Question

A soil sample is subjected to a hydrostatic pressure $\sigma$. The Mohr circle for any point in the soil sample would be

• A. A circle of radius $\sigma$ and center at the origin
• B. A circle of radius $\sigma$ and center at a distance $\sigma$ from the origin
• C. A point at a distance $\sigma$ from the origin
• D. A circle of diameter $\sigma$ and center at the origin

Answer 1

The correct option is C A point at a distance $\sigma$ from the origin

Radius of Mohr circle = $\sqrt{{\left(\frac{{\sigma }_x-{\sigma }_y}{2}\right)}^2+{\tau }^2}$

Given :
${\sigma }_x={\sigma }_y={\sigma }_z=\sigma and\tau =0$

$R=\sqrt{{\left(\frac{\sigma -\sigma }{2}\right)}^2+0^2}=0$

$Centre=\frac{{\sigma }_x+{\sigma }_y}{2}=\frac{\sigma +\sigma }{2}=\sigma$

Mohr circle is a point at a distance of $\sigma$ from orgin.