A method for estimating jrc based on hausdorff distance

Abstract

This invention discloses a method for JRC estimation based on Hausdorff distance. The method involves extracting the coordinates of 10 standard profiles of Barton's structural surfaces with a sampling interval of dx. Based on the extracted x and y coordinate data, the cumulative slope of each standard profile is calculated, forming a cumulative slope data sequence of standard curves. The structural surface curves are then measured in the field, and the coordinates of the measured curves are extracted with a sampling interval of dx. The cumulative slope of the measured curves is calculated, forming a cumulative slope data sequence of measured data. The Hausdorff distance between the cumulative slope of the measured curves and the cumulative slope of the standard curves is calculated. The standard profile of the structural surface most similar to the measured curve is identified, and its corresponding JRC value is assigned to the measured curve, ultimately estimating the JRC value of the measured curve. This invention achieves JRC value estimation based on the self-similarity of the cumulative slope of the curves, avoiding the arbitrariness and subjectivity in determining the JRC value caused by comparing visual observation with standard profiles.

Description

Technical Field

[0001] This invention belongs to the field of engineering geological exploration technology, specifically relating to a method for JRC estimation based on Hausdorff distance. Background Technology

[0002] In 1977, Barton and Choubey proposed using the surface roughness coefficient (JRC) to quantitatively describe the differences in surface roughness undulations of rock joints in their paper "BARTONN, CHOUBEY V. The shear strength of rock joints in theory and practice [J]. Rock Mechanics, 1977, 10(1 / 2): 1-54". They constructed 10 standard surface profiles, each corresponding to a specific JRC value, such as... Figure 1 As shown. The standard sections corresponding to these 10 standard structural plane outlines have been included in the ISRM specification.

[0003] In practical fieldwork, the visual comparison method is commonly used. This involves comparing the actual structural surface morphology with the Barton standard profile and determining the JRC value of the standard profile that most closely resembles the actual surface based on visual differences. This method is intuitive, requires no calculation, and is widely used in determining the roughness coefficient of structural surfaces in the field. However, due to the complex and varied geometry of rock mass structural surfaces, which differ in length, the visual comparison method often results in surfaces that are similar to multiple curves or dissimilar to all standard curves. Therefore, the JRC score obtained using this method often depends on the user's experience, is difficult to accurately determine, and is highly arbitrary, frequently leading to human estimation errors.

[0004] To reduce the subjectivity and arbitrariness of the visual comparison method, many researchers have established quantitative calculation formulas between JRC and the root mean square of slope Z2, as shown in Table 1.

[0005] Table 1 summarizes the calculation formulas for JRC value and Z2.

[0006]

[0007] However, the above method also has the following drawbacks:

[0008] 1) Current quantitative calculation formulas for JRC are derived from a fitting formula based on the relationship between the root mean square slope of Barton's 10 standard curves and the JRC value. This fitting formula only has 10 data points, which limits its applicability. When using this formula, JRC values ​​may be less than 0 or greater than 20, as shown in Tables 1-3. If JRC is less than 0, it does not match the actual situation; if JRC is greater than 20, it will lead to some shear strength calculation formulas based on JRC values ​​resulting in an overestimation of the shear strength, which is detrimental to engineering safety.

[0009] 2) For the same curve, regardless of the calculation formula used, there should be only one JRC value, or the calculated results should be similar. However, the root mean square slope Z2 in the JRC value fitting formula is closely related to the sampling interval of the profile. If different sampling intervals are used, multiple JRC values ​​may appear for one curve depending on the calculation formula, as shown in Table 4.

[0010] According to the study in Reference 3, the root mean square of the slope Z2 is closely related to the sampling interval of the profile. Therefore, when using the empirical formula to calculate the JRC value of the measured curve, the sampling interval of the profile must be consistent with the sampling interval used when deriving the empirical formula. Otherwise, the error in calculating JRC may be as high as 100% (see Reference 4).

