1. Shear Strength GLE/CEE 330 Lecture Notes Soil Mechanics
William J. Likos, Ph.D. Department of Civil and Environmental Engineering University of Wisconsin-Madison

2. Applications Slope Stability Bearing Capacity Retaining Walls Others…
Tunnel Linings
Roadway Base
Excavations
(USC)
(bp0.blogger.com)

3. Consider Bearing Capacity
s’h t uw
s’v
Is there a plane within the soil mass where the induced shear stresses exceed the shear strength of the soil (c’, f’) ?
Will a “failure plane” develop?
How does shear strength depend on effective stress?

4. Shear Strength Dilation s’v t Failure plane
Particles must move to create shear plane
Results in positive (increase) in volume
Total resistance depends on confining pressure
Angular particles result in more dilation (so more shear resistance.
Failure plane
occurs at particle contacts
particles themselves generally
do not fail high s’)
Sources of shear resistance:
1) Dilation & frictional resistance:
Dependent on effective stress (s’)
Captured with material property f’
2) Cohesive resistance:
Independent of stress
Captured with material property c’
Important for clays (“cohesive soils”)

5. Mohr-Coulomb Failure Criterion
s’v
shear
strength
frictional component
(dependent on s’, the effective stress on the shear surface)
cohesive component
c’ = effective cohesion intercept (units of stress – kPa, psf, psi, etc.))
f’ = effective angle of internal friction (degrees)

6. Mohr-Coulomb Failure Criterion
c’ = effective cohesion intercept
f’ = effective friction angle
s’ = effective stress on failure plane
This is a straight line in s’-t space t
failure
M-C Failure Envelope
no failure
s’1 t s’
s’3 f’
Mohr’s Circle c’
s’3
s’1 s’

7. Factors Affecting f’ Mineralogy (e.g., quartz vs. mica)
Grain shape (e.g., angular vs. rounded)
Grain size distribution (e.g., well-graded vs. poorly-graded)
Void ratio, density, porosity (e.g., compacted vs. loose)
Organic material (very weak)
(mica)
(Coduto, 1999)

8. (Bardet, 1997)

9. Cohesion Factors affecting c’: 1) Cementation (e.g., CaCO3)
2) Electrostatic attraction – van der Waals forces
appreciable for small, high-surface area materials
3) Negative pore pressure (unsaturated soils)
4) Interlocking
Caliche layer exposed in
southern Kansas (KGS)

10. (Bardet, 1997)

11. Mohr-Coulomb Failure Criterion
c’ = effective cohesion intercept
f’ = effective friction angle
s’ = effective stress on failure plane
This is a straight line in s’-t space t
failure
M-C Failure Envelope
no failure
s’1 t s’
s’3 f’
Mohr’s Circle c’
s’3
s’1 s’

12. Consider a triaxial shear test:
First apply isotropic compression (s1’ = s3’)
Hold s3’ constant and increase s1’ until failure
s’1 tf
s’f
s’3 a
M-C Failure Envelope t
Stress on failure plane
(s’f, tf)
Mohr’s Circle at Failure f’ f’ c’ 2a s’
s’3
s’1f
So, the higher c’ and f’, the stronger the soil

13. Consider stress-strain response for loose sand and dense sand
Loose Sand (Dr = 38%)
Dense Sand (Dr = 100%) ea
s’3 ev
Observations:
Loose sand: ductile
Dense sand: brittle
Low s3: brittle
High s3: ductile
Loose: compressive
Dense: dilative
Dense: low failure ea
Same strength and small volume change
at “critical state”
compression
dilation
compression
dilation
(Bardet, 1997)

14. How do we define failure?
Loose
Peak strength
(Use to find f’p) ea
Peak strength
Dense
(Use to find f’p)
Residual strength
(Use to find f’res)
f’p> f’res
(see table 4)
Want to use strength
appropriate for problem! ea

15. Consider a laboratory “direct shear” (DS) test on loose sand
failure plane
(Coduto, 1999)
sC’ > sB’ > sA’ tC tC
Test C
Test C (sC’ = P/A) f’
Test B
Construct M-C
failure envelope
to determine
f’ and c’ tB tB
Test B (sB’ = P/A)
Shear Stress (t = V/A)
Shear Stress (t )
Test A tA tA
Test A(sA’ = P/A)
sA’
sB’
sC’
Shear Displacement
Effective Normal Stress, s’

16. (Coduto, 1999)

17. Sensitivity – Rissa Landslide (Norway)
Occurred 1978
~0.13 square miles
7-8 million cubic yards
45 minutes
1 fatality
(Sukumaran)

