function to the amplitude of the rail surface frequency response function is calculated at the resonant frequency to obtain the relative stiffness ratio of the edge and rail surfaces.

[0041] Preferably, a critical switching accessibility index is generated based on the relative stiffness ratio of the edge to the surface, the equivalent intrusion of the edge contact, and the equivalent intrusion of the surface contact, including:

[0042] Multiply the relative stiffness ratio of the edge to the surface by the equivalent intrusion of the edge contact, and then subtract the equivalent intrusion of the surface contact to obtain the critical switching value.

[0043] When the critical switching value is not less than zero, it is determined that the critical state has been reached;

[0044] The incident angle of the vehicle and the lateral clearance between the vehicle and the guardrail are statistically analyzed to construct a joint distribution of the incident state of the vehicle and the guardrail.

[0045] By integrating the joint distribution of vehicles and incident states on the barrier that meet the critical state, the critical switching accessibility index is obtained.

[0046] Preferably, the protective test results of the concrete guardrail are generated based on the critical switching accessibility index, including:

[0047] The arc length of the expansion joint is discretized to obtain a set of discrete arc length positions;

[0048] Within a preset detection time interval, the accessibility index of critical switching corresponding to each discrete arc length position is averaged over time to obtain accessibility density data corresponding to the arc length coordinate position.

[0049] Within the preset detection time interval, for each discrete arc length position, the product of the normal micro-misalignment and the cosine of the incident small deflection angle is statistically averaged to obtain the geometric contribution of the normal micro-misalignment.

[0050] Within the preset detection time interval, for each discrete position of arc length, the product of the tangential step difference and the sine value of the incident small deflection angle is statistically averaged to obtain the geometric contribution of the tangential step difference.

[0051] The reachability density value, normal micro-misalignment geometric contribution, and tangential step difference geometric contribution corresponding to each discrete position of arc length are combined to generate the protection test results of the arc length section of the concrete guardrail.

[0052] Compared with the prior art, the beneficial effects of the present invention are:

[0053] 1. This invention establishes a detection system that describes the spatial morphology of the guardrail connection area and the relationship between the vehicle approach path and the concrete guardrail surface and expansion joints through three-dimensional scanning, combined with the actual driving posture of the vehicle on the road. It can quantify the stress risk of the guardrail during the vehicle approach process based on real traffic operation data. It can not only reflect the geometric changes of the guardrail surface and joint edges, but also combine the directional factors of the vehicle's driving direction and the tire approach path, thereby accurately depicting the possible contact state changes that may occur when the vehicle advances to the guardrail, making the detection results more consistent with the actual operating conditions.

[0054] 2. This invention, by setting up measuring points in the expansion joint area and constructing vibration response functions at different locations, can reflect the local stiffness difference between the guardrail surface and the joint edge under dynamic action. Based on the geometric proximity calculated from the vehicle's incident path, a comprehensive analysis is performed to form a quantitative index for determining the change in contact state. This quantitative index maintains consistent judgment rules under different vehicle operating conditions, enabling automatic identification of weak sections of the guardrail and significantly improving the objectivity of the detection results.

[0055] 3. This invention discretizes the guardrail connection area along the arc length of the expansion joint, averages the critical switching accessibility indices corresponding to each discrete arc length position over time to form accessibility density data, and combines the normal displacement projection and longitudinal step difference projection to obtain the normal geometric contribution and tangential geometric contribution of each arc length segment. The above quantitative results are combined to generate the arc length segment protection detection results, realizing the spatial segmental characterization and risk visualization of the protective performance of guardrails adjacent to the expansion joint. It can distinguish high-risk and low-risk parts of different arc length segments under a unified index system, providing an objective basis for formulating targeted reinforcement and repair, thereby improving the accuracy and effectiveness of the assessment of the protective performance of concrete guardrails in the expansion joint connection area without significantly increasing the detection cost. Attached Figure Description

[0056] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0057] Figure 1 A flowchart illustrating a method for testing the protective performance of highway concrete guardrails according to an embodiment of the present invention;

[0058] Figure 2 This is a functional module diagram of a highway concrete guardrail protective performance testing system provided in an embodiment of the present invention. Detailed Implementation

[0059] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0060] Example: This example provides a method for testing the protective performance of concrete guardrails on highways. See [link / reference]. Figure 1 Specifically, including:

[0061] S1. Perform three-dimensional measurement on the concrete guardrail surface and expansion joints, establish a reference plane based on the three-dimensional measurement point set, and calculate the normal micro-misalignment and tangential step difference from the edge of the expansion joint to the reference plane.

[0062] In an embodiment of the present invention, three-dimensional measurements are performed on the concrete guardrail surface and expansion joints. A reference plane is established based on the set of three-dimensional measurement points, and the normal micro-misalignment and tangential step difference from the edge of the expansion joint to the reference plane are calculated, including:

[0063] Establish a three-dimensional rectangular coordinate system in the concrete guardrail connection area adjacent to the expansion joint, and define the arc length coordinate on the center line of the expansion joint;

[0064] Temperature sensors were installed in the concrete guardrail connection area near the expansion joint to obtain temperature data.

[0065] At each temperature, the concrete guardrail surface and the edge of the expansion joint are scanned using a three-dimensional measurement device to obtain a set of three-dimensional measurement points for the guardrail surface area and a set of three-dimensional measurement points for the edge area.

[0066] Specifically, expansion joints refer to linear separation joints installed in highway concrete guardrails or bridge structures. They are used to provide necessary deformation space between concrete components under the action of temperature changes, load changes, or structural deformation, allowing adjacent structures to elongate or contract along the joint line, thereby avoiding excessive internal forces or damage caused by restraint. Expansion joints are usually arranged longitudinally along the road, and their positions form the boundary lines between components. The joint edge is the most sensitive area for structural deformation and is also the prominent location where geometric discontinuities occur in guardrail connection sections. In the protection performance test, it is necessary to focus on analyzing the spatial morphology, displacement, and deformation behavior of the expansion joint location. Arc length coordinates refer to positional parameters marked sequentially along the centerline of the expansion joint according to the length of the line segment, used to represent the positional relationship of any position on the joint edge in the direction of the centerline; the three-dimensional measurement point set of the railing area refers to a set of spatial point data obtained by scanning the surface of the concrete railing, used to characterize the geometry of the railing; the three-dimensional measurement point set of the joint edge area refers to a set of spatial point data obtained by scanning the boundary position of the expansion joint, used to describe the position of the joint edge in space; the joint edge spatial position data refers to the spatial position sequence formed by corresponding the three-dimensional measurement points of the joint edge according to the arc length coordinates, used to establish the spatial distribution relationship of the joint edge along the direction of the expansion joint.

[0067] Specifically, a spatial range covering the concrete guardrail surface and the expansion joint edge is selected on-site. A reference origin that can completely describe the spatial location of this area is determined, and a three-dimensional rectangular coordinate system is established with this reference point as the origin. Within this rectangular coordinate system, a first coordinate axis aligned with the longitudinal direction of the road, a second coordinate axis aligned with the transverse direction of the road, and a third coordinate axis set along the vertical direction are determined. This ensures that the subsequent sets of three-dimensional measurement points for both the guardrail surface and the expansion joint edge can be expressed within a unified spatial reference system. After establishing the three-dimensional rectangular coordinate system, continuous point acquisition is performed along the centerline of the expansion joint. The lengths of the line segments between each continuous point are accumulated to obtain the length distribution along the centerline of the expansion joint. This length distribution is used as the arc length coordinate of the expansion joint centerline, thus allowing any position on the expansion joint to be uniquely identified by an arc length coordinate. Within the concrete guardrail connection area adjacent to the expansion joint, considering the expansion joint's characteristic as a structural deformation sensitive area, representative locations capable of characterizing local structural temperature changes are selected. Multi-point temperature sensors are installed at these locations, with the sensing ends of the temperature sensors in direct contact with the concrete guardrail surface or the edge of the expansion joint. Temperature sensors continuously record temperature measurements at various times and output temperature data in the acquisition sequence, enabling the structural state under different temperature conditions to be directly correlated with subsequent three-dimensional measurements, thereby providing a reliable basis for analyzing the spatial deformation of the expansion joint area caused by temperature changes.