[0011] Furthermore, patents CN105678786A, CN105716545A, and CN105737768A disclose methods for evaluating the surface roughness coefficient based on Jaccard similarity, Dice similarity, and Cosine similarity metrics, respectively. The main steps are: extracting the coordinates of 10 standard profile curves of Barton, calculating adjacent undulation angles, statistically analyzing the frequency distribution of undulation angles within each statistical interval, and reconstructing the undulation angle feature vector of the standard profile curves; then calculating the similarity between the undulation angle feature vector of the test curve and the undulation angle feature vectors of each standard curve based on the Jaccard similarity, Dice similarity, or Cosine similarity metrics, and selecting the roughness coefficient of the curve corresponding to a similarity of 1 as the JRC value of the test curve.

[0012] However, the above methods also have a number of drawbacks:

[0013] 1) The similarity calculation of the above method requires statistical analysis of the fluctuation angle distribution interval, construction of a new fluctuation angle feature vector, and vector operation. The calculation method and process are relatively complex.

[0014] 2) The above method for evaluating the surface roughness coefficient of similarity measurement not only requires that the sampling interval of the test curve and the curve spacing of the standard curve be the same, but also that the statistical interval of the undulation angle be the same, which places strict requirements on the calculation conditions.

[0015] 3) The accuracy of the evaluation results is low.

[0016] Taking the test curve example disclosed in the embodiment of patent CN105737768A as an example, according to its calculation method, the JRC value of the test curve is 2 to 4. However, through intuitive comparison with Barton's 10 standard curves, based on engineering experience, it can be intuitively judged that the JRC value of the test curve should be 18 to 20.

[0017] Taking the test curve example disclosed in the embodiment of patent CN105678786A as an example, according to its calculation method, the JRC value of the test curve is 10 to 12. However, through intuitive comparison with Barton's 10 standard curves, based on engineering experience, the JRC value of the test curve should also be 18 to 20.

[0018] Taking the test curve example disclosed in the embodiment of patent CN105716545A as an example, according to its calculation method, the JRC value of the test curve is 10 to 12. However, through intuitive comparison with Barton's 10 standard curves, based on engineering experience, the JRC value of the test curve should also be 18 to 20.

[0019] Furthermore, to verify the error in the calculation results based on the similarity of the curve undulation angle feature vector in the above method, the test curve case published in the embodiment of CN105737768A is used as an example for further verification. The verification method is as follows: extract the coordinates of the test curve in CN105737768A (sampling interval dx = 0.5 mm), calculate its root mean square slope (Z2), and then calculate its JRC value according to the methods in references 3, 4, and 5, as shown in Table 1. The calculation results show that the JRC value of the test curve is greater than 20. According to the same method, the JRC values ​​in the other two published patents are calculated (see Tables 2 and 3), and they are also greater than 20. According to Barton's 10 standard curves, the range of JRC value is between 0 and 20. For those calculated to have a JRC greater than 20, the value should be 20. It can be seen that there is a significant difference between the JRC value calculated according to the method published in the above three patents and the JRC value calculated by experience and the root mean square slope Z2.

[0020] Based on the above engineering experience verification and slope root mean square verification, it can be concluded that the structural surface roughness coefficient evaluation method based on the similarity measure of curve undulation angle feature vector in the above three published patents is inaccurate and has a large error.

[0021] Calculation of JRC values ​​for the test curves in Table 1 CN105737768A

[0022]

[0023] Calculation of JRC values ​​for the test curves in Table 2CN105678786A

[0024]

[0025] Calculation of JRC values ​​for the test curves in Table 3 CN105716545A

[0026]

[0027] Table 4 shows the different JRC values ​​calculated for the same curve using different sampling intervals.

[0028]

[0029] Note: The root mean square (Z2) data of the standard curve are from publicly published literature 6: Li Rui, Xiao Weimin. Research on new formula for calculating JRC of rock joints based on fine digital processing of Barton standard profile [J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(S1):3515-3522, and the calculation formula is from literature 3. Summary of the Invention

[0030] The purpose of this invention is to provide a method for JRC estimation based on Hausdorff distance. This invention, based on Hausdorff distance, achieves JRC value estimation using the self-similarity of the cumulative slope of a curve, avoiding the arbitrariness and subjectivity in determining the JRC value caused by comparing visual observation with standard profiles.

