test #1 - cive 462 sp 04
120
100
110
90
100
80
90
70
80
60
70
50
60
50
40
40
30
0
10
20
30
40
50
Soil Stresses
(ch10)
Stress
Assumptions
Continuous material
Homogeneous (eng. props. = at all locations)
Isotropic (Modulus and n are = in all directions)
Linear-elastic stress-strain properties
Stress Concept
Stress Concept
sz
x
s normal stresses
 zx
z
Ten (-), Comp (+)
 xz
sx
sx
 xz
 zx
 shear stresses
sz
Clock (+), CC (-)
Strain Concept

g
normal strain
P
shear strain
g
dL
L
 dL

L
g = shear strain [radians]
Stress vs. Strain = Modulus
s
E


G
g
p
n 
 pa
Stresses in Soils
1. Geostatic Stresses
Due to soil’s self weight
2. Induced Stresses
Due to added loads (structures)
3. Dynamic Stresses
0.248811
0.4
0.2
e.g., earthquakes
AS
i
0
g
0.2
0.241673 0.4
0
0
10
20
30
40
50
t
i
60
70
80
90
81.95
Geostatic Stresses
TOTAL VERTICAL STRESS AT A POINT
Ground surface
z = depth = 5 m
Soil , g = 18 kN/m3
A
s A  g  zA
“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
Ground surface
z=5m
Soil , g = 18 kN/m3
hpA
A
u A  g w  hp A
“pore water pressure at A”
Geostatic Effective Stress
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Example
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Special Case
Board – submerged soils
Induced Stresses
P
g
z
A
sA = g z
A = 0
g
z
A
sA = g z + ?
A = ?
Bousinnesq - point loads
Point load
zf
A
See page 324 of your book…
Area loads
P
B
L
g
z
Area, A
A
Terminology:
q = bearing pressure = P/A
B < or = to L
Area loads – sz below corner
B
L
zf
sz below corner of a loaded
area: see page 327 (book)
Area loads – sz below center
Circular loaded area
q
zf
A
 
 
 
1


s z  q 1
   B
  1  
   2 z f

1.5




2
 
 
 
 








Area loads – sz below center
Square loaded area
Strip loads
Rectangular area
See page 332 (text)
Lateral Stresses
Ground surface
z
Soil , g = 18 kN/m3
A
s'
= Vertical effective stress =
s 'h
= Horiz. eff. stress = ?
sv'
Lateral Stresses
“Coefficient of lateral earth pressure”
s 'h
K
s 'v
Superposition
We can only add total stresses
Stresses on other planes…
So far we have sx and sz
Now we want
sz
sx
sx
sz
Stresses acting on other planes
The Mohr Circle
Describes 2-D stresses at a point in a material
Plots s and  on an = scale
Each point on the MC represents the s 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

A2
A1
sB2
sB1

B2
B1
If we change
A

s
sA2
sA1
B
we will get two more points on the same MC.
The Mohr Circle
1
21
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
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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