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8/11/2019 Notes for Retaining Wall Design
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RETAINING
•,IALL
DESIGN
NOTES
INDEX
SECTION
1
INTRODUCTION
1.1
Scope
1.2
Definitions
and
Symbols
1,3
Design
Principles
1,3,1
Free
Standing
Retaining
Walls
1,3,2
Other
Retaining
Structures
1,4 Lo•d
Cases
1,4,1
Basiq
Loadings
1,4,2
Other
onsiderations
SEG•ION
2
SOIL
PROPERTIES
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2°9
2.10
2.11
General
Selection
and
Use
of
Backfil
Density
Effective
Stress
and Pore
Pressures
Shearing
Strength
Base
Friction
Modulus
of
Elastici•and
Poisson's
Ratio
Coefficient
of
Subgrede
Reaction
Swelling
and
Softening
of
Clays
Permeability
Liquefaction
SECTION
3
STATIC
EARTH
PRESSURE
3;-1' States
of
Stress
3.2 Amount
and
•ype
of
Wall
Movement
3.3 Limiting
Equilibrium
onditions
3 3.1
The
Rankine Earth
Pressure
Theory
3.3.2
3.3.3
3.3.4
3.3.5.
3.3.6
3.4
The
Coulomb
Earth
Pressure
Theo[y
Passive Pressures
using
Equations.
The
Trial
Wedge
Method
Geometrical
Shape
of
the
Retaining
Structure
Limlte•-Backfill
Elastic
Equilibrium
onditions
3,4,1 At-rest Pressures
3.4,2
Over-consolidation
Pressures
3.4.3
Elestic
Theory
Methods
SECTION
4
EARTHQUAKE
EARTH
PRESSURE
4.1 Method
of
Analysis
4,2
Selection
of
Seismic
Coefficient
Page
I
1
1
i
2
2
2
3
3
4
4
6
7
7
10
I0
11
11
12
12
12
13
13
14
15
16
17
17
18
18
18
19
2O
20
20
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4.3
4.4
Limiting
Equilibrium Conditions for Earthquake
Loading
4.3.1
General
•
4.3,2
Mononobe Okabe Equations
4.3.3
Trial
Wedge for
Earthquake
Seismic
At rest Pressures
SECTION 5 EFFECT
OF
SURCHARGES
5.1
Uniform
Surcharges
5.2
Line
Loads
5 3
Point
Loads
SECTION 6
EFFECTS
OF
WATER
6.1,
Static
Water Level
6.2
Seepage Pressure
6.3
Dynamic
Water
Pressuwe
6.4
Drainage
Provisions
SECTION
7 STABILITY
OF RETAINING
WALLS
Page
21
21
?_
21
22
23
23
23
23
24
24
25
25
27
7.1
General
7.2
Sliding
Stability
7.2.1
Base
Without
a
Key
7.2.2
Base Wit•
•..KRy
7.3
Overturning Stability
7.4
Foundation
Bearing Pressures
7.5
7.4.1
7.4.2
7.4.3
7.4.4
7.4.5
7.4.6
Slip
Vertical Central
Loads
Eccentric
Loads
Inclined
Loads
Eccentric
Inclined
Loads
Foundations
onZa
Slope
Effect
of Ground
Water Level
Circl.e.-Stab•l.ity
SECTION
8
STRUCTURAL
DESIGN
8.1
8.2
8.3
General.
8.1.1
8.1.2
8.1.3
8.1.4
8.1.5
Codes
Material
Strength
and Allowable
Stresses
Ultimate
Strength
Cover
to
Reinforcement.
Selection
of Wall
Type
Toe
Design
S em
Design
8.3.1
Stem
Loading
8.3.2
Lower
Section
of Counterfort
Stem
8.3.3
Horizontal
Moments
in
Counterfort
Stem
27
28
28
28
28
28
28
29
30
30
30
31
31
33
33
33
33
33
34
34
34
35
35
35
35
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8 4
8 5
8 6
8 7
Heel Slab
Design
8 4 1
Loading
8 4 2
Heel
Slabs
for
Counterfort
Walls
Counterfort
Design
Key
Desig9
Control of
Cracking
SECTION
SPECIAL PROVISIONS
FOR
CRIB
WALLS
9 1
General
9 2
Design
L•ading
9 3
Foundation Depth
9 4
Drainage
9 5
Multiple
Depth
Walls
9 6
Walls
Curved
in
Plan
APPENDIX
.References
APPENDIX
II
Figures
Page
35
35
36
37
37
38
38
38
38
38
38
39
40
42
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B
B
CF
C
Cb
c
D
dc,dq•dT
Is
Fs
H,H
,etc
SYMBOLS
effective
re
of base
base
width
of wall
effective
base
width
design
seismic
coefficient
including
importance
factor)
cohesion of
soil in
terms
of total
stress
dhesion
at
base
cohesion
of
soil in
terms
of
effective
stress
foundation
depth
foundetion
depth
correction
f ctors
modulus
of
elasticity
of
soil
eccentricity
of load
on
base
f ctor
•f
safety
vertical
height
of
plane
on
which
earth
pressure
is
c lcul ted
(from
underside
of base
or
bottom of
key
to
ground
surface)
vertical
height of
wa,ll
piezometric head
foundation
load
inclin tion
f ctors
coefficient
of
earth
pressure
at rest
..
coefficient
of
active
earth
pressure
coefficient of
ctive
earthquake
eaF•h
pressure
coefficient
of
passive
earth
pressure
coefficient
of
subgrad9
re ction
coefficient
of
permeability
length
of-b-•6
effective
length
of base
l@ngth of
f•ilure
surf ce
.'normal
reaction
on
a
soil
f ilure surf ce
bearing
capacity
f ctors
slope
stabi.lity
number
resultant
lateral
pressure
ctive
lateral
earth
pressure
active
lateral
earthquake'earth
pressure
(PA+APAE)
horizontal
component
of
later•l
earth
pressure
at-rest
earth
pressure
passive
earth
pressure
lateral
earth pressure
due to line
or
point surcharge
load
(per
Unit
length
of
wall)
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ii)
Pv
APAE
PA
Pc
Pw
QL
Qp
q
qa
qult
qu
R,
RA, Rp,
Rw,
etc
S
S
Sc,Sq,Sy
T
U
U
V
W
Wb
Ww
Wt
Yo
•A
vertical
component
Of
lateral
ea th
pressure
hydrostatic
water
pressure
increment
in
active
earth
pressure
due
to
an
earthquake
intensity
of
active earth
pressure
consolidation
pressur•
intensity
af
water
pressure
total
load
line
load
point load
intensity
of
load
on
base
or
surcharge
load
allowable
soil bearing
pressure
intensity
ultimate
soil bearing
pressure
intensity
unconfined
compressive
strength
resultant
forces
total
shearing
resistance
at underside
o f
base
shearingstrength
of soil
foundation
shape
correction factors
tangential
force
along
a
fail•ure
surface
resultant
of
pore
water
pressures
intensity
of
pore water
pressure
.vertical
component
of
resultant
of
loading
on
the
base
weight
of
soil
wedge
used
in calculation
of
earth
pressgres
weight
of
backfill
ov r
heel
of wall
weight
of
wall
total
weight
of
wall,
soil
above
toe
and
soil
above
bee
vertical
depth
of tension
crack
in
cohesive
soil
angle
of failure
plane
from
the horizontal
for active
state
(degrees)
slope
of
back
of
the wall
(degrees)
density
of
Soil
(force
units
submerged
soil
density
Ysat
Yw
dry
soil
density
density
of
saturated
soil
density
of
water
increment;
settlement
angle
of wall
friction
(degrees)
angle
of
base
friction
(degrees)
angle
tan
-I
CF
Poisson's
ratio
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iii)
angle measured
clockwise
from
vertical to
direction
ofP
A
total
normal stress
effective
normal
stress
shear
stre•s
angle
Of
shearing
resistance
in
terms
of total
stress
angle
of shearing resistance
in
terms
of
e fective stress
angle
of
inclination
of
loading
on
base
angle
of
ground
slope
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1-
SECTION
NTRODUCTI
ON
I.
SCOPE
These
notes
are
intended
as a
guide
for
use
in
the
estimation
of
earth
pressure
forces
and
the
design
and
construction of
retaining
walls end
similar
earth
retaining
structures.
Recommended
methods
are
given
for
r•st
aspects of design,
however
if
a
more
detailed
knowledge
of
a
particular
subject
is
required,
the
references
given
should
prove
helpful.
Reference
is
also
made
to
standard texts for
detailed methods
such
as
the
construction
of-flow
nets.
for
pore
water
pressure
determination,
and
reinforced
concrete
design
methods.
Aspects
such
as:
the
use
of
classical earth
pressure
equations;
the
effect
of
earthquakes
on
earth
pressures;
and
allowable
bearing
pressures
under
inclined
loads,
which
are
not
readily
available
in
standard
texts
are
covered in
detail.
Engineering
judgement
must always
be
used when
applying the
theories
an•
methods
given
in
these
notes
and strict
notice
must
be taken
of the
limitations
of
the
various
assumptions.
1.2
DEFINITIONS
•ND
SYMBOLS
Throughout
these
n6•es,•'•tatic earth
pressure me ns
the
pressure
exerted
by
the
earth
due
to
gravity
forces.
Earthquake
earth
pressure
me ns
the
combined
static and
dynamic
earth
pressure
which
acts
during
or
because
of
an
earthquake.
A
list
of
symbols
used
with their meanings,
is
included
in
the
front
of
these
notes.
1o3
•_DES GN
PRINCIPLES
1.3.1
Free
Standing
Retaining
Walls
In
iZhe
design.of
free
standing
retaining
wails, the
following
aspects
need
to be
investigated:
a)
the
stability
of the
soil
containing the
wall;
b)
the
stability
of
the retaining
wall
itself;
and
the
structural
strength .of the
wall.
For
these
walls
it is
usual
to
a@sume
that
some
outward movement
of
the
wall takes
place
so
that the
lateral
earth
pressure
from the
retained
soil is
a
minimum
active
c•ndition)
for
both static and
earthquake
loadings.
However
the
designer
should check that the
required
movement
can
take
p•ace
and
that
it
does not affect the
serviceability
or
appearance
of.the
wall. If
the
deformation
that
is required
to
reduce
the
earth
pressure
to
the active
c se
is
not
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1.3.2
available
due to
the
r gid
nature
of
the structureor
foundation,
either the
wall
must
be
designed
to .withstand
a
higher
pressure
or
some
change
made to
the
structure
or
foundation.
If cohesive
back-
fill
is
used the large
displacements
necessary
for the active
condition
means
that
the lataral
earth
pressure
will almost
al•ays
be higher
than the
active
value.
For the
determination
of
eai-•h
pressures
it
is usual
to consider
only
a
unit length
of the
cross•section
of
the wall
and
retained
Soil.
A unit length
is
also
used
in
the
structural
design
of
cantilever
walls
and
other
walls
with
a
uniform
cross-section.
Other
Retaining
Structures
Where
an
earth
retaining
wall
is
part
of
a
mor•
extensive
structure
(e.g.
a
basement
wall
in
a
building
or
an
abutment
wall
of
a
portal
structure
or
is
connected to
another
structuro
(e.g.
a
bridge
abutment
connected
to the
•uperstructure)
the
wall
is usually
subject
to static
earth
pressures
greater
than
active since
the
structure
does
not
allow
full
"yielding"
of
the
soil.
In these
cases,
the
main structure
generally
provides
the
stability
for
the
wall
which
then only
needs
to
have adequate
structural
strength.
The
earth
pressure
on
this
type
of
structure
under earthquake
conditions
depends
on
the
movements of
the structure
and the
forces
exerted
on
the wall
by
the
rest
of
the
structure
as
well
as
the
inertia
forces
from
the
soil.
1.4.1 Basic
Loadings
Twe
basic
earth
pressure
loadings
are
considered
for
design.
These
a)
b)
Normal
loading
Static
earth
pressure
+
water
pressure
+
pressure
due
to
live
loads
or
surcharge.
Earthquake
loading
Earthquake
earth
pressure
+
water
pressure
+
surcharge
but
not
live
loads).
However,
earth
retaining
structures
should
be designed
for
not
less
than
the
pressure
due
to
a
fluid
with
a
density
of
25
Ibs
per
cubic
-•oot.
400
kg/m3).
For
many
walls
of lesser
importance,
earthquake
loading
need
not
be
applied
see
section
4.
Other
Considerations
Consideration
should
als•
be
given
to the
possible
occurrence
of
other
design
cases
or
variations
within the
two
design
cases
given
bove,
caused
by construction
sequence
or
future
development
of
surrounding
areas
For
instance
additional
surcharges
should be
considered in
calculating
active
pressures
and
allowance
made for any
possible
future
removal
of
ground
i•
front
of
the
•all if the passive
resistance
of.this
material
is
included.
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3
SECTION
2
SOIL
PROPERTIES
2.1
GENERAL
Tests
should
preferably be
carried out
on
the proposed backfill
material
and natural
ground
behind and
under
an
earth retaining
structure in
advance
of
design. It is
good
practice to make further soil
tests
on
the
material
exposed after
excavation.
For
all walls higher than
20 feet
(6
metres), e•pecially
those
with
sloping
backfill,
the
soil
properties
of
the natural
ground
and
backfill
should
be
estimated from tests
on
samples
of
the
m•terials
involved.
For
less
important
wails,
an
estimation
of
the
soil
properties
may
be
made from
previous
tests
on
similar
materials. However
a
careful
visual examination
of
the
material,
particularl•/
that
at the
proposed
foundation
level,
should
be
made
with
the
help of
identification tests to
ensure
that the assumed
•terial
type
is
correct.
2.2
SELECTION
AND USE OF BACKFILL
The
ideal backfill is
a
free
draining granular material o2
high
shearing
strength.
However
the
final choi0e
of
material should
be based
on
the costs
and
availability
balanced
against the desired
properties.
In
general the
use
of
cohesive
backfills
is
not recommended. Clays
"ar•subject
•o
seasonal
vaF•atiohs•
•welling
(see
2.9),
and
deteriorat on
which
all lead to
an
increase
in
pressure
on
a
wall. They
are
difficult
to
consolidate
and
long
te•m settlement
problems
are
considerably greater
than
with
cohesionless
materials.
