CN112577450A - Engineering rock mass structural surface roughness coefficient determination method based on multiple regression analysis - Google Patents

Engineering rock mass structural surface roughness coefficient determination method based on multiple regression analysis Download PDF

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CN112577450A
CN112577450A CN202011182987.5A CN202011182987A CN112577450A CN 112577450 A CN112577450 A CN 112577450A CN 202011182987 A CN202011182987 A CN 202011182987A CN 112577450 A CN112577450 A CN 112577450A
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roughness coefficient
fractal dimension
length
sample
roughness
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杜时贵
雍睿
罗战友
王昌硕
林杭
章子华
刘文连
杨小聪
李泽
夏才初
郑荣跃
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Ningbo University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/30—Measuring arrangements characterised by the use of optical techniques for measuring roughness or irregularity of surfaces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
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Abstract

Method for determining roughness coefficient of engineering rock mass structural surface based on multivariate regression analysis, and dimensional effect fractal dimension D is accurately obtainednBased on multiple regression analysis processing, obtaining potential slip surface roughness coefficient fractal dimension D corresponding to length KkThe roughness coefficient is divided into a number of dimensions DkPotential slip plane actual length K, and roughness coefficient fractal dimension D20、D30、D40The obtained value is substituted into a JRC size effect fractal model to obtain a potential slip surface roughness coefficient JRC corresponding to the length Kk. The method ensures the reliability of the prediction result of the roughness coefficient of the large-scale structural surface, and avoids the traditional method that D is replaced by an empirical valuenCausing a problem of large error of the prediction result.

Description

Engineering rock mass structural surface roughness coefficient determination method based on multiple regression analysis
Technical Field
The invention belongs to the technical field of engineering, and relates to a method for determining a rough coefficient of a structural surface of an engineering rock, in particular to a multivariate regression model constructed based on the relationship between the dimensional effect fractal dimension of the structural surface roughness coefficient and the size of a sample, which can provide the dimensional effect fractal dimension more consistent with the actual measurement result, and ensure the reliability of the roughness prediction result of the structural surface of the engineering rock.
Background
The shear strength of the rock mass structural plane is one of the key factors for controlling the stability of the rock slope. The shear strength properties of the structural surface are mainly determined by the morphology, continuity, cement filling characteristics and wall rock properties of the structural surface, secondary changes, stress history (repeated shearing times) and the like. For hard structural surfaces, surface morphology is a determining factor in controlling the mechanical properties of the structural surface. The structural surface roughness coefficient (JRC) is a mechanical index describing the influence of the surface roughness relief morphology on the structural surface shear strength. Meanwhile, the JRC-JCS model is the only empirical estimation method of the structural plane shear strength parameter which can be applied to engineering practice at present. Therefore, the method for accurately obtaining the roughness coefficient of the engineering rock mass structural plane has important significance for accurately evaluating the stability of the rock slope.
The change of the mechanical properties of the structural surface with the increase of the sampling size is a well-known phenomenon, and the size effect becomes a part for researching the mechanical behavior of the structural surface to be non-negligible. A large number of scholars prove the objective fact that the structural surface roughness coefficient has the size effect through experimental research. However, in order to directly apply the measurement result of the roughness coefficient of the small-scale structural surface to the large-scale structural surface of the engineering, people usually apply the measurement result of the roughness coefficient of the small-scale structural surface, which is manually reduced by 70%, to the determination of the shear strength of the specific slope rock structural surface, and the measurement result covers the objective property that the roughness coefficient of the structural surface has the size effect, and is neither scientific nor reasonable, and has low reliability. In order to solve the problem of difficulty in evaluating the roughness coefficient of the engineering scale structural surface, domestic and foreign scholars develop research on the structural surface roughness coefficient acquisition method based on the size effect rule, wherein the representative research is as follows:
barton and Bandis (1980) have, based on a number of experiments, derived a JRC calculation that takes into account the size effect:
Figure BDA0002750662190000021
in the formula, L0Represents the length of the structural plane of the laboratory sample, i.e. 100 mm; l isnRepresenting the length of the engineering rock mass structural plane; JRC0The roughness coefficient of the structural surface under the length (100 mm); JRCnThe coefficient of roughness of the engineering rock mass structural plane.
