Q$3)(16\%)$:

Direct shear test was done under a vertical load of $2124$ N$,$ on a dense, dry, clean $($without fines$)$ sand specimen that is initially $6$ cm by $6$ cm square. The shear stress vs$.$ horizontal deformation data from this test are given in the figure.

a$)(4\%)$ Determine the peak friction angle of this dense sand specimen.

b$)(4\%)$ Illustrate the Mohr circle at peak shear stress, at the middle of the specimen. Also draw the peak strength envelope on the same figure.

c$)(4\%)$ Determine the magnitudes and orientations of principal stresses at peak shear stress, at the middle of the specimen.

d$)(4\%)$ Estimate the friction angle for a loose specimen of the same sand. Sketch shear stress vs$.$ shear deformation plot you expect for such a test.