Geoscience Reference
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and lengths. However, the effect is most pronounced in the case of direct sliding
with horizontal combined with vertical accelerations.
For direct sliding mechanism, the coefficient of yield acceleration of
reinforced soil block is determined as (Ling and Leshchinsky, 1998)
W
B
C
ds
tan f
þ
W
A
tan
ð
f
2
a
Þ
L
k
hy
¼ð
2
k
v
Þ
ð
Þ
1
13
W
B
þ
W
A
L
where
1
2
C
ds
tan dtan f
L
¼
ð
14
Þ
1
2
tan dtan
ð
f
2
a
Þ
W
A
and W
B
are the weights of reinforced soil and potential sliding backfill soil, d
is the interwedge friction angle (equal to relevant values such as for f/2). ais
the angle of inclination of the most critical failure plane, which may be
determined numerically or using the expression of Richards and Elms (1992). For
the design where only horizontal acceleration is used,
the permanent
displacement limit is straightforward, employing
Fig. 6
.
A comparison is given in Table 1 for a 6-m vertical wall designed statically
and seismically with k
h
¼
4 and 0.65. The lengths against tieback and direct
sliding, and the total reinforcement force, are given. The analysis showed that
equilibrium against direct sliding is not attainable for k
h
¼
0
:
65 and is
excessively long for internal stability. However, by allowing a displacement of
6.4 cm, a design can be conducted using k
h
¼
0
:
0
:
4
:
The required lengths of the
geosynthetic become practically acceptable.
4 PERMANENT DISPLACEMENT UNDER VERTICAL
ACCELERATION
The vertical acceleration may be required for the design of earth structures, such
as in Orange County, California. Under a combined vertical and horizontal
acceleration, the equations to determine permanent displacement require k
hy
and
Table 1
Design of Vertical Wall
ð
f
¼
35
8;
g
¼
18 kN
=
m
3
;
C
ds
¼
0
:
8
;
k
ho
¼
0
:
65
Þ
Tieback
length (m)
Direct sliding
length (m)
Total reinforcement
force (kN/m)
Permanent
displacement (cm)
k
h
0.0
3.1
0.7
88
—
0.4
6.9
6.6
188
6.4
0.65
22.3
Infinity
346
0.0
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