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CE 240
Soil Mechanics & FoundationsLecture 11.1
Shear Strength of Soil I
(Das, Ch. 11)
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Shear strength in soils Introduction
Definitions
Mohr-Coulomb criterion
Introduction
Lab tests for getting the shear strength
Direct shear test
Introduction Procedure & calculation
Critical void ratio
Class Outlines
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Shear Strength The strength of a material is the
greatest stress it can sustain;
So that the unit of strength is the same
as stress (Pa in SI unit system);
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Significance of Shear Strength
The safety of any geotechnical structureis dependent on the strength of the soil;
If the soil fails, the structure founded onit can collapse.
Understanding shear strength is thebasis to analyze soil stability problemslike:
lateral pressure on earth retainingstructures (Chs. 12, 13),
slope stability (Ch. 14), and
bearing capacity (Ch. 15).
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Shear Failure in Soils
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Slope Failure in Soils
Failure due to inadequatestrength at shear interface
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Static: Transcosna Grain Elevator
Canada (Oct. 18, 1913)
West side of foundation sank 24-ft
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Bearing Capacity Failure
D i F d ti f il b li f ti
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Dynamic: Foundation failure by liquefaction
after the 1964 Niigata Earthquake. (USGS)
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Dynamic: Lateral Spreading caused by the 1906 San
Francisco Earthquake at Moss Landing, CA
(USGS Professional Paper 993)
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Shear Strength in Soils
The shear strength of a soil is its resistance toshearing stresses.
It is a measure of the soil resistance to
deformation by continuous displacement of itsindividual soil particles
Shear strength in soils depends primarily on
interactions between particles Shear failure occurs when the stresses between
the particles are such that they slide or roll past
each other
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Shear Strength in Soils
(cont.) Soil derives its shear strength from two
sources: Cohesion between particles (stress
independent component)
Cementation between sand grains
Electrostatic attraction between clay particles
Frictional resistance between particles (stressdependent component)
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Shear Strength of Soils: Cohesion
Cohesion (C), is a measure of the forces thatcement particles of soils
Dry sand with no cementation
Dry sand with some cementation Soft clay
Stiff clay
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Shear Strength of Soils; Internal
Friction Internal Friction angle (), is the measure of the
shear strength of soils due to friction
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Mohr-Coulomb Failure Criteria
This theory states that a material fails
because of a critical combination ofnormal stress and shear stress, and not
from their either maximum normal orshear stress alone.
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Mohr-Coulomb Failure
Criterion
ShearStrength,S
=
C
Normal Stress, n = = h
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' '
tan (11.2)
tan ' (11.3)
f n n
f n n
c c
c c
= + = +
= + = +
f
whereshear strength
c = cohesion; c =effective cohesion
= angle of internal friction; = effective angle of internal friction
= coefficient of friction; ' = effective coefficient of frictio
=
n.
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=tan
0.51-0.58
0.58-0.70
0.70-0.78
0.58-0.700.70-0.84
0.84-1.00
0.67-1.110.49-0.70
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Mohr-Coulomb shear failure criterion
1
1
33n
f
1
3
2
f=c+
n
c
Failed Zone
(, )
ff
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From trigonometric equalities we have
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Way 1: Increase the normal
stress in one direction
1
1 major principle stress
n
f3 3
Minor principle stress
Confining stress
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Way 2: directly apply the shear stress
Consider the following situation:
- A normal stress is appliedvertically and held constant- A shear stress is then applied
until failureShear
stress
Normal stress n
Normal stress n
D t i ti f Sh St th P t
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Determination of Shear Strength Parameters
The shear strength parameters of a soil aredetermined in the lab primarily with two types
of tests: 1) Direct Shear Test; and 2) Triaxial
Shear Test.(1) (2)
Soil
Normal stress n
Shear stress 3
3
1
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Direct Shear Test
Direct shear test is Quick and Inexpensive
Shortcoming is that it fails the soil on adesignated plane which may not be theweakest one
Used to determine the shear strength ofboth cohesive as well as non-cohesive
soils
ASTM D 3080
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Direct Shear Test (cont.)
The test equipment consistsof a metal box in which thesoil specimen is placed
The box is split horizontallyinto two halves
Vertical force (normalstress) is applied through ametal platen
Shear force is applied bymoving one half of the boxrelative to the other tocause failure in the soilspecimen
Soil
Normal stress n
Shear stress 3
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Direct Shear Test
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Direct Shear Test
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Direct Shear Test
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Direct Shear Test Data
Shearstress
Residual Strength
Peak Strength
Direct Shear Test Data:
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Direct Shear Test Data:
Volume change
H
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Direct Shear Test: Procedure
1.Measure inner side or diameter of shear box and find thearea
2.Make sure top and bottom halves of shear box are in
contact and fixed together.3.Weigh out 150 g of sand.
4.Place the soil in three layers in the mold using the funnel.
Compact the soil with 20 blows per layer.5.Place cover on top of sand
6.Place shear box in machine.
7.Apply normal force. The weights to use for the three runsare2 kg, 4 kg, and 6 kg if the load is applied through a lever arm,or 10 kg, 20 kg, and 30 kg, if the load is applied directly.
Note: Lever arm loading ratio 1:10 (2kg weight = 20 kg)
Direct Shear Test: Procedure
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Direct Shear Test: Procedure
8. Start the motor with selected speed (0.1 in/min) so thatthe rate of shearing is at a selected constant rate
9. Take the horizontal displacement gauge, verticaldisplacement gage and shear load gage readings.
Record the readings on the data sheet.
10. Continue taking readings until the horizontal shear loadpeaks and then falls, or the horizontal displacement
reaches 15% of the diameter.
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Calculations
1. Determine the dry
unit weight, d
2. Calculate the void
ratio, e
3. Calculate the normal
stress & shearstress
1=d
wGse
A
V
A
N== ;
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Figures
Peak Stress
s3
s2
s1
Shear
stress,s
N3 = 30 kg
N2 = 20 kg
N1 = 10 kg
Horizontal displacement, H
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Figures (cont)
S
hear
Stres
s,s
(psf)
C
(1,s1)
(3,s3)(2,s2)
Normal Stress , psf
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Figures (cont)
Verticaldisplacemen
t
Horizontal displacement
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Reading Assignment:
Das, Ch. 11
HW: Problem 11.1