METHOD FOR QUANTITATIVELY EVALUATING THE ANISOTROPY OF ROUGHNESS COEFFICIENT OF ROCK JOINTS

Abstract

A method for quantitatively evaluating the anisotropy of joint roughness coefficient of rock joints is provided, comprising the following steps: selecting a joint sample of an engineering rock mass to be analyzed; uniformly arranging rock joint measurement segments in different orientations; recording each joint profile by a profilograph;

measuring joint roughness coefficient of each measurement segment; calculating a statistical mean value of the joint roughness coefficients in each orientation under same dimensional conditions, and obtaining a roughness coefficient class ratio in each orientation; transforming each item in the roughness coefficient class ratio by R.sub.1(i)=r.sub.0(i).sup.1/m; fitting the processed roughness coefficient of the rock joints by anisotropic ellipse function; determining a major axis a and a minor axis b of the anisotropic ellipse, Θ representing a direction of rotation, where a ratio of the major axis to the minor axis indicates a difference between the maximum roughness coefficient and the minimum roughness coefficient on the anisotropic ellipse, and Θ indicates a dominant orientation for roughness development of the rock joints. The present invention can effectively and quantitatively determine the degree of the anisotropy of joint roughness coefficient of the rock joints.

Claims

1. A method for quantitatively evaluating the anisotropy of joint roughness coefficient of natural rock joint samples, comprising the following steps of: (1) selecting a joint sample of an engineering rock mass to be analyzed; (2) uniformly arranging rock joint measurement segments in different orientations; (3) drawing each joint profile by a profilograph; (4) extracting coordinate data on the profile curve by an image processing method, so as to measure a roughness coefficient of the rock joints in each of the measurement segments; (5) calculating a statistical mean value of the roughness coefficients of the rock joints in each orientation under same dimensional conditions, and obtaining a roughness coefficient class ratio r.sub.0(r.sub.0(1), r.sub.0(2), . . . , r.sub.0(t)) in each orientation, where t represents the number of measurement orientations, r.sub.0(1) is a roughness coefficient in the first measurement orientation, r.sub.0(2) is a roughness coefficient in the second measurement orientation, and r.sub.0(t) is a roughness coefficient in the t.sup.th orientation; (6) transforming each item in the roughness coefficient class ratio by using R.sub.1(i)=r.sub.0(i).sup.1/m until $J=\left[\frac{R_0\left(1\right)}{R_0\left(2\right)},\frac{R_0\left(2\right)}{R_0\left(3\right)},\mathrm{.Math.}.Math.,\frac{R_0\left(t-1\right)}{R_0\left(t\right)}\right]$ meets J∈[e.sup.−2/(t+1),e.sup.2/(t+1)], where m≧1 and m is an exponential term, r.sub.0(i) represents a roughness coefficient in the i.sup.th orientation, R.sub.0(i) represents a transformed value of the roughness coefficient in the i.sup.th orientation, wherein the value of m is denoted by m.sub.0, m.sub.0 representing the smoothness of the roughness coefficient of the rock joints in each orientation and called a roughness smooth coefficient; (7) fitting the processed roughness coefficient R.sub.0(R.sub.0(1), R.sub.0(2), . . . , R.sub.0(t)) of the rock joints by using an anisotropic ellipse:
Ax.sup.2+Bxy+Cy.sup.2+Dx+Ey+F=0 where x=R.sub.0 cos θ, y=R.sub.0 sin θ, θ represents a measurement orientation, and A, B, C, D, E and F all are elliptic coefficients; (8) determining a major axis a and a minor axis b of the anisotropic ellipse by the following formula, Θ representing a direction of rotation: $\{\begin{array}{c}{a^2\left(\sin .Math..Math.\Theta \right)}^2+{b^2\left(\cos .Math..Math.\Theta \right)}^2-A=0\\ 2.Math.\left(b^2-a^2\right).Math.\sin .Math..Math.\Theta .Math..Math.\cos .Math..Math.\Theta -B=0\\ {a^2\left(\cos .Math..Math.\Theta \right)}^2+{b^2\left(\sin .Math..Math.\Theta \right)}^2-C=0\\ 2.Math.{\mathrm{Ax}}_c+{\mathrm{By}}_c+D=0\\ {\mathrm{Bx}}_c+2.Math.{\mathrm{Cy}}_c+E=0\end{array}.$ where a ratio of the major axis to the minor axis indicates a difference between the maximum roughness coefficient and the minimum roughness coefficient on the anisotropic ellipse, and Θ indicates a dominant orientation for roughness development of the rock joints.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] FIG. 1 is a diagram of the anisotropy of joint roughness coefficient;

[0022] FIG. 2 is a diagram of the anisotropy of joint roughness coefficient when a class ratio transform coefficient m is 3, i.e., m=3;

[0023] FIG. 3 is a diagram of the anisotropy of joint roughness coefficient when the class ratio transform coefficient m is 5, m=5; and

[0024] FIG. 4 is a diagram of the anisotropy of joint roughness coefficient after the roughness smooth coefficient transform, and the anisotropic ellipse fitting.

DETAILED DESCRIPTION OF THE INVENTION

[0025] The present invention will be further described with reference to the accompanying drawings.

[0026] With reference to FIGS. 1-4, a method for quantitatively evaluating the anisotropy of joint roughness coefficient of rock joints is provided, comprising the following steps of:

[0027] (1) selecting a joint sample of an engineering rock mass to be analyzed, and determining a potential slip orientation;

[0028] (2) uniformly arranging rock joint measurement segments in different orientations;

[0029] (3) drawing each joint profile by a profilograph;

[0030] (4) extracting coordinate data on the profile curve by an image processing method, so as to measure a roughness coefficient of the rock joints in each of the measurement segments;

[0031] (5) calculating a statistical mean value of the roughness coefficients of the rock joints in each orientation under same dimensional conditions, and obtaining a roughness coefficient class ratio r.sub.0=(r.sub.0(1),r.sub.0(2) , . . . , r.sub.0(t)) in each orientation, where t represents the number of measurement orientations, r.sub.0(1) is a roughness coefficient in the first measurement orientation, r.sub.0(2) is a roughness coefficient in the second measurement orientation, and r.sub.0(t) is a roughness coefficient in the t.sup.th orientation;

[0032] (6) transforming each item in the roughness coefficient class ratio by using R.sub.1(i)=r.sub.0(i).sup.1/m until

[00003]$J=\left[\frac{R_0\left(1\right)}{R_0\left(2\right)},\frac{R_0\left(2\right)}{R_0\left(3\right)},\mathrm{.Math.}.Math.,\frac{R_0\left(t-1\right)}{R_0\left(t\right)}\right]$

meets J∈[e.sup.−2/(t+1), e.sup.2/(t+1)], where m≦ and m is an exponential term, r.sub.0(i) represents a roughness coefficient in the i.sup.th orientation, r.sub.0(i) represents a transformed value of the roughness coefficient in the i.sup.th orientation, wherein the value of m is denoted by m.sub.0, m.sub.0 representing the smoothness of the roughness coefficient of the rock joints in each orientation and called a roughness smooth coefficient, this parameter reflecting a difference between roughness coefficients of the rock joints in different orientations;

[0033] (7) fitting the processed roughness coefficient R.sub.0=(R.sub.0(1), R.sub.0(2), . . . , R.sub.0(t)) of the rock joints by using an anisotropic ellipse:

Ax.sup.2+Bxy+Cy.sup.2+Dx+Ey+F=0

where x=R.sub.0 cos θ, y=R.sub.0 sin θ,θ represents a measurement orientation, and A, B, C, D, E and F all are elliptic coefficients;

[0034] (8) determining a major axis a and a minor axis b of the anisotropic ellipse by the following formula, Θ representing a direction of rotation:

[00004]$\{\begin{array}{c}{a^2\left(\sin .Math..Math.\Theta \right)}^2+{b^2\left(\cos .Math..Math.\Theta \right)}^2-A=0\\ 2.Math.\left(b^2-a^2\right).Math.\sin .Math..Math.\Theta .Math..Math.\cos .Math..Math.\Theta -B=0\\ {a^2\left(\cos .Math..Math.\Theta \right)}^2+{b^2\left(\sin .Math..Math.\Theta \right)}^2-C=0\\ 2.Math.{\mathrm{Ax}}_c+{\mathrm{By}}_c+D=0\\ {\mathrm{Bx}}_c+2.Math.{\mathrm{Cy}}_c+E=0\end{array}.$

[0035] where a ratio of the major axis to the minor axis indicates a difference between the maximum roughness coefficient and the minimum roughness coefficient on the anisotropic ellipse, and Θ indicates a dominant orientation for roughness development of the rock joints.

[0036] An embodiment: A method for quantitatively evaluating the anisotropy of roughness coefficient of rock joints is provided. The process is as follows.

[0037] First, a representative granite rock joint is measured in the field. The roughness coefficients of the rock joints measured in different orientations are as shown in Table 1, and the anisotropy graph is shown in FIG. 1. In this case, the value of m is 0.

TABLE-US-00001 TABLE 1 Measurement orientation JRC 0 9.818 15 12.471 30 11.688 45 20.395 60 18.865 75 16.306 90 12.212 105 11.652 120 14.051 135 10.955 150 11.071 165 10.737 180 9.818 195 12.471 210 11.688 225 20.395 240 18.865 255 16.306 270 12.212 285 11.652 300 14.051 315 10.955 330 11.071 345 10.737 360 9.818

[0038] Second, due to the large difference in the roughness coefficient in each orientation, the fitting may not be directly performed by an elliptic equation, and in this case, the experimental data will be processed by class ratio analysis. When the values of m are 3 and 5, respectively, the difference in the processed roughness coefficients in each orientation is reduced significantly, and the irregular shape gradually tends to an elliptic shape. However, the conditions of the class ratio analysis are not met. Accordingly, it is required to continuously increase the value of m.

[0039] Then, when the value of m is 7.3, the processed roughness coefficients meet the conditions of the class ratio analysis. In other words, m.sub.0=7.3 is a roughness smooth coefficient of the rock joints, and may be used for representing the anisotropy of the joint roughness coefficient.

[0040] Finally, in accordance with the anisotropy elliptic equation, it can be obtained that a ratio of the major axis to the minor axis is 1.045, and the dominant orientation of the roughness coefficient of the rock joints is 63.88°.