For cohesive
backfills,
special attention
must
be
paid to the
provision
of drainage
to
prevent
the
build-up of
water
pressure.
Free draining
cohesionless materials
do
not rgquire the
same
amount
of
attention in
this respect•
The
wall
deflection
required to produce the active state
in
cohesive
•mterials
may
be
up
to •O ti• greateF•than
that for
cohesionless
materials.
• •,is, together
with
the fact
that the former
generally
have
lower values
of
shearing strength,
means
that the
amount of shearing
strength mobilised for
any
given
wall
movement •s
Considerably
lower
for cohesive materials
than
for
cohesionless
materialsZ The corresponding active earth
pressure
for
a
particular
wall
movement
•ill
therefore
be
higher'if
cohesive soil is used
for backfill.
In'cases•of
a
high
S•ismic
coefficient
and for
a
steeply
sloping
back-
fill,
the active
earth
pressure
will be
substantially
reduced
if the failure
plane
occurs
in
a
material with
a
high angle
of
shearing
resistance.
(See
figures
20 to
27).
In
some
circumstances
it
may
be economical
to
replace
weaker
material
so
that
the
above
situation
occurs.
However also
see
3.3.6.
It is
essential
to
•pecify
and supervise
the
placing
of backfill
to
ensure
tnat
its properties
•,
c
and
y)
agree
with
the design assumptions
bo•h
for
lateral
earth
pressure
and
d@ad
weight
calculations..
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2.3
DENSITY
The
density
of •oil
depends
on
the
specific
gravity
of
the
solid
articles
and
the
propo•ions
of
solid,
air
and
water
in
the
soil.
The
verage
specific
gravity
of
the
soil
particles
is
about
2.65
for
sand
or
rock
and
2.70
for
clays,
however
this
will
va
y
• um
area
to
area.
The
roportion
of
the
total volume
that
is
made
up
of
this
solid
material
is
dependent
on
the
degree
of
compaction
or
consolidation.
An
estimate
of-the
density
of
backfill
material
•o
be
used
behind
a
retaining
structure
•y
be
obtained
from
standard
laboratory
compaction
ests
on
samples
of
the
material.
The
density
chosen
must
correseond
to
the
compaction
and
mo.isture
conditions.that
will
apply
in
the
actu•l
ituation.
The
density
of
natural
soll
should
be
obtained
from
undisturbed
samples
kept
at
the
field
moisture
cantent,
and
volume.
For
low,
relatively
nimportant,
walls
the
density
o•
the
soil
behind
the
wall
may
be
estimated
from
the
typical
values
given
in table • In
general
the
saturated
density
hould
be
used
in
calculations
involving
clay
filling.
•0•:
In
eaF-•h
pressure
calculations
using
metric
quantities,
density
m•s•
e
in
force
units,
i.e.
mass
densities
in
k•/m
•
must
be
multiplied
y
9.81
to
give
the
equivalent
force
in
N/m•).
2.4
EFFECTIVE
STRESS
AND
PORE
PRESSURES
An
effective
stress
is
the
stress
or
p•6s•u•e)
transmitted
through
•he
oints
of
contact
between
the
solid
particles
of
the
soil.
It
is
this
stress
that
determines
the
shearing
resistance of
the
soil.
T
tres•
at
any
point
in
the
soil
mass
•
•
•-•
he
effective
• • •.•u Dy suaTracting
the
ressure
transmitted
by
water
in
the
voids
pore
water
pressure)
from
the
otal
stress,
i.e.:
positive
pore
water
pressure
means
a
reduced
effective
stress
and
there-
fore
a
reduced
soil
shearing
strength
which
leads
to
an
increase
in
earth
pressure in
the
active
case. A
negative
pore
pressure
gives
an
increase
in
soil
strength.
Pore
water
pressures
result
from
a
number
of
factors.
ohesive
soils
may
retain
pore
pressures
due
to
a
previous
loading
since
the
dissipation
of
pore
pressures
in
these
materials
takes
months
or
even
yearsunder
some
conditions.
Negative
pore
ware
r•ssur
P
es
may
be
induced
by
capillary
tension
in
moist
sand.
This
particular
effect
is
however
transitory
as
it
is
destroyed
if
the
sand
dries
or
if
it
is
saturated
with
water.
Positive
pore
pressures
can
develop
due
to
static
water
pressure,
seep-
age
of
water,
the
effect
of
shock
or
vibration
in
Some
soils,
or
if
the
stress
increases
more
rapidly
than
the
pore
water
can
flow.
Pore
pressures
due
to
static
water
pressure
and
seepage of
water
are
covered
in
section
6.
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5
TABLE
I
REPP•SENTATIVE
VALUES
FOR
DENSITIES
OF
SOILS
(Basic
Data
from
References
3 and
5)
MATERIAL
Clean
gravel
or
rock
loose
dense,
poorly
graded
dense, well
graded
Well graded, clean
sands,
m-avelly sands
•loose
dense
Poorly
graded
clean
sand,
sand-
gravel
mix
loose
dense
Clayey
sand
loose,
poorly
graded
dense,
poorly
graded
Fine
and silty
sands
and.
silt
loose
dense
Sand-si
It
clay
mixed
with
•gh_t• l_y
plas•tic
fines
C'layey
gravel,
psorly
graded
grave
l-sand
clay
Silty
gravel,
poorly
crade'd
gravel-sand
si
It
Glacial
t-ill
very
mixed
grained
Glacial
clay
soft
stiff
Organic
clay
so'ft
slightly
organic
sof
•ery
organ
c
DENSITIES
Dry,
Yd
Saturated,
Ysat
(Ib/ft
3
(kg/m•)
100-110
1600-1760
115-125
1840-2000
125-135
2000-2160
90-100 1440-1600
1107130
1760-2080
100-I 10
1600-1760
110-120
1760-1920
90-105
1440-1680
105-115
1680-1840
90-100
1440-1600
110-120
1760-1920
110-130
1760-2080
115-130
1840-2080
120-135
1920-216 0
130-135
2080-2160
(lb/ft 3
(kg/mS)
120-130
1920-2080
130-140
2080-2240
120
1920
130
208O
125
2000
135
2160
145
2320
I00-120
1600-1920
125-135
2000-2160
95-100
1520-1600
85-
90
1360-1440
Dams;Ties
must
be
converted
to force
units for
use
in
earth
pressure
alculations.
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2.5
SHEARING
STRE;•GTH
The
sheari.ng
strength
of
a
sol
is
important
ateral
deformations
of
the
soil
boundary
occur
in
s tuatio•s
•here
The
maximum
shear
stress
hat
a
sample
of the
soil
can
sustain
under
different
normal
stresses
should
e
obtained
by
compression
or
shear
box
testing.
The
sample
must
be
at
a
density
and
moisture
content
corresponding
to
that
of
the
backfill
or
natural
ground.
The
plotted
results
of
these
tests
will
give
an
envelope
f
shearing
strength
at
failure
or
yielding
of
the
soil.
This
envelope
is
sually
represented
by
a
straight
line,
which
is
expressed
as:
s
c
+
•
tan
(in
terms
of
total
stress),
or
s
c'
+-•
tan
9T
(in
terms
of
effective
stress).
This
method.of
representing
the
shearing
strength
of the
soil,
is
usedn
these
notes.
An
effective
stress
analysis
should
generally
be
used.
In
this
case
c'
and
•
are
used
in
place
of
c
and
•
in all
calculations.
Tests
must
be
onducted
in
such
a
way
fhat
the
shearing
strength
is
given
in
terms
of
ffective
stress.
This
me ns
that,
either
the
test
loading
must
be
applied
lowly
and
drainage
provided
so
that
any
pore
water
can
adapt
itself
to"
the
hanged
stress
conditions
(drained
test),
or
measurements
of
pore
water
ressures
must
be
taken
during
consolidated-undrained
tests
and
the
normal
tress
adjusted
accordingly
(see
2.4).
If
c'
and
•
(effective
stress
soiltrength
parameters)
are
used
in
the
calculations
for
lateral
earth
pressure,
earing
pressure,
etc.,
the
effect
of
any
field
pore
water
pressures
must
be
ncluded
in
the
analysis.
In
certain
soils,
the
field
pore
water
pressures
may
be
simulated
by
he
undrained
tests
mentioned
above. In this
case
no
further allowance
eed
be
made
for
field
pore
water
pressures and
the
analysis
of
the
earth
ressure
forces
may
be
carried
out
in
terms
of
total
stress.
Saturated
undisturbed
soils
with
relatively
low
permeability,
such
as
silt
and
silty
sand,
ar@ likely
to
fail
in
the
field
under
conditions
imilar
to
those
under
which
the
consolidated-undrained
tests
are
made,
and
hear
failuFe--in-saturated-sand
due
to
the
rapid
draw-down
of
the
water
able
also
corresponds
to
the
consolidated-undrained
condition.
Therefore
n
these
cases,
the
consolidated-undrained
shearing
strength
parameters
ould
be
usedwith
a
total
stress
analysis.
A
condition
that
may
be
approached
in
constructions
using clay
filling
hich
becomes
saturated
or
in
a
saturated
undisturbed
clay
m ss
is
that
of
he
stress
changing
m•re
rapidly
than
the
pore
water
can
flow.
If
the
hearing
strength
of
the
saturated
clay
in
this
condition
is
determined
by
sing
an
undrained
triaxial
t•st
it
is
usually
found
to
be
independent
of
he
normal
pressure
(i.e.
•
o).
Since
there
re
uncertainties
in
the
pplication
of
these
results,
an
unconfined
compression
test
is
usually
mployed,
where
theoretically
c
qu/2
if
•
o.
This
value
of
c
is
used
ith
a
total
stress
analys
s
for
the
situations
described.
Representative
values
for
the
angle
of
shearing
resistance
in
terms
of
ffective
stress,
•
and
total
stress
•
are
given
in
table
2.
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7
For
any
particular
material,
the
shearing
resistance
depends
on
the
degree
Of
compaction
or
consolidation.
For loose
sand
•
is
approximately
equal
to
the
angle
of
repose
in the
dry
state.
TABLE
2
REPRESENTATIVE
VALUES
FOR
THE
ANGLE
OF
SHEARING
RESISTANCE
(Values
Obtained
Mainly
from
Reference
5
c
o
in
all
the
cases
except
clay
where
c
qu/2)
Material
Sandy
gravel
or
rock
filling
and
loose,
round
gr•ins,
uniform
dense,
round
grains,
uniform
-loose,
angular
grains,
well
graded
dense,
angular
grains,
well
graded
Silt
and
silty
s•nd
loose
dense
Clayey
sand
Clay,
normally
loaded
or
slightly
preconsolidated
(Degrees)
35-45
28
34
33
45
27-30
3O-35
20-25
22-30
•
(Degrees)
(Saturated)
20-22
25-30
14-20
2.6
BASE
FRICTION
•,
Typical
value•
of -f-ri•ib-h--•-ngle
T•b)
end
adhesion
(c
b)
for
calculating
ae
shearing
resistance
between
a
concrete
base
and
the
foundation
material
re
given
in
table
3.
These
values
may
be
used
for
low
walls
in
the
absence
f
specific
test
data.
Ifa--base
key
is
used
the
failure
plane
wi
enerally
be.
through
the
foundation
soil
and therefore
the
shearing
esistance
i•
that
of the
soil
•b
• and
Cb
c•.
2.7
MODULUS
OF
•LASTICITY-AND
POISSON S
RATIO
The
relations
between
stress
and
strain
in
soils
are
important
in
the
ettlement
of
soil-supported
foundation•.
They
also
determine
the
change
n
earth
pressure
due
to
small
movements
of retaining
walls
or
other
earth
upports.
These
relationships
are
complex
since
they
depend
on
stress,
train,
time,
inltiel
decree
of
saturation
and
Various
other
factors.
How-
ver
it
is
often
convenient
to
express
them
in
terms
of
•odulus
of
elasticity
nd
Poisson s
ratio,
since
for
small
stress
differences
the
soil
behaviour
losely
e•proxlmates
that
for
a
perfectly
elastic,
homog=neous
material.
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8
The modulus
of elasticity of
the
soils
E
s
is
important
in
problems
where displacements
are
to
be calculated
The
value
is
usually
determined
from
triaxial
compression tests,
but plate bearing
tests
may
be
used.
Seismic
methods
may
be
used
to check
a
larger
mass
of
material,
however
the
values
obtained must
be
corrected
since
seismic
values
of E
s
are
always
onsiderably
higher •han
slatic
values particularly
•n jointed
rock,
and
ar•
not applicable
to
problems
o• static
loading.
For
all
soils the
elastic
mddulus
increases
with
increasing
onsolidation
p[essure,
Pc
For loose
sand
E
s
approximately
equals
100
Pc
A
range
of
values for
the modulus
of
elasticity
in
compression
for
selected
soils
is
given
in table
4.
TABLE 3
TYPICAL
FRICTION
•GLES •D
ADHESION
VALUES
FOR
BASES
WITHOUT
KEYS
(Valbes Taken
from
Reference
3)
Interface
Materials
Mass
concrete
on
the
following
foundation
material:
Clean
sound
rock
Cle
gravel,
gravel-sand
mixtures,
•:
coarse
sand
Clean
fine to
medium
sand,
silty
medium
to
coarse
sand, silty
or
clayey
gravel
Clean
fine
sand,
silty
or
clayey
fine
to.
medium
sand
Fine
sandy
silt,
non-plastic
silt
Very
stiff
and
hard
residua.l
or
preconsolidated
clay
Mediu•
stiff
and
Stiff
clay
and silty
clay
Formed
concrete
on
the
following
foundation
mater•al:
Clean
g•avel,
gravel-sand
mixtures,
well
graded
rock fill
with
spalls
Clean
sand,
silty
sand-gravel
mixture,
single
size
hard
rock
fill
Silty
sand,
gravel
or
sand
mixed
with
silt
or
clay
Fine
sandy
sil•,
non-plastic
silt
Soft
clay
and
clayey
silt
Stiff
and hard
clay
and
clayey
silt
Friction
Angle
6b)
Degrees
35
to
45
29
to
31
24 to
29
19
to 24
17
to 19
22
to
26
17
to
19
22
to
26
17
to
22
17
14
•Adhesion
Cb
Ib/ft
z
(kN/m 2)
200
to 700
(9.6
to
33.5)
700
to
1200
(33.5
to
57.5)
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-9
Poisson s
ratio,
•
is
very
important
in
Stress
oriented
problems
(e.g.
tresses
on
retaining
walls
for
no
wall
moven•nt)
since
it
controls
the
Fela•ionship
between
orthogonal
stresses.
