CN115711587A - Method for determining minimum sample number of section line strips for structural surface three-dimensional roughness evaluation - Google Patents
Method for determining minimum sample number of section line strips for structural surface three-dimensional roughness evaluation Download PDFInfo
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Abstract
A minimum sample number determining method for section line strips for structural surface three-dimensional roughness evaluation comprises the following steps: s1, determining the measuring direction of the three-dimensional roughness and the optimal width of a section line strip; s2, measuring a section line strip on the surface of the structural surface; s3, establishing a section line strip triangularization model; s4, calculating the mean value and standard deviation of the three-dimensional roughness basic indexes of the structural surface; s5, inversely calculating the minimum sample number of the section line strips according to the three-dimensional roughness measurement error of the structural surface allowed by engineering; s6, repeating the steps S4 and S5 until the number of the section line strips obtained by measurement meets the requirement of the minimum sample number of the required section line strips obtained by inverse calculation, and finally, the number of the section line strips obtained by measurement is the minimum sample number of the section line strips. The invention solves the problems that the dimension difference between the two-dimensional section line and the three-dimensional structure surface appearance cannot be eliminated, the sampling interval is difficult to accurately determine, and the number of measurement samples has no quantitative index.
Description
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a minimum sample number determination method for section line strips for structural plane three-dimensional roughness evaluation.
Background
The structural surface roughness has obvious influence on the mechanical and hydraulic characteristics of rock mass, is a key parameter in rock mass stability analysis, and can be generally characterized by Joint Roughness Coefficient (JRC), fractal dimension and statistical parameters. In engineering practice, these roughness parameters can be conveniently estimated using two-dimensional section lines. However, the surface topography of a structural surface has three-dimensional characteristics, and it remains controversial whether the three-dimensional roughness of a structural surface can be characterized using a single or multiple two-dimensional section lines, given the dimensional differences between two-dimensional roughness and three-dimensional roughness.
When evaluating the roughness of a structural surface using two-dimensional section lines, some geometric features located within the section line interval may be ignored, and researchers have therefore attempted to improve the accuracy of the roughness evaluation by reducing the sampling interval of the section lines. In previous studies, the cross-sectional line was typically measured using a sampling interval of 0.1mm to 15 mm. Although studies have verified the effect of the cross-sectional line sampling intervals on the roughness evaluation results, there are still results that are inconsistent with each other in terms of cross-sectional line optimal sampling intervals. For example, bao et al found that when the sampling interval of the cross-sectional lines was less than 4mm, the average roughness of the cross-sectional lines remained constant regardless of the roughness of the structural plane. However, ge et al found that both the size and roughness of the structured surface had a significant effect on the optimal sampling interval of the profile line. Therefore, the optimal sampling interval of the two-dimensional section line still needs to be further explored.
Although the accuracy of the structural surface roughness evaluation can be improved by reducing the sampling interval of the two-dimensional section lines, measuring excessive section lines is time-consuming and labor-consuming, and is not beneficial to engineering practice. It is therefore important to determine the minimum number of cross-hatching (RMN) required to obtain a sufficient degree of structural surface roughness. Yong et al performed scale ratio analysis on a 100cm long section line of a slate structural surface and found that at least 65 section lines were required to accurately evaluate the roughness of the structural surface. Bao et al studied the geometric non-uniformity of the structural surface roughness and suggested that the sampling interval of the structural surface section lines should be less than 4mm. Prior studies provide insights into the RMN of the identified section lines, however the above work was analyzed under defined conditions. In this state, a large number of structural surface roughness measurements have been made, and statistical information of the structural surface roughness is known. The RMN of the section lines is evaluated by analyzing the existing database, and a reference can be provided for the structural surfaces with similar roughness. However, research on Du Shi and the like shows that the structural surface roughness has non-uniformity and has significant difference at different positions. In most cases, no reliable a priori statistical information about the roughness of the structural surface is available. In fact, statistical information on the roughness of the structural surface can only be revealed gradually during the roughness measurement. Therefore, it is necessary to dynamically judge whether the measured profile line is sufficient to reliably evaluate the roughness of the structural surface during the measurement.
