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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
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
Soil Physics 2010
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 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
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
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
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
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
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
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
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
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)
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
Soil Physics 2010
Direct shear(unconfined shear)
Soil Physics 2010
Direct shear(unconfined shear)