It
may
be
determined
from
triaxial
tests;•however
like
the
elastic
modulus,
it
is
dependent
on
the
confining
pressure
and rate
of
loading
amongst
other
factors.
For
granular
or
normally
consolidated
materials,
• may
be
estimated
from
the
relation-
ships
for
at-rest
pressure
coefficients
see
3.4.
Representative
values
are
given in
table
5.
TABLE_____•
t•DULUS
OF
ELASTICITY
FOR
SELECTED
SOILS
(COMPRESSION)
(Values
Taken
from
Reference
3)
Soil
Very
soft clay
Soft
clay
Medium
clay
Hard
clay
Sandy
clay
Silty
sand
Loose
sand
Dense
sand
E
s
psi)
Dense
•and
and
gravel
14,000-
Loess
• •i•,000
Sandstone
Limestone
Basalt
50-
400
250-
600
600-
1,200
I•000-
2,500
4,000-
6,000
1,000-
3,000
1,500-
3,500
7,000-
12,000
28,000
18,000
1,000,000- 3,000,000
2,000,000-
6,000,000
7,000,000-13,000,000
E
s
(•/m
z)
0.35
2.75
1.72
4.14
4.14
8.27
6.89
17.2
27.5
41.4
6.89
20.6
10.3
24.1
48.2
82.7
96.5
193
96.5
124
6
900
20
600
13
800
41 300
48
200
89
500
TABLE
5
TYPICAL
VALUES
FOR
POISSON S
RATIO
Va]ues
Taken
from
Reference
3)
Soil
Ciay,
saturated
Clay,
unsaturated
Sandy
clay
0.4
-0.5
0.1
-0.3
0.2
-0.3
Silt
Sand
dense
co rse
(void
ratio
0.4-0.7)
fine-grained
(void
ratib
0.4-0.7)
Rock
0.3
-0.35
0.2
-0.4
0.15
0.25
O.
-0.4
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2.8
COEFFTCIENT
OF
SUBGRADE
REACTION
In
the design
of
footings
and
wall
f
subgrade
reaction
is
often
used
to
determine
foundation
pressures.
his
concept
is
based
on
the
assumption
that
the
settlement,
•
o•
any
element
of
a
loaded
re
is
entire ly
independent
of
the
load
on
the
djoining
elements.
It
is
further
assumed
that
the
ratio
•KS
=2_
foundations,
the
simplified
Concept
between
the
intensity,
p
of
the
foundation
pressure
on
the
element
and the
orresponding
settlement
is
a
constant,
Ks.
This
foundation
pressure is
alled
the
subgrade
reaction.
The
coefficient
K
s
;s
known
as
the
oefficient
of
subgrade
reaction.
Representative
values
of
K
s
for
oundation
design
ere
given
in
table
6.
NOTE:
TABLE
6
COEFFICIEN•
OF
SUBGRADE
REACTION
(VERTICAL)
Soil
Type
Dens•
gravel
and
gravelly
soils
(no
lay
fines)
•ense
sand
and
sandy
soils
including
layey
sand,
clayey
gravel
Silts,
clays
of
low
compressibility
Clays
of
high
compressibility
K
S
lblin2/in
>300
200-300
100-200
55-100
kN/m21mm
>8O
55-80
25-55..
15-25
For
clays
K
s
may
be
assumed
to
vary
linearly
with
qu,
from0
Ib/in2/in
for
qu
of
14.5
Ib•in
2
to
330
Ib/in2/in
for
qu
of
5
Ib/in
2
In
metric
units
K
s
varies
from
8
kN/m2/mm
for
qu
of
100
kN/m
z
to
0
kN/m2/mm
for
qu
of
380
kN/m
2.
2.9
SIqELLING
AND
SOFTENING
OF
CLA•S
Some
clays,
particularly
those
with
high
plasticity
(plasticity
index
exceeding
20)
tend
to
expand
in
the
presence
of
water
and
if
restrained
by
a
structure
can
develop
very
high
earth
pressures
e•ceeding
10,000
Ib/ft
2
480
kN/m2).
These
pressures
are
not
related
to
soil
strength,
but
to
the
mineralogy
and
initial,
moisture
of
the
clay.
Swelling
pressures
can
be
estimated
from
laboratory
swell
tests,
but
at
present
such
predictions
are
not
too
reliable.
These
pressures
usually
only
develop
in
the
zone
of
weathering
which
is
to
a
depth
of
3
to
5
feet.
(I
bove
pressures
should
be
con -
d•r•
•
.to
I.•
metres).
The
non-yieldina,
walls
•--•7
.-.cohesive
so•l
•s
to
be
used behind
eea
not
De
allowed
for
n
the
case
of fre•
sTanding
walls
t;here
a
small
yield
can
be
tolerated.
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When
a
natural
deposit
of clay
or
silt
is disturbed
by
an
excavation
for
a
retaining
wall
the
change in stress
conditions
and
water
content
may
lead to
a
change
in
shearing
strength
with
time.
With
stiff
fissured
clays
it has been shown
that
progressive
softening
c n
reduce the
shearing strength
to
a
small
fraction
of its
original
value.
This
is
usually
d,,•
to
Water
percolating
into
the
fissures
which
open
at
the
time
of
excavation
for
the
wall.
Earth
pressures
should
therefore
be calculated
using
a
'residual'
strength to
allow
for this
deterioration.
References
5
and 28
should
be
consulted.
In
fissured
clays
and
clay
filling
the
rate
of
softening
is
reduced by
adequate
drainage
and
if the wall is
prevented
from
yielding
progressively.
However
the
latter
requirement
will
me n
that lateral
earth
pressures
higher
han
activewill
result.
•-•.•.10
PERMEABILITY
The
permeabiliti•s
of
soi
s
in
broad terms
are
givenin
table
7.
The
permeebiIities
of
granular
materials
are
given
in greeter
detai
in figure
5,
•ccording
to
the
pahticle
grading.
TABLE
7
PERMEABILITIES
OF
SOILS
Clean
gravel
Cl•an
sand,
clean
sand
andlgravel
mixture
Wery
fine
sand,
organic
and
inorganic
silt,
mixture
of
sandy
silt
and
clay,, glacial
till,
stratified
clay
deposits,
etc.
Homogeneous
clays
below
zone
of
weathering
Value•
Tgken
from
Reference
5
Soil
Type
Coefficient
of
Permeability,
k cm/sec)
100
-I.0
1.0-i0-3
2.11
LIQUEFACTION
In
materials
with
no
cohesion,
if the
pore
pressure
is
made
to
increase
so
as
to
reduce the
effective
stress
t•
zero,
a
condition
known
as
liquefaction
m•y
result
•here the
material has
no
shearing
strength
an•
there-
fore
behaves
like
a
fluid.
This
can
happen
in
saturated
loose
sands
and
silts
where
a
shock
or
vibration
c uses
spontaneous
collapse
of the
grain
•ructure
(densification)
and therefore
an
increase
in the
pore
water
•ressure.
Saturated
sandv
soil
layers
which
are
within
•0
#eat
9
metres)
f
the
ground
surface,
have
a
standard
penetratio•
temt
N-value
less than
•have
a
coefficient
of
uniformity
less
than
6 and
also
have
a
D20-value
be-
ween
0.04
mm
and 0.5
mm,
have
a
high
potential
for
liquefaction
during
earth-
uakes.
Saturated
sandy soil
l.ayers
which
have
a
D20
value
between
0.004
mm
and
0.04
mm
or
between
0.5
mm
and 1.2
mm
may
liquefy
during
earthquakes.
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SECTION
3
STATIC
EARTH
PRESSURE
3.1
STATES
OF
STRESS
The
stresses
at
any
point
within
a
soil
m ss
may
be
represented
on
the
ohr
co-ordinate
system
in
terms
of
shear
stress,
•
and
effective
normal
tress,
o'
(see
references
or
6
for
the
plotting
of
stresses
and
use
of
the
system).
On
this
system,
the
shearing
strength
of
the
soil
at
various
ffective
normal
stresses
gives
an
envelope
of the
ossible
combinations
of
shear
end
normal
stress.
When
the
maximum
shearing
strength
is
fully
mobilised
along
a
surface
within
a
soil
mass,
a
failure
condition
known
as
a
state
of
plastic
(or
imiting)
equilibrium
is
reached.
Rankine's
active
and
passive
states
of
stress
result
when
Shear
stresses
equal
to
the
maximum
shearing
strength
of
the
soil
develop uniformly
and
unhindered
in
two
major
directions
through-
ut
a
soil
mass
due
to
lateral
extension
or
compression.
Where
the
combinations
of
shear
and
normal
stress
within
a
soil
m•s
ll
lie
below
the
limiting
envelope
the
soil
is
in
a
state
of
elasticquilibrium.
A
special
condition
of
elastic
equilibrium
is
the
at-rest
tate,
where
the
soil
is
prevented
from
expanding
or
compressing
laterally
ith
changes
in
the
vertical
stress.
3.2
AMOUNT
AND
TYPE
OF
NALL
MOVEMENT
.,•
The
limiting
eqdilibrium
theories
all
require
that
the
maximum
shearingtrength
of
the
soil
is
mobilised.
This
however
reouires
deformation
in
the
soil.
The
deformation
of
a
supporting
structure
only
has
a
local
effect
n
the
state
of
stress
in
the
soil.
The
remainder
of
the
soil
remains
in
state
of
elastic
equilibrium.
The
state
of
stress
in
the
locally
isturbed
zone
end the shape
of
this
zone
is
dependeqt
on
the
amount
and
.type
of
wall
deformation.
This
also
determines
the
shape
of
the
pressur•
istribution-on'the--wall
•n-d
the
intensity
of
the
pressure.
For
no mOvement
of
a
retai•ing
wall.system
at-rest
earth
pressures
(or
ressures
due
to.compaction)
ac,
on
the
•..all..
When
a
wall
moves
ou
ward,
the.
shearing
strength
of
the
retained
sell
resists
the
correspondina
outward
ovement
of
the
soil
and
reduces
the
earth
pressures
on
the wall.
The earth
pressure
calculate•
for the
active
state
is
the
absolute
minimum
value.
When
the
Wall
movement
is
towards
the
retained
soil
the
shearinc
streneth
of
the
soil
resists
the
corresponding
soil
movement
and
increases
•ne
earth
ressure
on
the
wall.
The
earth
pressure (or
resistance)
calculated
for
the
passive
state
is
the
maximum
value
that
can
be
developed.
TABLE
8
MOVEMENT
OF
WALL
NECESSARY
TO
PRODUCE
ACTIVE
PRESSURES
S0il
Cohesionless,
dense
Cohesionless,
loose
Clay,
firm
Clay,
soft
Wall
Y•eld
0.001
H
;
O.
O01-0.
002
0.01
-0.02
H
0.02
-0.05
H
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The
amount
of
movement required to produce the active
or
passive•
states in the
soil
fs
dependent mainly
on
the type of
backfill material.
Table
8 gives the outward movement of
a
wail
which is
necessary
to produce
an
active state of stress in the
retained soil.
The movements
required to
produce
fell
•assive
resistance
are
considerably
larger,
especially in
cohesionless
material.
These
requirements
apply
whether
the
mevement
is
a
lateral
translation of •he whole
wall
or
a
rotation about the
base.
The
pressure
distributions for
full
active and passive states
are
basically
triengular
for constantly sloping ground
(see
3.3 .
If
a
wall
rotates
about its
top
in the direction
away
from
the
soil•
the
soil
between
the
wall
and
the surface
of sliding
does
not
all
pass
into
th•
active
state.
The soil
near
the top
of
the
wall
stays
near
the at-
res•
state.
This
condition
arises
in cuts
that
are
braced
as
excavation
proceeds
downwards
from
the
top.
The
distribution
of
pressure
may
be
represented
by
a
trepezium w•th
dimensions
which
vary
according to the
soil
type
see
figure 18.
(• •i
The amount Of wall
m•vement
which will
take
place depends mainly
upon
•The
foundation conditions
end the flexibility
of
the wall.
The designer
must
ensure
that
the
calculated
earth
pressures
correspond to the available
wall
movement.
A
free
standing
wall
need only be
designed for
active
each
pressure as
far
as
stability
is concerned since,
if it starts
to
slide
or
overturn
under
higher
pressures,
the
movement
will be
sufficient
to
reduce
the
pressures
to active.
Flowever if it
is
on
a
strong
foundation
or
otherwise
fixed
so
that adequate
stebility
is provided,
the
stem
may
be
subject
to
pressures
near
those for the
at-rest state.
The following
pressure
coefficlents shoul•be,
used for
rigid
foundation
cenditions unless
mere
exact
analysis of
movements
is made:
Ca)
(b)
(c)
CounterforT
or
gravity
type
walls founded
on
rock
or
piles
K
o
Cantilever
walls less than 16
feet
(5
metres)
high
founded
on
rock
or
piles
0.5 (Ko+K
A)
Any
wall
on
soil foundations
or
cantilever
walls higher
KA
han 16
feet
(5
me• •
Bridge abutment walls
tha•
are
not
included
in
the
above categories
should
be
designed
for at-rest
pressures.
Where
abutment walls
are
framed
in
with the
superstruclure, temperature
movements
may
produce
higher
pressures
•.see
reference 26.
T•e
tilting
movement that will
result
when earth
pressures
act
on
a
retaining
well
may
be
estimated
by
simulating
the
foundation
soil
as
a
series of
spFings with
an
appropriate coefficient
of
subgrade
reection
see
2.7.
The base rotation
(in
radians
is then given
by:
8
b
12Ve/KsL•
3.3
LIMITING
EQUILIBRIUM
CONDITIONS
3•3.1
The Rankine
Earth Pressure
Theory
If
Rahklne s•
active
or
passive states of stress
exist
throughout
a
zone
in
a
soil
mass
en
exact
solution (fully
satisfying
both static
equilibrium
and
the
condition
for failure)
may
be
obtained for
the
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3.3.2
14
earth
pressure
from
that
zone
However,
useabie
equations
result
only
if
the
surfaces
of
failure
are
planar.