Researchers and engineers often use the average roughness of the section lines as a representative roughness value for the structural surface, taking into account the variability of the two-dimensional section line roughness. In order to study the effectiveness of section lines in characterizing the three-dimensional roughness of a structural surface, researchers have done extensive work in comparing the differences between two-dimensional roughness and three-dimensional roughness. For example, belem et al found that the rougher the structured surface, the lower the average two-dimensional roughness estimated the three-dimensional roughness. However, both Tatone and Grasselli find that the average two-dimensional roughness may either overestimate or underestimate the three-dimensional roughness. These findings indicate that the average roughness of the section lines may not be effective in evaluating the three-dimensional roughness of the structural surface. Therefore, some researchers have proposed other processing methods regarding two-dimensional roughness to evaluate the three-dimensional roughness of the structural surface. For example, liu et al analyzed their experimental results using the maximum two-dimensional roughness of the section lines, while \37063. The above-described treatment of the profile line two-dimensional roughness (i.e., average roughness, maximum roughness, and weighted average roughness) facilitates the use of profile lines in evaluating the three-dimensional roughness of a structural surface. However, the results obtained by different treatment methods are inconsistent, and the practicability of the section line is weakened. The consequence of this inconsistency is likely to be because dimensional differences between two-dimensional section lines and three-dimensional structure surface topography cannot be eliminated by simply increasing the number of section lines. Therefore, how to effectively evaluate the three-dimensional roughness of the structural plane using the section lines requires further research.
The two-dimensional section line of the structural surface is widely applied to the evaluation of the roughness of the structural surface in engineering practice at present due to the convenience of acquisition and measurement. Although the section line is successfully applied to the aspect of evaluating the two-dimensional roughness of the structural surface, the problems that the sampling interval is difficult to accurately determine, the measurement quantity has no quantitative index, and the dimension difference between the two-dimensional section line and the three-dimensional structural surface appearance cannot be eliminated are still faced in the aspect of evaluating the three-dimensional roughness. Therefore, when the three-dimensional roughness of the structural surface is evaluated by using the two-dimensional section line, the reliability of the evaluation result is insufficient, and the accuracy of the evaluation result of the mechanical and hydraulic characteristics of the structural surface is directly affected.
Disclosure of Invention
In order to solve the problems that the dimensional difference between a two-dimensional section line and the appearance of a three-dimensional structure surface, which is faced by the evaluation of the three-dimensional roughness of the structure surface by the two-dimensional section line in the prior art, cannot be eliminated, the sampling interval is difficult to accurately determine, and the measurement quantity has no quantitative index, the invention provides the minimum sample number determination method of the section line strip for the evaluation of the three-dimensional roughness of the structure surface.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a section line strip minimum sample number determination method for structural surface three-dimensional roughness evaluation, the method comprising the steps of:
s1, selecting a structural surface outcrop, and determining the measurement direction of the three-dimensional roughness and the optimal width of a section line strip; the section line strip is composed of two adjacent section lines, and the width of the section line strip is equal to the distance between the two adjacent section lines;
s2, measuring the section line strip on the surface of the structural surface based on the measuring direction and the optimal width of the section line strip;
s3, adopting a high-precision scanner and an image processing technology to carry out digital processing on the measured hatching strips, and establishing a hatching strip triangularization model;
s4, calculating the mean value and the standard deviation of the three-dimensional roughness basic index of the structural surface based on the established section line strip triangularization model;
s5, inversely calculating the minimum sample number of the section line strips according to the engineering-allowed three-dimensional roughness measurement error of the structural surface and the following formula (1);
wherein, delta is the three-dimensional roughness measurement error of the structural surface, s is the standard deviation of the three-dimensional roughness basic index of the section line strip, mu is the average value of the three-dimensional roughness basic index of the section line strip, n is the measurement quantity of the section line strip, beta is the confidence level,
is the upper quantile of t distribution with the degree of freedom of n-1;
s6, repeating the steps S4 and S5 in the section line strip measuring process until the number of the measured section line strips meets the requirement of the minimum sample number of the required section line strips obtained by inverse calculation, and finally, the number of the measured section line strips is the minimum sample number of the section line strips.
