Civil Engineering Reference
In-Depth Information
It is seen therefore that for a smooth wall where
δ
=
0° the Rankine theory can be used for the evalu-
ation of passive pressure. If wall friction is mobilised then
δ
≠
0° and the coefficients of Table
7.2
should
be used (unless
δ
≤
φ
′
/3 in which case the Coulomb equation can be used directly).
7.7.2 The effect of cohesion
As has been discussed, a clay has a non-linear stress-strain relationship and its shear strength depends
upon its previous stress history. Add to this the complications of non-uniform strain patterns within a
passive resistance zone and it is obvious that any design approach must be an empirical approach based
on experimental work.
A similar equation to that of Bell can be used for passive pressure values when the effect of wall friction
and adhesion are taken into account.
The passive pressure acting normally to the wall at a depth of h can be defined as:
p
K h cK
=
γ
+
ph
p
pc
where
c
=
operating value of cohesion
K
pc
=
coeficient of passive earth pressure.
Various values of K
p
and K
pc
are given in Table
7.3
for the straightforward case of
β
=
0,
ψ
=
90°. As with
the active pressure coefficients given in Table
7.1,
they give the value of the pressure acting normally to
the wall.
An alternative to using the values set out in Table
7.3
is that of the work of Sokolovski (
1960)
, part of
which is presented in Table
7.4.
This offers a more realistic set of values than those listed in Tables
7.2
and
7.3.
The K
pc
values were obtained from the approximate relationship:
{
}
c
c
w
K
=
2
K
1
+
pc
p
This relationship has been used in the
earth pressure coefficients.xls
spreadsheet which can be used to
determine intermediate values of K
p
and K
pc
.
It should be noted that, in the case of passive earth pressure, the amount of wall movement necessary
to achieve the ultimate value of
φ
′
can be large, particularly in the case of a loose sand where one cannot
reasonably expect that more than one half the value of the ultimate passive pressures will be
developed.
Table 7.3
Values of K
p
and K
pc
for a cohesive soil for
β
=
0;
ψ
=
90°.
Values of
φ
′
Values
of c
w
/c
Coefficient
Values of
δ
0°
5°
10°
15°
20°
25°
K
p
0
All
1.0
1.2
1.4
1.7
2.1
2.5
φ
′
values
1.0
1.3
1.6
2.2
2.9
3.9
K
pc
0
0
2.0
2.2
2.4
2.6
2.8
3.1
0
2.4
2.6
2.9
3.2
3.5
3.8
1
2
0
1
2.6
2.9
3.2
3.6
4.0
4.4
φ
′
2.4
2.8
3.3
3.8
4.5
5.5
1
2
φ
′
1
2.6
2.9
3.4
3.9
4.7
5.7
