Stress distribution in soil

Stress Distribution in soil

1. Stress Distribution in Soil

2. Vertical Stress Due to Concentrated Load 1. Boussinesq Equation: 1885, Boussinesq gave the theoretical solution for the stress distribution in an elastic medium subjected to concentrated load on its surface. Assumptions Soil Mass in elastic Soil is homogenous and isotropic Soil id Semi infinite Soil is weight less and unstressed before application of load

3. Using logathemic stress functions for the solution of elastic problems, Boussinesq proved that the polar stress sigma R at any point P(x, y, z) given by

4. Shear Stress

5. It should me noted that, the vertical stress at certain depth z is dependent only on the r/z ratio and independent of material (E, mu) The Vertical Stress decreases rapidly with an increase in the r/z ratio Boussinesq euation can be applied to actual field problems, provided the distance Z is measured from the point of application of load This equation can be used for the negative upward load i.e , vertical decreases due to an excavation.

6. Vertical Pressure Under a Uniformly loaded circular Area

7. Integrating Over the entire ring of radius r, the vertical stress delta sigma z is given by The Total Vertical pressure sigma z due to the entire loaded area is given by integrating the above expression between the limits r=0 to r=a

8. Vertical Stress due to a line Load The load intensity q per unit length Acting on semi – infinite elastic medium. Y axis be the direction of load The vertical stress at any point P having coordinated (x, y, z) Consider a small length in line load delta y The elementary load is equal to the load intensity * delta y

9. Vertical Stress Under Strip Load

10. Vertical Pressure Under a Uniformly Loaded Rectangular Area