According to analysis of physical significance of fractal dimension D and structural surface roughness of a fractal geometry-based code scale method in Du-Shi-Gui (1997), the fact that inevitable correlation does not exist between the fractal dimension and JRC is considered, but a JRC size effect fractal model constructed on the basis of actual measurement data statistical analysis can objectively and really describe the rule that the roughness coefficient is reduced along with the increase of sampling length, and the JRC size effect fractal model is as follows:
Figure BDA0002750662190000022
in the formula, JRCn、DnRespectively the structural surface roughness coefficient and the dimension effect fractal dimension, L, corresponding to the engineering rock structural surfacenIs the size of the rock mass structural plane.
In contrast to the empirical formula proposed by Barton, Bandis (1980) above, the prediction model of Duchen (1997) uses the size effect fractal dimension DnSubstitution empirical coefficient 0.02JRC0The method has clear physical significance, and the prediction result of the roughness coefficient of the engineering rock mass structural plane is more accurate in principle. However, whether the prediction result is reliable or not depends directly on obtaining the size-effect fractal dimension DnThe accuracy of (2).
Fractal dimension D to account for size effectsnThe value problem of (D) is proposed successively30The method comprises a method of obtaining a fractal dimension D of the size effect of the roughness coefficient corresponding to a sample with the size of 30cm by comparing an expected value obtained by a sample with the size of 30cm with an expected value obtained by a sample with the size of 10cm and estimating the attenuation tendency, and a weighted average method30By D30In place of DnAnd then predicting the mechanical parameters of the large-scale engineering material. However, it has been found that the attenuation trend is estimated only by comparing the expected value obtained for a 30cm sample with the expected value obtained for a 10cm sample. The latter obtains the attenuation rule of the mechanical parameters of the small-scale engineering material according to the test result by measuring the roughness coefficient of the structural surface samples with the sizes of 10cm, 20cm, 30cm and 40cm, and divides the corresponding size effect of the roughness coefficient into dimensions D20、D30、D40Weighted average replacing Dn. Weighted average method and "D30Compared with the method, the method considers a plurality of fractal dimension values of the roughness coefficient of the small-size structural surface, assigns the weight of the dimension effect fractal dimension of samples with different sizes, and calculates the precision ratio D30The method is obviously improved. However, both of these methods have a fundamental limitation, and they ignore the size-effect fractal dimension DnThe rule that the sample size changes is a certain fixed value (D)30Or D20、D30、D40Weighted average) instead of DnNeglecting D in different sizesnThe difference in value.
In addition, based on the Barton and Bandis models, the Ficker (2017) provides an improved large-scale structural surface roughness coefficient prediction model according to a fractal theory:
Figure BDA0002750662190000031
the value of fractal dimension D in the model is 1+0.02JRC0. It also replaces D with some fixed value obtainednNeglecting D in different sizesnThe difference in the values.
