A method for establishing a three-dimensional equivalent porous medium model for karst cave formations

Abstract

The present invention relates to the technical field of structural reconstruction, and in particular to a method for establishing a three-dimensional equivalent porous medium model of a karst-type cavity formation, comprising the following steps: step 1, obtaining two-dimensional cross-sectional images of different sections of the karst-type cavity formation; step 2, identifying two-dimensional pore parameters in the two-dimensional cross-sectional images based on a two-dimensional parameter recognition model of a karst cavity, performing equivalent processing on the two-dimensional pore parameters to obtain equivalent two-dimensional pore parameters; step 3, converting the equivalent two-dimensional pore parameters into three-dimensional pore parameters based on a probability analysis method; step 4, reconstructing and generating a three-dimensional equivalent porous medium model using the three-dimensional pore parameters; the present invention ensures the high efficiency of model establishment, effectively uses the two-dimensional karst cavity parameters directly for three-dimensional simulation through the probability conversion method, and accurately reflects the distribution of three-dimensional karst cavities.

Description

Technical Field

[0001] The invention relates to the technical field of structural reconstruction, and in particular to a method for establishing a three-dimensional equivalent porous medium model of a karst-type hollow stratum. Background Art

[0002] Karst, also known as karst, was first named after the limestone plateau on the Istrian Peninsula in northwestern Yugoslavia. It is a unique geomorphic form with a large number of underground cavities formed by the mutual dissolution of surface water or groundwater and rollable rocks. It is widely distributed in the world, and China is also one of the main distribution areas; there are a large number of small karst cavities distributed in the karst strata, which are difficult to detect by geophysical methods, and the core recovery rate of the rock mass in this stratum is very low, and it is not easy to estimate the location of the karst cavities by drilling. The distribution of karst cavities in the slopes or tunnels of karst strata will inevitably reduce the overall stability. In the existing numerical simulation process, the consideration of pores only stays at the scale of the sample; for the analysis of the overall project, whether through finite element or discrete element method, homogenization treatment is used, and the distribution of karst cavities in karst strata is not considered. As a result, the calculated value of the engineering safety factor is too high, which is very likely to cause hazards such as landslides and tunnel instability and collapse.

[0003] At present, the main methods for reconstructing porous media models are direct reconstruction and statistical equivalent reconstruction. For the overall project, the scale is relatively large, but the direct reconstruction method consumes a lot of manpower and material resources, and the detection is difficult. The statistical equivalent reconstruction method and the image-based pore feature extraction methods mostly stay at the microscopic scale, which is difficult to apply to the karst cavity feature extraction at the engineering scale. In addition, the result of the two-dimensional image extraction is that the local two-dimensional cavity feature deviates from the three-dimensional cavity distribution;

[0004] Therefore, it is necessary to design a porous media model establishment method that can obtain a three-dimensional equivalent porous media model of the karst stratum through simple two-dimensional image recognition. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the prior art and provide a method for establishing a three-dimensional equivalent porous medium model of a karst-type hollow stratum.

[0006] The present invention provides a method for establishing a three-dimensional equivalent porous medium model of a karst-type hollow stratum, which is characterized in that it comprises the following steps:

[0007] Step 1, obtaining two-dimensional cross-sectional images of different cross sections of the karst cavity stratum;

[0008] Step 2: identifying the two-dimensional pore parameters in the two-dimensional cross-sectional image based on the two-dimensional parameter recognition model of karst cavities, performing equivalent processing on the two-dimensional pore parameters to obtain equivalent two-dimensional pore parameters;

[0009] Step 3: Convert the equivalent two-dimensional pore parameters into three-dimensional pore parameters based on the probability analysis method;

[0010] Step 4: Reconstruct and generate a three-dimensional equivalent porous medium model using the three-dimensional pore parameters.

[0011] Furthermore, in step 2, the method for obtaining the two-dimensional karst cavity parameter identification model comprises the following steps:

[0012] Step 2.1: preprocessing the two-dimensional cross-sectional image to obtain a preprocessed two-dimensional cross-sectional image set;

[0013] Step 2.2: Using the preprocessed two-dimensional cross-sectional image set, a two-dimensional parameter recognition model for karst cavities is established based on a neural network algorithm.

