A collapsible loess area highway underground cavity GPR forward model construction method

Abstract

The application provides a collapsible loess area highway underground cavity GPR forward model construction method, and relates to the technical field of forward simulation. The method comprises the following steps: step S1, a multi-layer geological model is established for the collapsible loess area highway; step S2, a cavity model is established in the bottom layer of the multi-layer geological model, including a regular cavity model and an irregular boundary cavity model; step S3, according to the ground dry and wet state, random parameters of each stratum are generated, and the establishment of the underground cavity GPR forward model is completed; and step S4, forward simulation is performed in gprMax, and a forward result is obtained. The application can quickly generate a cavity model, dynamically simulate the parameters (such as dielectric constant, conductivity, etc.) of the stratum in the dry and wet states of the collapsible loess area, improve the establishment efficiency of various forward models, expand the required data sample size of GPR research, and provide more comprehensive data support for underground cavity detection under complex geological conditions.

Description

Technical Field

[0001] This invention relates to the field of forward modeling technology, and in particular to a method for constructing a GPR forward model of underground cavities in highways in collapsible loess areas. Background Technology

[0002] The development of underground cavities in highways in collapsible loess areas is a key contributing factor to roadbed settlement, pavement collapse, and structural instability, seriously threatening transportation safety and sustainable economic development. Loess is characterized by its tendency to disintegrate when exposed to water, making it more prone to forming hidden cavities and soil holes. Furthermore, the distribution of these cavities exhibits significant randomness and spatial heterogeneity.

[0003] Ground-penetrating radar (GPR), as an efficient non-destructive testing method, analyzes the characteristics of underground anomalies by analyzing electromagnetic wave reflection signals and has been widely used in highway defect detection. However, most existing GPR forward modeling models are based on deterministic medium assumptions, which oversimplify the medium model, usually simplifying loess layers as homogeneous or layered media, and lack sufficient modeling of parameter stochasticity.

[0004] The parameters of collapsible loess (such as dielectric constant and electrical conductivity) are influenced by factors such as water content and density, exhibiting strong spatiotemporal variability. Simultaneously, the morphology, size, and location distribution of underground cavities also exhibit significant randomness and spatial heterogeneity. Existing methods, employing fixed parameter sets for forward modeling, struggle to reflect the statistical characteristics of parameter distribution, failing to accurately characterize the complexity of collapsible loess strata and the randomness of cavity formation. This results in limited accuracy in cavity identification and insufficient ability to classify cavities.

[0005] Therefore, it is urgent to construct a GPR forward model that integrates the theory of stochastic cavitation media with multiphysics coupling to improve the accuracy and robustness of underground cavity detection in collapsible loess areas and provide a more reliable scientific basis for highway maintenance decisions. Summary of the Invention

[0006] The purpose of this invention is to provide a method for constructing a forward model of underground cavities in collapsible loess areas, which can quickly generate cavity models and dynamically simulate parameters (such as dielectric constant and conductivity) of strata in collapsible loess areas under both dry and wet conditions. This improves the efficiency of establishing various forward models, expands the amount of data samples required for GPR research, and provides more comprehensive data support for the detection of underground cavities under complex geological conditions.

[0007] To achieve the above objectives, a method for constructing a GPR forward model of underground cavities in highways in collapsible loess areas includes the following steps:

[0008] Step S1: Establish a multi-layer geological model for highways in collapsible loess areas;

[0009] Step S2: Establish a cavity model in the bottom layer of the multi-layer geological model, including a regular cavity model and an irregular boundary cavity model;

[0010] Step S3: Based on the dry and wet conditions of the ground, generate random parameters for each stratum to complete the establishment of the underground cavity GPR forward model;

[0011] Step S4: Perform forward modeling in gprMax to obtain the forward modeling results.

[0012] Preferably, the specific process of step S1 is as follows:

[0013] Step S101: Collect geological survey data of the target area. Based on the actual distribution characteristics of collapsible loess layers, initially establish a six-layer geological model including two asphalt structural layers for road surface, a waterproof layer, a cement crushed stone layer, a gravel layer, and a rammed loess layer.

[0014] Step S102: Based on the geological survey data, parameterize the thickness of each stratum in the six-layer geological model;

[0015] Step S103: Set the grid resolution to complete the establishment of the multi-layer geological model.

