A geotechnical problem uses Primary consolidation settlement. Given compression index (Cc) = 0.4900; layer thickness (H) = 21.5000 ft; initial void ratio (e0) = 1.1000; initial effective stress (sigma0) = 3,390 psf; stress increase (dsigma) = 940.0 psf, determine the settlement (Sc) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Primary consolidation settlement.
• Everything except Sc is given, so isolate Sc 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:

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

3. Step 3 — List the givens: compression index (Cc) = 0.4900, layer thickness (H) = 21.5000 ft, initial void ratio (e0) = 1.1000, initial effective stress (sigma0) = 3,390 psf, stress increase (dsigma) = 940.0 psf.

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

5. Step 5 — Evaluate:

   $$Sc = 0.5332\ \text{ft}$$

6. Step 6 — Check: returning Sc = 0.5332 ft to

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

Why the other options are there

• 1.0664 — kept a factor of two that cancels in the correct rearrangement.
• 0.2666 — dropped that same factor in the other direction.
• 0.5865 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Ultimate consolidation settlement in soil layer

ultimate consolidation settlement in a soil layer supporting a mat foundation Given compression index (C_c) = 0.3200; clay layer thickness (H) = 8.2000 m; initial void ratio (e_0) = 1.3800; final effective stress (sigma_f) = 275.0 kPa; initial effective stress (sigma_0) = 89.0000 kPa, determine the consolidation settlement (S_c) in m.

Start with the thinking

• The governing relation printed in this handbook section is Ultimate consolidation settlement in soil layer.
• Everything except S_c is given, so isolate S_c 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.
• Ultimate consolidation settlement in a soil layer estimates long-term compression of a clay layer under added surcharge.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

3. Step 3 — List the givens: compression index (C_c) = 0.3200, clay layer thickness (H) = 8.2000 m, initial void ratio (e_0) = 1.3800, final effective stress (sigma_f) = 275.0 kPa, initial effective stress (sigma_0) = 89.0000 kPa.

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

5. Step 5 — Evaluate:

   $$S_{c} = 0.5402\ \text{m}$$

6. Step 6 — Check: returning S_c = 0.5402 m to

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

Why the other options are there

• 1.0803 — kept a factor of two that cancels in the correct rearrangement.
• 0.2701 — dropped that same factor in the other direction.
• 0.5942 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultimate consolidation settlement in soil layer

A geotechnical problem uses Primary consolidation settlement. Given layer thickness (H) = 20.0000 ft; initial void ratio (e0) = 0.9800; initial effective stress (sigma0) = 1,750 psf; stress increase (dsigma) = 2,350 psf; settlement (Sc) = 2.8530 ft, determine the compression index (Cc).

Start with the thinking

• The governing relation printed in this handbook section is Primary consolidation settlement.
• Everything except Cc is given, so isolate Cc 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:

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

3. Step 3 — List the givens: layer thickness (H) = 20.0000 ft, initial void ratio (e0) = 0.9800, initial effective stress (sigma0) = 1,750 psf, stress increase (dsigma) = 2,350 psf, settlement (Sc) = 2.8530 ft.

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

5. Step 5 — Evaluate:

   $$Cc = 0.7639$$

6. Step 6 — Check: returning Cc = 0.7639 to

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

Why the other options are there

• 1.5278 — kept a factor of two that cancels in the correct rearrangement.
• 0.3819 — dropped that same factor in the other direction.
• 0.8403 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Ultimate consolidation settlement in soil layer

ultimate consolidation settlement in a soil layer of soft clay under fill loading Given clay layer thickness (H) = 5.8000 m; initial void ratio (e_0) = 1.0200; final effective stress (sigma_f) = 340.0 kPa; initial effective stress (sigma_0) = 88.0000 kPa; consolidation settlement (S_c) = 0.0420 m, determine the compression index (C_c).