[0014] Further, in step 2.1, the two-dimensional cross-sectional image is preprocessed to obtain a preprocessed two-dimensional cross-sectional image set; specifically, the following steps are included:

[0015] S2.1.1: Manual labeling: Manual labeling of the two-dimensional cross-sectional image is performed.

[0016] S2.1.2: Image normalization: convert the pixels of the annotated two-dimensional cross-sectional image from 0-255 to 0-1 using formula (1);

[0017]

[0018] Among them, input is the input image pixel value, output is the output image pixel value, input max 、input min Respectively represent the maximum and minimum values ​​of the input pixels;

[0019] S2.1.3: Image enhancement: Rotate, mirror and add noise to the normalized two-dimensional cross-sectional image.

[0020] Further, in step 2, the two-dimensional pore parameters include two-dimensional karst cavity area distribution and porosity;

[0021] The two-dimensional pore parameters are processed equivalently, including:

[0022] The karst cavity is treated as a circle, and the two-dimensional karst cavity equivalent radius distribution is obtained according to the area equivalence relationship.

[0023] Furthermore, in step 3, the equivalent two-dimensional pore parameters are converted into three-dimensional pore parameters based on a probability analysis method, specifically including:

[0024] S3.1: Convert the two-dimensional karst cavity equivalent radius r into the three-dimensional karst cavity radius R;

[0025] S3.2: Convert the two-dimensional karst cavity porosity P2 corresponding to the two-dimensional karst cavity equivalent radius r into the three-dimensional karst cavity porosity P3.

[0026] Furthermore, in S3.1, the two-dimensional karst cavity equivalent radius r is converted into the three-dimensional karst cavity radius R, specifically including:

[0027] S3.1a: Simplify the karst cavity into a sphere. Take any cross section through the center of the 3D sphere. Fix a point A on the circumference and another point B on the circumference. Half the length of the chord AB corresponds to the equivalent radius r of the 2D karst cavity. Let the central angle corresponding to the chord length AB be δ. The area of ​​the 2D karst cavity corresponding to the chord AB is: S = πr 2 =πRsin 2 (δ / 2);

[0028] The expected area of ​​the two-dimensional karst cavity is: Among them, δ ranges from 0 to π, and d is the diameter of the two-dimensional karst cavity;

[0029] S3.1b: The expected cross-sectional area of ​​a three-dimensional sphere formed by random cuts is:

[0030] S3.1c: The relationship between the radius R of a three-dimensional karst cavity and the equivalent radius r of a two-dimensional karst cavity is:

[0031]

[0032] Further, in S3.2, the two-dimensional karst cavity porosity P2 corresponding to the two-dimensional karst cavity equivalent radius r is converted into the three-dimensional karst cavity porosity P3, specifically including:

[0033] S3.2a: The porosity of karst cavities in two-dimensional state is:

[0034] The porosity of karst cavities in three-dimensional state is:

[0035] The two-dimensional karst cavity is set as a cube; l is the side length of the two-dimensional karst cavity, R is the radius of the three-dimensional karst cavity, n2 is the number of voids on the surface of the two-dimensional karst cavity, and n3 is the total number of karst cavities in the cube;

[0036] Set the karst cavity distribution density from the karst cavity surface to the inside to be linear distribution, and set the linear coefficient to k;

[0037] Then there is get

[0038] The geometric analysis yields:

[0039] Will and Through integration, we get

[0040] S3.2b: Combining equation (3) with equation (2), the conversion relationship between the two-dimensional karst cavity porosity P2 and the three-dimensional karst cavity porosity P3 is obtained as follows:

[0041] Furthermore, in step 4, the three-dimensional pore parameters are used to reconstruct and generate a three-dimensional equivalent porous medium model through numerical simulation software, and the numerical simulation software is discrete element simulation software PFC or matlab software.