This
is
the
case
in
a
semi-infinite
mass
of
coheslonless
soil
with
the
ground
surface
at
any constant
slope,
and
also
in
cohesive
soil
with
a
horizontal
round
surface.
RangineSs
equations
give
the
earth
pressure
on
a
vertical
plane,
hich
is
sometimes
called
the
virtual
back
of
the
wall. The
equations
for
cohesionless
soil
are
giver
in
figure
2.
The
earth
pressure
on
the
vertical
plane
acts
in
a
direction
parallel
to
the
ground
surface
andis
directly
proportional
to
the
vertica.l
distance
below
the
ground
surface
(i.e.
a
triangular
pressure
distribution
ith
the
resultant
acting
at
I/3
Equations
for
Rankine s
conditions
in
cohesive
soils
with
a
horizontal
ground
surface
are
given
in
figure
iO.
The earth
ressure
on
tile
vertical
plane
acts
horizontally.
The
pressure
distribution
is
similaP
to
that
for
cohesionless
soil
except
that
a
zon•
of
tension
at
the
top
is
neglected
siace
soil
cannot
sustain
ension.
Rankine
active
earth
pressure
coefficients
for
cohesion-
less
soil
are
presented in
graphical
form
in
figure
3.
If
Rankine s
states
of
stress
exist
in
cohesive
soil
with
a
uniformly
sloping
ground
surface,
useable
equations
do
not
result,
since
the
failure
surfaces
are
curved,
and
the
pressure
distributio•
is
not
theoretical
y
a
linear
function
of
depth.
An
exact
o
ution
for
this
case
can
be
obtaine•
by
using
the
M•hr
diagram
ee
the
circle
of
stress
method
in
reference
I.
Rankiners
conditions
are
theoreticaIl.y.•nl•y
applicable
to
•etaining
alls
when
the
wall
does
net
interfere
with
the
formation
of
any
part
of
the
failure
wedges
that
form
on
either
side
of
the
vertical
plane,
or
where
an
imposed
boundary
produces
the
conditions
of
stress
that
would
exist
in
the
uninterrupted
soil
wedges.
The
vertical
plane
on
which
the
pressures
are
calculated
is
not
normally
a
failure
plane
(only
in
the
case
where
•
•).
However
a
vertical
wall
would
satisfy
the
Rankine
conditions
if
the
angle
of
wall
friction,
•
is
equal
to
the
backfi•ll
slope.
In
many
cases
this
would
not
represent
a
practical
situation
since
it
implies
a smooth
wall
for
horizontal
backfi-•l.
The
Coulomb
Earth
Pressure
Theory
This
theory
di•ectly
gives
the
resultant
pressure
against
the
back
of
e
retaining
structure
for
any
sI•pe
of
the
wall
and
for
a
range
of
wall
friction angles.
It
assumes that
the
soil
slides
on
the
back
of
the
wall
and
mobilises
the
shearing
resistance
between
the
back
the
wall
and
the
soil
as
well
as
that
on
the
failure
surface.
The
•oulomb
equations
reduce
to
those
of
the
Rankine
theory
if
a
vertical
wall
surface
with
an
angle
gf
wall
friction
equal
to
the
backfiI|
slope
is
used.
Other
Cases of
wall
slope
or
wa
•riction
require
CUrved
surfaces.of
sliding
to
satisfy
static
equilibrium.
The
degree
of curvature may
be
Quite
marked
especially
for
passive
conditions.
However
Coulomb•s
theory
aSSumes
that
the
failure
wedge
is
always
bounded
by
a
plane
surface,
and
.it
is
therefore
only
an
approximation
usuaJ.ly
on
the
unsafe
side).
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15
d•rect•on
and
magnitude
for
the.wall
friction
angle
for
passive
pressure.
However
for
large
pos
tive backfill
sloes
or
la
rge
values
the
error
due
to
the
assumpTion
of
a
plane
fai
ure
surface
leads
to
a
large
over-estimat
on'
of th•
Dassive
resistan
Th•s
is
accentuated
further
when the
back
of
the
wall
has
a
negative
The
simplifying
assumption
also
me ns
that
static
equilibrium
.is
not
always
completely
satisfied,
i.e.
the
fQrces
actihg
on
the
soil
wedge
cannot
all
be
resolved
to
act
through
a
common
point. The
error
from
an
'exact'
solution
is
proportional
to
the
amount by which
static
equilibcium
is
not
satisfied.
Equations
for
Coulomb•s
conditions
in
cohesionless
soil with
e
constant
ground slope
re
given
in figure
4.
In the
active
c se
the
soil tends
to slip
downward
along
the
back
of
the wall
causing
the
resultant
earth
pressure
to
be inclined
at
a
positive
angle
(see
figure
4)
to
the
normal
to
the wall.
t
is
recommended
that
an
angle
of
wall
friction
of
+2/3
@ be
used
in
the
equation
for
active
pressure
for
concrete
walls which
have
been
cast
against
formwork.
Coulomb
active
earth
pressure
coefficients
re
given
in
figures
5 to
8
and the
corresponding
failure
planes
in
figure
9
for
selected
values
of
angle
of
internal
friction,
@.
Linear
interpolation
may
e
used to
fi.nd
the
earth
pressure
coefficient
or
failure
plane
angle
or
intermediate
values
of
@.
Passive
Pressures.Using
Equations
The
movement
required
to
produce
passive
pressure
leads
to
the
soil
sliding
upward
on
the
failure
surfaces
including
the
back
of
a
wall
or
anchor
block).
There'foce
Rankine's
equation
does
not
theoretic-
ally
apply
for
passive
resistance
of
soil
with
a
positive
ground
lope
against
a
vertical
wall because
it
ssumes
a
positive
angle
of
wall
friction
equal
to
the
ground
slope,
when
in
fact
the
wall
friction
angle
would
be
negative.
The
use of
Rankine's
equation
in
this
situation
gives
an
under-estimation
of
the
passive
resistance.
Equations
for
Coulomb s
conditions
allow
the
use
of
the
correct
slope.
In
the.ca•e•
of
a
vertical
wall
the
Rankine
equatiQn
should
e
used.instead
to
give
a
conservative
estimate
of
the
passive
esistance.
For
other
wall
slopes
the
passive
resistance
c n
be
aken
as
Rankine s
passive
pressure
on
the
ve•ical plane
plus
the
eight
of the
soil
wedge
between
the
vertical
plane
and the
pressure
urface.
Alternatively
methods
based
on
curved
failure
surfaces
such
as
the logarithmic
spiral
method
(references
and 5)
may
be
used.
eference
3
chapter
I0
gives
values,
of
KD based
on
the
logarithmic
piral
method
for
the
c se
of
a
vertical-wall
and
sloping
backfill
nd
for
a
sloping
wa•land
level
backfi•l.
For
negative
backfill
lopes,
the
conditions
for
Rankine's
passive
state
may
be
fuifilled
3c
that
a
good
estimation
of the
passive
resistance
may
be
obtained.
he
equation
for
Coulomb's
conditions
also
•ives
a
good
approximation
f.the
passive
resistance
in
this
case,
although
it
wil
generally
T,
I• be •light•y
on
the
unsafe
side.
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For
;•ost
Cases
involving
passive
pressures
encountered
in
retaining
wall
design,
the
ground
surface
is
horizontal
and
the
pressure
surface
may
be
assumed
to
be
vertical.
If
the
angl&
of
wall
friction
is
taken
as
zero
under
these
conditions,
the
Rankine
and
Coulomb
equations
are
the
same
and
the
resulting
passive
resistance
is
on
the
•onservative
side
(since
there
would
be
some
wall
friction
Which
•nCreases
the
passive
resistance).
3.3.4
The
Trial
Wedge
Metho
d
Where
the
ground
surface
is
irregular
or
where
it
is
constantly
sloping
in
cohesive
soil
a graphical
procedure
USing
the
assumption
of
planar
failure
SUrfaces
is
the
simplest
approach.
This
procedure
is
known
as
the
trial
Wedge
method
(see
figures
The
backfill
is
divided
into
wedges
by
selecting
planes
through
th•
heel
of
the
wall.
The
forces
acting
on
each
of
these
wedges
ere
combined
in
a
force
polygon
so
that
the
magnitude
of
the
resultant
earth
pressure
can
be
obtained.
A
force
polygon
is
constructed
even
• •
although
She
forces
acting
on
the
wedge
are
often
not
in
•ment
' ',•_•
equilibrium.
This
method
is
therefore
an
apProximation
with
the
same
assumptions
as
the
equations
for
Coulomb•s
conditions
and,
for-
..•
a
ground
surface
with
a
constant
slope,
will
give
the
same
resu'It.
If
the
conditions
are
the
same
as
those
for
Rankine's
equations,
the
trial
wedge
earth
pressures
will
Correspond
to
these
also.
The
limitations
On
wall
friction
and
passive
pressures
mentioned
in
the
use
of
the
Rankine
and
Coulomb
equations
also
app:M
to
the
trial
wedge
method.
The
adhesion
of
the
soil
to
the
back
of
the
wall.in
cohesive
soils
is
neglected
since
it
increases
the
tension
crack
depth
and
hence
reduces
the
active
pressure.
i:
For
the
active
case
•he
maximum
va
ue
of
the
earth
pressure
.
calculated
for
the
ver
ous
wedees
is
nterpolating
between
required.
This
is
The
re
uired
values.
Fo
Y
i
q
m•nlmum
value
•s
similarly
obtained,
r
the
passive
case
The
direction
of
the
res ultant
earth
pressure
in
he
force
polygons
•..
should
be
obtained
from
he
considerations
of
3.3.1
to
3.3.3
(•)
the
cases
where
this
force
substitute
constant
•
•ct•
p•rallel
to
the
erou•
For
•
so
both
w•+h
•P•
snoula
be
used
as
•h•,.,• •
o•Tace
a
•
WITHOUT
cohesion.
in
Tlgure
15
for
For
cohesion•es•
material,
Culmann,s
graphical
construction
(figure
12)
provides
a
•compact
method
of
plotting
the
resultant
earth
pressures
for
the
various
wedges
and
obtaining
the
maximum
value with
the
COrresponding
failure
plane.
In
cohesive
soils,
according
to
theoretical
considerations,
tension
exists
to
a
depth
of
2c
o
•-tan
(45 °
+
•/2)
for
both
horizontal
and
slopin•
ground
surfaces.
Vertical
tension
Cracks
will
develop
in
this
Zoae
since
soil
cannot
sustain
tension.
One
of
these
cracks
will
extend.down
to
the
failure
Surface
and
so
reduce
the
length
on
which
Cohesion
acts.
The
effect
of
this,
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3.3.5
17
3.3.6
together
with
the
slightly
smaller
wedge
weight
is
the same
as
neglecting
the
reduction
in
total
pressure
provided
by
the
tension
zone
according
to
the
Rankine
and
Coulomb
equations.
For
an
irregular
ground
surface
the
pressure
distribution
is
not
triangular.
However
if
the
ground
does
not
depart
significantly
from
a
plane
surface,
a
linear
pressure
distribution
may
be
assumed,
and
the
construction
given
in
figure
16
used.
A
more
accurate
method
is
given
in
figure
17.
The
latter
should
be
used
when
there
ere
abrupt
changes
in
the
ground
surface
or
there
are
non-uniform
surcharges.
Geometrical
Shape
of
the
Retaining
Structure
The
geometrical
shape
of
the
retaining
struct6re largely
determines
which
of
Rankine s
or
Coulomb s
conditions
are
satisfied
or
•ost
nearly
satisfied
for
a
particular
soil
and hence
how
the
pressure
should
be
determined.
Rankine s
conditions
may
be
taken
as
applying
to
cantilever
and
counterfort retaining
walls with
heel
lengths equal
to at
least
half
the
wall
height.
The
earth
pressure
is
calculated
on
the
vertical
plane
through
the
re r
of the
heel
which
is
sometimes
referred
to
as
the
Virtual
back
of
the
wall.
Coulomb s
conditions
may
be
applied
to
gravity
type
walls
and
walls
with
small
heels,
since
it
will
usually be
found
that
the
soil
siiUes
on
the
back
of
the
wall.
For
further
information
on
the
application
of
Rankine s
or
Coulomh s
conditions,
see
reference
I.
Limited Backfill
The
limiting
equilibrium
methods
given
above
ssume
that the
sol
is
homogeneous
for
a
sufficient
distance
behind
the
wall
to
enable
an
inner
failure
surface
lto
form
in
the
position
where
static
equilibrium
is
satisfied.
Where
an
excavation
is
made
to
accommodate
the
wall,
the
undis•r•ed
m•erial
may
have
a
different
strength
from
that
of
the
backfill.
If
equations
are
used
the
position
of
two
failure
planes
should
be
calculated
one
using
the
properties
of the
back-
fill
material
and
one
using
the
properties
of the
undisturbed
material.
If
both
fall
within
the
physical
limit
of the
backfill
the
critical
failure
plane
is
obviously
the
one
calculated
using
the
backfill
properties.
Similarly
if
they
both
come
within
the
undisturbed
material,
the
critical
one
is
that
for
the
undisturbed
material
properties.
Two
other
possible
situations
may
however
arise
one
where
critical
failure
planes
occur
in
both
materials
(the
one
gi•ng
the
maximum
earth
pressure
is
used),
and
the
other
where
the
failure
plane
calculated
with
the
backfill
properties
would
fall
within
the.
undisturbed
material
and
the
failure
plane
for
undisturbed
material
would
fall
within the
backfill.
In
the
latter
case,
which
occurs
when the
undisturbed
material
has
a
high
strength,
the
backfill
may
be
assumed
to
slide
on
the
physical
boundary
between
the
two
materials.
The
earth
pressure
equations
do
not
apply in
this
case,
but
The
trlcl
wedge
metho,
may
be
used
with the
already
selected
critical
faiiure
plane
and
the
backfill
soil
properties.
The
total
pressure
thus
calculated
will
be
less
than the full active
value
however
the
variation
of
pressure
with
depth
is
not
linear
it
should
be
deter-
mined by
the
procedure
given
in
figure
17.
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18-
This
is
a
form
of
ever-consolidation.
In
Coarse
grained
soils
the
lateral
pressures
produced
are
equal
to
or
Slightly
higher
than
the
at-rest
pressures.
The
boundary
between
the
two
materials
should
b•
constructed
so
•h•
there
is
no
inherent
loss
of
friction
(or
cohesion)
on
the
failure
SUrface.
Benching
the
undisturbed
material
will
ensure
that
the
failure
surface
is
almost
entirely
through
solid
backfill
material.
ELASTIC
EQUILIBRIUM
CONDITIONS
At-rest
Pressures
The
special
state
of
elastic
equilibrium
known
as
the
at-rest
state
is
useful
as
a
reference
point
for
calculation
of
earth
pressures
Where
only
sma•l
wall
mOvements
occur.
For
the
Case
of
a
Vertical
wall
and
a
horizontal
ground
SUrface
the
coefficient
of
at-rest
earth
pressure
may
be
taken
as:
for
normally
consolidated
mater
als.
as
not
any
bu,,t
,n
Over conso.lidotio T oossume
that
the
material
ngles
and
backfi•l
slopes,
it
may
be
assumed
=- •ss.
rot
other
wall
roportional
to
KA.
At=rest
ea
that
K
o
varies
•re•s•
linearly
With
de•th
•__rth
pressures
may
be •SSumed
to
u•Terlals.
-.um
Zero
at
the
ground
surface
for
al
The
total
at-rest
earth
pressure
force
is
given
by:
o
½
K
o
y
H•
This
acts
at
H/3
from
the
base
of
the
wall
(or
bottom
of
th•
key
fQr
walls
with
ke•s).
For
gravity
type
retaining
walls
the
at-rest
pressure
should
be
taken
as
aC•ing
normal
to
the
back
of
the
wall
(i.e.
•
= o).
For
canti-
lever
and
Counterfort
walls
it
should
be
calculated
on
the
vertical
plane
through
the
rear
of
the
heel
and
taken
as
acting
parallel
with
the
ground
surface.
In
cohesionless
soils,
full
he
mos•
rigidly
•unaort=•
•a?•rest
pressures
will
occur
only
with
ressures
approa•hina
=
In
highly
plastic
clays,
ont•nu:'with
• •
•---esr
may
develop
Unless
wall
movement
can
Over conso]idat•on
Pressures
Several
factors
produce
a
coefficient
greater
than
that
given
in
3.4.1
above.
If
a
braced
excavation
is
Constructed
in
over-
Consolidated
clay,
the
built-in
ever-consolidation
produces
lateral
pressures
in
excess
of
those
that
would
be
obtained
by
USing
the
existing
depth
of
material.
This
is
a
rt
cu•arly
marked
at
shallow
existing
depths.
If
some
wall
mOvement
takes
place
these
high
pressures
dhop
rapidly.
Compaction
of
backfill
in
a Confined
wedge
behind
a
restrained
wall
also
tends
to
increase
lateral
pressures.
In
fine
grained
soils
the
lateral
pressures
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all
ra
low
the
the
3 4 3
produced
by
compaction
may
be
higher
still.
Some
further
Information
on
actual
pressures
for
unyielding
retaining
structures
Is
given
in
references
and
8
Elastic
•heo•y
Methods
When
the
solution
of
a
lateral
pressure
problem
requires
the
estimate
of
some
deformations
or
the
relation
between
load and
deformation,
elastic
methods
of
analvsis
may
be
considered.
Usually
only
the
linear
theory
is
used.
Particular
care
and
judgement is
required
in
order
to
select
appropriate
elastic
constants
and
boundary
conditions.
Currently
available
general
computer
programs
based
on
the
finite
element
method
of
analysis
are
ICES=STRUDL-II
and
the
Ministry
of
Works' plane
stress
or
plane
strain
program
STQUAD2D,
From
elastic
theory
the
coefficient
of
at-rest
pressure
for
a
vertical
wall
and
horizon#al
ground
surface
is
given
by:
Ko
(for
plain
strain).
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20
SECTION 4
EARTHQUAKE
EARTH
PRESSURE
4.1
IdETHOD
OF ANALYSIS
The
most
common
method
of
obtaining forces
due
to
earthquake
loading
is
the
pseudo-static
seismic
coefficient
method.
In this
method,
a
force
equal
to
the weight
of
a m ss
multiplied
by
a
specified
value
of
seismic
coefficient
is
assumed
to
act
statically
at the
centre
of
gravity of
the
m ss°
b)
This
approach
has been
extensively
used
to
determine the
pressure
on
earth
retaining
structures
under earthquakes
see references
9,
I0,
11
and
12)
and
at
this
stage
of
knowledge
it
is the
recommended method.
A
horizontal seismic
coefficient
only
need be
used
s•nce typical vertical
accelerations
have
a very
small
effect
on
earth
pressures
4.2
SELECTION
OF
SEISMIC
COEFFICIENT
The
design
seismic
coefficients
for
use
in
earth
pressure
calculations.
ere
given
in
table
9.
These
are
determined
without
regard
to
the
dynamic
haracteristics
of th•
retaining
structure
or
soil
•
They
are,
however,
dependent
on
the
seismic
zoning
of the
re
and the
importance
of
the
structure.
The
seismic
zone
should
be
determined
from
NZS 1900
chapter
8:
1965 reference
13).
Earth
retaining
structures
should
be placed
in
one
of the
three
importance
categories
as
follows
depend
ng
on
the
size of
the structure,
the
effect
of failure
in
The
structure,
and the
cost
of
reconstruction:
a)
Importance
category
1
Major retaining
walls
supporting
important
structures,
developed
property
or
services,
and the
like,
and
where
failure
would
have
disastrous
consequences
such
as
cutting
vital
communications
or
services,
serious
loss
of life,
etc
Importance
category 2
Free
standing
structures
of
at least
20
feet
6
metres)
in height
in
locations
other
•han
in a)
above
where
replacement
would
be
difficult
or
costly
and/or
where
other
consequences
of
failure
would
be serious.
Importanc•
category
3
For
all
other
retaining
structures
no
specific
provision
for
earthquake
loading
need
be
considered
except that
the
seismic
coefficient
to
be
applied
for
earth
pressure
on.bridge
members
should
be
in
accordance
with
the Highway
Bridge
Design
Brief
reference
14).
TABLE
9
SEISMIC
COEFFICIENTS,
CF FOR
EARTH
RETAL,
IrIG
STRUCTURES
Importance
Category
2
Zone
A
Zone
B
Zone
C
0.24
0.18
0.12
0.17
0.13
0.09
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22
The
pressure
distribution
end
point
of
applicatioq
of
the
resultant
ressure
should
be
determined
by
superimposing
the
dynamic
increment
n
earth
pressure,
4PA•
on
the
static
pressure
diagram
similar
to
the
ethod
given
in
figure•19.
For
the
determination
of
PA
for
this
ase,
the
full
static
pressure
diagram
including
the
part
in
tension
hou
d
be
used
for
cohesive
soils.
For
an
irregular
ground
surface,
he
static
pressure
diagram
may
not
be
a
linear
variation
with
depth
i.e.
the
point of
application
of
PA
may
not
be
at
H/3).
However
he
dynamic
increment
PAE
should
always
be
applied
at
the
2/3H
oint
to
give
a
distribution
varying
linearly
from
a
maximum
at
the
op
to
zero
at the
bottom
of
the
wall (or
key,
for
walls
wi•h
keys).
4.4
SEISMIC
AT-REST
PRESSURES
For
a
completely
rigid
retaining
wall,
the
force
from
the
earthquake
arth
pressure
may
be
approximated
by:
PE
½
Y.H
2
(Ko
+
2
KAE)
where
•KAE
KAE
KA
Where
mevemeny
is
sufficient
for
the
fully
active
c se
to
develop
see
lause
3.2),
the
force
from
the
ea•hquake
earth
pressure
should
be
taken
as
PE
½
Y
H
•
(K
A
+4KAE)
For
wails
of
intermediate
rigidity,
the
earthquake
earth
pressure
should
be
etermined
by
estimating
the
displacement
of
the
top
of
the
wa•I
under
earth-
uake
loading
and interpolating
between
the
values
from
the
two
•quations
iven
above.
The
following
pressure coefficients
should
be
used
for
rigid
oundation
conditions
unless
a
more
exact
analysis
of
movements
is
made;.
(a)
Counterfor•
or
gravity
type
wails
founded
on
•ock
r
piles
Ko
+
AKAE
Cantilever
walls
le•s
than
16
feet
(5
metres)
igh
founded
on
rock
or
piles
(K
o
+
+
(C)
• y
wall
on
soil
foundations
or
cantilever
walls
igher
than
16
feet
(5
metres)
K
A
+ •KAE
The
point
of
application
of
the
resultant
of
the
ea'rth
pressure and
hence
he
pressure
distribution
shou
d
be
de•ermlned
similar
to
figure
19 with
•PAE
a•
2/3H).
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be
23-
SECTION
5
THE
EFFECT
OF
SURCHARGES_
5.1
UNIFO•4
SURCHARGES
Uniform surcharge
loads
may
be
Converted
to
an
equivalent
height
of
fill
and
the
earth
pressures
calculated
for
the
correspondingly
greater
height.
The
equivalent
height
is
given
by:
be
•
cos
B
•
cos
6
•)
The
depth
of
the
tension zone
in
cohesive
material
is
calculated
from
the
top
of
the
equivalent
additional
fill.
The
distribution
of
pressure
for
the
greater
height
is
determined
from
the
procedures
given
in
sections
3
and
4.
The
total
lateral
earth
pressure
is
calculated
from
the
pressure
diagram
neglecting
the
part
in
tension
and/or
the
part
in
the
height
of
{ill
equivalent
to
the
surcharge.
Concrete
buildings may
be
represented
as
a
uniform
surcharge
of
200
Ib/ft2
(10
kN/m
2)
per
storey.
Timber
buildings
may
be
taken
as
half
the
above.
Traffic
Ioadina,
when
at
a
greater
distance
than
2/3
ti•es
the
height
of
the
wa•t
from
the
back
face
of
the
wa•l
may
be
represented
as
a
uniform
surcharge
of
250
lb/f
tz
[12
kN/m
2)-
The
two
loading
cases
shown
in
figure
29
need
to
be
considered.
5.2
LINE
LOADS
Where
there
is
a
superimposed
line
load
running
a
considerable
length
of
this
load
can
be
added
wed
e
to
which
it
is
applied
see
arallel
to
the
wall
the
weight
per
unit
length
hl
to
the
weight
of
the
part•c•l•r,t[•h
o
•ssur
will
be
given
fro•
t•e
[..;i
•n
The
increased
TOTa•
•r
-h=n•e
the
Do
nT OT
K
f•gure
line
load
wi•
a s
•
trial
wedge
procedur
rut
•
e
method
given
in
figure
17
may
be
•i•
application
of
th•s
TOTal
•,•==•'•
Th_
u•d
to
give
the
distributlon
ot
pressure.
•hen
the
line
load
is
small
in
comparison
with
active
earth
pressure,
the
effect
of
the
line
load
on
its
own
shguld
be
determined
by
the
method
given
in
figure
31.
This is based
on
stresses
in
an
elastic
medium
modified
by
experiment.
The
pressures
thus
determined
are
supeFimposed
on
those
due
to
active
earth
pressure
and
other
effects.
5.3
POINT
LOADS
Point
loads
cannot
be
taken
into
account by
trial
wedge
procedures.
•he
method
based
on
Boussinesq'S
equations
given
in
figure
31
should
be
used.
A
similar
method
is
given
in
appendix
H
of
reference
2.
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24
SECTION
6
E•FFECTS
OF
WATER
6.1
STATIC
WATER
LEVEL
Where
part
or
all
of
the
soil
behind
a
wall
is
subm•rged
below
a
statig
ater
level,
the
earth
pressure
is
changed
due
to
the
hydrostatic
poreressures
set
up
in
the
soil.
The
water
itself
also
exerts
lateral
ressure
on
the wail
equal
to
the
depth
below
the
water
table
times
the
ensity
of
water.
If
cohesionless
soil
is
fully
saturated,
and
the
water
in
the
voids
is
ot
flowing,
the
pore
water
pressure
at
a
depth,
y
b'elow
the
water
table
is
equal
to
Yw
Y
where
Xw
is
the
density
of
water.
This
means
that
the
ffective
vertical
pressure
due
to
the
amount
of
soil
that
is
submerged
issat Y
Yw
Y
The
effect
of
the
h•dr
•
w aJlc
pore
water
pressure may
be
•Ken
•nTO
account
by
using
the
submerged
density
of
soil,
y',
for
f
the
earth
pressure
diagram
which
is
below
the
water
table
see
that
part
figure
2.
Alternatively
all
t:•e
forces
acting
on
e
soil
wedge
including
the
hydrostatic
normal
uplift
pressure
on
the
failure
plane
and
the
lateral
ydrostatic
pressure
may
be
included
in
the
trial
wedge
procedure
see
figure
14.
In
cohesive
soils
the
pore
water
pressures
set
up
during
construction
will
override
any
hydrostatic
pore
pressure
Where
tension
cracks
occur,
lateral
hydrostatic
water
pressure
should
be
included
for
the
full
depth
of
the
crack
as
given
in
3.3.4
or
for
H/2
•hichever
is less.
If however
shrinkage
cracks
are
l able
to
form
to
a
depth
greater
than
that
given
above,
water
pressure should
be
allowed
for
the
full
depth
of
such
shrinkage
cracks.
The
maximum
depth
varies
with
soil
and
climate
but
may
be
taken
as
5
feet
1.5
metres).
Full
lateral
ater
pressure
must
be
allowed
for
below
the
highest
level
of
the
soffit
of
the
weep
holes
or
other
drainage
outlets.
Static
water
pressure
always
acts
normal
to
the
surface
of
the
wall.
6.2
SEEPAGE
PRESSURE
If
the
water
in
the
soil voids
is
flowing,
the
pore
water
pressures
will
be
changed from
the
hydrostatic
values
by
an
amount
proportional
to
the
flow
of
water.
For
major
s
•ructures,
the
pore
water
pressures
under
seepage
conditions
should
be
determined
by
flow
he+
procedures
see
references
I
5
or
6.
The
pore
water
pressures
normal
to
the
failure
surface
of
active
or
passive
wedges
affects
the
earth
pressure
act
ng
on
a
wall.
The
resuliant
uplift
force
on
the
fai
ure
surface
determined
from
a
flow
net
is
applied
in
the
force
polygon
for
the
soil
wedge
together
with
any
lateral
water
pressure
at
the
wall
see
figure
14.
