Fracture surrounding rock grouting plugging method based on fracture opening intelligent identification

By intelligently identifying the crack opening of surrounding rock and establishing a two-dimensional diffusion model, the theoretical and practical disconnection of fracture grouting and blindness of parameters in the existing technology are solved, and the optimization of the reinforcement effect of surrounding rock grouting and precise control of parameters is achieved.

CN120298964APending Publication Date: 2025-07-11JIANGXI UNIV OF SCI & TECH
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Patent Information

Application Number
CN202510361908.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-26
Publication Date
2025-07-11

AI Technical Summary

Technical Problem

The existing technology has problems in the disconnection between theory and practice, insufficient grouting pressure, numerical simulation does not conform to the actual situation on site, unrefined crack network modeling, and blind parameter selection, resulting in waste of grouting materials and poor sealing effect.

Method used

By intelligently identifying the crack opening of surrounding rock, using MATLAB image processing and improved crack midline algorithm, an accurate crack binary map is obtained, a two-dimensional crack network slurry diffusion model is established, and the grouting pressure and slurry usage are adjusted to optimize the slurry diffusion filling effect.

Benefits of technology

The optimization of the grouting reinforcement effect of surrounding rocks is achieved, the utilization rate and sealing effect of grouting materials are improved, and accurate grouting parameters are provided.

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Abstract

The invention relates to the technical field of surrounding rock reinforcement, and discloses a method comprising the following steps: 1, obtaining a complete surrounding rock fracture image, and processing the image to obtain an accurate fracture binary image; step 2, utilizing an improved fracture center line algorithm to carry out fracture opening calculation on the fracture binary image; and 3, establishing a two-dimensional fracture network slurry diffusion filling model, endowing the model with the calculated surrounding rock fracture opening degree information, and simulating the slurry diffusion process under the real surrounding rock fracture opening degree. According to the method, firstly, surrounding rock fracture images are obtained through intelligent drilling imaging, then the opening degree information of surrounding rock fractures is measured through a fracture opening degree intelligent identification method, then measured parameters are applied to surrounding rock fracture grouting diffusion numerical simulation, and on the basis, the filling and diffusion rules of grout in fractured surrounding rock are calculated and analyzed; and the best surrounding rock grouting reinforcement effect is sought. And the method is of great significance to reasonable optimization of fracture surrounding rock grouting reinforcement.
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Description

Technical Field

[0001] The present invention relates to the technical field of surrounding rock reinforcement, and particularly to a grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture. Background Art

[0002] At present, the optimization and improvement of grouting for fractures mainly focus on theoretical derivation, experimental research, and numerical simulation, etc.

[0003] (1) In terms of theoretical analysis, mainly by studying the diffusion and migration process of grout in the rock mass fracture network, conclusions about the variation of grout pressure, penetration distance, etc. with time are obtained.

[0004] (2) In experimental research, the visualization study of the migration and diffusion of grout in fractures can be realized, which can intuitively reflect the seepage phenomenon and deposition law of grout.

[0005] (3) In numerical simulation, the commonly used method is to obtain the probability distribution law of fracture occurrence through geological investigation and statistical analysis, and on this basis, use numerical means to simulate the fracture network in the rock mass, and calculate the grout flow based on this.

[0006] The above technologies also have the following disadvantages respectively:

[0007] In terms of theoretical analysis: At present, the grouting theory for fractured rock masses lags far behind the development of grouting practice. The diffusion and migration mechanism of grout in the rock mass fracture network is still in the exploratory stage. In actual grouting engineering sites, the grout mixture ratio, grouting hole layout, and grouting diffusion distance, etc. still rely too much on experience, often resulting in waste of grouting materials and poor reinforcement and plugging effects.

[0008] In terms of experiments, except for a few experimental models that can simulate the grout diffusion under higher grouting pressure, most grouting models can withstand lower grouting pressure, while high-pressure grouting is often required in actual engineering applications.

[0009] In terms of numerical simulation, the current grouting numerical simulation research does not fit well with the actual conditions of on-site engineering, and there is less research considering the coupling effect of grout pressure and fracture aperture change during the grout flow process.