[0016] Preferably, the specific process of step S2 is as follows:

[0017] Step S201: Set up multiple void models, including regular void models and irregular boundary void models;

[0018] Among them, the regular void models include cylindrical void models, triangular prism void models, cubic void models, trapezoidal prism void models, and elliptical prism void models;

[0019] Step S202: Set the parameters for each cavity model;

[0020] Step S203: Place the various types of cavity models into the six-layer geological model of step S101 according to their center positions to complete the preliminary modeling;

[0021] Step S204: Visualize the modeling results and output the model results.

[0022] Preferably, the parameter settings in step S202 are as follows:

[0023] For cylindrical cavity models, the center position and base radius need to be set; for triangular prism cavity models, the center position, base length, and height need to be set; for cube cavity models, the center position and lengths of the major and minor sides need to be set; for trapezoidal prism cavity models, the center position, lengths of the top and bottom bases, and height need to be set; for elliptical prism cavity models, the center position and lengths of the major and minor axes need to be set; for irregular boundary cavity models, the center position and irregularity need to be set, with the base upper and lower boundary range being 0.6m × 0.32m, the parameter selection range being 0 to 1, and the default value being 0.3.

[0024] The preferred construction process for the irregular boundary void model is as follows:

[0025] After obtaining the coordinates of the cavity center point, the cavity center point (x, y) in the physical coordinate system is... center ,y center Convert to grid index coordinates (c) x ,c y The specific expression is:

[0026]

[0027] Where Δx and Δy represent the grid resolution;

[0028] In the polar coordinate system, 50 angles are uniformly sampled to generate an angle sampling sequence, the specific expression of which is:

[0029]

[0030] Where, θ k represents the k-th sampling angle in polar coordinates; i represents the total number of angle sampling points.

[0031] The basic radius is calculated using the following expression:

[0032]

[0033] Where, r x Indicates the lateral foundation radius; r y Represents the longitudinal base radius; ∈ represents the irregularity parameter controlling the overall expansion of the shape; n x ,n y Indicates the grid size;

[0034] Random perturbations are superimposed along the basic radius direction to generate an instantaneous radius with normally distributed noise; different standard deviations σ are used in the x and y directions respectively. x σ y This generates asymmetric fluctuations; the specific expression is:

[0035]

[0036] in, Indicates the instantaneous lateral radius; Represents the instantaneous longitudinal radius; θ k The value represents the sampling angle in polar coordinates; k represents the index value of the angle sampling sequence; e represents the perturbation coefficient. This indicates that the mean is 0 and the variance is 0. The normal distribution function; This indicates that the mean is 0 and the variance is 0. The normal distribution function;

[0037] The vertex sequence is obtained through polar coordinate to Cartesian coordinate transformation, and the specific expression is as follows:

[0038]

[0039] Where, x k y k This represents the coordinates of the k-th vertex of the cavity boundary in the Cartesian coordinate system. The instantaneous radius function in the x-direction; The instantaneous radius function in the y-direction is represented by T; T represents the instantaneous time at the k-th vertex.

[0040] This ultimately resulted in a sequence of closed polygonal outlines. Where ζ represents the total number of vertices of the closed polygonal contour.

[0041] Preferably, the parameters in step S3 include relative permittivity, conductivity, relative permeability, and magnetic loss rate.

[0042] Preferably, the specific process of step S3 is as follows:

[0043] Step S301: Set the parameters of each stratum under dry conditions and determine their value range;

[0044] Step S302: Set the parameters of each stratum under wetland conditions and determine their value range;

[0045] Step S303: Before modeling, the dry / wet state of the ground needs to be selected, and the value range of the corresponding parameters needs to be determined according to the selected dry / wet state of the ground.

[0046] Step S304: Randomly generate specific parameter values ​​within the selected parameter value range, and assign the generated specific parameter values ​​to the corresponding formation.

[0047] Preferably, the specific process of step S4 is as follows:

[0048] Step S401: Export the random parameters of each stratum and the names of their corresponding strata generated in step S3 as txt format files and store them.

[0049] Step S402: Save the underground cavity GPR forward model results generated in step S3 as an h5 file;

[0050] Step S403: Write the in file required by gprMax, and import the txt file in step S401 and the h5 file in step S402 to set up the model;

[0051] Step S404: Set the model size, resolution, time window, initial position of the electromagnetic wave transmitter, initial position of the receiver, dielectric constant reading, electromagnetic wave transmission frequency, transmitter and receiver movement step size, and absorption boundary width information in the in file; Step S405: Perform forward modeling simulation using gprMax software, generate an out file, and output the forward modeling result B-Scan image after integration.

