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TOPIC 1 :
SHEAR STRENGTH OF SOIL
FACULTY OF CIVIL ENGINEERING & EARTH RESOURCES
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Mohr-Coulomb criterion*
Laboratory test for shear strength parameters *
- Direct Shear Test- Triaxial Test
- Vane Shear Test
Effective overburden pressure*
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TOPIC OUTLINE
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LEARNING OUTCOMES
Understand the concept of shearstrength
Briefly explain Mohr-Coulombcriterion and the relationship to the
soil shear strengthDetermine the soil shear strength
using various methods
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SHEAR STRENGTH OF SOIL
Soils derive their strength from contact between particlescapable of transmitting normal as well as shear forces. Thecontact between soil particles is mainly due to friction and thecorresponding stress between the soil grains is called theeffective (or inter-granular) stress .
Thus, the shear strength of a soil is mainly governed by theeffective stress. Besides the effective stress between soil grains,the pore water contained in the void spaces of the soil also exertspressure which is known as pore pressure, u.
The sum of the effective stress and pore pressure acting an anygiven surface within a compacted earth embankment is calledthe total stress .
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SHEAR STRENGTH OF SOIL
Shear strength of the soil is the internal frictionresistance per unit area that the soil mass can offer toresist failure and sliding along any plane inside.
The capability of the following comes from the soilshear strength :
Support loading from structure
Support its own overburden
Sustain slope in equilibrium
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WHY THE SHEAR STRENGTHPARAMETER IS IMPORTANT??
- As an important property to evaluate:
1) Bearing capacity of foundation
2) Stability of slope3) Design of a dam, embankment andect.
4) Lateral pressure onearth retaining
structure
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Soil derives its shear strength from two sources:
Cohesion between particles (stress independent
component) - c
Cementation between particle grains
Electrostatic attraction between clay particles
Predominant in clayey soils
Frictional resistance between particles (stressdependent component) -
Strength gained from internal frictional resistance
(interlocking action among soil particles)
Predominant in granular soils
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COHESION vs FRICTION
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COHESION
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INTERNAL FRICTION
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Shear strength is not aunique property of a soil butdepends on many factors.
Factors ??
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1. Mineralogy of grains
2. Particle shape, size distribution and configuration
3. Void ratio and water content
4. Previous stress history
5. Existing stress in-situ6. Stress change imposed during sampling
7. Initial state of the sample
8. Stresses applied prior to test
9. Rate at which loading is applied10. whether drainage is allowed during test
11. Resulting pore pressure
12. Criterion adopted for determining the shear strength
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FACTORS THAT INFLUENCE SHEAR STRENGTH
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Peak strength
Residual strength
Point of failurePoint of failure
Residual strength
Peak strength
** normal stress is constant DAA3513 : GEOTECHNICAL ENGINEERING
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tsn
The limiting shear stress (soil strength) is given by :
t = c + s tan where
c = cohesion
= angle of internal friction
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MOHR COULOMB CRITERION
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Charles Mohr Charles Coulomb
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Shear
Strength, t
Normal Stress, s= s
C
=
Gradient of the line
Interception of y-axis
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Mohr-Coulomb
envelope
REPRESENTATION OF SHEARSTRENGTH OF SOIL
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'tan' st c
c and are known as the effective (or drained) strength
parameters.
If the soil is at failure the effective stress failure criterion will
always be satisfied.
Soil behavior is controlled by effective stresses, and the effective
strength parameters are the fundamental strength parameters. But
they are not necessarily soil constants.
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EFFECTIVE STRESS FAILURECRITERION
Where, s = s -u and u ispore water pressure
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t s cu n utan
If the soil is taken to failure at constant volume (undrained) then
the failure criterion can be written in terms of total stress as
cu and u are known as the undrained strength parameters
These parameters are not soil constants, they depend stronglyon the moisture content of the soil.
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TOTAL STRESS FAILURE CRITERION
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LETS TRY THIS
t
t
s'
s'c
This soil would probably be..??
Sandy/course grain soil??
Clayey/ fine grained soil??
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How can wedetermine the soil
shear strength??
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Laboratory test for testing shear strength of soil are:
1. Direct shear test
2. Triaxial compression test
3. Unconfined compression test
Field test for testing shear strength of soil are:
1. Cone penetration test
2. Standard penetration test
3. Vane shear test
4. Dilatometer test
For cohesive &cohesionless soil
For cohesive soil only
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DIRECT SHEAR TEST (ASTM D3080)
Motor
drive
Load cell to
measure
Shear Force
Normal load
Rollers
Soil
Porous plates
Top platen
Measure relative horizontal displacement, dx
vertical displacement of top platen, dy
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PROCEDURES
Soil specimen (round or square) is placed in arelatively flat box and subjected to a verticalload
The box consists 2 parts (upper and lower)
If 1 part of the box held while another onebeing pushed, the specimen will experienceshear failure along the horizontal surface
Vertical load and shear force that induced thefailure of the specimen is recorded
The failed sample is discarded and anothersample is placed in the box
Experiment is repeated several time
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T pical drained direct shear
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Typical drained direct shear
results
Horizontal displacement (dx)
ShearLoad(F)
Normal load
increasing
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Shear load, FVS
Displacement, dx
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Shearstress
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1. Draw suitable axes (x and y) on a graph paper. The
same scale should be used for both axes
2. Using the axes, plot shear stress vs normal stress
3. Draw a best fit line connecting all the pointsplotted
4. c value obtained from the y-axis while value
obtained from the gradient of the strengthenvelope
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Based on the plot, the following parameters obtained :
1) Cohesion, c interception at y-
axis2) Angle of internal friction, =
gradient of the straight line
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Advantages of direct shear test
Most easiest and quickest test
Large samples may be tested in large shear boxes.Small samples may give misleading results due to
imperfections (fractures and fissures) or the lack ofthem.