[0031] The technical solution of this invention is: a method for JRC estimation based on Hausdorff distance, which involves extracting the coordinates of 10 standard profile lines of Barton's structural surfaces with a sampling interval dx as the precision; calculating the cumulative slope of each standard profile line based on the extracted x and y coordinate data to form a cumulative slope data sequence of standard curves; measuring the structural surface curves in the field and extracting the coordinates of the measured curves with a sampling interval dx as the precision, calculating the cumulative slope of the measured curves to form a cumulative slope data sequence of measured data; calculating the Hausdorff distance between the cumulative slope of the measured curves and the cumulative slope of the standard curves; finding the standard profile line of the structural surface most similar to the measured curves and assigning its corresponding JRC value to the measured curves, thus finally estimating the JRC value of the measured curves.

[0032] In the aforementioned method for JRC estimation based on Hausdorff distance, the calculation method for Hausdorff distance is as follows:

[0033] Let: Curve coordinate data sequence C = [x1y1, x2y2, x3y3, ..., x... n y n ], where x n y n Let x and y be the x and y coordinates of the nth sampling point on the curve under the sampling interval dx;

[0034] Let: (x) i y i ), (x i+1 y i+1 () represents the coordinates of two adjacent points on the curve;

[0035] Then: the absolute value of the slope of the curve, k i The calculation formula is as follows:

[0036]

[0037] The formula for calculating the cumulative slope of the curve, Sumki, is as follows:

[0038]

[0039] The formula for calculating the cumulative slope data series is as follows:

[0040] C_sumk=[x1sumk1, x2sumk2, x3sumk3,···,x n-1 sumk n-1 ];

[0041] Based on the above formula, the cumulative slope data sequence of the measured curves is calculated under the same sampling interval dx. and the cumulative slope data sequence S of each structural surface standard contour line 1_sumk S 2_sumk S 3_sumk S 10_sumk ;

[0042] Let curve A consist of n points, and let curve B also consist of n points.

[0043] Then the point set A = {a1, a2, ..., a...} n}, point set B = {b1, b2, ..., b} n}, then the Hausdorff distance between point sets A and B is:

[0044] H(A,B) = max[h(A,B),h(B,A)]

[0045]

[0046]

[0047]

[0048] In the formula: h(A,B) and h(B,A) are called the one-way Hausdorff distance from point set A to B and the one-way Hausdorff distance from B to A, respectively; H(A,B) is called the Hausdorff distance between point sets A and B; |a i -b j | and |b j -a i | represents the Euclidean distance between two points;

[0049] Will With S 1_sumk , With S 2_sumk … With S 10_sumk Substituting the values ​​into the formulas above, we can calculate the results. respectively with S 1_sumk S 2_sumk S 3_sumk S 10_sumk Hausdorff is located at distances from Hd1, Hd2, Hd3, ..., Hd 10 .

[0050] In the aforementioned method for JRC estimation based on Hausdorff distance, when H d =H dmin =min[Hd1, Hd2, Hd3,···,Hd 10 When H d The corresponding standard profile of the structural surface is most similar to the measured curve.

[0051] In the aforementioned method for JRC estimation based on Hausdorff distance, the standard contour lines of the structural surfaces are digitally processed using Photoshop and MATLAB to remove noise points and fill in fracture surfaces before the cumulative slope calculation.

[0052] In the aforementioned method for JRC estimation based on Hausdorff distance, the sampling interval is 1 mm.

[0053] In the aforementioned method for JRC estimation based on Hausdorff distance, in the field environment, the measured curves are obtained by acquiring the contour and coordinate data of the structural surface through a shape extractor, profilometer, or scanner.

