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