[0042] Furthermore, the three-dimensional pore parameters are reconstructed by discrete element simulation software PFC to generate a three-dimensional equivalent porous medium model; specifically, the following steps are included:

[0043] S4.1. Import the overall rock mass contour as geometry through the stl file, use the rblock distribute command to generate rblocks with corresponding gradation and porosity in the rock mass contour, and generate the rblock distribution state;

[0044] S4.2, exporting the rblock distribution state into a corresponding geometry, and then deleting the rblock to generate a karst cavity geometric space geometry image;

[0045] S4.3, calibrate the parameters of the complete on-site rock;

[0046] S4.4. Establish a slope without karst cavities according to the calibrated parameters, generate particles within the geometry range by using the ball distributerange geometry space command, calculate the balance, and generate a slope without karst cavities;

[0047] S4.5. In the slope without karst voids, the particles in the karst void geometry range are grouped and deleted by using the ball group range geometry space command, and the three-dimensional equivalent porous geological model corresponding to the karst void stratum is obtained after balancing;

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] (1) The present invention obtains the two-dimensional pore parameters of karst cavities through on-site photography and neural network algorithms, and constructs a three-dimensional equivalent porous medium through a probability statistical method, thereby ensuring the high efficiency of model establishment. The two-dimensional pore parameters are converted into three-dimensional pore parameters based on probability analysis, and the two-dimensional karst cavity parameters are effectively used directly for three-dimensional simulation through the probability conversion method, without causing deviations in cavity size and porosity, and more accurately reflecting the distribution of three-dimensional karst cavities;

[0050] (2) The present invention can generate a three-dimensional equivalent porous medium model by importing three-dimensional pore parameters into discrete element software PFC or randomly generating geometric figures through MATLAB software and importing them into the finite element model, so as to more accurately reflect the overall impact of karst cavities on slopes and tunnel projects, avoid the safety factor calculation caused by homogenization, and ensure the overall safety of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The following drawings are only used to illustrate and explain the present invention, and are not used to limit the scope of the present invention, wherein:

[0052] Figure 1 : Schematic diagram of the process of establishing a three-dimensional equivalent porous medium model of a karst-type hollow stratum in an embodiment of the present invention;

[0053] Figure 2 : Schematic diagram of an arbitrary cross section through the center of a three-dimensional sphere of the present invention;

[0054] Figure 3 : The hypothetical distribution diagram of karst cavities in the rock mass of the present invention;

[0055] Figure 4 : A diagram showing the relationship between karst cavities and coordinates in the rock mass of the present invention;

[0056] Figure 5 : The rblock position diagram generated by the present invention in the PFC software;

[0057] Figure 6 : The karst cavity geometry map derived by rblock in PFC of the present invention;

[0058] Figure 7 : The complete slope without karst cavities generated by the present invention in PFC software;

[0059] Figure 8 : The karst slope map after the karst cavity parts are grouped in the present invention. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution, design method and advantages of the present invention clearer, the present invention is further described in detail by specific embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0061] In specific implementation, Figure 1 As shown, the present invention provides a method for establishing a three-dimensional equivalent porous medium model of a karst stratum, comprising the following steps:

[0062] Step 1: Select a suitable location through on-site survey to obtain two-dimensional cross-sectional images of different sections of the karst-type hollow stratum;

[0063] Specifically, through on-site investigation, a suitable location is selected to shoot and obtain two-dimensional cross-sectional images of different sections of the karst-type hollow stratum. The specific acquisition process is as follows:

[0064] First, through on-site investigation, suitable locations are selected to obtain two-dimensional cross-sectional images of different sections of the karst cavity strata; the area where a three-dimensional karst cavity model needs to be established is surveyed to determine whether there are large open sections containing karst cavities. If there are few natural open surfaces, a small amount of excavation can be carried out to obtain the excavation surface information, and the location and estimated size of the section can be recorded.

[0065] Secondly, when marking the section location information on the map, attention should be paid to the accuracy of the marking information.

[0066] Then, select the sections to be photographed. In the selection process, it is necessary to pay attention to the location of the sections to be photographed as evenly as possible to avoid excessive concentration of sections in local areas. At the same time, the sections to be photographed should have a certain size to reflect the distribution law of karst cavities.

[0067] Finally, take photos from the front of the selected section. The shooting distance is flexibly adjusted according to the on-site terrain. The principle is to take photos of as large a part of the section as possible. The picture should be clear and complete, with obvious color difference between the karst cavity and the rock mass, so as to facilitate the identification of the two-dimensional parameters of the karst cavity in step 2;

[0068] Step 2. Identify the two-dimensional pore parameters in the two-dimensional cross-sectional image based on the two-dimensional parameter identification model of karst cavities, perform equivalent processing on the two-dimensional pore parameters, and obtain equivalent two-dimensional pore parameters;

[0069] Wherein, the two-dimensional pore parameters include two-dimensional karst cavity area distribution and porosity;

[0070] The two-dimensional pore parameters are processed equivalently, including:

[0071] The karst cavity is treated as a circle, and the two-dimensional karst cavity equivalent radius distribution is obtained according to the area equivalence relationship.