[0054] Beneficial effects

[0055] Compared with existing technologies, this invention addresses the shortcomings of the field visual comparison method for determining JRC values, which suffers from arbitrariness and subjectivity. It refines Barton's 10 standard structural surface curves, extracting their coordinates with a precision of dx. Based on the extracted x and y coordinate data, the cumulative slope of the curves is calculated, forming a cumulative slope data sequence for the standard curves. Structural surface curves are then measured in the field, and their coordinates are extracted with the same precision of dx. The cumulative slope of the measured curves is calculated, forming a cumulative slope data sequence for the measured data. By calculating the Hausdorff distance between the cumulative slope of the measured curves and the cumulative slope of the standard curves, the standard profile most similar to the measured curves is identified. This achieves accurate JRC value estimation based on the similarity of the cumulative slopes, avoiding the arbitrariness and subjectivity of manually determining JRC values.

[0056] Compared with the method of calculating the root mean square of the slope Z2, the present invention has the following advantages:

[0057] 1) This invention overcomes the shortcoming of the JRC calculation formula where the calculated result exceeds the JRC boundary. The JRC value estimation method based on Hausdorff distance proposed in this invention calculates JRC values ​​between 0 and 20, avoiding the shortcoming of the JRC value calculated using the root mean square slope Z2 formula which exceeds 20.

[0058] 2) This invention overcomes the problem of multiple JRC values ​​for the same curve due to different sampling intervals. Analysis shows that while the sampling interval has a significant impact on the JRC calculation results, the root mean square slope Z2 is positively correlated with the JRC value regardless of the sampling interval. Therefore, to overcome the influence of sampling interval on JRC calculation errors, this invention proposes a JRC estimation method based on the similarity of cumulative slopes of curves. This method only requires ensuring that the sampling interval of the measured curve is consistent with that of the standard curve to obtain the estimated JRC value of the measured curve. See Tables 5 and 6.

[0059] Furthermore, compared with similarity calculation methods based on fluctuating angle feature vectors, the present invention has the following advantages:

[0060] 1) Simple requirements for calculation conditions. This invention only requires ensuring that the sampling interval of the test curve and the sampling interval of the standard curve are the same to obtain the corresponding estimation results.

[0061] 2) The evaluation results are highly accurate. Taking the test curve case published in the CN105737768A embodiment as an example, the Hausdorff distance of the cumulative slope between the test curve and the standard curve was calculated, and the JRC value of the test curve at a sampling interval of 0.5 mm and 1 mm was calculated to be 18-20. The specific calculation results are shown in Tables 5 and 6.

[0062] Table 5. JRC values ​​of the test curves in CN105737768A calculated according to this invention (sampling interval 0.5 mm).

[0063]

[0064] Table 6. JRC values ​​of the test curves in CN105737768A calculated according to this invention (sampling interval 1 mm).

[0065]

[0066] Comparison revealed that the calculation results based on cumulative slope similarity proposed in this invention are more accurate than the calculation results based on undulation angle feature vector similarity proposed in patent CN105737768A.

[0067] In summary, this invention achieves JRC value estimation based on the similarity of cumulative slope of curves, avoiding the arbitrariness and subjectivity in determining JRC values ​​caused by comparing with standard profiles using visual observation, and also achieving higher calculation accuracy. Attached Figure Description

[0068] Figure 1 These are the standard curves of Barton's 10 structural surfaces and their corresponding JRC values;

[0069] Figure 2 It is a standard Barton curve profile obtained after refined processing;

[0070] Figure 3 This is a schematic diagram of the in-situ shear failure surface of mudstone, where (a) represents τ. 1-2 Photographs of the shear failure surface of the specimen, (b) is τ 1-3 Photographs of the shear failure surface of the test block;

[0071] Figure 4 It extracts the profile curve on the failure surface, where (a) is τ 1-2 The profile curve on the failure surface, (b) is τ 1-3 The profile curve on the damaged surface;

[0072] Figure 5 It is the test curve fitted with a sampling interval of dx = 1 mm.

[0073] Figure 6 Field measured profile of structural surface curves. Detailed Implementation

[0074] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0075] Example 1. A method for JRC estimation based on Hausdorff distance, comprising the following steps:

[0076] Step 1: Obtain the Barton standard profile. In 1997, Barton and Choubey published "The Shear Strength of Rock Joints in Theory and Practice" in the journal *Rock Mechanics*, and the corresponding PDF version can be downloaded online. The original standard profile image can be obtained from this article. Figure 1 ).

