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Gabion Retaining Walls
62 CHAPTER 4
GABION RETAINING WALLS INTRODUCTION
The modern g a b i o n especially weirs, lies
for
groynes
in
that
stability
have a f u r t h e r ment does n o t
tive
as t h e y
date
Olivier they
(1967)
The use o f
in
the
cost
riprap
per
(about
tically
the
tipped
stone.
f i l l ,
gabion
Up t o
energy
or
subsided
level
to drop.
This
assess. gabion of
of
When f l o w
in
gabions
verified
for
various
of
move-
some
relatively
the wire of
ex-
attrac-
gabions this by
This
o r mesh
at
need r a r e l y Izbash
arises.
(1970),
in
remote
locations,
during
throughflow.
slopes
be c o n s t r u c t e d
to
dams
basket.
stability
not
over
with
consider-
but
as c o n c r e t e
more e x p e n s i v e
is
than
(about
stone
pitching
The s t a b i l i t y
considerably
volume would
better
be r e q u i r e d
for
is
than
practhat
tipped
of
stone
water. dams r e q u i r e
through
an
impermeable
where a f r e e - d r a i n i n g temporarily
a pool,
or
as e x p e n s i v e
dumped r i p r a p ) .
however,
avoids
or the
stagnant
for
water
through
structures
routing. thereby
or a s i l t
dry
a gabion
fill
occurs
A theoretical is
is
presented
is
upstream
useful.
to assist After
allowing
the
in flood
the
water
trap. relatively the
study in
core or
weir
dam u p w a t e r
flood
rockfill,
retaining
to estimate.
hydraulic
experimentally.
and s l i g h t to
yet
They
to ensure
considerably price
structures
becomes more d i f f i c u l t
of
Fortunately
and permanent
although
rockfill
flow
turn
life
dams w e r e a d v o c a t e d
c a n be u s e d t o
of water
size.
replace
are
a new l a y e r
wire.
steeper
the gabion
the form of
gabion
They
Gabion w a l l s
advantage
pressures)
stone
are f l e x i b l e
stability.
with
slopes
flowing
the water w i l l
The s t a b i l i t y
is
the
water,
weir in
they
Their
water
individual
and
linings,
rockfill.
situations,
rockfill
dissipation
1979).
releasing
the
limited
o f mass c o n c r e t e ,
fast
retain
There are
the
cofferdams
metre)
5 times in
in
rocktip
enables
times
same as t h a t
When u s e d t o membrane.
has
cubic
and even more
A gabion
for
structure,
three
or
packing.
resistant
downstream
the volume of
The f i n i s h e d
or
flat
that
by r e - s u r f a c i n g
stacked gabions
savings
half
lies
corrosion
and o t h e r s
fairly
of
structures channel
appearance.
overf1ow-throughf1ow
require
able
using
stone
gabions
be o v e r c o m e or
in
retaining
(Stephenson,
(therefore that
the appearance
have a n a t u r a l
however
concrete
of dry
of
than
earth
such as r e v e t m e n t s ,
works,
permeable
units
over
from
art
The d i s a d v a n t a g e
Although
larger
used f o r
works
dissipation
they are
of
detract
t h e now d y i n g
a later
engineering
advantage
tent
could
advantageously
and e n e r g y
the f a c t
have t h e
is
hydraulic
the
simple
stability of
the
chapter
of
to the
stability and was
63
Fig.
4.1
STABILITY
Gabion
situations
a through-flow
due t o w a s h i n g as a f i l t e r . be d e s i g n e d criteria
Note however to
resist
of
of
coverage
The e q u a t i o n s
for
the
is
of
than
stacked
as
to
can be p l a c e d
in
the the of
Fig.
gabion
is
The g a b i o n s granular
into
will
reduce
material,
intermediate
washing
that
material
but
individual
obtained
laid
(Fig. per
plane
gabions
filter
the
next
i.e.
face erosion
they
layers
act
should
using
filter
if
slopes
4.4)
area
of
the
retains
the
stability
is
the
is
permeability due t o
n o t as g r e a t
arrangement
the
is
more
as
when
economical
gabion.
applicable
t o an
subsequently.
to a slope
but
the slope
where
gabion
rocks.
unit
applies
the
has a h i g h e r
parallel
below are also
indicated
and
one l a y e r
gabions
position
90°
4.1.
underlying
on a s l o p e d d o w n s t r e a m
cloth.
gabions
developed
not applicable
qualifications
that
similar
on a h o r i z o n t a l
(The t h e o r y fore
or
in a horizontal
as g r e a t e r
of
filter
gabions
The s t a b i l i t y
thickness
forces
gabions
particles
advantage
rockfill
higher weight
stacked
body
s u c h as
piping
or a s u i t a b l e
a tipped
where
structure
away o r
The p r i n c i p l e of
with
OF G A B I O N SLOPES I N WATER
There are of
slope
taken
to a gabion as
infinitely
height
is
zero, high
finite).
layer
i.e. slope
of
finite
as f o r
a
and
there-
is
There a r e ,
weir.
however,
64
Sliding stability In o r d e r slope,
t o p r o d u c e an a n a l y t i c a l
i t i s necessary
assumed t h a t water
ence across force
is horizontal,
the gabion
Now c o n s i d e r
i s expended
the internal
where S i s t h e r e l a t i v e weight
of
tending
of water,
(d) that
t h e head
and ( e ) t h a t
forces
per unit width namely
or wab(S-1)/(1+e)
density
o f a gabion
t o cause s l i d i n g
acting
i s no
depicted
acting
vert-
horizontally.
i s t h e submerged w e i g h t ratio
of the gabion,
and w i s t h e
t h e components
down t h e s l o p e
of the forces
should
be l e s s
by t h e f r i c t i o n
( 1 ) and ( 2 ) i n F i g . than
t h e components
coefficient
t a n φ:
S-1 S-1 vhr-r a b s i n Θ + w i a b c o s Θ S t a n φ ( ν / τ — a b s i n Θ - ww i a b s i n Θ )
(4.1)
tan φ - tan 0
,1+e
Values o f i ( 1 + e ) / ( S - 1 )
tained
differ-
there
on t h e gabions
t h e submerged w e i g h t
of the stone, e is the void
to the slope m u l t i p l i e d
value of f r i c t i o n
be
(c) the
water.
For e q u i l i b r i u m
perpendicular
It will
are full
i n d r a g on t h e s t o n e ,
downwards, and t h e seepage f o r c e a c t i n g
Note t h a t w a b ( S - 1 ) ( n - 1 )
4.1
is zero,
on a
on t h e s l o p e .
i n F i g . 4 . 1 . There a r e two body f o r c e s ,
specific
o f gabions
assumptions.
(b) the voids
on t h e e x p o s e d d o w n s t r e a m f a c e
between gabions
ically
for the stability
t o make a number o f s i m p l i f y i n g
(a) the flow
pressure
solution
versus
(4.2)
Θ are plotted
φ may be f a i r l y
by w i r e mesh r e d u c e s
in Fig. 4.2 f o r φ = 35°.
low f o r r o c k f i l l ,
the friction
angle
the fact
t o about
this
that
Whereas
t h e rock
is
this con-
value.
Overturning The seepage f o r c e
also
tends
to overturn
the gabion about
the toe ( A ) . For
equilibrium,
w a b ( |+ j
tan 0)cos
Rearranging,
i-ς-τ- ^
Θ ύ w ^ - a b ( |- | b/a - t a n 0 1 + (b/a)tan
Values o f i ( 1 + e ) / ( S - 1 ) various
values
of b/a.
from t h i s
tan 0)cos
0
(4.3)
(4.4)
0
equation were l i k e w i s e
plotted
on F i g . 4 . 2 f o r
65
stone relative void ratio - e
SYMBOLS:
density - s
a/sine
(Λ
\
τ» 5 3 0
\
\
S.
\
V
20
Ν
—/* NO'.
Sä. NT
10
s
Nix! i
\
^
^
S*
\ \
0.2
Fig.
OA
4 . 2 S t a b i l i t y
0.6
of gabions
0.8
on a slope
«(lit)
(φ= 35
c
Assessment of results It
will
be observed f r o m F i g . 4 . 2 t h a t
criterion is sliding, b/a,
overturning
Laboratory (S-1) for
tests
at failure
this
butting
is that
that
i s independent
failure
f o r b/a greater
and t h i s
0.7 the limiting
of b / a . For smaller
values o f
0.7 the value o f i(1+e)/ condition.
was n o t p o s s i b l e
The reason
owing t o one gabion
I t was assumed f o r t h e a n a l y s i s
I t w o u l d be s a f e condition
than
andoverturning
by s l i d i n g
o n e down t h e s l o p e . force.
than
criterion.
between t h e s l i d i n g
complete
on t h e n e x t
however,
indicate
lies
was n o i n t e r - g a b i o n limiting
and t h e slope
is the limiting
f o r b/a greater
t o adopt
is likely
c r i t e r i o n as
t o be t h e l i m i t i n g
one f o r long
s l o p e s w h e r e t h e r e w o u l d have t o b e c o n s i d e r a b l e movement down t h e s l o p e to
transmit
restraining
For small
slope angles
accurate as there assess i . as f o l l o w s
thrust
is flow
that
the sliding
there
i n order
up t h e s l o p e .
approaching
the horizontal
upwards as w e l l
t h e above t h e o r y
as h o r i z o n t a l l y
I t becomes n e c e s s a r y t o a n a l y s e t h e s t r u c t u r e f o r a gabion on a h o r i z o n t a l p l a n e .
becomes i n -
and i t i s d i f f i c u l t using
basic
to
principles
66
Fig
4.3 Gabion
STABILITY
the stability
conditions
of a single
such as F i g . 4 . 3 .
stream of t h e gabion as
plane
OF GABIONS ON HORIZONTAL PLANES I N WATER
Consider lified
on a h o r i z o n t a l
is zero,
gabion
on a h o r i z o n t a l
plane,
Here i t
i s assumed t h a t
the water depth
and t h a t
uplift
and t h e i n t e r n a l
water
under
simpdown-
surface are
depicted.