[0052] Therefore, the present invention employs the above-mentioned method for constructing a GPR forward model of underground cavities in highways in collapsible loess areas, and the beneficial technical effects are as follows:

[0053] This invention effectively solves the key problem of detecting underground cavities in highways in collapsible loess areas through an innovative technical solution.

[0054] In terms of modeling methods, it breaks through the limitations of the traditional homogeneous medium assumption and establishes a multi-layer geological model based on terrain features. Through the bottom-level cavity model, it supports the generation of cavities in six basic forms, such as cylinders and triangular prisms, and can dynamically adjust the cavity size and spatial distribution characteristics, realistically simulating the randomness and heterogeneity of cavities in actual engineering.

[0055] In terms of parameter settings, an innovative random generation mechanism for dry and wet dual-condition parameters was developed. By performing multi-parameter coordinated perturbation within a reasonable range of key parameters such as dielectric constant and conductivity, the complex response of sudden changes in water content to soil disintegration and porosity changes was accurately simulated, significantly improving the simulation accuracy of electromagnetic wave scattering attenuation caused by changes in water content.

[0056] This invention features stable operation and simple principle. Verified by actual engineering, it can quickly and accurately generate a large number of GPR forward models of underground cavities in highways in collapsible loess areas according to specific needs. It not only greatly improves the efficiency of establishing various forward models, but also provides rich data support for GPR-related research. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the overall algorithm for constructing a GPR forward model of underground cavities in highways in collapsible loess areas, as described in this invention.

[0058] Figure 2 This is a general technical roadmap for the construction of a GPR forward model of underground cavities in highways in collapsible loess areas according to the present invention.

[0059] Figure 3 This is a schematic diagram of the road simulation structure model of the present invention;

[0060] Figure 4 This is a simulation model diagram of a cylindrical cavity; among which, Figure 4 (a) in the figure is a cross-sectional view of the three-dimensional model of the cylinder; Figure 4 (b) in the figure is a three-dimensional model of the cylinder; Figure 4 (c) in the image is a result of the cylindrical B-scan radar image;

[0061] Figure 5 This is a simulation model diagram of a cube with a cavity; among them, Figure 5 (a) in the figure is a cross-sectional view of the 3D model of the cube; Figure 5 (b) in the diagram is a 3D model of the cube; Figure 5 (c) in the figure is a result of the cube B-scan radar image;

[0062] Figure 6 This is a simulation model diagram of a hollow triangular prism; among which, Figure 6 (a) in the figure is a cross-sectional view of the three-dimensional model of the triangular prism; Figure 6 (b) in the diagram is a three-dimensional model of a triangular prism; Figure 6 (c) in the image is a result of the triangular prism B-scan radar image;

[0063] Figure 7 This is a simulation model diagram of a trapezoidal cavity; among which, Figure 7 (a) in the figure is a cross-sectional view of the trapezoidal 3D model; Figure 7 (b) in the diagram is a three-dimensional model of the trapezoid; Figure 7 (c) in the figure is a trapezoidal B-scan radar image result;

[0064] Figure 8 This is a simulation model diagram of an elliptical cylinder cavity; among which, Figure 8 (a) in the figure is a cross-sectional view of the 3D model of the elliptical cylinder; Figure 8 (b) in the diagram is a three-dimensional model of an elliptical cylinder; Figure 8 (c) in the image is the result of the B-scan radar image of the elliptical cylinder;

[0065] Figure 9 This is a simulation model diagram of an irregularly shaped boundary cavity; among which, Figure 9 (a) in the figure is a cross-sectional view of the 3D model with irregular boundaries; Figure 9 (b) in the figure is a 3D model diagram of an irregular boundary;

[0066] Figure 9 (c) in the image is a B-scan radar image of an irregular boundary. Detailed Implementation

[0067] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0068] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0069] Example 1

[0070] like Figure 2 As shown, this invention provides a method for constructing a GPR forward model of underground cavities in highways in collapsible loess areas, comprising the following steps:

[0071] Step S1: Establish a multi-layer geological model for highways in collapsible loess areas. The specific process is as follows:

[0072] Step S101: Collect geological survey data for the target area. The geological survey data includes the road layer structure, the average dielectric constant of each stratum, and the thickness of each stratum.

