Civil Engineering Reference
In-Depth Information
than or equal to the total vertical stress (
σ
stb; d
) at the bottom of the column, or the submerged unit
weight
(
G
stb d
of the same column, i.e.
u
≤
′
)
≤
σ
or S
G
;
dst d
;
stb d
;
dst d
;
stb d
;
The EQU, GEO and STR limit states are the most likely ones to be considered for routine design. Further-
more, in the design of retaining walls and foundations it is likely that limit state GEO will be the prevalent
state for determining the size of the structural elements.
5.6 The EQU limit state
To check this limit state, the equilibrium of the structure when considered as a rigid body is assessed. The
procedure is shown in Fig.
5.10.
There are two sides of the analysis to consider represented by the large
shaded areas:
destabilising
actions and effects and
stabilising
actions and effects.
For both the destabilising and the stabilising aspects, the representative actions are combined with the
appropriate partial factors of safety to yield the design values. The analysis (typically a moment equilibrium
analysis for the EQU state) is then performed and the magnitudes of the effects of the actions are com-
pared to assess stability.
An example of this limit state is the overturning of a gravity retaining wall resting on a rigid layer, with
no contribution to stability from any adjacent soil. In the case of such a wall (e.g. Fig.
5.8a
), the
destabilis-
ing actions
are the forces tending to push the wall over (e.g. the active thrust behind wall) and the
stabilis-
ing actions
are the forces resisting the overturning (i.e. the self-weight of the wall). The effects of the
actions (both the stabilising and the destabilising) are the moments created by the actions. Thus, verifica-
tion that the limit state requirement against overturning is satisfied requires that the overturning moment
(E
dst; d
) is less than or equal to the restoring moment (E
stb; d
).
i . .
E
E
≤
dst d
;
stb d
;
The partial factors for use in the EQU limit state are listed in Eurocode 7 Part 1 Annex A, and are
reproduced in Table
5.1.
It is important to remember that the National Annex can provide alternative
values to those published in Annex A and indeed the UK National Annex publishes different material
partial factors for the EQU limit state (NA to BS EN 1997-1:2004).
Destabilising actions and effects
Stabilising actions and effects
Representative destabilising
actions, F
dst; rep
Representative stabilising
actions, F
stb; rep
Partial factors,
γ
F dst
Partial factors,
γ
F stb
Design destabilising
actions, F
dst;d
Design stabilising
actions, F
stb;d
GEOTECHNICAL ANALYSIS
Design effect of
destabilising actions, E
dst;d
Design effect of
stabilising actions, E
stb;d
Verify E
dst;d
≤ E
stb;d
Fig. 5.10
Verification of EQU limit state for stability.
