1. CHAPTER 4
SOIL STRESSES

3. Introduction
We have to know the distribution of stress at a given depth to analyze the:
Compressibility of soils
Bearing capacity of foundations
Stability of embankments
Lateral pressure on retaining structure

4. Introduction
In determining the stress distribution, we have to know the stress that will be carried by water and the stress to be carried by the solid (soil skeleton).
It is involved the effective stress concept

5. STRESS DISTRIBUTION IN SOILS
Stresses at a point in a soil layer are caused by:
Added load (such as buildings, embankments, rail track
Self weight of the soil layers (Geostatic stresses)

6. Effective stress concept
1. Water level is far away from the soil surface A h1 B h2 C

7. Effective stress concept
1. Water level is at the soil surface A h1 B h2 C

8. Effective stress concept
1. Water level is above the soil surface hw A h1 B h2 C

9. Effective stress concept
1. Water level is far away from the soil surface + uniform load
q (kN/m2) A h1 B h2 C

10. Stresses in saturated soil with seepage
The effective stress in soil is different from static condition when there have upward or downward seepage of water.
The effective stress for downward seepage is higher than upward seepage
Upward seepage

11. Stresses in saturated soil with seepage
Downward seepage

12. Stresses in saturated soil with seepage
Example 1
A 9 m thick of stiff saturated soil clay underlain by a layer of sand. The sand is under artesian pressure. Calculate the maximum depth of cut H that can be made in the clay.

13. Stresses in saturated soil with seepage
Solution
Heave occur when ’A is 0

14. Stresses in saturated soil with seepage
Example 2
A cut is made in a stiff, saturated clay that is underlain by a layer of sand. What should be the height of the water, h, in the cut so that the stability of the saturated clay is not lost.

15. Stresses in saturated soil with seepage
Solution
For loss of stability, ’ = 0

16. VERTICAL STRESS DUE TO LOADING

17. Stress Due To a Point Load
assumed that the soil is elastic, homogeneous and isotropic

18. Stress Due To a Point Load
X - AXIS
Horizontal stress in x direction
Horizontal stress in y direction
Vertical stress, z
Poisson’s Ratio is when a sample of material is stretched in one direction, it tends to get thinner in the other two directions. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load.
NOTE:
 = Poisson’s Ratio

19. Stress Due To a Point Load
X - AXIS
Vertical stress
Poisson’s Ratio is when a sample of material is stretched in one direction, it tends to get thinner in the other two directions. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load.
NOTE:

20. Stress Due To a Line Load
X - AXIS
Poisson’s Ratio is when a sample of material is stretched in one direction, it tends to get thinner in the other two directions. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load.

21. Stress Due To a Line Load
X - AXIS
Poisson’s Ratio is when a sample of material is stretched in one direction, it tends to get thinner in the other two directions. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load.
Note: The value of  does not include the overburden pressure of the soil above point A

22. Stress Due To a Uniformly Loaded Circular Area
X - AXIS
Example: circular foundation, water tank

23. Stress Due To a Uniformly Loaded Circular Area
X - AXIS

24. Stress Due To a Rectangular Loaded Area
X - AXIS
Many structural foundations are rectangular. The increase in stress below the corner of a rectangular are
Where;
q = Load per unit area
In radian
Note: If the m’2+n’2+1< m’2n’2, add  to the angle.

25. Stress Due To a Rectangular Loaded Area
X - AXIS
The value of I3 also can be determine using this chart

26. Stress Due To a Rectangular Loaded Area
The increase in stress below the center of a rectangular are
Where; q = Load per unit area

27. Stress Due To a Rectangular Loaded Area

28. Lateral Earth Pressure

29. Lateral Earth Pressure
Lateral earth pressure can be divided into:
At- rest pressure
Active Pressure
Passive Pressure

30. Coefficient of earth pressure at rest
At-rest Pressure
Coefficient of earth pressure at rest
Researchers K0
Note
Jaky (1944)
’ is drained friction angle
Mayne & Kulhawy (1982)
For over consolidated coarse grained soil
Massarsch (1979)
For fine grained , normally consolidated soils

31. How to calculate the total force per unit length of the wall (Po)?
Po = ½ Ko’H2
1/3H
Ko’H

32. Rankine’s Theory of active and passive earth pressures
Rankine’s theory assumes that:
No friction on the wall
The wall at the soil interface is vertical
Can be used for horizontal and sloping backfill

33. Rankine’s active earth pressures

34. Rankine’s active earth pressures
For cohesionless soil, c’=0
So,

35. Rankine’s active earth pressures
For cohesion soil

36. Rankine’s passive earth pressures

37. Rankine’s passive earth pressures
For cohesionless soil, c’=0
So,

38. Rankine’s passive earth pressures
For cohesion soil

39. Rankine’s active pressure with sloping granular backfill

40. Coulomb’s Earth Pressure
Coulomb’s theory assume that:
Consider the wall friction
Consider sloping wall
Consider sloping backfill

41. Coulomb’s Earth Pressure

42. Coulomb’s Earth Pressure