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1
Shear Strength of Soils
ChihChih--Ping LinPing Lin
NationalNational ChiaoChiao TungTung Univ.Univ.
cplin@mail.nctu.edu.twcplin@mail.nctu.edu.tw
Soil Mechanics −
2
Outline
Shear FailureShear Failure
Soil StrengthSoil Strength
MohrMohr--Coulomb Failure CriterionCoulomb Failure Criterion
Laboratory Shear Strength TestLaboratory Shear Strength Test
Direct shearDirect shear
TriaxialTriaxial
Stress PathStress Path
Pore Pressure ParametersPore Pressure Parameters
3
Shear failure
Soils generally fail inSoils generally fail in shearshear
strip footing
embankment
At failure, shear stress along the failure surface
reaches the shear strength.
failure surface mobilised shear
resistance
Shear Failure
4
Shear failure
The soil grains slide over
each other along the
failure surface.
No crushing of
individual grains.
failure surface
Shear Failure
5
Shear failure
σ
τ
τ
At failure, shear stress along the failure surface
(τ) reaches the shear strength (τf).
Shear Failure
6
Soil (Shear) Strength
Soils are essentiallySoils are essentially frictional materialsfrictional materials
the strength depends on the applied stressthe strength depends on the applied stress
Strength is controlled byStrength is controlled by effective stresseseffective stresses
water pressures are requiredwater pressures are required
Soil strength depends onSoil strength depends on drainagedrainage
different strengths will be measured for a given soildifferent strengths will be measured for a given soil
a)a) deforms at constant volume (deforms at constant volume (undrainedundrained) and) and
b)b) deforms without developing excess pore pressuresdeforms without developing excess pore pressures
(drained)(drained)
Soil Strength
7
Mohr-Coulomb Failure Criterion
τ
σ’
'tan'' φστ += cf
c’
φ
failure envelope
cohesion
friction angle
τf is the maximum shear stress the soil can take
without failure, under normal stress of σ’.
τf
σ’
τ σ’
Mohr-Coulomb
8
Mohr-Coulomb Failure Criterion
'tan'' φστ ff c +=
Shear strength consists of two
components: cohesive and frictional.
σ’f
τf
φ’
τ
σ’
c’
σ’f tan φ
c cohesive component frictional
component
Mohr-Coulomb
9
c’ and φ’ are measures of shear strength.
Higher the values, higher the shear strength.
The parameters c’, φ’ depend on
Soil composition
Stress state of the soil (OCR)
The MohrThe Mohr--Coulomb criterion is an empirical criterion,Coulomb criterion is an empirical criterion,
and the failure locus is only locally linear.and the failure locus is only locally linear.
Extrapolation outside the range of normal stressesExtrapolation outside the range of normal stresses
for which it has been determined is likely to be unreliable.for which it has been determined is likely to be unreliable.
Mohr-Coulomb
10
Mohr Circles & Failure Envelope
Y
Initially, Mohr circle is a point
σ’c
σ’c
σ’c
∆σ’
σ’c+∆σ’
∆σ’
The soil element does not fail if
the Mohr circle is contained
within the envelope
GL
Mohr-Coulomb
11
Mohr Circles & Failure Envelope
Y
σ’c
σ’c
σ’c
∆σ’
GL
As loading progresses, Mohr
circle becomes larger…
.. and finally failure occurs
when Mohr circle touches the
envelope
Mohr-Coulomb
12
Orientation of Failure Plane
Y
σ’c
σ’c
σ’c
∆σ’
GL
σ’c+∆σ’
90+φ’
φ’
45 + φ’/2
Failure plane
oriented at 45 + φ/2
to horizontal (σ’1)
45 + φ’/2
Y
Mohr-Coulomb
13
Mohr circles in terms of σ & σ’
X X X
σv
σh
σv’
σh’
u
u
= +
total stresses
effective stresses
σvσhσv’σh’
u
Mohr-Coulomb
14
Envelopes in terms of σ & σ’
Identical specimens
initially subjected to
different isotropic stresses
(σc) and then loaded
axially to failure
σc
σc
σc
σc
∆σf
Initially… Failure
uf
At failure,
σ3 = σc; σ1 = σc+∆σf
σ3’ = σ3 – uf ; σ1’ = σ1 - uf
c, φ
c’, φ’
in terms of σ
in terms of σ’
Mohr-Coulomb
15
Effective stress failure criterion
tanφστ ′+=c
c′ and φ′ are known as the effective (or drained) strength
parameters.
Soil behaviour is controlled by effective stresses, and the
effective strength parameters are the fundamental strength
parameters. But they are not necessarily soil constants.
If the soil is at failure the effective stress failure criterion will
always be satisfied.
