effect of overburden pressure on compacted landfill waste settlement Given unit weight of waste/cover (gamma) = 14.5000 kN/m^3; depth of overburden (z) = 30.5000 m, determine the overburden pressure (sigma_v) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except sigma_v is given, so isolate sigma_v 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for sigma_v:

   $$\sigma_{v} = \gamma z$$

3. Step 3

   $$List the givens: unit weight of waste/cover (gamma) = 14.5000 kN/m^3, depth of overburden (z) = 30.5000 m$$

4. Step 4 — Substitute the given values:

   $$\sigma_{v} = 14.5000 30.5000$$

5. Step 5 — Evaluate:

   $$\sigma_{v} = 442.3\ \text{kPa}$$

6. Step 6 — Check: returning sigma_v = 442.3 kPa to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

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

Reference: FE Handbook — Effect of Overburden Pressure

overburden pressure at the base of a landfill cell Given depth of overburden (z) = 19.5000 m; overburden pressure (sigma_v) = 98.0000 kPa, determine the unit weight of waste/cover (gamma) in kN/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except gamma is given, so isolate gamma 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for gamma:

   $$\gamma = \dfrac{\sigma_v}{z}$$

3. Step 3

   $$List the givens: depth of overburden (z) = 19.5000 m, overburden pressure (sigma_v) = 98.0000 kPa$$

4. Step 4 — Substitute the given values:

   $$\gamma = \dfrac{\sigma_v}{19.5000}$$

5. Step 5 — Evaluate:

   \gamma = 5.0256\ \text{kN/m^3}

6. Step 6 — Check: returning gamma = 5.0256 kN/m^3 to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

• 10.0513 — kept a factor of two that cancels in the correct rearrangement.
• 2.5128 — dropped that same factor in the other direction.
• 5.5282 — rounded an intermediate value before the final step.

Reference: FE Handbook — Effect of Overburden Pressure

effect of overburden pressure on waste density with increasing depth Given unit weight of waste/cover (gamma) = 14.3000 kN/m^3; overburden pressure (sigma_v) = 138.0 kPa, determine the depth of overburden (z) in m.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except z is given, so isolate z 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for z:

   $$z = \dfrac{\sigma_v}{\gamma}$$

3. Step 3 — List the givens: unit weight of waste/cover (gamma) = 14.3000 kN/m^3, overburden pressure (sigma_v) = 138.0 kPa.

4. Step 4 — Substitute the given values:

   $$z = \dfrac{\sigma_v}{14.3000}$$

5. Step 5 — Evaluate:

   $$z = 9.6503\ \text{m}$$

6. Step 6 — Check: returning z = 9.6503 m to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

• 19.3007 — kept a factor of two that cancels in the correct rearrangement.
• 4.8252 — dropped that same factor in the other direction.
• 10.6154 — rounded an intermediate value before the final step.

Reference: FE Handbook — Effect of Overburden Pressure

effect of overburden pressure on compacted landfill waste settlement Given unit weight of waste/cover (gamma) = 11.6000 kN/m^3; depth of overburden (z) = 19.0000 m, determine the overburden pressure (sigma_v) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except sigma_v is given, so isolate sigma_v 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for sigma_v:

   $$\sigma_{v} = \gamma z$$

3. Step 3

   $$List the givens: unit weight of waste/cover (gamma) = 11.6000 kN/m^3, depth of overburden (z) = 19.0000 m$$

4. Step 4 — Substitute the given values:

   $$\sigma_{v} = 11.6000 19.0000$$

5. Step 5 — Evaluate:

   $$\sigma_{v} = 220.4\ \text{kPa}$$

6. Step 6 — Check: returning sigma_v = 220.4 kPa to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

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

Reference: FE Handbook — Effect of Overburden Pressure

overburden pressure at the base of a landfill cell Given depth of overburden (z) = 10.5000 m; overburden pressure (sigma_v) = 256.0 kPa, determine the unit weight of waste/cover (gamma) in kN/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except gamma is given, so isolate gamma 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for gamma:

   $$\gamma = \dfrac{\sigma_v}{z}$$

3. Step 3

   $$List the givens: depth of overburden (z) = 10.5000 m, overburden pressure (sigma_v) = 256.0 kPa$$

4. Step 4 — Substitute the given values:

   $$\gamma = \dfrac{\sigma_v}{10.5000}$$

5. Step 5 — Evaluate:

   \gamma = 24.3810\ \text{kN/m^3}

6. Step 6 — Check: returning gamma = 24.3810 kN/m^3 to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

• 48.7619 — kept a factor of two that cancels in the correct rearrangement.
• 12.1905 — dropped that same factor in the other direction.
• 26.8190 — rounded an intermediate value before the final step.

