A possible slope failure is shown in the figure. Three soil samples are taken from different locations (I, II and III) of the potential failure plane. Which is the most appropriate shear strength test for each of the sample to identify the failure mechanism? Identify the correct combination from the following options:
P : Triaxial compression test
Q : Triaxial extension test
R : Direct shear or shear box test
S : Vane shear test
Consider that a force P is acting on the surface of a half-space (Boussinesq’s problem). The expression for the vertical stress (σz) at any point (r, z), within the half-space is given as,
$\rm \sigma_z=\frac{3P}{2\pi} \frac{z^3}{_{(r^2+z^2)}\frac{5}{2}}$
where, r is the radial distance, and z is the depth with downward direction taken as positive. At any given r, there is a variation of σz along z, and at a specific z, the value of σz will be maximum. What is the locus of the maximum σz ?