Effective Stress
No Flow Condition
C
B
A
hw
A
B L
L/2
C
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No Flow Condition
σ '= σ − u
At Point A
σ A = γ wH w
μA = γ wH w
σ A ' = γ wH w − γ wH w = 0
No Flow Condition
At Point C
σ C = γ w H w + γ sat L
μC = γ w ( H w + L) = γ w H w + γ w L
σ C ' = γ w H w + γ sat L − γ w H w − γ w L
σ C ' = γ sat L − γ w L = (γ sat − γ w ) L = γ ' L
where γ ' = (γ sat − γ w ) = effective or bouyant unit weight
σC '= γ ' L
2
Upward Flow Condition
C
B
A
h
hw
A
B L
L/2
C
Upward Flow Condition
At Point C
σ C = γ w H w + γ sat L
μ C = γ w ( H w + L + h) = γ w H w + γ w L + γ w h
σ C ' = γ w H w + γ sat L − γ w H w − γ w L − γ w h
σ C ' = γ sat L − γ w L − γ w h = (γ sat − γ w ) L − γ w h = γ ' L − γ w h
σ C ' = γ ' L − γ wh
Note: effective stress decreased below static level (γ’L)
Upward flow decreases particle to particle contact
3
Upward Flow Condition
σ C ' = γ ' L − γ wh
Note σc’ =0 when
γ ' L = γ wh
γ' h
= = icritical = critical hydraulic gradient (σ ' = 0)
γw L
At critical hydraulic gradient we have quick sand – (shear stress =0)
Soil particles have no stress transmitted through the grain contacts
Downward Flow Condition
C
B
A
h
hw
A
B L
L/2
C
4
Downward Flow Condition
At Point C
σ C = γ w H w + γ sat L
μ C = γ w ( H w + L − h) = γ w H w + γ w L − γ w h
σ C ' = γ w H w + γ sat L − γ w H w − γ w L + γ w h
σ C ' = γ sat L − γ w L + γ w h = (γ sat − γ w ) L + γ w h = γ ' L + γ w h
σ C ' = γ ' L + γ wh
Note: effective stress increased above static level (γ’L)
Downward flow increases particle to particle contact
Summary
To find effective stress always calculate the
total stress and pore water pressure then
subtract porewater pressure from the total
stress
For flow conditions determine porewater
pressure by determining the total head at
the point of interest.
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