Sliding Consider
the external
der f o r the gabion
= (wTTë
ab
+
(Note t h a t
t o be s a f e a g a i n s t
Μ
S i m p l i f y i n g , £ <;
π ? 2
and body f o r c e s
S
y b
a
^
e
in this
on t h e g a b i o n
s l i d i n g , we m u s t
(Fig.4.3).
"
1
In o r -
have
'w ^ T ) t an Φ
for simplicity
yQ elsewhere
acting
·
tan φ
5 () 4
(4.6)
we u s e y h e r e a n d i n t h e f o l l o w i n g
section
in place of
chapter).
Overturning In o r d e r have
f o r the gabion
t o be s a f e a g a i n s t
overturning
about
t h e t o e A , we m u s t
67
Simplifying,^
Equs.
4.6
gabions
(4.8)
and 4 . 8 were f o u n d
even f o r
The e q u a t i o n s various
relatively
4.6
high
and 4 . 8 w i l l
downstream water should
STABILITY
OF STACKED GABIONS
A logical
of
is
stack
the gabions
that
the
slope,
gabions, stability
so t h e
individual
4.4
in
fact
as w i l l of
overall
blocks
a horizontal
Fig.
and
For
Stacked
depths use f o r
relatively
arrangement
of
gabions
each o t h e r
in question the
the
(up t o
limiting 50% o f
analysing
equilibrium
the
gabion
of
upstream
depth).
structures
with
deep downstream w a t e r
steeper
at
improves the angle
to
resist
a batter the
however,
of
structure the
up t h e w a l l . be u s e d t o
gabions
with
the overall
forces
soil The
against
the
following.
should
The p r e v i o u s
check
water
stability
as a w h o l e
structure
(or
(Fig. 4.4).
the greater
be s e e n f r o m t h e a n a l y s i s
stability
base c o u l d
predict
the
I N WATER
the w a l l - l i k e
making
be o f
to
anew.
t h e m on t o p o f
above any one
and o v e r t u r n i n g individual
be a n a l y s e d
and e f f i c i e n t
to
tailwater
thus
depths.
situation
ssures)
by e x p e r i m e n t
reduces
for
stability.
weight
sliding
stability Note the
single
of
the
however
steeper
be c h e c k e d as w e l l
theory
pre-
as
gabions
the for on
68
Sliding of individual blocks From F i g . 4 . 4 i t w i l l the f r i c t i o n for
due t o s e l f
be o b s e r v e d weight
that
the lateral
and weight
water
o f t h e gabions
force
i s r e s i s t e d by
above,
less
uplift,
so
equilibrium;
. ^ r uS+e w ι a b -, [w a b ^
-1+e /
η · Rearranging,
The r e l a t i o n s h i p values also
2
2
a b t a n Ox S+e,b tan Θ 2 ~ " FTärTÖ — ä ' "
+
1+(b/a)tan ( b ) 2a ) + t an
between
be a t l e a s t
.φ
n
Ο , 0 t a n Φ
i(1+e)/(S+e)
o f b / a , and φ = 3 5 ° .
2
- b η7 . Γ ^
λ
w
\
9)n
(
(4
,« * \ ( 4 . 1 0 η) and Ο i s p l o t t e d
Note t h a t
t a n 35° f o r t h i s
·
the friction
relationship
in F i g . 4.5 f o r various
coefficient
on t h e base
should
to hold.
Overturning stability of individual blocks Consider For
t h e o v e r t u r n i n g moments a b o u t t h e t o e Ά '
o f a gabion
(Fig. 4.4).
equilibrium; 3
, -a ,S+e b S+e/b , w a b Λ j - w a b ^ - ^ - ^j^i^-tan
Rparranaina Rearranging,
This
i i
1 +e
^
relationship
< ^
b
+
2
and f o r l a r g e r
2
than about
2
b a> . b 2b „ ^—) + w î - ^ - y - ^ 0n
(2 2 b / 23 a ) t a n (H2b /3a )
is also plotted
observed f o r b/a less ing,
/ a2
2
„ θ
Q
j ]) 2
4
in F i g . 4.5 f o r various 0.7 the individual
b/a they f a i l
,,χ (4.11)
Λ
blocks
b/a values. will
fail
It will
be
by o v e r t u r n -
by s l i d i n g .
EMBANKMENT LOAD
If
there
i s an uncontained
fill
material
force
on t h e g a b i o n s .
I t is often
arily
to retain
(granular
sures
little,
a fill
tion will co-incides
stability.
fully
active
w i t h minimum l a t e r a l o f gabions
retaining walls,
thickness
pressure
has an added a d v a n t a g e
ensure that
The b u l k w e i g h t crete
or cohesive)
i f any, groundwater
The g a b i o n w a l l
The w e i g h t
soil
a gabion wall
and t h e p o r o s i t y
i t will
exert a
is erected
prim-
o f the gabions e n -
build up. in that
i t is flexible.
conditions
Outward
are developed.
This
deflec-
condition
p r e s s u r e on t h e w a l l .
adds t o t h e o v e r a l l
on a c c o u n t
and a r e designed
behind the gabions,
t h e case t h a t
of their
cost,
slope
have t o be k e p t
t o a c t in bending, gabions
of a battered
gabion wall
stability.
rely
i s taken
con-
t o a minimum
on t h e i r partly
Whereas
weight f o r
by t h e s o i l
mass,
ί
d.
Fig. thus
4.6
Gabion
improving
Various lecting ive
(but
lateral
the
retaining frictional
arrangements
the
self
weight
uneconomic), soil
pressures
U s i n g wedge t h e o r y , for
the active
cohesive
fill
gabion
of
the wall
then
bulk
retaining for
the following
on t h e Coulomb
unit
arrangements
resistance.
for
horizontal of
wall
Tilted
walls
nearly
are depicted
vertical
theory
walls
in
which
may b e e m p l o y e d
to
Fig. is
4.6.
Neg-
conservat-
estimate
the
wall. (Capper,
pressure weight
at
1969)
derived
any d e p t h ,
Wg ( R e f e r
to
h,
Fig.
the following
below 4.7
the
for
expression
surface
symbols):
of
a non-
71
WW
Fig.
4.7
Embankment
f i l l
against
retaining
wall
2
sin (0-(i))
W sh
(4.13) sin
2
For most θ is
+
0
structures
less
friction
5 ΐ η
ι η$ ( θ + 6 ) { 1 + // 1 ^ ^ Φ | : [ Φ - β | } ^ / sin(0+6)sin(e-B)
than
or
angle
the
equal
δ = 0,
surface to
90°
is
horizontal
it
is
i.e.
reasonable
so t h e e x p r e s s i o n
3 = 0 ,
and
if
and c o n s e r v a t i v e
simplifies
the wall
angle
t o assume
the
to
2
W $h s i n ( 0 - 0 ) p
If
~ sTn
0(sin
θ + sin
the wall
is
W sh ( 1
sin
p
-
(1 + s i n
φ)
vertical
(4.14)
2
0 = 90°
and
φ) (4.15)
φ)
K W h a s
where Κ
a
Κ
= (1 s i n φ ) / ( 1 + s i n φ) = 0.3 f o r s a n d . a is termed the a c t i v e pressure c o e f f i c i e n t . It
vertical is
to
movement of
soil
reduce the
the wall
pressure. the
lateral
coefficient the
fully
The e f f e c t pressure becomes
developed
of
permitting
significantly. approximately
resistance
of
0.5 the
is
the
ratio
of
outward d e f l e c t i o n For
instance
and f o r soil,
for
large
termed
no
lateral of
the
wall
outward
inward
the
to
movement
passive
resis-
72
tance,
can
result
Allowing
for
a t e an a c t i v e
in a c o e f f i c i e n t
cohesion
pressure
c of
at
as
the
high
soil,
any d e p t h
as
the
3.
t h e o r y was m o d i f i e d
h on a v e r t i c a l
wall
with
by B e l l
to
no f r i c t i o n
indicas
f o l 1ows:
(4.16)
This h h
c c
equation
indicates
= 2c/W / K ~ , w h i c h i s s a i s z e r o , so t h a t t h e
Ρ = ! K W (Η -
wall
is
of
friction
plays
superimposed
the
factors
impossible. active
It
thrust
stress
should
on t h e w a l l
be a s s u m e d
on t h e w a l l
that
down
the
to
pressure
above
becomes
(4.17)
relatively
statics the
are
tensile
L
Where w a l l there
or
2
h )
a b
or
a negative
of
an
loads
important,
system needs safety
with
important
part,
above
top
the
to
the
simple
to
if
the wall
the w a l l ,
equations
be a n a l y s e d
respect
or
of
slopes
or
significantly
the weight
a b o v e do n o t
graphically
overturning
or
suffice.
numerically
and s l i d i n g
of
of
The
to
the
the
determine
retaining
wal 1 . Coulomb d e v e l o p e d it
is
assumed
Trial
that
a method
failure
wedges a r e a n a l y s e d
Many c o n f i g u r a t i o n s a retaining about
sliding the
wall
a point out
of
the
t o e and w i t h Methods
(Taylor,
log
spiral
the
radius of
A slice
of
slices.
Each
weight)
and c o m p u t e r circles. circle
of
the
unit
imaginary on a l l
programs Fig. for
4.8
about
is
the the
along a f a i l u r e
arc
to
the
the
lowest
the
wall.
occur
t o p may
for
rotate
e m b a n k m e n t may f a i l passing
embankment
to
find
by
through face.
the most
critical
have been p r o p o s e d ,
stability
ratio
of
i.e.
resistance.
formed,
curve
of
heel
t o e as w o u l d
at
circles
the w a l l ,
analysis
factor
of
of
to
safety.
the f r i c t i o n
the a c t u a l l y
is
e.g. find
The
plus
co-
developed
fric-
considered.
favour with is
geotechnical
divided
into
summated v e c t o r i a l l y . an
the
the
thus
behind
least
a sloping
the f a i l u r e
The o b j e c t with
ideal
illustrates
analysis
for
circle
arc
is
slip
strength
slices
provide
plane
to
failure
through
somewhere above
slip
is
soil
or anchored
Similarly
arc.
thickness in
braced
slip
of
surface with
analysing
shapes
respect
analysis
the
rotation
a circular
with
on a p l a n e
toe.
for
c a n be d e v e l o p e d
and s e l f
slip
Various
and c e n t r e safety
One m e t h o d o f
a slip
of
o f wedges
by r o t a t i o n
A cut
the
A circular
centre
simply
fail
tilted.
toe.
