Civil Engineering Reference
In-Depth Information
5.7.2 The over-design factor and the degree of utilisation
When checking the ultimate limit state (for any of the five ultimate limit states) it may be helpful to rep-
resent the degree of safety of the system by either the
over-design factor
or the
degree of utilisation
.
These expressions are quite simply the ratio of the design resistance to the effects of the actions (ODF)
and its reciprocal (DoU).
i.e.
Over-design factor,
Γ =
R
E
d
d
Degree of utilisation,
∆=
E
R
d
d
Example 5.6:
GEO limit state: forward sliding
Return to the retaining wall of Example
5.3.
Assume now that the wall is founded upon
a clay of characteristic undrained strength 75 kPa. Check the safety of the wall against
forward sliding by checking the GEO limit state of Eurocode 7 for all three design
approaches.
Solution:
(a) Design Approach 1
1.
Combination 1: (A1
+
M1
+
R1)
(iii)
Design Material Properties:
75
75
1
c
;
=
=
=
75
kPa
u d
γ
cu
(iii)
Design Actions and effect of actions:
The active and surcharge thrusts are unfavourable.
Active Thrust: P
a;d
=
66.5
×
γ
G
=
66.5
×
1.35
=
89.8 kN/m
Surcharge Thrust: P
q:d
=
15.1
×
γ
Q
=
15.1
×
1.5
=
22.7 kN/m
Total Sliding force, E
d
=
89.8
+
22.7
=
112.5 kN/m
(iii)
Design Resistance:
R
=
c
× = × =
B
75 2
150
kN/m since
(
γ
=
1 0
.
,
see Table
5 1
. )
d
u d
;
Rh
150
112 5
Γ =
=
1 33
.
.
1
1 33
∆=
=
75
%
.
2.
Combination 2: (A2
+
M2
+
R1)
75
75
1 4
c
=
=
=
53 6
.
kPa
u d
;
γ
.
cu
P
=
66 5
.
× =
γ
66 5 1 0
.
×
.
=
66 5
.
kN/m
a d
;
G
P
15 1
.
15 1 1 3
.
.
19 6
.
kN/m
=
× =
γ
×
=
q d
:
Q
