Civil Engineering Reference
In-Depth Information
Active pressure at top of wall,
−
′
P
=
γ
h K
c K
=
(
20 3 75 0 44
×
.
×
.
)
−
(
10 1 78
×
.
)
=
15 2
.
kPa
a
e
a
ac
0
Active pressure at base of wall,
−
′
P
=
γ
(
H h K
+
)
c K
=
20 5
(
+
3 75 0 44 17 8
.
)
.
−
.
=
59 2
.
kPa
a
e
a
ac
5
The pressure diagram on the back of the wall is shown in Fig.
7.23c
. Remembering
that these are the values of pressure acting normal to the wall, the maximum horizontal
thrust will be the area of the diagram.
15 2 59 2
2
.
+
.
Maximum horizontal thrust
=
× =
5
186
kN/m run of wall
.
7.8.2 Line load
The lateral thrust acting on the back of the wall as a result of a line load surcharge is best estimated by
plastic analysis.
It is possible to use a Boussinesq analysis (see Chapter
3
) to determine the vertical stress increments
due to the surface load and then to use these values in the plastic analysis combined with the design
With the Culmann line construction the weight of the line load, W
L
is simply added to the trial wedges
affected by it (Fig.
7.24)
. The Culmann line is first constructed as before, ignoring the line load. On this
basis the failure plane would be BC and P
a
would have a value 'ed' to some force scale.
Slip occurring on BC
1
and all planes further from the wall will be due to the wedge weight plus W
L
. For
plane BC
1
, set off (W
1
+
W
L
) from X to
d
1
and continue the construction of the Culmann line as before
(i.e. for every trial wedge to the right of plane BC
1
, add W
L
to its weight). The Culmann line jumps from
e
1
to
e
1
and then continues to follow a similar curve.
The wall thrust is again determined from the maximum ed value by drawing a tangent, the maximum
value of ed being in this case
e
1 1
If W
L
is located far enough back from the wall it may be that ed is still
′
′
′
′
greater than
e
1 1
in this case W
L
is taken as having no effect on the wall.
Fig. 7.24
Culmann line construction for a line load.
