METHODS FOR PROCESSING DATA FROM THE STUDY OF ROCK FRACTURING USING UNORIENTED CORE

V. V. NIKOLAEV

(Presented by Prof. A. M. Kuzmina)

The study of fracturing from core differs substantially from its study in rock outcrops. The specificity of the investigations consists mainly in the fact that measurements of fracture orientation are made in unoriented cores; boreholes are often not straight, and intersect thick strata with variable lithological composition, while the tectonic structure and the elements of bedding of the rocks differ in different intervals of the borehole. These features have determined a certain distinctiveness in the methods for processing measurements of fracture orientation that we used in studying the fracturing of rocks from core in Kuzbass.

Core documentation was carried out in accordance with the form adopted in Kuzbass; the geological description of each bed was supplemented by measurements of fracture orientation and of the dip angles of bedding [1], by characterization of systems and individual fractures with determination of their genetic type, and also by the degree of disturbance of the rocks.

Experience shows that the pattern of rock fracturing is satisfactorily outlined with 100–150 measurements of fracture orientation. In all lithological varieties of the sandy-clayey complex of rocks, the same systems of fractures of identical orientation were observed. Therefore, fracturing diagrams were constructed primarily for separate intervals of boreholes intersecting a series of beds of homo- and monoclinal occurrence, within which the tectonic structure (elements of bedding, jointing, fracturing, etc.) does not undergo substantial changes.

Construction of fracturing diagrams was carried out with the aid of polar and equatorial nets of stereographic projection, combined on a single drawing so that the pole of the equatorial net has an azimuth of 90°. The azimuthal scale of the net was numbered clockwise. Before work, tracing paper was firmly fastened onto the polar-equatorial net; on it the conventional north direction was recorded. In constructing fracturing diagrams the following cases occurred.

1. A straight interval of the borehole intersects a series of beds with identical elements of bedding.

The orientation of fractures was represented on the diagram by points, the positions of which were determined with the aid of the polar net on the basis of measurements of the conditional orientation of the fractures.

1. A rectilinear interval of a borehole, perpendicular to the strike line of the rocks, intersects a series of beds having the same strike but different dip angles.

Using a polar net, the projection of the pole of bedding of one of the beds, the projections of the poles of schistosity, and of those fractures measured in the first bed whose orientation depends on the elements of bedding attitude, were plotted on tracing paper. The projection of the pole of schistosity was superposed on the projection of the pole of bedding of one of the beds; in doing so, the projections of the fracture poles were shifted along the corresponding parallels of the equatorial net in the same direction and through the same angle as the projection of the pole of schistosity. The reduced position of the projections of the fracture poles was marked on the tracing paper in ink. In exactly the same way, the projections of the poles of fractures measured in other beds of the given borehole interval were plotted on the diagram.

The projections of the poles of feather fractures in the wings of disjunctives and of fractures of the general stress field, whose orientation is uniform within large tectonic blocks, were plotted on the diagram in the same way as described for case 1.

1. A borehole interval, curved in the plane of dip of the rocks, intersects a series of beds with identical elements of attitude.

The construction of the fracture-orientation diagram was performed in the same way as described for case 2; in this case, the reduced position of the projections of the poles of feather fractures and fractures of the general stress field was determined on the diagram exactly as was the reduced position of the projections of the poles of fractures geometrically rigidly connected with bedding.

1. A borehole interval, curved in the plane of dip of the rocks, intersects a series of beds having the same strike but different dip angles.

The reduced position of the projections of the poles of fractures geometrically rigidly connected with bedding was determined by superposing the projections of the poles of bedding of each bed with the projection of the pole of bedding of one of the beds, as described for case 2.

The reduced position of the projections of the poles of feather fractures and fractures of the general stress field was determined as follows. The curvilinear interval of the borehole was divided into rectilinear segments. The projections of the poles of bedding and of fractures measured on the first segment were plotted on the diagram. The projection of the bedding pole was shifted along the line of the conventional dip direction of the rocks in the direction opposite to the azimuth of inclination of the first segment, through an angle equal to its zenith angle; the projections of the fracture poles were then shifted along the corresponding parallels of the Wulff net in the same direction and through the same angle as the projection of the conventional bedding pole. The reduced position of the projections of the poles of fractures measured on other rectilinear segments of the given borehole interval was determined analogously.

On fracture diagrams, the projections of the poles of fractures of different genetic groups, as well as of feather fractures in the hanging and footwall wings of different disjunctives, were designated by different conventional symbols.

Fracture systems were identified by statistical-graphical processing of point fracture diagrams. To determine the character of the distribution of fracture poles, we used a template consisting of a stereographic projection of a hemisphere divided into 400 equal-area, nearly equidimensional figures (Fig. 1).

The principle of calculating the template is as follows. If \(s\) is the area of the counting figure on the sphere, then the side of the square equal to it will be \(a\). If \(n\) whole segments equal to \(a\) are laid off in one quarter of the circumference of the great circle of the sphere, then the area of the first zone, whose stereographic projection is the peripheral ring of the template, will be \(2ns\), and its height \((h)\) will be \(\dfrac{ns}{\pi R}\) (where \(R\) is the radius of the sphere). The radius of the circumference of the upper base of the first zone is equal to \(\sqrt{R^{2}-h^{2}}\). If \(n_1\) whole segments equal to \(a\) are laid off in one quarter of this circumference, then the area of the second zone will be \(4n_1s\), and its height will be \(\dfrac{2n_1s}{\pi R}\). The number of counting areas and the height for each subsequent zone are determined in exactly the same way.

Fig. 1. Template for statistical-graphic processing of diagrams of rock fracturing, constructed using a Wulff net.

The construction of a template for a Wulff net 20 cm in diameter can be carried out according to the calculated data given in the table, analogously to the construction of the polar net of a stereographic projection [2].

To identify the maxima of fracture systems, the diagram was superimposed on a stencil; in each cell of the stencil the number of points was counted. Points in opposite cells of the peripheral ring of the stencil were summed, and the number was entered at the ends of the diameter passing through the centers of the given counting areas. Isolines of point density were drawn in the usual way. In those cases where distribution fields of the poles of fractures of different genetic groups overlapped, in each cell of the stencil the number of points belonging to systems of different genetic groups was counted separately, and isolines of point density were drawn individually for each system of a definite genetic group.

With this method of graphical-statistical processing of fracture-orientation diagrams, the isolines of density of the projections of fracture poles acquire real meaning, reflecting the actual character of the distribution of fracture poles; and the materials of the preliminary processing of fracturing diagrams can serve as initial data for determining distribution parameters by exact methods of mathematical statistics [2].

The method of processing fracturing diagrams on the Schmidt net, and the methods of A. V. Pronin and V. V. Sukhoruchkin [2, 3], do not have a rigorous mathematical justification. Repeated counting of the same points on the diagram contradicts the rule of addition of probabilities and complicates the process of processing diagrams. The method in which points are counted in ten-degree cells of a polar equidistant (4) or stereographic projection grid does not ensure a correct representation of the character of the distribution of fracture poles because of the inequality of the counting areas on the sphere. Inequality of the counting areas also occurs when fracturing diagrams are processed by V. V. Sukhoruchkin’s method.

Taking into account the shortcomings of the noted methods for processing fracturing diagrams constructed with the aid of the nets of Schmidt, Kavraisky, and Sukhoruchkin, one may recommend the use of similar stencils made in the appropriate (equal-area, equidistant, orthogonal) projection according to the calculated parameters given in the table.

The statistical processing of fracturing diagrams and their geological interpretation completed the preliminary analysis of field observations. As information was received on the elements of occurrence of rocks in the intervals of fracturing study, the maxima of fracture systems were spatially oriented.

If this problem were solved by means of modeling, then the sphere with the image of the bedding pole and the maxima of fracture systems (in a conventional coordinate system) would have to be rotated, while keeping the coordinate system fixed, first about one of the horizontal diameters in the direction opposite to the azimuth of inclination of the borehole axis, through an angle equal to its zenith angle, and then the semi-

the sphere about the borehole axis so that the bedding plane would correspond to the true azimuth and dip angle; if only the strike of the rocks is known, then the hemisphere should be rotated about the borehole axis so that the strike lines of the bedding would correspond to the true strike azimuth. These operations for orienting the maxima of fracture systems were carried out by us graphically with the aid of the polar–equatorial net of a stereographic projection [2, 5].

To determine the actual orientation of the systems of feathering fractures and fractures of the general stress field (the four cases of diagram construction), it is sufficient to recode the diagram so that the projection of the conventional pole of the bedding corresponds to the true dip azimuth.

REFERENCES

1. I. A. Ocheretenko. A method for measuring the azimuth and dip angle of fractures in core with the aid of a transparent grid. Razvedka i okhrana nedr, No. 9, 1958.

2. A. B. Vistelius. Structural Diagrams. Publishing House of the Academy of Sciences of the USSR, 1958.

3. A. E. Mikhailov. Field Methods for Studying Fractures in Rocks. Gosgeoltekhizdat, 1956.

4. Manual on Geological Documentation of Underground Workings in the Mines of the Kuzbass. VNIMI Publishing House, Leningrad, 1959.

5. E. I. Patalakha. A method for determining the orientation of planar structural elements from the core of a deviated borehole. Publishing House of the Academy of Sciences of the Kazakh SSR, geological series, issue 2 (47), 1962.