Fdr
an
approximate
analysis
the
uplift
intensity
may
be
taken
as
being
equa
to
the
pressure
of
the
vertical
height
of
water
between
ground
water
table
level
(may
be
sloping)
and
a
point
directly
beneath
on
the
failure
surface.
Figure
32
shows
a
flow
net
for
seepage
from
the
ground
surface
behind
a
wall
with
a
vertical
drain.
For
C
C
S
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stat
c
is
is
s
be
rt
I-
H/2.
a
for
of
to
6.
passive
uplift
the
heigh•
for
For
25
cohesionless materials
sustained
seepage
under
the
conditions
shown
would
Increase
the
active
force
20
to 40
percent
over
that
for
dry
backfill,
depending
on
the
backfill shearing
strength.
6.3
DYNAMIC WATER
PRESSURE IN
EARTHQUAKES
Yhe
dynamic
pressure
of
any
water
in
the
backfill
should
be
taken into
account
by
applying the
seismic
coefficient
•o
the
weight
of
water
in
the
failure
wedge
as
well
as
to
the
soil.
If
the
•nonobe-Okabe
equations
are
used
with
the
Submerged
density
Of
the
soil below
the water
table,
the
seismic coefficient
must
be
scaled
up
by
Ysat/Y
to
allow fop
the
mass
of
the water.
The
dynamic
pressure
of
water in
front of
a
wall
e.g.
a
quay
wall)
is
usually
not
taken into
consideration
because
this
usually
acts
in
a
direction
opposite
to
the
pressures
from the
backfill material.
6.4
DRAINAGE PROVISIONS
Water
pressures
must
be
included in the forces acting
on
the
wall
unless
adequate drainage
is
provided.
For
walls
less than
6 feet
2
metres)
high, drainage
material
is
usually
only provided
on
the back face
of the
wall,
with
weep
holes
to
relieve water
pressure see
figure 34. In
these
circumstances
it
may
be
desirable
or
more
economic
to
design
for
hydrostatic
water
pressure.
In
general, if the drainage
system
shown in
figure
33 is
used
water
pressures
may
be
neglected both
on
the wall itself and
on
the soil
failure
plane.
Adequate
drainage
reduces the rate of
softening of
clay
filling
and of
stiff-fissured
clays
and
lessens
the
likelihood
of
reductions in
the
strength
of
the
foundations, and
is
therefore
very
desirable for
clay
soils.
It
Is worth noting
that in
cohesionless
soils,
the active force
on
a
wall with
static
water
level
at
the top
of the
backfill is approximately
double
that
for
a
dry
backfill. For walls
over
20
feet
6
metres) high,
particular
care
should be
taken
to
ensure
that the
drainage
system
will
control the effects
of water
according to
the
assumptions
made
in
design.
Many recorded wall
failures
seem
to
be the
result
of
inadequate drainage.
Water should
•Feferably
be
prevented
from
entering
the
backfill from
the
surface,
otherwise
any
resulting
seepage
pressures
must
be allowed for
in
design.
Drainage
material
should have
a
permeability
at least
100 times
that
of the material
it
is
meant
to
drain. If this
is achieved,
pore
water
pressures
due
to
seepage
will be
minimised
at the
boundary
and the
soil
mass
will drain
as
though it had
a
free
boundary.
Permeabilities of
granular
drainage)
materials
are
given
in figure
35.
The filter
principle
must be
used
when
seepage
is
from
fine
grained
to
coarser
grained
materials, to prevent movement
of the fines and
possible
choking
of
the
coarser more
permeable
material.
The following
particle
size
ratios should
generally
be
provided:
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26
D15C
DSO
C
D15
C
-•SF
_•
5,
25,
• <
40
50
F
DIS
F
where
D15
C
size
at
which
15%
by
weight
of
the
coarse
material
is
fi•er
I5F
15$
-
fine
,,
,,
,,
DSOC
505
,,
,,
Coarse
,,
,,
,,
DSOF
,t
,,
50%
fine
.
.
D85F
85%
fine
,,
,,
,,
For
clay
soils
the
D15
C
size
should
not
be
less
than
0.2
mm
and
the
DSO
criterion
may
be
disregarded
but
•he
filter
(coarse)
material
must
be
well
graded
such
that:
D60C
20
io
C
The
filter
material
must
also
have
sufficient
permeabi
ity
so
that
the
seepage
can
pass
through
to
the
drainage
material
or
drain.
To
avoid
head
loss
in
the
filter
the
following
additional
provision must
be
met:
DI5C
------>5
I5F
To
avoid
internal
movement
of
•ines,
the
filter
should
have
0-5
passing
the
No.
200
s,eve,
and
to
avoid
segregation
it
should
not
contain
sizes
larger
than
3
inches.
The
above
criteria
mean
that the
following
grading
is
the
finest
equired
for
any
filter
materia
rotected:
regardless
of
the
material
that
is
being
Sieve
S•ze
3i16
No.
7
No.
14
No.
25
No.
52
No•
100
No.
200
Percent
Passing
100
92
74
5O
25
.8
0
Material
surrounding
a
perforated
subsoil
drain
pipe
must
have
a
D85
size
9reater
than
the
diameter
of
the
pipe
perforations•
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net
D50
be
we
being
a
D85
27
SECTION 7
STABILITY
OF
RETAINING
WALLS
7.1 GENERAL
The stability
of
a
free
standing
retaining structure
end the
soil
containing
it is
determined
by
computing
factors
of
safety
or
stability
factors
which
may
be
defined
in
general terms
as:
Moments
or
forces
aiding
stabi.lity
s
Moments
or
forces
causing
instability
Factors
of
•afe•y
should
be
calculated
for the
following
separate
modes
of
failure:
a)
Sliding
of the
wall
outwards
from
the
retained
soil.
b)
Overturning of the
retaining
wall
about
its
toe.
c)
Foundation
bearing failure.
d)
Slip
circle failure
in the
surrounding
soil.
The
forces that
produce
overturning
and
sliding
are
also
producing
the
foundation bearing
pressures
and therefore
(a)
end
(b)
above
are
inter-
related
with foundation
bearing
failure
in most
soils.
In
c ses
where the
foundation is
soil,
overturning
stability
will
usually
be satisfied
if
bearing
criteria
are
satisfied.
However
it
may
be critical
for
strong
foundetion
materials
such
as
rock,
or
when
the base
of•the
wall
is
small,
which is
the
c se
with
crib walls.
From
settlement
and
•ilting
considerations in
soil
materials,
the
resultant of
the
loading
on
the
base should
be
within
the middle
third for
static
loading
and
within the
middle
half
for
earthquake
loading.
For
rock foundation
material,
the
resultant
should
be
within the
middle
half
of
the
base
for
both
static and
earthquake
loading.
When
ca-lculating
overall
stability
of the
wall.the
lateral
earth
pressure
is
calculated
to
the bottom
of the
blinding
layer,
or
in the
c se
of
a
basw
with
a
key, to
the
bottom
of the
key.
The
vertical
component
(if any)
of
the
resultant
earth
pressure
is
added
to the
weight
of the
wall
system
when
computing
stability
factors.
If
the
•essive resistance
of
the
soil in
front
of
a
wall
is
included in
calculations
for stability,
either
the
top 18
inches
(0.5
metres) of the
soil
should
be neglected,
or
only
2/3
of
the calculated
passive
resistance
should
be
used..
Stability
criteria
for free
standing
retaining
wal
fl•ure
36.
s
re
summarised in
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7.4.2
The
recommended
method
of
calculating
the
bearing
capacity
applies
o
both
earthquake
loading
and
static
loading.
No
consideration
need
be
made for
the
cyclic
effects
of
dynamic
load
or
the
dynamic
roperties
of the
soil.
The
ultimate
bearing
capacity
for
a
shallow
(D
•
B)
strip
foundation
s
given
In
general
terms
by:
-Q-=
cN
c
s•d
c
+
D
Nq
Sqdq
+ BNy
sydy
ult
BL
Y
½
Y
The
bearing
capacity
factors
Nc,
Ng
and
Ny
(for
a
horizontal
strip
oundation
under
vertical
concentric
loading),
are
calculated
from
he
angle
of
shearing
resistance
of
the
foundation
material.
This
ssumes
that
the
material
is
reasonably
dense
so
that
failure
would
ccur
by
general
shearing.
If
the
material
is loose
c
and
¢
should
e
reduced
to
2/3
of
the
actual
values,
i.e.
c 2/3c
and tan
¢'
/3
tan
•. The
ultimate
bearing
capaqity
for
a
shallow
foundation
hat
is
not
a
continuous
•trip
is
obtained
by
multiplying
the
earing
capacity
factors
by
corresponding
empirical
shape
factors
s
c,
Sq
and
sy).
The
bearing
capacity
factors
may
be
further
multiplied
by
depth
actors
(dc,
dq
and dy)
which
take
into
account the
shearing
..resistance
of the
soil
above
foundation
level.
Bearl•g
capacity
factors,
shape
factors
and depth
factors
based
on
eyerhof s
assumptions
(references
16
or
19)
are
given
in
figure
37.
imilar
factors
according
to
Hansen
are
given
in
referenqe
27.
Eccentric
Loads
If
the
load
on
the
foundation
is
eccentric
this
can
substantially
educe
the
bearing
capacity.
To
allow
for
this
the
base
width,
B
s
reduced
to
an
effective
width B'
given
by:
B
t
B
2e
Where
e-is
the--load
eccentricity.
For
a
footing
eccentrically
loaded
in
two
directions
(el,
eb)
the
ffective
dimensions
of the
base
become
such
that
the
centre
of
an
rea
A
coincides
with
the
vertical
component
of the
applied
load,
A
B
x
L'
where L'
L 2e
B
B 2e
b
U
and
B
replace
L
and B
in
all
equations.
The
factor
of safety
is
given
by:
Fs
(bearing)
qul•t
where
q
A •
q
for
a
rectangular
footing
for
a
continuous
strip
footing.
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7.4.3
7.4.4
?.4.5
Inclined
Loads
Where
the
load
on
a
horizontal
continuous
strip
foundation
is
inclined,
which
is
the
case
for
most
retaining
wails,
the
vertical
Component
of
the
ultimate
bearing
capacity
is
compared
with
the
bearing
pressure
from
the
vertical component
of
the
applied
loading
to
obtain
the
factor
of
safety.
According
to
Meyerhof,
the
vertical
component
of
the
ultimate
bearing
capacity
is
given
by:
qult(v).
CNcq
+
½
y
B
Nyq
where
Ncq
(depending
on
N
c
and
Nq
and
Nyq
(depending
on
Ny
and
Nq
are
beari.fig
c•)pacity
factors
n•odified
for
the
degree
of
inclination.
f
the
inclination
of
the
applied
loading
is
large
and the
oundation
depth,
D
is
small,
a
sliding
failure
may
occur
first.
variation
of
the
above
situation
is
where
the
base
is
inclined
so
that
the
applied
loading
is
normal
to
it.
In
this
ease
the
bearing
pressures
are
calculated
normal
to
the
base,
and
Meyerhof,s
ultimate
bearing
capacity
is
•iven
by:
qult
cNcq
+
½
y
B
Nyq
The
bearing
capacity
factors
Nc•
and
Nyg
for
the
two
cases
mentioned
are
given
in
figure
38
for
embe•ment
rafios,
D/B
of
0
and
I.
The
factors
for
intermediate
embedment
ratios
may
be
obtained
by
linear
interpolation.
In
the
particular
ase
where
@
o,
Meyerhof s
ultimate
bearing
Capaci.ty
(or
the
vertical
component
of
it)
is
given
by:
qult
or
qult. _9)•cN•_+
yD--
As
an
approximate
alternative
to
the
above
method,
the
terms
in
the
ultimate
bearing
C•pacity
equation
in
7.4.1
may
be
modified
by
inclination
factors
to
allow
for
the
inclined
load
see reference
19
(Meyerhof s
method)
and
27
(Hansen•s
method).
The
bearing
Capacity
of
a
rectangular
footing
is
approximately
the
same
as
a
strip
footing
at
a
load
inclination
angle
of
15
°
to
the
vertical.
ccentri•
Inclined
Loads
When
a
foundation
carries
an
eccentric
inclined
load,
an
estimate
of
the
ultimate
bearing
Capacity
may
be
obtained
by
combining
the
methods
given
in
7.4.2
and 7.4.3.
The
procedure
in
.the
ase of
a
horizontal
base
is
given
in
figure
38
but
it
also
applies
when
the
base
is
inclined
see reference
17.
Foundations
on
a
Slope
When
a
shallow
foundation
Is
located
on
the
face
of
a
slope
or
at
the
+op
of
a
slope,
ultimate
bearing
Capacity
is
reduced
see
reference
18.
For
slopes
less
than
30
°
the
decrease
in
bearing
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7.4.6
capacity Is
small
for
clays
but
can
be
considerable
for
sands
and
gravels. However
in
clays
the
bearing capacity
of
a
shallow
foundatibn
may
be
limited by
the
stability of the
whole.slope.
The
ultimate
bearing
capacity
according to
Meyerhof'Is
given by:
qult
cNcq
+
Y
B
Nyq
•.
The'bearing
capacity
factors,
Ncq
and
•yq
for
a
strip
fo•,'•dation
wlth concentric vertical
load ng
re
g•ven
in
figure
39.
If the
foundation is
located
on
the face of
a
clay
slope
less
then
half
way
up
the
slope
the stability of the slope
will not
affect
the
bearing
capacity
and
a
stability number,
Ns,
of
zero
should
be used.
If
the
foundation
is
located
on
top of
the
•lope
the
bearing
capacity
varies
with the distance
from
the
slope.
When the
foundation
material is
cohesive, the
ultimate
bearing
capacity
also depends
on
the
slope stability,
number,
which must
be
calculated for
the
particular
situation
In the particular
c se
of
a
purely cohesive
soil @
o) the
slope
stability
number
is
given by:
N
s
¥
H/C
and
qult
=.
cNcq
+
yD
The
ultimate
bearing
capacity of
a
foundation located
more
than
half
way
up a
clay slope
may
be estimated by
using
a
slope stabiiity
number intermediate
between
zero
and
that
appropriate to
the
c se
of
a
foundation at
the top
of the slope.
