Shear Strength of Soil
© 2004 Brooks/Cole Publishing / Thomson Learning™
Direct shear test in sand: (a) schematic
diagram of test equipment; (b) plot of test
results to obtain the friction angle φ’
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© 2004 Brooks/Cole Publishing / Thomson Learning™
Variation of friction angle φ’ with void ratio for Chattachoochee River
sand (after Vesic, 1963)
Soil Sampling
σ’1
σ’3
σ’3 = K σ’1
σ’1
2
Sequences of stress application in
triaxial test
© 2004 Brooks/Cole Publishing / Thomson Learning™
Triaxial Test Equipment
3
© 2004 Brooks/Cole Publishing / Thomson Learning™
Plot of deviator stress vs. axial strain-drained triaxial test
Triaxial Testing
‡
Application of cell pressure (sigma 3):
„
UNCONSOLIDATED (U) –
‡
‡
No drainage allowed
e constant (fixed) if Sr =1
- CONSOLIDATED (C) –
‡
‡
Drainage allowed when applying cell pressure
e decreases due to sample consolidation.
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Triaxial Testing
Application of deviatoric stress (σ1):
‡ Deviator stress = σ1 – σ3
‡
„
Undrained (U)
‡
‡
No drainage allowed
e constant (fixed) if Sr =1
- Drained (D)
‡
‡
‡
Drainage allowed when applying cell deviator stress
e decreases due to consolidation.
Stress applied so slow no excess pwp
Triaxial Tests
UU – Unconsolidated Undrained
‡ UD – Unconsolidated Drained
‡ CU - Consolidated Undrained
‡ CD - Consolidated Drained
‡
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Undrained Soil Strength
Parameters (Su, φ = 0)
Note: Always test soil at
void ratio on the field
Skempton’s Porewater Coefficients
B=
‡
Δμ
Δσ 3
Developed “B” for a
measure of degree
of Water saturation
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© 2004 Brooks/Cole Publishing / Thomson Learning™
Peak- and residual-strength envelopes for clay
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Skempton’s Porewater Coefficients
‡
Developed “A” parameter for
indication of sample OCR
A=
Δμi
(σ 1 − σ 3 )i
where :
Δμi = ( μi − μ o )
μ o = initail pore pressure
μi = pore pressure at point of interest
(σ 1 − σ 3 )i = deviatoric stress at point of interest
What about negative values of Af
Soil Strength
M-C Failure Envelope
Test 1 Failure Circle
Sample will fail at intersection
with envelope
τfailure (2)
τ’
τfailure (1)
Test 2 Failure Circle
c’
σ1(2)
σ3(1)
σ1(1)
σ1(3) σ1(Failure)
σ3(2)
σ1(1)
σ1(2) σ1(3)
σ1(Failure)
σ’n
NOTE: all stresses are effective
Each test is performed at a set void ratio
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Drained Soil Strength Parameters (c’, φ’)
Soil Strength Envelope
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Soil Strength
Stress Path of Sample
sinφ’ = tanα’
(σ1 - σ3)/2 = t
Radius of Circle
3
α’
2
t
t = d' + S tan α'
1
S
d
d = c' cos φ'
tan ψ = sin φ'
s
s = (σ1' + σ3')/2
Centre of Circle
Unconfined compression test in progress (courtesy of Soiltest, Inc., Lake Bluff, IL)
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© 2004 Brooks/Cole Publishing / Thomson Learning™
Unconfined compression test:
(a) soil specimen; (b) Mohr’s circle for the test; (c) variation of qu with
the degree of saturation
© 2004 Brooks/Cole Publishing / Thomson Learning™
Variation of friction angle φ’ with plasticity index for several clays
(after Bjerrum and Simons, 1960)
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