CHAPTER THREE

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CHAPTER THREE

• SOIL STRENGTH AND SOIL FORCES

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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.

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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.

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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.
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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  
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Measurement of Internal Soil Properties
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MICKLETHWAITE EQUATION
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SHEAR STRENGTH
Shear Strength is defined as the maximum
resistance of the soil to shearing stress under
any given conditions
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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
  constant rate of strain until the sample fails.

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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 Coulomb equation.

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Diagrams of the Triaxial Test
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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.

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Solution
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  
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Graphical Soln and Analytical Solution
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Analytical Solution Concluded
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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.
  

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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.

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(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.

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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.

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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.

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Role of Soil Pores
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Example and Solution
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Solution Contd.
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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.
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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.

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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.
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ACTIVE AND PASSIVE RANKINE STATES CONTD

• If is the major principal stress ( i..e.
  
• gt ), 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.

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SUMMARY
If 1 gt , then 3
and the soil is said to be ACTIVE
If 1 gt , 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.
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Active Rankine State
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Active Rankine State Contd.
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Passive Rankine State
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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
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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.
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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.  
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Active and Passive Earth Forces Contd.
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Active Earth Forces
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Active Earth Forces Contd.
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Passive Earth Forces
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Passive Earth Forces Contd.
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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.
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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.
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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.
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COULOMB-TRIAL WEDGE ANALYSIS - For active cases
only.
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COULOMB-TRIAL WEDGE ANALYSIS Contd.
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COULOMB-TRIAL WEDGE ANALYSIS Contd.
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COULOMB-TRIAL WEDGE ANALYSIS Contd.
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Case Where Cohesion and Adhesion are Present
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Case Where Cohesion and Adhesion are Present
Contd.
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THE GENERAL SOIL MECHANICS EQUATION
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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.

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Solution
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Solution Contd.
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