[0072] Specifically, S2.1 preprocesses the two-dimensional cross-sectional image to obtain a preprocessed two-dimensional cross-sectional image set;

[0073] S2.1.1. Manual labeling: Manually label the two-dimensional cross-sectional images used in the training model. The information that needs to be labeled includes the outline of the karst cavity.

[0074] S2.1.2. Image normalization: convert the pixels of the annotated two-dimensional cross-sectional image from 0 to 255 to 0 to 1 using formula (1);

[0075]

[0076] Among them, input represents the input image pixel value, output represents the output image pixel value, input max 、input min Represent the maximum and minimum values ​​of the input pixels respectively;

[0077] S2.1.3. Image enhancement: Rotate, mirror and add noise to the normalized 2D cross-sectional image to improve the generalization of the model;

[0078] Step 2.2: using the pre-processed two-dimensional cross-sectional image set to establish a two-dimensional parameter recognition model for karst cavities based on a neural network algorithm;

[0079] 70% of the preprocessed image data set is taken as the training set, the remaining 20% ​​is taken as the validation set, and 10% is taken as the test set; the training set is used to establish a two-dimensional parameter recognition model for karst strata karst voids, and it is trained. The two-dimensional parameter recognition model for karst voids is used to recognize the subsequent images, and the two-dimensional karst void area distribution and porosity in the image can be obtained; since most karst void parameters are approximately circular, the karst voids are treated as circular, and according to the area equivalence relationship, the radius distribution of the equivalent two-dimensional karst voids can be obtained, and the overall porosity does not change;

[0080] Step 3: Convert the equivalent two-dimensional pore parameters into three-dimensional pore parameters based on the probability analysis method;

[0081] S3.1: Convert the two-dimensional karst cavity equivalent radius r into the three-dimensional karst cavity radius R;

[0082] In S3.1, the two-dimensional karst cavity equivalent radius r is converted into the three-dimensional karst cavity radius R, specifically including:

[0083] The karst cavity is simplified as a sphere. Therefore, the three-dimensional radius of the karst cavity is the radius of the sphere, and the two-dimensionally identified karst radius corresponds to the radius of a circular section of the sphere, which is smaller than the three-dimensional karst cavity radius; the two-dimensional karst cavity size identified on the rock surface based on the neural network can be regarded as the cross section formed by any section cutting the three-dimensional sphere. Figure 2 As shown, in a three-dimensional sphere, take any section through the center of the circle, fix a point A on the circumference, and B is another point on the circumference. Half the length of the chord AB corresponds to the radius of the two-dimensional section.

[0084] Assume that the central angle corresponding to the chord length AB is δ, then the two-dimensional karst cavity area corresponding to the chord AB is S = πr 2 =πRsin 2 (δ / 2), since δ is uniformly distributed in the range of 0 to π, the expected area of ​​the two-dimensional karst cavity is

[0085] The expected cross-sectional area formed by randomly cutting a three-dimensional sphere through probability analysis is Therefore, the conversion formula between the three-dimensional actual radius R of the cavity and the two-dimensional karst cavity radius r is:

[0086]

[0087] S3.2 Conversion of two-dimensional porosity to three-dimensional porosity:

[0088] like Figure 3 Take a representative karst cavity cube with a side length of l and a karst cavity radius of R. n2 is the number of surface voids, and n3 is the total number of karst cavities in the cube. Since the formation of karst cavities starts from the surface, the karst cavities on the outer surface are densely distributed. Figure 4 , assuming that the density of karst cavities from the surface to the inside is distributed linearly, and the linear coefficient is k.