[0073] Highways in collapsible loess areas adopt a typical layered structure system, mainly divided into two parts: the upper pavement structure consists of surface layer, base layer and subbase layer; the lower roadbed structure includes roadbed and embankment.

[0074] Based on the actual distribution characteristics of collapsible loess layers, a preliminary six-layer geological model was established, comprising two asphalt structural layers for the road surface, a waterproof layer, a cement-aggregate layer, a gravel layer, and a compacted loess layer.

[0075] Step S102: Based on the geological survey data, parameterize the thickness of each stratum in the six-layer geological model.

[0076] The specific parameters are as follows: fine asphalt layer 0.04m, coarse asphalt layer 0.06m, waterproof layer 0.004m, base course 0.2m, subbase course 0.8m, road base course 2m.

[0077] Step S103: Set the grid resolution Δx=Δy=Δz=0.01m to meet the requirements of various ground-penetrating radar parameters for simulation experiments, and complete the establishment of a multi-layer geological model.

[0078] Step S2: Establish a cavity model in the bottom layer of the multi-layer geological model, including regular cavity models and irregular boundary cavity models. The specific process is as follows:

[0079] Step S201: Set up multiple void models, including regular void models and irregular boundary void models.

[0080] The regular void models include cylindrical void models, triangular prism void models, cubic void models, trapezoidal prism void models, and elliptical prism void models.

[0081] Step S202: Set the parameters for each void model.

[0082] For cylindrical cavity models, the center position and base radius need to be set; for triangular prism cavity models, the center position, base length, and height need to be set; for cube cavity models, the center position and lengths of the major and minor sides need to be set; for trapezoidal prism cavity models, the center position, lengths of the top and bottom bases, and height need to be set; for elliptical prism cavity models, the center position and lengths of the major and minor axes need to be set; for irregular boundary cavity models, the center position and irregularity need to be set, with the base upper and lower boundary range being 0.6m × 0.32m, the parameter selection range being 0 to 1, and the default value being 0.3.

[0083] To address irregular cavities formed by natural erosion, this invention proposes a method combining polar coordinate parameterization and random perturbation to construct irregular closed shapes. The global size and local fluctuation intensity of the shape are simultaneously adjusted by the parameter ∈. The core idea is to generate random shapes based on weights, while the random number generation employs a normal distribution perturbation strategy for random size generation, thereby generating the irregular boundaries of the cavities. The specific process is as follows:

[0084] After obtaining the coordinates of the cavity center point, the cavity center point (x, y) in the physical coordinate system is... center ,y center Convert to grid index coordinates (c) x ,c y The specific expression is:

[0085]

[0086] In the polar coordinate system, 50 angles are uniformly sampled to generate an angle sampling sequence, the specific expression of which is:

[0087]

[0088] Where, θ k represents the k-th sampling angle in polar coordinates; i represents the total number of angle sampling points.

[0089] The basic radius is calculated using the following expression:

[0090]

[0091] Where, r x Indicates the lateral foundation radius; r y Represents the longitudinal base radius; ∈ represents the irregularity parameter controlling the overall expansion of the shape; n x ,n y Indicates the grid size.

[0092] A random perturbation is superimposed along the basic radius direction to generate an instantaneous radius with normally distributed noise; different standard deviations, σ, are used in the x and y directions respectively. x =0.2, σ y =0.25, to generate asymmetric fluctuations; the specific expression is:

[0093]

[0094] in, Indicates the instantaneous lateral radius; Represents the instantaneous longitudinal radius; θ k The value represents the sampling angle in polar coordinates; k represents the index value of the angle sampling sequence; e represents the perturbation coefficient. This indicates that the mean is 0 and the variance is 0. The normal distribution function; This indicates that the mean is 0 and the variance is 0. The normal distribution function.

[0095] The vertex sequence is obtained through polar coordinate to Cartesian coordinate transformation, and the specific expression is as follows:

[0096]

[0097] Where, x k y k This represents the coordinates of the k-th vertex of the cavity boundary in the Cartesian coordinate system. The instantaneous radius function in the x-direction; The instantaneous radius function in the y-direction is represented by T; T represents the instantaneous time at the k-th vertex.

[0098] This ultimately resulted in a sequence of closed polygonal outlines. Where ζ represents the total number of vertices of the closed polygonal contour.

