Retaining walls - Piling Engineering - page 241

Figure 6.20 Anchored or propped wall: idealized pressure diagram for rotation about point O.
cantilever wall) or the reaction T (in the case of an anchored or propped wall). This
procedure establishes the penetration of the wall below excavation that represents an
incipient failure condition. However, this is of passing interest in terms of the required
wall penetration for stability and is used, for reasons to be described later, only in the
establishment of bending moments in the wall.
The procedure is then continued until some desired ratio is achieved between the
restoring moment acting on the wall and the disturbing moment. This ratio is fre-
quently described as a factor of safety, but for the reason that at this stage in design
the wall length has not finally been determined in the case of a cantilever, and because
there are other ways in which this factor can be expressed in other methods of analysis,
the term 'factor of safety' is not entirely satisfactory and hence it should be regarded
rather as a method related 'rotational stability factor'.
In practice this factor, F p , can conveniently be introduced by simply dividing the
passive earth pressure at all levels by F p , but of course the water pressures acting on
the passive side of the wall are not so treated.
Once the notional rotation point has been found in the case of a cantilever under
this condition, the force R is determined, and reversing the roles of active and pas-
sive pressure, so that passive pressure appears on the active side below this point, an
additional length of wall is added to provide the balancing force R .
In the case of the anchored wall, the rotation point in the design is constrained to be
at the anchor level, and hence the length of the wall can be determined simply using
a similar factor F p applied to the passive earth pressure. Once this has been done, the
force in the prop or anchor is determined as before from the horizontal equilibrium
conditions.
When using an effective stress method of design such as is outlined above, the
values F p that are applicable to both cantilever and anchored walls are necessarily
related to the soil properties; appropriate values for F p are in the ranges shown in
Table 6.3.
There are a number of limit state equilibrium programs that can deal with cantilever
and single propped or tied retaining wall cases. Many of these have been developed by
companies 'in house' but one which is generally available with a variety of options has
been developed by British Steel and Geocentrix Limited under the name REWARD.
In addition to the normal limit state equilibrium method it has features that allow
approximate wall deflections to be calculated.