Further, in the step S1, the measurement direction of the three-dimensional roughness is consistent with the shearing direction of the structural surface or the seepage direction of the fracture; when the size of the structural surface is less than or equal to 300mm, the optimal width of the section line strip is 3mm; when the structural face dimension is greater than 300mm, the cross-sectional strip has an optimum width of 5mm.
And further, in the step S3, when the section line strip is subjected to triangularization modeling, the distance between the adopted sampling points is consistent with the distance between the sampling points of a calculation formula of the structural surface three-dimensional roughness basic index.
Furthermore, in the step S4, the three-dimensional roughness basic index is a three-dimensional average inclination angle θ of the structural plane s Three-dimensional slope root-mean-square Z of structural plane 2s And the area projection ratio R of the structural surface s The calculation formula is as follows:
wherein M is x 、M y Number of sampling points, alpha, uniformly distributed along the X and Y axes, respectively i Is the inclination angle of the outer normal vector of the ith triangular element, i.e. the angle between the outer normal of the triangular plane and the Z axis, A t Is the actual area of the surface of the structural plane, A n Is the projection area of the structural plane on the X-Y plane, a i SI is the sampling pitch of the point cloud, which is the area of the ith triangle element.
Compared with the prior art, the invention has the following beneficial effects: the three-dimensional local topography of the structural surface is characterized by a section line strip consisting of adjacent section lines instead of a single section line, so that the dimension difference between the two-dimensional section line and the three-dimensional topography of the structural surface can be effectively eliminated; different optimal widths of section line strips are adopted for structural surfaces with different sizes, so that the measurement time can be greatly reduced on the premise of ensuring the three-dimensional roughness measurement precision of the structural surfaces; in the measuring process, whether the measured section line strip sample number meets the requirement of the minimum sample number of the required section line strip obtained by inverse calculation or not is dynamically judged, a quantitative index can be provided for the minimum sample number of the section line strip required by the structural surface three-dimensional roughness evaluation, the resource waste is avoided while the structural surface three-dimensional roughness is accurately evaluated, and the engineering application of the two-dimensional section line in the structural surface three-dimensional roughness evaluation is effectively promoted.
Drawings
FIG. 1 is a partial triangle cell and section line strip extracted from a structural surface triangularization model, where (a) is the structural surface triangularization model, (b) is the partial triangle cell, and (b) is the section line strip;
FIG. 2 is a graph showing the effect of the width of a cross-sectional strip on the results of three-dimensional roughness evaluation;
FIG. 3 is a schematic illustration of cross-sectional strip measurements;
fig. 4 shows the position of the hatching strip, in which only one hatching is shown on the left side of the hatching strip, the width of which is 3mm.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 4, a structural surface three-dimensional roughness evaluation method based on section line strips comprises the following steps:
s1, selecting a structural surface outcrop, and determining the measurement direction of the three-dimensional roughness and the optimal width of a section line strip; the section line strip consists of two adjacent section lines, and the width of the section line strip is equal to the distance between the two adjacent section lines;
s2, measuring the section line strip on the surface of the structural surface based on the measuring direction and the optimal width of the section line strip;
s3, performing digital processing on the measured section line strip by adopting a high-precision scanner and an image processing technology, and establishing a section line strip triangularization model;
specifically, the surface topography of the structural surface is usually constructed on the measurement point cloud by a triangulation method, and the triangulation treatment can be performed on the section line strip obtained by measurement by a Delaunay triangulation algorithm; through the triangulation process, the surface topography of the structured surface can be discretized into a limited number of triangles, as shown in fig. 1 (a); the method is widely used for representing the geometric characteristics of the surface of the structural surface and has remarkable advantages in the aspect of evaluating the three-dimensional roughness of the structural surface; when the three-dimensional roughness of the structural surface is evaluated, the geometric characteristics of the structural surface can be conveniently represented by the inclination angle and the area of a triangular unit on a triangular surface model; two local triangle units extracted from the triangulated model of the structural surface are shown in fig. 