What is Westergaard equation?

Based on this criterion of no lateral displacement, Westergaard derived the following equation for a point load, Q, at a depth z from the surface: σ z = Q Z 2 π [ 1 1 + 2 ( r z ) 2 ] 3 / 2. ∴ Westergaard’s analysis for stress distribution beneath loaded areas is more suitable to stratified or layered soils.

What is isobar of vertical stress?

An isobar or pressure bulb is a stress contour or a line which connects all points below the ground surface at which the vertical pressure is the same. A system of isobars indicates the decrease in stress intensity from the inner to the outer ones.

How do you calculate horizontal stress and vertical stress?

In other words the vertical stress (σv) and horizontal stress (σH) are principal stresses. The horizontal stress is customarily expressed as a proportion of the vertical stress σH = K’o σv = K’o ρd gz (3.2) where K’o = coefficient of earth pressure at rest in terms of effective stresses (see equation (3.7)).

What are the assumptions made in Boussinesq theory?

The soil mass is semi-infinite, homogeneous and isotropic. The soil has a linear stress-strain relationship, The soil is weightless. The load is a point load acting on the surface.

What is K0 in Geotech?

The at-rest earth pressure coefficient K0, i.e. the ratio σ′h /σ′v between the horizontal and the vertical effective geostatic stresses at a point in a semi-infinite soil mass bounded by a horizontal plane, is a fundamental parameter in soil mechanics.

What is Boussinesq stress?

Abstract. 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.

What are the assumptions made in Boussinesq formula for stress distribution in soil?

Explanation: 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. Therefore, the soil is considered to be elastic and of homogeneous nature.

What is Boussinesq influence factor?

It may be noted that the Boussinesq influence factor for vertical stress is a function of the ratio r/z and is independent of soil properties. It is maximum when r = 0, that is, below the concentrated load, and is equal to 0.4775.

What is the formula for calculating vertical stress?

V ertical stress,σz = 3Q 2πz2 1 [1+(r/z)2]5/2 = Q z2 I B V e r t i c a l s t r e s s, σ z = 3 Q 2 π z 2 1 [ 1 + ( r / z) 2] 5 / 2 = Q z 2 I B r = the horizontal distance between an arbitrary point P below the surface and the vertical axis through the point load Q.

What is the formula for Boussinesq’s equation?

Boussinesq’s Formula Equation At point P of above figure due to a point load Q, V ertical stress,σz = 3Q 2πz2 1 [1+(r/z)2]5/2 = Q z2 I B V e r t i c a l s t r e s s, σ z = 3 Q 2 π z 2 1 [ 1 + (r / z) 2] 5 / 2 = Q z 2 I B

What is the vertical stress computed by the Boussinesq theory?

The vertical stress computed by the Boussinesq theory for a point load is infinite when z = 0, that is, at the ground surface, where the load is applied. a.

What is the Boussinesq equation for stress on a wall calculator?

The Boussinesq Equation for Stress on a Wall calculator computes the stress on a wall based on a load on the ground surface and the relative location of that stress to the point in the wall. INSTRUCTIONS: Choose units and enter the following: