Question

As per Rankine Theory, the coefficient of active earth pressure ($K_a$) is given by:

• A. $K_a = \frac{1 - \sin \theta}{1 + \sin \theta}$
• B. $K_a = \frac{1 + \sin \theta}{1 - \sin \theta}$
• C. $K_a = \frac{1 - \tan \theta}{1 + \tan \theta}$
• D. $K_a = \frac{1 + \tan \theta}{1 - \tan \theta}$

Hint:

\[ K_a = \frac{1 - \sin \theta}{1 + \sin \theta} \quad \text{(Active State)}, \quad K_p = \frac{1 + \sin \theta}{1 - \sin \theta} \quad \text{(Passive State)}. \]

Answer 1

The Correct Option is A

The coefficient of active earth pressure ($K_a$) as per Rankine’s Theory is derived based on the lateral pressure exerted by soil in its active state. The formula is:
\[K_a = \frac{1 - \sin \theta}{1 + \sin \theta},\]
where $\theta$ is the angle of internal friction of the soil. This formula is widely used in geotechnical engineering to calculate lateral earth pressure.