Civil Engineering Reference
In-Depth Information
δ
is the angle of shearing resistance between the soil and the wall and
U
is
the force due to pore pressures acting over the base area
B
. The wall cannot overturn
provided that the normal stress at the upstream edge remains positive (i.e. in compres-
sion) and it can be shown by simple statics that this requires that the resultant
R
passes
through the middle third of the base, as shown in Fig. 24.14(b). The resulting trian-
gular distribution of normal stress shown in Fig. 21.14(c) implies that the maximum
stress at the toe is given by
where
2
W
B
q
=
(24.19)
The possibility of failure of the foundation due to excessive bearing pressure is really
a problem of bearing capacity and is discussed in Chapter 22.
24.10 Soil strength and factors for design of
retaining walls
So far I have described analyses for earth pressures, prop or anchor forces and over-
all stability of retaining walls using a friction angle
φ
or an undrained strength
s
u
.
As discussed in Sec. 24.4, if the wall is supporting an excavation and the soil is ini-
tially undrained it will become less safe with time and the drained case is most critical.
However, if the wall is supporting a fill and the soil is initially undrained it will become
safer with time and the undrained case is most critical. The question now is should
the critical state strengths or the peak strengths be used to calculate the ultimate limit
state and what factors should be applied.
Design of a retaining wall is something like a problem in slope stability where there
must be an adequate margin against ultimate failure states and something like a prob-
lem in bearing capacity where it is necessary to limit movements. There are a number
of standards, codes and advice notes which deal with selection of design parameters
and factors for design of retaining walls and many of these give different designs. I am
not going to deal with these; the issues are far too complicated for this simple book
and you will have to consult topics specializing in retaining walls for details. Instead
I will describe some simple and logical procedures.
Firstly you should assume the wall is strong and stiff and demonstrate that it is in
equilibrium with active and passive pressures calculated from the critical state strength
and the worst credible groundwater and free water conditions. You can add partial
factors to the critical state strength and water pressures to account for any uncertainties
you may have in your estimates of them. This is the procedure for slope stability
analyses described in Chapter 21.
Next you should repeat the stability analyses with active and passive pressures cal-
culated from the peak strength with a load factor to limit ground movements. The
load factor will probably be in the region of 2 to 3, depending on whether you took
worst credible, moderately conservative or average values of measured peak strengths.
This is the procedure described in Chapter 22 for design of shallow foundations.
You will then have to calculate the loads on props or anchors and shear forces
and bending moments in the wall. A major difficulty here is that the distributions