Eccentric
applied
loads
may
be
taken
into
account
by
the
methods
of
7.4.2.
Effect of
Ground
Water
Level
The
equations
given'in
7.4.1 to 7.4.5
apply when
the
ground
water
table
is
at
a
distance
of
at
least
B below
the
base
of
the
foundatT•o•.
---•n
the--water
table
is
•t
the
s me
level
as
the
foundation, the
submerged
unit weight
of
the
soil
below
the
foundation
should be used.
For intermediate
levels of the
water
table the
Ultimate
bearing
Capacity should
be interpolated
between
the
above
limiting
values
7.5 SLIP CIRCLE FAILURE
For
walls
higher
than
30 feet (9
metres), slip
circle failure
in
the
soil
containing the wall should be investigated.
The
slip
circle
stability
factor:
F
s
(slip
circle)
N tan
•
+
cl
T
should
be
•t
least
1.5
for
static loading
and
at
least
1.3
for
earthquake
loading.
An
effective
stress
analysis
using
appropriate
pore
water
pressures
Is
recommended
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Earthquake
loading
should
be
allowed
for
y
applying
a
static
orizontal
force
to
the
soil
m ss
s
described
in
4.1
using
the
design
eismic
coefficient
determined
from
4.2.
Computer
programs
currently
available
for
this
type
of
analysis
includeCES-LEASE
and
the
Ministry
of
Works
SOILS
program.
The
former
is
onsidered
to
be
mor
accurate
however
at
present
it
does
not
have
theapability
for
including
the
horizontal
force
for
the
earthquake
loading
hich
SOILS
allows.
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8.1
GENERAL
SECTION 8
STRUCTURAL
DESIGN
8•1.1
Codes
Reinforced
concrete
design
should
be
in
accordance with NZS
3101P
(reference
20)
with
reference
to
ACI
3i8-71
reference
21)
for
those
requirements
not covered
by
the New Zealand
code.
8. .2 Material
Strengths
and
Allowable
Stresses
The
following
material
strengths (with
the
corresponding
allowable
stresses)
re
recommended.
However in
some
c ses
an
increased
concrete strength
with
correspondingly increased
allowable
stresses
may
give
some
economy:
Reinforcement,
Deformed
structural
grade
to
NZS i693:1962
Yield
stress,
fy
40,O00Ib/in
2
(275
MN/m
2
'Allowable
tensile
stress, fs 20,000 Ib/in
2
(138
MN/m•).
Concrete
Nominal
compressive strength,
f'c
3,000
Ib/in
2
(20
MN/m
2
Allowable
compressive
stress,
fc
1,350
Ib/in
2
(9.3
MN/m
2
Allowable
shear
stress,
fv
60
Ib/in
2
(0.41MN/m
2
Modular
ratio,
n
9.
For
earthquake
loading the
above
stresses
may
be increased
by
33%.
8.1.3
Ultimate
Strength
If
ult•n•a•e.•zength
d •ign
methods
are
used
for
proportioning
a
structural
section,
the
design
load•
shall
be
computed
so
thai the
capacity
of
the
section
shall
not
be
less
than:
U
1.35
(DL
+
1.35
EP
+
W);
or
U
1.08 (kDL
÷
I..25
(EQ
+
W))
where
DL
EP
dead
load
of
the
structural
element
static
earth
pressure
acting
on
the
element
(inclJdine
the
effects
of
any
surcharge
loads)
EQ
earthquake
earth
pressure
acting
on
the
element
W
hydrostatic
water
pressure
k ='1.2
or
0.8
whichever
is
more
severe,
to allow
for
vertical acceleration.
If
USD
is
used,
a
serviceability
check
on
"crack
widths
at
working
loads
shall
be
made
to
ensure
that
the limits
given
in
clause
3.1.9
of
NZS 3101P
are
not
exceeded.
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q
8.1.4
8.1.5
8.2.2
Reference
23
gives
an
example
of
USD
of
a
cantilever
retaining
wall.
Cover
to
Reinforcement
a)
Concrete
below
ground
i)
ii)
. b)
cast
against
natural
ground
cast
egainst
formwork
or
blinding
concrete
Above
ground
inches
mm
3.0
75
2.0
50
i)
cast-in-situ
concrete
1.5
40
ii)
precast
components
•
1.25
30
•
CY/•:
•he
thickness
of
architectural
finishes
is
neglected
when
ca
culating
Fover
to
steel
or
stresses.
Selection
of
Hall
Type
For
walls
up
to
25
feet
7.5
m)
high
where
crib
walling
is
not
suit-
ble,
a
cantilever
wall
will
usually
be
found
@o
be
the
most
conomical.
For
higher
walls
en
investigation
should
be
made
for
the
relative
conomies
of
using
a
counterfort
or
cantilever
wall.
This
should.
ake
into
account
unit
costs
for
formwork,
reinforcing
steel,
and
oncrete,
end
not
just
all
in
cost per
cubic
yard
of
final
wall..
ounterfort
walls
should
have
approximately
a
30
ft.
(9
metre)
bay
ength
varied
to
suit
architectural
finish
etc.)
with
three
counter
orts
per
bay.
The
position
of
the
counterforts
is
obtained
by
onsidering
the
stresses
in
the
stem.
TOE
DESIGN
For
Length
of toe
Effective
depth
at
face
of
support
I,
design
according
to
NZS
3101P.
face
of
support.
Shear
may
be
taken
at
Wd'
out
from
LenQth
of
toe
Effective
depth
at
face
of
support
•
I,
design
as
a
0racket
in
accordance
with
section
II.14
of
ACI
318:71.
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8.3
STEM
DESIGN
8.3.1
Stem
Leading
For
the stem
design in
cantilever
and
counterfort
walls,
t•e
earth
pressure
acting
on
the
vertical plene
through the
rear
of
the heel
Is•projected onto
the stem.
8.3.2
Lower
Section of
Counterfort
Wall
Stem
Th•
bottom
LS 2
of
the
stem
is
to
be
reinforced
fer
vertical
spanning action in
addition
to
horizontal spanning.
Bending
-re
M
re
M
wLs
2
-re
M
=-25--
where
w
is the
considered.
moments
per
unit
height
of
stem
may
be
assumed
as:
•Ls
14
WLs___•
22
horizontal
steel)
horizontal
steel)
vertical
steel)
lateral
design
pressur
e
at the level being
8.3.3
Horizontal Moments in Counterfort
Wall
Stem
Bending
moments
in
the
top part
of the
stem
may
be
celculated from:
-re
M
wLs
horizontal
steel)
+ve
M
wLs2
horizontal
steel)
16
Use continuous
horizontal steel
in
both
faces.
Horizontal
B.M.
variations
with
height should
be
catered
for
by
varying the
reinforcement spacing in preference
to
changing
the bar sizes.
When
caFculating-the bending
moments for
the
stem,
the
span
should
be
taken
as
.the clear
span
between
counterforts
Ls).
8.4
HEEL
SLAB
DESIGN
8.4.1
Loading
The
design
loading
on
fhe
heel
slab is shown
in
figure
40.
The
foundation
bearing
pressures
may
be calculated
by
using
the
theory
of
subgrade
reaction see 2.7).
For
a
rigid
base
slab this
theory
gives bearing
pressures
whlzh
vary
linearly
across
the
base
width.
The
pressures
for
use
in structural
design
are
not the
same
as
those
used
to check
the
factor
of safety
against ultimate
bearing
failure
section
7.4).
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If
the
resultant
cuts
the
base
within
the
m•dd•e
third
the
toe
and
eel
pressures
for
structural
design
may
be
calculated
from:
p
V/BL
±
6
Ve/B2L
8.4.2
8.5
where
V
the
vertical
component
of
the
resultant
loading
on
the
base
B
the
base
width
L
the
length
of
wall
for
which
the
resultant
earth pressure
s
calculated
(usually
unity).
If
th•
resultant
lies
outside
the
middle
third:
2V
max
B/2
e)
L
Heel
Slabs
for
Counterfort
Walls
The
heel
siab
for
counterfori-
wails
shouI•
be
designed
as
a
•lab
panning
in
two
directions
if
a
key
is
included
at
the
rear
The
esig•
bending
moments
may
be
obtained
from
tables
in
reference
15.
Alternatively,
the
heel
slab
can
be
divided
into
or
5
strips,
of
pproximate
width
3.5
feet
(I
metre)
to
5
feet
(1.5
metres)
spanning
etween
counterforts.
The
outermost
strip
including
the
key
can
be
esigned
as
a•
L-beam
for
bending,
its
breadth
equal
to
the
strip
idth.
The
width
of the
key
strip
resisting
shear
should
be
ssumed
as
the
maximum
width
of the
key
plus
half
the
thickness
of
he
heel
slab.
Bending
moments
mey
be
calculated
as
in
8.3.3.
Each
strip
should
be
designed
for
the
average
load occurring.
Th•
ritical
section
is
at
the
face
of
the
counterforts
where
shear
tresses
are
not
to
exceed
stresses
in
section
8.1.2.
This
shearill
usually
govern
the
heel
thickness.
The
heel
slab
should
also
be
considered
as
strips
spanning
at
right
ngles
to
that
mentioned
above,
i.e.,
between
stem
line
and
keytrip.
Simple
aSsumptions
can
be
made
as
to
end
fixity
of
these
trips
and
an approximate
amount
of
reinforcing
provided.
COUNTERFORT
DESIGN
Vertical
steel
in
the
counterfort
is
required
to
carry
the
net
load
from
each
strip
of
the
heel
slab.
The
main
moment
reinforcement
for
the-
wall
is
usually
concentrated
at
the
back
of
the
counterfort.
Where
itoins
the
heel
slab, the
above
steel
should
be
considered
as
taking
only
that
load
o•currlng
on the
outermost
strip
incorporating
the
key,
as
defined
in
8.4.2
above.
Horizontal
steel
in
the
counterfort
is
required
to
carry
the
net
load
n
each
horizontal
strip
of
stem.
Cut-off
positions
for
the
main
tensile
steel
in
the
counterforts
is
shown
in
figure
41.
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8.6 KEY
DESIGN
In
general
the depth
to
width
ratio of
the
key
should be
approximately
one
It
is difficult
to predict
what the force
acting
on
the
key
will
be.
An
epproxlmate design horizontal
load
on
the
hey
is:
•
horizontal
loads
causing
sliding
0.4
x
total
vertical
loads above
blinding
layer.
This
load
acts
at
I/3
key
height
frombottom
of key.
Design
the
key
as
e
bracket
refer 8.2
above.
Note
some
stresses
are
carried
from
the
key
lnto
the
bottom
of
the
heel
slab,
and
will
call
for
some
reinforcement
In that
area
8.7
CONTROL
OF
CRACKING
a)
To
mlnimise
cracking
in the
retaining
structure:
Provide
shrinkage
and
temperature
reinforcement
equal
to
0.25
of the
gross
concrete
area
as
a
minimum
in
both
directions
in
all
members.
In
the
stem:
b)
c)
d)
2/3
of
this
steel
to
be
on
the
outside
face
I/3
of
this
steel
to
be
on
the
earth
face.
Specify
that
the
coscrete
placing
and
temperature
is
to
be
kept
as
low
as
practical
especially
in
the
summer
period.
Specify
successive
bay
construction.
Specify
early
curing
for
the
purpose
of
cooling
so as
to
minimise
the
heat rise.
e)
f)
Place
the steel
in
bar
sizes
to
limit
crack
width to
0.01
inch (0.25
(see
code
requirements).
Added
protection
can
be
given
by
painting
the
earth
face
with
say
two
c•ats
of
Mulseal•J_or
F..intcoat
(reference
24).
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38
SECTION
9
S•PECIAL
PROVISIONS
FOR
CRIB
WALLS
9.1
GENERAL
A
considerable
amount
of
llterature
is
available
from
Crlbwal
Unit
anufacturers
e.g.
Hume, I.C.B.,
Cement
Products)
and
also
Portland Cementssociation
on
the
design
of
crib
walls.
However,
care
must be
exercised
in
interpretatlon
of
this
data.
Crib
alls
must
be
checked
for
stability
in
accordance
with
section
7.
Figures
3 to
46
may
be
used
as
an
aid
In
determining
the
maximum
height
for
ifferent
well
thicknesses.
The
crib
units
and
wall
construction
should
be
in
eccordence
with
the
urrent
Ministry
of
Works
stendard
speclflcetion
for
this
work
MOW
7562).
9,2
DESIGN
LOADING
The
pressures
ecting
on
a
typical
crib
well
are
shown
In
figure
42.
hese
pressures
are
calculated
by
the
methods
of
sectlon
3.
Earthquake
oeding
will
usually
not
be
applied
to
crib
wells,
but
if
it
is
the
methodsf
section
4
should
be
used.
9.3
FOUNDATION
DEPTH.
The
minimum
•epth
of
foundation
shall
be
as
shown
in
figure
42
which
ncludes
a
continuous
concrete
foundation
slab.
A
minimum
slab
thickness
f
6
inches
150
ram)
reinforced
with
one
layer
of
655
mesh
is
recommended
o
prevent
differential settlement
of
the
wali
structure.
The
onsequences
of
such
settlement
are
described
in
reference
25.
F•] 9.4
DRAINAGE
A
continuous
6
In•cb__ •5.0_•)
diameter
minimum)
subsoil
drain
should
e
provided
at
the
reer
of
the
foundetion
slab,
to
ensure
a
dry
foundatlcn.
(•-• •
This
should
be
provided
for
all
heights
of
crib
wall.
Adequate
drainage
Of
the
whole
crib
structure
is
essential.
Many
of
the
failures
in
crib
walls
heve
oCcurred
because
material
of
low
permeability
as
used
as
backfill
thus
developing
high
static
or
seepage
water
ressures
.A free
draining
backfill
should
always
be
used
if
possible,
therwise
the
effect
of
water
should
be
allowed
for.
Unless
effectively
drained
ov r
the
full
height•
crib
walls
should
be.
esigned
to
resist
lateral
hydrostatic
pressures in
addition
to
sell
ressures
9.5
MULTIPLE
DEPTH
WALLS
Walls
of
more
than
single
depth
should
be
checked
at
the
changes
from
Single
to
double
and
double
to
triple
depth
to
satlsfy
the
followingtabillty
crlterla:
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For
normal
conditions
resultant
to be within
middle
I/3.