[0068] Specifically, after obtaining temperature data from the temperature sensor, a 3D scan is triggered for each temperature data point. A 3D measuring device fixed to the roadside or vehicle platform continuously scans the concrete guardrail surface area, recording multiple spatial points to form a 3D measurement point set for the guardrail area. Simultaneously, the 3D measuring device is adjusted to a scanning angle that fully covers the edge of the expansion joint, scanning the joint edge area and recording the resulting spatial points as a 3D measurement point set for the joint edge area. During the scanning process, by controlling the scanning accuracy, scanning distance, and point cloud density of the 3D measuring device, the resulting 3D measurement point set fully reflects the subtle geometric differences between the guardrail surface area and the joint edge area. This ensures that the point data completely covers the entire surface area of ​​the guardrail and the entire position of the expansion joint edge, providing a continuous, dense, and repeatable spatial point data foundation for subsequent reference plane fitting and calculations of normal micro-misalignment and tangential step difference.

[0069] Based on the spatial orientation of the expansion joint, a correspondence is established between the three-dimensional measurement points of the joint edge and the arc length coordinates to obtain the spatial position data of the joint edge;

[0070] Plane fitting is performed on the three-dimensional measurement point set of the railing area to obtain the reference plane of the concrete railing surface;

[0071] Determine the normal direction perpendicular to the concrete guardrail surface in the reference plane;

[0072] Determine the tangential direction within the reference plane of the concrete guardrail surface that extends longitudinally along the road.

[0073] Specifically, the spatial orientation of an expansion joint refers to the continuous linear path formed by the expansion joint along the road direction. Its spatial extension is used to identify the longitudinal arrangement of the joint edges. The three-dimensional measurement points of the joint edges refer to the spatial point data obtained by 3D scanning equipment at various locations along the boundary line of the expansion joint. These points record the actual spatial position of the joint edges. The spatial position data of the joint edges refers to the data sequence formed by sequentially corresponding and recording the three-dimensional measurement points of the joint edges according to the spatial orientation of the expansion joint, allowing the shape and elevation changes of the joint edges to be expressed under a stable parametric coordinate system. The set of three-dimensional measurement points for the guardrail area refers to the multiple spatial points formed by scanning the concrete guardrail surface, used to express the overall shape of the guardrail. Body shape; Plane fitting refers to finding the plane that best represents the overall posture of the fence among the three-dimensional measurement points of the fence area, so that the geometry of the fence can be expressed through a unified reference plane; The reference plane of the concrete guardrail refers to the reference plane obtained by fitting the three-dimensional measurement points of the fence area, which is used as a unified reference for calculating the changes in joint height and lateral changes; The normal direction refers to the direction perpendicular to the reference plane, which is used to represent the positional relationship of the fence surface pointing positively into space; The tangential direction refers to the direction extending longitudinally along the road in the reference plane, which is used to represent the extension trend of the fence in the road direction and to describe the lateral change law of the joint relative to the fence in the road direction.

[0074] Specifically, based on the established three-dimensional rectangular coordinate system and the arc length coordinates of the expansion joint centerline, the three-dimensional measurement points of the seam edge obtained through the three-dimensional measurement equipment are first imported into the data processing program. For each seam edge three-dimensional measurement point, its spatial coordinate components in the three-dimensional rectangular coordinate system are extracted. Then, a series of continuous points are discretized on the spatial curve model of the expansion joint centerline according to the arc length coordinates, forming a sequence of centerline reference points arranged in ascending order of arc length coordinates. For each seam edge three-dimensional measurement point, a nearest-point matching operation is performed, calculating the spatial distance from the seam edge three-dimensional measurement point to each point in the centerline reference point sequence. The centerline reference point with the smallest distance is selected, and the arc length coordinate value corresponding to this reference point is designated as the arc length coordinate of the seam edge three-dimensional measurement point. Through the above processing, each seam edge three-dimensional measurement point simultaneously carries three-dimensional spatial coordinate and arc length coordinate information, thereby forming seam edge spatial position data sorted by arc length coordinates, used to describe the spatial shape changes and elevation fluctuations of the expansion joint seam edge along the seam direction.

[0075] Specifically, when establishing a plane fitting model on the three-dimensional measurement point set of the guardrail area, the measurement points located in the exposed area of ​​the front of the guardrail are first selected as the effective point set for fitting, based on the geometric distribution range of the concrete guardrail surface. A plane fitting algorithm based on the least squares principle is then used on this effective point set to construct a reference plane equation. By calculating the sum of the squares of the distances from all effective measurement points to the target plane, the plane parameters that minimize the sum of the squares of the distances from each measurement point to the target plane are solved, thus obtaining a uniquely determined plane equation and corresponding plane normal direction in the three-dimensional rectangular coordinate system. This plane is used as the reference plane for the concrete guardrail surface. All height, distance, and direction quantities related to the guardrail surface are referenced to this reference plane. By calculating the offset of the joint edge spatial position data relative to this reference plane, geometric quantities such as normal micro-misalignment and tangential step difference can be further obtained, providing a unified geometric benchmark for the testing of the protective performance of concrete guardrails.

[0076] By orthogonally projecting the spatial position of the seam edge onto the reference plane, the spatial offset of the seam edge relative to the reference plane is obtained.

[0077] The component of the spatial offset in the normal direction is defined as the normal micro-misalignment of the seam edge relative to the railing surface;

[0078] The component of spatial offset in the tangential direction is defined as the tangential step difference between the seam edge and the fence surface;

[0079] Specifically, the normal micro-misalignment refers to the height obtained by comparing the distance difference between the projected point and the actual point of the joint edge in the normal direction of the reference plane after projecting the spatial position of the joint edge onto the reference plane of the concrete guardrail surface. It is used to characterize the degree of slight vertical misalignment of the joint edge relative to the guardrail surface. The tangential step difference refers to the distance difference in the tangential direction between the spatial position of the joint edge and the projection point of the reference plane. This direction extends along the longitudinal direction of the road and is used to characterize the forward and backward misalignment or displacement change of the joint edge relative to the guardrail surface along the road direction. These two quantities can reflect the slight vertical misalignment and longitudinal displacement of the expansion joint area caused by temperature changes or structural deformation.

[0080] Specifically, after obtaining the spatial location data of the seam edge and the reference plane of the concrete guardrail surface, the coordinate information of each spatial location point of the seam edge is first read in a three-dimensional rectangular coordinate system, along with the plane equation, normal direction, and tangential direction of the reference plane. Based on this, each spatial location point of the seam edge is treated as an independent data input. Its orthogonal projection point on the reference plane is determined through the plane equation of the reference plane; that is, by finding the unique point along the normal direction of the reference plane that allows the projection point to lie on the reference plane, the orthogonal projection process from the spatial location point of the seam edge to the reference plane is completed. After the orthogonal projection is completed, the spatial offset of the seam edge relative to the reference plane is obtained by calculating the three-dimensional coordinate difference between the spatial location point of the seam edge and its corresponding projection point. This offset can fully characterize the minute relative displacement of the seam edge point in the vertical, elevation, and longitudinal directions. After obtaining the spatial offset of the seam edge relative to the reference plane, in order to extract the core geometric quantities used for protective performance testing, the spatial offset is further decomposed along the normal direction of the reference plane. Based on the normal direction determined during the reference plane fitting process, the projected value of the offset in this direction is taken as the normal micro-misalignment of the seam edge relative to the railing surface. This quantity reflects the vertical protrusion or subsidence of the seam edge position relative to the railing reference surface, and its magnitude directly reflects the degree of discontinuity between the railing surface and the seam edge in the vertical direction. By retaining the normal micro-misalignment data of all seam edge position points, the elevation variation trend along the seam line of the expansion joint area can be comprehensively described, providing basic data support for subsequent calculations of the equivalent intrusion of surface contact and edge contact.

