Introduction to Soils

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Soil Stresses(ch10)
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Stress
Assumptions
Continuous material
Homogeneous (eng. props. at all locations)
Isotropic (Modulus and n are in all directions)
Linear-elastic stress-strain properties
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Stress Concept
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Stress Concept
s normal stresses
Ten (-), Comp ()
t shear stresses
Clock (), CC (-)
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Strain Concept
g shear strain
e normal strain
g shear strain radians
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Stress vs. Strain Modulus
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Stresses in Soils
1. Geostatic Stresses
Due to soils self weight
2. Induced Stresses
Due to added loads (structures)
3. Dynamic Stresses
e.g., earthquakes
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Geostatic Stresses
TOTAL VERTICAL STRESS AT A POINT
Ground surface
z depth 5 m
Soil , g 18 kN/m3
A
total vertical stress at A
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Geostatic Stresses
SHEAR STRESSES
If ground surface is flat, all geostatic shear
stresses zero
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Geostatic Stresses
PORE WATER PRESSURE AT A POINT
z 5 m
Soil , g 18 kN/m3
A
pore water pressure at A
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Geostatic Effective Stress
board
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Example
board
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Special Case
Board submerged soils
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Induced Stresses
sA g z
sA g z ?
tA 0
tA ?
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Bousinnesq - point loads
Point load
A
See page 324 of your book
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Area loads
B
L
Area, A
Terminology B lt or to L
q bearing pressure P/A
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Area loads sz below corner
B
L
zf
sz below corner of a loaded area see page 327
(book)
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Area loads sz below center
Circular loaded area
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Area loads sz below center
See page 332 (text)
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Lateral Stresses
Ground surface
z
Soil , g 18 kN/m3
A
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Lateral Stresses
Coefficient of lateral earth pressure
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Superposition
We can only add total stresses
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Stresses on other planes
So far we have sx and sz
Now we want
Stresses acting on other planes
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The Mohr Circle
Describes 2-D stresses at a point in a material
Plots s and t on an scale
Each point on the MC represents the s and t 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
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The Mohr Circle
t
A
?
s
sA2sA1
B
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The Mohr Circle
?1
2?1
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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.
s1 major principal stress
s3 minor principal stress
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The Mohr Circle
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Direction of max principal stresses is 17 degrees
c.c. from the vertical
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Effective Stress Mohr Circle
board
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Seepage Force
board
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Seepage Force - Example
board