Slide 1 of 55 Revised 04/2013 14.330 SOIL MECHANICS Shear Strength of Soils STRESSES IN A SOIL ELEMENT Analyze Effective Stresses (´) “Load carried by Soil” Stresses in a Soil Element after Figure 8.1a. Das FGE (2005). ´ v ´ v ´ H ´ H Where: ´ = Normal Effective Stress on Failure Plane f = Shear Stress on Failure Plane ´ v = Vertical Effective Stress ´ H = Horizontal Effective Stress = Shear Stress
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Slide 1 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
STRESSES IN A SOIL ELEMENTAnalyze Effective Stresses (´)
“Load carried by Soil”
Stresses in a Soil Elementafter Figure 8.1a. Das FGE (2005).
Theory of Rupture in Materials. A material fails due to because ofa critical combination of normaland shear stress, not frommaximum normal or shear stress.Functional Relationship:
Mohr Functional Relationshipafter Figure 8.1b. Das FGE (2005).
)( ff
Where:
f = Shear Stress on Failure Plane´ = Normal Stress on Failure Plane
Normal Effective Stress (´)
f = f(´)Failure Envelope
Failure –Cannot Exist
Stable
Shea
r Str
ess
()
Slide 3 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
MOHR-COULOMB FAILURE CRITERIAFailure Envelope is approximated by
a linear relationshipMC Failure Criteria(Effective Stresses)
MC Failure Criteriaafter Figure 8.1b. Das FGE (2005).
tancfWhere:f = Shear Stress on Failure Plane´ = Normal Effective Stress on Failure Planec´ = Effective Cohesion´ = Effective Friction Angle
Normal Effective Stress (´)
FailureEnvelope
Stable
Shea
r Str
ess
() MC Failure
Criteria
c´
tan cf
MC Failure Criteria(Total Stresses)
Where: = Normal Total Stress on Failure Planec = Cohesion = Friction Angle
´1 = Major Principal Stress´3 = Minor Principal Stress
´1
´1
´3´3
Normal Stress (´)
Shea
r Str
ess
() MC Failure
Criteria
c´
a ´1´3
Normal Stress (´)
Inclination of Failure Plane with Major Principal PlaneFigure 8.2. Das FGE (2005).
f
d
h
be
g
O
Slide 8 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Normal Stress (´)
Shea
r Str
ess
() MC Failure
Criteria
c´a ´1´3
Normal Stress (´)
Figure 8.2. Das FGE (2005).
f
d
h
be
g
2cot
2sin
2
2cot
sin
245
31
31
31
31
c
ad
cOafOfa
faad
o
Angle dab = 2 = 90° + ´ or
From Figure 8.2
Substituting
INCLINATION OF FAILURE PLANEPRINCIPAL STRESSES
Slide 9 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Normal Stress (´)
Shea
r Str
ess
()
MC FailureCriteria
c´a ´1´3
Normal Stress (´)Figure 8.2. Das FGE (2005).
f
d
h
be
g
245tan2
245tan
245tan
sin1cos
245tan
sin1sin1
sin1cos2
sin1sin1
2cot
2sin
231
2
31
31
31
oo
o
o
c
c
c
From Previous Slide
or
Trigonometry Identities
and
ThereforeMC Failure Criteria in Terms of
Failure Stresses
INCLINATION OF FAILURE PLANEPRINCIPAL STRESSES
Slide 10 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
SHEAR STRENGTH LABORATORYTESTING SUMMARY
Test ASTMPore Pressure Soil TypesDrained Undrained Coarse
GrainedFine
Grained
Direct Shear D3080 Y N Y See Note 1
TriaxialCD - WK3821CU – D4767UU – D2850
Y Y Y Y
Unconfined Compression D2166 N Y N Y
NOTES:1. Possible, but not recommended. Takes 2 -5 days to allow for drained conditions.
Slide 11 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
DIRECT SHEAR TESTING
Figure 8.3. Das FGE (2006).
´ = Confining Stress= Normal Force/Area
Slide 12 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Oldest, Simplest Shear Test
Typically performed on coarse grained soils
Drained conditions (i.e. no pore pressure buildup)
Failure occurs on fixed plane
Shear stress distribution not uniform
Can be Stress or StrainControlled (typically strain)
Measure Shear Force, Horizontal Displacement,
Vertical DisplacementFigure 8.3. Das FGE (2006).
´ = Confining Stress= Normal Force/Area
DIRECT SHEAR TESTING
ASTM D3080
Slide 13 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Figure 8.3. Das FGE (2006). Area sectional-CrossForceShear StressShear
Area sectional-CrossForce Normal
Stress Normal
Normal Stress
Shear Stress
´ = Confining Stress= Normal Force/Area
NOTE: Cross-sectional Area (A)is from start of test
DIRECT SHEAR TESTING
Slide 14 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Figure 8.5. Das FGE (2006).
Direct Shear Test Results – Dry SandsComponents of Shear Strength forCohesionless Soils (Rowe, 1962)
• Friction Resistance:Resistance due to particle sliding andpossibly rolling.
• Dilation:Expansion required to overcomeparticle interlocking. Increase in volume.