[0081] Specifically, after decomposing the normal micro-misalignment, to simultaneously extract the minute displacement changes of the joint edge relative to the guardrail in the longitudinal direction of the road, it is also necessary to decompose the spatial offset along the tangential direction. The tangential direction is the direction extending longitudinally along the road within the reference plane, obtained from the orientation calibration results during guardrail fitting. The projection value of the spatial offset in the tangential direction is determined as the tangential step difference of the joint edge relative to the guardrail. This quantity is used to characterize the forward and backward offset of the joint edge in the road extension direction, reflecting the displacement differences along the line caused by temperature deformation, structural relaxation, or connection construction effects of the expansion joint. By obtaining the tangential step difference data of all discrete points of the joint edge, a continuous distribution value along the arc length coordinate can be formed, which can then be used in the subsequent intrusion calculation to characterize the relative influence between the vehicle incident direction and the geometric inconsistency of the joint edge.

[0082] Specifically, through the above-mentioned orthogonal projection, direction decomposition, and parameter formation process, the complex spatial geometric relationship between the seam edge and the railing surface can be transformed into two types of structured geometric quantities: normal micro-stagger and tangential step difference. These geometric quantities have clear directional orientation, can be accurately calculated, and can be repeatedly measured, providing direct quantitative input for modeling the interaction behavior between the vehicle's incident state and the geometric discontinuity of the seam edge.

[0083] S2. Based on the vehicle's heading angle, the geometric center of the front wheels, and the road direction, calculate the small incident angle of the vehicle relative to the road and the normal geometric distance from the vehicle's front wheels to the reference plane.

[0084] In embodiments of the present invention, the calculation of the small incident angle of the vehicle relative to the road and the normal geometric distance from the front wheel of the vehicle to the reference plane, based on the vehicle's heading angle, the geometric center of the front wheel, and the road direction, includes:

[0085] Acquire the vehicle's heading angle and the spatial position data of the geometric center of the vehicle's front wheels in a three-dimensional Cartesian coordinate system;

[0086] The spatial position data of the highway centerline in a three-dimensional rectangular coordinate system is obtained, and the centerline is parameterized according to the arc length coordinate to obtain the spatial coordinate data of the centerline at different arc length positions and the corresponding road direction angle data.

[0087] Specifically, the heading angle of a vehicle refers to the angle between the vehicle's forward direction and the reference direction of the road plane, used to describe the degree of deviation of the vehicle's forward orientation during driving; the geometric center of the front wheels of a vehicle refers to the representative center point obtained by averaging the positions of the left and right wheels of the front axle, used to reflect the overall position of the front of the vehicle on the road.

[0088] Specifically, the vehicle's driving status is collected in real time using a vehicle positioning device. This device includes a heading angle acquisition module for determining the vehicle's attitude and a spatial positioning module for determining the geometric center position of the vehicle's front wheels. The heading angle acquisition module measures the vehicle's orientation and outputs the heading angle data for the current moment. The spatial positioning module, using a ranging sensor unit and a satellite positioning unit installed at the front or top of the vehicle, records the spatial position of the vehicle's front wheel geometric center in a three-dimensional Cartesian coordinate system as coordinate values ​​in three directions, enabling the vehicle's front position in space to be recorded using a unified coordinate system. To obtain the spatial location data of the road centerline in a three-dimensional rectangular coordinate system, high-precision road surveying data or point cloud acquisition of the highway center area is performed using 3D scanning equipment. The acquired centerline spatial point set is sorted according to the road direction, and a continuous spatial curve model describing the road centerline is obtained through curve fitting algorithm. Based on this spatial curve model, with the curve's starting point as the arc length zero point, the length values ​​are accumulated sequentially according to the curve's path length to generate an arc length coordinate sequence for the road centerline, so that any spatial point on the road centerline can be clearly identified with its corresponding arc length coordinates. To obtain the difference between the vehicle's driving direction and the road direction, the road direction angle is calculated at each arc length position. The road direction angle is obtained by solving for the tangential direction of the road centerline at that arc length position. This tangential direction is the directional derivative of the road centerline spatial curve at the corresponding arc length coordinate point, representing the road's extension direction in three-dimensional space. This tangential direction is projected onto the horizontal plane, and its angle value relative to the road reference direction is calculated to obtain the road direction angle corresponding to each arc length coordinate.

[0089] The road arc length coordinates of the vehicle are determined based on the minimum distance between the spatial position data of the geometric center of the vehicle's front wheels and the spatial position data of the road centerline.

[0090] Obtain the road direction angle data corresponding to the road arc length coordinates of the vehicle, and use the difference between the vehicle's heading angle data and the road direction angle data as the small incident deflection angle of the vehicle relative to the road direction.

[0091] Specifically, after acquiring the spatial position data of the vehicle's front wheel geometric center in a three-dimensional Cartesian coordinate system and the spatial position data of the highway centerline in a three-dimensional Cartesian coordinate system, the road centerline is discretized on the spatial curve model of the road centerline according to the arc length coordinates. The road centerline is divided into several adjacent arc length discrete points, each with a unique road arc length coordinate and a corresponding three-dimensional spatial coordinate. Subsequently, at any moment during the vehicle's journey, the spatial position data of the vehicle's front wheel geometric center at that moment is read, and the distance between this spatial position and the spatial coordinates of all the arc length discrete points is calculated one by one to obtain the spatial distance value from the front wheel geometric center to each arc length discrete point. The target arc length discrete point with the smallest distance value is then determined, and the road arc length coordinate corresponding to the target arc length discrete point is determined as the vehicle's road arc length coordinate at that moment. This achieves a one-to-one correspondence between the three-dimensional spatial position of the vehicle's front wheel geometric center and the arc length parameter of the road centerline, enabling the vehicle's position in the longitudinal direction of the road to be uniformly represented by road arc length coordinates.

[0092] Specifically, after obtaining the road arc length coordinates of the vehicle at each moment, to obtain the incident small deflection angle of the vehicle relative to the road direction, the road direction angle data at the same arc length position as the road arc length coordinates is read from the parameterized data of the road centerline. This road direction angle data is used to represent the extension direction of the road centerline at that arc length position. At the same moment, the vehicle's heading angle data is read, and the difference between the vehicle's heading angle data and the corresponding road direction angle data is calculated. The resulting angle difference is defined as the incident small deflection angle of the vehicle relative to the road direction. This incident small deflection angle can characterize the degree of deviation between the vehicle's forward direction and the direction of the road centerline. By recording the incident small deflection angles of different times or different vehicle samples, a unified directional parameter can be provided for subsequent calculations of the relative collision incident state and equivalent intrusion behavior between the vehicle and the concrete guardrail.

[0093] Based on the spatial relationship between the reference plane of the concrete guardrail surface and the geometric center of the vehicle's front wheels, calculate the normal geometric distance of the geometric center of the vehicle's front wheels relative to the reference plane of the concrete guardrail surface.

[0094] Based on the spatial position data of the road centerline and the spatial position data of the geometric center of the vehicle's front wheels, the lateral geometric offset distance of the vehicle relative to the road centerline is calculated in the lateral direction of the road.

[0095] The lateral geometric offset distance is used as the lateral clearance between the vehicle and the guardrail;

[0096] Specifically, the normal geometric distance refers to the distance obtained by projecting the position of the geometric center of the vehicle's front wheels along the normal direction of the reference plane in a three-dimensional rectangular coordinate system, using the concrete guardrail surface as the reference plane. It represents the degree of approach or departure of the vehicle's front wheel geometric center in the direction perpendicular to the guardrail surface. This distance is a key geometric quantity for subsequent judgment of whether the vehicle has made surface contact intrusion. The lateral geometric offset distance refers to the lateral distance obtained by projecting the position of the vehicle's front wheel geometric center relative to the road centerline in the road plane, using the lateral direction of the road centerline as the reference direction. It describes the offset of the vehicle on the road cross-section. This distance can reflect the lateral approach of the vehicle relative to the guardrail.

[0097] Specifically, after obtaining the reference plane of the concrete guardrail surface and the spatial position data of the vehicle's front wheel geometric center in a three-dimensional rectangular coordinate system, the plane equation parameters of the reference plane and the normal direction perpendicular to the reference plane are extracted from the fitting results of the reference plane. An arbitrary point on the reference plane is selected as a reference point, and the spatial coordinates of this reference point are subtracted from the spatial coordinates of the vehicle's front wheel geometric center to obtain a spatial vector pointing from the reference plane to the vehicle's front wheel geometric center. This spatial vector is projected along the normal direction of the reference plane, and the resulting projection length is taken as the normal geometric distance of the vehicle's front wheel geometric center relative to the reference plane of the concrete guardrail surface. According to the orientation convention of the reference plane's normal direction, the distance towards the guardrail is recorded as a negative value, and the distance away from the guardrail is recorded as a positive value. This ensures that the normal geometric distance reflects both the proximity of the vehicle's front wheel to the guardrail surface and can be directly used as an input to determine whether the vehicle has intruded into the normal region of the guardrail surface when calculating the equivalent intrusion amount of surface contact.

[0098] Specifically, when calculating the lateral geometric offset distance of a vehicle relative to the road centerline, firstly, based on the vehicle's road arc length coordinates determined in the previous step, a centerline spatial point corresponding to these coordinates is selected from the parameterized road centerline data. This centerline spatial point is used as the reference position of the vehicle in the longitudinal direction of the road at the current moment. A spatial vector is constructed in a three-dimensional Cartesian coordinate system, pointing from the centerline spatial point to the geometric center of the vehicle's front wheels. A lateral direction is defined within the road plane, perpendicular to the tangential direction of the road centerline and pointing towards the guardrail. The spatial vector is then projected onto the lateral direction of the road, and the resulting projection length is the lateral geometric offset distance of the vehicle relative to the road centerline. According to the orientation convention of the lateral direction, the distance offset towards the guardrail is recorded as a positive value, and the distance offset away from the guardrail is recorded as a negative value. This ensures that the lateral geometric offset distance accurately represents the vehicle's lateral offset position on the road cross-section and can be directly used as the basic data for the lateral clearance between the vehicle and the guardrail. This provides a quantitative basis for subsequently determining the risk area where the vehicle may come into contact with the concrete guardrail, and the lateral geometric offset distance is used as the lateral clearance between the vehicle and the guardrail.

[0099] S3. Determine the equivalent intrusion amount of surface contact based on the normal geometric distance of the vehicle's front wheels, and determine the equivalent intrusion amount of edge contact by combining the normal micro-misalignment, tangential step difference and incident small deflection angle.

[0100] In embodiments of the present invention, the equivalent intrusion amount of surface contact is determined based on the normal geometric distance of the vehicle's front wheels, and the equivalent intrusion amount of edge contact is determined by combining the normal micro-misalignment, tangential step difference, and small incident deflection angle, including:

[0101] If the normal geometric distance of the front wheel of the vehicle is negative, the absolute value of the normal geometric distance is taken as the equivalent intrusion amount of the surface contact; otherwise, the equivalent intrusion amount of the surface contact is zero.

[0102] The geometric correction amount of the normal micro-misalignment along the incident direction is obtained by multiplying the normal micro-misalignment step by the cosine of the incident small deflection angle.

[0103] The geometric correction of the tangential step along the incident direction is obtained by multiplying the tangential step by the sine of the incident small deflection angle.

[0104] The equivalent intrusion amount of surface contact is added to the geometric correction amount of the normal micro-misalignment along the incident direction and the geometric correction amount of the tangential step along the incident direction to obtain the equivalent intrusion amount of edge contact.

[0105] Specifically, the equivalent intrusion amount of surface contact refers to the intrusion amount obtained by calculating the distance along the normal direction of the geometric center of the vehicle's front wheel along the reference plane, with the reference plane of the concrete guardrail surface as a reference. When the normal geometric distance is negative, it indicates that the geometric center of the vehicle's front wheel has entered the normal space region of the guardrail surface. Its absolute value is used as the equivalent intrusion amount of surface contact, which is used to describe the degree of direct intrusion of the vehicle into the guardrail in the vertical contact state. The equivalent intrusion amount of edge contact refers to the equivalent intrusion amount obtained by superimposing the synthetic effect between the vehicle's incident direction and the geometrical change of the joint edge, based on the equivalent intrusion amount of surface contact, while also considering the normal micro-misalignment, tangential step difference and directional component of the small incident angle of the vehicle at the joint edge. This amount is used to characterize the degree of edge contact intrusion caused by the local geometrical discontinuity of the joint edge when the vehicle is incident at an oblique angle.

[0106] Specifically, the absolute value of the negative normal geometric distance of the vehicle's front wheels is used as the equivalent intrusion amount for surface contact. This is because in distance calculations using the reference plane of the concrete guardrail surface as a reference surface, a negative normal geometric distance means that the geometric center of the vehicle's front wheels has entered the inner region of the guardrail surface in the normal direction. This indicates that the vehicle and the guardrail surface have actually approached and penetrated each other in the vertical direction. Therefore, its absolute value is needed to record the intrusion depth of the vehicle relative to the guardrail surface. When the normal geometric distance is positive, it means that the geometric center of the vehicle's front wheels is located outside the guardrail surface in the normal direction, and no form of normal penetration has occurred. The vehicle and the guardrail still maintain a safe distance. Therefore, in this case, the equivalent intrusion amount for surface contact is taken as zero to clearly distinguish between the two states of actual intrusion and no intrusion.

[0107] Specifically, the calculation of the equivalent intrusion amount of edge contact is based on the directional decomposition relationship of the vehicle's incident path in space. This is achieved by separately calculating the components of the normal micro-misalignment along the incident direction and the tangential step difference along the incident direction, and then adding them to the equivalent intrusion amount of surface contact. This allows for a unified measurement of the overall intrusion depth generated when the vehicle deviates from the guardrail, all within the same incident direction. The product of the normal micro-misalignment and the cosine of the incident small deflection angle represents the actual approach amount formed by the projection of the height change of the joint edge perpendicular to the guardrail surface along the vehicle's incident direction. The product of the tangential step difference and the sine of the incident small deflection angle represents the additional approach amount formed by the horizontal step of the joint edge along the road direction on the vehicle's incident path. The contact between the vehicle and the guardrail is not a one-way contact, but a comprehensive approach process dominated by the vehicle's actual deflection angle. Therefore, by adding the equivalent intrusion amount of surface contact, the geometric correction amount of the normal micro-misalignment along the incident direction, and the geometric correction amount of the tangential step difference along the incident direction, the comprehensive intrusion depth of the vehicle relative to the joint edge in the current incident state can be obtained, which is the equivalent intrusion amount of edge contact. This method can fully project the impact of the geometrical abrupt change in the seam edge on the vehicle's approach behavior onto the vehicle's actual approach direction, truly reflecting the degree of lateral contact that the vehicle may have with the guardrail.

[0108] S4. Vibration measuring points are set up at the joint edge of the expansion joint and the concrete guardrail surface, and the relative stiffness ratio of the edge surface is obtained based on the vibration response.

[0109] In an embodiment of the present invention, vibration measuring points are arranged at the edge of the expansion joint and the surface of the concrete guardrail. The relative stiffness ratio of the edge surfaces is obtained based on the vibration response, including:

[0110] A first vibration measuring point is set at the edge of the expansion joint, and a second vibration measuring point is set at the surface of the concrete guardrail.

