Westergaard's Equation

November 08, 2024 Post a Comment

Westergaard's equation

Explanation: 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 difference between Boussinesq theory and Westergaard's theory?

Boussinesq's theory considers that the medium of soil is isotropic while Westergaard's theory considers that the medium of soil is anisotropic.

What is Boussinesq equation in soil mechanics?

Boussinesq's equation for vertical stress σ z = Q Z 2 × 3 2 π × [ 1 1 + ( r Z ) 2 ] 5 2. Where, σZ = vertical stress in kN/m2. Q = concentrated load in kN. Z = point below the ground level where stress has to be calculated.

What are the assumptions 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 are the assumptions of Westergaard's theory?

Westergaard assumed an elastic soil to be laterally reinforced by numerous closely spaced, horizontal sheets of negligible thickness but of infinite rigidity that allow only vertical movement but prevent the mass as a whole from undergoing any lateral strain.

What is 2 1 stress distribution method?

Vertical Ratio 2:1 Method For a non-rectangular footing, the stress is calculated by computing the area of the load at the surface. With increasing depth, the area over which the load is applied increases at a 2:1 ratio and the magnitude of the loading stress decreases correspondingly.

Why is Boussinesq important?

The Boussinesq approximation was a popular method for solving nonisothermal flow, particularly in previous years, as computational costs were lower when solving this method and convergence was more likely to be achieved.

What is terzaghi theory?

Terzaghi's Principle states that when stress is applied to a porous material, it is opposed by the fluid pressure filling the pores in the material.

What is Boussinesq coefficient?

Boussinesq's Formula Equation where, r = the horizontal distance between an arbitrary point P below the surface and the vertical axis through the point load Q. z = the vertical depth of the point P from the surface. IB = Boussinesq stress coefficient = 32π1[1+(r/z)2]5/2.

What is the difference between compaction and consolidation?

Compaction is the compression of soil by the expulsion of air from the voids of the soil. Consolidation is the compression of soil by the expulsion of water from voids of the soil. It is a quick process. It is a slow process.

What are the assumptions in terzaghi bearing capacity theory?

1. The soil is homogeneous and isotropic and its shear strength is represented by Coulomb's equation. 2. The strip footing has a rough base, and the problem is essentially two-dimensional.

What is sand boiling condition?

Sand boils or sand volcanoes occur when water under pressure wells up through a bed of sand. The water looks like it is boiling up from the bed of sand, hence the name.

What are the factors affecting compaction?

Factors affecting compaction Nature and type of soil, i.e. sand or clay, grading, plasticity. Water content at the time of compaction. Site conditions, e.g. weather, type of site, layer thickness. Compactive effort: type of plant (weight, vibration, number of passes)

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. Thin layers of sand are usually embedded in a homogeneous clay deposit. Westergaard's theory assumes that thin sheets of rigid material are sandwiched in a homogeneous soil mass.

What is the formula for stress ratio?

The stress ratio R is usually defined as minimum stress value divided by maximum stress value, which leads to values between -∞ and +1.

What is normal stress formula?

The dashed lines are the projections of the principal stress axes onto a deviatoric plane (i.e. a plane normal to the hydrostatic axis σ1 = σ2 = σ3, also called the π-plane) passing through the point (σ1,σ2,σ3).

What is direct stress formula?

Direct stress (σd) is produced when applied load acts on a body. Mathematically, σd= Axial applied compressive or tensile load/Area of cross section = P / A.

Which is correct equation for line load?

Diode load line. The curve shows the diode response (I vs VD) while the straight line shows the behaviour of the linear part of the circuit: I=(VDD-VD)/R. The point of intersection gives the actual current and voltage.

What is the eddy viscosity hypothesis?

The eddy viscosity hypothesis is that this dissipativity can be modelled by a viscosity term with particular flow features captured by a turbulent viscosity coeffi- cient. These assumptions are the foundation most turbulence models used in practical computations.