1 (b), which shows that the geometric features of the two local triangle units T1 and T2 are controlled by two adjacent two-dimensional section lines P1 and P2; however, the inclination of the section line does not coincide with the inclination of the triangular unit, and thus the inclination of the section line is not the same as the inclination of the triangular unit; these observations confirm that a single section line cannot accurately reflect the three-dimensional morphological characteristics of the surface of the structural plane; in contrast, the local three-dimensional morphological characteristics of a structural surface can be accurately characterized by the combined morphology of two adjacent two-dimensional section lines, which is called a section line strip, as shown in fig. 1 (c); the width of each section line strip is equal to the distance between two adjacent two-dimensional section lines; generally, the three-dimensional morphology of the structural plane can be broken down into a series of section line strips, the number of which depends on the width of the section line strips; thus, the roughness of the plurality of cross-hatched strips can potentially be used to approximate the three-dimensional roughness of the entire surface of the structural plane;
s4, calculating the mean value and the standard deviation of the three-dimensional roughness basic index of the structural surface based on the established section line strip triangularization model;
s5, inversely calculating the minimum sample number of the section line strips according to the three-dimensional roughness measurement error of the structural surface allowed by engineering and the following formula (1);
wherein, delta is the three-dimensional roughness measurement error of the structural surface, s is the standard deviation of the three-dimensional roughness basic index of the section line strip, mu is the average value of the three-dimensional roughness basic index of the section line strip, n is the measurement quantity of the section line strip, beta is the confidence level,
is the upper quantile of t distribution with the degree of freedom of n-1;
specifically, in engineering practice, the measurement error delta of the three-dimensional roughness of the structural surface can be set to 5%, the confidence level beta can be set to 95%, and the degree of freedom is the upper quantile of t distribution of n-1
The value of (2) can be obtained by table look-up or calculation according to the number of the measured section line strips;
s6, repeating the steps S4 and S5 in the section line strip measuring process until the number of the measured section line strips meets the requirement of the minimum sample number of the required section line strips obtained by inverse calculation, and finally, the number of the measured section line strips is the minimum sample number of the section line strips.
Preferably, in the step S1, the measurement direction of the three-dimensional roughness is consistent with the shearing direction of the structural surface or the seepage direction of the crack; when the size of the structural surface is less than or equal to 300mm, the optimal width of the section line strip is 3mm; when the structural face dimension is greater than 300mm, the cross-sectional strip has an optimum width of 5mm.
Specifically, 5 kinds of section line strip widths (i.e., 1mm, 2mm, 3mm, 4mm and 5 mm) are usedThe influence of the section line strip width on the three-dimensional roughness evaluation accuracy of the structural surface is researched; under the condition that the three-dimensional roughness measurement error delta of the structural surface is set to be 5% and the confidence level beta is set to be 95%, 30 times of random sampling tests are carried out on each width of the section line strips, and the measurement error of the three-dimensional roughness of the structural surface obtained under each width of the section line strips is calculated after the measurement is finished, as shown in figure 2; the graph shows that the average sampling rate for different sized facets decreases with increasing cross-hatch strip width, indicating that increasing the cross-hatch strip width can effectively reduce the measurement time; the figure also shows that the measurement error of the three-dimensional roughness of the structural surface is reduced along with the increase of the size of the structural surface, but is increased along with the increase of the width of the section line strip; when the size of the structural surface is larger than 300mm, the three-dimensional roughness basically indicates the three-dimensional average inclination angle theta of the structural surface s Three-dimensional slope root-mean-square Z of structural plane 2s And the area projection ratio R of the structural surface s The measurement error of (a) is less than 5% under all section line strip width conditions; however, when the structural surface size is less than 300mm, the three-dimensional roughness basic index Z 2s The measurement error of (2) is more than 5% when the bandwidth of the profile line is 5 mm; thus, for structural surfaces with dimensions less than or equal to 300mm, an optimum width of the section line strip of 3mm is recommended, and for structural surfaces with dimensions greater than 300mm, an optimum width of the section line strip of 5mm is recommended.
