Question

Which of the following is true for the cohesion of soils?

• A. It varies directly with surface tension and directly with particle size
• B. It varies inversely with surface tension and inversely with particle size
• C. It varies directly with surface tension and inversely with particle size
• D. It varies inversely with surface tension and directly with particle size

Hint:

Clay has very small particles $\implies$ High specific surface $\implies$ High cohesion. Sand has large particles $\implies$ Negligible cohesion (cohesionless).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Apparent cohesion in unsaturated soils is generated by capillary meniscus water films bridging adjacent soil grains, governed by the Young-Laplace capillary equation.
Key Formula or Approach:
\[ P_c = \frac{2\sigma \cos \theta}{r} \]
where \(\sigma\) is the surface tension of water and \(r\) is the pore radius particle contact radius.

Step 2: Detailed Explanation:
Capillary attractive force between adjacent soil particles is given by:
\[ F_{\text{cohesion}} \propto \frac{\sigma}{d} \]
where:
- \(\sigma\) is the surface tension of water (increasing surface tension increases cohesive tensile meniscus pull).
- \(d\) is the soil particle diameter (finer particles have much smaller pore radii and higher specific surface area, generating stronger cohesive suction forces).
Thus, soil cohesion varies directly with water surface tension and inversely with particle size.

Step 3: Final Answer:
Therefore, cohesion varies directly with surface tension and inversely with particle size, matching option (C).