[0099] Step S203: Place the various types of cavity models into the six-layer geological model of step S101 according to their center positions to complete the preliminary modeling.

[0100] Step S204: Visualize the modeling results and output the model results.

[0101] Step S3: Based on the surface wet / dry conditions, generate random parameters for each stratum to complete the establishment of the GPR forward model for underground cavities. The specific process is as follows:

[0102] Step S301: Set the parameters of each stratum under dry conditions and determine their value range.

[0103] The parameters include relative permittivity, conductivity, relative permeability, and magnetic loss rate.

[0104] Step S302: Set the parameters of each stratum under wetland conditions and determine their value range;

[0105] Step S303: Before modeling, the dry / wet state of the ground needs to be selected, and the value range of the corresponding parameters needs to be determined according to the selected dry / wet state of the ground.

[0106] Step S304: Randomly generate specific parameter values ​​within the selected parameter value range, and assign the generated specific parameter values ​​to the corresponding formation.

[0107] Table 1 is a table of random parameters.

[0108] Table 1 Random Parameter Table

[0109] Material Relative permittivity electrical conductivity relative permeability Magnetic loss rate Material code Air 1.00 0.00 1.0 0.0 6 Fine asphalt 2.11 0.00 1.0 0.0 0 coarse asphalt 3.12 0.00 1.0 0.0 1 Waterproof membrane 4.37 0.01 1.0 0.0 2 grassroots 6.28 0.00 1.0 0.0 3 Subbase 6.96 0.09 1.0 0.0 4 Roadbed 8.93 0.04 1.0 0.0 5

[0110] Step S4: Perform forward modeling in gprMax to obtain the forward modeling results. The specific process is as follows:

[0111] Step S401: Export the random parameters of each stratum and the names of their corresponding strata generated in step S3 as txt format files and store them.

[0112] Step S402: Save the underground cavity GPR forward model results generated in step S3 as an h5 file;

[0113] Step S403: Write the in file required by gprMax, and import the txt file in step S401 and the h5 file in step S402 to set up the model;

[0114] Step S404: Set the model size, resolution, time window, initial position of electromagnetic wave transmitter, initial position of receiver, dielectric constant reading, electromagnetic wave transmission frequency, transmitter and receiver movement step size, and absorption boundary width information in the in file.

[0115] like Figure 3 As shown, the model in this embodiment adopts a three-dimensional structure of 6m (length) × 0.5m (width) × 3.25m (height), with survey lines laid out along the X-axis. The model adopts a seven-layer geological structure, from top to bottom: 0.1m air layer, 0.04m fine asphalt layer, 0.06m coarse asphalt layer, 0.004m waterproof membrane layer, 0.2m base course, 0.8m subbase course, and 2.0m road base course.

[0116] Step S405: Perform forward modeling using gprMax software, generate an out file, and output the forward modeling result B-Scan image after integration.

[0117] Example 2

[0118] like Figure 1As shown, the main program of the system in this embodiment adopts a modular flow design, and the specific execution steps are as follows:

[0119] (1) Initialize 3D mesh parameters.

[0120] (2) Create the basic geological structure.

[0121] (3) Obtain user input.

[0122] The system includes a user interaction module, which mainly contains the following functional settings:

[0123] Obtain the ground condition: dry or wet;

[0124] Get Shape Type: Block Shape Selection;

[0125] Obtain coordinate parameters: Input center coordinates;

[0126] Get size parameters: Input the boundary range.

[0127] (4) Generate custom modules.

[0128] The system includes a geometry generation module: select the shape type (cylinder / cube / triangular prism / trapezoidal prism / random) and generate a Boolean mask.

[0129] (5) Applied to 3D models.

[0130] (6) Generate material parameter files.

[0131] The system includes a material parameter generation module that, based on the input ground conditions, selects a set parameter range, randomly generates specific parameters, and produces a material TXT file.

[0132] (7) Visualization of intermediate slices.

[0133] (8) Save the H5 and TXT files.

[0134] Example 3

[0135] This embodiment uses cavity models with different geometric shapes for system simulation, including various typical cavity structures such as cylinders, cubes, triangular prisms, trapezoidal prisms, elliptical cylinders, and irregular boundaries. The simulation results are as follows: Figures 4-9 As shown.

