The document explains the concept of effective stress in soil mechanics, emphasizing the multi-phase nature of soil and its behavior under load. It outlines how total stress is calculated from the weight of the soil and water above a point, and how stress is transmitted through water and soil solids. Effective stress is critical in understanding stress distribution and is defined as the sum of vertical forces at points of contact per unit area.

1. 1
Effective Stress
• Soil is a multi phase system
• To perform any kind of analysis - we must
understand stress distribution
• The concept of effective stress:
• The soil is “loaded” (footing for example)
• The resulting stress is transmitted to the
soil mass
• The soil mass supports those stresses at the
point to point contacts of the individual soil
grains

2. 2
Effective Stress
Water
Soil
A
HA
H

3. 3
Effective Stress
The total stress at A is calculated from:
The weight of the soil above A
The weight of the water above A
 = Hw + (HA - H) sat
 = Total Stress at A
w = Unit Weight of Water (62.4 pcf)
sat = Saturated Unit Weight
HA = Height of A to Top of water
H = Height of water

4. 4
Effective Stress
•  is the stress applied to the soil by its own
weight
• As you go deeper in the soil mass, the stress
increases
• Like in a swimming pool, as you go deeper, the
stress of the weight of the water increases
• The soil carries the stress in 2 ways:
• A portion is carried by the water (acts
equally in all directions)
• A portion is carried by the soil solids at
their point of contact.

5. 5
Effective Stress
• The sum of the vert. components of the forces at
their points of contact per unit of X- sectional area is
the effective stress.
Cross Sectional Area = A
a2
P1
a3 a4
a1
P2 P3 P4
an = Area of points of contact
A = Cross Sectional area of soil mass
Pn = Forces acting at points of contact

6. 6
Effective Stress
• The sum of vertical components of forces over the area is
the effective stress ’
’= (P1v+P2v+P3v .....+Pnv) / A
If as = a1 + a2 + a3 +...an
Then the space occupied by water = A - as
Assume u = HA * w Ht of water * w = stress due
to water (ft*pcf = psf =
stress)
 = ’ + u(A - as) / A Since as is very small,
assume 0

7. 7
Effective Stress
Recall the following equation:
 = Hw + (HA - H) sat
Now, ’ =  - u
Substituting: ’ = [Hw + (HA - H) sat] - HA * w
Rearranging: ’ = (HA - H)(sat - w)
Height of Soil Column * ’
Where ’
= sat - w
’
= EFFECTIVE UNIT WEIGHT
Effective Stress is independent of height of water
In the equation:  = ’ + u
’ is the soil skeleton stress
u is the stress in the water, or pore
water pressure