shear strength of soil - national chiao tung · pdf filenormally consolidated clays 2 (1 3)f...
TRANSCRIPT
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
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
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 −
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
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
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
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 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
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
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
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
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
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
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
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