SOIL STRENGTH AND SOIL FORCES

1. CHAPTER THREE
SOIL STRENGTH AND
SOIL FORCES

2. 3.1 INTRODUCTION
 In terms of Soil Mechanics, there are two
groups of soil properties:
 3.1.1 Internal properties:
 i) Friction in the soil is a factor and depends
on the normal load.
 It is between soil and soil and is called angle
of shearing resistance or internal friction ( )
 ii) The force of adherence between the
particles of the soil - cohesion.
 The cohesion(C) is the attraction of soil
properties for each other.

3. External Soil Properties
 i) Friction between soil and an external
material e.g. a moldboard plough.
 This is called external friction or soil metal
friction. The symbol is
 ii) Adhesion: The attraction between soil
and some other material e.g. plough.
 The symbol is Ca. These four properties
control the soil behaviour as a mechanical
entity.

4. Measurement of Soil Mechanical
Properties
3.2.1 External Properties: In the soil surface, put a slider.
Apply a normal force, N and apply a shear force, F.

5. Measurement of External Soil
Properties Contd.
If the soil moisture content is increased, another set of points are
obtained as shown in the second line. There is now adhesion
between the metal plate and the soil. In this general case,
where: is N/A = normal stress
  
 
Ca tan


6. Measurement of Internal Soil Properties

7. MICKLETHWAITE EQUATION

8. SHEAR STRENGTH
Shear Strength is defined as the maximum resistance of the soil to
shearing stress under any given conditions

9. Triaxial Compression Test
Apparatus
 This is the most common method used to determine
soil shear strength.
 A soil specimen is extruded from a 37.5 mm
diameter cutting tube, capped top and bottom and
covered with a rubber membrane to minimize loss of
moisture.
 The sample is placed in position (see diagram) and
pressure head is applied to the water in the
transparent cylinder surrounding the specimen.
 This pressure is applied to the soil and is called
lateral pressure or cell pressure and is termed
minimum principal stress.
 A vertical load is now applied to the sample at a

10. Triaxial Compression Test
Apparatus Contd.
 The vertically applied stress at failure, called
the deviatoric stress, may be measured on
the proving ring, and when added to the cell
pressure gives the maximum principal stress.
 With the maximum ( 1) and minimum
principal stresses (3) be drawn.
 The procedure is repeated with different cell
pressures( 3 ) and a series of Mohr circles
drawn.
 These circles have a common tangent called
the Mohr envelope which defines the


11. Diagrams of the Triaxial Test

12. Example
 The following data refer to three triaxial tests
performed on representative undisturbed
samples of a soil.
 Test Cell pressure (kN/m2 ) Axial load dial reading
 (divisions) at failure
 1 50 66
 2 150 106
 3 250 147
 Load dial calibration factor is 1.4 N per division.
Each sample is 75 mm long and 37.5 mm diameter.
Find by graphical means the value of apparent
cohesion and the degree of internal friction.

13. Solution
 x
mm m
37 5
4
1104 0 001104
2
2 2
.
.
 
Cross-sectional area of sample =
Additional vertical pressure =
Cell pressure(kN/m2 ) Additional vertical pressure (kN/m2 ) Total vertical
pressure
50 84 134
150 134 284
250 186 436
14
0 001104 1000
1268
. Re ,
.
. Re
N x ading kN
x
x ading




14. Graphical Soln and Analytical
Solution

15. Analytical Solution Concluded

16. Types of Triaxial Test
 The types of Triaxial Test that we can do
depend on the drainage conditions of the
soils to be tested.

 i) Undrained Test: There is no dissipation
of pore pressure during the application of
of cell pressure or deviatoric stress.
 No hole or connection is at the bottom plate
of the soil cylinder.
 The pore pressure is then difficult to
dissipate.

17. Undrained Test Contd.
 This is called the quick undrained test and
involves the total stress analysis.
 This applies to fast soil failures where there
is insufficient time for drainage to occur eg.
tillage and rapid construction of a large
embankment.
 It is also the standard test for bearing
capacity of foundation which is a short term
case, since after initial loading, the soil will
consolidate and gain in strength.

18. (ii) Consolidated-Undrained Test or
Consolidated Slow Quick Test:
 Drainage is permitted during the application of the
cell pressure .
 Pore pressure that builds up during the application
of cell pressure is allowed to drain.
 The sample becomes fully consolidated. No
drainage is allowed during the application of the
deviatoric stress.
 The effective stress analysis applies and may apply
to a building which has consolidated as drainage
has taken place and the building fails eg. the failure
of footings or foundations with suddenly applied
load.

19. iii) Drained Test
 Drainage is permitted during the application
of the cell pressure and the deviatoric stress.
 It is a slow test as the pore pressures are
allowed to dissipate.
 This is called the slow test and the effective
stress analysis applies.
 This pattern applies to the soil slope failure
which is slow.

20. Drained Test Concluded.
 For excavated or natural slopes that are
exposed for long periods of time, it is
necessary to use the drained strength
because of unloading produced by erosion
or excavation eventually reduces the
effective stress on the soil and thereby the
strength.
 Drained test is used for long term values of
shear strength e.g. if a motorway cutting is
being envisaged.
 The Triaxial Test holds the key to the
Mohr-Coulomb Soil Mechanics
Knowledge.