1948).
or
hesion which tion.
not
have been e v o l v e d
one
factor
would occur
up t h a n
the
analysis
to determine
will
which
higher
of
method o f
an embankment
by t h e m e t h o d o f
engineers slices
and t h e
the method forces
The p r o c e d u r e
analysis
of
slope with
slices.
is
Taylor
is
a large forces (1948)
of
(external
laborious
number
of
on s l i c e s published
in a
73
t r i a l
centre
/
WY^"/^
Ι
/
\
1
^
—
^
WT Γ
χ
3
,
N
A \
r.
factor
ET
^ s h e a r
Fig.
4.8
Slip c i r c l e analysis by m e t h o d o f slices
set
of
out
drainage
stability
Where
for
is
seepage
in
the
effective
soil
the
pressure
total
(Chapter should are
for
analysis
gabion
of
simple
a
n
F(
^
n
component
component
of
t
safety =
of
weight
retained
cases
of
F
s 3
embankment
embankment
s-lope
slopes
with-
forces.
there
be a l l o w e d
curves
normal
of
6).
stresses
similarly
determined
rather
minus
Soil
through
stability
than
the water
properties,
be o b t a i n e d
with
aid
the
of
embankment
analysis. total
in
terms
triaxial
angle of
is
stresses.
pressure,
namely,
and w a t e r
Analysis
which of
effective
obtained
on
in
soil
and
of
stress
is
net
cohesion,
The s o i l
laboratory
should
terms
from a flow
friction
stresses.
tests
these
accurate
The e f f e c t i v e is
internal
compression
pressures,
more
properties
samples
of
soi 1. If
an e m b a n k m e n t
stability
i)
ii)
cases
During
or
the
soil
be
high.
which
likely need
to
immediately will
Immediately Water
is
not
after
pressures
to
construction
consolidated
drawdown
will
inundated
be c o n s i d e r e d .
after
have
be
cause
of
saturated,
The most
of
reverse
level flow
there
important
are
the
At
pore-water
adjacent and
low
to
various
are:
an embankment.
much and
the water
high
or
this
pressure
an
effective
time will
embankment. soil
stresses.
74 iii)
Under e x t e r n a l bankment
if
considered
l o a d and s t e a d y
high in
superimposed
the
seepage. loads
the
normal
life
and seepage a r e
During
likely
these
of
the
em-
should
be
analysis.
Anchored embankments To i m p r o v e into
the
exposed
the
embankment. rockface
ling
rocks
this
but
type of
resistant,
retaining
walls
stabilization
w i r e mesh t o
could also
avert
of
the
it
is
this
nature
face.
a major
possible
This
slide.
is
is
to
anchor
the
wall
the protection
primarily
Rock a n c h o r
to
bolts
of
an
catch
are
fal-
used
for
anchoring. can a l s o
reinforcing.
reinforcing
of
Slope
by t y i n g
it
Gabion w a l l s embedded
stability
strips
be a n c h o r e d
If
the
into
embankment
may b e l a i d
high-friction-grip
in
t h e embankment w i t h is
the f i l l
built
up w i t h
and t i e d
and l o w - s t r e t c h
to
tension
ground
anchors
the gabion w a l l ,
the
gabions.
member
is
A
or then
corrosion
required.
FOOTINGS
Vertical ings,
loads
designed
ment.
to
deflection,
from the
pores
of
The b e a r i n g cohesion
and
internal
footing.
such as t r i a x i a l Pressures the
load
is
tact
is
to
underlying
to
reduce of
contact
soils
yield,
are
foundation pressures complex,
material
via
foot-
and m i n i m i z e
and
and c o n s o l i d a t i o n
settle-
in addition
as w a t e r
to
is
expelled
soil. of
soil
friction
The s t r e n g t h compression
Thus
foundation twice
the
plastic
is of
the f o o t i n g ,
spread.
equal
load
also the
dependent
soil
of
soil
the
or extrapolated
vertical
the footing
the
content
to
depth
safe the
width.
is
Not o n l y
but
also
and t h e
from f i e l d
plate
the contact
therefore
and most d e f l e c t i o n
the
tests
loaded
as
footing
within
pressures place
tests.
surface
pressure
takes
the
bearing
from the
the
flexibility
from laboratory
under a uniformly
10% o f It
load, soil
and d i s t a n c e
pressure
about
face which are o f most c o n c e r n ,
of
may b e d e t e r m i n e d
reduce with
reduces
on many f a c t o r s .
decide
the water
tests
under a f o o t i n g
on an e l a s t i c depth
there
the
of
the
to
characteristics
capacity
d e p t h and w i d t h the
transmitted
spread
The s e t t l e m e n t
elastic
of
are
at
in
a
the
the
con-
upper
strata. Failure ure
conditions
surface.
under
The u l t i m a t e
Terzaghi
in
Ρ
+ iW bN + W dN s w s q
u
= cN
c
where c is
the following
the cohesion,
a foundation bearing
form,
may be c a l c u l a t e d
capacity
of
a long
assuming
footing
t o w h i c h m u s t be a p p l i e d
a shear
was e x p r e s s e d
a factor
of
failby
safety.
(4.18) b the
breadth
and d t h e d e p t h o f
founding.
The Ν
factors
75
are functions
TABLE
of
bearing
capacity
Ν /2
_
φ
Ν _c_
0 15° 30°
5.7 9 18
Ν
W
0 0 3
For a f i r s t
TABLE
angle
as
indicated
by T a b l e 4 . 1 .
4.1
Terzaghi
ings
the f r i c t i o n
coefficients
g
1.0 3 8
approximation,
on d i f f e r e n t
types
of
the
soils
typical is
surface
tabulated
bearing
with
capacity
impunity
in
for
Table
wide
foot-
4.2.
4.2
Typical safe soil bearing ( R e f . BS C o d e o f P r a c t i c e
capacities CP101, 1963)
2
kN/m S o f t c l a y s and s i l t s S t i f f and sandy c l a y s Loose sand d r y submerged Compact sand o r l o o s e g r a d e d Compacted g r a v e l - s a n d
sand
mixture
kN/m
2
= 0.01
kg/cm
The p r e s s u r e s will
be u n i f o r m a n d l i n e a r
The p r e s s u r e s sand w i l l
The g r e a t e s t soil
the centre
will
where shear
settle
a slight
edges o f tual
4.9 f o r
will
occur. at soil
footing
the
the
loaded
there
be a t
uniformly.
cohesive
a rigid
under a f l e x i b l e
since
will
resistance
conditions
100 400 200 100 400 200 600 300 2000 4000 10000
ft)
(see F i g .
consequently
failure
On a h i g h l y
ton/sq
due to a u n i f o r m l y
be s i m i l a r ,
less
rock
to to to to to to to to to to to
footing
on an e l a s t i c
pressure
distributions
foundation under
foot-
soils).
settlement
near
then
= 0.01
immediately
i n g s on d i f f e r e n t
less
2
dry submerged
dry submerged
Shale and s o f t s a n d s t o n e L i m e s t o n e and hard s e d i m e n t a r y Sound i g n e o u s r o c k (1
50 200 100 50 200 100 400 200 1000 3000
There w i l l pressure If
the
though.
footing
on
cohesion-
transmission
of
load.
footing
resistance
be h i g h e r
were founded
to
than below
on a
cohesion-
compression
at
the
edges
surface
level
result.
be a r e s i s t a n c e
stresses
footing
A rigid
be a h i g h
here w i l l
edges would
under a s e m i - f 1 e x i b l e
flexible
c a n be no l a t e r a l
the edges
there will
and t h e
perfectly
developed
rockfill
to
settlement
there will
footing
will
at
be h i g h .
be b e t w e e n
the The
the
ac-
two
76 Uniformly
distributed
load
f oo t i η g
[^contact pressure Elastic
b .
foundation
1 !
11 ^
settlement
c.
Non cohesive foundation
Cohesive
Rigid Fig.
Fig.
foundation
4.9
Pressure 1 oad
4.10
distribution
Pressure lateral
f.
Flexible
footings under
distribution and
vertical
a
under load
footings
uniformly
a
1
rigid
distributed
footing
with
77 cases,
depending
which mesh
is
If
there
is
of
lateral
use
lateral
the w a l l ,
the w a l l .
on an e l a s t i c
ing weight
to
to y i e l d
assumed
soil
footing
that
the
edges o f
the
the
soil
tends
to
wall
contact
the
in
upthrust
are
edge.
hand t h e
4.10b.
compress
the outer under
self
and
sliding toe
the footing
4.10.