[0089] Porosity of karst cavities in two-dimensional state

[0090] Porosity of karst cavities in three-dimensional state

[0091] Assuming the linear coefficient is k, we have

[0092] Can get

[0093] Geometric analysis yields

[0094] Will and Through integration, we get because It is small in itself, and its value after square can be ignored. Combining the conversion formula of two-dimensional void radius and three-dimensional void radius, we can get

[0095] Step 4: Reconstruct and generate a three-dimensional equivalent porous medium model using the three-dimensional pore parameters through numerical simulation software; wherein, the karst rock equivalent porous medium is generated based on the three-dimensional pore parameters obtained in step 3 through discrete element numerical simulation software PFC and imported into the numerical model for calculation;

[0096] The specific process is as follows:

[0097] S4.1. Import the entire rock mass contour as geometry through the stl file, and use the rblock distribute command to generate rblocks with corresponding gradation and porosity in the rock mass contour. The generated rblock distribution state is as follows: Figure 5 .

[0098] S4.2. Export the rblock distribution obtained in the above steps to the corresponding geometry, and then delete the rblock to prevent it from participating in the calculation. The obtained karst cavity geometry space geometry picture is as follows: Figure 6 .

[0099] S4.3. Parameter calibration is performed on the complete on-site rock. The parameters obtained in this process can reflect the influence of the rock's mesoscopic pores. The model mesoscopic parameters obtained in the calibration process are shown in Table 1:

[0100] Table 1: Mesoscopic parameters of the discrete element model of karst intact rock:

[0101]

[0102] S4.4 Establish a slope without karst voids based on the calibrated microscopic parameters. The ball distributerange geometry space command can be used to generate particles within the geometry range, calculate the balance, and generate a slope without karst voids. Figure 7 .

[0103] S4.5. In the slope without karst cavities, the ball group range geometry space command can be used to group and delete the particles in the karst cavity geometry range. After balancing, the three-dimensional equivalent porous geological model corresponding to the stratum can be obtained, such as Figure 8 ;

[0104] It is worth noting that the present invention obtains the two-dimensional pore parameters of karst cavities through photography and neural network algorithms, which greatly saves manpower and material resources compared to existing geophysical survey technologies.

[0105] The present invention constructs a three-dimensional equivalent porous medium through a probability statistics method. Compared with the traditional direct generation method, it greatly reduces the amount of tasks in the reconstruction process while ensuring the similarity of the model, thereby ensuring the high efficiency of model establishment.

[0106] The equivalent two-dimensional pore parameters are converted into three-dimensional pore parameters based on probability analysis. The probability conversion method effectively solves the problem of small cavity size and porosity caused by directly using two-dimensional karst cavity parameters for three-dimensional simulation, and more accurately reflects the distribution of three-dimensional karst cavities.

[0107] A three-dimensional equivalent porous medium model can be generated by importing three-dimensional pore parameters into the discrete element software PFC or by randomly generating geometric figures through MATLAB software and importing them into the finite element model. Compared with the homogeneous rock mass model in the existing technology, it can more accurately reflect the overall impact of karst cavities on slopes and tunnel projects, avoid the excessive calculation of safety factors caused by homogenization, and ensure the overall safety of the project.