Further, in the step S3, when triangulating the cross-section line strip, the sampling point pitch used is consistent with the sampling point pitch of the calculation formula of the structural plane three-dimensional roughness basic index.
Specifically, the point cloud data of the profile line strips can be subjected to regularization processing, so that the point cloud spacing of the established triangulated profile line strip model is consistent with the point spacing required by the calculation formula of the basic index of the three-dimensional roughness of the structural surface to be calculated.
Preferably, in the step S4, the three-dimensional roughness basic index is a three-dimensional average inclination angle θ of the structural plane s Three-dimensional slope root-mean-square Z of structural plane 2s And the area projection ratio R of the structural surface s The calculation formula is as followsThe following:
wherein, M x 、M y Number of sampling points, alpha, uniformly distributed along the X and Y axes, respectively i Is the inclination of the outer normal vector of the ith triangular element, i.e. the angle between the outer normal of the triangular plane and the Z axis, A t Is the actual area of the surface of the structural plane, A n Is the projection area of the structural plane on the X-Y plane, a i SI is the sampling pitch of the point cloud, which is the area of the ith triangle element.
Specifically, the three-dimensional roughness basic index θ s 、Z 2s And R s The method can respectively reflect the average dip angle characteristic, the local dip angle characteristic and the size characteristic of a surface convex body of the surface of the structural surface, and the inclination degree and the size of the concave-convex body of the surface of the structural surface are basic roughness factors influencing the mechanical and hydraulic performances of the structural surface, so that the selected basic index of the three-dimensional roughness is enough to quantify the three-dimensional roughness of the structural surface; in addition, in order to further improve the evaluation accuracy of the three-dimensional roughness of the structural surface, more three-dimensional roughness parameters (such as the undulation height parameter) can be included in the three-dimensional roughness basic index.
Example (c): a structural surface three-dimensional roughness evaluation method based on section line strips comprises the following steps:
firstly, selecting the exposed end of the sandstone structural surface in the landslide region of the Yamajiaguo ditch of Guizhou county, yichang City, hubei province, wherein the measuring direction of the three-dimensional roughness is consistent with the shearing direction of the structural surface; the dimension of the structural surface is about 100mm, so the optimal width of the section line strip is 3mm;
then, based on the measuring direction and the optimal width of the section line strip, measuring the section line strip on the surface of the structural surface by using a profile curvometer, digitizing the measured section line strip by using a high-precision scanner and an image processing technology, triangulating the measured section line strip by using a Delaunay triangulation algorithm, and establishing a section line strip triangularization model by using a sampling interval of 0.5mm, wherein the section line strip triangularization model is shown in FIG. 3; three-dimensional average dip angle theta of structural surface s Three-dimensional slope root-mean-square Z of structural plane 2s And the area projection ratio R of the structural surface s Calculating the mean value and standard deviation of the three-dimensional roughness basic index of the structural surface based on the established section line strip triangularization model as the basic index of the three-dimensional roughness; setting the measurement error delta of the three-dimensional roughness of the structural surface to be 5%, setting the confidence level beta to be 95%, and carrying out inverse calculation according to the formula (1) to obtain the minimum sample number of section line strips; repeating the steps S4 and S5 in the section line strip measuring process until the number of the measured section line strips meets the requirement of the minimum sample number of the required section line strips obtained by inverse calculation, the number of the finally measured section line strips is 9, and the positions of the section line strips are shown in FIG. 4, so that the minimum sample number of the section line strips required by the structural plane three-dimensional roughness evaluation is 9.