The
to
Two
the downward
t h e moment due t o
toe.
the of
of
a rigid in F i g .
pressure
act-
the
and e c c e n t r i c
The e q u a t i o n s
be s u b t r a c t e d
implying
the
from s t a t i c s .
upthrust
the
to
tension,
zero
wall
are
water
solved
uplift.
pressure
assuming a t r i a n g u l a r pressure
material
Fig.
at
the pressure
4.10a
pressures
soil
and o u t w a r d
will
foundations
is
distribut-
section.
since
the
under a r i g i d
The p r e s s u r e s the
say
the
backfill,
illustrated
and w a t e r
negative
foundation in
total
to
In a d d i t i o n
near
from which must
loaded
like
shape as
load
gabion
the d i s t r i b u t i o n
due t o t h e
and one e q u a t i n g
repeated
of
load,
distribution
the
bending
such as w i t h
transmitted
b a s e may be c a l c u l a t e d
about,
is
and amount o f
footing
load.
pressures
pressure
soil
pressure
footing
the
cause o v e r t u r n i n g
pressures,
be m o r e
Fig.
of
outside
one e q u a t i n g
lateral
cohesionless
in
to
be t r a p e z o i d a l
base w i d t h
will
the
l o a d on t h e w a l l ,
of
On t h e o t h e r
be as
tend
and t h e e x e r c i s e
unknown
the of
as a v e r t i c a l
at
The c o n t a c t
both
resulting
footing
yield. will
is
toe and heel
In a real
as w e l l
pressures
the f i l l
t h e moment o f
there
ion w i t h
at
effect
transfer
on a r e t a i n i n g
established;
plus
the
either
rigid
of
base w i l l
are
overturning weight
of
of
Reinforcing
t h e r e may be d o w n w a r d f r i c t i o n
The r e s u l t
vertical pressure
flexibility
lateral
thrust
are magnified.
equations
in
The t h r u s t s
pressures
footing
If
of
a concentration
weight
relative
can a c c o m o d a t e .
therefore
be e c c e n t r i c . with
on t h e
the footing
under
the
distribution
soil
at
footing
in
the edges w i l l
edges
to
ensure
the
soil
as
base
a
will
cohesive
increase
that
under
t h e edges
the
remains
piane. Under a f l e x i b l e relative loaded
rigidity
the f o o t i n g
as
in gabions
sures If
there
upwards
may t h e r e f o r e will
pressure
the f o o t i n g .
yield
assist
in
is
saturation
or
in
strength.
keep t h e w a t e r
Chapter
Thus
thereby
be o f
distribution
will
be c o n t r o l l e d
under a very
flexible
reducing
l o a d and t h e e x t e n d e d
little
distributing
use. the
the
footing
by
The use o f w i r e load outwards
the
the
highly toe
reinforcing
thereby
reducing
such pres-
capacities
under water of
situation,
tipping
table
seepage In
the
upward
case of
down and a v o i d
into
the
seepage,
piping
or
foundation, drainage
strength
t h e r e may be a
should
be
provided
deterioration
(see
6).
Footings
the
the
considerably.
deterioration to
of
edges w i l l
of
footing
sediments
require often
even causing
rockfill
in.
c a n be a n t i c i p a t e d
at
special
very
scour.
consideration.
low,
but
In
loose
the
D r e d g i n g may b e w o r t h w h i l e a reasonable
depth.
flow
beds, if
Not
only
of water
the
silt
a harder
Alternatively
are
the
a l s o may
bearing
aggravate
may b e d i s p l a c e d foundation
piling
may be
by
material required
78
Fig.
4.11
Wire
in deep s i l t s
basket
where
high
loads
are
to
be t a k e n w i t h
little
settlement.
WIRE STRENGTH
The w i r e
diameter
and r o c k f i l l
loads
ditions
respect
ssure
with
Then t h e in
total
the
to
the
outward
gabion),
force like
b a s k e t may be e s t i m a t e d
basket.
rockfill
Κ = (1 -sin
an a r r a n g e m e n t
a wide
gabion
i m p o s e d on t h e
= KSwh/(1+e)where
stacked (i.e.
for
in
It
the
(J>)/(1+sin
on a u n i t in Fig.
is
reasonable
gabion,
i.e.
φ) and h i s
width
4.4 with
of
from the
t o assume a c t i v e
horizontal depth
basket
in
hydraulic
below the F i g . 4.11
the diaphragms
if
and s i d e s
£ ^t
this
to
where f
the d i r e c t i o n
the force is
it
is
neglected
is
2
2
pre-
surface.
1-sin φ S a . , TWÔ- + w ι a b 1 + s i n φ 1+e 2
Equate
con-
rockfill
the wire
* \ ( 4 . 1 9n )
Λ
per
unit
stress,
perpendicular
to
width t
of wire
the wire
the f l o w .
(top
diameter
Thus
and b o t t o m ) and
the wire
k is
2 x 2
cos
45°
t h e mesh s p a c i n g
diameter
is
given
by
the
i
79
equation
, *
=
/wak /a 1 - s i n φ S , . . χ ( + 1b ) A f c o s 4 5 ° 2 πΤΓηφ ü ?
Where t h e r e ance
a r e superimposed
should also
be r e q u i r e d
loads
these
b e made f o r r u s t i n g ,
in conjunction
with
(Λ
οη\
· 2 0)( 4 should
be a l l o w e d
f o r in (4.19).
and f o r heavy pressures
a gabion
facing
steel
Allow-
t i e b a r s may
(see Chapter 3 ) .
EXAMPLE
Calculate fill
such as a t a i l i n g s
a flow is
t h e safe angle
The embankment 1 0 0 mm s t o n e ,
dam w i t h
an angle
3
o f water
eliminated
of a battered
o f 0.1 m /s/m of wall
by d r a i n s . height
Calculate
i s 5 m.
factor
to retain
of internal
friction
across
the surface
the freeboard
Assume g a b i o n s
Κ = 3 for rockfill
Friction
gabion wall
height
a
cohesionless
o f 2 5 ° . There
but subsurface t o ensure
no o v e r t o p p i n g .
1 m high χ 1.5 m wide f i l l e d
and η = 0 . 3 5and S = 2 . 6 f o r r o c k f i l l
ings
f i l l .
on r o c k f i l l
base
i)
Bulk unit weight of saturated fill = ( 1 - n ) w S + n w
Overturning moment about toe\ f r o m 2
W.sin (0-0)h
M1 =
sin 0(sin
= 0.5.
(4.14)
due t o thrust
x (h/2) χ (h/3)
θ + sin φ]
2
2
=
20000 s i n ( 0 - 2 5 ° ) χ 1 2 5 / 6 2 sin 0(sin Θ + s i n 25°)
Stabilizing
M2
moment o f g a b i o n s
Equating Θ
d u e t o w e i g h t Wa
= 5 χ 1.5 χ 0 . 6 5 χ 9800 χ 2 . 6 χ ( 2 . 5 / t a n = 124000(2.5/tan
Mi a n d M2 a n d s o l v i n g
i i i ) Sliding force on gabions 2
Θ +0.75)
Θ + 0.75)
= 81°
20000 s i n ( 0 - 2 5 ° )
χ 25/2
with
and t a i l -
= 0 . 6 5χ 9800 χ 2 . 6 + 0 . 3 5 χ 9800
ii)
is
seepage
f o r Θ by t r i a l ,
F
x
= 20000 N / m
(Fig. 4.12)
3
Resisting
force:
Assume t h e w e i g h t
o f t h e gabions
acts
down o n a g a b i o n
foot-
ing .
Friction
resistance
F 2 = 0 . 5 χ 5 χ 1.5 χ 0 . 6 5χ 9800 χ 2 . 6 = 62000
Equating
Fi a n d F2 a n d s o l v i n g
f o rΘ,
Θ = 63°.
A lower angle would demonstration
be s e l e c t e d
to allow
a factor
of safety,
say 45° f o r
purposes.
Top water depth
Depth a t c r e s t
of tailings
= y
c
=
3
2
; / g
8
ΓΓΤ χ Q 35?
Assuming a slope o f 1 / 1 , then upstream face
=
°*
20
m
i s 0.75 m back,
(2.21) anddepth
0.75 m
back ; 3Kb/d .*.
= 3 χ 3 χ 0.75/0.1
y = 4.1
= 67.5
χ 0 . 2 = 0.82 m
so u s e a 1 m h i g h g a b i o n
(Fig. 2.4)
retaining
wall.
Sliding stability of top gabion under water pressure
Z
=
^
2
=
0
. 5 5 < ^ i t a n *
(4.6)
_ 2 χ 2 . 6 χ 1/0.82 - 1 1 + 0.54 =
3.47
Overturning stability of top gabion
^0.55
(4.8)
χ 2 . 6 χ 1/0.82 -~2 1+0.54
2.21
The t o p g a b i o n
is therefore
safe as long as t h e f i l l
is level
with
i t s base.
81 REFERENCES Capper, P.L. and C a s s i e , W . F . , 1969. The M e c h a n i c s o f E n g i n e e r i n g S o i l s , 5 t h E d . , S p o n , L o n d o n , 309 p p . I z b a s h , S.V. and K h a l d r e , Kh. Y u . , 1970. H y d r a u l i c s o f R i v e r Channel C l o s u r e , T r a n s i . C a i r n s , G . L . , B u t t e r w o r t h s , L o n d o n , 174 p p . O l i v i e r , H., 1967. Through and o v e r f l o w r o c k f i l l dams, P r o c , I n s t . C i v i l Engrs., London, March: 433-471. Stephenson, D., 1979. S t a b i l i t y o f g a b i o n w e i r s , W a t e r P o w e r a n d Dam C o n s t r u c t i o n , IPC P r e s s , A u g . T a y l o r , D.W., 1948. F u n d a m e n t a l s o f S o i l M e c h a n i c s , J . W i l e y & S o n s , NY, 700 p p . T e r z a g h i , Κ., 1943. T h e o r e t i c a l S o i l M e c h a n i c s , J . W i l e y & S o n s , NY, 510 p p . NOTATION a b d e h H i k Κ Ν ρ Ρ S t w ws
depth of gabion width of gabion or foundation depth of founding void ratio d e p t h below t o p o f embankment embankment h e i g h t o r w a l l h e i g h t hydraulic gradient wire spacing soil lateral pressure coefficient bearing capacity factor pressure thrust r e l a t i v e density of rock wire diameter unit weight of water unit weight of rock
Ws
bulk
y 3 δ φ Θ
water angle angle angle slope
unit
weight
of
earth
or
rockfill
depth o f t o p o f embankment f r o m t h e o f f r i c t i o n on w a l l of internal friction angle from the horizontal
horizontal
toe Fig.
4.12
Gabion
retaining
wall
design
Plate
5.
R o c k f i l l gabion drop s t r u c t u r e ( P h o t o by M a c c a f e r r i ) .
Plate
6.
Gabion w e i r
after
a stilling
in
basin
a
channel.
