Shear strength parameters

2. Shear strength
 Shear strength is a term used in soil mechanics to describe the magnitude of
the shear stress that a soil can sustain.
 The shear resistance of soil is a result of friction and interlocking of particles,
and possibly cementation or bonding at particle contacts.
 Shear failure occurs when the stresses B/W the particles are such that they
slide or roll past each other

3. Types of shear failure
 General shear failure
 Local shear failure
 Punching shear failure

4. shear failure

5. Shear Strength in Soils parameters
 Soil derives its shear strength from two sources:
 Cohesion (C)
 Frictional resistance (ϕ)

6. Cohesion (C)
 The attraction between the molecules of the same material is called cohesion.
 Cohesion (C), is a measure of the forces that cement particles of soils
 Dry sand is cohesion less.
 Addition of water in the dry and induces, a little cohesion in it.
 Clayey soil has maximum cohesion
 The cohesion of soil depends on:
 1. Fineness of clay particles
 2.Amount of clay
 3.Water content of soil

7. Internal Friction(ϕ)
Internal friction
 The frictional resistance between the individual soil particles at their contact
point is known as internal friction.
Angle of Internal friction : Ф
 It represents the frictional resistance between the soil particles, which is
directly proportional to the normal stress

8. Cohesion less soil (Ф- Soil)
 These are the soils which do not have cohesion.
(C=0)
 These soils derive the shear strength from the
intergranular friction.
 These soils are also called frictional soils.
 Examples: Sands and gravels.
 Equation for strength
is, S= σ . Tan Ф

9. 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.
 The relationship between normal stress and shear is given as
 s = c¢ +s ¢ tanf ¢
 angle of internal friction
 c cohesion
 s shear strength

10. Shear
Strength,S
Normal Stress, n =  =  h
C
 = 
Mohr-Coulomb Failure
Criterion

11. Mohr-Coulomb Failure Criterion
’f
f
’
Shear strength consists of two
components: cohesive and frictional.

'
c’
’f tan ’
c’
 f  c''f tan'

12. Mohr-Coulomb Failure Criterion
(in terms of total stresses)

f is the maximum shear stress the soil can take without
failure, under normal stress of .

c
 f  c  tan

f


13. f is the maximum shear stress the soil can take without
failure, under normal effective stress of ’.
Mohr-Coulomb Failure Criterion
(in terms of effective stresses)

’
c’
 f  c' 'tan'
’
Effective
cohesion Effective
friction angle
f
’
 '
  u
u = pore water
pressure

14. 4
MOHR CIRCLE OF STRESS

’
'
' '
1 3
2
m
1 3
2
'
'
'
3
 1
'

PP = Pole w.r.t.plane

’
’
’ ’
' 

Major principal stress: σ1
Minor principal stress: σ3
Mean principal stress: σm
Maximum shear stress: τmax
max ’ 
2 2
   
 
2

2
2
 1 3
  1 3

Equation of Mohr Circle
Compare it’s formulation with equation of circle

15. MOHR CIRCLE AND FAILURE ENVALOPE
Failure surface
X X
Y
Y
Soil elements at different locations
Y ~ stable
X ~ failure


’
  ctan
f

16. MOHR CIRCLE AND FAILURE ENVALOPE
Y h
h
Mohr circle before
external loading
v
 +
Soil element does not fail if the Mohr circleis
contained within the envelope
GL

v
v


17. MOHR CIRCLE AND FAILURE ENVALOPE
Y
h
GL
As loading progresses, Mohr
circle becomes larger…
.. and finally failure occurs
when Mohr circle touches
the envelope

v
h
v

18. MOHR CIRCLE IN TERMS OF TOTAL AND
FFECTIVE STRESSES
X
h’
X
u
u
= +
h’
u
v
v’ h
X
v v’
h

 or ’
If X is on
failure
Failure envelope in
terms of total stresses

c’ c
Failure envelope in terms
of effective stresses
’
Effective Stresses Total Stresses

19. MOHR-COULOMB FAILURE CRITERION WITH
MOHR CIRCLE OF STRESS