Civil Engineering Reference
In-Depth Information
Irrespective of the earth retaining system used, two requirements must be satis-
fied: The stability of the retention system as a whole (external stability) and the
strength and stability of the retaining structure itself (internal stability).
2.2 The Development of Earth Pressure Theory
The earth pressure problem dates back to the beginning of the 18
th
century. Gau-
tier (1717) lists five areas requiring research, one of which was the dimensions of
gravity-retaining walls needed to hold back soil. A number of engineers such as
Bullet (1691), Couplet (1726, 1727, 1728), Belidor (1729), and Rondelet (1812),
appear to have worked on the problem, and published their findings. It was Cou-
lomb, in a paper read to the
Academie Royale des Sciences in Paris
on the 10
th
of
March and the 2
nd
of April 1773, who was to make the first lasting impression in
the field.
Coulomb (1776) introduced two ideas essential in soil mechanics, when he
separated the strength of materials into two components, namely cohesion and
friction. This concept introduced by Coulomb, and later refined by Terzaghi to in-
clude the effective stress concept, remains the basis of soil-strength theory today.
Coulomb also considered the case of a rigid soil mass sliding upon a shear
failure surface, which formed the basis for his equations to calculate the lateral
earth-pressure on retaining walls (Heyman 1997).
In 1808 Mayniel extended the work of Coulomb (1776) and others namely
Woltmann (1794) and Prony (1802) to give a general solution for a frictional,
non-cohesive soil, with wall friction.
Müller-Breslau (1906) expanded further on Mayniel's work to give a general
solution for a frictional cohesionless soil that allows for sloping backfill behind
frictional retaining walls. Müller-Breslau's equation took the following form:
1
2
γ
f
1
H
2
Q
a
=
(2.1)
sin
α
.cos
δ
sin
2
(
α + ϕ
). cos
δ
where,
f
1
=
2
sin(
ϕ + δ
)sin(
ϕ
-
β
)
sin
α
.sin(
α
-
δ
) 1
+
sin(
α
-
δ
)sin(
α + β
)
Figure 2.1 illustrates Müller-Breslau's solution for a frictional cohesionless soil
in active state. This solution could also be obtained for the passive state.
The previous solutions, however, were all developed in term of total stress for a
rigid soil mass that was defined on a critical discrete planar shear surface. In 1857
Rankine extended on this earth pressure theory in his paper “
On the stability of
loose earth
” by deriving a solution for a complete soil mass in a state of failure. In
his analysis, however, Rankine assumed that the resultant force on the vertical
place acts parallel to the ground surface.