GABION RETAINING WALLS INTRODUCTION
The modern g a b i o n especially weirs, lies
for
groynes
in
that
stability
have a f u r t h e r ment does n o t
tive
as t h e y
date
Olivier they
(1967)
The use o f
in
the
cost
riprap
per
(about
tically
the
tipped
stone.
f i l l ,
gabion
Up t o
energy
or
subsided
level
to drop.
This
assess. gabion of
of
When f l o w
in
gabions
verified
for
various
of
move-
some
relatively
the wire of
ex-
attrac-
gabions this by
This
o r mesh
at
need r a r e l y Izbash
arises.
(1970),
in
remote
locations,
during
throughflow.
slopes
be c o n s t r u c t e d
to
dams
basket.
stability
not
over
with
consider-
but
as c o n c r e t e
more e x p e n s i v e
is
than
(about
stone
pitching
The s t a b i l i t y
considerably
volume would
better
be r e q u i r e d
for
is
than
practhat
tipped
of
stone
water. dams r e q u i r e
through
an
impermeable
where a f r e e - d r a i n i n g temporarily
a pool,
or
as e x p e n s i v e
dumped r i p r a p ) .
however,
avoids
or the
stagnant
for
water
through
structures
routing. thereby
or a s i l t
dry
a gabion
fill
occurs
A theoretical is
is
presented
is
upstream
useful.
to assist After
allowing
the
in flood
the
water
trap. relatively the
study in
core or
weir
dam u p w a t e r
flood
rockfill,
retaining
to estimate.
hydraulic
experimentally.
and s l i g h t to
yet
They
to ensure
considerably price
structures
becomes more d i f f i c u l t
of
Fortunately
and permanent
although
rockfill
flow
turn
life
dams w e r e a d v o c a t e d
c a n be u s e d t o
of water
size.
replace
are
a new l a y e r
wire.
steeper
the gabion
the form of
gabion
They
Gabion w a l l s
advantage
pressures)
stone
are f l e x i b l e
stability.
with
slopes
flowing
the water w i l l
The s t a b i l i t y
is
the
water,
weir in
they
Their
water
individual
and
linings,
rockfill.
situations,
rockfill
dissipation
1979).
releasing
the
limited
o f mass c o n c r e t e ,
fast
retain
There are
the
cofferdams
metre)
5 times in
in
rocktip
enables
times
same as t h a t
When u s e d t o membrane.
has
cubic
and even more
A gabion
for
structure,
three
or
packing.
resistant
downstream
the volume of
The f i n i s h e d
or
flat
that
by r e - s u r f a c i n g
stacked gabions
savings
half
lies
corrosion
and o t h e r s
fairly
of
structures channel
appearance.
overf1ow-throughf1ow
require
able
using
stone
gabions
be o v e r c o m e or
in
retaining
(Stephenson,
(therefore that
the appearance
have a n a t u r a l
however
concrete
of dry
of
than
earth
such as r e v e t m e n t s ,
works,
permeable
units
over
from
art
The d i s a d v a n t a g e
Although
larger
used f o r
works
dissipation
they are
of
detract
t h e now d y i n g
a later
engineering
advantage
tent
could
advantageously
and e n e r g y
the f a c t
have t h e
is
hydraulic
the
simple
stability of
the
chapter
of
to the
stability and was
63
Fig.
4.1
STABILITY
Gabion
situations
a through-flow
due t o w a s h i n g as a f i l t e r . be d e s i g n e d criteria
Note however to
resist
of
of
coverage
The e q u a t i o n s
for
the
is
of
than
stacked
as
to
can be p l a c e d
in
the the of
Fig.
gabion
is
The g a b i o n s granular
into
will
reduce
material,
intermediate
washing
that
material
but
individual
obtained
laid
(Fig. per
plane
gabions
filter
the
next
i.e.
face erosion
they
layers
act
should
using
filter
if
slopes
4.4)
area
of
the
retains
the
stability
is
the
is
permeability due t o
n o t as g r e a t
arrangement
the
is
more
as
when
economical
gabion.
applicable
t o an
subsequently.
to a slope
but
the slope
where
gabion
rocks.
unit
applies
the
has a h i g h e r
parallel
below are also
indicated
and
one l a y e r
gabions
position
90°
4.1.
underlying
on a s l o p e d d o w n s t r e a m
cloth.
gabions
developed
not applicable
qualifications
that
similar
on a h o r i z o n t a l
(The t h e o r y fore
or
in a horizontal
as g r e a t e r
of
filter
gabions
The s t a b i l i t y
thickness
forces
gabions
particles
advantage
rockfill
higher weight
stacked
body
s u c h as
piping
or a s u i t a b l e
a tipped
where
structure
away o r
The p r i n c i p l e of
with
OF G A B I O N SLOPES I N WATER
There are of
slope
taken
to a gabion as
infinitely
height
is
zero, high
finite).
layer
i.e. slope
of
finite
as f o r
a
and
there-
is
There a r e ,
weir.
however,
64
Sliding stability In o r d e r slope,
t o p r o d u c e an a n a l y t i c a l
i t i s necessary
assumed t h a t water
ence across force
is horizontal,
the gabion
Now c o n s i d e r
i s expended
the internal
where S i s t h e r e l a t i v e weight
of
tending
of water,
(d) that
t h e head
and ( e ) t h a t
forces
per unit width namely
or wab(S-1)/(1+e)
density
o f a gabion
t o cause s l i d i n g
acting
i s no
depicted
acting
vert-
horizontally.
i s t h e submerged w e i g h t ratio
of the gabion,
and w i s t h e
t h e components
down t h e s l o p e
of the forces
should
be l e s s
by t h e f r i c t i o n
( 1 ) and ( 2 ) i n F i g . than
t h e components
coefficient
t a n φ:
S-1 S-1 vhr-r a b s i n Θ + w i a b c o s Θ S t a n φ ( ν / τ — a b s i n Θ - ww i a b s i n Θ )
(4.1)
tan φ - tan 0
,1+e
Values o f i ( 1 + e ) / ( S - 1 )
tained
differ-
there
on t h e gabions
t h e submerged w e i g h t
of the stone, e is the void
to the slope m u l t i p l i e d
value of f r i c t i o n
be
(c) the
water.
For e q u i l i b r i u m
perpendicular
It will
are full
i n d r a g on t h e s t o n e ,
downwards, and t h e seepage f o r c e a c t i n g
Note t h a t w a b ( S - 1 ) ( n - 1 )
4.1
is zero,
on a
on t h e s l o p e .
i n F i g . 4 . 1 . There a r e two body f o r c e s ,
specific
o f gabions
assumptions.
(b) the voids
on t h e e x p o s e d d o w n s t r e a m f a c e
between gabions
ically
for the stability
t o make a number o f s i m p l i f y i n g
(a) the flow
pressure
solution
versus
(4.2)
Θ are plotted
φ may be f a i r l y
by w i r e mesh r e d u c e s
in Fig. 4.2 f o r φ = 35°.
low f o r r o c k f i l l ,
the friction
angle
the fact
t o about
this
that
Whereas
t h e rock
is
this con-
value.
Overturning The seepage f o r c e
also
tends
to overturn
the gabion about
the toe ( A ) . For
equilibrium,
w a b ( |+ j
tan 0)cos
Rearranging,
i-ς-τ- ^
Θ ύ w ^ - a b ( |- | b/a - t a n 0 1 + (b/a)tan
Values o f i ( 1 + e ) / ( S - 1 ) various
values
of b/a.
from t h i s
tan 0)cos
0
(4.3)
(4.4)
0
equation were l i k e w i s e
plotted
on F i g . 4 . 2 f o r
65
stone relative void ratio - e
SYMBOLS:
density - s
a/sine
(Λ
\
τ» 5 3 0
\
\
S.
\
V
20
Ν
—/* NO'.
Sä. NT
10
s
Nix! i
\
^
^
S*
\ \
0.2
Fig.
OA
4 . 2 S t a b i l i t y
0.6
of gabions
0.8
on a slope
«(lit)
(φ= 35
c
Assessment of results It
will
be observed f r o m F i g . 4 . 2 t h a t
criterion is sliding, b/a,
overturning
Laboratory (S-1) for
tests
at failure
this
butting
is that
that
i s independent
failure
f o r b/a greater
and t h i s
0.7 the limiting
of b / a . For smaller
values o f
0.7 the value o f i(1+e)/ condition.
was n o t p o s s i b l e
The reason
owing t o one gabion
I t was assumed f o r t h e a n a l y s i s
I t w o u l d be s a f e condition
than
andoverturning
by s l i d i n g
o n e down t h e s l o p e . force.
than
criterion.
between t h e s l i d i n g
complete
on t h e n e x t
however,
indicate
lies
was n o i n t e r - g a b i o n limiting
and t h e slope
is the limiting
f o r b/a greater
t o adopt
is likely
c r i t e r i o n as
t o be t h e l i m i t i n g
one f o r long
s l o p e s w h e r e t h e r e w o u l d have t o b e c o n s i d e r a b l e movement down t h e s l o p e to
transmit
restraining
For small
slope angles
accurate as there assess i . as f o l l o w s
thrust
is flow
that
the sliding
there
i n order
up t h e s l o p e .
approaching
the horizontal
upwards as w e l l
t h e above t h e o r y
as h o r i z o n t a l l y
I t becomes n e c e s s a r y t o a n a l y s e t h e s t r u c t u r e f o r a gabion on a h o r i z o n t a l p l a n e .
becomes i n -
and i t i s d i f f i c u l t using
basic
to
principles
66
Fig
4.3 Gabion
STABILITY
the stability
conditions
of a single
such as F i g . 4 . 3 .
stream of t h e gabion as
plane
OF GABIONS ON HORIZONTAL PLANES I N WATER
Consider lified
on a h o r i z o n t a l
is zero,
gabion
on a h o r i z o n t a l
plane,
Here i t
i s assumed t h a t
the water depth
and t h a t
uplift
and t h e i n t e r n a l
water
under
simpdown-
surface are
depicted.