Disclosure of Invention
In order to solve the problem of low value precision of the size effect of the roughness coefficient of the large-scale structural surface of the engineering rock mass at present, the invention accurately obtains the fractal dimension D of the size effectnThe method for determining the roughness coefficient of the engineering rock mass structural surface is provided based on multiple regression analysis, the reliability of the prediction result of the roughness coefficient of the large-scale structural surface is ensured, and the traditional method is prevented from adopting an empirical value to replace DnCausing a problem of large error of the prediction result.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for determining the roughness coefficient of a structural surface of an engineering rock mass based on multivariate regression analysis comprises the following steps:
(1) carrying out grading analysis on the slope stability of the surface mine, determining a slope potential failure mode, determining a potential slip plane, and finding a structural plane corresponding to the potential slip plane;
(2) investigating a structural surface corresponding to the potential slip surface, searching a large-area exposed structural surface, and acquiring surface point cloud data of the structural surface by adopting a handheld three-dimensional laser scanner;
(3) judging the potential slip direction of the side slope according to the grading analysis result, and extracting a large-scale structural surface contour curve along the potential slip direction based on the structural surface point cloud data;
(4) acquiring roughness coefficients of each contour curve under different sizes by adopting a global search method, and carrying out first-level statistical analysis, namely statistical analysis on the calculation results of the roughness coefficients of each contour curve under different sizes obtained by the global search method, and respectively acquiring the statistical average value of the roughness coefficients of each contour curve under different sizes;
(5) calculating the fractal dimension D of the roughness coefficient of the series dimension structural surface according to the following formula according to the obtained statistical average value of the roughness coefficient of each profile curvenMeasured value:
Figure BDA0002750662190000041
wherein JRC10Is the length L of the structural surface10A statistical average of roughness coefficients at 10 cm; JRCnIs a structural plane with a length of LnThe statistical average value of the corresponding roughness coefficient;
(6) summarizing the series of size roughness coefficient fractal dimensions of all measured profile curves, and carrying out second-level statistical analysis, namely, the statistical analysis of the roughness coefficient fractal dimensions of all profile curves under each size condition, so as to obtain the average value of the roughness coefficient fractal dimensions of each size of the structural surface
Figure BDA0002750662190000042
And the relation with the size of the sample reflects the general trend of fractal dimension of each size roughness coefficient along with the change of the size of the sample, and is expressed by the following matrix:
Figure BDA0002750662190000043
Figure BDA0002750662190000044
for all contour curve dimensions, i.e. the length L of the structural plane20Fractal dimension of roughness coefficient corresponding to 20cm sample;
Figure BDA0002750662190000045
for all contour curve dimensions, i.e. the length L of the structural plane30Fractal dimension of roughness coefficient corresponding to a sample of 30 cm;
Figure BDA0002750662190000046
for all contour curve dimensions, i.e. the length L of the structural planen-1Fractal dimension of roughness coefficient corresponding to (n-1) × 10cm sample;
Figure BDA0002750662190000047
for all contour curve dimensions, i.e. the length L of the structural planenFractal dimension of roughness coefficient corresponding to sample of n × 10 cm;
(7) drawing a relation scatter diagram of the series size roughness coefficient fractal dimension and the sample size according to the relation between the summarized series size roughness coefficient fractal dimension and the sample size, and selecting two contour curves which are close to the upper limit and the lower limit of the change rule of the series size roughness coefficient fractal dimension along with the sample size, namely, the fractal dimensions of the roughness coefficients of all sizes of the contour curve M and the contour curve N are respectively expressed by a matrix as follows:
Figure BDA0002750662190000051
Figure BDA0002750662190000052
Figure BDA0002750662190000053
length L of structural surface corresponding to profile curve M20Fractal dimension of roughness coefficient corresponding to 20cm sample;
Figure BDA0002750662190000054
length L of structural surface corresponding to profile curve M30Fractal dimension of roughness coefficient corresponding to a sample of 30 cm;
