Boussinesq's Equations - Free MCQ Practice Test with solutions, GATE Civil

Boussinesq in 1885 studied and solved the problems of stress distribution in soils due to a concentrated loads acting at the ground surface. Darcy gave the law of flow of water through soils. The stress function was introduced by G.B Airy in 1862.

Boussinesq solved the problems of stress distribution in soils due to a concentrated loads acting at the ground surface. The assumptions made are based on theory of elasticity. Therefore, the soil is considered to be elastic.

Semi-infinite condition is when one of the dimension extends to infinity. If XY pane is considered to be ground surface and the z-axis as depth, then this condition is known as semi-infinite.

Boussinesq showed that the polar radial stress is given by,

Boussinesq’s vertical stress σ_z is given by,
σ_z = σ_Rcos² β
where, σ_z is the vertical stress
Q is the point load acting at the ground surface
r is the radial horizontal distance
z is the vertical distance.

The Boussinesq influence factor is given by,  where the K_B = Boussinesq influence factor which is a function of r/z ratio which is a dimensionless factor.

Boussinesq in 1885 studied and solved the problems of stress distribution in soils due to a concentrated loads acting at the ground surface, by assuming a suitable stress function. The assumptions made are based on theory of elasticity.

Boussinesq solved the problems of stress distribution in soils due to a concentrated loads acting at the ground surface. The assumptions made are based on theory of elasticity. Therefore, the soil is considered to be elastic and of homogeneous nature.

Boussinesq showed that the polar radial stress is given by,  where σ_R is the polar radial stress

R is the polar radial coordinate=√(r² + z²).

Boussinesq showed that the polar radial stress is given by,

Boussinesq’s tangential stress σz is given by,

where, τ_rz is the tangential stress
Q is the point load acting at the ground surface
r is the radial horizontal distance
z is the vertical distance.

Boussinesq’s vertical stress σ_z is given by,

Substituting r = 0,
We get,