Geotechnical Engineering

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DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 471


Coulomb’s theory considers the soil behind the wall as a whole instead of as an element
in the soil. If a wall supporting a granular soil were not to be there, the soil will slump down to
its angle of repose or internal friction. It is therefore reasonable to assume that if the wall only
moved forward slightly a rupture plane would develop somewhere between the wall and the
surface of repose. The triangular mass of soil between this plane of failure and the back of the
wall is referred to as the ‘sliding wedge’. It is reasoned that, if the retaining wall were sud-
denly removed, the soil within the sliding wedge would slump downward. Therefore, an analy-
sis of the forces acting on the sliding wedge at incipient failure will reveal the thrust from the
lateral earth pressure which is necessary for the wall to withstand in order to hold the soil
mass in place. This is why Coulomb’s theory is also called the ‘Wedge theory’, implying the
existence of a plane repture surface. However, Coulomb recognised the possibility of the exist-
ence of a curved rupture surface, although he considered a plane surface for the sake of math-
ematical simplicity. In fact, it is now established that the assumption of a plane repture sur-
face introduces significant error in the determination of passive earth resistance, a curved
rupture surface being nearer to facts, as demonstrated by experiments.


In the course of time Coulomb’s theory underwent some alternations and new develop-
ments. The theory is very adaptable to graphical solution and the effects of wall friction and
batter are automatically allowed for. Poncelet (1840), Culmann (1866), Rebhann (1871) and
Engesser (1880) are the notable figures who contributed to further development of Coulomb’s
theory.


The significance of Coulomb’s work may be recognised best by the fact that his ideas on
earth pressure still prevail in their principal points with a few exceptions and are considered
valid even today in the design of retaining walls.


13.7.1 Assumptions


The primary assumptions in Coulomb’s wedge theory are as follows:



  1. The backfill soil is considered to be dry, homogeneous and isotropic; it is elastically
    underformable but breakable, granular material, possessing internal friction but no
    cohesion.

  2. The rupture surface is assumed to be a plane for the sake of convenience in analysis.
    It passes through the heel of the wall. It is not actually a plane, but is curved and
    this is known to Coulomb.

  3. The sliding wedge acts as a rigid body and the value of the earth thrust is obtained
    by considering its equilibrium.

  4. The position and direction of the earth thrust are assumed to be known. The thrust
    acts on the back of the wall at a point one-third of the height of the wall above the
    base of the wall and makes an angle δ, with the normal to the back face of the wall.
    This is an angle of friction between the wall and backfill soil and is usually called
    ‘wall friction’.

  5. The problem of determining the earth thrust is solved, on the basis of two-dimen-
    sional case of ‘plane strain’. This is to say that, the retaining wall is assumed to be of
    great length and all conditions of the wall and fill remain constant along the length
    of the wall. Thus, a unit length of the wall perpendicular to the plane of the paper is
    considered.

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