Figure BDA0002750662190000055
length L of structural surface corresponding to profile curve Mn-1Fractal dimension of roughness coefficient corresponding to (n-1) × 10cm sample;
Figure BDA0002750662190000056
length L of structural surface corresponding to profile curve MnFractal dimension of roughness coefficient corresponding to sample of n × 10 cm;
Figure BDA0002750662190000057
length L of structural surface corresponding to profile curve N20Fractal dimension of roughness coefficient corresponding to sample of 220 cm;
Figure BDA0002750662190000058
length L of structural surface corresponding to profile curve N30Fractal dimension of roughness coefficient corresponding to a sample of 30 cm;
Figure BDA0002750662190000059
length L of structural surface corresponding to profile curve Nn-1Fractal dimension of roughness coefficient corresponding to (n-1) × 10cm sample;
Figure BDA00027506621900000510
length L of structural surface corresponding to profile curve NnFractal dimension of roughness coefficient corresponding to sample of n × 10 cm;
(8) respectively in matrix A0、AM、ANThe independent variable x and all elements in the corresponding column of the second row, the dependent variable y, are fitted using the following model:
y＝fⅠln(x)+fⅡx+fⅢ
in the formula fⅠ、fⅡ、fⅢFor the fitting coefficients, a total of 3 different sets of f were obtainedⅠ、fⅡ、fⅢ；
(9) Construction of the fitting coefficient fⅠ、fⅡ、fⅢFractal dimension D of roughness coefficient of structural surface with the length of 20cm, 30cm and 40cm20、D30、D40The system of equations of the ternary equation:
Figure BDA0002750662190000061
extraction of A0In
Figure BDA0002750662190000062
AMIn
Figure BDA0002750662190000063
ANIn
Figure BDA0002750662190000064
Figure BDA0002750662190000065
Combined with the 3 groups f obtainedⅠ、fⅡ、fⅢSolving to obtain the coefficient A of the ternary linear equation setⅠ、AⅡ、AⅢ、BⅠ、BⅡ、BⅢ、CⅠ、CⅡ、CⅢ。
(10) Obtaining a roughness coefficient size effect fractal dimension D according to the stepsnThe multiple regression prediction model of (1):
Dn(L,D20,D30,D40)＝fⅠln(L)+fⅡL+fⅢ
Figure BDA0002750662190000066
(11) obtaining a profile curve with the length of 40cm on the potential slip surface by adopting a structural surface roughness coefficient directional statistical measurement method, and obtaining a statistical average value D of fractal dimensions of roughness coefficients of the sizes of 20cm, 30cm and 40cm of the potential slip surface to be measured according to the steps (4) and (5)20、D30、D40；
Will potentially slipThe actual length K of the surface and the fractal dimension D of the roughness coefficient obtained in the step (11)20、D30、D40Namely, the fractal dimension D of the roughness coefficient of the potential slip surface corresponding to the length K is obtainedkThe obtained data is substituted into a JRC size effect fractal model to obtain a potential slip surface roughness coefficient JRC corresponding to the length Kk，
Figure BDA0002750662190000067
Further, in the step (2), the area of the structural surface is larger than 1m × 1 m.
Still further, in the step (3), the interval between the profile curves of the structural surface is preferably greater than 10cm, and the total number of the profile curves is preferably greater than 30.
The technical conception of the invention is as follows: in order to solve the problem of accurate shear strength parameters of the engineering rock mass structural plane, the method must avoid replacing D with an empirical approximate single valuenShould objectively reflect the fractal dimension D of the size effectnAnd the roughness coefficient of the engineering rock mass structural plane can be accurately obtained according to the rule of sample size change.
The invention has the following beneficial effects: the reliability of the prediction result of the roughness coefficient of the large-scale structural surface is ensured, and the traditional method that the empirical value is adopted to replace D is avoidednCausing a problem of large error of the prediction result.
Drawings
FIG. 1 is a diagram showing the relationship between the fractal dimension of the dimensional roughness coefficient of the contour curve series and the size of a sample.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1, a method for determining the roughness coefficient of a structural plane of an engineering rock based on multivariate regression analysis comprises the following steps:
(1) carrying out grading analysis on the slope stability of the surface mine, determining a slope potential failure mode, determining a potential slip plane, and finding a structural plane corresponding to the potential slip plane;
(2) investigating a structural surface corresponding to the potential slip surface, searching a large-area exposed structural surface (the area should be larger than 1m multiplied by 1m), and acquiring surface point cloud data of the structural surface by adopting a handheld three-dimensional laser scanner;