[0111] Vibration response data of the first and second vibration measuring points at different frequencies were collected to construct the edge frequency response function at the seam edge and the fence surface frequency response function at the fence surface.

[0112] A common resonant frequency is determined in the amplitude spectra of the edge frequency response function and the rail surface frequency response function. At the resonant frequency, the ratio of the amplitude of the edge frequency response function to the amplitude of the rail surface frequency response function is calculated to obtain the relative stiffness ratio of the edge and rail surfaces.

[0113] Specifically, the relative stiffness ratio refers to the ratio between the vibration response amplitudes of the expansion joint edge and the concrete guardrail surface under the same excitation conditions. It characterizes the overall resistance to deformation of the edge relative to the surface under stress. Due to differences in structural connection methods, geometry, and material continuity, the deformation degree of the edge under external dynamic forces usually differs from that of the surface. When vibration measuring points are set up at both locations and the corresponding vibration amplitudes are measured under the same frequency excitation, if the frequency response amplitude of the edge is significantly greater than that of the surface, it indicates that the edge is more prone to deformation and its stiffness is relatively lower; conversely, it indicates that the edge is more rigid and has stronger resistance to deformation. Therefore, dividing the frequency response function amplitude of the edge by that of the surface yields the degree of stiffness comparison between the two, which is the relative stiffness ratio. This quantity can intuitively reflect the true resistance level of the geometrically weak points of the expansion joint, providing a basic parameter for determining the key structural response during edge contact.

[0114] Specifically, a first vibration measuring point is fixedly installed on the exposed surface of the expansion joint edge of the concrete guardrail, ensuring that the sensing axis of this measuring point is aligned with the vibration direction of the joint edge surface. Simultaneously, a second vibration measuring point is fixedly installed on a flat area of ​​the concrete guardrail surface, ensuring that the sensing axis of the second measuring point is aligned with the main vibration direction of the guardrail surface. To ensure the stability of the measurement results, both the first and second vibration measuring points are installed using secure adhesive or mechanical fastening to prevent relative slippage during subsequent excitation. After the two types of vibration measuring points are deployed, excitation signals of different frequencies are applied to the joint edge and guardrail surface locations using an external excitation device, and vibration response data of the first and second measuring points at each frequency are collected simultaneously. The vibration response data includes the response amplitude and phase information at the corresponding frequency, and the acquisition system records the data according to a fixed sampling frequency and recording format. To cover the main range of structural energy response, the excitation frequency increases sequentially from low to high frequencies, ensuring that both measuring points produce stable response data at the same set of frequencies.

[0115] Specifically, after acquiring complete vibration response data, the response amplitudes of the first vibration measuring point under excitation at various frequencies are organized into a sequence varying with frequency, constructing the edge frequency response function at the seam edge location. Noise interference is filtered to ensure the frequency response function is continuous and usable for subsequent analysis. Simultaneously, the response amplitudes of the second vibration measuring point under excitation at the same frequency are organized into another sequence varying with frequency, constructing the railing frequency response function at the railing location. Both frequency response functions are plotted with frequency on the x-axis and vibration amplitude on the y-axis to reflect the mechanical response characteristics of the structure at different locations. After obtaining the edge frequency response function at the seam edge location and the railing frequency response function at the railing location, the frequency response data for both are organized from low to high frequency. The vibration response amplitudes corresponding to each frequency point are plotted as amplitude spectrum curves with frequency on the x-axis and amplitude on the y-axis. By observing the peak distribution of amplitude variation with frequency, frequency points with significantly amplified amplitudes in both the edge frequency response function and the railing frequency response function are identified. Frequency points in the two amplitude spectra that are close in frequency position and simultaneously exhibit amplitude peaks are selected as candidate resonant frequencies. Multiple candidate frequencies are compared one by one, and the frequency point with the most obvious amplitude peak and sharpest peak shape is selected as the common resonant frequency. This frequency represents the main resonant characteristics of both the seam edge and the railing surface. After determining the common resonant frequency, the vibration response amplitude of the edge frequency response function at that resonant frequency is read and used as the response amplitude of the seam edge in the resonant state. Simultaneously, the vibration response amplitude of the railing surface frequency response function at the same resonant frequency is read and used as the response amplitude of the railing surface in the resonant state. Dividing the response amplitude of the seam edge by the response amplitude of the railing surface yields the amplitude ratio of the two at the same resonant frequency. This amplitude ratio is defined as the relative stiffness ratio of the edges and surfaces. Since, under the same excitation frequency and input energy conditions, a larger response amplitude indicates a smaller local stiffness, and a smaller response amplitude indicates a larger local stiffness, comparing the response amplitudes of the seam edge and the fence surface at the same resonant frequency and calculating their ratio can quantitatively reflect the difference in the deformation resistance of the seam edge relative to the fence surface. Thus, the relative stiffness ratio of the edge and the fence surface can be used as a quantifiable index of stiffness for subsequent critical switching evaluation and protective performance analysis.

[0116] S5. Generate critical switching accessibility index based on the relative stiffness ratio of edge and surface, the equivalent intrusion amount of edge contact, and the equivalent intrusion amount of surface contact;

[0117] In embodiments of the present invention, a critical switching reachability index is generated based on the edge-to-surface relative stiffness ratio, the equivalent intrusion amount of edge contact, and the equivalent intrusion amount of surface contact, including:

[0118] Multiply the relative stiffness ratio of the edge to the surface by the equivalent intrusion of the edge contact, and then subtract the equivalent intrusion of the surface contact to obtain the critical switching value.

[0119] When the critical switching value is not less than zero, it is determined that the critical state has been reached;

[0120] Specifically, the critical switching value refers to a judgment quantity calculated based on the numerical relationship between the relative stiffness ratio of the edge and surface, the equivalent intrusion amount of edge contact, and the equivalent intrusion amount of surface contact during the process of a vehicle approaching a concrete guardrail. This judgment quantity is used to measure the tendency of the vehicle to make contact along the seam edge in its current incident state. When the critical switching value is not less than zero, it means that the approach tendency of the vehicle along the incident direction, after considering the deformation resistance of the seam edge, is still greater than or equal to its approach degree along the normal direction of the guardrail surface. At this time, the approach relationship of the vehicle reaches the boundary condition of transitioning from surface contact to edge contact. The magnitude of the critical switching value reflects the sensitivity of the vehicle approaching the seam edge position and is an important indicator for judging the impact risk of local weak points in the concrete guardrail. The critical state refers to the state in which the vehicle's incident contact relationship, judged according to the critical switching value, is at the boundary position. This state indicates that the vehicle's incident direction and intrusion tendency have reached the transition boundary between surface contact and edge contact. In this state, the distance relationship between the vehicle and the concrete guardrail and the actual deformation resistance of the seam edge position together make the contact mode at the critical point between the two paths. Further deviation of the vehicle will preferentially result in edge contact at the seam edge position rather than surface contact along the normal direction of the guardrail surface. Identifying critical states helps analyze whether there are high-risk areas in expansion joints and their adjacent structures, providing a basis for guardrail performance evaluation and maintenance.

[0121] Specifically, when calculating the relative stiffness ratio of the edge and surface, the equivalent intrusion amount of edge contact, and the equivalent intrusion amount of surface contact, the relative stiffness ratio of the edge and surface is first multiplied by the equivalent intrusion amount of edge contact. The purpose is to scale the intrusion tendency in the edge contact direction according to the deformation resistance of the seam edge region, based on the deformation bearing capacity of the edge position relative to the surface position. This scaled value reflects the effective intrusion degree when the vehicle contacts the edge. A larger relative stiffness ratio of the edge and surface indicates stronger deformation resistance at the seam edge, resulting in a smaller effective intrusion amount under the same intrusion tendency; a smaller relative stiffness ratio indicates that the seam edge is more easily deformed, resulting in a larger effective intrusion amount under the same intrusion tendency. Therefore, multiplication links the intrusion tendency with local deformation resistance. After obtaining the effective intrusion amount in the edge contact direction, the equivalent intrusion amount of surface contact is subtracted to compare the intrusion risk of the edge contact path and the surface contact path at the same scale. The effective intrusion amount in surface contact represents the degree of intrusion when the vehicle directly presses against the guardrail in the normal direction, while the effective intrusion amount in the edge contact direction represents the intrusion tendency when the vehicle deviates towards the seam edge area in the incident direction. By subtracting the two, it can be determined whether the vehicle's incident state is more inclined to cause edge contact. When the difference is not less than zero, it indicates that the vehicle's approach tendency in the incident direction, after considering the seam edge's deformation resistance, still exceeds the intrusion degree of the surface contact path, that is, the vehicle's approach relationship has entered a critical state of deviating towards the seam edge.