[0010] In addition, on the one hand, due to the fact that the current research on grouting in fractured rock masses is far from mature, a large number of scientific research results are difficult to be transformed into practical grouting engineering applications, and there is still blindness in the selection of grouting parameters for roadway surrounding rock fractures; on the other hand, there are still deficiencies in aspects such as the refined modeling of fracture networks and the characterization of fracture interface effect parameters in the slurry diffusion theory and numerical simulation of fracture networks. The flow law of slurry in fracture networks is affected by various factors such as grouting pressure, grouting speed, the properties of the slurry itself, the aperture and roughness of rock fractures, and groundwater. However, in current experimental research and numerical simulation, there are few parameters such as the aperture of rock fractures in the surrounding rock directly measured to improve the numerical simulation of grouting diffusion. Based on this, the present technical method proposes a grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture. Summary of the Invention

[0011] To solve the technical problems proposed in the background art, the present invention provides a grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture.

[0012] The present invention is implemented by the following technical solutions: The grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture includes the following steps:

[0013] Step 1: Obtain a complete image of the surrounding rock fractures, and process the image to obtain an accurate binary fracture map;

[0014] Step 2: Calculate the fracture aperture of the binary fracture map using an improved fracture centerline algorithm;

[0015] Step 3: Establish a two-dimensional fracture network slurry diffusion filling model, and assign the calculated surrounding rock fracture aperture information to the model to simulate the slurry diffusion process under the actual surrounding rock fracture aperture;

[0016] Step 4: By adjusting adjustable parameters such as the grouting pressure and slurry consumption of the model, when the best slurry diffusion filling effect is achieved, record the corresponding model parameters.

[0017] Specifically, the image processing in Step 1 includes grayscale binaryzation, threshold segmentation, denoising, and smoothing bridging.

[0018] Specifically, the operation of Step 1 is as follows:

[0019] Step 1.1: Grayscale binaryzation; Read the color image of rock fractures into MATLAB, and process the image using image enhancement technology based on the transformed grayscale histogram. Specifically:

[0020] Construct a grayscale value function f(x, y);

[0021]

[0022] Where: m and n respectively represent the number of rows and columns of the grayscale image;

[0023] Since each pixel point of the grayscale image represents a grayscale value, and the range of the grayscale value is 0 - 255, correspondingly, the grayscale image constitutes a grayscale matrix. The grayscale value of each pixel point contains position information, thus constituting the grayscale value function f(x, y). The values of x and y respectively represent the positions corresponding to the grayscale values in the grayscale image, that is, the row and column numbers of the matrix.

[0024] Step 1.2, threshold segmentation; when the function f(x, y) in the image grayscale matrix is greater than the threshold, the value of this point is 1 and shows white; when the function f(x, y) is less than the threshold, the value of this point is 0 and shows black; finally, when the threshold segmentation ends, the grayscale matrix becomes a matrix only containing values of 0 or 1;

[0025] Step 1.3, denoising; removing noise from the crack image; using the medfilt2 function in MATLAB to implement median filtering to remove the miscellaneous points in the image;

[0026] Step 1.4, smoothing and bridging; using the imfill filling function in MATLAB to fill the black points in the white area of the image, then filling the white points in the background area of the image, and finally using the bwselect function to select the real crack area to obtain an accurate binary crack image.

[0027] Specifically, before the step 1.4, it is also necessary to use the dilation function imdilate and the erosion function imerode to smooth the boundary of the binary crack image first to reduce the interference of crack boundary burrs.

[0028] Specifically, the crack aperture is the vertical distance between the upper and lower boundaries of the crack, that is, the distance between the intersection points of the normal line of the midline at any point on the midline of the crack and the upper and lower boundary lines of the crack.

[0029] Specifically, the operation of the step 2 is as follows:

[0030] Step 2.1, determining the initial crack midline; using the bwmorph function of the MATLAB platform to skeletonize the crack as the initial midline of the crack;

[0031] Step 2.2, determining the accurate crack midline; identifying and deleting the left and right boundaries of the crack to eliminate the boundary effect, counting the number of midline points P(i) on the i-th column. If P(i) is greater than 1, then remove all the midline points on this column, and take the average value of the coordinates (i, F(i, k)) of all the midline points on this column as the coordinates of the midline points on this column, where L(i) is the number of crack pixel points on the i-th column, and k = 1, 2, 3,..., L(i);

[0032]

[0033] At this time, the point corresponding to the coordinates (i, M(i)) is the final midline point on the i-th column, successfully eliminating the burr phenomenon of the crack midline and obtaining an improved crack midline that can finally reflect all the shape information of the original image.