(3) judging the potential slip direction of the side slope according to the grading analysis result, extracting a large-scale structural surface contour curve along the potential slip direction based on the structural surface point cloud data, and obtaining 30 structural surface contour curves with the length of 330cm in total;
(4) acquiring roughness coefficients of each contour curve under different sizes by adopting a global search method, and carrying out first-level statistical analysis, namely statistical analysis on the calculation results of the roughness coefficients of each contour curve under different sizes obtained by the global search method, and respectively acquiring the statistical average value of the roughness coefficients of each contour curve under different sizes;
(5) calculating the fractal dimension D of the roughness coefficient of the series dimension structural surface according to the following formula according to the obtained statistical average value of the roughness coefficient of each profile curvenMeasured value:
Figure BDA0002750662190000081
wherein JRC10Is the length L of the structural surface10A statistical average of roughness coefficients at 10 cm; JRCnIs a structural plane with a length of LnThe statistical average value of the corresponding roughness coefficient;
(6) summarizing the series of size roughness coefficient fractal dimensions of all measured profile curves, and carrying out second-level statistical analysis, namely, the statistical analysis of the roughness coefficient fractal dimensions of all profile curves under each size condition, so as to obtain the average value of the roughness coefficient fractal dimensions of each size of the structural surface
Figure BDA0002750662190000082
And the relation with the size of the sample reflects the general trend of fractal dimension of each size roughness coefficient along with the change of the size of the sample, and is expressed by the following matrix:
Figure BDA0002750662190000083
Figure BDA0002750662190000084
for all contour curve dimensions, i.e. the length L of the structural plane20Fractal dimension of roughness coefficient corresponding to 20cm sample;
Figure BDA0002750662190000085
for all contour curve dimensions, i.e. the length L of the structural plane30Fractal dimension of roughness coefficient corresponding to a sample of 30 cm;
Figure BDA0002750662190000086
for all contour curve dimensions, i.e. the length L of the structural planen-1Fractal dimension of roughness coefficient corresponding to (n-1) × 10cm sample;
Figure BDA0002750662190000087
for all contour curve dimensions, i.e. the length L of the structural planenFractal dimension of roughness coefficient corresponding to sample of n × 10 cm;
(7) drawing a relation scatter diagram (shown in figure 1) of the fractal dimension of the series size roughness coefficient and the size of the sample according to the relation between the fractal dimension of the series size roughness coefficient and the size of the sample, and selecting the fractal dimension of each size roughness coefficient of two contour curves (contour curve 17 and contour curve 25) which are close to the upper limit and the lower limit of the change rule of the fractal dimension of the series size roughness coefficient along with the size of the sample, wherein the fractal dimension of each size roughness coefficient is expressed by a matrix as follows:
Figure BDA0002750662190000088
Figure BDA0002750662190000091
L20is 20 cm; l is30Is 30 cm; l is320Is 320 cm; l is330Is 330 cm;
Figure BDA0002750662190000092
length L of structural plane corresponding to contour curve 1720Fractal dimension of roughness coefficient corresponding to 20cm sample;
Figure BDA0002750662190000093
length L of structural plane corresponding to contour curve 1730Fractal dimension of roughness coefficient corresponding to a sample of 30 cm;
Figure BDA0002750662190000094
length L of structural plane corresponding to contour curve 17320Fractal dimension of roughness coefficient corresponding to 320cm sample;
Figure BDA0002750662190000095
length L of structural plane corresponding to contour curve 17330Fractal dimension of roughness coefficient corresponding to 330cm sample;
Figure BDA0002750662190000096
length L of structural plane corresponding to profile curve 2520Fractal dimension of roughness coefficient corresponding to 20cm sample;
Figure BDA0002750662190000097
length L of structural plane corresponding to profile curve 2530Fractal dimension of roughness coefficient corresponding to a sample of 30 cm;
Figure BDA0002750662190000098
length L of structural plane corresponding to profile curve 25320Fractal dimension of roughness coefficient corresponding to 320cm sample;
Figure BDA0002750662190000099
corresponding to the profile curve 25Length of structural plane L330Fractal dimension of roughness coefficient corresponding to 330cm sample;
