Civil Engineering Reference
In-Depth Information
Table 24.1
Calculation of earth pressures (see Example 24.1)
(a) Active side
σ
z
(kPa)
σ
a
(kPa)
Depth (m)
Soil
σ
z
(kPa)
u (kPa)
σ
a
(kPa)
0
Sand
80
0
80
27
27
2
Sand
120
0
120
40
40
7
Sand
220
50
170
57
107
7
Clay
220
140
10
Clay
280
200
(b) Passive side
σ
z
(kPa)
σ
p
(kPa)
Depth (m)
Soil
σ
z
(kPa)
u (kPa)
σ
p
(kPa)
2
Water
0
0
0
0
0
5
Water
30
30
0
0
30
5
Sand
30
30
0
0
30
7
Sand
70
50
20
60
110
7
Clay
70
150
10
Clay
130
210
the line of action of a force is through the centre of area of each pressure distribution
diagram.
The best way to avoid making mistakes is to set up a table and draw the distribution
of earth pressure with depth, as shown in Table 24.1 in Example 24.1 below. This gives
calculations for the horizontal stresses on a wall bedded into sand over clay as shown
in Fig. 24.17(a). The calculations use Eqs. (24.3) and (24.4) for the stresses in the
sand and Eqs. (24.9) and (24.10) for the stresses in the clay: in the free water the
horizontal and vertical total stresses are equal. Notice how the pore pressures come
into the calculations in the drained sand but not in the undrained clay. There is a step
in the earth pressures at the sand-clay junction, so it is necessary to calculate separately
the stresses just in the sand and just in the clay.
Overall, a wall is considered to be stable if the forces and moments are in equilibrium
and this is examined by resolving horizontally and taking moments about a convenient
point. In most analyses the variable (or unknown) is the depth of embedment, which
is increased until a suitable margin of safety is achieved. Selection of factors of safety
for a retaining wall design is very difficult and will be considered in a later section: for
the present I will simply consider the overall stability of a retaining wall at the point
of collapse, such that the horizontal stresses are everywhere the full active and passive
pressures. It is necessary to consider propped or anchored walls, cantilever walls and
gravity walls separately.
(a) Anchored or propped walls
Figure 24.12 shows a simple propped wall with depth of embedment
d
. The active
and passive pressures are as shown and from these the magnitudes
P
and depths
z
