Soil Stresses (ch10) Stress Assumptions Continuous material Homogeneous (eng. props. = at all...
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Transcript of Soil Stresses (ch10) Stress Assumptions Continuous material Homogeneous (eng. props. = at all...
test #1 - cive 462 sp 04
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Soil Stresses(ch10)
Stress
Assumptions
Continuous material
Homogeneous (eng. props. = at all locations)
Isotropic (Modulus and are = in all directions)
Linear-elastic stress-strain properties
Stress Concept
Stress Concept
xz
x
z
normal stresses
xx
xz
zx
zx
z
z
shear stresses
Ten (-), Comp (+)
Clock (+), CC (-)
Strain Concept
dL
P
L
dL
normal strain
L
shear strain
= shear strain [radians]
Stress vs. Strain = Modulus
E
Gpa
p
Stresses in Soils
1. Geostatic Stresses
Due to soil’s self weight
2. Induced Stresses
Due to added loads (structures)
3. Dynamic Stresses
e.g., earthquakes
0.248811
0.241673
ASi
g
81.950 ti
0 10 20 30 40 50 60 70 80 900.4
0.2
0
0.2
0.4
Geostatic Stresses
TOTAL VERTICAL STRESS AT A POINT
z = depth = 5 m
A
Ground surface
Soil , = 18 kN/m3
AA z “total vertical stress at A”
Geostatic Stresses
SHEAR STRESSES
If ground surface is flat, all geostatic shear stresses = zero
Geostatic Stresses
PORE WATER PRESSURE AT A POINT
z = 5 m
A
Ground surface
Soil , = 18 kN/m3
ApwA hu “pore water pressure at A”
hpA
Geostatic Effective Stress
board
Example
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Special Case
Board – submerged soils
Induced Stresses
z
A
z
A
P
= z = z +
= =
Bousinnesq - point loads
zf
A
Point load
See page 324 of your book…
Area loads
q = bearing pressure = P/A
z
A
P
Area, A
B
L
Terminology:
B < or = to L
Area loads – z below corner
zf
B
L
z below corner of a loaded area: see page 327 (book)
Area loads – z below center
Circular loaded area
zf
A
q
5.1
2
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f
z
zB
q
Area loads – z below center
Square loaded area
Strip loads
Rectangular area
See page 332 (text)
Lateral Stresses
z
A
Ground surface
Soil , = 18 kN/m3
' = Vertical effective stress = 'v
h' = Horiz. eff. stress = ?
Lateral Stresses
v
hK'
'
“Coefficient of lateral earth pressure”
Superposition
We can only add total stresses
Stresses on other planes…
So far we have x and z Now we want
xx
z
z
Stresses acting on other planes
The Mohr Circle
Describes 2-D stresses at a point in a material
Plots and on an = scale
Each point on the MC represents the and on one side of an element oriented at a certain angle
The angle between two points in the MC is = 2 times the angle between the planes they represent
The Mohr Circle
A 1
A 2B 1
B 2
B2
B1
A2
A1
A2
A1
B2
B1
If we change we will get two more points on the same MC.
A
B
The Mohr Circle
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The Mohr Circle – Principal Stresses
Planes A and B are called principal planes when there are no shear stresses (only normal stresses) acting on them.
1 = major principal stress
3 = minor principal stress
The Mohr Circle
Direction of max principal stresses is 17 degrees c.c. from the vertical
Effective Stress Mohr Circle
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Seepage Force
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Seepage Force - Example
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