• Interference:Due to particle interlocking (like dilation),but occurs even at a constant volumecondition (unlike dilation). Particlescannot go in straight line, must go aroundeach other.
Ultimate = Residual
DIRECT SHEAR TESTING
Slide 15 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Typical Direct Shear Results – Dry Sand (c = 0)Peak Results Only
Figure 8.3. Das FGE (2006).
• Test typically performed at a minimum of three (3) confining stresses.
• Density of sample should be within ±2% of field value.
• Plots of peak (p) and residual (r) MC criteria should be presented.
DIRECT SHEAR TESTING
Slide 16 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
TestConfining Stress
()(psi)
Shear Stress ()(psi)
Peak Residual
1 14.4 11.1 8.4
2 17.5 14.0 11.8
3 23.1 18.4 16.7
Determine the peak friction angle (peak) and residualFriction angle residual) for this material.
GIVEN:
REQUIRED:
A Poorly Graded Sand (SP) from a Local Sand Pit with the following Direct Shear Test Results.
DIRECT SHEAR TESTINGEXAMPLE #1
Slide 17 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
0 5 10 15 20 25 30 35 40Confining Stress () (psi)
0
5
10
15
20
Shea
r Str
ess
() (
psi)
DIRECT SHEAR TESTINGEXAMPLE #1
Slide 18 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
0 5 10 15 20 25 30 35 40Confining Stress () (psi)
0
5
10
15
20
Shea
r Str
ess
() (
psi)
Direct Shear Peak ValuesPeak Best Fit Line( = 38°, c = 0)Direct Shear Residual ValuesResidual Best Fit Line( = 34°, c = 0)
DIRECT SHEAR TESTINGEXAMPLE #1 SOLUTION
Slide 19 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
TestConfining Stress
()(psf)
Shear Stress ()(psf)
Peak Residual
1 604 657 549
2 926 875 734
3 1248 1092 920
Determine the peak friction angle (peak) and residualFriction angle residual) for this material.
GIVEN:
REQUIRED:
A Clayey Sand (SC) from a Local Sand Pit with the following Direct Shear Test Results.
Direct Shear Peak ValuesBest Fit Line (p = 34°, cp = 250 psf)Direct Shear Residual ValuesBest Fit Line (r = 30°, cr = 200 psf)
Plot of Provided Data
DIRECT SHEAR TESTINGEXAMPLE #2 SOLUTION
Slide 22 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
SOIL
FOUNDATION
Interfacial Shear between Foundation and Soil
after Figure 8.7. Das FGE (2006).
APPLICATION EXAMPLES:
DeepFoundations
Retaining Walls
tanaf cWhere:f = Shear Stress on Failure Plane´ = Normal Effective Stress on Failure Planeca´ = Adhesion´ = Effective Interfacial Friction Angle
DIRECT SHEAR TESTINGINTERFACIAL SHEAR
Slide 23 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Direct Shear Interfacial Testing for Geomembranes(after Mofiz, 2000)
ASTM D5321-12 Standard Test Method for Determining the Shear Strength of Soil-Geosynthetic and Geosynthetic-Geosynthetic Interfaces by Direct ShearBS EN 13738:2004 Geotextiles and geotextile-related products. Determination of pullout resistance in soil (British Standard)ISO 12957-1:2005 Geosynthetics - Determination of friction characteristics - Part 1: Direct Shear Test
DIRECT SHEAR TESTINGINTERFACIAL SHEAR STANDARDS
Slide 24 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
INTERFACIAL FRICTION ANGLE
Table 1. NAVFAC DM 7.02 (1986).
General Rule of Thumb
Relating and
1/3 < < 2/3Other Interfacial Testing
Methods: The Dual Interface Apparatus -
Paikowsky et al. (1995)1996 ASTM Hogentogler Award
Slide 25 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Considered to be the most reliable soil shear test
Provides more information on stress-strain behavior than
direct shear testing
Allows soil to fail along preferred failure plane
Provides more flexibility in terms of loading conditions
Allows measurement of vertical stress, confining
stress, vertical displacement, pore pressure, and volume
change.Figure 7-7a. FHWA NHI-01-031.
TRIAXIAL SHEAR TESTING
Slide 26 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Test Samples:
Diameter: 35 to 75 mm2 ≤ D/L Ratio ≤ 2.5
D = DiameterL = Length
Figure 7-7d. FHWA NHI-01-031.
TRIAXIAL SHEAR TESTING
Slide 27 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Axial Load
PressureSource
TriaxialCylinder(Plexiglass)
Soil Sample
BaseInlet forFilling
DrainageConnection
Pore PressureMeasurement
Figure 8.9. Das FGE (2006).
