Effective stress

Effective Stress

1. Effective Stress

2. Geostatic Stresses Total Stress Effective Stress Pore Water Pressure Total Stress= Effective Stress+ Pore Water Pressure s total = s eff + u Bossinisque Equations Point Load Line Load Strip Load Triangular Load Circular Load Rectangular Load Added Stresses (Point, line, strip, triangular, circular, rectangular) Stress Distribution in Soils Influence Charts Newmark Charts Stress Bulbs Westergaard’s Method (For Pavement) Approximate Method 1:2 Method A By: Kamal Tawfiq, Ph.D., P.E Added Stress Geostatic Stress s y s x t xy

3. Introduction Water may influence the nature of the mineral surface chemically and consequently affect the bonding forces between adjacent soil grain. This kind of interaction between the soil and water is called chemical interaction. The other kind of interaction is physical interaction between solid and water. Volume of the soil skeleton as a whole can change due to the rearrangement of the soil particles into new positions mainly by rolling and sliding due to force acting between particle. This physical interaction is studied when we study the effective stress concept.

4. Effective stress concept was developed by Terzaghi. Effective stress concept applies to a fully saturated soil and relates three types of stress Total Stress Neutral Stress Effective Stress

5. Total Stress When a load is applied to soil, it is carried by the solid grains and the water in the pores. The total vertical stress acting at a point below the ground surface is due to the weight of everything that lies above, including soil, water, and surface loading. Total stress thus increases with depth and with unit weight. Total Stress = unit weight of the soil * depth (Z or H)

6. TOTAL VERTICAL STRESS in homogeneous soil Ground Level Depth, z SOIL ELEMENT σ v σ v

7. TOTAL VERTICAL STRESS below a river or lake Ground Level z Water Level z w

8. Ground Level z 1 Soil 1 z 2 Soil 2 Soil 3 z 3 TOTAL VERTICAL STRESS in multi-layered soil

9. TOTAL VERTICAL STRESS with a surface surcharge load Ground Level z Very ‘wide ’ surcharge, q (kN/m 2 )

10. Pore Water Pressure The pressure of water in the pores of the soil is called pore water pressure (u). The magnitude of pore water pressure depends on : the depth below the water table. the conditions of seepage flow. Under hydrostatic conditions, no water flow takes place, and the pore pressure at a given point is given by u = ɣ w .h

11. Ground Level Water Table z PORE WATER PRESSURE under hydrostatic conditions (no water flow)

12. Effective Stress The principle of effective stress was enunciated by Karl Terzaghi in the year 1936 . This principle is valid only for saturated soils , At any point in a soil mass, the effective stress (represented by σ ' or s ' ) is related to total stress (s) and pore water pressure (u) as. σ ' = σ - u

13. Effective Stress in Unsaturated Zone Above the water table, when the soil is saturated, pore pressure will be negative (less than atmospheric). The height above the water table to which the soil is saturated is called the capillary rise , and this depends on the grain size and the size of pores. In coarse soils, the capillary rise is very small .

14. EFFECTIVE STRESS CONCEPT (Terzaghi, 1923) where = Total Vertical Stress = Effective Stress = Pore Water Pressure

15. VERTICAL EFFECTIVE STRESSES Ground Level z Water Table

16. Salient points about Effective Stress It should be noted that some times effective stress is also called as intergannular stress ( ) which is not actually true. The actual contact stress or intergannular stress is very large, as the contact area between the particles is very small. Effective stress is an imaginary parameter which is sum of the contact force divided by the gross area. This is the reason why effective stress is not measured, hence it is not a physical parameter. Effective stress is a function of normal force acting at the contact points of grains and pore pressure.  

17. Effective Stress can only be computed by subtracting pore water pressure form the total stress , both of which are physical parameters. Even though Effective stress is not a measurable quantity, it is very important parameter in soil mechanics, because Effective stress is a parameter on which compressibility, consolidation, settlements, shear stress and bearing capacity depends. These parameters do not depend on total stress directly. Incase of clay mineral particles in soil mass, mineral crystals are not in direct contact, since they are surrounded by absorbed layer of water. But it is observed that inter – granular force can be transformed through the absorbed layer. The principal of effective stress is valid for coarse grained and clayey soils.

18. Effective Stress In soil when No flow takes place

19. STRESSES WHEN FLOW TAKES PLACE THROUGH THE SOIL FROM TOP TO BOTTOM

20. STRESSES WHEN FLOW TAKES PLACE THROUGH THE SOIL FROM BOTTOM TO TOP