[0122] The incident angle of the vehicle and the lateral clearance between the vehicle and the guardrail are statistically analyzed to construct a joint distribution of the incident state of the vehicle and the guardrail.

[0123] By integrating the joint distribution of the vehicle and the incident state of the barrier that meet the critical state, the critical switching accessibility index is obtained.

[0124] Specifically, to construct a joint distribution of the incident states of vehicles and guardrails, firstly, within a preset detection time interval, the incident small deflection angle values ​​of all vehicles entering the detection area and the lateral gap values ​​between the vehicles and the guardrails are extracted sequentially. The preset detection time interval can be determined based on the representativeness of vehicle traffic volume and the stability requirements of guardrail deformation changes, ensuring that the acquired data fully reflects the actual incident state distribution of the expansion joint area under typical traffic loads. These two types of data are numbered according to the vehicle passage time to form an original sample set. Subsequently, the incident small deflection angle values ​​are discretized and divided according to preset angle intervals to form a set of discrete angle segments; simultaneously, the lateral gap values ​​are discretized and divided according to lateral distance intervals to form a set of discrete gap segments. Furthermore, a correspondence is established between the discrete segment of the incident angle of each vehicle and the discrete segment of the lateral clearance. By statistically analyzing the frequency of different combinations of discrete segments of different angles and different discrete segments of different clearances, the probability value of each combination is calculated, thereby generating a joint distribution of the vehicle and barrier incident states with the incident angle as the horizontal axis and the lateral clearance as the vertical axis. This joint distribution can fully describe the incident trend of the vehicle under different incident angles and clearance conditions, providing basic data for subsequent critical state probability analysis.

[0125] Specifically, after obtaining the joint distribution of the incident states of vehicles and guardrails, it is necessary to filter out all combinations of incident small deflection angles and lateral clearances that satisfy the critical state based on the judgment results of the critical state. For each combination of discrete angle segments and discrete clearance segments, when its corresponding critical switching value is not less than zero, the combination is marked as a critical state combination, and the probability value corresponding to the combination is extracted from the joint distribution. Subsequently, the probability values ​​of all critical state combinations are accumulated and integrated according to the two-dimensional coordinate range of the joint distribution, that is, the area of ​​the region satisfying the critical state is summed on the probability density plane of the joint distribution. The resulting integral is the critical switching accessibility index. This index represents the overall probability level of vehicles reaching the critical state in actual traffic operation, reflects the potential collision risk of concrete guardrails in the expansion joint area, and provides a quantitative basis for the structural reliability assessment and safety maintenance of this area.

[0126] S6. Generate the protection test results of the concrete guardrail based on the critical switching accessibility index;

[0127] In an embodiment of the present invention, generating the protection test results of the concrete guardrail based on the critical switching accessibility index includes:

[0128] The arc length of the expansion joint is discretized to obtain a set of discrete arc length positions;

[0129] Within a preset detection time interval, the accessibility index of critical switching corresponding to each discrete arc length position is averaged over time to obtain accessibility density data corresponding to the arc length coordinate position.

[0130] Specifically, based on the arc length coordinates defined on the centerline of the expansion joint, the total arc length of the expansion joint is statistically analyzed from the starting arc length to the ending arc length to obtain the total arc length value. Then, according to the detection accuracy requirements and the spatial scale of vehicle incident state changes, a uniform arc length step is set within the total arc length range. The expansion joint is divided into several arc length segments at equal intervals along the centerline direction, such that the arc length difference between the endpoints of adjacent arc length segments equals the set arc length step. Using the center arc length position of each arc length segment as a representative point, the arc length coordinates corresponding to these representative points are organized into a set of discrete arc length positions, so that each discrete position on the expansion joint is identified by a unique arc length coordinate, facilitating the subsequent mapping of vehicle incident state and critical switching accessibility index to specific positions. Within the detection time interval, several time slices are divided according to a uniform time step. Critical state statistics and joint distribution integration are performed on vehicle samples passing through the discrete arc length position within each time slice to obtain the critical switching accessibility index corresponding to that time slice. Subsequently, the accessibility index of the critical switching at the same discrete location of arc length across all time slices is arithmetically averaged, and the resulting average value is used as the accessibility density data corresponding to that arc length coordinate location. The accessibility density data reflects the time-averaged probability level of a vehicle reaching the critical state at that location within the complete detection time interval, thus forming a continuously distributed risk density sequence along the arc length direction, providing a quantitative basis for identifying high-risk areas in different arc length segments of the expansion joint.

[0131] Specifically, within a preset detection time interval, the critical switching accessibility index value for each discrete arc-length location is statistically analyzed at different time slices. The preset detection time interval can be determined based on the representativeness of vehicle traffic volume and the stability requirements of guardrail deformation changes, ensuring that the acquired data fully reflects the actual incident state distribution of the expansion joint area under typical traffic loads. Specifically, the detection time interval is divided into several time slices with a uniform time step. For vehicle samples passing through the discrete arc-length location within each time slice, critical state statistics and joint distribution integration are performed to obtain the critical switching accessibility index corresponding to that time slice. Subsequently, the critical switching accessibility index of the same discrete arc-length location is arithmetically averaged across all time slices, and the resulting average value is used as the accessibility density data corresponding to that arc-length coordinate location. The accessibility density data reflects the average probability level of a vehicle reaching the critical state at that location within the complete detection time interval, thus forming a continuously distributed risk density sequence along the arc length direction, providing a quantitative basis for identifying high-risk areas in different arc-length segments of the expansion joint.

[0132] Within the preset detection time interval, for each discrete arc length position, the product of the normal micro-misalignment and the cosine of the incident small deflection angle is statistically averaged to obtain the geometric contribution of the normal micro-misalignment.

[0133] Within the preset detection time interval, for each discrete position of arc length, the product of the tangential step difference and the sine value of the incident small deflection angle is statistically averaged to obtain the geometric contribution of the tangential step difference.

[0134] The reachability density value, the geometric contribution of the normal micro-misalignment, and the geometric contribution of the tangential step difference corresponding to each discrete position of arc length are combined to generate the protection test results of the arc length section of the concrete guardrail.

[0135] Specifically, based on the aforementioned set of discrete arc-length positions, each discrete arc-length position on the expansion joint is treated as an independent statistical unit. For each vehicle sample passing through that position within the detection time interval, its corresponding data record is retrieved. In each vehicle data record, the normal micro-misalignment value and the incident small deflection angle value at that discrete arc-length position are read. The cosine value of the incident small deflection angle is obtained through trigonometric function calculations. Multiplying the normal micro-misalignment value by the cosine value of the incident small deflection angle yields the single normal projection of the vehicle at that discrete arc-length position. The above calculation steps are repeated for all vehicles passing through that discrete arc-length position within the detection time interval, forming a set of normal projection sample values. Subsequently, a statistical averaging operation is performed on this sample set, for example, using an arithmetic mean. The sum of all normal projection values ​​is divided by the number of vehicle samples to obtain the geometric contribution of the normal micro-misalignment corresponding to that discrete arc-length position. The geometric contribution of the normal micro-misalignment is statistically averaged by multiplying the normal micro-misalignment by the cosine of the incident small deflection angle because the contact between the vehicle and the guardrail does not always occur perpendicularly. Instead, the effective component of the contact action in the normal direction of the guardrail surface is determined by the vehicle's incident direction. The normal micro-misalignment itself only describes the vertical undulation of the seam edge relative to the guardrail surface, while the vehicle does not always approach the guardrail directly. The cosine of the incident direction and the guardrail surface normal reflects the degree of the vehicle's approach to the guardrail. Multiplying the normal micro-misalignment by the cosine of the incident direction is equivalent to extracting the normal contact contribution that actually occurs during the vehicle's approach. Statistically averaging this product at each time point within the detection time interval reflects the typical normal geometric influence of the discrete arc-length position under actual traffic conditions, thus forming the geometric contribution of the normal micro-misalignment.

