A geotechnical problem uses Void ratio–porosity relation. Given porosity (n) = 0.5700, determine the void ratio (e).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except e is given, so isolate e symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3

   $$List the givens: porosity (n) = 0.5700$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = 1.3256$$

6. Step 6 — Check: returning e = 1.3256 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2.6512 — kept a factor of two that cancels in the correct rearrangement.
• 0.6628 — dropped that same factor in the other direction.
• 1.4581 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity

A geotechnical problem uses Void ratio–porosity relation. Given void ratio (e) = 0.9480, determine the porosity (n).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except n is given, so isolate n symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that n stands alone on the left-hand side.

3. Step 3

   $$List the givens: void ratio (e) = 0.9480$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$n = 0.4867$$

6. Step 6 — Check: returning n = 0.4867 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.9733 — kept a factor of two that cancels in the correct rearrangement.
• 0.2433 — dropped that same factor in the other direction.
• 0.5353 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity

A geotechnical problem uses Void ratio–porosity relation. Given porosity (n) = 0.4700, determine the void ratio (e).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except e is given, so isolate e symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3

   $$List the givens: porosity (n) = 0.4700$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = 0.8868$$

6. Step 6 — Check: returning e = 0.8868 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1.7736 — kept a factor of two that cancels in the correct rearrangement.
• 0.4434 — dropped that same factor in the other direction.
• 0.9755 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity

A geotechnical problem uses Void ratio–porosity relation. Given void ratio (e) = 0.3960, determine the porosity (n).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except n is given, so isolate n symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that n stands alone on the left-hand side.

3. Step 3

   $$List the givens: void ratio (e) = 0.3960$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$n = 0.2837$$

6. Step 6 — Check: returning n = 0.2837 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.5673 — kept a factor of two that cancels in the correct rearrangement.
• 0.1418 — dropped that same factor in the other direction.
• 0.3120 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity

A geotechnical problem uses Void ratio–porosity relation. Given porosity (n) = 0.3700, determine the void ratio (e).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except e is given, so isolate e symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3

   $$List the givens: porosity (n) = 0.3700$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = 0.5873$$

6. Step 6 — Check: returning e = 0.5873 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1.1746 — kept a factor of two that cancels in the correct rearrangement.
• 0.2937 — dropped that same factor in the other direction.
• 0.6460 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity

A geotechnical problem uses Void ratio–porosity relation. Given void ratio (e) = 1.3850, determine the porosity (n).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except n is given, so isolate n symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that n stands alone on the left-hand side.

3. Step 3

   $$List the givens: void ratio (e) = 1.3850$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$n = 0.5807$$

6. Step 6 — Check: returning n = 0.5807 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1.1614 — kept a factor of two that cancels in the correct rearrangement.
• 0.2904 — dropped that same factor in the other direction.
• 0.6388 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity

A geotechnical problem uses Void ratio–porosity relation. Given porosity (n) = 0.3200, determine the void ratio (e).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except e is given, so isolate e symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3

   $$List the givens: porosity (n) = 0.3200$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = 0.4706$$

6. Step 6 — Check: returning e = 0.4706 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.9412 — kept a factor of two that cancels in the correct rearrangement.
• 0.2353 — dropped that same factor in the other direction.
• 0.5176 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity

A geotechnical problem uses Void ratio–porosity relation. Given void ratio (e) = 0.9800, determine the porosity (n).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except n is given, so isolate n symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that n stands alone on the left-hand side.

3. Step 3

   $$List the givens: void ratio (e) = 0.9800$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$n = 0.4949$$

6. Step 6 — Check: returning n = 0.4949 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.9899 — kept a factor of two that cancels in the correct rearrangement.
• 0.2475 — dropped that same factor in the other direction.
• 0.5444 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity

A geotechnical problem uses Void ratio–porosity relation. Given porosity (n) = 0.4300, determine the void ratio (e).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except e is given, so isolate e symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3

   $$List the givens: porosity (n) = 0.4300$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = 0.7544$$

6. Step 6 — Check: returning e = 0.7544 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1.5088 — kept a factor of two that cancels in the correct rearrangement.
• 0.3772 — dropped that same factor in the other direction.
• 0.8298 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity

A geotechnical problem uses Void ratio–porosity relation. Given void ratio (e) = 1.3420, determine the porosity (n).

Start with the thinking

• The governing relation printed in this handbook section is Void ratio–porosity relation.
• Everything except n is given, so isolate n symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$e = n / (1 - n)$$

2. Step 2 — Rearrange the relation so that n stands alone on the left-hand side.

3. Step 3

   $$List the givens: void ratio (e) = 1.3420$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$n = 0.5730$$

6. Step 6 — Check: returning n = 0.5730 to

   $$e = n / (1 - n)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1.1460 — kept a factor of two that cancels in the correct rearrangement.
• 0.2865 — dropped that same factor in the other direction.
• 0.6303 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Porosity