Calculating three-dimensional gradient root-mean-square Z of structural plane according to established section line strip triangularization model 2s (ii) a Then, calculating a three-dimensional joint roughness coefficient JRC according to a formula (5) provided by Mo and Li, wherein the calculation result is 11.1; obtaining a true value of the three-dimensional JRC of the structural surface by inverse calculation according to the direct shear test, wherein the true value is 11.8; the relative error between the structural surface three-dimensional roughness evaluation result based on the section line strips and the true value is only-5.9%, which shows that the invention can conveniently and accurately evaluate the three-dimensional roughness of the structural surface.
The embodiments described in this specification are merely illustrative of implementations of the inventive concepts, which are intended for purposes of illustration only. The scope of the present invention should not be construed as being limited to the particular forms set forth in the examples, but rather as being defined by the claims and the equivalents thereof which can occur to those skilled in the art upon consideration of the present inventive concept.
Claims (4)
1. A minimum sample number determination method for section line strips for structural surface three-dimensional roughness evaluation is characterized by comprising the following steps of:
s1, selecting a structural surface outcrop, and determining the measurement direction of the three-dimensional roughness and the optimal width of a section line strip; the section line strip consists of two adjacent section lines, and the width of the section line strip is equal to the distance between the two adjacent section lines;
s2, measuring the section line strip on the surface of the structural surface based on the measuring direction and the optimal width of the section line strip;
s3, performing digital processing on the measured section line strip by adopting a high-precision scanner and an image processing technology, and establishing a section line strip triangularization model;
s4, calculating the mean value and the standard deviation of the three-dimensional roughness basic index of the structural surface based on the established section line strip triangularization model;
s5, inversely calculating the minimum sample number of the section line strips according to the three-dimensional roughness measurement error of the structural surface allowed by engineering and the following formula (1);
wherein, delta is the three-dimensional roughness measurement error of the structural surface, s is the standard deviation of the three-dimensional roughness basic index of the section line strip, mu is the average value of the three-dimensional roughness basic index of the section line strip, n is the measurement quantity of the section line strip, beta is the confidence level,
is the upper quantile of t distribution with the degree of freedom of n-1;
s6, repeating the steps S4 and S5 in the section line strip measuring process until the number of the measured section line strips meets the requirement of the minimum sample number of the required section line strips obtained by inverse calculation, and finally, the number of the measured section line strips is the minimum sample number of the section line strips.
2. The method for determining the minimum sample number of section line strips for structural surface three-dimensional roughness evaluation according to claim 1, wherein in the step S1, the measurement direction of the three-dimensional roughness coincides with the shearing direction of the structural surface or the seepage direction of the cracks; when the size of the structural surface is less than or equal to 300mm, the optimal width of the section line strip is 3mm; when the structural face dimension is greater than 300mm, the cross-sectional strip has an optimum width of 5mm.
3. The method for determining the minimum sample number of the section line strips for evaluating the three-dimensional roughness of the structural surface according to claim 1 or 2, wherein in the step S3, when the section line strips are triangulated, the adopted sampling point intervals are consistent with the sampling point intervals of the calculation formula of the basic index of the three-dimensional roughness of the structural surface.
4. The method for determining the minimum sample number of section line strips for structural surface three-dimensional roughness evaluation according to claim 1 or 2, wherein in the step S4, the three-dimensional roughness basic index is the structural surface three-dimensional average inclination angle θ s Three-dimensional slope root-mean-square Z of structural plane 2s And the area projection ratio R of the structural surface s The calculation formula is as follows:
wherein M is x 、M y Number of sampling points, alpha, uniformly distributed along the X and Y axes, respectively i Is the inclination angle of the outer normal vector of the ith triangular element, i.e. the angle between the outer normal of the triangular plane and the Z axis, A t Is the actual area of the surface of the structural plane, A n Is the projection area of the structural plane on the X-Y plane, a i SI is the sampling pitch of the point cloud, which is the area of the ith triangle element.
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