[0136] Specifically, within the preset detection time interval, to obtain the geometric contribution of the tangential step difference for each discrete arc-length position, based on the set of discrete arc-length positions, all vehicle samples at each discrete arc-length position within the detection time interval are statistically analyzed one by one. In each vehicle data record, the tangential step difference value and the incident small deflection angle value of the vehicle at that discrete arc-length position are read. The sine value of the incident small deflection angle is obtained through trigonometric function calculations. The tangential step difference value is multiplied by the sine value of the incident small deflection angle to obtain the single tangential projection of the vehicle at that discrete arc-length position. The above calculation is repeated for all vehicles passing through that discrete arc-length position within the detection time interval, resulting in a set of tangential projection sample values. A statistical average is then performed on this sample set. The sum of all tangential projection values ​​is divided by the number of vehicle samples to obtain the geometric contribution of the tangential step difference corresponding to that discrete arc-length position. The geometric contribution of the tangential step difference is statistically averaged by multiplying the tangential step difference by the sine of the incident small deflection angle because the tangential step difference is distributed along the longitudinal direction of the road, and its direction of action is not consistent with the incident direction of the vehicle. The sine of the incident small deflection angle of the vehicle relative to the road direction characterizes the effective projection of the vehicle's incident direction in the tangential direction. The influence of the tangential step difference on the contact state depends only on the tangential component of the vehicle's incident direction. Multiplying the tangential step difference by the sine of the incident direction yields the effective portion of the tangential step difference that can truly be converted into vehicle contact geometric intrusion. Taking the statistical average of this effective portion within the detection time interval reflects the typical tangential geometric influence corresponding to the discrete position of that arc length under actual traffic incident behavior, thus obtaining the geometric contribution of the tangential step difference.

[0137] Specifically, the accessibility density data refers to the value obtained by averaging the critical switching accessibility index corresponding to each discrete arc-length position within a preset detection time interval, using discrete arc-length positions as statistical units. This data represents the overall probability level of a vehicle reaching the critical switching state at that arc-length position. It quantifies the cumulative effects of factors such as vehicle incident state, lateral clearance, and structural response in a single quantitative form, reflecting the risk exposure degree of that arc-length position under long-term operating conditions. The normal micro-misalignment geometric contribution refers to the value obtained by multiplying the normal micro-misalignment at a specific discrete arc-length position by the cosine of the vehicle's small incident angle within a preset detection time interval, and averaging the results over all vehicle samples. This value describes the average vertical geometric abrupt change intensity along the vehicle's incident direction at that arc-length position. This contribution reflects the long-term cumulative effect of the subtle height difference between the seam edge and the barrier surface in the vertical direction during the vehicle's approach path. The tangential step geometric contribution refers to the value obtained by multiplying the tangential step at a specific arc length discrete position within a preset detection time interval by the sine of the small incident angle of the vehicle and averaging it over all vehicle samples. It is used to describe the average longitudinal geometric discontinuity intensity at that arc length position along the incident direction of the vehicle. This contribution reflects the cumulative effect of the horizontal displacement generated by the seam edge in the road direction on vehicle operation.

[0138] Specifically, after obtaining the accessibility density data, normal micro-misalignment geometric contribution, and tangential step difference geometric contribution corresponding to each discrete arc length position on the expansion joint, the system first uses the set of discrete arc length positions as an index to read the accessibility density value, normal micro-misalignment geometric contribution value, and tangential step difference geometric contribution value for each discrete arc length position. These three values ​​are then arranged in a fixed order to form a ternary evaluation data entry for that discrete arc length position. To facilitate lateral comparisons between different arc length positions, the values ​​in the ternary evaluation data entry are uniformly scaled according to a pre-set reference range, ensuring that the accessibility density value, normal micro-misalignment geometric contribution, and tangential step difference geometric contribution are numerically comparable. Based on this, according to engineering experience or design requirements, weight coefficients are assigned to the accessibility density value, the geometric contribution of the normal micro-misalignment, and the geometric contribution of the tangential step difference. The three indicators are weighted and combined to obtain the comprehensive protection evaluation value corresponding to the discrete position of the arc length. The discrete positions of the arc length that are adjacent along the arc length direction and have similar comprehensive protection evaluation values ​​are merged into segments. The comprehensive protection evaluation value, accessibility density level, and corresponding geometric contribution information of each merged arc length segment are output as the protection test result of that arc length segment. This forms the distribution of concrete guardrail arc length segment protection test results covering the entire expansion joint area, which is used to guide on-site maintenance and local reinforcement decisions.

[0139] like Figure 2The diagram shown is a functional block diagram of a highway concrete guardrail protection performance testing system provided in an embodiment of the present invention.

[0140] In this embodiment, the functions of each module / unit are as follows:

[0141] The parameter reconstruction module is used to perform three-dimensional measurements on the concrete guardrail surface and expansion joints. It establishes a reference plane based on the set of three-dimensional measurement points and calculates the normal micro-misalignment and tangential step difference from the edge of the expansion joint to the reference plane.

[0142] The incident attitude module is used to calculate the small incident angle of the vehicle relative to the road and the normal geometric distance from the front wheel of the vehicle to the reference plane based on the vehicle's heading angle, the geometric center of the front wheel, and the road direction.

[0143] The equivalent intrusion module is used to determine the equivalent intrusion amount of surface contact based on the normal geometric distance of the vehicle's front wheels, and to determine the equivalent intrusion amount of edge contact by combining the normal micro-misalignment, tangential step difference and incident small deflection angle.

[0144] The relative stiffness ratio module is used to set up vibration measuring points at the joint edge of the expansion joint and the concrete guardrail surface, and obtain the relative stiffness ratio of the edge surface based on the vibration response.

[0145] The accessibility index module is used to generate critical switching accessibility indices based on the relative stiffness ratio of the edge to the surface, the equivalent intrusion of the edge contact, and the equivalent intrusion of the surface contact.

[0146] The performance testing module is used to generate protection test results for concrete guardrails based on the critical switching accessibility index.

