14.330 Shear Strength - Faculty Server...

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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).

´v

´v

´H´H

Where:

´ = Normal Effective Stress onFailure Plane

f = Shear Stress on Failure Plane

´v = Vertical Effective Stress´H = Horizontal Effective Stress = Shear Stress



MOHR FAILURE ENVELOPEMOHR (1900):

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

()



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


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


NOTE:c´ ≈ 0 for sands, inorganic silts,& NC clays



FACTORS AFFECTING EFFECTIVE FRICTION ANGLE (´)Cohesionless Soils (c´ ≈ 0)

MC Failure Criteriaafter Figure 8.1b. Das FGE (2005).

tancf


Stable

Shea

r Str

ess

() MC Failure

Criteria

SANDS: Peak effective friction angle (´p) a function of particle mineralogy, level of

effective confining stresses, and the packing arrangement (Bolton, 1986).


c´ ≈ 0 for sands, inorganic silts,& NC clays

Factor Effect

Void Ratio (e) e

Angularity (A) A

Grain Size Distribution Cu

Water Content (w) w (slightly)

Particle size No effect (with constant e)

Overconsolidation or prestress Little Effect

Table 11-3. Holtz and Kovacs (1981).



Soil Dr ´ (°)

Sand(Rounded)

Loose 27 – 30Medium 30 – 35Dense 35 - 38

Sand(Angular)

Loose 30 – 35Medium 35 – 40Dense 40 - 45

Gravels(w/ some sands)

34 – 48

Silts 26 - 35

Table 8.1. Das FGE (2005).

TYPICAL DRAINED FRICTION ANGLES (´)COARSE GRAINED SOILS



Figure 7. NAVFAC DM 7.01 (1986).

TYPICAL DRAINED FRICTION ANGLES (´)COARSE GRAINED SOILS



INCLINATION OF FAILURE PLANEPRINCIPAL STRESSES

Where:

´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



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




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




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.



DIRECT SHEAR TESTING


´ = Confining Stress= Normal Force/Area



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).



ASTM D3080



Figure 8.3. Das FGE (2006). Area sectional-CrossForceShear StressShear

Area sectional-CrossForce Normal

Stress Normal

Normal Stress

Shear Stress


NOTE: Cross-sectional Area (A)is from start of test





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




Typical Direct Shear Results – Dry Sand (c = 0)Peak Results Only


• 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.




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



0 5 10 15 20 25 30 35 40Confining Stress () (psi)

0

5

10

15

20

Shea

r Str

ess

() (

psi)




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



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.




0 400 800 1200 1600 2000 2400Confining Stress () (psf)

0

200

400

600

800

1000

1200

Shea

r Str

ess

() (

psf)




0 400 800 1200 1600 2000 2400Confining Stress () (psf)

0

200

400

600

800

1000

1200

Shea

r Str

ess

() (

psf)

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



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



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



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



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



Test Samples:

Diameter: 35 to 75 mm2 ≤ D/L Ratio ≤ 2.5

D = DiameterL = Length

Figure 7-7d. FHWA NHI-01-031.




Axial Load

PressureSource

TriaxialCylinder(Plexiglass)

Soil Sample

BaseInlet forFilling

DrainageConnection

Pore PressureMeasurement


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.

ValveValve

Connection determines cheap or good triaxial

setupTRIAXIAL SHEARTESTING SETUP




3

1 = P/AApplied Stress

Soil

u

u

Measurement Instrumentation

Axial Load (Stress) 1 Load Cell

Axial Deformation vDial Gauges,

LVDT’s, DCDT’s

Confining Pressure 3Pressure Transducers,

Water Levels

Pore Pressure uPressure Transducers,

Water Levels

Volume Change w Graduated Cylinder

d 1 - 3





3

1

Soil

u

u

BASIC TRIAXIAL TESTS

Test Type ASTMSimpleAbbr.

Letter

Consolidated Drained WK3821 CDS

“Slow”

Consolidated Undrained D4767 CUR

“Rapid”

Unconsolidated Undrained D2850 UUQ

“Quick”

Full Test Abbreviations (Example):C I D C (L)

Consolidation State(Consolidated/Unconsolidated)

Consolidation Condition(Isotropic, Anisotropic (e.g. Ko))

Loading/Unloading

Compression/Extension

Drained/Undrained




3cuB

Where:

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).



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:

and




Normal Stress(´)

Shea

r Str

ess

()

´

´1f´3f´3f ´1f´3f ´1f

Test 1Test 2Test 3

(d)f

c´ ≈ 0

Total Stress Envelope = Effective Stress Envelopef = ´tan ´ + c´

Total and Effective Stress Failure Envelope from CD TestsFigure 8.13. Das FGE (2006).