[0108] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A method for establishing a three-dimensional equivalent porous medium model of a karst-type hollow stratum, characterized in that: It is characterized by comprising the following steps: Step 1, obtaining two-dimensional cross-sectional images of different sections of the karst cavity stratum; Step 2: identifying the two-dimensional pore parameters in the two-dimensional cross-sectional image based on the two-dimensional parameter recognition model of karst cavities, performing equivalent processing on the two-dimensional pore parameters to obtain equivalent two-dimensional pore parameters; The two-dimensional pore parameters include two-dimensional karst cavity area distribution and porosity; The two-dimensional pore parameters are subjected to equivalent processing, specifically comprising: treating the karst cavity as a circle, and obtaining a two-dimensional karst cavity equivalent radius distribution according to an area equivalent relationship; Step 3: Convert the equivalent two-dimensional pore parameters into three-dimensional pore parameters based on the probability analysis method; S3.1: Convert the two-dimensional karst cavity equivalent radius r into the three-dimensional karst cavity radius R, specifically including: S3.1a: Simplify the karst cavity into a sphere. Take any cross section through the center of the 3D sphere. Fix a point A on the circumference and another point B on the circumference. Half the length of the chord AB corresponds to the equivalent radius r of the 2D karst cavity. Let the central angle corresponding to the chord length AB be δ. The area of ​​the 2D karst cavity corresponding to the chord AB is: S = πr 2 =πRsin 2 (δ / 2); The expected area of ​​the two-dimensional karst cavity is: Among them, δ ranges from 0 to π, and d is the diameter of the two-dimensional karst cavity; S3.1b: The expected cross-sectional area of ​​a three-dimensional sphere formed by random cuts is: S3.1c: The relationship between the radius R of a three-dimensional karst cavity and the equivalent radius r of a two-dimensional karst cavity is: S3.2: Convert the two-dimensional karst cavity porosity P2 corresponding to the two-dimensional karst cavity equivalent radius r into the three-dimensional karst cavity porosity P3, specifically including: S3.2a: The porosity of karst cavities in two-dimensional state is: The porosity of karst cavities in three-dimensional state is: The two-dimensional karst cavity is set as a cube; l is the side length of the two-dimensional karst cavity, R is the radius of the three-dimensional karst cavity, n2 is the number of voids on the surface of the two-dimensional karst cavity, and n3 is the total number of karst cavities in the cube; Set the karst cavity distribution density from the karst cavity surface to the inside to be linear distribution, and set the linear coefficient to k; Then there is get The geometric analysis yields: Will and Through integration, we get S3.2b: Combining equation (3) with equation (2), the conversion relationship between the two-dimensional karst cavity porosity P2 and the three-dimensional karst cavity porosity P3 is obtained as follows: Step 4: Reconstruct and generate a three-dimensional equivalent porous medium model using the three-dimensional pore parameters.

2. The method for establishing a three-dimensional equivalent porous medium model of a karst-type hollow stratum according to claim 1 is characterized in that: In step 2, the method for obtaining the two-dimensional karst cavity parameter identification model includes the following steps: Step 2.1: preprocessing the two-dimensional cross-sectional image to obtain a preprocessed two-dimensional cross-sectional image set; Step 2.2: Using the preprocessed two-dimensional cross-sectional image set, a two-dimensional parameter recognition model for karst cavities is established based on a neural network algorithm.

3. The method for establishing a three-dimensional equivalent porous medium model of a karst-type hollow stratum according to claim 2 is characterized in that: In step 2.1, the two-dimensional cross-sectional images are preprocessed to obtain a preprocessed two-dimensional cross-sectional image set; specifically, the following steps are included: S2.1.1: Manual labeling: Manual labeling of the two-dimensional cross-sectional image is performed. S2.1.2: Image normalization: convert the pixels of the annotated two-dimensional cross-sectional image from 0-255 to 0-1 using formula (1); Among them, input is the input image pixel value, output is the output image pixel value, input max 、input min Respectively represent the maximum and minimum values ​​of the input pixels; S2.1.3: Image enhancement: Rotate, mirror and add noise to the normalized two-dimensional cross-sectional image.

4. The method for establishing a three-dimensional equivalent porous medium model of a karst-type hollow stratum according to claim 1 is characterized in that: In step 4, the three-dimensional pore parameters are used to reconstruct and generate a three-dimensional equivalent porous medium model through numerical simulation software, and the numerical simulation software is discrete element simulation software PFC or matlab software.

5. The method for establishing a three-dimensional equivalent porous medium model of a karst-type hollow stratum according to claim 4 is characterized in that: The three-dimensional pore parameters are reconstructed by discrete element simulation software PFC to generate a three-dimensional equivalent porous medium model; specifically, the following steps are included: S4.

1. Import the overall rock mass contour as geometry through the stl file, use the rblock distribute command to generate rblocks with corresponding gradation and porosity in the rock mass contour, and generate the rblock distribution state; S4.2, exporting the rblock distribution state into corresponding geometry, and then deleting the rblock to generate a karst cavity geometric space geometry image; S4.3, calibrate the parameters of the complete on-site rock; S4.

4. Establish a slope without karst voids according to the calibrated parameters, generate particles within the geometry range through the balldistributerangegeometryspace command, calculate the balance, and generate a slope without karst voids; S4.

5. In the slope without karst voids, the particles in the karst void geometry range are grouped and deleted through the ballgrouprangegeometryspace command, and the three-dimensional equivalent porous geological model corresponding to the karst void stratum is obtained after balancing.

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