(8) respectively in matrix A0、A17、A25The independent variable x and all elements in the corresponding column of the second row, the dependent variable y, are fitted using the following model:
y＝fⅠln(x)+fⅡx+fⅢ
in the formula fⅠ、fⅡ、fⅢFor the fitting coefficients, a total of 3 different sets of f were obtainedⅠ、fⅡ、fⅢ；
(9) Construction of the fitting coefficient fⅠ、fⅡ、fⅢFractal dimension D of roughness coefficient of structural surface with the length of 20cm, 30cm and 40cm20、D30、D40The system of equations of the ternary equation:
Figure BDA00027506621900000910
extraction of A0In
Figure BDA00027506621900000911
AMIn
Figure BDA00027506621900000912
ANIn
Figure BDA00027506621900000913
Figure BDA00027506621900000914
Combined with the 3 groups f obtainedⅠ、fⅡ、fⅢSolving to obtain the coefficient A of the ternary linear equation setⅠ＝0.00734、AⅡ＝0.01461、AⅢ＝-0.01775、BⅠ＝-2.43567、BⅡ＝-8.41599、BⅢ＝9.536345、CⅠ＝3.73650、CⅡ＝12.01443、CⅢ＝-12.94406。
(10) Obtaining a roughness coefficient size effect fractal dimension D according to the stepsnThe multiple regression prediction model of (1):
Dn(L,D20,D30,D40)＝fⅠln(L)+fⅡL+fⅢ
Figure BDA0002750662190000101
(11) obtaining a profile curve with the length of 40cm on the potential slip surface by adopting a structural surface roughness coefficient directional statistical measurement method, and obtaining a statistical average value D of fractal dimensions of roughness coefficients of the sizes of 20cm, 30cm and 40cm of the potential slip surface to be measured according to the steps (4) and (5)20、D30、D40；
The actual length of a potential slip surface is 15m, JRC012, and the fractal dimension D of the roughness coefficient obtained in step (11)20＝0.15862、D30＝0.23590、D400.28565, obtaining the fractal dimension D of the roughness coefficient of the potential slip surface corresponding to the length of 15mk0.15848, the method is substituted into a JRC size effect fractal model, namely a potential slip surface roughness coefficient JRC corresponding to the length of 15m is obtainedk
Figure BDA0002750662190000102
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 (3)

1. A method for determining the roughness coefficient of a structural surface of an engineering rock mass based on multivariate regression analysis is characterized by comprising the following steps:
(1) carrying out grading analysis on the slope stability of the surface mine, determining a slope potential failure mode, determining a potential slip plane, and finding a structural plane corresponding to the potential slip plane;
(2) investigating a structural surface corresponding to the potential slip surface, searching a large-area exposed structural surface, and acquiring surface point cloud data of the structural surface by adopting a handheld three-dimensional laser scanner;
(3) judging the potential slip direction of the side slope according to the grading analysis result, and extracting a large-scale structural surface contour curve along the potential slip direction based on the structural surface point cloud data;
(4) acquiring roughness coefficients of each contour curve under different sizes by adopting a global search method, and carrying out first-level statistical analysis, namely statistical analysis on the calculation results of the roughness coefficients of each contour curve under different sizes obtained by the global search method, and respectively acquiring the statistical average value of the roughness coefficients of each contour curve under different sizes;
(5) calculating the fractal dimension D of the roughness coefficient of the series dimension structural surface according to the following formula according to the obtained statistical average value of the roughness coefficient of each profile curvenMeasured value:
Figure FDA0002750662180000011
wherein JRC10Is the length L of the structural surface10A statistical average of roughness coefficients at 10 cm; JRCnIs a structural plane with a length of LnThe statistical average value of the corresponding roughness coefficient;
(6) summarizing the series of size roughness coefficient fractal dimensions of all measured profile curves, and carrying out second-level statistical analysis, namely, the statistical analysis of the roughness coefficient fractal dimensions of all profile curves under each size condition, so as to obtain the average value of the roughness coefficient fractal dimensions of each size of the structural surface
Figure FDA0002750662180000017
And sample sizeThe general trend of fractal dimension of each size roughness coefficient along with the change of the sample size is reflected by the relationship of (A) and (B), and the relationship is expressed by the following matrix:
Figure FDA0002750662180000012
Figure FDA0002750662180000013
for all contour curve dimensions, i.e. the length L of the structural plane20Fractal dimension of roughness coefficient corresponding to 20cm sample;
Figure FDA0002750662180000014
for all contour curve dimensions, i.e. the length L of the structural plane30Fractal dimension of roughness coefficient corresponding to a sample of 30 cm;
