UPSC MainsGEOLOGY-PAPER-II201910 Marks
Q22.

What is meant by pitch and plunge of an ore body? Calculate average grade of a Pb-ore body from the given data.

How to Approach

This question requires a demonstration of understanding of fundamental concepts in ore deposit geology and practical application of calculations. The answer should begin by defining pitch and plunge, explaining their significance in describing ore body geometry. Then, it should clearly demonstrate the calculation of average grade using the provided data, showing all steps. A well-structured answer will include a clear presentation of the data and the formula used.

Model Answer

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Introduction

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.

Additional Resources

Key Definitions

Ore Reserve
The economically mineable portion of a measured or indicated mineral resource.
Geostatistics
A branch of statistics focused on spatial or spatiotemporal data, used extensively in ore reserve estimation to predict values at unsampled locations.

Key Statistics

Global lead production in 2022 was approximately 4.9 million metric tons (Source: US Geological Survey, Mineral Commodity Summaries 2023).

Source: US Geological Survey, Mineral Commodity Summaries 2023

India holds approximately 3.8% of the world’s lead reserves (as of 2022). (Source: Ministry of Mines, Annual Report 2022-23)

Source: Ministry of Mines, Annual Report 2022-23

Examples

Broken Hill, Australia

The Broken Hill ore deposit in Australia is a classic example of a massive sulfide deposit with complex ore body geometry, requiring detailed analysis of pitch and plunge for effective mining.

Frequently Asked Questions

What is the difference between ore reserve and mineral resource?

Mineral resources are all minerals that have been identified and estimated, while ore reserves are the economically viable portion of those resources that can be mined profitably.

Topics Covered

GeologyEconomic GeologyOre DepositsOre Body GeometryResource EstimationGeostatistics