stress-strain resistance for soils
DESCRIPTION
Good explication of Stress-strain Resistance for SoilsTRANSCRIPT
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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.
0.1 kg
1 m
1 g
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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)
0.1 kg
1 m1 g
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Soil Physics 2010
Stresses
• 4 Stresses commonly encountered:
•Compressive s
• Tensile s
• Shear t
• Torsion (not typical in soil)
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Soil Physics 2010
Kinds of behavior under stress
• Elastic materials regain their pre-stress formExample: rubber
• Plastic materials remain in stressed formExample: modeling clay
• Viscous materials deform slowlyExample: tar
• Brittle materials fracture under stressExample: brick
• Soils have aspects of all of these
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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
L0
DL
Original height
L0 – DL:
Height after compression
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Soil Physics 2010
Stress – strain curves I
Hooke’s Law:
e sFor elastic materials:
L0
DL
F
Strain e, DL/L0
Str
ess s,
F/A
Slope is E: Young’s modulus
E ≡ s / e, so
e = s / E
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L0
DL
F
Strain e, DL/L0
Str
ess s,
F/A
Soil Physics 2010
Stress – strain curves IIFor many materials
(including soil, sometimes):Ela
stic
FailurePlastic Material has
sheared or fractured
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Soil strength
1.2
1.6
2.0
2.4
5 10 15 20w
rb
saturation, mass basis
w
r b 100%
75%
90%
Soil Physics 2010
Proctor Compaction
Test
Water gets in the way
No lubrication
Optimal
• Soil strength is resistance to shear stress
• Strength depends mainly on:
1. Bulk density
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Soil strength
1.2
1.6
2.0
2.4
5 10 15 20w
rb
w
r b 100%
75%
90%
Soil Physics 2010
More force needed
Less force needed
Harder to compact when dry
• Soil strength is resistance to shear stress
• Strength depends mainly on:
1. Bulk density
2. Wetness
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Soil strength
• Soil strength is resistance to shear stress
• Strength depends mainly on:
1. Bulk density
2. Wetness
Soil Physics 2010
When the soil is saturated, some stress is borne by the water:
se = st – p se: effective stress (Terzaghi’s
st: total stress equation)
p: water pressure
st
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Soil Physics 2010
Soil strength
• Soil strength is resistance to shear stress
• Strength depends mainly on:
1. Bulk density
2. Wetness
3. Particle size distribution
10110010-110-210-310-4
GradualAbruptPoorly GradedGradual distributions
tend to be stronger: tighter grain packing
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Soil Physics 2010
Basic laws of friction:
Pull
1. friction normal force
Normal force
Support
Friction
2. friction is not affected by contact area (ideal case)
3. friction is not affected by velocity (for small velocities)
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Soil Physics 2010
Shear test How strong is this soil?How hard is it to break this soil?
Measure force needed to breakRepeat for different normal forces
Apply normal
force
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Soil Physics 2010
Direct shear(unconfined shear)
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Soil Physics 2010
Direct shear(unconfined shear)