Mohr-Coulomb
16
Total stress failure criterion
uuc φστ tan+=
If the soil is taken to failure at constant volume (undrained) then the
failure criterion can be written in terms of total stress as
cu and φu are known as the undrained strength parameters
These parameters are not soil constants, they depend strongly on the
moisture content of the soil.
The undrained strength is only relevant in practice to clayey soils
that in the short term remain undrained. Note that as the pore
pressures are unknown for undrained loading the effective stress
failure criterion cannot be used.
Mohr-Coulomb
17
Laboratory Tests for Shear Strength Parameters
Direct shear testDirect shear test
TriaxialTriaxial testtest
Direct simple shear testDirect simple shear test
Plane strainPlane strain triaxialtriaxial testtest
TorsionalTorsional ring shear testring shear test
Shear Strength Test
18
Direct Shear Test
Motor
drive
Load cell to
measure
Shear Force
Normal load
Rollers
Soil
Porous plates
Top platen
Measure relative horizontal displacement, dx
vertical displacement of top platen, dy
Direct Shear
19
Sand
Direct Shear
20
Clay
Direct Shear
21
Pros:
Simplest and most economical for sandy soil
Applicable for soil/structure interface
Cons:
Soil not allowed to fail along the weakest plane.
Shear stress distribution is not uniform.
Direct Shear
22
Triaxial Test Apparatus
porous
stone
impervious
membrane
piston (to apply deviatoric stress)
O-ring
pedestal
perspex cell
cell pressure
back pressure
pore pressure or
volume change
water
soil sample at
failure
failure plane
Triaxial
23
Types of Triaxial Tests
Under all-around
cell pressure σc
Shearing
(loading)
Is the drainage valve open? Is the drainage valve open?
deviatoric stress (∆σ)
yes no yes no
Consolidated
sample
Unconsolidated
sample
Drained
loading
Undrained
loading
Triaxial
24
Types of Triaxial Tests
Depending on whether drainage is allowed
or not during
initial isotropic cell pressure application, and
shearing,
there are three special types of triaxial tests
that have practical significances. They are:
Consolidated Drained (CD) test
Consolidated Undrained (CU) test
Unconsolidated Undrained (UU) test
Triaxial
25
Granular soils have
no cohesion.
c = 0 & c’= 0
For normally consolidated
clays, c’ = 0 & c = 0.
For unconsolidated
undrained test, in
terms of total
stresses, φu = 0
Triaxial
26
CD, CU and UU Triaxial Tests
no excess pore pressure throughout the test
very slow shearing to avoid build-up of pore
pressure
Consolidated Drained (CD) Test
gives c’ and φ’
Can be days!
∴ not desirable
Use c’ and φ’ for analysing fully drained
situations (e.g., long term stability,
very slow loading)
Triaxial
27
Loose sand / NC clay Dense sand / OC Clay
Triaxial
28
Triaxial
29
Triaxial
30
CD, CU and UU Triaxial Tests
pore pressure develops during shear
faster than CD (∴preferred way to find c’ and φ’)
Consolidated Undrained (CU) Test
gives c’ and φ’
Measure σ’
Triaxial
31
Triaxial
Loose sand / NC clay
Dense sand / OC Clay
32
Triaxial
33
CD, CU and UU Triaxial Tests
pore pressure develops during shear
very quick test
Unconsolidated Undrained (UU) Test
analyze in terms of σ gives cu and φu
Not measured
∴σ’ unknown
= 0; i.e., failure envelope
is horizontal
Use cu and φu for analysing undrained
situations (e.g., short term stability,
quick loading)
Triaxial
34
UU test on saturated clay
Triaxial
35
©2001Brooks/Cole,adivisionofThomsonLearning,Inc.ThomsonLearning™isatrademarkusedhereinunderlicense.
The φ=0 concept
Triaxial
36
Unconfined compression test on saturated clay
Triaxial
37
σ’1 and σ’3 at Failure
Triaxial
38
Stress Point
t
s
τ
σσh
σv
(σv-σh)/2
(σv+σh)/2
stress point stress point
2
hv
s
σσ +
=
2
hv
t
σσ −
=
X
σv
σh
Stress Path
39
Stress Path
t
s
Stress path is
the locus of
stress points
Stress path
Stress path is a convenient way to keep track of the
progress in loading with respect to failure envelope.
During loading…
τ
σ
Stress Path
40
Failure Envelopes
τ
σ
t
s
c
φ
c cos φ
tan-1 (sin φ)
failure
During loading (shearing)….
stress path
Stress Path
41
Pore Pressure Parameters
Y
∆σ1
∆σ3
∆u = ?
A simple way to estimate the pore
pressure change in undrained
loading, in terms of total stress
changes ~ after Skempton (1954)
[ ])( 313 σσσ ∆−∆+∆=∆ ABu
Skempton’s pore pressure
parameters A and B
Pore Pressure Parameters
42
Pore Pressure Parameters
For saturated soils, B ≈ 1.
