Soil Stress
Air Hockey Game
A = area of puck
Air Hockey Table
W
W
W/A=σ
∑F
z
= 0 if static
N =W
N
N/A=σN
σN =
W
= table surface total stress due to the puck
A
1
Air Hockey Game with Fan on
A = area of puck
upwards air pressure
W
Air Hockey Table
U = μ air A = air force acting on bottom of puck
Air Hockey Game with Fan on
A = area of puck
∑F
z
=0
N'= W −U
N' W U
= −
A A A
σ ' = σ − μ air
upwards air pressure (μair)
W = weight of puck
U = μ air A = air force acting on bottom of puck
N’ = effective normal force of puck on table
In force form
In stress form
2
Shear Resistance
• Shear resistance is controlled by normal
stress the table feels (effective stress) not
the total stress created by the puck.
If W = U N' = 0
If σ = μ σ ' = 0
• Effective stress is the net stress difference
between the downward total stress and
the upward stress reduction created by the
air pressure acting on the puck
Stress in Soil mass
σ’v
σ’h
σ’h = K0 σ’v
σ’v
Note: If no soil movement there will be no shear stress
3
Stresses on Soil Element
σ’v
τ=0
τ=0
σ’h=Kσ’v
σ’h=Kσ’v
τ=0
τ=0
σ’v
Earth Pressure Coefficient
K=
σ 'h
σ 'v
Ko = lateral earth pressure coefficient at rest
Ka = Active Earth pressure coefficient
Kp = Passive earth pressure coefficient
4
Vertical Total Stress
P
σA =
∑ (P + P
∑ (a + a
1v
2v
1
2
+ P3v + ...Pn v
+ a3 + ...an )
)≈ P =γ
A
total
HA
P
Vertical Total Stress
• We do not know the actual particle to particle load or contact area
• We can determine the average total stress at Point A using the soil total unit
weight
σ A = γ total H A = γ total z
Total stress (σ)
z
σ A = γ total H A
σ z = γ total z
Depth z
5
Total Stress
• Saturated soil (Sr = 1) saturated unit weight = total unit weight
σ A = γ sat H A = γ sat z
Total stress (σ)
z
σ A = γ sat H A
σ z = γ sat z
Depth z
Positive Porewater Pressure
+μ acts normal to soil particles and is equal in all directions
• pushes soil grains apart resulting in a decrease in soil particle
to particle contact
+μ
+μ
6
Static (no flow)
Porewater Pressure (μ)
μ = γ w hw = γ w z = porewater pressure
Porewater Pressure (μ)
μ = γ wH
z
μA = γ wH A
μz = γ wz
Depth z
Soil Effective Stress
Average stress soil particles feel at grain to grain contact
σ 'A =
∑ (P + P
∑ (a + a
1v
2v
1
2
+ P3v + ...Pn v
+ a3 + ...an )
)
7
Total Stress
P = P'+ ( A − Ac ) μ
P P' ( A − Ac )
= +
μ
A A
A
σ = σ '+(1 −
if
Ac
)μ
A
Ac
is very small ≈ zero
A
σ = σ '+ μ
Soil Effective Stress
Average stress soil particles feel at grain to grain contact
σ = σ '+ μ
Terzaghi’s effective stress equation
σ '= σ − μ
8
Ground Water Table
Definition:
• Surface on which the fluid pressure in the
pores of the porous media is exactly
atmospheric
• Location is revealed by the level at which
water stands in a shallow open well
Aquifers
• In an unconfined aquifer the water table forms
the upper boundary of the aquifer
• A confined aquifer is an aquifer confined by two
aquitards – water level
surface is a
potentiometric surface
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