Figure FDA0002750662180000015
for all contour curve dimensions, i.e. the length L of the structural planen-1Fractal dimension of roughness coefficient corresponding to (n-1) × 10cm sample;
Figure FDA0002750662180000016
for all contour curve dimensions, i.e. the length L of the structural planenFractal dimension of roughness coefficient corresponding to sample of n × 10 cm;
(7) drawing a relation scatter diagram of the series size roughness coefficient fractal dimension and the sample size according to the relation between the summarized series size roughness coefficient fractal dimension and the sample size, and selecting two contour curves which are close to the upper limit and the lower limit of the change rule of the series size roughness coefficient fractal dimension along with the sample size, namely, the fractal dimensions of the roughness coefficients of all sizes of the contour curve M and the contour curve N are respectively expressed by a matrix as follows:
Figure FDA0002750662180000021
Figure FDA0002750662180000022
Figure FDA0002750662180000023
length L of structural surface corresponding to profile curve M20Fractal dimension of roughness coefficient corresponding to 20cm sample;
Figure FDA0002750662180000024
length L of structural surface corresponding to profile curve M30Fractal dimension of roughness coefficient corresponding to a sample of 30 cm;
Figure FDA0002750662180000025
length L of structural surface corresponding to profile curve Mn-1Fractal dimension of roughness coefficient corresponding to (n-1) × 10cm sample;
Figure FDA0002750662180000026
length L of structural surface corresponding to profile curve MnFractal dimension of roughness coefficient corresponding to sample of n × 10 cm;
Figure FDA0002750662180000027
length L of structural surface corresponding to profile curve N20Fractal dimension of roughness coefficient corresponding to sample of 220 cm;
Figure FDA0002750662180000028
length L of structural surface corresponding to profile curve N30Fractal dimension of roughness coefficient corresponding to a sample of 30 cm;
Figure FDA0002750662180000029
length L of structural surface corresponding to profile curve Nn-1Fractal dimension of roughness coefficient corresponding to (n-1) × 10cm sample;
Figure FDA00027506621800000210
length L of structural surface corresponding to profile curve NnFractal dimension of roughness coefficient corresponding to sample of n × 10 cm;
(8) respectively in matrix A0、AM、ANThe independent variable x and all elements in the corresponding column of the second row, the dependent variable y, are fitted using the following model:
y＝fⅠln(x)+fⅡx+fⅢ
in the formula fⅠ、fⅡ、fⅢFor the fitting coefficients, a total of 3 different sets of f were obtainedⅠ、fⅡ、fⅢ；
(9) Construction of the fitting coefficient fⅠ、fⅡ、fⅢFractal dimension D of roughness coefficient of structural surface with the length of 20cm, 30cm and 40cm20、D30、D40The system of equations of the ternary equation:
Figure FDA00027506621800000211
extraction of A0In
Figure FDA00027506621800000212
AMIn
Figure FDA00027506621800000213
ANIn
Figure FDA00027506621800000214
Figure FDA00027506621800000215
Combined with the 3 groups f obtainedⅠ、fⅡ、fⅢSolving to obtain the coefficient A of the ternary linear equation setⅠ、AⅡ、AⅢ、BⅠ、BⅡ、BⅢ、CⅠ、CⅡ、CⅢ。
(10) Obtaining a roughness coefficient size effect fractal dimension D according to the stepsnThe multiple regression prediction model of (1):
Dn(L,D20,D30,D40)＝fⅠln(L)+fⅡL+fⅢ
Figure FDA00027506621800000216
(11) obtaining a profile curve with the length of 40cm on the potential slip surface by adopting a structural surface roughness coefficient directional statistical measurement method, and obtaining a statistical average value D of fractal dimensions of roughness coefficients of the sizes of 20cm, 30cm and 40cm of the potential slip surface to be measured according to the steps (4) and (5)20、D30、D40；
The actual length K of the potential slip surface and the fractal dimension D of the roughness coefficient obtained in the step (11)20、D30、D40Namely, the fractal dimension D of the roughness coefficient of the potential slip surface corresponding to the length K is obtainedkThe obtained data is substituted into a JRC size effect fractal model to obtain a potential slip surface roughness coefficient JRC corresponding to the length Kk，
Figure FDA0002750662180000031
2. The method for determining the roughness coefficient of the structural surface of the engineering rock mass based on the multiple regression analysis as claimed in claim 1, wherein in the step (2), the area of the structural surface is more than 1m x 1 m.
3. The method for determining the roughness coefficient of the structural face of the engineering rock mass based on the multiple regression analysis as claimed in claim 1 and 2, wherein in the step (3), the interval of the profile curves of the structural face is more than 10cm, and the total number of the profile curves is more than 30.
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