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This article provides an example to illustrate and explain the problem on borehole.
Three boreholes are sunk at 3 points of an equilateral triangle whose sides are 480 m each. Is West of Q and R is North of midpoint PQ. Boreholes and R-reach the upper surface of a rich coal seam at 100 m, 220 m, and 260 m depths respectively.
(a) Determine the attitude (dip and strike) of the coal seam.
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(b) Another borehole is sunk at S, midpoint of QR. Determine at what depth the borehole S reaches the coal seam.
Gradient of PQ
120/480 = 1 in 4
Gradient of PR
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160/480 = 1 in 3
Procedure:
Construct an equilateral triangle with a suitable scale. Show the positions of the boreholes. The coal seam is reached at point P and Q at 100 m and 220 m. So the coal seam dips from P to Q. To determine the inclination (gradient) along PQ construct trough sketch depth diagram and determine the gradient, it is 120 m in 480 m. So it is 1 in 4.
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Similarly, construct the depth diagram along PR it is 160 m in 480 m i.e., 1 in 3. Take convenient scale and mark 4 units (cms) along PQ and 3 units (cms) along PR from P. They are A and B. Join AB and extend. It is the true strike direction (TSD).
Draw a perpendicular to AB from P. It cuts AB at C. Measure PC it is 2.85 cms i.e., the gradient is 1 in 2.85. It is true dip.
To determine the direction of true dip, measure the angles CPQ = 45°. So direction of true dip is the complementary angle from north direction so (90° – 45°) 45°. So it is N45°E or NE.
True dip 1 in 2.85 along NE.
Strike = SE and NW.
To determine the depth at which the borehole 5 reaches the coal seam, join PS it intersects AB line (true strike direction) at T. Measure PT with units selected it is 3 cms. So the gradient along PT ‘is 1 in 3. Measure PS it is 4.2 cms = 420 m.
Depth Horizontal distance PS x Gradient + Depth of Borehole at P
= 420 x 1/3 + 100 = 140 + 100 = 240 m
To check whether this calculation is correct or not, let us find out the gradient of coal seam along QR.
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Draw depth diagram.
The Gradient is 1 in 12 from Q, QS is 240 m.
Depth = (Horizontal distance x Gradient) + Depth of Borehole Q
= 240 x 1/12 + 220
= 20 + 220 = 240 m
Scale 1 cm = 100 m
Gradient 1 cm = 1 unit.
2. Three boreholes are sunk at SW, SE, and NW corners of square level ground. The side of the square is 150 m long. The boreholes are X, Y, Z respectively. The boreholes meet the coal seam at 15 m in X, 45 m in Y, and 60 m in Z.
(a) Determine the attitude of the coal seam.
(b) Fourth borehole is proposed at P, the NE corner of the square land. Calculate at what depth, the borehole encounters the coal seam.
Depth Diagram (Not to Scale):
Gradient of XY = 30/150 = 1 in 5
Gradient of XZ = 50/150 = 1 in 3
Scale 1cm= 30 m
Gradient Scale 1 cm = 1unit
True depth = 1 in 2.55 along North 30°E
Strike = N60°W and S60°E
Depth of unknown point P = Horizontal distance x Gradient + Depth of borehole at minimum depth
= 216 x 1/2.7 + 15
= 80 + 15 = 95 m