Geoscience Reference
In-Depth Information
l
c
and l
ds
are the required length to resist tieback/compound failure and
direct sliding, respectively.
t
j
is the required strength of the jth layer to ensure local stability.
K is analogous to conventional earth pressure coefficient.
In a design, it is practical to select the required length at the top layer based on L
c
and at the bottom based on the greater length of L
c
and L
ds
, whereas length of
other layers is obtained by interpolation. The construction may use a constant
length, based on the greater value of L
c
and L
ds
, for all geosynthetic layers.
To ensure global stability, where the failure surface extends from the wall
face through the reinforced soil zone and into the retained backfill soil, a
geosynthetic having allowable strength greater than or equal to that calculated
from tieback analysis is specified for each layer. Typically, at the jth layer, the
specified geosynthetic has an allowable strength, t
j-allowable
, larger than the
required strength, t
j
. It is, thus, practically required that only the bottom m layers
be designed against compound failure. That is,
X
n
X
n
t
j-allowable
$
t
j
ð
11
Þ
j
¼
1
j
¼
1
The required anchorage length of each layer, l
e,j
, is determined using t
j
or t
j-
allowable
, whichever the greater, to prevent pullout failure:
t
j
or
t
j-allowable
l
e
;
j
¼
ð
12
Þ
2
ð
1
2
k
v
Þ
s
v
;
j
C
i
tan f
where f, C
i
, s
v,j
are the internal friction angle, soil-geosynthetic interaction
coefficient, and average overburden pressure acting on the jth layer, respectively.
C
i
is expressed as the ratio of the soil -geosynthetic pullout strength to the soil
strength, i.e., tan f.
Figures 7a-c
show the required geosynthetic strength and lengths for a
vertical wall with franging from 20 to 45
under static and seismic loadings. The
analysis was conducted using the ReSlope program (Leshchinsky, 1995) on a
5-m-high wall having 20 layers of geosynthetics, and the results were normalized.
The results for direct sliding were for a coefficient C
ds
¼
8
tan f
is the interaction coefficient, which expresses the ratio of frictional strength
between soil-geosynthetic to that of soil. It is seen that an increase in the lengths
and strength of geosynthetic is required following seismic loading. A smaller f
also resulted in a longer and stronger geosynthetic. For instance, at fequal to 30
0
:
8
:
C
ds
¼
tan f
s
=
,
two times tieback length and strength may be needed when comparing static and
seismic designs at k
h
¼
8
The difference between the length of static and
seismic designs is much larger for direct sliding along the base of the wall. In fact,
small soil friction angle and large acceleration may require an excessively long
geosynthetic or may render design impossible because equilibrium is not
0
:
3
:
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