ADVANCED SOIL SHEAR

STRENGTH – Fine-grained SoilsSTRENGTH – Fine-grained SoilsDonald C. Wotring, Ph.D., P.E.

December 2008

CLAY MINERALOGYCLAY MINERALOGY

Bonding

• Primary Chemical Bonds – a net attractive force between atoms▫ Ionic – removal and gain of electron(s) from one atom

to the otherto the other▫ Covalent – sharing of electrons to complete outer shell

of electrons for both atoms• Secondary Hydrogen Bond – intermolecular force

between hydrogen atom of one molecule and an electron of another molecule (dipoles)

• Secondary van der Waals forces – instantaneous dipole attraction forces due to fluctuating electrons

Structural Units – Sheet Silicates

G

B

Kaolinite – Mineralogical Composition

G

G

7Å

Interlayer - Hydrogen bonding and van der Waals forces

t = 1000Å (140 layers)

L = 10,000Å = 1µm

• L/t = 5-10• SSA = 5-15 m2/g• EAR = 12%

Kaolinite – SEM photo

Illite - Mineralogical Composition

G or B

G or B

10Å

• 1/6 of Si+4 in tetrahedral replaced by Al+3 � Net unbalanced charge deficiency• K+ ions in the hexagonal holes of the tetrahedral surfaces • Basal cleavage, tearing and tattering

t = 100Å (10 layers)L = 3,000Å = 0.3µm

• L/t = 30• SSA = 80-100 m2/g• EAR = 6%

Illite – SEM photo

Montmorillonite - Mineralogical

Composition

G or B

G or B

9.6Å

t = 10Å (1 layer)L = 1,000-4,000Å = 0.1-0.4µm

• L/t = 100-400• SSA = 800 m2/g• EAR = 2%

• Much less isomorphic substitution of Al+3

for Si+4 than Illite• Fe+2 or Mg+2 substitution for Al+3 in Gibbsite sheet• Na+ or Ca+2 cations balance net negative charge but don’t bind layers

Montmorillonite (Na) – SEM photo

Adsorbed Water – Possible Mechanisms

H O

HH O

+

Increased ion concentration

H

H O

H

1) Hydrogen Bonding

+

2) Ion Hydration 4) Dipole Attraction

3) Osmosis

Inward diffusion of H20

5) van der Waals Forces 3-4 molecular layers 10-15Å

Double Layer Water

+

+

+ +

+

+

+

+

+

+

-

-

-

-- -

-

-

-

Con

cen

trat

ion

CationsBulk free water

Stern’s layer

-+

++ +

+

++

-

-

--

- -C

once

ntr

atio

n

Distance

Anions

water

Debye Length

220

0

2 υε

en

DkTtd =

ε0 – permittivity of a vacuum (ease of polarization) (8.854x10-12 C2/J*m)D – Dielectric constant (force between electric charges)k – Boltzmann constant (1.38x10-23 J/oK)T – temperature (oK)n0 – bulk concentration (number/m3)e – electric charge (1.60x10-19 C)v – cation valence

Double Layer Thickness

0

02.0)(

c

DTAtd υ

=&

c0 – cation concentration in bulk water (moles/liter)1.E-02

1.E-01

1.E+00

Ca

tio

n c

on

cen

tra

tio

n (

mo

les/

lite

r)

Na+

Ca+20

1.E-06

1.E-05

1.E-04

1.E-03

0 500 1000 1500

Ca

tio

n c

on

cen

tra

tio

n (

mo

les/

lite

r)

Debye Length (Angstrom)

Ca+2

Intergranular Pressure

Intergranular Pressureσa – force from applied stress

ua – hydrostatic pressure including double layer repulsion

Aa – long-range van der Waals attraction

A’ac – short-range attractive forces: primary valence (chemical); edge-to-face electrostatic; and short-range van derWaals.

Cac – short-range repulsive forces: adsorbed water and Born repulsion

cc CauaaAAaa +=++ 'σ

Intergranular Pressure

Aua

aAC c −+−= )'(σ

cc CauaaAAaa +=++ 'σa

aAC c

i )'( −≡σ

uAi −+= σσ

Define intergrain force, σi

Water Pressure

ht = he + hp + hv + hs + htemp

If we assume no change in temperature or elevation and that the velocity is negligible, we can reduce this to

h = h + h

If no water flow occurs between location of intergranular contact and piezometer ht0 = (hp0 + hs0) =htcontact = (hpc+hsc) and hs0 in piezometer ~0

hp0 = (hp+hs)c

Solving for pressure head at the intergranular contact hp = hp0 – hs ,or in terms of pressure

ht = hp + hs

u = uo - hsγw

Itergranular Pressure

uAi −+= σσ and u = uo – hsγw combine to form

wsi huA γσσ +−+= 0• Osmotic pressure hsγw will be negative

and is termed R• σ’ = σ-uo

)(' ARi −+= σσ STRENGTH IS A FUNCTION OF EFFECTIVE STRESS

Practical Implication

Kaolinte

Illite

Montmorillonite

)(' AR −=σ

Montmorillonite

Mineralogy to Shear Strength

STRENGTH IS A FUNCTION OF

EFFECTIVE STRESS

An increase in effective normal stress produces an increase in interparticlecontact area, which produces and increase in bonds and thus an increase in shearing resistance.

Soil Fabric

Orientation of Particles

N ature of Particles

Dispersed Flocculated (Aggregated)

RandomRandom

Highly Oriented

Atterberg LimitsMeasure of soils ability to hold water

Shrinkage Limit Plastic Limit Liquid Limit

plastic state fluid statesemi-solid statesolid state

su ~ 2kPa

wω −

pl

pL

wI

ωωω

−−

=

CF

IA p=

Ip

CF

SOIL SAMPLINGSOIL SAMPLING

Ideal Soil Laboratory Testing Criteria

• High quality samples with minimum disturbance

• Reconsolidation to in-situ stress (K0)• Reconsolidation to in-situ stress (K0)• Account for mode of shear

▫ Intermediate principal stress▫ Direction of applied major principal stress at

failure• Test at strain rate approaching field conditions• Strain compatibility

“Undisturbed” Shelby Tube Sampling

σ’ vo = ur

σ’ ho = ur

−ur

0

0

Total, σ Neutral, u Effective, σ’

Residual (capillarity) pressure, after sampling

= +

Minimize Sampling Disturbance

+

−+−=

z

zsK

z

z w

w

b

v

Euw

w

m

γγ

σγγ

0

)(0 '

21

Drilling (A-B) - Use appropriate drilling mud

If OCR Soil:

( ) 8.0

0

)(

0

)(

''OCR

ss

NCv

Eu

OCRv

Eu

=

σσ

( ) ( ) )1(00

0 pKpOCR OCRKK −=

Minimize Sampling Disturbance

Tube Sampling and Extraction (C-D)• Fixed piston sampler (standard in NE)• Min. outside diameter (76 mm)• D0/t >450

• Insert tube, allow setup (20 min), slowly rotate, and slowly withdraw

• Radiography• Germaine (2003) tube extrusion• Prepare samples in a humid room• Moist stones

Reconsolidate to In-Situ Stress

Conditions

Volumetric strain kept to between 1.5% and 4% at σ’v0

Volumetric Strain (%)

SQD

< 1 A

1-2 B

2-4 C

4-8 D

>8 E

Modes of Shear and Strain

Compatibility

σ'1f

σ'1f σ'1f

TC TE

DSS

σ'1f

s(PSC) ~ 1.1 s(TC)s(PSE) ~ 1.2 s(TE)

Strain Rate Effects

Difficult to account for, sometimes use corrections or hope for compensating errors.

VOLUMETRIC BEHAVIOR DURING

SHEARSHEAR

Volumetric Response of Soils During

Shear - UNDRAINED

If water cannot be readily expelled upon applying τ, a volume change won’t occur and excess pore pressures develop

uo + ue

Volumetric Response of Soils During

Shear - DRAINED

If water can be readily expelled upon applying τ, a volume change will occur and excess pore pressures won’t develop

uo

u0

Shear Induced Pore Water Pressure

A

εa

NC Skempton’s A-coefficient

Triaxial compression testB=1.0 (saturated)∆σ = 0OC

Af

OCR

1.0

-0.3

∆σ3 = 0∆σ1 = σ1 – σ3

31 σσ −∆= u

A

q

p’

A=1 0.5 0

Volumetric Behavior During Shear

DRAINED SHEAR STRENGTHDRAINED SHEAR STRENGTH

Drained Shear Strength

If shear stress is applied at such a rate and/or the boundary conditions are such that zero shear-induced pore water pressure is developed on failure, then failure has taken place under drained conditions and the drained shear strength of the soil has been mobilized.

Normally Consolidated Clay

)'tan(' φσ ns =

σ1-σ3

εa σn

sφ’NC

Overconsolidated Clay – Peak Intact

')'tan(' cs pn += φσ

σ1-σ3

εa σn

sφ’NC

)1(

'

')'tan('

m

n

pNCns

−

=

σσ

φσ

Peak φ’p

c’

Overconsolidated Clay - Fissuring

• Micro or macro fissures provide avenues for local drainage

• Soil along fissures has softened (increased water content) and is (increased water content) and is softer than intact material

• Intact Strength is significantly modified by fissuring and softening, even for first time failures

• Use of intact strength is often overestimating the available strength that can be mobilized in field problems

Overconsolidated Clay – Fully Softened

)'tan(' FSns φσ=

σ1-σ3

εa σn

sφ’NC = φ’FSFS

Peakφ’p

c’

• Increased face-to-face particle orientation

Overconsolidated Clay – Fully Softened

Overconsolidated Clay – Residual

)'tan(' Rns φσ= • Face-to-face particle orientation

• Rapid pore pressure equilibration due to

σ1-σ3

εa σn

sφ’NC = φ’FSFS

Peakφ’p

c’φ’RResidual

• Rapid pore pressure equilibration due to small shear zone

Overconsolidated Clay – Residual

( ) ( ) 254.2037.00003.0 2 +−= ASTMASTMASTM

BM CFCFCF

CF 23.1003.0 )()(

)( += ASTML

ASTML

BML ww

w

UNDRAINED SHEAR STRENGTHUNDRAINED SHEAR STRENGTH

Undrained Shear Strength

If shear stress is applied so quickly and/or the boundary conditions are such that no dissipation of shear-induced pore water pressure occurs upon failure, then failure has taken place under undrained conditions and the undrained shear strength of the soil has been mobilized.

Undrained Shear Strength - Field Vane

)()( FVumobu ss µ=

Undrained Shear Strength - Field Vane

0.25

0.30

0.35

0.40

22.0)()( == FVumobu ssµ

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80 100

s u/σσ σσ

' p

Ip

22.0''

)()( ==p

FVu

p

mobu ss

σµ

σ

Undrained Shear Strength – Lab Testing

σ'1f

σ'1f σ'1f

TC TE

DSS

tp

TEu

p

DSSu

p

TCu

p

mobu ssssµ

σσσσ

++=

'''3

1

')()()()(

Undrained Shear Strength – Lab Testing

0.25

0.30

0.35

0.40

σ'1f

22.0'''3

1

')()()()( =

++= t

p

TEu

p

DSSu

p

TCu

p

mobu ssssµ

σσσσ0.00

0.05

0.10

0.15

0.20

0.25

0 20 40 60 80 100

s u(m

ob

)/σσ σσ

' p

Ip

σ'1f σ'1f

TC TE

DSS

Data Normalized to σ’p

σ’pσ’vo

oo

vo

p

m

vo

p

m

vo

p

vo

uo

vo

uo Sss

=

=

=

'

'

'

'

''1

'

' σσ

σσ

σσσσ

Ss

p

uo ='σAt mo = 1

Example New Baltimore Data

0

0 1 2 3

Stress (tsf)

10

20

30

De

pth

(ft

)

Suo(HP)

Suo(FV)

Suo(DSS)σ’vo

22.0'

)( =p

mobus

σ

Stress History and Normalized Soil

Engineering Parameters (SHANSEP) and

Recompression

SHANSEP

SHANSEP

m

vc

p

m

vc

p

vc

u

vc

u Sss

vc

p

=

=

=

'

'

'

'

''1

'

' σσ

σσ

σσσσ

SHANSEP and Recompression

SHANSEP - Mechanical (constant σ’p-σ’vo) overconsolidation only, not applicable for dessication, secondary compression, or physicochemical

Recompression – Destruction of Recompression – Destruction of bonds and sample disturbance outweigh strength gain due to decrease in water content. Good for OC soils.

Triaxial Compression Test

UU – Unconsolidated Undrained

CIU – Isotropically Consolidated CIU – Isotropically Consolidated Undrained

CKoU – Ko Consolidated Undrained

Mohr’s Circle Review

αααα

p’ = (σ’1+σ’3)/2(p’,q)

Pole

q = (σ1-σ3)/2

p’ = (σ’1+σ’3)/2

What is Failure?

Common Failure Criterion

Peak Deviator Stress, (σ1-σ3)max

Peak Obliquity, (σ’1/σ’3)max

Peak pore pressure, uPeak pore pressure, umax

Ā = 0 or ∆u = 0

Reaching Kf line

Limiting strain

Definition of Undrained Shear Strength

φ’τ ∆σf

τ

αf

σ, σ’σ’hf

τf

c=qf=(σ1-σ3)/2

τf qf

τf=qfcos(φ’)

Unconsolidated Undrained

Compression (UUC) Test

σ’ vo = ur

−u

0

Total, σ Neutral, u Effective, σ’

Residual (capillarity) pressure, after sampling

= +

After sampling

σ’ ho = ur−ur0

After sampling

σ’ vc = σc+ur-σc=ur

σ’ hc = ur

−ur+∆uc = -ur+σcσc

After cell

pressure

At failure

σc

σc

σc

∆σf = (σ1-σ3)f -ur+σc+∆uf

σ’ vf =∆σf+σc+ur-σc-+∆uf

σ’ hf =σc+ur-σc-+∆uf

UUC Test

φ’φT=0

τ

φT=0

At failure

σ3=σc

σc

∆σf = (σ1-σ3)f -ur+σc+∆uf

σ’ vf =∆σf+ur-+∆uf

σ’ hf =ur-+∆uf

σ, σ’

τf=c

σ’hf σc1 σc2

σ1

UUC Test

ESP

q

TSP-0TSP-1 TSP-2

qf

p, p’p’op’f po1 po2

qf

Initial Conditions At Failure

Total Stresses

po qo pf qf

σc,i 0 ∆σf/2+σc,i ∆σf/2

Effective Stresses

p’o qo p’f qf

ur 0 ∆σf/2+ur-∆uf ∆σf/2

UUC Test

Reliance on UUC tests to estimate su(mob) depends on fortuitous cancellation of three errors:

1. Fast rate of shearing (60%/hr) causes an increase in su;2. Shearing in compression mode (ignoring the effect of anisotropy) causes an 2. Shearing in compression mode (ignoring the effect of anisotropy) causes an

increase in su; and3. Sample disturbance causes a decrease in su.

Ladd and DeGrootUUC are generally a waste of time and money over strength index testing (hand torvane, fall cone). The cost saving should be spent on consolidation tests and Atterberg Limits.

Consolidated Undrained(CU) Test

σ’ vc = σvc

Total, σ Neutral, u Effective, σ’= +

After

consolidation σvc+uo

uoσ’ hc = σhcA

fter

consolidation

At failure

σhc

σvc

∆σf = (σ1-σ3)f

uo+∆uf

σ’ vf =∆σf+σvc-uo-+∆uf

σhc+uo

uo

σ’ hf =σhc-uo-+∆uf

UU and CIU Test Stress Path

σ’vo σ’pσ’sq/σ’vo

1

2

3

4

5

In-situ

Lab UUC – perfect sample

Lab UUC – small disturbance

Lab UUC – large disturbance

CIUC – σ’c = σ’vo

εvol

log(σ’vc)

In-situ Ko

Lab Ko

Lab Kc = 11

2

3

4

5

p’/σ’vo

1.0

q(mob)/σ’vo

σ’psσ’sσ’s

5

CIUC tests do NOT give a correct design strength for undrained stability – DISCONTINUE and replace with CKoU

Coefficient of Earth Pressure at Rest

( ) )1(00

0 pKp OCRKK −= )'sin(10 φ−=pK

Stress Path to Failure CKoUTXC/E

Stress Path to Failure

Sophistication Levels of Undrained

Stability Evaluations

Level Analysis MethodStrength Input

StrengthTesting

Stress History

FS

CCircular Arc(Isotropic su)

su(avg) vs. zFVT or

Mesri/SHANSEPDesireableRequired

>1.5

BCircular Arc(Isotropic su)

su(avg) vs. zEach zone

CKoUTC & CKoTEOr CKoUDSS

Essential 1.3-1.5

ANon-circular Surface

(Anisotropic su)su(α) vs. zEach zone

CKoUTC & CKoTEand CKoUDSS

Essential 1.25-1.35

Level C and B Evaluations

Plot the Following Data versus elevation• su(FV); su(HT); su(HP); su(UUC); su(CPT)• Atterberg limits and water content• Vertical effective stress and maximum past pressure (consolidation

test results)test results)• su(mob) = 0.22σ’p and SHANSEP relationship

Circular arc

Isotropic su

Level B• su(DSS) or su(TX) and su(TE)

Level A Evaluation

1.2

90 60 30 0 -30 -60 -90

1.2

0.8

1.0

0.9

1.1

D

C

E

s u(α

)/s u

(D)

α

COMPRESSIBILITYCOMPRESSIBILITY

Compressibility

e

e0 e0 σ’ v0 k0

CR 1

σ’p

v

v

tv t

e

dt

de

dt

de

'

'

' σ

σσ

∂∂+

∂∂=

log(k) log(σ’ v)

Terzaghi Theory Assumption

Ck

CC

1

1

1

Compressibility

vt

e

dt

de

dt

de v

tv '

'

' σ

σσ

∂∂+

∂∂=

∫∫

∂+

∂+

∂∂=∆

t

t

t

tv p v

p

v

dtdt

edt

dt

e

dt

deee

'0 '' σσσ

0'

=

∂∂

vt

e

σv

tv

ae −=

∂∂

'σ

For Primary Consolidation, Terzaghi Theory Assumes

Secondary Compression

e

(σ’ v, t, e)1 Slope CC,1 Slope Cα,1

log(σ’ v)

log(t)

Slope CC,2

Slope Cα,2

(σ’ v, t, e)2

(Cα/CC)1 = (Cα/CC)2

Secondary Compression Index

Material Cαααα/Cc

Granular soils, including rockfill 0.02+0.01

Shale and mudstone 0.03+0.01

Inorganic clays and silts 0.04+0.01

Organic clays and silts 0.05+0.01

Peat and muskeg 0.06+0.01

Constant Rate of Strain (CRS)

Consolidation Test

pv Ck ασε

'0=&

Theoretical strain rate to develop zero excess pore pressure (EOP)

Cw

p

C

C

vP C

C

H

k

k

C

α

γσ

ε'

2 2

0

=&

)1log( max,20

)*38(u

w

vaLI RH

kpe −−= −

γε&

Strain Rate and Pore Pressure

ue σ’v

Becker Method

σ‘p = 1.96 ksc – 2.08 kscAt imposed strain rate

CRS Test Results

1

)'log(

)log()log(

)'log( v

vv

vk

c k

e

ke

C

C

σσ ∆∆=

∆∆

∆∆=

1

CcCk

Cc = 0.3 Ck = 0.58 e0 = 0.91 Ck/eo= 0.64 Cc/Ck= 0.52 Cα/Cc~ 0.05

Adjust for EOP conditions

[ ][ ] 94.0

'

'=

=

C

I

pC

C

I

p

p

p

α

εε

σ

σ

ε

ε

&

&

&

&

Iε&

EOP Maximum Past Pressure

σ’p = 1.88 kg/cm2