stress and strains in soil and...
TRANSCRIPT
Stress and Strains in Soil and Rock
Hsin-yu ShanDept. of Civil Engineering
National Chiao Tung University
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
Disturbance,Remold
She
ar s
treng
th
Aging
Remolded strength
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 solutionTest 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 testTime, t
Stra
in
cycle log/% 203log
)( 31 −≈∆
−∆
ftσσ
f)( 31 σσ −
1 10 100 1000 10000Time, logtf (min)
Anisotropy
Lean sensitive clays are more affected by “rotation of principal planes” than highly plastic clays of low sensitivity
σ1f σ1f
Ladd and Foott (1974)
0.19Plane strain “passive” (σ1fhorizontal)
0.20Direct simple shear
0.16Triaxial extension(σ1fhorizontal)
0.33Triaxial compression (σ1fvertical)
0.34Plane strain “active” (σ1fvertical)
τf/σ’vcType of test/Loading condition
σ1f
Factors Influencing Undrained Shear 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 shearFor 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
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 Test
Increase 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
su
φττ cosmax, fff =
σ
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
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
01 σσ =
03 σσ ==
)]1(1[
)1(
)]()([
)(
0
0
0000
0031
KA
KA
KAuuuu
uu
vc
vcvc
vcvcvc
vcvc
−−=
−−=
+−++−−−=∆−=
∆−+−===
σ
σσ
σσσ
σσσσσ
In the lab. Before setup.
vco AK σσσσ 5.0 ,0.1 ,5.0For 031 =====
vco AK σσσσ 32 ,3
2 ,5.0For 031 ===== (Elastic)
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%
fieldv,σ cσ σlog
To Obtain “Field” Undrained Shear Strength of N.C. clay
ComputeMeasure shear strength in the labCompute field strength
vc
f
στfieldv,σ
fieldvlabvc
fus ,)( σ
στ
×=
O.C. clays
Virgin consolidation curve(actually, we don’t have it)e or w%
labmax,σfieldv,σ fieldmax,σ labv,σσlog
To Obtain “Field” Undrained Shear Strength of O.C. clay
ComputeMeasure shear strength in the lab for the field OCR
Compute field strengthvc
f
στ
fieldv,σ
fieldvlabvc
fus ,)( σ
στ
×=
fieldmax,σ
constant≈vc
f
στ
For a given OCR
constant≈vc
f
στ
For a given OCR
vc
f
στ
OCR
Failure Criteria
Mohr-CoulombTresca (Extended Tresca)von Mises
Mohr-Coulomb
For σ1 > σ2 > σ3φσσσσ sin)()( 3131 +=−
Independent of σ2σa
T.E.
0]sin)()[(
]sin)()[(
]sin)()[(
213
213
232
232
221
221
=+−−
×+−−
×+−−
φσσσσ
φσσσσ
φσσσσ
T.C.
T.E.
σb σcT.E.T.C. T.C.
For c=0σa
If c is not 0, but φ is, the shape would be a hexagonal column
σb
σc
Tresca
octασσσσασσ =++
=−3
)( 32131
Often used for c=0 and φ=0αis the Trescaparameterequivalent to φExtended Tresca for φ > 0
σaT.C.
T.E.
octac
octcb
octba
σασσ
σασσ
σασσ
⋅≤−
⋅≤−
⋅≤−
T.E.
σb σcT.E.T.C. T.C.
Von Mises (φ = 0) 22222 )
3(2)()()( cba
accbbaσσσασσσσσσ ++
=−+−+−
σaT.C.c = 0 coneφ = 0 cylinerT.E.T.E.
σb σcT.E.T.C. T.C.
σaT.C.
T.E.T.E.
σb σcT.E.T.C. T.C.