Sliding Consider
the external
der f o r the gabion
= (wTTë
ab
+
(Note t h a t
t o be s a f e a g a i n s t
Μ
S i m p l i f y i n g , £ <;
π ? 2
and body f o r c e s
S
y b
a
^
e
in this
on t h e g a b i o n
s l i d i n g , we m u s t
(Fig.4.3).
"
1
In o r -
have
'w ^ T ) t an Φ
for simplicity
yQ elsewhere
acting
·
tan φ
5 () 4
(4.6)
we u s e y h e r e a n d i n t h e f o l l o w i n g
section
in place of
chapter).
Overturning In o r d e r have
f o r the gabion
t o be s a f e a g a i n s t
overturning
about
t h e t o e A , we m u s t
67
Simplifying,^
Equs.
4.6
gabions
(4.8)
and 4 . 8 were f o u n d
even f o r
The e q u a t i o n s various
relatively
4.6
high
and 4 . 8 w i l l
downstream water should
STABILITY
OF STACKED GABIONS
A logical
of
is
stack
the gabions
that
the
slope,
gabions, stability
so t h e
individual
4.4
in
fact
as w i l l of
overall
blocks
a horizontal
Fig.
and
For
Stacked
depths use f o r
relatively
arrangement
of
gabions
each o t h e r
in question the
the
(up t o
limiting 50% o f
analysing
equilibrium
the
gabion
of
upstream
depth).
structures
with
deep downstream w a t e r
steeper
at
improves the angle
to
resist
a batter the
however,
of
structure the
up t h e w a l l . be u s e d t o
gabions
with
the overall
forces
soil The
against
the
following.
should
The p r e v i o u s
check
water
stability
as a w h o l e
structure
(or
(Fig. 4.4).
the greater
be s e e n f r o m t h e a n a l y s i s
stability
base c o u l d
predict
the
I N WATER
the w a l l - l i k e
making
be o f
to
anew.
t h e m on t o p o f
above any one
and o v e r t u r n i n g individual
be a n a l y s e d
and e f f i c i e n t
to
tailwater
thus
depths.
situation
ssures)
by e x p e r i m e n t
reduces
for
stability.
weight
sliding
stability Note the
single
of
the
however
steeper
be c h e c k e d as w e l l
theory
pre-
as
gabions
the for on
68
Sliding of individual blocks From F i g . 4 . 4 i t w i l l the f r i c t i o n for
due t o s e l f
be o b s e r v e d weight
that
the lateral
and weight
water
o f t h e gabions
force
i s r e s i s t e d by
above,
less
uplift,
so
equilibrium;
. ^ r uS+e w ι a b -, [w a b ^
-1+e /
η · Rearranging,
The r e l a t i o n s h i p values also
2
2
a b t a n Ox S+e,b tan Θ 2 ~ " FTärTÖ — ä ' "
+
1+(b/a)tan ( b ) 2a ) + t an
between
be a t l e a s t
.φ
n
Ο , 0 t a n Φ
i(1+e)/(S+e)
o f b / a , and φ = 3 5 ° .
2
- b η7 . Γ ^
λ
w
\
9)n
(
(4
,« * \ ( 4 . 1 0 η) and Ο i s p l o t t e d
Note t h a t
t a n 35° f o r t h i s
·
the friction
relationship
in F i g . 4.5 f o r various
coefficient
on t h e base
should
to hold.
Overturning stability of individual blocks Consider For
t h e o v e r t u r n i n g moments a b o u t t h e t o e Ά '
o f a gabion
(Fig. 4.4).
equilibrium; 3
, -a ,S+e b S+e/b , w a b Λ j - w a b ^ - ^ - ^j^i^-tan
Rparranaina Rearranging,
This
i i
1 +e
^
relationship
< ^
b
+
2
and f o r l a r g e r
2
than about
2
b a> . b 2b „ ^—) + w î - ^ - y - ^ 0n
(2 2 b / 23 a ) t a n (H2b /3a )
is also plotted
observed f o r b/a less ing,
/ a2
2
„ θ
Q
j ]) 2
4
in F i g . 4.5 f o r various 0.7 the individual
b/a they f a i l
,,χ (4.11)
Λ
blocks
b/a values. will
fail
It will
be
by o v e r t u r n -
by s l i d i n g .
EMBANKMENT LOAD
If
there
i s an uncontained
fill
material
force
on t h e g a b i o n s .
I t is often
arily
to retain
(granular
sures
little,
a fill
tion will co-incides
stability.
fully
active
w i t h minimum l a t e r a l o f gabions
retaining walls,
thickness
pressure
has an added a d v a n t a g e
ensure that
The b u l k w e i g h t crete
or cohesive)
i f any, groundwater
The g a b i o n w a l l
The w e i g h t
soil
a gabion wall
and t h e p o r o s i t y
i t will
exert a
is erected
prim-
o f the gabions e n -
build up. in that
i t is flexible.
conditions
Outward
are developed.
This
deflec-
condition
p r e s s u r e on t h e w a l l .
adds t o t h e o v e r a l l
on a c c o u n t
and a r e designed
behind the gabions,
t h e case t h a t
of their
cost,
slope
have t o be k e p t
t o a c t in bending, gabions
of a battered
gabion wall
stability.
rely
i s taken
con-
t o a minimum
on t h e i r partly
Whereas
weight f o r
by t h e s o i l
mass,
ί
d.
Fig. thus
4.6
Gabion
improving
Various lecting ive
(but
lateral
the
retaining frictional
arrangements
the
self
weight
uneconomic), soil
pressures
U s i n g wedge t h e o r y , for
the active
cohesive
fill
gabion
of
the wall
then
bulk
retaining for
the following
on t h e Coulomb
unit
arrangements
resistance.
for
horizontal of
wall
Tilted
walls
nearly
are depicted
vertical
theory
walls
in
which
may b e e m p l o y e d
to
Fig. is
4.6.
Neg-
conservat-
estimate
the
wall. (Capper,
pressure weight
at
1969)
derived
any d e p t h ,
Wg ( R e f e r
to
h,
Fig.
the following
below 4.7
the
for
expression
surface
symbols):
of
a non-
71
WW
Fig.
4.7
Embankment
f i l l
against
retaining
wall
2
sin (0-(i))
W sh
(4.13) sin
2
For most θ is
+
0
structures
less
friction
5 ΐ η
ι η$ ( θ + 6 ) { 1 + // 1 ^ ^ Φ | : [ Φ - β | } ^ / sin(0+6)sin(e-B)
than
or
angle
the
equal
δ = 0,
surface to
90°
is
horizontal
it
is
i.e.
reasonable
so t h e e x p r e s s i o n
3 = 0 ,
and
if
and c o n s e r v a t i v e
simplifies
the wall
angle
t o assume
the
to
2
W $h s i n ( 0 - 0 ) p
If
~ sTn
0(sin
θ + sin
the wall
is
W sh ( 1
sin
p
-
(1 + s i n
φ)
vertical
(4.14)
2
0 = 90°
and
φ) (4.15)
φ)
K W h a s
where Κ
a
Κ
= (1 s i n φ ) / ( 1 + s i n φ) = 0.3 f o r s a n d . a is termed the a c t i v e pressure c o e f f i c i e n t . It
vertical is
to
movement of
soil
reduce the
the wall
pressure. the
lateral
coefficient the
fully
The e f f e c t pressure becomes
developed
of
permitting
significantly. approximately
resistance
of
0.5 the
is
the
ratio
of
outward d e f l e c t i o n For
instance
and f o r soil,
for
large
termed
no
lateral of
the
wall
outward
inward
the
to
movement
passive
resis-
72
tance,
can
result
Allowing
for
a t e an a c t i v e
in a c o e f f i c i e n t
cohesion
pressure
c of
at
as
the
high
soil,
any d e p t h
as
the
3.
t h e o r y was m o d i f i e d
h on a v e r t i c a l
wall
with
by B e l l
to
no f r i c t i o n
indicas
f o l 1ows:
(4.16)
This h h
c c
equation
indicates
= 2c/W / K ~ , w h i c h i s s a i s z e r o , so t h a t t h e
Ρ = ! K W (Η -
wall
is
of
friction
plays
superimposed
the
factors
impossible. active
It
thrust
stress
should
on t h e w a l l
be a s s u m e d
on t h e w a l l
that
down
the
to
pressure
above
becomes
(4.17)
relatively
statics the
are
tensile
L
Where w a l l there
or
2
h )
a b
or
a negative
of
an
loads
important,
system needs safety
with
important
part,
above
top
the
to
the
simple
to
if
the wall
the w a l l ,
equations
be a n a l y s e d
respect
or
of
slopes
or
significantly
the weight
a b o v e do n o t
graphically
overturning
or
suffice.
numerically
and s l i d i n g
of
of
The
to
the
the
determine
retaining
wal 1 . Coulomb d e v e l o p e d it
is
assumed
Trial
that
a method
failure
wedges a r e a n a l y s e d
Many c o n f i g u r a t i o n s a retaining about
sliding the
wall
a point out
of
the
t o e and w i t h Methods
(Taylor,
log
spiral
the
radius of
A slice
of
slices.
Each
weight)
and c o m p u t e r circles. circle
of
the
unit
imaginary on a l l
programs Fig. for
4.8
about
is
the the
along a f a i l u r e
arc
to
the
the
lowest
the
wall.
occur
t o p may
for
rotate
e m b a n k m e n t may f a i l passing
embankment
to
find
by
through face.
the most
critical
have been p r o p o s e d ,
stability
ratio
of
i.e.
resistance.
formed,
curve
of
heel
t o e as w o u l d
at
circles
the w a l l ,
analysis
factor
of
of
to
safety.
the f r i c t i o n
the a c t u a l l y
is
e.g. find
The
plus
co-
developed
fric-
considered.
favour with is
geotechnical
divided
into
summated v e c t o r i a l l y . an
the
the
thus
behind
least
a sloping
the f a i l u r e
The o b j e c t with
ideal
illustrates
analysis
for
circle
arc
is
slip
strength
slices
provide
plane
to
failure
through
somewhere above
slip
is
soil
or anchored
Similarly
arc.
thickness in
braced
slip
of
surface with
analysing
shapes
respect
analysis
the
rotation
a circular
with
on a p l a n e
toe.
for
c a n be d e v e l o p e d
and s e l f
slip
Various
and c e n t r e safety
One m e t h o d o f
a slip
of
o f wedges
by r o t a t i o n
A cut
the
A circular
centre
simply
fail
tilted.
toe.
