Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 537

2. The limiting values of lateral pressure occur when the wall yields away from the backfill (or
   moves toward the fill); these are known as the ‘active’ and the ‘passive’ states. The pressure
   exerted when there is no movement is called the ‘at-rest’ pressure, which is intermediate be-
   tween the active and the passive values.
   Very little yield is adequate to cause active conditions, but relatively greater movement is neces-
   sary to mobilised passive resistance.


3. The classical earth pressure theories of Rankine (1857) and Coulomb (1776) stood the test of
   time. Rankine considered the plastic equilibrium of a soil when there is stretching and compres-
   sion of the mass, and applied the relationships between the principal stresses so derived for
   determining the pressure on the wall. Coulomb considered straightaway a wall and a backfill
   and the equilibrium of the sliding wedge for deriving the total thrust on the wall. The former
   neglected wall friction, while the latter considered it.
   The distribution of pressure is considered to be triangular with depth; in the case of uniform
   surcharge, however, it will be rectangular.


4. Rankine assumes a conjugate relationship between stresses in the case of an inclined backfill
   surface.


5. There will exist a ‘tensile’ zone near the surface of a cohesive fill. The depth of this zone is given

by^2 c N

γ φ

.. and the ‘critical’ depth or the depth up to which the soil may stand unsupported is

4 c

N

γ φ

.. Tension cracks occur in the tension zone and these may cause some relief of pressure

in the active case.

6. The Coulomb wedge theory which assumes a plane rupture surface introduces significant errors
   in the estimation of passive earth resistance, although the error is small in the estimation of
   active thrust. Thus, it is generally recomemended that analysis based on curved rupture surface
   (for example, Terzaghi’s logarithmic spiral method) be used for passive resistance.


7. The Poncelet construction based on Rebhann’s condition and Poncelet rule, and the Culmann’s
   graphical approach are versatile graphical solutions to Coulomb’s wedge theory and are popu-
   larly used in view of the complexity of the analytical expressions derived by Coulomb. The charts
   and tables prepared by Caquot and Kerisel, and Jumikis are also relevant in this context.


8. The angle of wall friction will usually range between^1
   2

φ and^3

4

φ; Terzaghi recommends^2

3

F

HG

I

KJ

φ

in the absence of data.

9. The stability considerations for gravity retaining walls are:
   (a) The maximum pressure on the base should be less than the safe bearing power of the founda-
   tion soil;
   (b) no tension should develop anywhere in the wall;
   (c) the factor of safety against sliding must be adequate; and
   (d) the factor of safety against overturing must be adequate.
   The nature of yield of the wall influences the wall design very much; for example, the yield at the
   bottom of a sheeting supporting a trench causes arching-active conditions, in which the distribu-
   tion of pressure varies significantly from the active case, although the total thrust value remains
   the same.