Samples may be sheared along predeterminedplanes. This is useful when the shear strengthsalong fissures or other selected planes are required.
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The shear failure is forced to occur along or across apredetermined plane which is not necessarily the weakestplane of the soil specimen tested
Non-uniform deformations and stresses in the specimen. Thestress-strain behavior cannot be determined. The estimatedstresses may not be those acting on the shear plane.
In practice shear box tests are used to get quick and crudeestimates of failure parameters
Since development of the much better triaxial test, the usedof the direct shear test has decreased
Disadvantages of direct shear test
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EXAMPLE
A direct shear test conducted on a soil sampleyielded the following results:
Normal Stress, s
(psi)
Max. Shear Stress, S
(psi)
10.0 6.5
25.0 11.0
40.0 17.5
Determine shear strength parameters of
the soil
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0
5
10
15
20
0 10 20 30 40 50
Normal Stress (psi)
Max.
ShearStres
s(psi
6.20)375.0(tan
375.0)1050(
)0.520(tan
5.2
1
psic
Lets try examples given
A
NSWE
R:
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TRIAXIAL TEST (ASTM D2850)
Cell
pressure Pore pressure
and volume
change
Rubbermembrane
Cell water
O-ring
seals
Porous filter
disc
Confining
cylinder
Deviator load
Soil
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PROCEDURES
Cylindrical soil specimen (wrapped in a rubbermembrane) is subjected to a vertical load
This test require the present of the confining / lateralpressure
which achieved by introducing water or compressed airinto the chamber to surround the soil specimen
The vertical load is applied and steadily increased untilthe specimen fails
The vertical load and the lateral pressure that cause thespecimen failed is recorded
The test is repeated several times
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TYPES OF FAILUREIN TRIAXIAL TEST
1. Complete shear failure2.Partial shear failure
3.Barrel or plastic failure
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Stresses in triaxial specimens
sr sr = Radial stress (cellpressure)
sa = Axial stress
F = Deviator load
sr
s sa rF
A
From equilibrium we have
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F/A is known as the deviator stress, and is given the
symbol q
q a r ( ) ( )s s s s1 3
where
s1 = axial pressure / major principal stress
s3 = lateral pressure / minor principal stress
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By plotting s1 and s3 in a graph, we can determine :
1. Cohesion, c
2. Angle of internal friction, HOW.??
Remember!!
s1 = axial pressure / major
principal stress
s3 = lateral pressure / minor
principal stress
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1. Draw suitable axes (x and y) in a graphpaper. The same scale should be used forboth axes
2. Using s1 and s3 values obtained fromseveral triaxial tests, draw a semicircle
3. Draw a straight tangent line (touch both
semicircles, if possible) to the semicircles
4. The straight line is called the StrengthEnvelope @ Failure Envelope @ MOHRS
Envelope5. c value obtained from the y-axis while
value obtained from the gradient of thestrength envelope
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Types of triaxial test
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There are many test variations. Those used most in practiceare:
UU (unconsolidated undrained) test.
Cell / lateral pressure is applied without allowingdrainage. Then keeping cell pressure constant, increasedeviator / axial load to failure without drainage.
CU (isotropically consolidated undrained) test.
Drainage allowed during cell pressure application. Thenwithout allowing further drainage increase deviator /
axial load, keeping cell pressure constant as for UU test.
CD (isotropically consolidated drained) test
Similar to CU except that as deviator stress is increased
drainage is permitted.
Types of triaxial test
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T t t St 1 St 2
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Test type Step 1 Step 2
Consolidated
drained,
CD
Apply chamber pressure, s3.
