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How much would 3 cubic miles of typical Nevada rock weigh?

To estimate the weight of 3 cubic miles of typical Nevada rock, we need to follow these steps:

1. Volume Conversion: Convert cubic miles to cubic feet, as rock density is often given in pounds per cubic foot.
2. Rock Density: Use an average density for typical rock found in Nevada. The density can vary significantly based on rock type, but common rocks in Nevada include sandstone, limestone, and granite. Average densities for these rocks can provide a reasonable estimate.
3. Weight Calculation: Multiply the volume in cubic feet by the average density to get the weight in pounds, and convert to tons if necessary.

Step 1: Volume Conversion

1 cubic mile = 5,280 feet/mile * 5,280 feet/mile * 5,280 feet/mile = cubic feet.

Step 2: Rock Density

• Sandstone: Typically around 150 lbs/ft³.
• Limestone: Around 160-170 lbs/ft³.
• Granite: About 165-175 lbs/ft³.

We can use an average density for these rock types. Let's estimate with a middle value of around 165 lbs/ft³, recognizing this is a simplification.

Step 3: Weight Calculation

• Volume in cubic feet * Density in lbs/ft³ = Weight in pounds.
• Convert pounds to tons, where 1 ton = 2,000 pounds.

Let's calculate the weight of 3 cubic miles of rock using these steps.

The volume of 3 cubic miles of rock is approximately 441,593,856,000 cubic feet. Using an average density of 165 pounds per cubic foot for typical Nevada rock, the total weight would be about 72,862,986,240,000 pounds, which is equivalent to approximately 36,431,493,120 tons.

How long would that take?

Estimating the time required for a modern team of thousands to excavate 3 cubic miles (approximately 441,593,856,000 cubic feet) of rock underground involves several factors, including:

1. Excavation Rate: This depends on the equipment used, the type of rock, and the efficiency of operations. Modern excavation equipment can vary widely in its capabilities.
2. Working Hours: Assuming a continuous 24/7 operation or a more standard work schedule impacts the total duration.
3. Team Size and Efficiency: The number of workers and their productivity, considering shifts and the potential for simultaneous operations in different sections.
4. Safety and Environmental Considerations: These can slow down operations, especially in sensitive or challenging environments.

Hypothetical Scenario

• Excavation Rate: Let's assume an average rate that includes drilling, blasting, removing debris, and reinforcing excavated sections. A high-capacity operation might move 10,000 cubic yards per day as a conservative estimate. This rate can vary significantly, so it's a rough approximation.
• Conversion Needed: Convert cubic feet to cubic yards for compatibility with the assumed rate (1 cubic yard = 27 cubic feet).

Let's calculate the estimated time based on these assumptions.

To excavate 3 cubic miles (approximately 441,593,856,000 cubic feet or 16,355,328,000 cubic yards) of rock underground, under the assumption of a daily excavation rate of 10,000 cubic yards, it would take approximately 1,635,533 days. This is equivalent to about 4,481 years.

This estimate is highly simplified and assumes continuous excavation at the stated rate without accounting for the complexities of underground operations, such as the need for additional structural support, variations in rock hardness, and potential logistical or environmental constraints. Real-world projects of this scale would require detailed planning and could see significant variations from this estimate based on the factors mentioned.