[0136] in, Figure 4 This is a simulation model diagram of a cylindrical cavity; among which, Figure 4 (a) in the figure is a cross-sectional view of the three-dimensional model of the cylinder; Figure 4 (b) in the figure is a three-dimensional model of the cylinder; Figure 4 (c) in the image is a result of the cylindrical B-scan radar image;

[0137] Figure 5 This is a simulation model diagram of a cube with a cavity; among them, Figure 5 (a) in the figure is a cross-sectional view of the 3D model of the cube; Figure 5 (b) in the diagram is a 3D model of the cube; Figure 5 (c) in the figure is a result of the cube B-scan radar image;

[0138] Figure 6 This is a simulation model diagram of a hollow triangular prism; among which, Figure 6 (a) in the figure is a cross-sectional view of the three-dimensional model of the triangular prism; Figure 6 (b) in the diagram is a three-dimensional model of a triangular prism; Figure 6 (c) in the image is a result of the triangular prism B-scan radar image;

[0139] Figure 7 This is a simulation model diagram of a trapezoidal cavity; among which, Figure 7 (a) in the figure is a cross-sectional view of the trapezoidal 3D model; Figure 7 (b) in the diagram is a three-dimensional model of the trapezoid; Figure 7 (c) in the figure is a trapezoidal B-scan radar image result;

[0140] Figure 8 This is a simulation model diagram of an elliptical cylinder cavity; among which, Figure 8 (a) in the figure is a cross-sectional view of the 3D model of the elliptical cylinder; Figure 8 (b) in the diagram is a three-dimensional model of an elliptical cylinder; Figure 8 (c) in the image is the result of the B-scan radar image of the elliptical cylinder;

[0141] Figure 9 This is a simulation model diagram of an irregularly shaped boundary cavity; among which, Figure 9 (a) in the figure is a cross-sectional view of the 3D model with irregular boundaries; Figure 9 (b) in the figure is a 3D model diagram of an irregular boundary; Figure 9 (c) in the image is a B-scan radar image of an irregular boundary.

[0142] Simulation results show that the method of the present invention can accurately simulate cavity structures with different geometric shapes, cover a variety of typical cavity structures, support full-scale simulation from standard geometries to random boundary anomalies, establish a mapping relationship library of geometric features and radar images, and provide a basis for discrimination for in-situ cavity morphology inversion.

[0143] Therefore, this invention employs the aforementioned method for constructing a GPR forward model of underground cavities in collapsible loess areas, establishing a multi-layered geological model that integrates actual terrain features. At the bottom layer of the model, it integrates cavity models of six typical shapes, including cylinders and triangular prisms. A random parameter generation mechanism under both dry and wet conditions is designed to achieve random assignment of physical properties such as dielectric constant and conductivity within reasonable ranges for each stratum. Forward modeling calculations of multi-scale underground cavity GPR models are implemented based on the gprMax software platform. This method overcomes the theoretical limitations of the traditional homogeneous medium assumption. Through a dynamic parameter system, it can rapidly generate a large number of GPR forward models of underground cavities in collapsible loess areas, significantly improving modeling efficiency. While systematically studying the influence of different cavity morphologies and parameters on ground-penetrating radar image waveforms, it also provides a reliable modeling solution for model establishment under complex geological conditions. This solves the problems of insufficient efficiency in establishing various forward models and the lack of data in GPR-related research, providing more comprehensive data support for underground cavity detection under complex geological conditions.

