(Solved): (a) Draw a typical Mohr circle diagram at failure for a cohesionless soil \( \left(c^{\prime}=0\ri ...

(a) Draw a typical Mohr circle diagram at failure for a cohesionless soil \( \left(c^{\prime}=0\right) \) with shear strength parameter \( \phi \), and show that the Mohr-Coulomb failure criterion can be expressed as: \[ \left(\sigma_{1}^{\prime}-\sigma_{3}^{\prime}\right)=\left(\sigma_{1}^{\prime}+\sigma_{3}^{\prime}\right) \sin \phi^{\prime} \text {. } \] (5 marks) (b) Consolidated drained triaxial tests were carried out on specimens of a saturated clay and the results at failure are given in Table Q7. The specimens were initially \( 38 \mathrm{~mm} \) in diameter and \( 76 \mathrm{~mm} \) long. Table Q7 i. Determine the effective stress shear strength parameters. (15 marks) ii. Using the appropriate equation, determine the deviator stress if a specimen of the same soil were consolidated under all-around pressure of \( 350 \mathrm{kN} / \mathrm{m}^{2} \). Check the obtained value graphically.