A highly sensitive volcanic clay was investigated in the laboratory and found to have the following properties: (i) gwet = 12.50 kN/m3 (ii) G = 2.75 (iii) e = 9.0 (iv) w = 311% In rechecking the above values, one was found to be inconsistent with the rest. Find the inconsistent value and report it correctly.

A highly sensitive volcanic clay was investigated in the laboratory and found to have the following properties: (i) gwet = 12.50 kN/m3 (ii) G = 2.75 (iii) e = 9.0 (iv) w = 311% In rechecking the above values, one was found to be inconsistent with the rest. Find the inconsistent value and report it correctly

Volcanic Clay Consistency Analysis (Civil Services Exam 2001)

Problem Statement (Civil Services Exam 2001)

A highly sensitive volcanic clay has the following properties:

Wet unit weight (\( \gamma_{\text{wet}} \)) = 12.50 kN/m³
Specific gravity (\( G \)) = 2.75
Void ratio (\( e \)) = 9.0
Water content (\( w \)) = 311%

One of these values is inconsistent. Identify and correct it.

Solution

1. Assumption (i): \( \gamma_{\text{wet}} \) is inconsistent

\( S = \frac{wG}{e} = \frac{3.11 \times 2.75}{9.0} = 0.95 < 1 \) (Valid)
\( \gamma_{\text{wet}} = \frac{G + eS}{1 + e} \cdot \gamma_w = \frac{2.75 + 9.0 \times 0.95}{1 + 9.0} \times 9.81 \approx 11.09 \, \text{kN/m}^3 \)

Computed \( \gamma_{\text{wet}} = 11.09 \, \text{kN/m}^3 \) ≠ Given \( \gamma_{\text{wet}} = 12.50 \, \text{kN/m}^3 \). Hence, \( \gamma_{\text{wet}} \) is inconsistent.

2. Assumption (ii): \( G \) is inconsistent

\( \gamma_d = \frac{\gamma_{\text{wet}}}{1 + w} = \frac{12.56}{1 + 3.11} \approx 3.06 \, \text{kN/m}^3 \)
\( G = \frac{\gamma_d (1 + e)}{\gamma_w} = \frac{3.06 \times (1 + 9.0)}{9.81} \approx 3.115 \)
\( S = \frac{wG}{e} = \frac{3.11 \times 3.115}{9.0} \approx 1.076 > 1 \) (Invalid)

Since \( S > 1 \), this assumption is invalid. \( G \) is consistent.

3. Assumption (iii): \( e \) is inconsistent

\( \gamma_d = \frac{\gamma_{\text{wet}}}{1 + w} = \frac{12.53}{1 + 3.11} \approx 3.06 \, \text{kN/m}^3 \)
\( e = \frac{G \gamma_w}{\gamma_d} – 1 = \frac{2.75 \times 9.81}{3.06} – 1 \approx 7.828 \)
\( S = \frac{wG}{e} = \frac{3.11 \times 2.75}{7.828} \approx 1.093 > 1 \) (Invalid)

Since \( S > 1 \), this assumption is invalid. \( e \) is consistent.

4. Assumption (iv): \( w \) is inconsistent

\( \gamma_d = \frac{G \gamma_w}{1 + e} = \frac{2.75 \times 9.81}{1 + 9.0} \approx 2.698 \, \text{kN/m}^3 \)
\( w = \frac{\gamma_{\text{wet}}}{\gamma_d} – 1 = \frac{12.56}{2.698} – 1 \approx 3.655 \)
\( S = \frac{wG}{e} = \frac{3.655 \times 2.75}{9.0} \approx 1.117 > 1 \) (Invalid)

Since \( S > 1 \), this assumption is invalid. \( w \) is consistent.

Result:

Inconsistent value: \( \gamma_{\text{wet}} = 12.50 \, \text{kN/m}^3 \)
Corrected value: \( \gamma_{\text{wet}} = 11.09 \, \text{kN/m}^3 \)

Explanation

Key Steps:

Checked consistency of each parameter using phase relationships.
Ensured saturation (\( S \)) does not exceed 1 (100%).
Verified calculations using dry density and void ratio relationships.

Physical Meaning

1. High Void Ratio (\( e = 9.0 \)):

Indicates extremely porous structure typical of sensitive clays.
Results in low density and high compressibility.

2. Water Content (\( w = 311\% \)):

Reflects high water absorption capacity of volcanic clay.
Leads to significant volume changes upon drying or wetting.

3. Corrected Wet Unit Weight:

11.09 kN/m³ aligns with high porosity and water content.
Ensures realistic saturation levels (\( S < 1 \)).

Engineering Significance:

Highlights importance of cross-verifying lab data.
Demonstrates sensitivity of volcanic clays to water content.
Reinforces need for accurate density measurements in geotechnical analysis.