A-parameter at failure (Af)
For normally consolidated clays Af ≈ 1.
B-parameter
B = f (saturation,..)
Af = f(OCR)
For heavily overconsolidated clays Af is negative.
Pore Pressure Parameters

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Tema 2 shear strengthofsoil

  • 1. 1 Shear Strength of Soils ChihChih--Ping LinPing Lin NationalNational ChiaoChiao TungTung Univ.Univ. cplin@mail.nctu.edu.twcplin@mail.nctu.edu.tw Soil Mechanics − 2 Outline Shear FailureShear Failure Soil StrengthSoil Strength MohrMohr--Coulomb Failure CriterionCoulomb Failure Criterion Laboratory Shear Strength TestLaboratory Shear Strength Test Direct shearDirect shear TriaxialTriaxial Stress PathStress Path Pore Pressure ParametersPore Pressure Parameters
  • 2. 3 Shear failure Soils generally fail inSoils generally fail in shearshear strip footing embankment At failure, shear stress along the failure surface reaches the shear strength. failure surface mobilised shear resistance Shear Failure 4 Shear failure The soil grains slide over each other along the failure surface. No crushing of individual grains. failure surface Shear Failure
  • 3. 5 Shear failure σ τ τ At failure, shear stress along the failure surface (τ) reaches the shear strength (τf). Shear Failure 6 Soil (Shear) Strength Soils are essentiallySoils are essentially frictional materialsfrictional materials the strength depends on the applied stressthe strength depends on the applied stress Strength is controlled byStrength is controlled by effective stresseseffective stresses water pressures are requiredwater pressures are required Soil strength depends onSoil strength depends on drainagedrainage different strengths will be measured for a given soildifferent strengths will be measured for a given soil a)a) deforms at constant volume (deforms at constant volume (undrainedundrained) and) and b)b) deforms without developing excess pore pressuresdeforms without developing excess pore pressures (drained)(drained) Soil Strength
  • 4. 7 Mohr-Coulomb Failure Criterion τ σ’ 'tan'' φστ += cf c’ φ failure envelope cohesion friction angle τf is the maximum shear stress the soil can take without failure, under normal stress of σ’. τf σ’ τ σ’ Mohr-Coulomb 8 Mohr-Coulomb Failure Criterion 'tan'' φστ ff c += Shear strength consists of two components: cohesive and frictional. σ’f τf φ’ τ σ’ c’ σ’f tan φ c cohesive component frictional component Mohr-Coulomb
  • 5. 9 c’ and φ’ are measures of shear strength. Higher the values, higher the shear strength. The parameters c’, φ’ depend on Soil composition Stress state of the soil (OCR) The MohrThe Mohr--Coulomb criterion is an empirical criterion,Coulomb criterion is an empirical criterion, and the failure locus is only locally linear.and the failure locus is only locally linear. Extrapolation outside the range of normal stressesExtrapolation outside the range of normal stresses for which it has been determined is likely to be unreliable.for which it has been determined is likely to be unreliable. Mohr-Coulomb 10 Mohr Circles & Failure Envelope Y Initially, Mohr circle is a point σ’c σ’c σ’c ∆σ’ σ’c+∆σ’ ∆σ’ The soil element does not fail if the Mohr circle is contained within the envelope GL Mohr-Coulomb
  • 6. 11 Mohr Circles & Failure Envelope Y σ’c σ’c σ’c ∆σ’ GL As loading progresses, Mohr circle becomes larger… .. and finally failure occurs when Mohr circle touches the envelope Mohr-Coulomb 12 Orientation of Failure Plane Y σ’c σ’c σ’c ∆σ’ GL σ’c+∆σ’ 90+φ’ φ’ 45 + φ’/2 Failure plane oriented at 45 + φ/2 to horizontal (σ’1) 45 + φ’/2 Y Mohr-Coulomb
  • 7. 13 Mohr circles in terms of σ & σ’ X X X σv σh σv’ σh’ u u = + total stresses effective stresses σvσhσv’σh’ u Mohr-Coulomb 14 Envelopes in terms of σ & σ’ Identical specimens initially subjected to different isotropic stresses (σc) and then loaded axially to failure σc σc σc σc ∆σf Initially… Failure uf At failure, σ3 = σc; σ1 = σc+∆σf σ3’ = σ3 – uf ; σ1’ = σ1 - uf c, φ c’, φ’ in terms of σ in terms of σ’ Mohr-Coulomb
