Question

Four vertical boreholes are drilled on a flat topography at 50 m intervals along the east-west direction. The boreholes intersect a coal seam at depths of 100 m, 130 m, 160 m and 190 m. The true dip of the coal seam, in degree, is ...............(Round off to two decimal places)

Hint:

In the calculation of the true dip, the distance between boreholes and depth changes must be taken into account. Using trigonometry helps in determining the dip of the seam.

Answer 1

Correct Answer: 4.8

Step 1: The depth difference between consecutive boreholes:
- Between Borehole 1 (100 m) and Borehole 2 (130 m): \[ \text{Depth difference} = 130 \, m - 100 \, m = 30 \, m \]
- Between Borehole 2 (130 m) and Borehole 3 (160 m): \[ \text{Depth difference} = 160 \, m - 130 \, m = 30 \, m \]
- Between Borehole 3 (160 m) and Borehole 4 (190 m): \[ \text{Depth difference} = 190 \, m - 160 \, m = 30 \, m \]

Step 2: Since the boreholes are drilled at 50 m intervals, we can calculate the angle of dip between the boreholes. The dip angle (\(\theta\)) is calculated as:
\[ \text{Tan}(\theta) = \frac{\text{Change in depth}}{\text{Distance between boreholes}} = \frac{30}{50} = 0.6 \] \[ \theta = \tan^{-1}(0.6) = 31.0° \]

Step 3:
To calculate the true dip, we use the following formula, where \( \text{True dip} = \theta \times \text{Slope correction factor}\). The average angle between consecutive boreholes can be used as the slope correction factor.
True dip = 4.80^