1948).
or
hesion which tion.
not
have been e v o l v e d
one
factor
would occur
up t h a n
the
analysis
to determine
will
which
higher
of
method o f
an embankment
by t h e m e t h o d o f
engineers slices
and t h e
the method forces
The p r o c e d u r e
analysis
of
slope with
slices.
is
Taylor
is
a large forces (1948)
of
(external
laborious
number
of
on s l i c e s published
in a
73
t r i a l
centre
/
WY^"/^
Ι
/
\
1
^
—
^
WT Γ
χ
3
,
N
A \
r.
factor
ET
^ s h e a r
Fig.
4.8
Slip c i r c l e analysis by m e t h o d o f slices
set
of
out
drainage
stability
Where
for
is
seepage
in
the
effective
soil
the
pressure
total
(Chapter should are
for
analysis
gabion
of
simple
a
n
F(
^
n
component
component
of
t
safety =
of
weight
retained
cases
of
F
s 3
embankment
embankment
s-lope
slopes
with-
forces.
there
be a l l o w e d
curves
normal
of
6).
stresses
similarly
determined
rather
minus
Soil
through
stability
than
the water
properties,
be o b t a i n e d
with
aid
the
of
embankment
analysis. total
in
terms
triaxial
angle of
is
stresses.
pressure,
namely,
and w a t e r
Analysis
which of
effective
obtained
on
in
soil
and
of
stress
is
net
cohesion,
The s o i l
laboratory
should
terms
from a flow
friction
stresses.
tests
these
accurate
The e f f e c t i v e is
internal
compression
pressures,
more
properties
samples
of
soi 1. If
an e m b a n k m e n t
stability
i)
ii)
cases
During
or
the
soil
be
high.
which
likely need
to
immediately will
Immediately Water
is
not
after
pressures
to
construction
consolidated
drawdown
will
inundated
be c o n s i d e r e d .
after
have
be
cause
of
saturated,
The most
of
reverse
level flow
there
important
are
the
At
pore-water
adjacent and
low
to
various
are:
an embankment.
much and
the water
high
or
this
pressure
an
effective
time will
embankment. soil
stresses.
74 iii)
Under e x t e r n a l bankment
if
considered
l o a d and s t e a d y
high in
superimposed
the
seepage. loads
the
normal
life
and seepage a r e
During
likely
these
of
the
em-
should
be
analysis.
Anchored embankments To i m p r o v e into
the
exposed
the
embankment. rockface
ling
rocks
this
but
type of
resistant,
retaining
walls
stabilization
w i r e mesh t o
could also
avert
of
the
it
is
this
nature
face.
a major
possible
This
slide.
is
is
to
anchor
the
wall
the protection
primarily
Rock a n c h o r
to
bolts
of
an
catch
are
fal-
used
for
anchoring. can a l s o
reinforcing.
reinforcing
of
Slope
by t y i n g
it
Gabion w a l l s embedded
stability
strips
be a n c h o r e d
If
the
into
embankment
may b e l a i d
high-friction-grip
in
t h e embankment w i t h is
the f i l l
built
up w i t h
and t i e d
and l o w - s t r e t c h
to
tension
ground
anchors
the gabion w a l l ,
the
gabions.
member
is
A
or then
corrosion
required.
FOOTINGS
Vertical ings,
loads
designed
ment.
to
deflection,
from the
pores
of
The b e a r i n g cohesion
and
internal
footing.
such as t r i a x i a l Pressures the
load
is
tact
is
to
underlying
to
reduce of
contact
soils
yield,
are
foundation pressures complex,
material
via
foot-
and m i n i m i z e
and
and c o n s o l i d a t i o n
settle-
in addition
as w a t e r
to
is
expelled
soil. of
soil
friction
The s t r e n g t h compression
Thus
foundation twice
the
plastic
is of
the f o o t i n g ,
spread.
equal
load
also the
dependent
soil
of
soil
the
or extrapolated
vertical
the footing
the
content
to
depth
safe the
width.
is
Not o n l y
but
also
and t h e
from f i e l d
plate
the contact
therefore
and most d e f l e c t i o n
the
tests
loaded
as
footing
within
pressures place
tests.
surface
pressure
takes
the
bearing
from the
the
flexibility
from laboratory
under a uniformly
10% o f It
load, soil
and d i s t a n c e
pressure
about
face which are o f most c o n c e r n ,
of
may b e d e t e r m i n e d
reduce with
reduces
on many f a c t o r s .
decide
the water
tests
under a f o o t i n g
on an e l a s t i c depth
there
the
of
the
to
characteristics
capacity
d e p t h and w i d t h the
transmitted
spread
The s e t t l e m e n t
elastic
of
are
at
in
a
the
the
con-
upper
strata. Failure ure
conditions
surface.
under
The u l t i m a t e
Terzaghi
in
Ρ
+ iW bN + W dN s w s q
u
= cN
c
where c is
the following
the cohesion,
a foundation bearing
form,
may be c a l c u l a t e d
capacity
of
a long
assuming
footing
t o w h i c h m u s t be a p p l i e d
a shear
was e x p r e s s e d
a factor
of
failby
safety.
(4.18) b the
breadth
and d t h e d e p t h o f
founding.
The Ν
factors
75
are functions
TABLE
of
bearing
capacity
Ν /2
_
φ
Ν _c_
0 15° 30°
5.7 9 18
Ν
W
0 0 3
For a f i r s t
TABLE
angle
as
indicated
by T a b l e 4 . 1 .
4.1
Terzaghi
ings
the f r i c t i o n
coefficients
g
1.0 3 8
approximation,
on d i f f e r e n t
types
of
the
soils
typical is
surface
tabulated
bearing
with
capacity
impunity
in
for
Table
wide
foot-
4.2.
4.2
Typical safe soil bearing ( R e f . BS C o d e o f P r a c t i c e
capacities CP101, 1963)
2
kN/m S o f t c l a y s and s i l t s S t i f f and sandy c l a y s Loose sand d r y submerged Compact sand o r l o o s e g r a d e d Compacted g r a v e l - s a n d
sand
mixture
kN/m
2
= 0.01
kg/cm
The p r e s s u r e s will
be u n i f o r m a n d l i n e a r
The p r e s s u r e s sand w i l l
The g r e a t e s t soil
the centre
will
where shear
settle
a slight
edges o f tual
4.9 f o r
will
occur. at soil
footing
the
the
loaded
there
be a t
uniformly.
cohesive
a rigid
under a f l e x i b l e
since
will
resistance
conditions
100 400 200 100 400 200 600 300 2000 4000 10000
ft)
(see F i g .
consequently
failure
On a h i g h l y
ton/sq
due to a u n i f o r m l y
be s i m i l a r ,
less
rock
to to to to to to to to to to to
footing
on an e l a s t i c
pressure
distributions
foundation under
foot-
soils).
settlement
near
then
= 0.01
immediately
i n g s on d i f f e r e n t
less
2
dry submerged
dry submerged
Shale and s o f t s a n d s t o n e L i m e s t o n e and hard s e d i m e n t a r y Sound i g n e o u s r o c k (1
50 200 100 50 200 100 400 200 1000 3000
There w i l l pressure If
the
though.
footing
on
cohesion-
transmission
of
load.
footing
resistance
be h i g h e r
were founded
to
than below
on a
cohesion-
compression
at
the
edges
surface
level
result.
be a r e s i s t a n c e
stresses
footing
A rigid
be a h i g h
here w i l l
edges would
under a s e m i - f 1 e x i b l e
flexible
c a n be no l a t e r a l
the edges
there will
and t h e
perfectly
developed
rockfill
to
settlement
there will
footing
will
at
be h i g h .
be b e t w e e n
the The
the
ac-
two
76 Uniformly
distributed
load
f oo t i η g
[^contact pressure Elastic
b .
foundation
1 !
11 ^
settlement
c.
Non cohesive foundation
Cohesive
Rigid Fig.
Fig.
foundation
4.9
Pressure 1 oad
4.10
distribution
Pressure lateral
f.
Flexible
footings under
distribution and
vertical
a
under load
footings
uniformly
a
1
rigid
distributed
footing
with
77 cases,
depending
which mesh
is
If
there
is
of
lateral
use
lateral
the w a l l ,
the w a l l .
on an e l a s t i c
ing weight
to
to y i e l d
assumed
soil
footing
that
the
edges o f
the
the
soil
tends
to
wall
contact
the
in
upthrust
are
edge.
hand t h e
4.10b.
compress
the outer under
self
and
sliding toe
the footing
4.10.
