Shear Strength of Soil Shear strength in soils Introduction Definitions Mohr-Coulomb criterion Introduction Lab tests for getting the shear strength Direct shear test Introduction Procedure & calculation Critical void ratio

1. CE 240
Soil Mechanics & Foundations
Lecture 11.1
Shear Strength of Soil I
(Das, Ch. 11)

2. • Shear strength in soils
– Introduction
– Definitions
• Mohr-Coulomb criterion
– Introduction
– Lab tests for getting the shear strength
• Direct shear test
– Introduction
– Procedure & calculation
– Critical void ratio
Class Outlines

3. Shear Strength
• The strength of a material is the
greatest stress it can sustain;
• So that the unit of strength is the same
as stress (Pa in SI unit system);

4. Significance of Shear Strength
• The safety of any geotechnical structure
is dependent on the strength of the soil;
• If the soil fails, the structure founded on
it can collapse.
• Understanding shear strength is the
basis to analyze soil stability problems
like:
– lateral pressure on earth retaining
structures (Chs. 12, 13),
– slope stability (Ch. 14), and
– bearing capacity (Ch. 15).

5. Shear Failure in Soils

6. Slope Failure in Soils
Failure due to inadequate
strength at shear interface

7. Static: Transcosna Grain Elevator
Canada (Oct. 18, 1913)
West side of foundation sank 24-ft

8. Bearing Capacity Failure

9. Dynamic: Foundation failure by liquefaction
after the 1964 Niigata Earthquake. (USGS)

10. Dynamic: Lateral Spreading caused by the 1906 San
Francisco Earthquake at Moss Landing, CA
(USGS Professional Paper 993)

11. Shear Strength in Soils
• The shear strength of a soil is its resistance to
shearing stresses.
• It is a measure of the soil resistance to
deformation by continuous displacement of its
individual soil particles
• Shear strength in soils depends primarily on
interactions between particles
• Shear failure occurs when the stresses between
the particles are such that they slide or roll past
each other

12. Shear Strength in Soils
(cont.)
• Soil derives its shear strength from two
sources:
– Cohesion between particles (stress
independent component)
• Cementation between sand grains
• Electrostatic attraction between clay particles
– Frictional resistance between particles (stress
dependent component)

13. Shear Strength of Soils: Cohesion
Cohesion (C), is a measure of the forces that
cement particles of soils
Dry sand with no cementation
Dry sand with some cementation
Soft clay
Stiff clay

14. Shear Strength of Soils; Internal
Friction
Internal Friction angle (φ), is the measure of the
shear strength of soils due to friction

15. Mohr-Coulomb Failure Criteria
• This theory states that a material fails
because of a critical combination of
normal stress and shear stress, and not
from their either maximum normal or
shear stress alone.

16. Mohr-Coulomb Failure
Criterion
Shear
Strength,S
φ = φ′
C′
Normal Stress, σn = σ′ = γ h

17. ' '
tan (11.2)
tan ' (11.3)
f n n
f n n
c c
c c
τ σ φ µσ
τ σ φ µ σ
= + = +
′ ′ ′= + = +
f
where
shear strength
c = cohesion; c =effective cohesion
φ = angle of internal friction; φ = effective angle of internal friction
= coefficient of friction; ' = effective coefficient of frictio
τ
µ µ
=
′
′
n.

18. µ=tanφ’
0.51-0.58
0.58-0.70
0.70-0.78
0.58-0.70
0.70-0.84
0.84-1.00
0.67-1.11
0.49-0.70

19. Mohr-Coulomb shear failure criterion
σ1
σ1
σ3
σ3σn
τf
σ1
σ3 σ
τ
2θ
τf = c’ + µ’σn’
c’
φ
φ
Failed Zone
(σ, τ)
σff

21. From trigonometric equalities we have

23. Way 1: Increase the normal
stress in one direction
σ1
σ1 major principle stress
σn
τf
σ3 σ3
Minor principle stress
Confining stress

24. Way 2: directly apply the shear stress
Consider the following situation:
- A normal stress is applied
vertically and held constant
- A shear stress is then applied
until failure
Shear
stress τ
Normal stress σn
Normal stress σn

25. Determination of Shear Strength Parameters
The shear strength parameters of a soil are
determined in the lab primarily with two types
of tests: 1) Direct Shear Test; and 2) Triaxial
Shear Test.
(1) (2)
Soil
Normal stress σn
Shear stress σ3
σ3
σ1

26. Direct Shear Test
• Direct shear test is Quick and Inexpensive
• Shortcoming is that it fails the soil on a
designated plane which may not be the
weakest one
• Used to determine the shear strength of
both cohesive as well as non-cohesive
soils
• ASTM D 3080

27. Direct Shear Test (cont.)
• The test equipment consists
of a metal box in which the
soil specimen is placed
• The box is split horizontally
into two halves
• Vertical force (normal
stress) is applied through a
metal platen
• Shear force is applied by
moving one half of the box
relative to the other to
cause failure in the soil
specimen
Soil
Normal stress σn
Shear stress σ3

28. Direct Shear Test

29. Direct Shear Test

31. Direct Shear Test

32. Direct Shear Test Data
Shearstress
Residual Strength
Peak Strength

33. Direct Shear Test Data:
Volume change
∆H

34. Direct Shear Test: Procedure
1.Measure inner side or diameter of shear box and find the
area
2.Make sure top and bottom halves of shear box are in
contact and fixed together.
3.Weigh out 150 g of sand.
4.Place the soil in three layers in the mold using the funnel.
Compact the soil with 20 blows per layer.
5.Place cover on top of sand
6.Place shear box in machine.
7.Apply normal force. The weights to use for the three runs
are
2 kg, 4 kg, and 6 kg if the load is applied through a lever arm,
or 10 kg, 20 kg, and 30 kg, if the load is applied directly.
Note: Lever arm loading ratio 1:10 (2kg weight = 20 kg)

35. Direct Shear Test: Procedure
8. Start the motor with selected speed (0.1 in/min) so that
the rate of shearing is at a selected constant rate
9. Take the horizontal displacement gauge, vertical
displacement gage and shear load gage readings.
Record the readings on the data sheet.
10. Continue taking readings until the horizontal shear load
peaks and then falls, or the horizontal displacement
reaches 15% of the diameter.

36. Calculations
1. Determine the dry
unit weight, γd
2. Calculate the void
ratio, e
3. Calculate the normal
stress & shear
stress
1−=
d
wGs
e
γ
γ
A
V
A
N
== τσ ;

37. Figures
Peak Stress
s3
s2
s1
Shearstress,s
N3 = 30 kg
N2 = 20 kg
N1 = 10 kg
Horizontal displacement, ∆H

38. Figures (cont)
ShearStress,s(psf)
C′
φ
(σ1,s1)
(σ3,s3)
(σ2,s2)
Normal Stress σ, psf

39. Figures (cont)
Verticaldisplacement
Horizontal displacement

40. Reading Assignment:
Das, Ch. 11
HW: Problem 11.1