[0147] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for testing the protective performance of highway concrete guardrails, characterized in that, include: S1. Perform three-dimensional measurement on the concrete guardrail surface and expansion joints, establish a reference plane based on the three-dimensional measurement point set, and calculate the normal micro-misalignment and tangential step difference from the edge of the expansion joint to the reference plane. S2. Based on the vehicle's heading angle, the geometric center of the front wheels, and the road direction, calculate the small incident angle of the vehicle relative to the road and the normal geometric distance from the vehicle's front wheels to the reference plane. S3. Determine the equivalent intrusion amount of surface contact based on the normal geometric distance of the vehicle's front wheels, and determine the equivalent intrusion amount of edge contact by combining the normal micro-misalignment, tangential step difference and incident small deflection angle. S4. Vibration measuring points are set up at the joint edge of the expansion joint and the concrete guardrail surface, and the relative stiffness ratio of the edge surface is obtained based on the vibration response. S5. Generate critical switching accessibility index based on the relative stiffness ratio of edge and surface, the equivalent intrusion amount of edge contact, and the equivalent intrusion amount of surface contact; The specific steps for generating critical switching accessibility indices based on the relative stiffness ratio of the edge and surface, the equivalent intrusion of edge contact, and the equivalent intrusion of surface contact are as follows: Multiply the relative stiffness ratio of the edge to the surface by the equivalent intrusion of the edge contact, and then subtract the equivalent intrusion of the surface contact to obtain the critical switching value. When the critical switching value is not less than zero, it is determined that the critical state has been reached; The incident angle of the vehicle and the lateral clearance between the vehicle and the guardrail are statistically analyzed to construct a joint distribution of the incident state of the vehicle and the guardrail. By integrating the joint distribution of the vehicle and the incident state of the barrier that meet the critical state, the critical switching accessibility index is obtained. S6. Generate the protection test results of the concrete guardrail based on the critical switching accessibility index; The specific steps for generating the protective test results of concrete guardrails based on the critical switching accessibility index are as follows: The arc length of the expansion joint is discretized to obtain a set of discrete arc length positions; Within a preset detection time interval, the accessibility index of critical switching corresponding to each discrete arc length position is averaged over time to obtain accessibility density data corresponding to the arc length coordinate position. Within the preset detection time interval, for each discrete arc length position, the product of the normal micro-misalignment and the cosine of the incident small deflection angle is statistically averaged to obtain the geometric contribution of the normal micro-misalignment. Within the preset detection time interval, for each discrete position of arc length, the product of the tangential step difference and the sine value of the incident small deflection angle is statistically averaged to obtain the geometric contribution of the tangential step difference. The reachability density value, normal micro-misalignment geometric contribution, and tangential step difference geometric contribution corresponding to each discrete position of arc length are combined to generate the protection test results of the arc length section of the concrete guardrail.

2. The method for testing the protective performance of highway concrete guardrails according to claim 1, characterized in that, Three-dimensional measurements were performed on the concrete guardrail surface and expansion joints. A reference plane was established based on the set of three-dimensional measurement points. The normal micro-misalignment and tangential step difference from the edge of the expansion joint to the reference plane were calculated, including: Establish a three-dimensional rectangular coordinate system in the concrete guardrail connection area adjacent to the expansion joint, and define the arc length coordinate on the center line of the expansion joint; Temperature sensors were installed in the concrete guardrail connection area near the expansion joint to obtain temperature data. At each temperature, the concrete guardrail surface and the edge of the expansion joint are scanned using a three-dimensional measurement device to obtain a set of three-dimensional measurement points for the guardrail surface area and a set of three-dimensional measurement points for the edge area. Based on the spatial orientation of the expansion joint, a correspondence is established between the three-dimensional measurement points of the joint edge and the arc length coordinates to obtain the spatial position data of the joint edge; Plane fitting is performed on the three-dimensional measurement point set of the railing area to obtain the reference plane of the concrete railing surface; Determine the normal direction perpendicular to the concrete guardrail surface in the reference plane; Determine the tangential direction within the reference plane of the concrete guardrail surface that extends longitudinally along the road. By orthogonally projecting the spatial position of the seam edge onto the reference plane, the spatial offset of the seam edge relative to the reference plane is obtained. The component of the spatial offset in the normal direction is defined as the normal micro-misalignment of the seam edge relative to the railing surface; The component of spatial offset in the tangential direction is defined as the tangential step difference of the seam edge relative to the railing surface.

3. The method for testing the protective performance of highway concrete guardrails according to claim 2, characterized in that, Based on the vehicle's heading angle, front wheel geometric center, and road direction, calculate the vehicle's incident angle relative to the road and the normal geometric distance from the vehicle's front wheels to the reference plane, including: Acquire the vehicle's heading angle and the spatial position data of the geometric center of the vehicle's front wheels in a three-dimensional Cartesian coordinate system; The spatial position data of the highway centerline in a three-dimensional rectangular coordinate system is obtained, and the centerline is parameterized according to the arc length coordinate to obtain the spatial coordinate data of the centerline at different arc length positions and the corresponding road direction angle data. The road arc length coordinates of the vehicle are determined based on the minimum distance between the spatial position data of the geometric center of the vehicle's front wheels and the spatial position data of the road centerline. Obtain the road direction angle data corresponding to the road arc length coordinates of the vehicle, and use the difference between the vehicle's heading angle data and the road direction angle data as the small incident deflection angle of the vehicle relative to the road direction. Based on the spatial relationship between the reference plane of the concrete guardrail surface and the geometric center of the vehicle's front wheels, calculate the normal geometric distance of the geometric center of the vehicle's front wheels relative to the reference plane of the concrete guardrail surface. Based on the spatial position data of the road centerline and the spatial position data of the geometric center of the vehicle's front wheels, the lateral geometric offset distance of the vehicle relative to the road centerline is calculated in the lateral direction of the road. The lateral geometric offset distance is used as the lateral clearance between the vehicle and the guardrail.

4. The method for testing the protective performance of highway concrete guardrails according to claim 3, characterized in that, The equivalent intrusion amount for surface contact is determined based on the normal geometric distance of the vehicle's front wheels, and the equivalent intrusion amount for edge contact is determined by combining the normal micro-misalignment, tangential step difference, and small incident deflection angle, including: If the normal geometric distance of the front wheel of the vehicle is negative, the absolute value of the normal geometric distance is taken as the equivalent intrusion amount of the surface contact; otherwise, the equivalent intrusion amount of the surface contact is zero. The geometric correction amount of the normal micro-misalignment along the incident direction is obtained by multiplying the normal micro-misalignment step by the cosine of the incident small deflection angle. The geometric correction of the tangential step along the incident direction is obtained by multiplying the tangential step by the sine of the incident small deflection angle. The equivalent intrusion amount of surface contact is obtained by adding the geometric correction amount of the normal micro-misalignment along the incident direction and the geometric correction amount of the tangential step along the incident direction.

5. The method for testing the protective performance of highway concrete guardrails according to claim 4, characterized in that, Vibration measuring points are installed at the edges of the expansion joints and on the concrete guardrail surface. The relative stiffness ratio of the edges is obtained based on the vibration response, including: A first vibration measuring point is set at the edge of the expansion joint, and a second vibration measuring point is set at the surface of the concrete guardrail. Vibration response data of the first and second vibration measuring points at different frequencies were collected to construct the edge frequency response function at the seam edge and the fence surface frequency response function at the fence surface. A common resonant frequency is determined in the amplitude spectra of the edge frequency response function and the rail surface frequency response function. The ratio of the amplitude of the edge frequency response function to the amplitude of the rail surface frequency response function is calculated at the resonant frequency to obtain the relative stiffness ratio of the edge and rail surfaces.

6. A highway concrete guardrail protective performance testing system, applied to the highway concrete guardrail protective performance testing method according to any one of claims 1-5, characterized in that, The system includes: The parameter reconstruction module is used to perform three-dimensional measurements on the concrete guardrail surface and expansion joints. It establishes a reference plane based on the set of three-dimensional measurement points and calculates the normal micro-misalignment and tangential step difference from the edge of the expansion joint to the reference plane. The incident attitude module is used to calculate the small incident angle of the vehicle relative to the road and the normal geometric distance from the front wheel of the vehicle to the reference plane based on the vehicle's heading angle, the geometric center of the front wheel, and the road direction. The equivalent intrusion module is used to determine the equivalent intrusion amount of surface contact based on the normal geometric distance of the vehicle's front wheels, and to determine the equivalent intrusion amount of edge contact by combining the normal micro-misalignment, tangential step difference and incident small deflection angle. The relative stiffness ratio module is used to set up vibration measurement points at the joint edge of the expansion joint and the concrete guardrail surface, and obtain the relative stiffness ratio of the edge surface based on the vibration response. The accessibility index module is used to generate critical switching accessibility indices based on the relative stiffness ratio of the edge to the surface, the equivalent intrusion of the edge contact, and the equivalent intrusion of the surface contact. The performance testing module is used to generate protection test results for concrete guardrails based on the critical switching accessibility index.

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