Membrane
PorousStone
PorousStone
ChamberFilled w/ water
or glycerine
Chamber Pressure: 3(a.k.a. c)
Applied Axial Stress: d(a.k.a. Deviator Stress, 1)Stress applied two ways:
1. Stress controlled:Load applied in equal increments until specimen fails.
1. Strain controlled:Application of axial deformation at constant rate until specimen fails.
B = Skempton’s Pore Pressure ParameterB ≈ 1 for Saturated Soils (see Table 8.2 below)uc = Pore Pressure Increase due to Confining Stress3 = Confining Stress
CONSOLIDATED DRAINED (CD) TEST
33
uc = 0(Drained prior to
test)
After IsotropicConsolidation
3
3
Prior to Drainageuc ≈ 3 (i.e. B ≈ 1)
“Water takes the Load”
Check for Saturation(Skempton’s Pore Pressure Parameter B)
Table 8.2. Theoretical Values of B at S = 100% (Das FGE 2006).
Slide 31 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
fffdf
ff
113
33
Where:
3f = Minor Principal Stress at Failure´3f = Minor Principal Effective Stress at Failure(d)f = Deviator Stress at Failure1f = Major Principal Stress at Failure´1f = Major Principal Effective Stress at Failure
33ud = 0
During AxialCompression
Loading
3
3
S “Slow” Testd
d
Allow drainage of sample during testing. Therefore, no pore pressures within the soil sample buildup during shear (i.e. ud = 0).
Since pore pressure developed during the test is completely dissipated:
CD Test – Volume Change with Time during Consolidation (Vc)Figure 8.11a. Das FGE (2006).
CONSOLIDATED DRAINED (CD) TEST
Slide 35 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Change in Deviator Stress (d)
vs. Axial Strain (v)Figure 8.11b. Das FGE (2006).
Volume Change (Vd) vs. Axial Strain (v)Figure 8.11d. Das FGE
(2006).
CONSOLIDATED DRAINED (CD) TESTLOOSE SANDS AND NC CLAYS
Slide 36 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Change in Deviator Stress (d)
vs. Axial Strain (v)Figure 8.11c. Das FGE (2006).
Volume Change (Vd)vs. Axial Strain (v)
Figure 8.11e. Das FGE (2006).
CONSOLIDATED DRAINED (CD) TESTDENSE SANDS AND OC CLAYS
Slide 37 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
d
duA
Where:
Ā = Skempton’s Pore Pressure Parameterud = Pore Pressure Increase due to Deviator Stressd = Deviator Stress
Skempton’s Pore Pressure Parameter Ā
33ud ≠ 0
3
3
d
d
Setup same as CD Test. Check for Saturation (Bparameter). Close drainage valve prior to test to make undrained (i.e. allow pore pressure buildup within sample). Pore pressure can be measured
during test to determine effective stresses.
CONSOLIDATED UNDRAINED (CU) TEST
Slide 38 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
3131
11
33
13
ffdf
ffdf
ffdf
u
u
Where:
3f = Minor Principal Stress at Failure´3f = Minor Principal Effective Stress at Failure(d)f = Deviator Stress at Failure(ud)f = Pore Pressure Increase at Failure1f = Major Principal Stress at Failure´1f = Major Principal Effective Stress at Failure
33
During AxialCompression
Loading
3
3
R “Rapid” Testd
d
DO NOT allow drainage of sample during testing. Therefore, pore pressures within the soil sample buildup during shear (i.e. ud ≠ 0). Therefore:
ud ≠ 0
CONSOLIDATED UNDRAINED (CU) TEST
Slide 39 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Normal Stress (´)
Shea
r Str
ess
()
(d)f
c & c´ ≈ 0
Total Stress Envelopef = tan + c´
Effective Stress Envelopef = tan´ + c´
3f´ 3f 1f´ 1f
(ud)f
* Still Need a Minimum of Three Tests!
(d)f (ud)f
CONSOLIDATED UNDRAINED (CU) TESTSANDS AND NORMALLY CONSOLIDATED CLAYS
CU Test – Volume Change with Time during Consolidation (Vc)(Still allowing drainage during Consolidation)
Figure 8.17a. Das FGE (2006).
CONSOLIDATED UNDRAINED (CU) TEST
Slide 43 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Change in Deviator Stress (d) vs. Axial Strain (v)Figure 8.17b. Das FGE (2006).
Pore Pressure Change (ud) vs. Axial Strain (v)Figure 8.17d. Das FGE (2006).
CONSOLIDATED UNDRAINED (CU) TESTLOOSE SANDS AND NC CLAYS
Slide 44 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
Change in Deviator Stress (d) vs. Axial Strain (v)Figure 8.17e. Das FGE (2006).
Pore Pressure Change (ud) vs. Axial Strain (v)Figure 8.17g. Das FGE (2006).
CONSOLIDATED UNDRAINED (CU) TESTDENSE SANDS AND OVERCONSOLIDATED CLAYS
Slide 45 of 55Revised 04/2013
14.330 SOIL MECHANICSShear Strength of Soils
)( 3133
ABABu
uuu
d
dc
Where:
3 = Minor Principal Stress1 = Major Principal Stressd = Deviator Stressud = Pore Pressure Increase due to Deviator Stress = Skempton’s Pore Pressure ParameterĀ = Skempton’s Pore Pressure Parameter
UNCONSOLIDATED UNDRAINED (UU) TEST
33
3
3
Q “Quick” Testd
d
Drainage of sample not permitted during application of confining stress 3 or during testing (i.e. application of d). Therefore, pore pressures within the soil sample at any stage of testing is: