Civil Engineering Reference
In-Depth Information
3: 12.20
×
9.55
=
116.4 kN
4: 13.25
×
9.55
=
126.5 kN
Weight of wedges:
1: 22.6
×
17.4
=
393 kN
2: 35.1
×
17.4
=
611 kN
3: 43.8
×
17.4
=
762 kN
4: 51.9
×
17.4
=
903 kN
Space and force diagrams are given in Figs
7.18b and 7.18c
.
a
=
′ ′
=
2 2
Maximum P
e d
314
kN/m
Kerisel and Absi (
1990
) published values of the horizontal components of K
a
and K
p
for a range of values
of
φ
,
β
,
δ
and
ψ
to ease calculation when using the Coulomb theory. In addition, the spreadsheet
earth
pressure coefficients.xls
is available for download, which can be used to determine the horizontal com-
ponents of K
a
and K
p
too. In this section we are concerned with the horizontal component of K
a
(i.e. K
a
The active pressure acting normally to the wall at a depth h can be defined by:
p
=
K h cK
γ
−
ah
a
ac
where
c
=
operating value of cohesion
K
ac
=
coeficient of active earth pressure.
Various values of K
a
and K
ac
are given in Table
7.1
for the straightforward case of
β
=
0 and
ψ
=
90°. Note
that, where appropriate,
φ
′
is the operating value of the angle of shearing resistance of the soil.
Intermediate values of K
a
and K
ac
can be obtained from the spreadsheet. It should be noted that the
values in both the spreadsheet and in Table
7.1
are for pressure components acting in the horizontal
direction, not at an angle
δ
to the horizontal as in the original Coulomb theory. The values in the spread-
sheet are derived from the following widely recognised formulae, which are sufficiently accurate for most
purposes:
K
a
=
Coulomb s value
'
×
cos
δ
c
c
w
K
=
2
K
1
+
ac
a
Table 7.1
Values of K
a
and K
ac
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
a
0
All
1.00
0.85
0.70
0.59
0.48
0.40
values
1.00
0.78
0.64
0.50
0.40
0.32
φ
′
K
ac
0
0
2.00
1.83
1.68
1.54
1.40
1.29
0
1
2.83
2.60
2.38
2.16
1.96
1.76
φ
′
2.45
2.10
1.82
1.55
1.32
1.15
1
2
φ
′
1
2.83
2.47
2.13
1.85
1.59
1.41
