The Boussinesq theory for the distribution of stresses in a half-space resulting from surface loads is largely used in road engineering. It is based on the assumption of linear-elastic homogeneous isotropic half-space for the soil media.
What is Westergaard theory?
Detailed Solution Westergaard’s Theory Assumptions: Elastic medium of semi-infinite extent but containing numerous, closely spaced horizontal sheets of a negligible thickness of an infinite rigid material which permits only downward deformation as a whole without allowing it to undergo any lateral strain.
What is boussinesq stress?
Boussinesq (1842 – 1929) evolved equations that can be used to determine stresses at any point P at a depth z as a result of a surface point load. Vertical pressure within an earth mass.
What is stress distribution in soil?
The soil stress distribution is caused by the self-weight of soil and surface loading on the structure. Self-weight causes the stresses below the soil at any depth. The equation used to determine the stress distribution caused due to self-weight is as shown below.
Why is Boussinesq important?
The Boussinesq approximation is a way to solve nonisothermal flow, such as natural convection problems, without having to solve for the full compressible formulation of the Navier-Stokes equations. The approximation is accurate when density variations are small as this reduces the nonlinearity of the problem.
What are differences between boussinesq’s and Westergaard’s theories?
5) Boussinesq’s influence factor is high Westergaard’s theory:- 1. ) Assumes that the soil medium is anisotropic 2) Deals with thin sheets of rigid material sandwiched in a homogeneous medium. 5) Westergaard’s influence factor is low compare to Boussinesq’s influence factor.
What are the assumptions involved in Boussinesq’s and Westergaard’s theory?
The Boussinesq theory assumes that the soil mass is isotropic. Actual sedimentary soils are generally anisotropic. Westergaard’s theory assumes that thin sheets of rigid material are sandwiched in a homogeneous soil mass.
What is Boussinesq influence factor?
In 1885, Boussinesq published equations to determine the state of stress in a subgrade material. He investigated the stresses in an elastic, semi-infinite, homogeneous, and isotropic soil solid medium. Boussinesq derived the equation of vertical stress and shear stress in a soil medium.
What is the significance of Boussinesq approximation?
The Boussinesq approximation is a way to solve nonisothermal flow, such as natural convection problems, without having to solve for the full compressible formulation of the Navier-Stokes equations.
What are the assumption of Boussinesq equation?
Boussinesq’s theory formula is based on following assumptions. The soil mass is semi-infinite, homogeneous and isotropic. The soil has a linear stress-strain relationship, The soil is weightless.
What is Boussinesq parameter?
Boussinesq Parameters contains inputs related to the Boussinesq model. This option appears only if Energy (in the Energy dialog box) and Gravity are enabled. This option appears only when Gravity is enabled. Specified Operating Density enables the specification of operating density.
Does Boussinesq reduce the attenuation of vertical stresses?
Results show that the plasticity reduces the attenuation of the vertical stresses in the soil mass, which means that the Boussinesq solution underestimates the stresses in an area which contributes to the soil settlement. To cite this article: M. Sadek, I. Shahrour, C. R. Mecanique 335 (2007).
What is the Boussinesq model used for?
The Boussinesq solution for the distribution of stresses in a half-space resulting from surface loads is largely used in geotechnical and road engineering. It is based on the assumption of a linear–elastic homogeneous isotropic half-space for the soil media.
Why is Boussinesq solution used in soil engineering?
The field measurements indicate that the actual stresses are generally smaller than the theoretical values given by Boussinesq’s solution at shallow depths. Thus, the Boussinesq solution gives conservative values and is commonly used in soil engineering problems. 1.
Does vertical stress depend on modulus of elasticity and Poisson’s ratio?
The vertical stress does not depend upon the modulus of elasticity (E) and the Poisson’s ratio (ν). But the solution has been derived assuming that the soil is linearly elastic. The stress distribution will be the same in all linearly elastic materials. 2.
