Model Answer
0 min readIntroduction
Ore bodies, the economically viable concentrations of minerals, are rarely found as simple, uniform shapes. Their geometry is crucial for resource estimation and mine planning. Describing this geometry accurately requires understanding parameters like pitch and plunge. These parameters define the orientation of a line within a plane, and in the context of ore bodies, they describe the direction and angle of inclination of the ore body’s elongation. Accurate determination of ore grade is equally vital for assessing the economic feasibility of mining operations.
Pitch and Plunge of an Ore Body
Pitch refers to the angle between the horizontal plane and the line of steepest descent on an inclined plane. In the context of an ore body, it represents the angle at which the ore body dips downwards from the horizontal. It is measured in degrees from 0° to 90°. A pitch of 0° indicates a horizontal ore body, while 90° indicates a vertical ore body.
Plunge refers to the angle between the horizontal plane and the direction of the ore body’s elongation. It indicates the direction of the ore body’s maximum extension. It is also measured in degrees from 0° to 90°. The plunge is typically measured in a compass direction (e.g., 30°NW means 30 degrees towards the Northwest).
These parameters are essential for creating 3D models of ore bodies, which are used for resource estimation, mine planning, and geotechnical analysis. They are determined through various methods, including core logging, surveying, and geophysical techniques.
Calculating Average Grade of a Pb-Ore Body
To calculate the average grade of a Pb-ore body, we need data on the concentration of lead (Pb) in different samples taken from the ore body. Let's assume we have the following data (this is example data as the question does not provide it):
| Sample ID | Weight (tonnes) | Pb Grade (%) |
|---|---|---|
| S1 | 100 | 2.5 |
| S2 | 150 | 3.0 |
| S3 | 80 | 2.0 |
| S4 | 120 | 3.5 |
The formula for calculating the average grade is:
Average Grade = (∑ (Weighti * Gradei)) / ∑ Weighti
Where:
- Weighti is the weight of the ith sample
- Gradei is the Pb grade of the ith sample
Applying this formula to our example data:
Average Grade = ((100 * 2.5) + (150 * 3.0) + (80 * 2.0) + (120 * 3.5)) / (100 + 150 + 80 + 120)
Average Grade = (250 + 450 + 160 + 420) / 450
Average Grade = 1280 / 450
Average Grade = 2.84%
Therefore, the average grade of the Pb-ore body, based on the given (example) data, is 2.84%.
It is important to note that this is a simplified calculation. In real-world scenarios, ore grade calculations are more complex and involve factors such as sampling errors, geological variations, and the use of geostatistical methods like kriging to estimate grades in unsampled areas.
Conclusion
Understanding pitch and plunge is fundamental to characterizing ore body geometry, while accurate grade calculation is crucial for economic viability assessment. The calculation demonstrated above provides a basic framework for determining average ore grade, but real-world applications require more sophisticated techniques. Continued advancements in geological modeling and analytical methods are essential for optimizing resource estimation and sustainable mining practices.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.