[0034] Step 2.3: Determine the normal line of the crack midline; Let C(i) be the slope of the midline tangent at a certain point on the crack midline, then C(i) is expressed as:

[0035]

[0036] The normal line equation at the point (i, Z(i)) on the midline can be expressed as:

[0037]

[0038] If the crack midline at the calculated point is horizontal, the slope C(i) of the tangent at this point is equal to 0, then the normal line of the midline is a vertical line segment, and the crack width at this point is the difference between the ordinate values of the upper and lower boundaries of the crack.

[0039] Step 2.4: Extract the crack boundary; Use the Roberts edge operator to extract the crack boundary through edge detection of the crack image; The operator is as follows:

[0040]

[0041] In the formula, f(x, y) is the coordinate matrix function of the digital image;

[0042] By selecting an appropriate threshold τ such that G((f(x, y)) > τ, the point (x , y) is considered to be an edge point of the graph; In MATLAB, the Roberts edge operator is called through the edge function.

[0043] Step 2.5: Calculate the intersection points of the crack midline normal line and the crack boundary; Since there is no fixed function expression for the upper and lower boundaries of the crack, the intersection points of the crack midline and the crack boundary are calculated by taking the difference at the same abscissa; Specifically:

[0044] Take the lower boundary point (x, C(x)); If the difference between the point (x, C(x)) and the ordinate of the crack midline normal line at the same abscissa is less than the predetermined value, that is:

[0045] |C(x) - f(x)| < ε

[0046] Then the point (x, C(x)) is the intersection point of the lower boundary of the crack and the midline normal line;

[0047] The calculation method of the upper boundary intersection point is the same as that of the lower boundary point;

[0048] Step 2.6: After obtaining the intersection points of the median line normal and the upper and lower boundaries of the crack;

[0049] The crack aperture corresponding to this point on the median line is expressed as:

[0050]

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] The present invention first uses intelligent borehole imaging to obtain the surrounding rock crack image, and then measures the aperture information of the surrounding rock crack through a method of intelligent identification of crack aperture. Then, the measured parameters are applied to the numerical simulation of grouting diffusion in the surrounding rock cracks. On this basis, the filling and diffusion law of the grout in the cracked surrounding rock is calculated and analyzed to seek the best effect of surrounding rock grouting reinforcement. It is of great significance for reasonably optimizing the grouting reinforcement of cracked surrounding rock. Brief Description of the Drawings

[0053] Figure 1 It is a flowchart of the grouting plugging method for cracked surrounding rock based on intelligent identification of crack aperture proposed by the present invention;

[0054] Figure 2 The flowchart of the crack median line aperture algorithm proposed by the present invention;

[0055] Figure 3 It is a schematic diagram of the process of obtaining the crack image proposed by the present invention;

[0056] Figure 4 The schematic diagram of the principle of the crack aperture median line algorithm proposed by the present invention;

[0057] Figure 5 It is a recognition result diagram of the crack median line and the upper and lower boundary lines proposed by the present invention;

[0058] Figure 6 It is a schematic diagram of crack aperture calculation proposed by the present invention. Detailed Embodiments

[0059] Next, in combination with the drawings and specific embodiments, the present invention will be further described. It should be noted that, on the premise of no conflict, the following described embodiments or technical features can be arbitrarily combined to form new embodiments.

[0060] Embodiment 1:

[0061] Referring to Figures 1-6 , the grouting plugging method for cracked surrounding rock based on intelligent identification of crack aperture proposed by the present invention includes the following steps:

[0062] Step 1: Use existing intelligent drilling tools such as intelligent drill rods to obtain a complete image of the surrounding rock fissures. Subsequently, read the color rock mass fissure image into MATLAB and process the image using image enhancement technology based on the transformed gray histogram. The purpose is to enhance the contrast between the fissure area and the background and maximize the separation of the fissure area from the background.

