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CH_4 _lect_01_

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Geo tech 2

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									GEOTECHNICAL ENGINEERING - II
                    Engr. Nauman Ijaz




   LATERAL EARTH PRESSURE
        Chapter # 04
   UNIVERSITY OF SOUTH ASIA
LATERAL EARTH
PRESSURE
  Lateral Earth pressure is an important
  parameter for the design of bridge abutment,
  different types of retaining walls (Such as
  gravity retaining walls, cantilever walls,
  counterforts or buttresses), sheet piles and
  other retaining structures.
GRAVITY RETAINING
      WALL
CANTILEVER WALL
COUNTERFORT OR BUTTRESS
RETAINING WALL
SHEET PILES
BRIDGE ABUTMENT
LATERAL EARTH PRESSURE
  AND WALL MOVEMENT
  Lateral earth pressure are the direct
  result of horizontal stresses in the soil.
  In order to understand the lateral earth
  pressure we have to define the
  Coefficient of lateral earth pressure, K.
    COEFFICIENT OF LATERAL
     EARTH PRESSURE “K”

It is defined as the;
 “Ratio of the horizontal effective stress to the
vertical effective stress at any point in a soil.”
               K = σ’x / σ’z
K   = Coefficient of lateral earth pressure.
σ’x = Horizontal effective stresses.
σ’z = Vertical effective stresses.
     K is important because it is an indicator
     of the lateral earth pressures acting on
     retaining wall.
     For purpose of describing lateral earth
     pressures, geotechnical engineers have
     defined three important soil conditions;
1.    At – rest Condition
2.    The Active Condition
3.    Passive condition
Two classic Earth pressure theories has
been put forward in the eighteen and
nineteen centuries by Coulomb and Rankine
respectively.

 1) Rankine (1857) Earth Pressure Theory
 2) Coulomb’s(1776) Earth Pressure Theory

These two theories are still in use in their original
form and in some modified forms to calculate the
earth pressure.
Consider an element of soil at depth z
below the ground surface level (GSL) as
shown in the figure.
The vertical stress due to the self weight of
soil, σ’z (also known as overburden pressure
or gravitational stress) is given by;

               σ’z = γz
Where;
γ = unit weight of in-situ soil
Figure # (a)
Figure # (b)
When confined (as in general case
below GSL due to the pressure of
surrounding soil), this vertical
stress,(σz) will tend to cause the
expansion of soil element and in doing
so a secondary lateral pressure is
generated.
These vertical (σz) and horizontal (σx)
stresses are the major and minor
principal stresses in this particular
case respectively.
The ratio of σx to σz is termed as the co-efficient
of earth pressure at rest and denoted by Ko.
Thus;
           Ko = σx / σz = σ3 / σ1………..(a)
Ko value in general is variable and depends upon t
soil type and its history of deposition
Numerous relations have been derived for its
evaluation, but the following relationships given by
Jaky (1948) is commonly used;

      Ko = 1 – SinΦ’ under root(OCR)……(b)
Φ’  = Effective angle of internal friction.
OCR = Over-consolidation Ratio.

For normally consolidated soils, the equation(b) is
reduced to;
              Ko = 1 – SinΦ’

								
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