Start with the thinking

• The governing relation printed in this handbook section is Ultimate consolidation settlement in soil layer.
• Everything except C_c is given, so isolate C_c 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.
• Ultimate consolidation settlement in a soil layer estimates long-term compression of a clay layer under added surcharge.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

3. Step 3 — List the givens: clay layer thickness (H) = 5.8000 m, initial void ratio (e_0) = 1.0200, final effective stress (sigma_f) = 340.0 kPa, initial effective stress (sigma_0) = 88.0000 kPa, consolidation settlement (S_c) = 0.0420 m.

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

5. Step 5 — Evaluate:

   $$C_{c} = 0.0249$$

6. Step 6 — Check: returning C_c = 0.0249 to

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

Why the other options are there

• 0.0498 — kept a factor of two that cancels in the correct rearrangement.
• 0.0125 — dropped that same factor in the other direction.
• 0.0274 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultimate consolidation settlement in soil layer

A geotechnical problem uses Primary consolidation settlement. Given compression index (Cc) = 0.5600; initial void ratio (e0) = 0.8100; initial effective stress (sigma0) = 1,650 psf; stress increase (dsigma) = 2,030 psf; settlement (Sc) = 2.0400 ft, determine the layer thickness (H) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Primary consolidation settlement.
• Everything except H is given, so isolate H 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:

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

3. Step 3 — List the givens: compression index (Cc) = 0.5600, initial void ratio (e0) = 0.8100, initial effective stress (sigma0) = 1,650 psf, stress increase (dsigma) = 2,030 psf, settlement (Sc) = 2.0400 ft.

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

5. Step 5 — Evaluate:

   $$H = 18.9273\ \text{ft}$$

6. Step 6 — Check: returning H = 18.9273 ft to

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

Why the other options are there

• 37.8545 — kept a factor of two that cancels in the correct rearrangement.
• 9.4636 — dropped that same factor in the other direction.
• 20.8200 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Ultimate consolidation settlement in soil layer

ultimate consolidation settlement in a soil layer beneath a new embankment Given compression index (C_c) = 0.5600; initial void ratio (e_0) = 0.8700; final effective stress (sigma_f) = 200.0 kPa; initial effective stress (sigma_0) = 83.0000 kPa; consolidation settlement (S_c) = 1.0190 m, determine the clay layer thickness (H) in m.

Start with the thinking

• The governing relation printed in this handbook section is Ultimate consolidation settlement in soil layer.
• Everything except H is given, so isolate H 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.
• Ultimate consolidation settlement in a soil layer estimates long-term compression of a clay layer under added surcharge.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

3. Step 3 — List the givens: compression index (C_c) = 0.5600, initial void ratio (e_0) = 0.8700, final effective stress (sigma_f) = 200.0 kPa, initial effective stress (sigma_0) = 83.0000 kPa, consolidation settlement (S_c) = 1.0190 m.

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

5. Step 5 — Evaluate:

   $$H = 8.9088\ \text{m}$$

6. Step 6 — Check: returning H = 8.9088 m to

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

Why the other options are there

• 17.8176 — kept a factor of two that cancels in the correct rearrangement.
• 4.4544 — dropped that same factor in the other direction.
• 9.7997 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultimate consolidation settlement in soil layer

A geotechnical problem uses Primary consolidation settlement. Given compression index (Cc) = 0.5500; layer thickness (H) = 5.5000 ft; initial void ratio (e0) = 1.0000; initial effective stress (sigma0) = 3,330 psf; stress increase (dsigma) = 920.0 psf, determine the settlement (Sc) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Primary consolidation settlement.
• Everything except Sc is given, so isolate Sc 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:

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

3. Step 3 — List the givens: compression index (Cc) = 0.5500, layer thickness (H) = 5.5000 ft, initial void ratio (e0) = 1.0000, initial effective stress (sigma0) = 3,330 psf, stress increase (dsigma) = 920.0 psf.