The
to
Two
the downward
t h e moment due t o
toe.
the of
of
a rigid in F i g .
pressure
act-
the
and e c c e n t r i c
The e q u a t i o n s
be s u b t r a c t e d
implying
the
from s t a t i c s .
upthrust
the
to
tension,
zero
wall
are
water
solved
uplift.
pressure
assuming a t r i a n g u l a r pressure
material
Fig.
at
the pressure
4.10a
pressures
soil
and o u t w a r d
will
foundations
is
distribut-
section.
since
the
under a r i g i d
The p r e s s u r e s the
say
the
backfill,
illustrated
and w a t e r
negative
foundation in
total
to
In a d d i t i o n
near
from which must
loaded
like
shape as
load
gabion
the d i s t r i b u t i o n
due t o t h e
and one e q u a t i n g
repeated
of
load,
distribution
the
bending
such as w i t h
transmitted
b a s e may be c a l c u l a t e d
about,
is
and amount o f
footing
load.
pressures
pressure
soil
pressure
footing
the
cause o v e r t u r n i n g
pressures,
be m o r e
Fig.
of
outside
one e q u a t i n g
lateral
cohesionless
in
to
be t r a p e z o i d a l
base w i d t h
will
the
l o a d on t h e w a l l ,
of
On t h e o t h e r
be as
tend
and t h e e x e r c i s e
unknown
the of
as a v e r t i c a l
at
The c o n t a c t
both
resulting
footing
yield. will
is
toe and heel
In a real
as w e l l
pressures
the f i l l
t h e moment o f
there
ion w i t h
at
effect
transfer
on a r e t a i n i n g
established;
plus
the
either
rigid
of
base w i l l
are
overturning weight
of
of
Reinforcing
t h e r e may be d o w n w a r d f r i c t i o n
The r e s u l t
vertical pressure
flexibility
lateral
thrust
are magnified.
equations
in
The t h r u s t s
pressures
footing
If
of
a concentration
weight
relative
can a c c o m o d a t e .
therefore
be e c c e n t r i c . with
on t h e
the footing
under
the
distribution
soil
at
footing
in
the edges w i l l
edges
to
ensure
the
soil
as
base
a
will
cohesive
increase
that
under
t h e edges
the
remains
piane. Under a f l e x i b l e relative loaded
rigidity
the f o o t i n g
as
in gabions
sures If
there
upwards
may t h e r e f o r e will
pressure
the f o o t i n g .
yield
assist
in
is
saturation
or
in
strength.
keep t h e w a t e r
Chapter
Thus
thereby
be o f
distribution
will
be c o n t r o l l e d
under a very
flexible
reducing
l o a d and t h e e x t e n d e d
little
distributing
use. the
the
footing
by
The use o f w i r e load outwards
the
the
highly toe
reinforcing
thereby
reducing
such pres-
capacities
under water of
situation,
tipping
table
seepage In
the
upward
case of
down and a v o i d
into
the
seepage,
piping
or
foundation, drainage
strength
t h e r e may be a
should
be
provided
deterioration
(see
6).
Footings
the
the
considerably.
deterioration to
of
edges w i l l
of
footing
sediments
require often
even causing
rockfill
in.
c a n be a n t i c i p a t e d
at
special
very
scour.
consideration.
low,
but
In
loose
the
D r e d g i n g may b e w o r t h w h i l e a reasonable
depth.
flow
beds, if
Not
only
of water
the
silt
a harder
Alternatively
are
the
a l s o may
bearing
aggravate
may b e d i s p l a c e d foundation
piling
may be
by
material required
78
Fig.
4.11
Wire
in deep s i l t s
basket
where
high
loads
are
to
be t a k e n w i t h
little
settlement.
WIRE STRENGTH
The w i r e
diameter
and r o c k f i l l
loads
ditions
respect
ssure
with
Then t h e in
total
the
to
the
outward
gabion),
force like
b a s k e t may be e s t i m a t e d
basket.
rockfill
Κ = (1 -sin
an a r r a n g e m e n t
a wide
gabion
i m p o s e d on t h e
= KSwh/(1+e)where
stacked (i.e.
for
in
It
the
(J>)/(1+sin
on a u n i t in Fig.
is
reasonable
gabion,
i.e.
φ) and h i s
width
4.4 with
of
from the
t o assume a c t i v e
horizontal depth
basket
in
hydraulic
below the F i g . 4.11
the diaphragms
if
and s i d e s
£ ^t
this
to
where f
the d i r e c t i o n
the force is
it
is
neglected
is
2
2
pre-
surface.
1-sin φ S a . , TWÔ- + w ι a b 1 + s i n φ 1+e 2
Equate
con-
rockfill
the wire
* \ ( 4 . 1 9n )
Λ
per
unit
stress,
perpendicular
to
width t
of wire
the wire
the f l o w .
(top
diameter
Thus
and b o t t o m ) and
the wire
k is
2 x 2
cos
45°
t h e mesh s p a c i n g
diameter
is
given
by
the
i
79
equation
, *
=
/wak /a 1 - s i n φ S , . . χ ( + 1b ) A f c o s 4 5 ° 2 πΤΓηφ ü ?
Where t h e r e ance
a r e superimposed
should also
be r e q u i r e d
loads
these
b e made f o r r u s t i n g ,
in conjunction
with
(Λ
οη\
· 2 0)( 4 should
be a l l o w e d
f o r in (4.19).
and f o r heavy pressures
a gabion
facing
steel
Allow-
t i e b a r s may
(see Chapter 3 ) .
EXAMPLE
Calculate fill
such as a t a i l i n g s
a flow is
t h e safe angle
The embankment 1 0 0 mm s t o n e ,
dam w i t h
an angle
3
o f water
eliminated
of a battered
o f 0.1 m /s/m of wall
by d r a i n s . height
Calculate
i s 5 m.
factor
to retain
of internal
friction
across
the surface
the freeboard
Assume g a b i o n s
Κ = 3 for rockfill
Friction
gabion wall
height
a
cohesionless
o f 2 5 ° . There
but subsurface t o ensure
no o v e r t o p p i n g .
1 m high χ 1.5 m wide f i l l e d
and η = 0 . 3 5and S = 2 . 6 f o r r o c k f i l l
ings
f i l l .
on r o c k f i l l
base
i)
Bulk unit weight of saturated fill = ( 1 - n ) w S + n w
Overturning moment about toe\ f r o m 2
W.sin (0-0)h
M1 =
sin 0(sin
= 0.5.
(4.14)
due t o thrust
x (h/2) χ (h/3)
θ + sin φ]
2
2
=
20000 s i n ( 0 - 2 5 ° ) χ 1 2 5 / 6 2 sin 0(sin Θ + s i n 25°)
Stabilizing
M2
moment o f g a b i o n s
Equating Θ
d u e t o w e i g h t Wa
= 5 χ 1.5 χ 0 . 6 5 χ 9800 χ 2 . 6 χ ( 2 . 5 / t a n = 124000(2.5/tan
Mi a n d M2 a n d s o l v i n g
i i i ) Sliding force on gabions 2
Θ +0.75)
Θ + 0.75)
= 81°
20000 s i n ( 0 - 2 5 ° )
χ 25/2
with
and t a i l -
= 0 . 6 5χ 9800 χ 2 . 6 + 0 . 3 5 χ 9800
ii)
is
seepage
f o r Θ by t r i a l ,
F
x
= 20000 N / m
(Fig. 4.12)
3
Resisting
force:
Assume t h e w e i g h t
o f t h e gabions
acts
down o n a g a b i o n
foot-
ing .
Friction
resistance
F 2 = 0 . 5 χ 5 χ 1.5 χ 0 . 6 5χ 9800 χ 2 . 6 = 62000
Equating
Fi a n d F2 a n d s o l v i n g
f o rΘ,
Θ = 63°.
A lower angle would demonstration
be s e l e c t e d
to allow
a factor
of safety,
say 45° f o r
purposes.
Top water depth
Depth a t c r e s t
of tailings
= y
c
=
3
2
; / g
8
ΓΓΤ χ Q 35?
Assuming a slope o f 1 / 1 , then upstream face
=
°*
20
m
i s 0.75 m back,
(2.21) anddepth
0.75 m
back ; 3Kb/d .*.
= 3 χ 3 χ 0.75/0.1
y = 4.1
= 67.5
χ 0 . 2 = 0.82 m
so u s e a 1 m h i g h g a b i o n
(Fig. 2.4)
retaining
wall.
Sliding stability of top gabion under water pressure
Z
=
^
2
=
0
. 5 5 < ^ i t a n *
(4.6)
_ 2 χ 2 . 6 χ 1/0.82 - 1 1 + 0.54 =
3.47
Overturning stability of top gabion
^0.55
(4.8)
χ 2 . 6 χ 1/0.82 -~2 1+0.54
2.21
The t o p g a b i o n
is therefore
safe as long as t h e f i l l
is level
with
i t s base.
81 REFERENCES Capper, P.L. and C a s s i e , W . F . , 1969. The M e c h a n i c s o f E n g i n e e r i n g S o i l s , 5 t h E d . , S p o n , L o n d o n , 309 p p . I z b a s h , S.V. and K h a l d r e , Kh. Y u . , 1970. H y d r a u l i c s o f R i v e r Channel C l o s u r e , T r a n s i . C a i r n s , G . L . , B u t t e r w o r t h s , L o n d o n , 174 p p . O l i v i e r , H., 1967. Through and o v e r f l o w r o c k f i l l dams, P r o c , I n s t . C i v i l Engrs., London, March: 433-471. Stephenson, D., 1979. S t a b i l i t y o f g a b i o n w e i r s , W a t e r P o w e r a n d Dam C o n s t r u c t i o n , IPC P r e s s , A u g . T a y l o r , D.W., 1948. F u n d a m e n t a l s o f S o i l M e c h a n i c s , J . W i l e y & S o n s , NY, 700 p p . T e r z a g h i , Κ., 1943. T h e o r e t i c a l S o i l M e c h a n i c s , J . W i l e y & S o n s , NY, 510 p p . NOTATION a b d e h H i k Κ Ν ρ Ρ S t w ws
depth of gabion width of gabion or foundation depth of founding void ratio d e p t h below t o p o f embankment embankment h e i g h t o r w a l l h e i g h t hydraulic gradient wire spacing soil lateral pressure coefficient bearing capacity factor pressure thrust r e l a t i v e density of rock wire diameter unit weight of water unit weight of rock
Ws
bulk
y 3 δ φ Θ
water angle angle angle slope
unit
weight
of
earth
or
rockfill
depth o f t o p o f embankment f r o m t h e o f f r i c t i o n on w a l l of internal friction angle from the horizontal
horizontal
toe Fig.
4.12
Gabion
retaining
wall
design
Plate
5.
R o c k f i l l gabion drop s t r u c t u r e ( P h o t o by M a c c a f e r r i ) .
Plate
6.
Gabion w e i r
after
a stilling
in
basin
a
channel.