A clay has a liquid limit of 58, a plastic limit of 24 and a natural water content of 41%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 1.35.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 58 - 24 = 34$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (41 - 24)/34 = 0.500$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 34/1.35 = 25.2$$

7. Interpretation

   $$LI = 0.50 indicates a stiff consistency$$

Why the other options are there

• PI = 82 (limits added)
• LI = -0.500 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index

A clay has a liquid limit of 40, a plastic limit of 26 and a natural water content of 45%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 1.25.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 40 - 26 = 14$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (45 - 26)/14 = 1.357$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 14/1.25 = 11.2$$

7. Interpretation

   $$LI = 1.36 indicates a very soft, near-liquid consistency$$

Why the other options are there

• PI = 66 (limits added)
• LI = 0.357 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index

A clay has a liquid limit of 34, a plastic limit of 20 and a natural water content of 42%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 0.95.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 34 - 20 = 14$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (42 - 20)/14 = 1.571$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 14/0.95 = 14.7$$

7. Interpretation

   $$LI = 1.57 indicates a very soft, near-liquid consistency$$

Why the other options are there

• PI = 54 (limits added)
• LI = 0.571 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index

A clay has a liquid limit of 30, a plastic limit of 15 and a natural water content of 51%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 1.30.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 30 - 15 = 15$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (51 - 15)/15 = 2.400$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 15/1.30 = 11.5$$

7. Interpretation

   $$LI = 2.40 indicates a very soft, near-liquid consistency$$

Why the other options are there

• PI = 45 (limits added)
• LI = 1.400 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index

A clay has a liquid limit of 73, a plastic limit of 17 and a natural water content of 21%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 1.15.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 73 - 17 = 56$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (21 - 17)/56 = 0.071$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 56/1.15 = 48.7$$

7. Interpretation

   $$LI = 0.07 indicates a stiff consistency$$

Why the other options are there

• PI = 90 (limits added)
• LI = -0.929 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index

A clay has a liquid limit of 30, a plastic limit of 25 and a natural water content of 54%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 0.70.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 30 - 25 = 5$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (54 - 25)/5 = 5.800$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 5/0.70 = 7.1$$

7. Interpretation

   $$LI = 5.80 indicates a very soft, near-liquid consistency$$

Why the other options are there

• PI = 55 (limits added)
• LI = 4.800 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index

A clay has a liquid limit of 42, a plastic limit of 27 and a natural water content of 35%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 0.65.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 42 - 27 = 15$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (35 - 27)/15 = 0.533$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 15/0.65 = 23.1$$

7. Interpretation

   $$LI = 0.53 indicates a soft consistency$$

Why the other options are there

• PI = 69 (limits added)
• LI = -0.467 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index

A clay has a liquid limit of 34, a plastic limit of 25 and a natural water content of 55%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 1.00.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 34 - 25 = 9$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (55 - 25)/9 = 3.333$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 9/1.00 = 9.0$$

7. Interpretation

   $$LI = 3.33 indicates a very soft, near-liquid consistency$$

Why the other options are there

• PI = 59 (limits added)
• LI = 2.333 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index

A clay has a liquid limit of 62, a plastic limit of 18 and a natural water content of 47%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 1.10.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 62 - 18 = 44$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (47 - 18)/44 = 0.659$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 44/1.10 = 40.0$$

7. Interpretation

   $$LI = 0.66 indicates a soft consistency$$

Why the other options are there

• PI = 80 (limits added)
• LI = -0.341 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index

A clay has a liquid limit of 63, a plastic limit of 17 and a natural water content of 35%. Compute the plasticity index and liquidity index, and estimate the clay fraction if the activity is 0.70.

Start with the thinking

• The plasticity index is the water-content band over which the soil behaves plastically.
• A liquidity index above 1 means the natural water content exceeds the liquid limit — the soil is essentially a slurry.

Step-by-step solution

1. Formula

   $$PI = LL - PL$$

2. Substituting

   $$PI = 63 - 17 = 46$$

3. Formula

   $$LI = (w - PL)/PI$$

4. Substituting

   $$LI = (35 - 17)/46 = 0.391$$

5. Formula

   $$A = PI / ($$

6. Rearranged

   $$clay fraction = PI/A = 46/0.70 = 65.7$$

7. Interpretation

   $$LI = 0.39 indicates a stiff consistency$$

Why the other options are there

• PI = 80 (limits added)
• LI = -0.609 (used LL in place of PL)

Reference: FE Reference Handbook — Geotechnical → Plasticity index