Civil Engineering Reference
In-Depth Information
Fig. 7.15
Symbols used in Coulomb's formula.
β
=
angle of inclination of surface of retained soil to the horizontal
φ
′
=
angle of shearing resistance.
=
2
γ
, where H
=
total height of the wall. This thrust is assumed to act at angle
δ
to the normal to the wall (see Fig.
7.15)
.
It is of interest to note that Coulomb's expression for K
a
reduces to the Rankine formula when
ψ
=
90°
and when
δ
=
β
, i.e.
Total active thrust
K H
a
′
cos
β
−
(cos
2
β
−
cos
2
φ
)
K
a
=
cos
β
×
′
cos
β
+
(cos
2
β
−
cos
2
φ
)
and further reduces to
1
1
−
sin
sin
φ
φ
′
K
a
=
′
+
when
ψ
=
90° and when
δ
=
0°.
Example 7.5:
Coulomb active thrust
=
′
Solve Example
7.1
using the Coulomb formula. Assume that
δ
.
1
2
Solution:
Coulomb's formula for K
a
is:
2
−
′
cosec
ψ
sin(
ψ φ
)
K
a
=
′
+
′
−
sin(
φ
δ
) sin(
φ
β
)
sin(
ψ δ
+ +
)
sin(
ψ β
−
)
