Boussinesq's Formula

Q. A concentrated load of 50 kN acts on the surface of ground. The increase in vertical stress directly below the load at a depth of 4 m will be (Value of influence factor is 0.48)

1. $1.5kN/m^2$
2. $1.5kN/m^2$
3. $150kN/m^2$
4. $0.15kN/m^2$

Q. A concentrated load of 50 t acts vertically at a point on the soil surface.If Boussinesq's equation is applied for computation of stress, then the ratio of vertical stresses at depths of 3 m and 5 m respectively vertically below the point of application of load will be

1. 0.36
2. 0.60
3. 1.66
4. 2.77

Q. ${\sigma }_z$ is the vertical stress at a depth equal to Z in the soil mass due to a surface point load Q. The vertical stress at depth equal to 2Z will be

1. $0.25{\sigma }_z$
2. $0.50{\sigma }_z$
3. $1.0{\sigma }_z$
4. $2.0{\sigma }_z$

Q. The vertical stress at depth, z directly below the point load P is (k is a constant)

1. $k\frac{P}{z}$
2. $k\frac{P}{z^3}$
3. $k\frac{P}{z^2}$
4. $k\frac{P}{\sqrt{z}}$

Q. A point load of 650 kN is applied on the surface of a thick layer of clay. Using Boussinesq's elastic analysis, what is approximate value of the estimated vertical stress at a depth 2 m and a radial distance of 1.0 m from the point of application of load?

1. $55kN/m^2$
2. $44kN/m^2$
3. $41kN/m^2$
4. $37kN/m^2$

Q. For a vertical concentrated load acting on the surface of a semi-infinite elastic soil mass, the vertical normal stress at depth 'z' is proportional to

1. $z$
2. $1/z$
3. $z^2$
4. $1/z^2$

Q. The vertical stress at point $P_1$ due to the point load Q on the ground surface as shown in figure is ${\sigma }_z$. According to Boussinesq's equation, the vertical stress at point $P_2$ Shown in figure will be

1. ${\sigma }_z/2$
2. ${\sigma }_z$
3. $2{\sigma }_z$
4. $4{\sigma }_z$

Q. A point load of 700 kN is applied on the surface of thick layer of saturated clay. Using Boussinesq's elastic analysis, the estimated vertical stress $\left({\sigma }_v\right)$ at a depth of 2m and a radial distance of 1.0 m from the point of application of the load is:

1. 47.5 kPa
2. 47.6 kPa
3. 47.7 kPa
4. 47.8 kPa

Q. A uniformly distributed line load of 500kN/m is acting on the ground surface. Based on Boussinesq's theory, the ratio of vertical stress at a depth 2 m to that at 4 m right below the line of loading is

1. 0.25
2. 0.5
3. 2.0
4. 4.0

Q. Stresses obtained from Boussinesq's theory are considered reasonably satisfactory in foundation engineering because

1. they represent stress distribution in inhomogeneous soils below loaded area
2. they account for anisotropy of soil property
3. they give due regard to plastic behaviour of soils, particularly for settlement analysis
4. they consider elastic soil medium, and the intensity of allowable stresses below foundations in most cases are quite small and justify elastic solutions

Q. A concentrated load of 500kN is applied on an elastic half space. The ratio of the increase in vertical normal stress at depth of 2m and 4m along the point of the loading, as per Boussinesq's theory, would be .

1. 4

Q. Two columns A and B are standing 5 m apart. The loads transferred from them taken as point loads of magnitude 50 t and 30 t respectively. The resultant vertical stress due to two loads on a horizontal plane 3 m below ground surface under column 'B' is in $t/m^2$.

1. 1.69
2. 2.85
3. 0.95
4. 7.45
   

Q. Consider a square-shaped area ABCD on the ground with this centre at M as shown in the figure. Four concentrated vertical loads of P = 5000 kN are applied on this area, one at each corner.


The vertical stress increment (in kPa up to one decimal place) due to these loads according to the Boussinesq's equation at a point 5m right below M is

1. 190.84

Q. Statement (I) : The stresses and strains in a soil mass depend on the stress-deformation characteristics, anisotropy and non-homogeneity of the soil and also on the boundary conditions.
Statement (II): Boussinesq's theory of stress distribution in soils deals with layered soils only.

1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
2. Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
3. Statement (I) is true but Statement (II) is false
4. Statement (I) is false but Statement (II) is true

Q. Assertion (A): Boussinesq equation is not suitable for sedimentary deposits.
Reason (R): Sedimentary deposits do not represent an iso-tropic-cum-homogeneous system.

1. Both A and R are true and R is the correct explanation of A
2. Both A and R are true but R is not a correct explanation of A
3. A is true but R is false
4. A is false but R is true