[0144] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for constructing a GPR forward model of underground cavities in highways in collapsible loess areas, characterized in that, Includes the following steps: Step S1: Establish a multi-layer geological model for highways in collapsible loess areas; Step S2: Establish a cavity model in the bottom layer of the multi-layer geological model, including a regular cavity model and an irregular boundary cavity model; Step S3: Determine the range of values ​​for relative permittivity, conductivity, relative permeability and magnetic loss rate of each stratum based on the dry and wet conditions of the ground. Randomly generate the above parameters for each stratum within the range of values ​​and assign them to the corresponding stratum to complete the establishment of the underground cavity GPR forward model. Step S4: Perform forward modeling in gprMax to obtain the forward modeling results; The specific process of step S1 is as follows: Step S101: Collect geological survey data of the target area. Based on the actual distribution characteristics of collapsible loess layers, initially establish a six-layer geological model including two asphalt structural layers for road surface, a waterproof layer, a cement crushed stone layer, a gravel layer, and a rammed loess layer. Step S102: Based on the geological survey data, parameterize the thickness of each stratum in the six-layer geological model; Step S103: Set the grid resolution to complete the establishment of the multi-layer geological model; The construction process of the irregular boundary void model is as follows: After obtaining the coordinates of the cavity center point, the cavity center point in the physical coordinate system ( Convert to grid index coordinates ( The specific expression is: ； in, , Indicates grid resolution; In the polar coordinate system, 50 angles are uniformly sampled to generate an angle sampling sequence, the specific expression of which is: ； in, Represents the first in polar coordinates Each sampling angle; This represents the total number of angle sampling points; The basic radius is calculated using the following expression: ； in, Indicates the lateral foundation radius; Indicates the longitudinal foundation radius; This parameter represents the irregularity that controls the overall expansion of the shape. Indicates the grid size; Random perturbations are superimposed along the basic radius direction to generate an instantaneous radius with normally distributed noise; where, in x direction and y Different standard deviations are used for each direction. , This generates asymmetric fluctuations; the specific expression is: ； in, Indicates the instantaneous lateral radius; Indicates the instantaneous longitudinal radius; This represents the sampling angle in polar coordinates. Indicates the index value of the angle sampling sequence; Indicates the disturbance coefficient; This indicates that the mean is 0 and the variance is 0. The normal distribution function; This indicates that the mean is 0 and the variance is 0. The normal distribution function; The vertex sequence is obtained through polar coordinate to Cartesian coordinate transformation, and the specific expression is as follows: ； in, , Indicates the boundary of the cavity. The coordinates of each vertex in the Cartesian coordinate system; express x The instantaneous radius function of the direction; express y The instantaneous radius function of the direction; Indicates the first The instantaneous time of each vertex; This ultimately resulted in a sequence of closed polygonal outlines. ,in, This represents the total number of vertices of the closed polygon outline; The specific process of step S3 is as follows: Step S301: Set the parameters of each stratum under dry conditions and determine their value range; Step S302: Set the parameters of each stratum under wetland conditions and determine their value range; Step S303: Before modeling, the dry / wet state of the ground needs to be selected, and the value range of the corresponding parameters needs to be determined according to the selected dry / wet state of the ground. Step S304: Randomly generate specific parameter values ​​within the selected parameter value range, and assign the generated specific parameter values ​​to the corresponding formation.

2. The method for constructing a GPR forward model of underground cavities in highways in collapsible loess areas according to claim 1, characterized in that, The specific process of step S2 is as follows: Step S201: Set up multiple void models, including regular void models and irregular boundary void models; Among them, the regular void models include cylindrical void models, triangular prism void models, cubic void models, trapezoidal prism void models, and elliptical prism void models; Step S202: Set the parameters for each cavity model; Step S203: Place the various types of cavity models into the six-layer geological model of step S101 according to their center positions to complete the preliminary modeling; Step S204: Visualize the modeling results and output the model results.

3. The method for constructing a GPR forward model of underground cavities in highways in collapsible loess areas according to claim 2, characterized in that, The specific parameter settings in step S202 are as follows: For cylindrical void models, the center position and base radius need to be set; for triangular prism void models, the center position, base length, and height need to be set; for cube void models, the center position and major and minor side lengths need to be set; for trapezoidal prism void models, the center position, top and bottom base lengths, and height need to be set; for elliptical prism void models, the center position and major and minor axis lengths need to be set; for void models with irregular boundaries, the center position and irregularity degree need to be set, and the range of the upper and lower boundaries is... The irregularity selection range is 0~1, and the default value is 0.

3.

4. The method for constructing a GPR forward model of underground cavities in highways in collapsible loess areas according to claim 1, characterized in that, The specific process of step S4 is as follows: Step S401: Export the random parameters of each stratum and the names of their corresponding strata generated in step S3 as txt format files and store them. Step S402: Save the underground cavity GPR forward model results generated in step S3 as an h5 file; Step S403: Write the in file required by gprMax, and import the txt file in step S401 and the h5 file in step S402 to set up the model; Step S404: Set the model size, resolution, time window, initial position of electromagnetic wave transmitter, initial position of receiver, dielectric constant reading, electromagnetic wave transmission frequency, transmitter and receiver movement step size, and absorption boundary width information in the in file; Step S405: Perform forward modeling using gprMax software, generate an out file, and output the forward modeling result B-Scan image after integration.

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