Question $6(10$ marks$)$

A soil element representing a stress condition of a soil mass is given below. Later, the vertical stress $({}_y)$ was changed from $100k\frac{N}{m^2}({}_{y,i})$ to $40k\frac{N}{m^2}({}_{y,f})$ and the horizontal stress $({}_x)$ from $40k\frac{N}{m^2}({}_{x,i})$ to $100k\frac{N}{m^2}({}_{x,f}),$ while the shear stress $()$ was held constant at $={}_i={}_f=40k\frac{N}{m^2}.$ By using Mohr's circle of stress, determine:

a$)$ Values of ${}_1$ and ${}_3$ before and after the changes of normal stresses.

b$)$ How many degrees the rotation of direction of ${}_1$ and the direction of rotation.

Remarks: Calculation without Mohr's circle and reading from scale will not be credited.