Allow complete drainage, so
pore water pressure (u = u0)
developed is zero
Apply axial stress, s, slowly. Allow
drainage, so pore water pressure (u =
ud) developed through application of
s is zero. At failure, s = sf ;
total pore water pressure, uf= ua + ud
= 0
Consolidatedundrained,
CU
Apply chamber pressure, s3.Allow complete drainage, so
pore water pressure (u = u0)
developed is zero
Apply axial stress, s. Do not allowdrainage (u = ud 0). At failure, s
= sf; pore water pressure,
u = uf= ua + ud = 0 + ud(f)
Unconsolidatedundrained,
UU
Apply chamber pressure, s3.Do not allow drainage, so pore
water pressure (u = u0)
developed through application
ofs3 is not zero
Apply axial stress, s. Do not allowdrainage (u = ud 0). At failure, s
= sf ; pore water pressure, u = uf=
ua + ud(f)
ADVANTAGES OF TRIAXIAL TEST
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Specimens are subjected to (approximately) uniformstresses and strains
The complete stress-strain-strength behavior can beinvestigated
Drained and undrained tests can be performed
Pore water pressures can be measured in undrainedtests, allowing effective stresses to be determined
Different combinations of cell pressure and axialstress can be applied
ADVANTAGES OF TRIAXIAL TEST
DAA3513 : GEOTECHNICAL ENGINEERING** read more in the textbook
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Typical triaxial results
s
e
Increasing cell
pressure
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Mohr Circles
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Mohr Circles
To relate strengths from different tests we need to use some results
from the Mohr circle transformation of stress.
t
s
s1s3
c
t s c tan
The Mohr-Coulomb failure locus is tangent to the Mohr
circles at failureDAA3513 : GEOTECHNICAL ENGINEERING
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EXAMPLE
The results of a trixial test are as follows :
No of test Chamber confining
pressure, kN/m
2
Deviator stress
at failure, kN/m
2
1 100 210
2 200 438
3 300 644
Draw the shear strength envelope anddetermine the shear strength parameters ofthe soil
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Hint : s s + s
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Solution :
1. Complete the table
2. Using the graph paper (same scale on both axis), drawthe mohr envelope and sketch the tangent line.
3. Check the interception on y-axis and the gradient ofthe line
No of test s3, kN/m2 s, kN/m2 s1, kN/m
2
1 100 210
2 200 438
3 300 644
Hint : s1 = s3 + s
Lets try examples given
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VANE SHEAR TEST (ASTM D2573)
Vane shear apparatus : consists of four thin,equal sized steel plates welded to a steel
torque rod DAA3513 : GEOTECHNICAL ENGINEERING
hi i d d i h h f h i
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This test is used to determine shear strength of cohesive
soils
Normally done in-situ ( field test) on a soft clayey soil
(cohesive soil)
The vane is pushed into the soil
Torque,T is applied at the top of the torque rod to rotate
the vane at a uniform speed A cylinder of soil (height h & diameter d) will resist the
torque until the soil fails
42
32dhd
Tcu
where = coefficient of shear strength
mobilization at the end of soil
cylinder.
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LEARNING OUTCOMES
Calculate the effective
overburden pressure of soil
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STRESS PATH
Results of triaxial tests can be represented by stresspath
Stress path = line that connects a series of point, eachof which represents a successive stress stateexperienced by a soil specimen during the process of atest
Stress path = diagrams/graphs of stress changes
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Types of stress path
1. Stress path in s/e space
2. Stress path in s1/s3 space
3. Stress path in t/s space
4. Stress path in q/p space
Advance
level
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SENSITIVITY CLAY
Sensitivity = the reduction in unconfinedcompression strength of clay soils due toremolding although no changes in the moisture
content
Degree of sensitivity, St =
)(
)(
remoldedu
undistubedu
q
q
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may range from 1 to 8 or might be reached as high as80 (flocculent marine clay deposits)
1 8 16 32 642 4
Slightly
sensitive
Medium
sensitive
Very
sensitive
Slightly
quick
Medium
quick
Very
quick
Extra
quick
Sensitivity, St (log scale)
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THIXOTROPHYCLAY
Thixotrophy = is a condition whereby a soil specimenwhich is kept in undisturbed condition (afterremolding) will experienced a continuous increased
in strength with time
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The loss of strength is gradually regained with timewhen the materials are allowed to rest
However most soils are partially thixotropic(part of the strength loss caused by remolding is neverregained with time)
The soils strength will never achieved the initialstrength although the specimen were preparedundisturbed
*** Refer to the handout given
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Effective Overburden Pressure
Factors affecting overburden pressure
i) Depth of the point of interest
deeper the point, larger the pressure
ii) Groundwater level same soil profile will give different pressure value
due to the water level
iii) Types of soil
soil with higher unit weight value (dense soil) give
larger overburden pressure
Lets try examples given DAA3513 : GEOTECHNICAL ENGINEERING
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Effective Overburden Pressure
Factors affecting overburden pressure
i) Depth of the point of interest
deeper the point, larger the pressure
ii) Groundwater level same soil profile will give different pressure value
due to the water level
iii) Types of soil
soil with higher unit weight value (dense soil) give
larger overburden pressure
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Effective Overburden Pressure
Calculate the effective stress at point A, B, C and D.
Take w = 9.81kN/m3
Lets try examples given DAA3513 : GEOTECHNICAL ENGINEERING
Claysat = 19.25kN/m313m
3m
Dry Sand
dry= 16.5kN/m3
Impermeable layer
A
B
C
D
3m
Q i
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Calculate the effective stress at 5m below the river bed
(Point A) which consist of sand. The depth of water in
the river was 2m. Take w = 9.8kN/m3
5 marks. DAA3513 : GEOTECHNICAL ENGINEERING
River bed
Sandsat = 20kN/m35m
-2m
A
River
w = 9.80kN/m3
Quiz.
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