CN101055175A - Simple measurement method for rock structural plane roughness coefficient - Google Patents

Abstract

The invention relates to a simple method for measuring roughness coefficient of rock structure surface, including the following steps of: measuring convex tooth amplitude Ryn of rock structure surface; calculating the relative convex tooth amplitude value RA of rock structure surface profile curve with sampling length Ln using the formula RA=RYn/Ln; obtaining the roughness coefficient of rock structure surface profile curve with sampling length Ln by substituting the RA into the formula JRCn=400RA. The method which is simple and convenient for operation and calculation quickly can be performed without the influence of human factor and have great value and social economical benefit with satisfied precision.

Description

Simple measurement method for rock structural plane roughness coefficient

(1) technical field

The present invention relates to simple measurement method for rock structural plane roughness coefficient, be applicable to that to sample length be L _nThe rock structural face surface outline curves measure roughness coefficient JRC _nThe occasion of value.

(2) background technology

Before the present invention made, the main mensuration that obtains structural plane roughness coefficient JRC at present was that the amplitude according to different sample length structural plane surface outline curves that Barton (1982) proposes is determined roughness coefficient JRC _nStraight flange figure method [3], as shown in Figure 1.Derived MAETHEMATICAL EXPRESSION formula (1) at present on the basis of the size effect of the physical significance of analysis corrections straight flange method and JRC:

${\mathrm{JRC}}_n=49.2114e^{\frac{29{\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="A20071006841400141.png"\; state="\{\{state\}\}">L</figure-callout>}}_0}{450L_n}}\arctan \left[\frac{8R_y}{L_n}\right]---\left(1\right)$

The measurement sample length is L _nRock structural face surface outline curves roughness coefficient JRC _nThe calculating of value or estimation technology are for revising straight flange method mathematical formulae computing method or revising straight flange method diagram estimation method: revising straight flange method mathematical formulae computing method is according to the specific assignment sampling length L _nThe rock mass discontinuity surface outline curves on the double wedge amplitude R that measures _Yn, utilize formula ${\mathrm{JRC}}_n=49.2114e^{\frac{{29\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="A20071006841400141.png"\; state="\{\{state\}\}">L</figure-callout>}}_0}{{450L}_n}}\arctan \left[\frac{{8R}_{\mathrm{Yn}}}{L_n}\right]$ The roughness coefficient value JRC of computing rock structural plane _n,, generally need by counter or program to calculate roughness coefficient JRC by computing machine because the formula complexity is calculated trouble _nValue, this is not suitable for the measurement of field condition structural plane roughness coefficient; Revising straight flange method diagram estimation method is according to the specific assignment sampling length L _nThe rock structural face surface outline curves on the double wedge amplitude R that measures _Yn, at L (horizontal ordinate)-R _yFind out L on (ordinate) graph of a relation _nWith R _YnIntersection point, and determine JRC by this intersection point _nValue, this technology formality is more loaded down with trivial details, and estimation speed is slower.Revise straight flange method mathematical formulae computing method and revise the rock structural face roughness coefficient JRC that straight flange method diagram estimation method all is not easy to each matter opposite sex of tool, anisotropy and heterogencity _nStatistical measurement.

(3) summary of the invention

Task of the present invention be overcome prior art computing formula complexity, be not easy to the mental arithmetic or the estimation technology is loaded down with trivial details, slow-footed shortcoming is measured in estimation, provide a kind of form simple, easy to use, measuring speed is fast, the simple measurement method for rock structural plane roughness coefficient that result of use is good.

Simple measurement method for rock structural plane roughness coefficient of the present invention comprises following steps:

(1) measuring sample length is L _nThe double wedge amplitude R of rock structural face surface outline curves _Yn

(2) by formula $R_A=\frac{R_{\mathrm{Yn}}}{L_n}$ The calculating sample length is L _nThe relative double wedge range value R of rock structural face surface outline curves _A

(3) with R _ASubstitution formula JRC _n=400R _APromptly getting sample length is L _nRock structural face surface outline curves roughness coefficient JRC _n

Above-mentioned formula is the geometric properties from straight flange figure, derives the simple and clear formula of said structure surface roughness coefficient B arton straight flange method.

Reach the unified needs of research for convenience, before research Barton straight flange figure, do 2 explanations:

(1) for for the purpose of the difference, will be identified at the ident value that data on the protruding amplitude of tooth are called the protruding amplitude of tooth on the straight flange figure, be identified at the ident value that data on the contour curve length are called contour curve length, and the corresponding measurement length of ident value is called its scale value;

(2) unit with the ident value of the ident value of the protruding amplitude of tooth among the straight flange figure and contour curve length all is scaled cm.

The basic characteristics of straight flange figure are as follows:

(1) ident value is inhomogeneous

No matter be the ident value of the protruding amplitude of tooth or the ident value of contour curve length, in straight flange figure, all demonstrate and dredge the close feature in back earlier, for example, in the drawings, can obviously find out, the gap ratio ident value 0.2cm of tooth protruding amplitude ident value 0.1cm and ident value 0.2cm and the spacing of ident value 0.3cm are long, contour curve length mark value 100cm is also long with the spacing of ident value 300cm than ident value 200cm with the spacing of ident value 200cm, and both density degree are basically identicals, if we are respectively with the protruding amplitude ident value of tooth 0.01cm, contour curve length mark value 10cm can obtain the protruding amplitude ident value of tooth by the ruler measurement and (use R as measuring starting point _yExpression) (uses L with the corresponding tables 1 of its scale value (representing) with contour curve length mark value with y _nExpression) with the corresponding tables 2 of its scale value (representing) with x

The protruding amplitude ident value of table 1 tooth R _yCorresponding tables with scale value y

The protruding amplitude ident value of tooth R y/cm	0.01	0.02	0.03	0.04	0.05	0.1	0.2	0.3	0.4	0.5	1	2	3	4	5	10
																	The protruding amplitude scale value of tooth y/cm	0	0.85	1.35	1.71	1.98	2.82	3.7	4.2	4.56	4.82	5.7	6.53	7.05	7.4	7.70	8.52

Table 2 contour curve length mark value L _nCorresponding tables with scale value x

Contour curve length mark value L n/cm	10	20	30	40	50	100	200	300	400	500	1000
												Contour curve length scale value x/cm	0	0.82	1.31	1.69	1.93	2.8	3.7	4.12	4.5	4.71	5.65

Analytical table 1, table 2, find the consistent logarithmic relationship of existence between the protruding amplitude ident value of tooth and its scale value, contour curve length mark value and its scale value, for obtaining the protruding amplitude ident value of tooth and its scale value relationship, list the relationship of the protruding amplitude ident value of tooth and its scale value and find the solution table 3, be the relationship that obtains contour curve length mark value and its scale value, list contour curve length

The relationship of ident value and its scale value is found the solution table 4.

The relationship of the protruding amplitude ident value of table 3 tooth and its scale value is found the solution table

The protruding amplitude ident value of tooth R y/cm	0.01	0.02	0.03	0.04	0.05	0.1	0.2	0.3	0.4	0.5	1	2	3	4	5	10
																	lg100R y	0	0.301	0.477	0.602	0.699	1	1.301	1.477	1.602	1.699	2	2.301	2.477	2.602	2.699	3
The protruding amplitude scale value of tooth y/cm	0	0.85	1.35	1.71	1.98	2.82	3.7	4.2	4.56	4.82	5.7	6.53	7.05	7.4	7.70	8.52
																	y/lg100R y	/	2.8	2.8	2.8	2.8	2.8	2.8	2.8	2.8	2.8	2.9	2.8	2.8	2.8	2.8	2.8

The relationship of table 4 contour curve length mark value and its scale value is found the solution table

Contour curve length mark value L n/cm	10	20	30	40	50	100	200	300	400	500	1000
												lg0.1L n	0	0.301	0.477	0.602	0.699	1	1.301	1.477	1.602	1.699	2
Contour curve length scale value x/cm	0	0.82	1.32	1.69	1.93	2.8	3.7	4.12	4.5	4.71	5.65
												x/lg0.1L n	/	2.7	2.7	2.8	2.8	2.8	2.8	2.8	2.8	2.8	2.8

From find the solution table 3, table 4 draws the protruding amplitude ident value of tooth R _yRelationship (2) and contour curve length mark value L with the protruding amplitude scale value of tooth y _nRelationship (3) with contour curve length scale value x

y＝2.8lg100R _y (2)

x＝2.8lg0.1L _n (3)

Express the protruding amplitude ident value of tooth R for investigating (2) formula _yWith the accuracy of the relation of the protruding amplitude scale value of tooth y, list the contrast table 5 of measuring scale value and computing scale value under the protruding amplitude ident value of same tooth.Express contour curve length mark value L for investigating (3) formula _nWith the accuracy of the mathematical relation of contour curve length scale value x, list the contrast table 6 of measuring scale value and computing scale value under the same contour curve length mark value.

The protruding amplitude ident value of the same tooth of table 5 is measured the contrast table of scale value and computing scale value down

The protruding amplitude ident value of tooth R y/cm	0.01	0.02	0.03	0.04	0.05	0.1	0.2	0.3	0.4	0.5	1	2	3	4	5	10
																	Amplitude measurement scale value y/cm	0	0.85	1.35	1.71	1.98	2.82	3.7	4.2	4.56	4.82	5.7	6.53	7.05	7.4	7.70	8.52
Amplitude computing scale value y/cm	0	0.84	1.34	1.69	1.96	2.80	3.64	4.14	4.49	4.76	5.60	6.44	6.94	7.29	7.56	8.40

Measure the contrast table of scale value and computing scale value under the same contour curve length mark of table 6 value

Contour curve length mark value L n/cm	10	20	30	40	50	100	200	300	400	500	1000
												Contour curve linear measure longimetry scale value x/cm	0	0.82	1.31	1.69	1.93	2.80	3.7	4.12	4.5	4.71	5.65
Contour curve length computation scale value x/cm	0	0.84	1.34	1.69	1.96	2.80	3.64	4.14	4.49	4.76	5.60

Analytical table 5, table 6 are found, no matter be protruding amplitude of tooth or contour curve length, measurement scale value under the same ident value and computing scale value goodness of fit height, as calculated, all in 2%, formula (2), formula (3) are portrayed the relational expression of the protruding amplitude ident value of tooth and its scale value respectively to error range and the relational expression between contour curve length mark value and its scale value is quite accurate.

(2) observing from figure and draw, (is laboratory size L when contour curve length mark value equals 10cm ₀=10cm) time, JRC ₀Ident value just is 40 times of the protruding amplitude ident value of the tooth on this contour curve (unit is cm) $({\mathrm{<figure-callout\; id="0"\; label="JRC"\; filenames="A20071006841400141.png"\; state="\{\{state\}\}">JRC</figure-callout>}}_0=40R_{y_0}),$ L for example ₀=10cm, ${\mathrm{<figure-callout\; id="0"\; label="R\; y"\; filenames="A20071006841400141.png"\; state="\{\{state\}\}">R</figure-callout>}}_{y_{}}=0.3\mathrm{cm},$ Cha Tude JRC ₀=12;

(3) all parallel and slope of all oblique lines among the figure is 1;

(4) the JRC ident value of being had a few on the same oblique line is all identical, and they are that this oblique line is at L _nThe JRC ident value at=1000cm place also is that this oblique line is at L simultaneously ₀The protruding amplitude ident value of the tooth at=10cm place R _Y040 times.If we (are contour curve length mark value L with the frame at figure insole binding contour curve length place ₀The straight line at=10cm place) as the x axle, the frame at the protruding amplitude of left side tooth place (is the protruding amplitude ident value of tooth $R_{y_{}}$ ${{}_0}_{}=0.01\mathrm{cm}$ The straight line at place), sets up plane right-angle coordinate, so intercept b (scale value b) the corresponding identification value R of oblique line on the y axle based on scale value as the y axle _YbBe exactly laboratory size L ₀The protruding amplitude ident value of tooth under=10cm R _Y0, the JRC value of being had a few on the oblique line by intercept b all equals the protruding amplitude ident value of this tooth R for this reason _Y040 times.

By above analysis, we can derive the simple and clear formula of structural plane roughness coefficient Barton straight flange method:

(I) based on the foundation of the plane right-angle coordinate of scale value

Frame with contour curve length place, base (is contour curve length mark value L ₀The straight line at=10cm place) as the x axle, the frame at the protruding amplitude of left side tooth place (is the protruding amplitude ident value of tooth $R_{y_{}}$ ${{}_0}_{}=0.01\mathrm{cm}$ The straight line at place), sets up plane right-angle coordinate (as Fig. 2) based on scale value as the y axle;

(II) conversion of the ident value of intersecting point coordinate and scale value

Under the general situation, given one group of contour curve length mark value L that obtains _nWith the protruding amplitude ident value of tooth R _y, then by L _nWith R _yCan determine an intersection point A, utilize formula (2) and formula (3), the scale value coordinate that obtains intersection point is A (2.81g0.1L _n, 2.81g100R _y), example: L ₀=10cm, R _y=0.01cm corresponding point scale value coordinate is (0,0);

(III) intercept asks for

Crossing some A, to make a slope be 1 straight line, and then the equation of this straight line is

y＝x+(2.81g100R _y-2.81g0.1L _n)，

Thereby obtain the intercept scale value b of this oblique line on the y axle, have

$b=2.81g100R_y-2.81g0.1L_n=2.81g\left(\frac{{1000R}_y}{L_n}\right)---\left(4\right)$

(IV) acquisition of JRC value

If the protruding amplitude ident value of the tooth of the correspondence of intercept scale value b is R _Yb, then get by formula (2)

$b=2.81g100R_{y_b}---\left(5\right)$

Contrast formula (4) and formula (5)

$2.81g\left(\frac{{1000R}_y}{L_n}\right)=2.81g100R_{y_b}$

Obtain contour curve length mark value L after the abbreviation arrangement ₀The protruding amplitude ident value of tooth during=10cm

$R_{y_b}=\frac{{10R}_y}{L_n}$

Basic characteristics (4) by straight flange figure get, for given R _yWith L _n, have

${\mathrm{JRC}}_n={40R}_{y_b}=40\&times;\frac{{10R}_y}{L_n}=400\&times;\frac{R_y}{L_n}---\left(6\right)$

If relative amplitude $R_A=\frac{R_y}{L_n},$

Thereby the simple and clear formula of Barton straight flange method

JRC _n＝400R _A (7)

The invention has the beneficial effects as follows: form is simple, use easy to operate, measuring speed is fast, not influenced by human factor and precision meets the demands, and measurement result has embodied the size effect influence of roughness coefficient, rock structural face roughness coefficient for each matter opposite sex of quantitative statistical analysis tool, anisotropy, heterogencity and size effect provides effective means simultaneously, be convenient to mental arithmetic, the rock structural plane roughness coefficient that is specially adapted to field condition is measured, and has bigger implementary value and economic results in society.

(4) description of drawings

The straight flange figure method of Figure 1B arton

The derivation graph of the simple and clear formula of Fig. 2 Barton straight flange method

(5) embodiment

Table 7 is embodiments of the invention.The protruding amplitude R of structural plane surface outline curves tooth according to the different sample lengths in Da Shigu eruptive tuff joint, Linan _YnMeasurement result, just can be by formula by counter or computing machine $R_A=\frac{R_{Y_n}}{L_n}$ The calculating sample length is L _nThe relative double wedge range value R of rock structural face surface outline curves _AWith formula JRC _n=400R _AThe sample length that calculates is L _nRock structural face surface outline curves roughness coefficient JRC _n, measurement result is listed in table 7.Table 7 is the roughness coefficient value of the different sample length structural planes in Da Shigu eruptive tuff joint, Linan.Assay shows, the roughness coefficient JRC of table 1 _nThe result who tries to achieve with correction straight flange method mathematical formulae computing method or correction straight flange method diagram estimation method is consistent.The JRC value that three kinds of methods obtain is very close, and error is within JRC measurement allowed band, and formula (7) can be used for the measurement of rock structural plane roughness coefficient JRC.

Table 7 diagram straight flange method, correction straight flange method mathematical expression and simple and clear formula are tried to achieve JRC

Sample length/cm	Statistics bar number	The protruding spoke degree of tooth statistical value R y/cm	Diagram straight flange method	MAETHEMATICAL EXPRESSION	Simple and clear formula
						10	70	0.21	8.4	8.6	8.4
20	35	0.35	7.2	7.0	7.0
						30	23	0.47	6.4	6.3	6.3
40	17	0.56	5.6	5.6	5.6
						50	14	0.78	6.4	6.1	6.2
60	11	0.88	5.9	5.8	5.9
						70	10	0.97	5.7	5.5	5.5
80	8	1.22	6.2	6.0	6.1
						90	7	1.26	5.8	5.5	5.6
100	7	1.15	4.7	4.5	4.6
						200	3	3.45	7.0	6.8	6.9
300	2	4.28	5.9	5.6	5.7
						400	1	4.92	5.0	4.8	4.9
500	1	7.34	6.1	5.8	5.9
						600	1	7.89	5.5	5.2	5.3
700	1	7.89	4.6	4.4	4.5

Analyzing above-mentioned table 7 can reduce to draw a conclusion:

(1) the Barton straight flange figure based on a large amount of tests makes the measurement of JRC enter the field of Quantitative study, and it has clear physical meaning, can objectively respond the mechanics effect of configuration of surface.In addition, it also has easy and simple to handle, measure intuitively, and the advantage of accuracy guarantee, but measuring speed is slower, is not suitable for the statistical measurement of big data quantity.

(2) mathematical expression of revising straight flange figure derives in physical mechanics Study on Mechanism basis and a large amount of Xiao Langdi case history, it has reflected the numerical solution of the JRC of straight flange figure exactly, and can carry out statistical measurement apace by computing machine, but cumbersome in form, be not suitable for open-air measurement fast.

(3) the simple and clear formula of Barton straight flange method is to serve as research basis with Barton straight flange figure, utilize mathematics geometry character to carry out that tight reasoning obtains, by practice test is the measurement requirement that meets JRC fully, and in actual engineering, use, and this formula is very simple and clear in form, need not to use counter just can be handled by mental arithmetic, be fit to the field condition statistical measurement, is the ideal tools of the directed statistical measurement of structural plane roughness coefficient.

Claims (1)

1, a kind of simple measurement method for rock structural plane roughness coefficient comprises following steps:

(1) measuring sample length is L _nThe double wedge amplitude R of rock structural face surface outline curves _Yn

(2) by formula $R_A=\frac{R_{\mathrm{Yn}}}{L_n}$ The calculating sample length is L _nThe relative double wedge range value R of rock structural face surface outline curves _A

(3) with R _ASubstitution formula JRC _n=400R _APromptly getting sample length is L _nRock structural face surface outline curves roughness coefficient JRC _n

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