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 ?
A square footing of size 2.5 m × 2.5 m is placed 1.0 m below the ground surface on a cohesionless homogeneous soil stratum. Considering that the groundwater table is located at the base of the footing, the unit weights of soil above and below the groundwater table are 18 kN/m3 and 20 kN/m3, respectively, and the bearing capacity factor Nq is 58, the net ultimate bearing capacity of the soil is estimated as 1706 kPa (unit weight of water = 10 kN/m3).
Earlier, a plate load test was carried out with a circular plate of 30 cm diameter in the same foundation pit during a dry season, when the water table was located beyond the plate influence zone. Using Terzaghi’s bearing capacity formulation, what is the ultimate bearing capacity (in kPa) of the plate?