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

5. Step 5 — Evaluate:

   $$Sc = 0.1602\ \text{ft}$$

6. Step 6 — Check: returning Sc = 0.1602 ft to

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

Why the other options are there

• 0.3205 — kept a factor of two that cancels in the correct rearrangement.
• 0.0801 — dropped that same factor in the other direction.
• 0.1763 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Ultimate consolidation settlement in soil layer

ultimate consolidation settlement in a soil layer supporting a mat foundation Given compression index (C_c) = 0.5700; clay layer thickness (H) = 4.5000 m; initial void ratio (e_0) = 1.0200; final effective stress (sigma_f) = 135.0 kPa; initial effective stress (sigma_0) = 77.0000 kPa, determine the consolidation settlement (S_c) in m.

Start with the thinking

• The governing relation printed in this handbook section is Ultimate consolidation settlement in soil layer.
• Everything except S_c is given, so isolate S_c 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.
• Ultimate consolidation settlement in a soil layer estimates long-term compression of a clay layer under added surcharge.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

3. Step 3 — List the givens: compression index (C_c) = 0.5700, clay layer thickness (H) = 4.5000 m, initial void ratio (e_0) = 1.0200, final effective stress (sigma_f) = 135.0 kPa, initial effective stress (sigma_0) = 77.0000 kPa.

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

5. Step 5 — Evaluate:

   $$S_{c} = 0.3096\ \text{m}$$

6. Step 6 — Check: returning S_c = 0.3096 m to

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

Why the other options are there

• 0.6193 — kept a factor of two that cancels in the correct rearrangement.
• 0.1548 — dropped that same factor in the other direction.
• 0.3406 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultimate consolidation settlement in soil layer

A geotechnical problem uses Primary consolidation settlement. Given layer thickness (H) = 8.0000 ft; initial void ratio (e0) = 1.1300; initial effective stress (sigma0) = 2,720 psf; stress increase (dsigma) = 500.0 psf; settlement (Sc) = 1.0270 ft, determine the compression index (Cc).

Start with the thinking

• The governing relation printed in this handbook section is Primary consolidation settlement.
• Everything except Cc is given, so isolate Cc 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:

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

3. Step 3 — List the givens: layer thickness (H) = 8.0000 ft, initial void ratio (e0) = 1.1300, initial effective stress (sigma0) = 2,720 psf, stress increase (dsigma) = 500.0 psf, settlement (Sc) = 1.0270 ft.

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

5. Step 5 — Evaluate:

   $$Cc = 3.7311$$

6. Step 6 — Check: returning Cc = 3.7311 to

   $$S_c = (C_c H)/(1+e_0) \log_{10}[(\sigma_0'+\Delta\sigma)/\sigma_0']$$

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

Why the other options are there

• 7.4621 — kept a factor of two that cancels in the correct rearrangement.
• 1.8655 — dropped that same factor in the other direction.
• 4.1042 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Ultimate consolidation settlement in soil layer

ultimate consolidation settlement in a soil layer of soft clay under fill loading Given clay layer thickness (H) = 7.2000 m; initial void ratio (e_0) = 0.7500; final effective stress (sigma_f) = 205.0 kPa; initial effective stress (sigma_0) = 84.0000 kPa; consolidation settlement (S_c) = 0.8560 m, determine the compression index (C_c).

Start with the thinking

• The governing relation printed in this handbook section is Ultimate consolidation settlement in soil layer.
• Everything except C_c is given, so isolate C_c 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.
• Ultimate consolidation settlement in a soil layer estimates long-term compression of a clay layer under added surcharge.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

3. Step 3 — List the givens: clay layer thickness (H) = 7.2000 m, initial void ratio (e_0) = 0.7500, final effective stress (sigma_f) = 205.0 kPa, initial effective stress (sigma_0) = 84.0000 kPa, consolidation settlement (S_c) = 0.8560 m.

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

5. Step 5 — Evaluate:

   $$C_{c} = 0.5370$$

6. Step 6 — Check: returning C_c = 0.5370 to

   $$S_c = \dfrac{C_c H}{1+e_0} \log\left(\dfrac{\sigma'_f}{\sigma'_0}\right)$$

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

Why the other options are there

• 1.0739 — kept a factor of two that cancels in the correct rearrangement.
• 0.2685 — dropped that same factor in the other direction.
• 0.5906 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultimate consolidation settlement in soil layer