Shear Strength of Soil

Hsin-yu ShanDept. of Civil Engineering

National Chiao Tung University

Normally Consolidated Clays2

)( 31 fus

σσ −=

c

uspc

σ=

3

1

σσ is the index of mobilization

of shear strengthThe shear strength is fully mobilized when this ratio reaches maximum.Normally, during R test, failure occurs at a axial strain of 1.0 – 6.0%

z

Drained Tests (Slow Tests)

)( 31 σσ −

%20≈aεexpansion

vε

contraction

Effective Stress Failure Envelope

φ

τ

0≈cσ

tends to decrease as P.I. increasesφ

cu determined from Q test is the “strength”not cohesionIt comes from the effect of locked-in stress or stress the soil had been subjected toIt has nothing to do with cohesion

S testOC clayStrain concentration tends to lead to dilation

NC clayStrain concentration tends to lead to compression

Water flows outward from shear zoneStrength increase

Water flows inward to shear zoneStrength decrease

OC clay – Undrained testsPlane strain

3

1

σσ

c3

31

σσσ −

c

u

3σ∆

εa~12%

Pore water pressure decreases as effective stress goes up

After peak the clay is still consolidating

Since the effective confining stress is increasing, the strength is still mobilizing in terms of absolute value of

3

1

σσ

31 σσ −

NC clay

R envelope31 σσ −

∆u

R envelope

f)( 31 σσ −

f3σ c3σ 3σ

vs. R envelopeR

Effective stress failure envelope

)( 31 σσ −

Total stress (R) failure envelope

3σ

Overconsolidated

Normally consolidated

Normally consolidatedOverconsolidated

f)( 31 σσ −

f3σc3σ

∆u

R

Due to ∆u < 0

σ3 or

Effective stress (S) failure envelope

)( 31 σσ −

3σ

Overconsolidated

Normally consolidated

Normally consolidatedOverconsolidated

f)( 31 σσ −

f3σc3σ

∆u

R > S

S vs. R envelope

Total stress (R) failure envelopeDue to ∆u < 0

σ3 or

NC (lightly OC) – S strength > R strengthStability during loading is critical

Heavily OC – R strength > S strengthStability during excavation is critical

)( 31 σσ −

NC Clay

)( 31 σσ −

Effective stress path for undrained testu increases

max31 )( σσ −max

3

1 )(σσ

σ3 or 3σ

OC Clay

Eff. stress path for undrainedtest, u decreases

)( 31 σσ −

max31 )( σσ −

max3

1 )(σσ

σ3 or 3σ

NC – at , the shear strength has not been fully mobilized, is still increasingOC – the difference is smaller than NC. reaches maximum first and is still increasingActually the difference in between NC and OC is not very large

)( 31 σσ −

max31 )( σσ −

)(3

1

σσ

)(3

1

σσ

max31 )( σσ −

Cohesionusually comes from the effect of fitting a

straight line through the data points to get the envelopeIts just the intercept on the vertical axisIt is usually the apparent cohesion, not the real cohesionTo test if the cohesion is real, just put the soil specimen in water if it holds, there is true cohesion

c

Factors Influencing UndrainedShear Strength

Initial effective stressEffective stress shear strength parameters

c and φ of N.C. clay show no anisotropyc and φ of O.C. clay has anisotropic effect

Pore water pressure generated during shear

For N.C. clay, the change of pore pressure is not affected by the orientation of principal stressThe pore water pressure of O.C. clay is dependent on the orientation of principal stress

Curved Failure Envelope

Dilatancy effect at lower stress levelCrushing of particles at high stress levelRearrangement of particle orientation under higher stress (tend to be more parallel)

Higher φ

Lower φ

Lee and Morrison (1970)

q

p’

Compacted Higgens clayCompacted kaolinite

psi 100=σ

psi 2500=σ °=19φ

°= 25φpsi 100=σ°= 26φ

°=12φ psi 1200=σ

Bishop, Webb, and Lewin (1965)

London clay

q

p’

°= 10φ°= 30φ

Sensitivity

Strength of the soil (in an undisturbed state) divided by the strength in a completely remolded state “at the same water content”For most soil, sensitivity, st, ranges between 1.5 ~ 10

Six Factors Affecting Sensitivity

Metastable soil structureCementationWeatheringThixotropic hardeningLeaching and ion exchangeEffect of addition of dispersive agents

1000S

ensi

tivity

, St(lo

g)

1Liquidity Index, L.I.

Effect of Salt Concentration

Effect on diffuse double layer

She

ar s

treng

thP.L.

L.L.

w %w %

Salt concentration Salt concentration

Thixotropy

An isothermal, reversible, time-dependent increase in strength at a constant water content

She

ar s

treng

th

Remolded strength

Aging

Disturbance,Remold

Time, t

Por

e pr

essu

re, u

shear

Time, t

Cementation

Effect of removal of the cementation bonds in the soil

4,000 psfEDTA(disodium salt of

ethylene diamenetetra acetic acid)

5

12,000 psfSea water3

11,000 psfOriginal pore liquid

4

Max. shear strength

Leaching solution

Test No.

Residual Strength

Peak strengthS

hear

stre

ngth

Residual strength

εa

Residual Strength Occurs:

At large shear strain/displacementUnder drained condition

S tests are appropriate tests for measuring the residual strength

Especially for clay

We should not use peak strength for design involving high-sensitivity clay

For overconsolidated clays, usually pr φφ >

τ

σ0≈rc

pφ

rφ

pc

Measuring Residual Strength

Direct shear (allowed displacement has to be large enough)Ring shearConsolidated-drained triaxial test

Strain-Rate Effect

Mainly for undrained loading

Equilibrium of pore water pressureCreep of soil structure under load

Undrained creep test Time, tS

train

cycle log/% 203log

)( 31 −≈∆

−∆

ftσσ

R test

f)( 31 σσ −

1 10 100 1000 10000Time, logtf (min)

8 – 21Cucaracha clay shale

7 – 10Oche bentonite

7 – 9Bearpaw clay shale

3 – 6Mexico City clay

Clay cycle) log/(% log

)( 31

ft∆−∆ σσ

Olson and Parola (1968) Q tests on compacted clay

226 milli sec1760 milli sec9600 milli sec56 sec41 min310 min

2 (+ increase)100 mintf )(% )( 31 σσ −∆

Seed and Chan (1966)Undisturbed S.F. Bay mudStf≈0.1sec ≈ 140 – 160% Sconventional,tf≈10-20 min

Compacted Vicsburg silty clay and Pittsburg sandy clayStf≈0.1sec ≈ 130 – 140% Sconventional,tf≈10-20 min

0.1 sec 10 min ≈ 3.8 log10 cycles

Effect of Stain Rate on Modulus

Negligible effect of strain rate on strain at failureNegligible effect of strain rate on modulus

Dynamic loading

Effect of loading frequencyTransient strength decreases as loading frequency increases

For compacted clays the strength remain almost the same For sensitive clays the strength decreases 10 – 20%

Strain at failure increases as loading frequency increases

Soft sensitive clays are more affected

Anisotropy

Lean sensitive clays are more affected by “rotation of principal planes” than highly plastic clays of low sensitivity

σ1f σ1f

Inherent anisotropyIsotropy in c, φ more obvious in OC clays, NC clays don’t have this effectDifference in inherent tendency for pore water pressure to be induced by shear more likely for OC clays, NC clays don’t have this difference

Stress-induced anisotropy

2.11Lierstronta

1.61Manglerud

1.51Drammen

1.1Slightly > 1Aserum

τfh/τfvOCRSite

Aas (1965) vane shearτfh

τfv

Why?

Ladd and Foott (1974)

0.19Plane strain “passive” (σ1fhorizontal)

0.20Direct simple shear

0.16Triaxial extension (σ1f horizontal)

0.33Triaxial compression (σ1f vertical)

0.34Plane strain “active” (σ1f vertical)

τf/σ’vcType of test/Loading condition

σ1f

σ1f

PSATC

σ1f

DSS

PSPTE

σ1f

Triaxial Extension Test

Decrease vertical stress (∆σvf) to induce failure

∆σ1f∆σ3f

∆σvf ∆σf

∆σ1f = 0

u0

σvc

σhc

033 uvcfvcfvf −−=−=∆ σσσσσ

)0()( 0303 uAuBu vcffvcff ++−+−−=∆ σσσσ

)()( 3103113 ffvcoffff uK σσσσσσσ −−+=−−=

if B =1

])1())[(1(

))(1(

31

03

vcofff

vcfff

KA

uAu

σσσ

σσ

−+−−=

++−−=∆

Mohr-Coulomb Equation:

φσσ

φσσσσsin]

2[sin

22)(

0313131

ffffff uu ∆−−

+=

+=

−

03131

33131

)(2

22

uK vcoffff

fffff

++−−−

=

+−

=+

σσσσσ

σσσσσ

pc

AKA

f

of

vc

fff

vc

f =−−−−

=−

=]sin)21(1[

sin)]1(1[2/)( 31

φφ

σσσ

στ

For N.C. clay, the parameters in the above equations are somehow independent of consolidation pressure

constant≈pc

Triaxial Compression TestIncrease vertical stress (∆σvf) to induce failure

∆σ1f∆σ3f

∆σvf ∆σf

∆σ3f = 00uvcvc += σσ

0uhchc +=σσu0

011 uvcfvf −−=∆=∆ σσσσ

03 =∆ fσ

if B =1

)( 01 uAu vcfff −−=∆ σσ

Mohr-Coulomb Equation:

φσσ

φσσσσsin]

2[sin

22)(

0313131

ffffff uu ∆−−

+=

+=

−

0313311 )()( uK vcoffffff ++−=+−= σσσσσσσ

031

33131

2

22

uK vcoff

fffff

++−

=

+−

=+

σσσ

σσσσσ

pc

AKAKf

ofo

vc

fff

vc

f =−−

−+=

−=

]sin)21(1[sin)]1([2/)( 31

φφ

σσσ

στ

For N.C. clay, the parameters in the above equations are somehow independent of consolidation pressure

constant≈pc

5.0 9.0 32 ==°= of KAφ

35.0≈vc

f

στ

Triaxial compression

20.0≈vc

f

στ

Triaxial extension

This is due to stress-induced anisotropy instead of inherent anisotropySpecimens of triaxial extension tests will experience larger shear deformationThe direction of major principal stress has to rotate 90°

Direct Simple Shear

Under the condition of the applied stresses, it can assumed that:

Pure shear applied to horizontal and vertical planesThe failure plane is not horizontal, α=φ/2The horizontal plane is the plane of maximum shear stress at failure

∆τ

τffτmax,f

φ/2τ

∆σv=∆σh=0

σ

Direct Shearσvc

σ1fσ3f

22.02/)(

19.0 31 =−

=∆

vc

f

vc

hf

σσσ

στ

vc

f

vc

hf

σσσ

στ 2/)(

25.0 31 −==∆

32.02/)(

19.0 31 =−

=∆

vc

f

vc

hf

σσσ

στ

DSS RoscoeFour platesPure shear is applied to horizontal and vertical plane

DSS NGIRubber membrane and circular ringsHorizontal plane is the plane of maximum shear stressFailure plane is not horizontal(Most reasonable)

Determination of Undrained Shear Strength

Take undisturbed samplesSubject specimens to all-around confining pressureShear the specimens to failure with no drainage

τff τmax,f

φ/2τ

σ

su

φττ cosmax, fff =

Lab. Strength is Probably Lower Than the Field Strength Because:

Specimens tested in the lab are “disturbed”Lab confining pressure is less than that in the fieldSome drainage will occur in the field (higher effective stress)

Lab. Strength is Probably Higher Than the Field Strength Because:

Strain rates in the lab are much higher than the strain rate in the fieldLab’s Q strengths based on triaxialcompression (sDSS < sT.C.)su (= τmax,f) > τff

SHANSEP procedure (Ladd and Foott)

Stress History And Normalized Soil Engineering PropertiesNormalized Soil Parameters NSPMajor advantages: as more and more NSP data become available, less tests are needed

vc

hf

στ

This value of a soil is a constant for assumed: (1) OCR and (2) loading path (e.g. TC, TE, or DSS)

NSP

)( 31 σσ −

Overconsolidated

Normally consolidated, OCR=1

OCR=2

OCR=4

σ3 or 3σ

The (c/p)=const concept have been recognized for NC clays for a long timeLadd and Foott extend the concept to OC clays

Consolidate the clay back onto the virgin curve, unload to the desired OCR, and get the shear strength

Effect of SamplingN.C. clay, OCR=1

e or w%

Swelling The sample swells and takes in water

Field consolidation (before sampling)

No swellingStress relief only (in sampling tube)

σlog

0uvcvc +=σσ0uvc +=∆ σσ

0uK vcohc += σσ0uK vco +=∆ σσ

u0 + ∆u

In the field During sampling

In the lab. Before setup.

vcσσ %200 ≈01 σσ =

03 σσ ==

)]1(1[

)1(

)]()([

)(

0

0

0000

0031

KA

KA

KAuuuu

uu

vc

vcvc

vcvcvc

vcvc

−−=

−−=

+−++−−−=∆−=

∆−+−===

σ

σσ

σσσ

σσσσσ

vco AK σσσσ 5.0 ,0.1 ,5.0For 031 =====

vco AK σσσσ 32 ,3

2 ,5.0For 031 ===== (Elastic)

NC Clay

After N.C. clay goes through the sampling process, it may behaves like O.C. clay

Virgin consolidation curve(actually, we don’t have it)e or w%

cσfieldv,σ σlog

To Obtain “Field” UndrainedShear Strength of N.C. clay

ComputeMeasure shear strength in the labCompute field strength

fieldv,σ

vc

f

στ

fieldvlabvc

fus ,)( σ

στ

×=

O.C. clays

Virgin consolidation curve(actually, we don’t have it)

Highly disturbed

e or w%

fieldv,σ fieldmax,σ labmax,σlabv,σσlog

To Obtain “Field” UndrainedShear Strength of O.C. clay

ComputeMeasure shear strength in the lab for the field OCR

Compute field strength

vc

f

στ

fieldv,σ

fieldvlabvc

fus ,)( σ

στ

×=

fieldmax,σ

constant≈vc

f

στ

For a given OCR

O.C. clays

Virgin consolidation curve(actually, we don’t have it)

in the lab

in the field

Sheare or w%

fieldv,σ fieldmax,σ labmax,σlabv,σσlog

constant≈vc

f

στ

For a given OCR

vc

f

στ

OCR

Comments

Ladd and Foott’s procedure eliminate the error of sampling, thus overestimate the shear strength on the unsafe sideSoil must have relatively insensitive structure, because using this procedure will consolidate and shear a lot of soil specimens