21. Role of Soil Pores

22. Example and Solution

23. Solution Contd.

24. ACTIVE AND PASSIVE RANKINE
STATES
Consider a soil element, with bulk density, . The shear stress
on the soil element exerted by a mass of soil on top of the
element ( i.e. vertical stress), , where Z is the distance
from the soil surface to the element.

z
V 
 

25. ACTIVE AND PASSIVE RANKINE
STATES CONTD.
 There is also a horizontal shear ( ) on the
element. can be located on the Mohr-
Coulomb diagram as shown below. As
values of the angle of internal friction and
cohesion (C) are known, the Coulomb line
can be drawn. To then proceed to draw the
Mohr circle, knowing ’s location, we need
to start drawing it leftwards or rightwards
depending on whether or is the major
principal stress.
h

v

v

v
 h


26. ACTIVE AND PASSIVE RANKINE
STATES CONTD
Note: At the point of soil failure, the Mohr circle will
just touch the Coulomb line at a tangent point.

27. ACTIVE AND PASSIVE RANKINE
STATES CONTD
 If is the major principal stress ( i..e.
> ), the circle will go leftwards as
= . being larger than means that the major
force causing failure on the soil element is
the vertical stress and then the soil above
the element is referred to as being ACTIVE
(See figure above) because it was doing the
work. If is larger like the bulldozer blade,
then the soil above the soil element acts as if
it is dormant waiting for a horizontal stress to
shear it. The soil is then said to be
PASSIVE.
v
 v

h
 v

1
 h

h


28. SUMMARY
If = 1 > , then = 3 and the soil is said to
be ACTIVE
If = 1 > , then = 3 and the soil is said to be
PASSIVE
NOTE: Soil normally fails at an angle to the
plane on which the major principal stress acts.

 h
 h

 h 
 v
 v

 
 
45 2
/

29. Active Rankine State

30. Active Rankine State Contd.

31. Passive Rankine State

32. Active and Passive Earth Forces
Consider a simple case of a retaining wall with a vertical back
supporting a cohesionless soil with a horizontal surface (see
figure below).
Let the angle of shearing resistance of the soil be and the
unit weight, be of a constant value.
The vertical stress acting at a point Z below the top of the wall
is equal to .
If the wall is allowed to yield i.e. move forward slightly, the soil
is able to expand and there will be an immediate reduction in
the value of lateral pressure at depth Z, but if the wall is
pushed slightly into the soil then the soil will tend to be
compressed and there will be an increase in the value of the
lateral pressure.


Z


33. Active and Passive Earth Forces
Contd.
The above indicates that there are two possible modes of failure
that can occur within the soil mass. If we assume that the value of
the vertical pressure at depth Z remains unchanged at Z during
these operations, then the minimum and maximum values of
lateral earth pressure that will be achieved can be obtained from
the Mohr circle diagram below.


34. Active and Passive Earth Forces
Contd.
The lateral pressure can reduce to a minimum value at
which the stress circle is tangential to the strength
envelope of the soil; this minimum value is known as
the active earth pressure.
The lateral pressure can rise to a maximum value (with
the stress circle again tangential to the strength
envelope) known as the passive earth pressure. It can
be seen from the Mohr circle diagram that the vertical
pressure due to the soil weight ( Z) is a major principal
stress when considering active pressure and that when
considering passive pressure, the vertical pressure due
to the soil weight ( Z) is a minor principal stress.



35. Active and Passive Earth Forces
Contd.

36. Active Earth Forces

37. Active Earth Forces Contd.

38. Passive Earth Forces

39. Passive Earth Forces Contd.

40. Point of Acting of Pp
For weighty and cohesive soil, take moments, Mo thus: Pr .
2/3 Z + Pc. Z/2 = (Pr + Pc)L . From this equation, L which
is the vertical distance, the force acts, can be obtained.

41. Effect of Friction
If friction exists on the wall, then the Rankine equations
break down. Wall friction produces shear stress i.e.
horizontal and vertical planes are no longer major and
minor principal planes.
In the active case, the friction at wall prevents the free sliding of the
soil down the wall and in the case of the passive one, the friction at
wall prevents free sliding of soil up the wall.

42. Effect of Friction Contd.
No Friction No Friction
Active Case Passive Case
In the presence of wall friction, for the active soil pressure, the
analysis can be done using the Coulomb Trial Wedge
Analysis. For the Passive Earth Pressures with wall friction,
especially for tillage and traction, the Log. Spiral or the
General Soil Mechanics Equation can be used.

43. COULOMB-TRIAL WEDGE ANALYSIS
- For active cases only.

44. COULOMB-TRIAL WEDGE ANALYSIS
Contd.

45. COULOMB-TRIAL WEDGE ANALYSIS
Contd.

47. COULOMB-TRIAL WEDGE ANALYSIS
Contd.

48. Case Where Cohesion and Adhesion are
Present

49. Case Where Cohesion and Adhesion are
Present Contd.

50. THE GENERAL SOIL MECHANICS
EQUATION

51. Example
 Determine the change in magnitude of
the passive force acting on a blade, 3
m long and 0.25 m deep as the value of
the soil/blade friction increased from
zero to 50 . The soil bulk density is 15
kN/m3; the angle of internal friction is
100 and the soil cohesion is 3.4 kN/m2
and the surcharge is 1 kN/m2 . Take
rake angle as 800.

52. Solution

53. Solution Contd.