List of top Geotechnical Engineering Questions on Stress distribution in soils asked in GATE CE

A building is proposed in an area having thick deposit of silty clay. The water table is at the ground surface. The saturated unit weight of soil is 18 kN/m3 and unit weight of water is 10 kN/m3. The maximum vertical load (\(P\)) on a column of the proposed building is 2000 kN.

Consider \(\sigma_z \leq 0.1\sigma_v'\) for computation of the minimum depth of soil exploration.

\(\sigma_v'\) is the effective vertical overburden stress. \(\sigma_z\) is the increase in the vertical stress at depth \(z\) below load \(P\) as per the Boussinesq's stress theory.

Based on above, the minimum depth (in m) of soil exploration required for the foundation design is (rounded off to two decimal places).

For the dual-wheel carrying assembly shown in the figure, \( P \) is the load on each wheel, \( a \) is the radius of the contact area of the wheel, \( s \) is the spacing between the wheels, and \( d \) is the clear distance between the wheels. Assuming that the ground is an elastic, homogeneous, and isotropic half space, the ratio of Equivalent Single Wheel Load (ESWL) at depth \( z = \frac{d}{2} \) to the ESWL at depth \( z = 2s \) is \(\underline{\hspace{1cm}}\) (round off to one decimal place). 

A concentrated vertical load of 3000 kN is applied on a horizontal ground surface. Points P and Q are at depths 1 m and 2 m below the ground, respectively, along the line of application of the load. Considering the ground to be a linearly elastic, isotropic, semi-infinite medium, the ratio of the increase in vertical stress at P to the increase in vertical stress at Q is \(\underline{\hspace{2cm}}\) (in integer).
Soil = 0.75
G = 2.68
Water content = 17% 
γw = 10 kg n /m3 
γd = ?