soil strength 2009
DESCRIPTION
TRANSCRIPT
![Page 1: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/1.jpg)
ADVANCED SOIL SHEAR
STRENGTH – Fine-grained SoilsSTRENGTH – Fine-grained SoilsDonald C. Wotring, Ph.D., P.E.
December 2008
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CLAY MINERALOGYCLAY MINERALOGY
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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
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Structural Units – Sheet Silicates
G
B
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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%
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Kaolinite – SEM photo
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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%
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Illite – SEM photo
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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
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Montmorillonite (Na) – SEM photo
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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
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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
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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
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Intergranular Pressure
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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
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Intergranular Pressure
Aua
aAC c −+−= )'(σ
cc CauaaAAaa +=++ 'σa
aAC c
i )'( −≡σ
uAi −+= σσ
Define intergrain force, σi
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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
![Page 18: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/18.jpg)
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
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Practical Implication
Kaolinte
Illite
Montmorillonite
)(' AR −=σ
Montmorillonite
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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.
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Soil Fabric
Orientation of Particles
N ature of Particles
Dispersed Flocculated (Aggregated)
RandomRandom
Highly Oriented
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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
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SOIL SAMPLINGSOIL SAMPLING
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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
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“Undisturbed” Shelby Tube Sampling
σ’ vo = ur
σ’ ho = ur
−ur
0
0
Total, σ Neutral, u Effective, σ’
Residual (capillarity) pressure, after sampling
= +
![Page 26: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/26.jpg)
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 −=
![Page 27: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/27.jpg)
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
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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
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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)
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Strain Rate Effects
Difficult to account for, sometimes use corrections or hope for compensating errors.
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VOLUMETRIC BEHAVIOR DURING
SHEARSHEAR
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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
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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
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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
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Volumetric Behavior During Shear
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DRAINED SHEAR STRENGTHDRAINED SHEAR STRENGTH
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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.
![Page 38: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/38.jpg)
Normally Consolidated Clay
)'tan(' φσ ns =
σ1-σ3
εa σn
sφ’NC
![Page 39: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/39.jpg)
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’
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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
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Overconsolidated Clay – Fully Softened
)'tan(' FSns φσ=
σ1-σ3
εa σn
sφ’NC = φ’FSFS
Peakφ’p
c’
• Increased face-to-face particle orientation
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Overconsolidated Clay – Fully Softened
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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
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Overconsolidated Clay – Residual
( ) ( ) 254.2037.00003.0 2 +−= ASTMASTMASTM
BM CFCFCF
CF 23.1003.0 )()(
)( += ASTML
ASTML
BML ww
w
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UNDRAINED SHEAR STRENGTHUNDRAINED SHEAR STRENGTH
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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.
![Page 47: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/47.jpg)
Undrained Shear Strength - Field Vane
)()( FVumobu ss µ=
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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
![Page 49: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/49.jpg)
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
')()()()(
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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
![Page 51: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/51.jpg)
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
![Page 52: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/52.jpg)
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
![Page 53: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/53.jpg)
Stress History and Normalized Soil
Engineering Parameters (SHANSEP) and
Recompression
![Page 54: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/54.jpg)
SHANSEP
![Page 55: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/55.jpg)
SHANSEP
m
vc
p
m
vc
p
vc
u
vc
u Sss
vc
p
=
=
=
'
'
'
'
''1
'
' σσ
σσ
σσσσ
![Page 56: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/56.jpg)
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.
![Page 57: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/57.jpg)
Triaxial Compression Test
UU – Unconsolidated Undrained
CIU – Isotropically Consolidated CIU – Isotropically Consolidated Undrained
CKoU – Ko Consolidated Undrained
![Page 58: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/58.jpg)
Mohr’s Circle Review
αααα
p’ = (σ’1+σ’3)/2(p’,q)
Pole
q = (σ1-σ3)/2
p’ = (σ’1+σ’3)/2
![Page 59: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/59.jpg)
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
![Page 60: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/60.jpg)
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’)
![Page 61: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/61.jpg)
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
![Page 62: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/62.jpg)
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
![Page 63: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/63.jpg)
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
![Page 64: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/64.jpg)
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.
![Page 65: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/65.jpg)
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
![Page 66: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/66.jpg)
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
![Page 67: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/67.jpg)
Coefficient of Earth Pressure at Rest
( ) )1(00
0 pKp OCRKK −= )'sin(10 φ−=pK
![Page 68: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/68.jpg)
Stress Path to Failure CKoUTXC/E
![Page 69: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/69.jpg)
Stress Path to Failure
![Page 70: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/70.jpg)
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
![Page 71: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/71.jpg)
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)
![Page 72: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/72.jpg)
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
![Page 73: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/73.jpg)
COMPRESSIBILITYCOMPRESSIBILITY
![Page 74: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/74.jpg)
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
![Page 75: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/75.jpg)
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
![Page 76: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/76.jpg)
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
![Page 77: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/77.jpg)
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
![Page 78: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/78.jpg)
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&
![Page 79: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/79.jpg)
Strain Rate and Pore Pressure
ue σ’v
![Page 80: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/80.jpg)
Becker Method
σ‘p = 1.96 ksc – 2.08 kscAt imposed strain rate
![Page 81: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/81.jpg)
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
![Page 82: Soil Strength 2009](https://reader033.vdocument.in/reader033/viewer/2022061214/549b1930b479590b098b46b3/html5/thumbnails/82.jpg)
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