[0063] More specifically, the specific image processing includes the following steps, which can be referred to Figure 3 ;

[0064] First of all, since each pixel point of a grayscale image represents a grayscale value, and the range of grayscale values is 0 - 255. Correspondingly, the grayscale image constitutes a grayscale matrix. The grayscale value of each pixel point contains position information, thus constituting the grayscale value function f(x, y). The values of x and y respectively represent the positions corresponding to the grayscale values in the grayscale image, that is, the row and column numbers of the matrix.

[0065]

[0066] In the formula: m and n respectively represent the number of rows and columns of the grayscale image.

[0067] In addition, further effectively remove the miscellaneous points in the non-fissure area of the image through threshold segmentation. That is, when the function f(x, y) in the image grayscale matrix is greater than the threshold, the value of this point is 1 and it shows white. When the function f(x, y) is less than the threshold, the value of this point is 0 and it shows black. Finally, when the threshold segmentation ends, the grayscale matrix becomes a matrix only containing values of 0 or 1.

[0068] And because during the process of collecting photos, affected by factors such as light intensity, the undulation of the fissure surface, and fissure filling materials, the fissure image is rich in a large amount of noise interference. To accurately obtain the mesoscopic characteristics of the fissures, it is necessary to remove the noise from the fissure image.

[0069] During the image processing process, use the pixel value output by median filtering as the median within the corresponding pixel neighborhood, which can reduce the influence of outliers without reducing the image contrast. Using the medfilt2 function in MATLAB can achieve median filtering to remove the miscellaneous points in the image.

[0070] It is worth mentioning that affected by the impurities on the surface of the rock mass fissures, if not removed, they will be automatically recognized as fissures during the intelligent identification of fissures. Here, we use the imfill filling function in MATLAB to fill the black dots in the white area, then fill the white dots in the background area, and finally use the bwselect function to select the true fissure area to obtain an accurate binary fissure image.

[0071] Due to various external factors such as filling and cementing inside the fracture area and the influence of light, there may still be some black shadows in the fracture under the above optimization treatment, which are misidentified as the background area. It is even possible to separate some originally continuous real fractures into several segments, resulting in an originally complete fracture being misidentified as multiple fractures. Here, we can use the dilation function imdilate and the erosion function imerode to first smooth the boundary of the fracture binary image to reduce the interference of fracture boundary burrs, and then perform bridging treatment on the fractures.

[0072] Step 2: Use the improved fracture centerline algorithm to calculate the fracture aperture of the fracture image processed through the above steps. For the principle of the fracture aperture centerline algorithm, see Figure 4 As shown, curves 1 and 2 are the upper and lower boundaries of the fracture respectively, and 3 is the centerline of the fracture. The fracture aperture is the vertical distance between the upper and lower boundaries of the fracture, that is, the distance between the intersection points of the normal line of any point on the fracture centerline and the upper and lower boundary lines of the fracture. Taking the G point on the fracture centerline as shown in Figure 2 as an example, the fracture aperture corresponding to the G point is the distance between the intersection points M and N of the normal line of the fracture centerline passing through the G point and the upper and lower boundary lines of the fracture.

[0073] The specific operation is to use the bwmorph function on the MATLAB platform to skeletonize the fracture as the initial centerline of the fracture. Identify and delete the left and right boundaries of the fracture to eliminate the boundary effect. Count the number of centerline points P(i) in the i-th column. If P(i) is greater than 1, then remove all the centerline points in that column, and take the average value of the coordinates (i, F(i, k)) of all the centerline points in that column as the coordinates of the centerline points in that column, where L(i) is the number of fracture pixel points in the i-th column, and k = 1, 2, 3, …, L(i);

[0074]

[0075] At this time, the point corresponding to the coordinate (i, M(i)) is the final centerline point in the i-th column, successfully eliminating the burr phenomenon of the fracture centerline and obtaining the improved fracture centerline that can finally reflect all the shape information of the original image.

[0076] After that is the determination of the normal line of the centerline. Let C(i) be the slope of the tangent line of the centerline at a certain point on the fracture centerline, then C(i) is expressed as:

[0077]

[0078] The normal line equation at the point (i, Z(i)) on the centerline can be expressed as:

[0079]

[0080] If the midline of the crack at the calculated point is horizontal, the slope C(i) of the tangent line at that point is equal to 0. Then the normal line of the midline is a vertical line segment, and the corresponding crack width at that point is the difference in the y-coordinates of the upper and lower boundaries of the crack.

[0081] After that, the extraction of the crack boundary is carried out. Here, we use the Roberts edge operator to extract the crack boundary through the edge detection of the crack image. The operator is as follows:

[0082]

[0083] In the formula, f(x, y) is the coordinate matrix function of the digital image.

[0084] By selecting an appropriate threshold τ such that G((f(x, y)) > τ, the point (x , y) is considered to be an edge point of the graph. In MATLAB, the Roberts edge operator is called through the edge function.

[0085] Step 3: After obtaining the positions of the midline and the boundary of the crack, the crack width, that is, the crack opening, can be calculated. Here, by calculating the intersection points of the normal line of the crack midline and the crack boundary, since there is no fixed function expression for the upper and lower boundaries of the crack, the intersection points of the crack midline and the crack boundary are calculated by taking the difference at the same abscissa.

[0086] Taking the lower boundary point (x, C(x)) as an example, if the difference in the y-coordinates between the point (x, C(x)) and the normal line of the crack midline at the same abscissa is less than the predetermined value, that is:

[0087] |C(x) - f(x)| < ε

[0088] Then the point (x, C(x)) is the intersection point of the lower boundary of the crack and the normal line of the midline, and the calculation method for the upper boundary intersection point is the same.

[0089] After obtaining the intersection points of the normal line of the midline and the upper and lower boundaries of the crack, the crack opening corresponding to this point on the midline is expressed as:

[0090]

[0091] By calculating the opening degrees of the points on the crack midline one by one, the crack opening distribution along the crack propagation direction can be obtained.

[0092] Step 4: To simulate and predict the diffusion process of grout in surrounding rock fissures, a two-dimensional fissure network grout diffusion and filling model is established. The information on the aperture of surrounding rock fissures obtained from the previous calculations is assigned to the model to simulate the grout diffusion process under the actual aperture of surrounding rock fissures. By adjusting adjustable parameters such as grouting pressure and grout volume, the best grout diffusion and filling effect is sought. Record the grouting simulation parameters such as grouting pressure under this best result. By accurately obtaining the image of surrounding rock fissures and calculating the information on the aperture of surrounding rock fissures through the improved midline algorithm, and finally applying it to the simulation of grout diffusion in fissures, the information on parameters such as the best grout volume and grouting pressure for grouting reinforcement and plugging of fissured surrounding rock is obtained, which helps to improve the effect of grouting reinforcement and plugging of fissured surrounding rock, accurately control the grouting filling parameters for fissured surrounding rock with different fissure apertures, and is of great significance for the optimization and improvement of grouting reinforcement and plugging of fissured surrounding rock.

[0093] The above embodiments are only the preferred embodiments of the present invention and cannot be used to limit the scope of protection of the present invention. Any non-substantial changes and substitutions made by those skilled in the art on the basis of the present invention belong to the scope of protection required by the present invention.

Claims

1. A grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture, characterized in that It includes the following steps: Step 1: Obtain a complete image of surrounding rock fractures, and process the image to obtain an accurate binary fracture map; Step 2: Use an improved fracture centerline algorithm to calculate the fracture aperture from the binary fracture map; Step 3: Establish a two-dimensional model of slurry diffusion and filling in the fracture network, and assign the calculated surrounding rock fracture aperture information to the model to simulate the slurry diffusion process under the actual surrounding rock fracture aperture; Step 4: By adjusting the parameters of the model, when the best slurry diffusion and filling effect is achieved, record the corresponding model parameters.

2. The grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture according to claim 1, characterized in that, The image processing in Step 1 includes grayscale binarization, threshold segmentation, denoising, and smoothing bridging.

3. The grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture according to claim 1, characterized in that, The operation of Step 1 is as follows: Step 1.1: Grayscale binarization; Read the color rock mass fracture image into MATLAB, and use the image enhancement technology based on the transformed grayscale histogram to process the image. Specifically: Construct a grayscale value function f(x, y); In the formula: m and n respectively represent the number of rows and columns of the grayscale image; Since each pixel point of the grayscale image represents a grayscale value, and the range of grayscale values is 0 - 255, correspondingly, the grayscale image forms a grayscale matrix. The grayscale value of each pixel point contains position information, thus constituting the grayscale value function f(x, y). The values of x and y respectively represent the positions corresponding to the grayscale values in the grayscale image, that is, the row and column numbers of the matrix. Step 1.2: Threshold segmentation; When the function f(x, y) in the image grayscale matrix is greater than the threshold, the value of this point is 1, showing white; when the function f(x, y) is less than the threshold, the value of this point is 0, showing black; finally, when the threshold segmentation ends, the grayscale matrix becomes a matrix containing only values of 0 or 1; Step 1.3: Denoising; Remove the noise from the fracture image; Use the medfilt2 function in MATLAB to implement median filtering to remove the miscellaneous points in the image; Step 1.4: Smoothing bridging; Use the imfill filling function in MATLAB to fill the black points in the white area of the image, then fill the white points in the background area of the image, and finally use the bwselect function to select the true fracture area to obtain an accurate binary fracture map.

4. The grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture according to claim 1, characterized in that, Before Step 1.4, it is also necessary to use the dilation function imdilate and the erosion function imerode to smooth the boundary of the binary fracture map first to reduce the interference of fracture boundary burrs.

5. The grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture according to claim 1, characterized in that, The fracture aperture is the vertical distance between the upper and lower boundaries of the fracture, that is, the distance between the intersection points of the midline normal of any point on the fracture centerline and the upper and lower boundary lines of the fracture.

6. The grouting plugging method for fractured surrounding rock based on intelligent identification of fracture aperture according to claim 1, characterized in that The operation of Step 2 is as follows: Step 2.1: Determine the initial fracture centerline; Use the bwmorph function on the MATLAB platform to skeletonize the fracture as the initial centerline of the fracture; Step 2.2: Determine the accurate fissure midline; identify and delete the left and right boundaries of the fissure to eliminate the boundary effect, count the number of midline points P(i) in the i-th column. If P(i) is greater than 1, then remove all midline points in this column, and take the average value of the coordinates (i, F(i, k)) of all midline points in this column as the coordinates of the midline points in this column, where L(i) is the number of fissure pixel points in the i-th column, and k = 1, 2, 3, …, L(i); At this time, the point corresponding to the coordinate (i, M(i)) is the final midline point in the i-th column, successfully eliminating the burr phenomenon of the fissure midline and obtaining an improved fissure midline that can finally reflect all the shape information of the original image; Step 2.3: Determine the normal line of the fissure midline; let C(i) be the slope of the midline tangent at a certain point on the fissure midline, then C(i) is expressed as: The normal line equation at the point (i, Z(i)) on the midline can be expressed as: If the fissure midline at the calculated point is horizontal, then the slope C(i) of the tangent at this point is equal to 0, and the normal line of the midline is a vertical line segment. The corresponding fissure width at this point is the difference in the vertical coordinates of the upper and lower boundaries of the fissure; Step 2.4: Fissure boundary extraction; use the Roberts edge operator to extract the fissure boundary through edge detection of the fissure image; the operator is as follows: where f(x, y) is the coordinate matrix function of the digital image; By selecting an appropriate threshold τ such that G((f(x, y)) > τ, the point (x , y) is considered an edge point of the graph; in MATLAB, the Roberts edge operator is called through the edge function; Step 2.5: Calculate the intersection points of the fissure midline normal line and the fissure boundary; since there is no fixed function expression for the upper and lower boundaries of the fissure, the method of taking the difference at the same abscissa is used to calculate the intersection points of the fissure midline and the fissure boundary; specifically: Take the lower boundary point (x, C(x)); if the difference between the point (x, C(x)) and the ordinate of the fissure midline normal line at the same abscissa is less than the predetermined value, that is: |C(x) - f(x)| < ε Then the point (x, C(x)) is the intersection point of the lower boundary of the fissure and the midline normal line; The calculation method of the upper boundary intersection point is the same as that of the lower boundary point; Step 2.6: After obtaining the intersection points of the midline normal line and the upper and lower boundaries of the fissure; The fissure opening corresponding to this point on the midline is expressed as: