Mining Geometry Skew Boreholes

This article on Skew Boreholes is intended as a review of the topic. The reason for selecting skew boreholes is, it is the only topic from Paper II(B) which appears on the higher level paper in text format only and for this reason students need to have a very good understanding of the principles involved to avoid making mistakes.

Background information:
The earth's surface is covered with a thin layer of soil and vegetation. Beneath this layer a series of stratified layers is found (strata-plural; stratum-singular). Most strata are inclined and cover only limited areas. The upper and lower surfaces of these strata are assumed to be parallel. Layered rock formations/strata/veins may contain valuable minerals, especially at the intersection of two strata. At times strata intersect the surface of the earth. The line along which a vein or stratum intersects the surface is called an outcrop line. Identification and location of outcrops is important for the exploration of valuable ores.

Contour maps are used to establish the limits of a particular ore deposit. The dip, strike and thickness of a stratum of rock describe its physical orientation.

The slope of a stratum is established by finding the angle it makes with the horizontal plane. The slope is referred to as the dip of the plane. The surface of a stratum can be found by three or more points, which in turn are found by drilling boreholes.

The dip and strike are measured as compass directions deviating from a north/south line towards the east or west.

Definitions:
The following definitions are also demonstrated graphically in figure 1 on the previous page.
Stratum:- a layer, vein or seam of ore usually at an angle to the horizontal plane.
The thickness of a stratum is the perpendicular distance between its surfaces.
Headwall:- the top surface of a stratum.
Footwall:- the bottom surface of a stratum.
Borehole:- the hole drilled from the surface to the stratum to establish the depth below the surface of a point on the stratum.
Contour:- Lines joining points that are at a constant height above sea-level.
Dip:- The angle that the stratum makes with the horizontal plane. The dip is measured at right angles to the strike.
Strike:- The bearing (direction) of a horizontal/level line resting on the surface of the stratum. The strike is measured from the north towards the east or west.
Outcrop:- A portion of a stratum that intersects the surface is called the outcrop. The outcrop line indicates the extent of the outcrop. In some instances, both the headwall and footwall intersect the surface resulting in two outcrop lines in plan.
Thickness:- The thickness of a stratum is the perpendicular distance between the headwall and footwall.

Sample Question
I will now take a look at the solution to typical question in an effort to explain the stages involved in arriving at the solution. The text of the question is as follows:-

On a contour map A and B are two points whose altitudes are 100m and 80m respectively. On the map B is located 130m south-east of A.

A skew bore-hole at A is drilled in a south-westerly direction in plan and has an actual inclination of 60º to the horizontal plane. It reveals the top and bottom surfaces of a stratum at altitudes of 75m and 30m respectively.

A skew-bore hole at B is drilled in a northerly direction in plan and has an actual inclination of 50º to the horizontal plane. It reveals the top and bottom surfaces of the stratum at altitudes of 50m and 25m, respectively.

• Determine the dip, strike and thickness of the stratum.
• Another skew bore-hole at B is drilled in a north-westerly direction in plan and meets the bottom of the stratum at a distance of 85m from B. Determine the inclination of this hole to the horizontal plane.            Scale 1:1000
(Source: Dept. of Ed. & Sc. - Leaving Certificate Examination 1991.)

The solution is divided into three stages. Fig. 2 shows the first stage which concentrates on setting up all the information. Beginning in plan, position A anywhere. Locate B in plan and draw lines in a south westerly and northerly direction from A and B, respectively. Locate A and B in elevation. Draw the true inclination of the skew borehole from A in elevation at 60 . Project the base of this line to plan to meet a line from A parallel to the vertical plane.

 Rotate this line in plan from A to meet the SW line. (As this line is being rotated it could be regarded as the generator of a cone with a base angle of 60 .) Project from plan to elevation to show the true elevation of this borehole. A similar procedure is used to draw the projections of the skew borehole at B. Care needs to be taken in locating the points on the stratum along the boreholes as some questions give the distances from the points on the surface (e.g. A and B) to the stratum. In this question altitudes are given.

Fig. 3 shows the second stage which concentrates on determining the dip, strike and thickness. I often feel that the question should ask for the strike, dip and thickness, as this is the sequence in which the solution evolves.

 The plane method is used in fig. 3 to determine the strike and the thickness is established in the dip view. The strike should be referenced as shown. Students would not normally have problems with this stage once the similarities between this and the Skew Lines section of Planes in Space from Paper I are adequately explained.
Fig. 4 shows the complete solution, in particular the solution to part (b).

An auxiliary view is projected from plan perpendicular to the north-westerly borehole from B. It should be noted that by continuing the direction of the skew borehole from B in plan, it coincides with point A. This has been the case to-date in a number of questions and while it is convenient later on, it is not totally necessary. Points A and B are now located in this new auxiliary. To determine the bottom of the stratum in the second auxiliary view it is necessary to return to the dip view. In this view, drill vertical boreholes from A and B. Points 3 and 4 represent the edge view of the bottom of the stratum. Extend points 3 and 4 to meet the vertical boreholes at points 'p' and 'q'.

These vertical boreholes will also project vertically in the second auxiliary. So, to locate the bottom of the stratum in the second auxiliary, transfer points 'p' and 'q' from the dip view. Swing a distance of 85m from B to intersect the footwall and give the angle of inclination to the horizontal. That completes the solution.

Consider, for a moment, the situation where point A might not be in the path of the north-westerly skew borehole from B in plan. This would mean that the vertical borehole from A would now be of no value in the second auxiliary.

One method of overcoming this would be to locate a vertical borehole somewhere along the north-westerly skew borehole from B. One obvious choice would be where the strike line intersects the borehole from B in plan. The height of this vertical borehole will be the same as the height of point 3 in the dip view (Fig. 4).

This height could then be projected to the second auxiliary and eliminate the need for point 'q' under A, should the need arise.