[0077] Step Two: Refined Digital Processing of Standard Profile Lines. Referring to Reference 2, professional graphics processing software such as Photoshop and MATLAB were used to perform refined digital processing on the 10 standard profile lines, including removing unwanted points and filling in breaks, to obtain 10 Barton standard profile lines (e.g., ...). Figure 2 Using the left endpoint of each curve as (0, 0), and sampling interval of dx = 1 mm, the coordinates of each curve are extracted in MATLAB for analysis and calculation.

[0078] Step 3: Obtain the measured structural surface curve profile and coordinate data. In the field, the profile and coordinate data of the structural surface can be obtained using a shape extractor, profilometer, or scanner.

[0079] Step 4: Under the dx sampling interval, obtain the coordinate data series of the curve as C, and calculate the slope k of the curve respectively. i Cumulative slope Sum ki The data sequence C_sumk reconstructed from the cumulative slope i .

[0080] Suppose a curve has coordinates C = [x1y1, x2y2, x3y3, ..., x... n y n ]in

[0081] The formula for calculating the absolute value of the slope of a curve is shown in Formula 1:

[0082]

[0083] Cumulative slope of the curve:

[0084]

[0085] The data sequence reconstructed by the cumulative slope is

[0086] C_sumk=[x1sumk1, x2sumk2, x3sumk3,···,x n-1sumk n-1 ]

[0087] Step 5: Under the same sampling interval, according to Step 4, obtain the cumulative slope data sequence of the test curves respectively. and the cumulative slope data series of each standard curve The cumulative slope data sequences of the 10 standard curves are S 1_sumk S 2_sumk S 3_sumk S 10_sumk .

[0088] Step Six: Calculate the Hausdorff distance between the cumulative slope of the measured structural surface curves and the Hausdorff distance of the Barton standard profile using the Hausdorff distance method. Calculate the Hausdorff distance between the cumulative slope sequence of the measured structural surface curves and the cumulative slope sequences of 10 standard Barton curves, namely Hd1, Hd2, Hd3, ..., Hd... 10 .

[0089] The formula for calculating Hausdorff distance is as follows:

[0090] Let there be a point set A = {a1, a2, ..., a...} n}, B={b1,b2,…,b n}, then the Hausdorff distance between point sets A and B is:

[0091] H(A,B)=max[h(A,B),h(B,A)] (11)

[0092]

[0093]

[0094]

[0095] In the formula: h(A,B) and h(B,A) are called the one-way Hausdorff distance from point set A to B and the one-way Hausdorff distance from B to A, respectively; H(A,B) is called the Hausdorff distance between point sets A and B; |a i -b j | and |b j -a i | represents the Euclidean distance between two points.

[0096] Step 7: Compare the Hausdorff distances of the curves. The smaller the Hausdorff distance (Hd), the higher the similarity between the test curve and the standard curve. Select the smallest Hausdorff distance (Hd). min The standard curve is the curve most similar to the measured curve, and the JRC value of the corresponding standard curve is the same as the JRC value of the measured curve.

[0097] Hd = Hd min =min[Hd1, Hd2, Hd3,···,Hd 10 ]

[0098] JRC 测 =JRC Hd .

[0099] Example 2. A method for JRC estimation based on Hausdorff distance. Taking Barton standard profile data as an example, the cumulative slope Hausdorff distance similarity of each curve with the other 9 curves is calculated. The sampling interval is dx = 1 mm. The calculation results are shown in Table 7 below.