  • 8. 15 Effective stress failure criterion tanφστ ′+=c c′ and φ′ are known as the effective (or drained) strength parameters. Soil behaviour is controlled by effective stresses, and the effective strength parameters are the fundamental strength parameters. But they are not necessarily soil constants. If the soil is at failure the effective stress failure criterion will always be satisfied. Mohr-Coulomb 16 Total stress failure criterion uuc φστ tan+= If the soil is taken to failure at constant volume (undrained) then the failure criterion can be written in terms of total stress as cu and φu are known as the undrained strength parameters These parameters are not soil constants, they depend strongly on the moisture content of the soil. The undrained strength is only relevant in practice to clayey soils that in the short term remain undrained. Note that as the pore pressures are unknown for undrained loading the effective stress failure criterion cannot be used. Mohr-Coulomb
  • 9. 17 Laboratory Tests for Shear Strength Parameters Direct shear testDirect shear test TriaxialTriaxial testtest Direct simple shear testDirect simple shear test Plane strainPlane strain triaxialtriaxial testtest TorsionalTorsional ring shear testring shear test Shear Strength Test 18 Direct Shear Test Motor drive Load cell to measure Shear Force Normal load Rollers Soil Porous plates Top platen Measure relative horizontal displacement, dx vertical displacement of top platen, dy Direct Shear
  • 11. 21 Pros: Simplest and most economical for sandy soil Applicable for soil/structure interface Cons: Soil not allowed to fail along the weakest plane. Shear stress distribution is not uniform. Direct Shear 22 Triaxial Test Apparatus porous stone impervious membrane piston (to apply deviatoric stress) O-ring pedestal perspex cell cell pressure back pressure pore pressure or volume change water soil sample at failure failure plane Triaxial
  • 12. 23 Types of Triaxial Tests Under all-around cell pressure σc Shearing (loading) Is the drainage valve open? Is the drainage valve open? deviatoric stress (∆σ) yes no yes no Consolidated sample Unconsolidated sample Drained loading Undrained loading Triaxial 24 Types of Triaxial Tests Depending on whether drainage is allowed or not during initial isotropic cell pressure application, and shearing, there are three special types of triaxial tests that have practical significances. They are: Consolidated Drained (CD) test Consolidated Undrained (CU) test Unconsolidated Undrained (UU) test Triaxial
  • 13. 25 Granular soils have no cohesion. c = 0 & c’= 0 For normally consolidated clays, c’ = 0 & c = 0. For unconsolidated undrained test, in terms of total stresses, φu = 0 Triaxial 26 CD, CU and UU Triaxial Tests no excess pore pressure throughout the test very slow shearing to avoid build-up of pore pressure Consolidated Drained (CD) Test gives c’ and φ’ Can be days! ∴ not desirable Use c’ and φ’ for analysing fully drained situations (e.g., long term stability, very slow loading) Triaxial
  • 14. 27 Loose sand / NC clay Dense sand / OC Clay Triaxial 28 Triaxial
  • 15. 29 Triaxial 30 CD, CU and UU Triaxial Tests pore pressure develops during shear faster than CD (∴preferred way to find c’ and φ’) Consolidated Undrained (CU) Test gives c’ and φ’ Measure σ’ Triaxial
  • 16. 31 Triaxial Loose sand / NC clay Dense sand / OC Clay 32 Triaxial
  • 17. 33 CD, CU and UU Triaxial Tests pore pressure develops during shear very quick test Unconsolidated Undrained (UU) Test analyze in terms of σ gives cu and φu Not measured ∴σ’ unknown = 0; i.e., failure envelope is horizontal Use cu and φu for analysing undrained situations (e.g., short term stability, quick loading) Triaxial 34 UU test on saturated clay Triaxial
  • 19. 37 σ’1 and σ’3 at Failure Triaxial 38 Stress Point t s τ σσh σv (σv-σh)/2 (σv+σh)/2 stress point stress point 2 hv s σσ + = 2 hv t σσ − = X σv σh Stress Path
  • 20. 39 Stress Path t s Stress path is the locus of stress points Stress path Stress path is a convenient way to keep track of the progress in loading with respect to failure envelope. During loading… τ σ Stress Path 40 Failure Envelopes τ σ t s c φ c cos φ tan-1 (sin φ) failure During loading (shearing)…. stress path Stress Path
  • 21. 41 Pore Pressure Parameters Y ∆σ1 ∆σ3 ∆u = ? A simple way to estimate the pore pressure change in undrained loading, in terms of total stress changes ~ after Skempton (1954) [ ])( 313 σσσ ∆−∆+∆=∆ ABu Skempton’s pore pressure parameters A and B Pore Pressure Parameters 42 Pore Pressure Parameters For saturated soils, B ≈ 1. A-parameter at failure (Af) For normally consolidated clays Af ≈ 1. B-parameter B = f (saturation,..) Af = f(OCR) For heavily overconsolidated clays Af is negative. Pore Pressure Parameters
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