Should use a Minimum of Three Tests

CONSOLIDATED DRAINED (CD) TESTSANDS AND NORMALLY CONSOLIDATED CLAYS



Normal Stress(´)

Shea

r Str

ess

()

c´´1f´3f ´3f ´1f3f´ ´1f

Test 1Test 2Test 3

(d)f

´= ´NC

Test 4

3f´ ´1f

´vm

OC NC

1´ = OC´

f = ´tan´ + c´

f = ´tan´

Total and Effective Stress Failure Envelope from CD TestsFigure 8.14. Das FGE (2006).

CONSOLIDATED DRAINED (CD) TESTOVERCONSOLIDATED CLAYS



CD Test – Volume Change with Time during Consolidation (Vc)Figure 8.11a. Das FGE (2006).




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



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



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



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




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



Normal Stress(´)

Shea

r Str

ess

()

c´´1f´3f ´3f ´1f3f´ ´1f

Test 1Test 2Test 3

(d)f

´= ´NC

Test 4

3f´ ´1f

´vm

OC NC

1´ = OC´

Effective Stress Failure Envelope from CU Tests

CONSOLIDATED UNDRAINED (CU) TESTOVERCONSOLIDATED CLAYS



Normal Stress ()

Shea

r Str

ess

()

c3f 1f

1 = OC

Total Stress Failure Envelope from CU TestsFigure 8.19. Das FGE (2006).

Total Stress Envelopef = tanOC + c

Total Stress Envelopef = tan

CONSOLIDATED UNDRAINED (CU) TESTOVERCONSOLIDATED CLAYS



CU Test – Volume Change with Time during Consolidation (Vc)(Still allowing drainage during Consolidation)

Figure 8.17a. Das FGE (2006).




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



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



)( 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:

u ≠ 0Therefore:



Normal Stress()

Shea

r Str

ess

()

1f3f 3f 1f 3f 1f

Test 1Test 2Test 3

Failure Envelope = 0

Total Stress Mohr’sCircles at Failure

cu

cu = SuUndrained Shear

Strength(d)f

(d)f constant regardless of confining stress (3)





´1f´3f 3f 1f3f 1f

Test 1Test 2

Total Stress Mohr’sCircles at Failure

cu

(d)f



3 = uc(ud)f

(d)f(d)f




Figure 11.34 . Das PGE (2006).

UNCONFINED COMPRESSION (UC) TESTCOHESIVE SOILS

UC Test Setup(Courtesy of Durham Geo)



Normal Stress (´)

Shea

r Str

ess

()

3 1 = qu

qu

Soil

1

1

Total Stress Mohr’sCircle at Failurecu = qu/2

Where:

qu = Unconfined Compression Strengthcu = Undrained Shear Strength



UNCONFINED COMPRESSION (UC) TESTCOHESIVE SOILS



General Relationship between Consistency and qu of Cohesive SoilsTable 8.3 Das FGE (2006)

Consistencyqu

(tsf)qu

(kN/m²)

Very Soft 0 – 0.25 0 – 25Soft 0.25 – 0.5 25 – 50

Medium 0.5 – 1 50 – 100Stiff 1 – 2 100 – 200

Very Stiff 2 – 4 200 – 400 Hard > 4 > 400

1 tsf = 95.8 kPa ≈ 100 kPa

UNCONFINED COMPRESSION (UC) TEST



UNCONFINED COMPRESSION (UC) ANDUNCONSOLIDATED UNDRAINED (UU)

TEST COMPARISON

Normal Stress(´)

Shea

r Str

ess

()

´ = 0

qu = 1f3 1 3 1

Test 1 - UCTest 2 - UUTest 3 - UU

cu

Theoretical Failure Envelope

Actual Failure Envelope




SENSITIVITY OF COHESIVE SOILS

Unconfined Compression Strength for Undisturbed and Remolded Clays

Figure 8.26. Das FGE (2006).)(

)(

disturbedu

dundisturbeut q

qS

Strength Shear DisturbedStrength Shear dUndisturbe

tS

Sensitivity (St)

Disturbed = Remolded

Example: Unconfined Compression



Sensitivity Classification of ClaysFigure 11.36. Das PGE (2006).

Strength Shear DisturbedStrength Shear dUndisturbe

tS

SENSITIVITY OF COHESIVE SOILS



Thixotropy:Time dependent reversible process in which soil gains strength with time after being remolded if left undisturbed.

THIXOTROPY OF COHESIVE SOILS



)(

)(

Hu

Vu

cc

K

Where:

K = Coefficient of Anisotropycu(V) = Undrained Shear Strength in Vertical Directioncu(H) = Undrained Shear Strength in Horizontal Direction

Strength Anisotropy in Cohesive SoilsFigure 8.27. Das FGE (2006).

Direction Variation of Undrained Shear Strength in Cohesive Soils

Figure 8.27. Das FGE (2006).Vertical/Horizontal

cu Ratio

ANISOTROPY OF COHESIVE SOILS

14.330 Shear Strength - Faculty Server...

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