[0100] Table 7. Results of cumulative slope calculation for Hausdorff distance using Barton standard profile data (dx = 1 mm)

[0101] Hd <![CDATA[JRC 0-2 ]]> <![CDATA[JRC 2-4 ]]> <![CDATA[JRC 4-6 ]]> JRC6-8 <![CDATA[JRC 8-10 ]]> <![CDATA[JRC 10-12 ]]> <![CDATA[JRC 12-14 ]]> <![CDATA[JRC 14-16 ]]> <![CDATA[JRC 16-18 ]]> <![CDATA[JRC 18-20 ]]> <![CDATA[JRC 0-2 ]]> 0 3.06603 4.71936 6.99331 9.72853 10.78038 11.77530 16.72914 17.48315 21.98502 <![CDATA[JRC 2-4 ]]> 3.06603 0 1.65487 3.92883 6.66266 7.71552 8.70938 13.66352 14.41866 18.92054 <![CDATA[JRC 4-6 ]]> 4.71936 1.65487 0 2.27396 5.01692 6.06138 7.05850 12.01084 12.76379 17.26566 JRC6-8 6.99331 3.92883 2.27396 0 2.74996 3.78792 4.78758 9.73776 10.48983 14.99171 <![CDATA[JRC 8-10 ]]> 9.72853 6.66266 5.01692 2.74996 0 1.05960 2.05117 7.00626 7.76283 12.26470 <![CDATA[JRC 10-12 ]]> 10.78038 7.71552 6.06138 3.78792 1.05960 0 1.40811 5.94990 6.70323 11.20510 <![CDATA[JRC 12-14 ]]> 11.77530 8.70938 7.05850 4.78758 2.05117 1.40811 0 4.95509 5.71166 10.21353 <![CDATA[JRC 14-16 ]]> 16.72914 13.66352 12.01084 9.73776 7.00626 5.94990 4.95509 0 1.30614 5.25844 <![CDATA[JRC 16-118 ]]> 17.48315 14.41866 12.76379 10.48983 7.76283 6.70323 5.71166 1.30614 0 4.50187 <![CDATA[JRC 18-20 ]]> 21.98502 18.92054 17.26566 14.99171 12.26470 11.20510 10.21353 5.25844 4.50187 0

[0102] As shown in Table 7, the similarity distance between each curve and its own cumulative curve data sequence is 0. The similarity distance increases with the increase or decrease of the JRC value, indicating a worse similarity. This verifies the correctness and accuracy of the method for estimating the surface roughness coefficient (JRC) based on cumulative slope similarity. The difference in cumulative slope between each curve and its two adjacent curves is the smallest, indicating the best similarity between these two adjacent curves. This demonstrates that the JRC value can be estimated based on the similarity of cumulative slope.

[0103] Example 3. A method for JRC estimation based on Hausdorff distance. Taking a set of mudstone in-situ shear tests at a hydroelectric power station in Tanzania as an example, photographs of the shear failure surface are shown below. Figure 3 As shown in (a) and (b), a 10cm cross-section of the structure along the shear direction was obtained using a surface profilometer. Figure 4 As shown in (a) and (b) in the figure.

[0104] By adjusting τ 1-2 The profile curve (test1) and τ on the failure surface 1-3The cross-sectional curve (test2) on the damaged surface was used in MATLAB software to extract its coordinates at a sampling interval of dx = 1 mm. The damaged surface curve was then refitted at a sampling interval of 1 mm as shown below. Figure 5 As shown in Tables 8 and 9, the Hausdorff distance between the cumulative slope data sequences of curves test1 and test2 and the cumulative slope data sequences of the 10 Barton profile curves is calculated based on the extracted curve coordinates.

[0105] Table 8 shows the calculation of the Hausdorff distance between the Test1 curve and the standard curve.

[0106]

[0107] Table 9 shows the calculation of the Hausdorff distance between the Test2 curve and the standard curve.

[0108]

[0109] As can be seen from Table 8, the cumulative slope of the test1 curve is the smallest with that of the fourth Barton standard profile curve, indicating that its JRC value is closest to that of the fourth Barton standard profile. Therefore, the JRC of the test1 curve is 6 to 8.

[0110] As can be seen from Table 9, the cumulative slope Hausdorff distance between the test2 curve and the 7th Barton standard profile curve is the smallest, indicating that its JRC value is closest to the JRC value of the 7th Barton standard profile. Therefore, the JRC of the test2 curve is 12 to 14.

[0111] Example 4. Taking a field-measured structural surface curve as an example, see... Figure 6 The Hausdorff distance of the cumulative slope between the measured structural surface curve and 10 standard curves was calculated using this invention, as shown in Table 10. The measured curve has the smallest Hausdorff distance of cumulative slope between it and the 5th Barton standard profile curve, indicating that its JRC value is closest to the JRC value of the 5th Barton standard profile. Therefore, the JRC of the measured curve is 8 to 10.

[0112] Table 10 shows the cumulative slope and Hausdorff distance calculation table for the measured curve and the standard curve.

[0113]

[0114] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for JRC estimation based on Hausdorff distance, characterized in that, The coordinates of the standard contour lines of 10 structural surfaces of Barton were extracted with a sampling interval dx as the precision. Based on the extracted x and y coordinate data, the cumulative slope of each standard contour line was calculated to form a cumulative slope data sequence of the standard curve. The structural surface curves were measured in the field, and the coordinates of the measured curves were extracted with a sampling interval dx as the precision. The cumulative slope of the measured curves was calculated to form a cumulative slope data sequence of the measured data. The Hausdorff distance between the cumulative slope of the measured curve and the cumulative slope of the standard curve is calculated. The standard profile of the structural surface most similar to the measured curve is then identified, and its corresponding JRC value is assigned to the measured curve, ultimately estimating the JRC value of the measured curve. The calculation method for the Hausdorff distance is as follows: Let: Curve coordinate data sequence C = [ x 1 y 1, x 2 y 2, x 3 y 3, ··· , x n y n ],in x n y n Let x and y be the x and y coordinates of the nth sampling point on the curve under the sampling interval dx; Let: (x) i y i (x) i+1 y i+1 () represents the coordinates of two adjacent points on the curve; Then: the absolute value of the slope of the curve ki The calculation formula is as follows: Cumulative slope of the curve Sumki The calculation formula is as follows: The formula for calculating the cumulative slope data series is as follows: C_ sumk =[ x 1sumk1 ， x 2sumk2 ， x 3sumk3 ， ··· ， x n-1sumkn-1 ]； Based on the above formula, under the same sampling interval dx, the cumulative slope data sequence T_ of the measured curve is calculated respectively. sumk i and the cumulative slope data sequence S1_ for each standard contour line of the structural surface. sumk S2_ sumk S3_ sumk , ··· S 10 _ sumk ; Let curve A consist of n points, and let curve B also consist of n points. Then the point set A = { a1 , a2 ,..., an }, point set B = { b1 , b2 ,..., bn }, then the Hausdorff distance between point sets A and B is: H(A, B) =max[h(A, B), h(B, A)] ， In the formula: h(A, B) and h(B, A) are called the one-way Hausdorff distance from point set A to B and the one-way Hausdorff distance from B to A, respectively; H(A, B) is called the Hausdorff distance between point sets A and B; | ai - bj| and | bj - ai | represents the Euclidean distance between two points; T_ sumk i With S1_ sumk T_ sumk i With S2_ sumk ... ... T_ sumk i With S 10 _ sumk Substituting these values ​​into the above formula, we can calculate T_. sumk i respectively with S1_ sumk S2_ sumk S3_ sumk , ··· S 10 _ sumk Hausdorf is located at distances from Hd1, Hd2, and Hd3. ··· Hd 10 .

2. The method for JRC estimation based on Hausdorff distance according to claim 1, characterized in that, When H d =H dmin =min[Hd1, Hd2, Hd3, ··· Hd 10 When H d The corresponding standard profile of the structural surface is most similar to the measured curve.

3. The method for JRC estimation based on Hausdorff distance according to claim 1, characterized in that, Before calculating the cumulative slope, the standard contour lines of the structural surfaces were digitally processed using Photoshop and MATLAB to remove noise and fill in fractures.

4. The method for JRC estimation based on Hausdorff distance according to claim 1, characterized in that, The sampling interval is 1 mm.

5. The method for JRC estimation based on Hausdorff distance according to claim 1, characterized in that, In the field, the measured curves are obtained by collecting the contour and coordinate data of the structural surface through a shape sampler, profilometer or scanner.

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