Reference: FE Handbook — Effect of Overburden Pressure

effect of overburden pressure on waste density with increasing depth Given unit weight of waste/cover (gamma) = 9.1000 kN/m^3; overburden pressure (sigma_v) = 498.0 kPa, determine the depth of overburden (z) in m.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except z is given, so isolate z 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for z:

   $$z = \dfrac{\sigma_v}{\gamma}$$

3. Step 3

   $$List the givens: unit weight of waste/cover (gamma) = 9.1000 kN/m^3, overburden pressure (sigma_v) = 498.0 kPa$$

4. Step 4 — Substitute the given values:

   $$z = \dfrac{\sigma_v}{9.1000}$$

5. Step 5 — Evaluate:

   $$z = 54.7253\ \text{m}$$

6. Step 6 — Check: returning z = 54.7253 m to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

• 109.5 — kept a factor of two that cancels in the correct rearrangement.
• 27.3626 — dropped that same factor in the other direction.
• 60.1978 — rounded an intermediate value before the final step.

Reference: FE Handbook — Effect of Overburden Pressure

effect of overburden pressure on compacted landfill waste settlement Given unit weight of waste/cover (gamma) = 18.0000 kN/m^3; depth of overburden (z) = 1.0000 m, determine the overburden pressure (sigma_v) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except sigma_v is given, so isolate sigma_v 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for sigma_v:

   $$\sigma_{v} = \gamma z$$

3. Step 3

   $$List the givens: unit weight of waste/cover (gamma) = 18.0000 kN/m^3, depth of overburden (z) = 1.0000 m$$

4. Step 4 — Substitute the given values:

   $$\sigma_{v} = 18.0000 1.0000$$

5. Step 5 — Evaluate:

   $$\sigma_{v} = 18.0000\ \text{kPa}$$

6. Step 6 — Check: returning sigma_v = 18.0000 kPa to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

• 36.0000 — kept a factor of two that cancels in the correct rearrangement.
• 9.0000 — dropped that same factor in the other direction.
• 19.8000 — rounded an intermediate value before the final step.

Reference: FE Handbook — Effect of Overburden Pressure

overburden pressure at the base of a landfill cell Given depth of overburden (z) = 9.5000 m; overburden pressure (sigma_v) = 462.0 kPa, determine the unit weight of waste/cover (gamma) in kN/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except gamma is given, so isolate gamma 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for gamma:

   $$\gamma = \dfrac{\sigma_v}{z}$$

3. Step 3

   $$List the givens: depth of overburden (z) = 9.5000 m, overburden pressure (sigma_v) = 462.0 kPa$$

4. Step 4 — Substitute the given values:

   $$\gamma = \dfrac{\sigma_v}{9.5000}$$

5. Step 5 — Evaluate:

   \gamma = 48.6316\ \text{kN/m^3}

6. Step 6 — Check: returning gamma = 48.6316 kN/m^3 to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

• 97.2632 — kept a factor of two that cancels in the correct rearrangement.
• 24.3158 — dropped that same factor in the other direction.
• 53.4947 — rounded an intermediate value before the final step.

Reference: FE Handbook — Effect of Overburden Pressure

effect of overburden pressure on waste density with increasing depth Given unit weight of waste/cover (gamma) = 10.6000 kN/m^3; overburden pressure (sigma_v) = 405.0 kPa, determine the depth of overburden (z) in m.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except z is given, so isolate z 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for z:

   $$z = \dfrac{\sigma_v}{\gamma}$$

3. Step 3 — List the givens: unit weight of waste/cover (gamma) = 10.6000 kN/m^3, overburden pressure (sigma_v) = 405.0 kPa.

4. Step 4 — Substitute the given values:

   $$z = \dfrac{\sigma_v}{10.6000}$$

5. Step 5 — Evaluate:

   $$z = 38.2075\ \text{m}$$

6. Step 6 — Check: returning z = 38.2075 m to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

• 76.4151 — kept a factor of two that cancels in the correct rearrangement.
• 19.1038 — dropped that same factor in the other direction.
• 42.0283 — rounded an intermediate value before the final step.

Reference: FE Handbook — Effect of Overburden Pressure

effect of overburden pressure on compacted landfill waste settlement Given unit weight of waste/cover (gamma) = 15.0000 kN/m^3; depth of overburden (z) = 6.0000 m, determine the overburden pressure (sigma_v) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Effect of Overburden Pressure.
• Everything except sigma_v is given, so isolate sigma_v 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.
• The effect of overburden pressure on landfill waste is estimated as the vertical stress from the overlying waste and cover depth.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma_v = \gamma \times z$$

2. Step 2 — Rearrange symbolically for sigma_v:

   $$\sigma_{v} = \gamma z$$

3. Step 3

   $$List the givens: unit weight of waste/cover (gamma) = 15.0000 kN/m^3, depth of overburden (z) = 6.0000 m$$

4. Step 4 — Substitute the given values:

   $$\sigma_{v} = 15.0000 6.0000$$

5. Step 5 — Evaluate:

   $$\sigma_{v} = 90.0000\ \text{kPa}$$

6. Step 6 — Check: returning sigma_v = 90.0000 kPa to

   $$\sigma_v = \gamma \times z$$

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

Why the other options are there

• 180.0 — kept a factor of two that cancels in the correct rearrangement.
• 45.0000 — dropped that same factor in the other direction.
• 99.0000 — rounded an intermediate value before the final step.

Reference: FE Handbook — Effect of Overburden Pressure