18. Sensitivity, St Sensitive or “Quick” clay:
Significant loss of strength
when disturbed (remolded)
Typically marine clay/silt that has been uplifted and leached with fresh water (Scandinavia).
Leads to an unstable flocculated structure
Edge-face particle
orientation

19. Shear Strength Measurement
Laboratory Methods:
Unconfined Compression Test (UCT)
Direct Shear Test (DS)
Ring Shear Test (residual strength)
Triaxial Compression Tests
Unconsolidated-Undrained (UU) (aka Q-test)
Consolidated-Undrained (CU) (aka R-Test)
Consolidated-Undrained with Pore Pressure Meas. (aka CU-bar test)
Consolidated-Drained (CD) (aka S-Test)
Note: First letter (U or C) describes consolidation phase, second letter (U or D) describes shear phase

20. Shear Strength Measurement
Field (In-situ) Methods:
Vane Shear Test
Pocket Penetrometer
Pocket Torvane
Standard Penetration Test (SPT)
Cone Penetration Test (CPT)
Undrained shear strength (su)
Empirical correlation to f’

21. Unconfined Compression Test
Specimen tends to bulge due to end constraint. A0
s 3 = 0 Af
s = P/A ea
Failure
plane
Trimmed Cylindrical Specimen (clay/silt) t
Loading Frame (CRS)
su = undrained shear strength
qu = unconfined compressive strength su
s3 = 0
qu = s1f s

22. (Bardet)

23. Triaxial Compression Testu
Control of s3, s1, and u
(effective stress)

24. Unconsolidated-Undrained (UU) Test (Q-Test)
Used for undrained shear strength (su) of fine-grained soils
Minimizing sample disturbance is critical
Relatively inexpensive because test is fast (~2 hours)
Better test than UCT (unconfined compression) because we can simulate field stress
Step 1: Sample Trimming
Step 2: Set up in triaxial cell

25. Unconsolidated-Undrained (UU) Test (Q-Test)
Step 3: Apply isotropic confining stress (s3 = s1)
no drainage allowed (so no consolidation occurs)
we do not know effective stress (but we know total stress)
confining stress selected to simulate stress from depth where sample taken
typically s3 (psi) = 0.75(z) (this assumes a total unit weight of ~100 pcf)
s 3
u= ?
z (ft)
g ~100 pcf
s (psi)~ 0.75(z)

26. Unconsolidated-Undrained (UU) Test (Q-Test)
Step 4: Apply deviator stress (s1) and monitor stress-strain until failure
typical axial strain rate is 1% per minute
typically go to about 15%-25% axial strain
Step 5: Calculate undrained shear strength (su)
s 1f
u= ?
shear
stress (t)
s 3 su
Test 1
Test 2 s3
s1f s3
s1f
total normal stress (s)

27. Consolidated-Undrained (CU) Test (R-Test)
Used to determine fcu
Sample is consolidated to some initial effective stress (to represent field)
Sheared with no drainage allowed
Must analyze in terms of total stress
Plot results from multiple tests to find fcu
shear
stress (t)
fcu
Test 1
Test 2 s3
s1f s3
s1f

28. Consolidated-Undrained Test with pore pressure measurements (CU-bar Test)
Used to determine c’ and f’
Sample is consolidated to some initial effective stress (to represent field)
Sheared with no drainage allowed BUT u measured with transducer
Can analyze in terms of effective stress
Plot results from multiple tests to find c’ and f’
shear
stress (t) f’ c’
Test 1
Test 2
s’3
s’1f
s’3
s’1f

29. Example of CU-bar test ….. (Coduto 13.10)

30. Vane Shear Test (Field Vane)
In-situ test for determining undrained shear strength (su)
Very common in soft clays and silts (ASTM D2573)
Typically conducted at bottom of borehole
Torque required to fail soil related to su
apply correction factors for failure mode, disturbance, rate effects, organics...
= correction factor
(Coduto Fig 13.35)
Tf = failure torque
d = vane diameter
torque rate:
1 deg per 10 sec
(Durham Geo)
(Geoengineer.org)

31. Pocket Penetrometer and Torvane
Commonly used in field on samples
At ends of Shelby tube after sampling
Side walls of test pits
Split spoon samples
“Chunk” samples
Applicable for soft to stiff clays and silts
Pocket penetetrometer estimates qu (su = qu/2)
Torvane estimates undrained shear strength (su)
Does not account for rate effects, failure mode, etc.
but good indication of strength variation with depth.
torvane
(source: ODP)
Pocket penetrometer

32. Standard Penetration Test (SPT)

33. Cone Penetration Test (CPT)