Retaining walls - Piling Engineering - page 240

Having established the general stability of a site, it is then necessary to consider
the need to satisfy the equilibrium of the vertical, horizontal and rotational forces on
the wall.
Two basic concepts have been used in calculating the stability of walls, namely the
so-called 'free earth' and 'fixed earth' methods. In the 'free earth' method the stability
of a wall is considered without making the assumption that the deflected form of the
wall is controlled by fixity in the ground. In the 'fixed earth' method it is assumed
that the rotation of the toe of a wall is constrained by fixity in the soil mass and a
consequence of this can be a reduction of moment in propped walls, but an increase
in the embedment length. However, for such a wall there is no relevant mechanism
that may be used to analyze the condition of rotation about the prop, and the method
relies on a pure empirical approach.
In a cantilever wall, equilibrium is not possible without involving a reaction force at
the wall toe and in practice the wall is lengthened after the basic analysis, in order to
provide this. Thus the analysis in this case involves 'fixed earth', but here a mechanism
of failure can be postulated to accord with the rotation of the wall at some point below
the excavated level.
The idealized and simplified soil pressure diagrams associated with the analysis of
cantilever and propped walls are as shown in Figures 6.18 and 6.19. In the initial stage
of calculation this is simplified further (Figure 6.20).
The procedure adopted in the calculation of retaining wall stability is in general
to progressively increase the embedment of the wall, analyzing the disturbing and
restoring moments, until a state of stability is reached, at which point the equilib-
rium of horizontal forces determines the value of the reaction R (in the case of a
Figure 6.18 Cantilever wall: idealized pressure diagram for rotation about point O.
Figure 6.19 Simplified pressure diagram at rotational failure.