Embed Size (px)
Citation preview
12/4/2014
1
L. 22-23-24Shear Strength of Soils
CIVE 431 SOIL MECHANICS & LAB
FALL 2014
Soils generally fail in shear
strip footing
embankment
At failure, shear stress along the failure surface reaches the shear strength.
failure surface mobilised shear resistance
Shear Failure in Soils
12/4/2014
2
The soil grains slide over each other along the failure surface.
failure surface
Shear Failure in Soils
1. 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
Tests to Measure Shear Strength
12/4/2014
3
Typical Direct Shear Machine
Typical Direct Shear Machine
T
Vertical load, N
Direction of Movement
12/4/2014
4
Horizontal displacement (dx)
She
ar L
oad
(F)
Normal load increasing
Test 1
Test 2
Typical Direct Shear Results
Actual Direct Shear Results
0
20
40
60
80
100
120
0 2 4 6 8
Shear Displacement (mm)
Sh
ear
Str
ess
(kP
a)
25 kPa
50 kPa
100 kPa
Total normal stress
12/4/2014
5
0 10000 20000
10000
20000
Normal Stress, psf
Sh
ear
Str
ess,
psf
0
C = 197 psf
= 42 degrees
Stress path
Failure point
Result of Shear Test on Dry Sand
tan cf
c
cohesion friction angle
f is the maximum shear stress the soil can take without failure, under normal stress of .
f
Mohr Coulomb Failure Criteria
12/4/2014
6
ExampleDirect Shear Test
Given:
A direct shear test conducted on a dry soil sample yielded the following results:
Normal Stress, (psi) Max. Shear Stress, (psi) 10.0 6.525.0 11.040.0 17.5
Required:
Determine shear strength parameters of the soil
Example 1Direct Shear Test Results
0
5
10
15
20
0 10 20 30 40 50
Normal Stress (psi)
Max
. S
hea
r S
tres
s (p
si
20)365.0(tan
365.048
)5.220(tan
5.2
1
psic
12/4/2014
7
• The Mohr-Coulomb Envelope that was shown before was for dry sands.
• Typically soils have some moisture in them. Pore water pressure is generated during shearing.
• If pore water pressures are positive, water moves out of the sample during shear (Compression).
• If pore water pressures are negative, water moves into the sample during shear (Dilation or Expansion)
• In Direct Shear Test, we try to shear the sample slow enough so that we have no generation of pore water pressure (Drained Test) .
Direct Shear Test
• Since we are conducting a drained test, the pore water pressures are ZERO, and the total stresses at failure are equal to the effective stresses.
Write the Mohr-Coulomb Equation as:
'tan'' cf
•The direct shear test is useful and reasonably economical for cases where we need the shearing properties under fully drained conditions.
Direct Shear Test
12/4/2014
8
• Usually only relatively slow drained tests are performed in shear box apparatus. For clays rate of shearing must be chosen to prevent excess pore pressures building up. For sands and gravels tests can be performed quickly
• Tests on sands and gravels are usually performed dry. Water does not significantly affect the (drained) strength.
• If there are no excess pore pressures and as the pore pressure is approximately zero the total and effective stresses will be identical.
• The failure stresses thus define an effective stress failure envelope from which the effective (drained) strength parameters c’, ’ can be determined.
Direct Shear Test
• Planar shear failure
─ may not be the plane of weakness
• Boundary condition
─ changing area
• NO control of pwp
• The failure Regarded as
− a drained shear test for sands
• Drained for clays only if rate of shearing is VERY slow
Limitations of Direct Shear Test
12/4/2014
9
2. The Triaxial Test
Cell pressure Pore pressure and
volume change
Rubber membrane
Cell water
O-ring seals
Porous filter disc
Confining cylinder
Deviatoric load
Soil
Tests to Measure Shear Strength
Triaxial Setup
12/4/2014
10
3 3 = Radial stress (cell pressure)
1 = Axial stress
F = Deviator load1
a rF
A From equilibrium we have
1 3
d = Deviatoric Stress
Stresses in Triaxial Specimen
Shear Failure
Triaxial Compression Test
12/4/2014
11
Triaxial Cell Panel for
Controlling Pressures
Soil Sample
Triaxial Compression Test
Measure Displacements
Measure Force
Soil Sample
Triaxial Cell
Triaxial Compression Test
12/4/2014
12
Apply a confining pressure, 3 in the sample from all directions
Start Increasing the Vertical Pressure in Small Increments until sample fails
STEP 1
STEP 2
STEP 3
Steps in Triaxial Test
d
a
Increasing cell pressure
Typical Triaxial Test Results
12/4/2014
13
Mohr circle represents combinations of and on different planes passing through a point
(3,0) (1,0)
,)
Mohr Circle
Failure Envelope
C
Cohesion
Soil Sample 1Soil Sample 2
Failure Points
Failure Points
Mohr-Coulomb Failure Envelope
12/4/2014
14
C
Failure Point
Failure plane oriented at an angle 2 = 90 + Failure plane oriented at = 45 +
Orientation of Failure Plane
Failure in Triaxial Test
12/4/2014
15
Y
c
c
c
GL
c+
90+
45 + /2
Failure plane oriented at 45 + /2to horizontal
45 + /2
Y
Orientation of Failure Plane
Under all-around cell pressure c
Shearing (loading)
Is the drainage valve open? Is the drainage valve open?
deviatoric stress ()
yes no yes no
Consolidatedsample
Unconsolidatedsample
Drained loading
Undrainedloading
Types of Triaxial Tests
12/4/2014
16
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) testConsolidated Undrained (CU) testUnconsolidated Undrained (UU) test
Types of Triaxial Tests
Granular soils have no cohesion.c = 0 & c’= 0
For normally consolidated clays, c’ = 0.
For unconsolidated undrained test, in
terms of total stresses, u = 0
Types of Triaxial Tests
12/4/2014
17
no excess pore pressure throughout the test very slow shearing to avoid build-up of pore
pressure
Consolidated Drained (CD) Test
gives c’ and ’
Can be days! not desirable
Use c’ and ’ for analysing fully drainedsituations (e.g., long term stability, very slow loading)
CD, CU, and UU Triaxial Tests
pore pressure develops during shear
faster than CD (preferred way to find c’ and ’)
Consolidated Undrained (CU) Test
gives c’ and ’
Measure ’
CD, CU, and UUTriaxial Tests
12/4/2014
18
pore pressure develops during shear
very quick test
Unconsolidated Undrained (UU) Test
analyze in terms of gives cu and u
Not measured’ unknown
= 0; i.e., failure envelope is horizontal
Use cu and u for analysing undrainedsituations (e.g., short term stability, quick loading)
CD, CU, and UU Triaxial Tests
• UU (Unconsolidated Undrained) test (Q-Test)
Cell pressure applied without allowing drainage. Then keeping cell pressure constant, increase deviatoric load to failure without drainage.
• CU (Consolidated Undrained) test (R-Test)
Drainage allowed during cell pressure application. Then without allowing further drainage increase d .
• CD (Consolidated Drained) test (S-Test)
Similar to CU except that as deviatoric stress is increased drainage is permitted.
Types of Triaxial Tests - Summary
12/4/2014
19
• The complete stress-strain-strength behavior can be investigated
• Drained and undrained tests can be performed
• Pore water pressures can be measured in undrained tests, allowing effective stresses to be determined
• Different combinations of cell pressure and axial stress can be applied
Advantages of Triaxial Tests
Sample Compresses During Shearing
Consolidated Drained Test on Normally Consolidated Clay or Loose Sand
12/4/2014
20
Sample Compresses and then expands During Shearing
Compression Dilation (Expansion)-5
Consolidated Drained Test on OC Clay or Very Dense Sand
’3 ’
’1 ’3 ’1
Sample 1Sample 2
Failure Envelope from CD-Triaxial Test:
’, c’
Results of CD-Triaxial Tests
12/4/2014
21
131 3
u
u
For any point in the soil a total and an effective stress Mohr circle can be drawn. These are the same size with
1 3 1 3
The two circles are displaced horizontally by the pore pressure, u.
Effective Stress Failure Envelope: c’ and ’
Total Stress Mohr Circle
Results of CU-Triaxial Tests
131 3
u (Positive)
u (Positive)
* For Normally Consolidated Clays and Loose Sands, the tendency to compress in Drained Tests reflects in a tendency to generate positive pore water pressure during Undrained Tests
Effective Stress Failure Envelope: c’ and ’
Total Stress Mohr Circle
CU Tests on NC Clays or Loose Sands
12/4/2014
22
13 1 3
u (Negative)
u (Negative)
* For Overconsolidated Clays and Dense Sands, the tendency to Dilate in Drained Tests reflects in a tendency to generate negative pore water pressure during Undrained Tests
Effective Stress Failure Envelope: c’ and ’
Total Stress Mohr Circle
CU Tests on OC Clays or Dense Sands
3
1 3 1
Sample 1Sample 2
Failure Envelope from UU Test: = su = c ; = 0
Undrained Shear Strength: Su = (1 – 3)/2
su
UU-Triaxial Tests on Saturated Clays (Samples have Same Water Content)
12/4/2014
23
3
1 3 1
Sample 1Sample 2
Failure Envelope from UU Test:
# 0
UU-Triaxial Tests on Unsaturated Clays (Samples have Same Water Content)
The Undrained Shear Strength is a function of the Void Ratio of the clay, which is a function of the vertical Effective Stress.
Sample 1 (’v)1, (su)1
Sample 2 (’v)2, (su)2
Sample 3 (’v)3, (su)3
Undrained Strength (su)
Ver
tica
l E
ffec
tive
Str
ess,
(’
v)
su/ ’v
Undrained Shear Strength of Clays (c, Su)
12/4/2014
24
Strength Ratio(su/ ’v or c/p)
The Strength Ratio (su/s’v) is a function of the Overconsolidation ratio (OCR) of the clay.
Undrained Strength (su)
Ver
tica
l E
ffec
tive
Str
ess,
(’
v)
su/ ’v
Normally Consolidated Clay
)(0037.011.0'
PIs
NCv
u
Overconsolidated Clay
m
NCv
u
OCv
u OCRss
''
0.75 – 0.85
Plasticity Index
1. Drained shear loading• In laboratory tests the loading rate is chosen so
that no excess water pressures will be generated, and the specimens are free to drain. Effective stresses can be determined from the applied total stresses and the known pore water pressure (Which is ZERO).
• Only the effective strength parameters c’ and ’ have any relevance to drained tests.
Interpretation of Laboratory Tests
12/4/2014
25
• Effective strength parameters are generally used to check the long term stability (that is when all excess pore pressures have dissipated) of soil constructions.
• For sands and gravels pore pressures dissipate rapidly and the effective strength parameters can also be used to check the short term stability.
• In principle the effective strength parameters can be used to check the stability at any time for any soil type. However, to do this the pore pressures in the ground must be known and in general they are only known in the long term.
Interpretation of Laboratory Tests
2. Undrained loading
• In undrained laboratory tests no drainage from the sample must occur.
• In the shear box this requires fast shear rates (basically impossible). In triaxial tests slower loading rates are possible because conditions are uniform and drainage from the sample is easily prevented.
• In a triaxial test with pore pressure measurement the effective stresses can be determined and the effective strength parameters c’, ’ evaluated. These can be used as discussed previously to evaluate long term stability.
Interpretation of Laboratory Tests
12/4/2014
26
• The undrained tests can also be used to determine the total (or undrained) strength parameters cu, u. If these parameters are to be relevant to the ground the moisture content must be the same. This can be achieved either by performing UU tests or by using CU tests and consolidating to the in-situ stresses.
• The total (undrained) strength parameters are used to assess the short term stability of soil constructions. It is important that no drainage should occur if this approach is to be valid. For example, a total stress analysis would not be appropriate for sands and gravels.
• For clayey soils a total stress analysis is the only simple way to assess stability. Note that undrained strengths can be determined for any soil, but they may not be relevant in practice
Interpretation of Laboratory Tests
• It is often found that a series of undrained tests from a particular site give a value of uthat is not zero (cu not constant). If this happens either:
– the samples are not saturated, or– the samples have different moisture
contents
• The undrained strength cu is not a fundamental soil property. If the moisture content changes so will the undrained strength.
Comments on Undrained Strength
12/4/2014
27
She
ar S
tres
s
Horizontal Displacement
Peak Strength
Residual Strength
Residual Drained Shear Strength
0 10000 20000
10000
20000
Normal Stress, psf
Sh
ear
Str
ess,
psf
0
Peak Strength c’, ’
Residual Strength cr’, r’
Peak vs Residual Shear Strength
12/4/2014
28
Shear Strength Properties
Shear Strength Properties
12/4/2014
29
Shear Strength Properties
Shear Strength Properties
