Transcript Stress

Outline
• Announcements
• Basic rheology
• Soil strength
• Triaxial test
Soil Physics 2010
Announcements
• New Homework, due Feb. 8
• Alert: Exam Feb. 12
Soil Physics 2010
Basic rheology
• The study of how materials
flow and deform
• Strength of materials
Pitch drop experiment:
1 drop every ~9 years!
Soil Physics 2010
Stress
• Stress is a force per unit area: N m-2
• This is also a pressure. The SI unit of pressure
is the Pascal: 1 Pa = 1 N m-2
• 1 N is the force required to accelerate 1 kg by 1
m s-2, so in earth’s gravity (g = 9.81 m s-2),
1/9.81 kg would exert a pressure of 1 Pa if
applied over 1 m2.
1g
0.1 kg
1m
Soil Physics 2010
Pressure
• 1 Pa = 1 N m-2 = 1 (kg m)/(s2 m2) = 1 kg m-1 s-2
• What is atmospheric pressure?
• g * (Mass of atmosphere above 1 m2) = 101,325 Pa
≈ 101.3 kPa ≈ 0.1 MPa
• Same force as a column of water 10.1 m high
• ≈ 14.7 psi (pounds / inch2)
1g
Soil Physics 2010
0.1 kg
1m
Stresses
• 4 Stresses commonly
encountered:
• Compressive s
• Tensile
s
• Shear
t
• Torsion (not typical in soil)
Soil Physics 2010
Kinds of behavior under stress
• Elastic materials regain their pre-stress form
Example: rubber
• Plastic materials remain in stressed form
Example: modeling clay
• Viscous materials deform slowly
Example: tar
• Brittle materials fracture under stress
Example: brick
• Soils have aspects
of all of these
Soil Physics 2010
Strain (elastic & plastic)
• Strain is deformation (e.g. in response to stress)
• Often given as e ≡ DL / L0 : a relative change in
length (dimensionless)
• Young’s modulus is the ratio: E ≡ s / e = s L0 / DL
DL
L0 – DL:
Original
height
Soil Physics 2010
L0
Height after
compression
Stress – strain curves I
For elastic materials: Hooke’s Law:
es
Slope is E: Young’s modulus
E ≡ s / e, so
Stress s, F/A
e=s/E
F
DL
Strain e, DL/L0
Soil Physics 2010
L0
Stress – strain curves II
For many materials
(including soil, sometimes):
Stress s, F/A
Failure
F
DL
Strain e, DL/L0
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Material has
sheared or
fractured
L0
Soil strength
• Soil strength is resistance to shear stress
• Strength depends mainly on:
1. Bulk density
2.4
Proctor
Compaction
Test
rb
rb
2.0
Optimal
100%
90%
1.6
75%
1.2
Soil Physics 2010
No
lubrication
5
10
Water gets
in the way
w
w
15
20
saturation,
mass basis
Soil strength
• Soil strength is resistance to shear stress
• Strength depends mainly on:
1. Bulk density
2.4
2. Wetness
rb
Harder to
compact
when dry
rb
2.0
More force
needed
1.6
100%
90%
75%
Less force
needed
1.2
Soil Physics 2010
5
10
w
w
15
20
Soil strength
• Soil strength is resistance to shear stress
• Strength depends mainly on:
1. Bulk density
2. Wetness
When the soil is saturated,
some stress is borne by the
water:
se = st – p
se: effective stress
st: total stress
p: water pressure
Soil Physics 2010
(Terzaghi’s
equation)
st
Soil strength
• Soil strength is resistance to shear stress
• Strength depends mainly on:
1. Bulk density
2. Wetness
3. Particle size distribution
Gradual distributions
tend to be stronger:
tighter grain packing
Soil Physics 2010
Gradual
Abrupt
Poorly Graded
10-4
10-3
10-2
10-1
100
101
Basic laws of friction:
1. friction  normal force
2. friction is not affected
by contact area (ideal
case)
Normal
force
Friction
Support
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3. friction is not affected
by velocity (for small
velocities)
Pull
Shear test
How strong is this soil?
How hard is it to break this soil?
Apply
normal
force
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Measure force needed to break
Repeat for different normal forces
Direct shear
(unconfined shear)
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Direct shear
(unconfined shear)
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A better shear test
(Allen presents the triaxial test)
Soil Physics 2010