This
will
ensure
that
no
part
of
the wall
structure
is in tension
For
earthquake
conditions
resultant
to
be within
the
section
of
the
wall
The
appropriate overturning
factor
of
safety
must
also
be
met at
these
s•ctions
9.6
HALLS
CURVED
IN
PLAN
Crlb
walls
with
a convex
front
face
re
much more
susceptible
to
m ge
by transverse
deformations
than
are
conc ve
walls
see
reference
25
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•
40
AhPENDIX
REFERENCES
4.
5.
6.
7.
Huntington,
W.
C.
(1957):
John
Wiley
and
Sons.
Earth
Pressures
and
Retaining
Institution
of
Structural
Engineers
(1951):
Earth
Retaining
Structures .
Civll
Engineering
Code
of
Prectice No.
2.
Prepared by
Civil
Engineering
Codes
of
Practice
Joint
Committe•.
US
Department
of
the Navy
(1971):
Design
Manual
Soil
Mechanics,
Foundations,
and
Earth
Structures . Navfac
DM-7.
TschebotariofF,
G.
P.
(1951):
Soil
Mechanics,
Foundations,
and
Earth
Structures .
McGraw-Hill Book
Co.
Terzaghi,
K.'and
R.
B.
Peck
(1967):
Soil
Mechanics
in
Engineering
Practice .
2nd
Edition.
John
Wiley
and
Sons..
Scott,
R.
F.
(1963):
Publishing
Co.
Principles of
Soil
Mechanics .
Addison-Wesley
Gould,
J.
P.
(1970):
Lateral Pressures
on
Rigid
Permanent
Structures . ASCE
Speciality
Conference
Lateral
Stresses
in
the
Ground
and
Earth
Retaining
Structures.
8.
Broms,
B.
(1971):
Lateral
Earth Pressures
due to
Compaction of
Cohesionless
•oils
Pro.
4th
Budapest
Conference
on
Soi'l
Mechanics
and
Foundation
Engineering.
9.
Tennessee
Valley
Authority 1951):
The
Kentucky
Project .
Technical
•eport No.
13..
10.
Kuesel,
T. R.
(1969):
Earthquake
Design
Criteriafor
Subways .
Proc.
ASCE
Structural
Division,
ST6,
pp.
1213-i231.
11.
lZ.
Japan
Society_o•_§•Engiqg•rs
(1968):
Earthquake
Resistant
Design
for
Civil Engineering
Structures, Earth
Structures
and
Foundations in
Japan .
Seed,
H.
B.
and
R.
V.
Whitman
(1970):
Design
of
Earth
Retaining
Structures
for
Dynamic
Loads .
ASCE Speciality
Conference
Lateral Stresses
in the
Ground and
Earth
Retaining
Structures.
13.
Standards
Association
of
New
Zealand
(1965):
NZS 1900
•del
Building.Bylaw
Chapter
8
Basic Design
Loads .
14.
N.Z.
Ministry
of Works
(1972):
Highway
Bridge
Design
Brief .
Issue B
with amendments
to
July
1973
or
Issue C
(metric
version).
15. Bowles, J. E.,
(1968):
Foundation
Analysis and
Design .
McGraw-Hil
Book CO.
16.
Meyerhof,
G.
G.
(1951):
The Ultimate
Bearing Capacity
of
Foundations
Geotechnique Volume
II.
8/11/2019 Notes for Retaining Wall Design
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17.
18.
19.
20.
21.
23.
Meyerhof,
G.
G.
(1953):
The
Bearing
Capacity
of
Foundations
under
Eccentric
and Inclined
Loads .
Proc.
3rd
International
onference
on
Soil
Mechanics
and
Foundation
Engineering.
Meyerhof;
.G.
6.
(1957):
The
Ultimate
Bearing
Capacity
of
Foundations on
Slopes .
Proc.
4th
International Conference
on
oil
Mechanics
and Foundation
Engineering.
Meyerh0f,
G.
G.
1963):
So6e
Recent
Research
on
the
Bearing
apacity
of
Foundations .
Canadian
Geotechnical
Journal,
olume
1,
No...].
Standards
Association
of
New
Zealand
1970):
NZS
3101P
Code
of
ractice
for
Reinforced
Concrete
Design .
American
Concrete
Institute (1971):
Building
Code
Requirements
for
einforced
Concrete
(ACI
31•-71) o
Urquhart,
L. C.;
C.
E.
O'Rourke;
and
G.
Winter
1958):
Design
of
oncrete
Structures .
6th
Edition.
McGraw-Hill.Book
Co.
Fergus0n,
P.
M.
(1958):
Reinforced
Concrete
Fundamentals .
2nd
dition.
John
Wiley
and
Sons.
Evans,
E.
P.
and
B. P.
Hughes
(1968):
Shrinkage
and
Thermal
racking
in
a
Reinforced
Concrete
Retaining
Wall .
Proc.
nstitution
of.
Civil
Engineers,
Volume
39.
Tschebotari0ff,
G.
P.
1965):
Analysis
of
a
High
Crib
Wall
Failure .
roc.
6th
International
Conference
on
•oil
Mechanics
and
oundation
Engineering.
Br0ms,
B.
B.
and
I.
Ingels0n
(1971):
Earth
Pressure
against
the
butments
of
a
Rigid
Frame
Bridge .
Geotechnique
Vol.
21,
No.
1.
Hansen,
J.
B.
1970):
A
Revised
and
Extended
Formula
for
Bearing
apacity
'';--
-The-Danish'Geotechnical
Institute,
Bulletin
No.
28.
Cullen,
R. M.
and
I.
B.
Donald
(1971):
Residual
Strength
etermination
in
Direct
Shear .
Proc.
Ist
Australian-New
Zealand
onference
on
Geomechanics.
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1
2
3
4
5
6
7
8
9,
10
11.
12
13
14
15
16.
17
18
19
2O
21
22
¸23
24
25
26
28
29
APPENDIX
II
FIGURES
Loading
on
typical
retaining
wall
Rankine
earth
pressure,
cohesionless
soil,
constant
backfil
slope
•Rankine
active
earth
pressure
coefficients
Coulomb.
earth
pressure,
cohesionless
soil•
constant
backfill
slope
Coulomb
active
earth
pressure
coefficients,
@
25
Coulomb
failure
plane for
active
pressure,
cohesionless
soil
with
uniform
slo•ing
backfill
Rankine
earth
pressure,
soil
with
cohesion,
horizontal
ground
surface
Trial wedge
method,
cohesionless
soil
Trial
wedge
method,
cohesionless
soil,
Culmann s
construction
Trial
wedge
method,
soil
with
cohesion
Trial
wedge
method,
layered
soil and
pore
water
pressures
Approximate
method
for
direction
of
Rankine
earth
pressure
Point of
application
of
active
pressure
Point
of
application
of
resultant
pressure
and
pressure
distribution
Braced
excavation
pressure
distributions
Mononobe-Okabe
earthquake
earth
pressure
Active
earthquake
earth
pressure
coefficients
for
pressure on a
vertical
plane,
@
25
°
Active
earthquake
earth
pressure
coefficients
for
pressure on
a
vertical
planes @
3•
Active
earthquake
earth
pressure
coefficients for
pressure on a
vertical
plane,
35
°
Active
earthquake
earth
pressure
coefficients
for
pressure
on a
vertical
plene,@
40
°
Active
earthquake
earth pressure coefficients
for
pressure
on
wall
with
B
•14
°
@
25o
Active
earthquake
earth
pressure
coefficients
for
pressure on
wall
with
B
-14
°
@
30
°
Active
earthquake
earth
pressure
coefficients for
pressure on
wall
wi•h
B
= 14
°
@
35
°
Active
earthquake
earth
pressure
coefficients
for
pressure
on
wall
wlth
B
-14
°
40
°
Earfhquake
loading,
trial
wedge
method,
soil with
or
without
cohesion
Uniform
surcharge
load
c ses
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RANKINE
EARTH
PRESSURE:
:'Io
H ESI
O
NLESS
SO•L
,
CONSTANT
BACKFILL
SLOPE:
•• - -.
FAILURE
PEANES
FOR
•
RANKIN•
•CTIVE
STATE
•
PRESSURE
ON
VERT
LANE
The
followin
9
equations
require
That
The
each
pressure
acts
af
he
backfi
1.
ACTIVE
PRgSSU•
H
•
PA
KAY
•
KA
cos
•
(cos
•
/•os
2
•
T
cos
2
eA
45
•
¢/2
•(•-•)
where
sin
•
•wifh
O<
•
<90
°
For
m
0
KA
•I-
sln
¢
÷
sin
¢
PASSIVE
PRESSURE
H
2
p
Kp
y
•
•A
45°
•/2
Kp
cos
•
2
•
cos2
)
ap
45
° ¢/2
½
•)
Note
the
angle
between
the
failure
planes
for
the
passive
pressure
case
is
90
°
•.
sin
s•
ep
45
°
•/2
For
•
0
Kp
sin
¢
FFI
GURE
2.
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R NKINE
CTIVE
E RTH
PRESSURE
COEFFICIENTS
FOR
COHESlONLESS
SOIL
WITH
UNIFORM
SLOPING
BACKFILL.
PRESSURES
ON
A
VERTICAL
PLANE :
0 90
0
-80
H
PA
•
H2
KA
cos •
7(COS
z
•
cosZ
¢) .
0.50
0 30
0
°
5
°
10
°
15
°
BACKFILL
SLOPE
20
°
25
°
50
°
IFIGURE
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COULOMB
EARTH
PRESSUR
COHESIONLESS
SOIL
CONSTANT
BACKFILL
SLOPE
•umed
fa•ure
plane
B
•---- i'•e,•
°
•
actual
failure
surface
FAILURE
WEDGE
FOR
AgTIVE
STATE
ACTIVE
PRESSURE
ON
BACK
OF
WALL.
The
following
equations
give
only
an
approximate
solution
for
the
earth
ressure
when
static
equilibrium
is
not
fully
satisfied.
The
departure
rom
an
exact
solution
is
usually
very
small
for
the
active
pressure
case
but
passive
resistance
may
be
da.ngerously
overestimated°
ACTIVE
PRESSURE
H•
cos
2
(•-IB)
cos(•+•)
•
(e-•)J-
cot
C•A-•)
-tan
(•+•+•-•)
+
sec
(•+•+•-•)
•
(•+6)
sin
(•+6)
cos
(•-•)
sin
(•-m)
If
the
pressure
su.rface
AB
is
projected
on
to
a
ve•ical
plane,
the
pressure
per
unit
of
ve•
cal
distance
at
a
ve•ical
depth,
y
below
the
top
of
the
wall
is p'
K
A
y
y.
for 6
m
and
•
O,
K
A
•
Rankine s
value.
PASSIVE
PRESSURE
Pp
I<p
T
2
Kp
cos•
•cos
(•+B)•1
L cos(•+8) cos(m-•)J
for
6
•
and
6
0,
Kp
•
Rankine s
value
FIGURE
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COULOMB
ACTIVE
EARTH
PRESSURE
COEFFI.CIENTS
COHESIONLESS
SOIL
WITH
UNIFORM
SLOPING
BACKFILL
0;8
0 5
0.4.
0.:5
0.2
20
I0
BACKFILL
SLOPE
0
I0
20
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Wt ILUIVI•
CTIVE
EIARTH
FOR
COHESIONLESS
SOIL
WITH
UNIFORM
SLOPING
BACNFILL.
0 9•
1-20
-I0
CKFILL
,0
SLOPE
I0
20
D
°
6
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r
COULOM
ACTIVE EARTI4
PRESSURE
COEFFI.C E NTS
FOR
COHESIONLESS SOIL
WITH
UNIFORM
SLOPING
BACKFILL.
•=
55
°
0"9
0"7
0; 2
20
-I0
BACKFILL
0
SLOPE
I0
20
50
40
I
GLIIE
7
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CuuILoMB
ACTIVE
EARTH
PRESSURE
COEFFIICtENTS
FOR
CONESIONLESS
SOIL
WITH
UNIFORM
SLOPIN
BACKFILL.
K
O
20
iO
BACKFILL
O
IO 20
SLOPE
.D
°
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COULOMB
FAILURE PLANE
COHESIONLESS
SOIL
WITH
BACKFILL
OR ACTIVE PRESSURE
UNIFORM
SLOPING
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•ANKINE
E RTH
PRESSURF
•OIL
WITH
COHESION
•ORIZONTAL
GROUND
SURFACF
A'
_Tension
zone
•
7]
/.j•
°
neglected.
i i
.
/
A
•-
KAY(H-y
J
FAILURE
PLANES
FOR
PRESSURE
ON
VERTICAL
ANKINE S
ACTIVE
STATE
PLANE
A-A
Water
pressure should
also
be
added
on
ALA
..
ACTIVE
PRESSURE
PA
½KA
•
(H
yo 2
sin
{
Yo
2•c
tan
(450
+
{
unit
pressure at
depth
y
below
top
of
wall,
p
KA
y(y
Yo
PASSIVE
PRESSURE
unit
pressure
at
depth
y
below
top
of
wall
p
Kp
y
y
+
2c/•
The
angle
between
the
failure
planes
for
the
passive
case
is
90
°
+
4-
FIGURE
I0
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TRIAL
WEDGE
METHOD
.COHESIONLESS
SOIL
IRREGULAR
GROUND
SURFACE
A
FORCES
ACTING
ON
WEDGE
FOR
ACTIVE
AND
PASSIVE
STATES
NOTES
FORCE
TRIANGLE
ACTIVE
(FULL
LINES)
PASSIVE
(DOTTED)
i.
The
lateral
earth
pressure
is obtained
by
selecting
a
number
of
trial
failure
planes
and
determining
corresponding
values
of PA
(or
.Pp).
For the
active
pressure
case,
the
minimum
value
of
PA
is
required.and
for the
passive
case,
the
maximum
PD
is
required.
These
.. limiting
values
are
obtgined
by
interpolating
between•
the
values
for
the
wedges
selected
2.
Culmann s
construction
(figure
12)
may
be
used to
determine
the
maximum value
of
PA
and
critical
failure
plane
for
cohesionless
soils.
•
3.
Lateral
earth
pressure
may
be
calculated
on
any
surface,
or
plane
hrough
the
soil.
4.
See clauses
3.3.1
to
3.3.4
for
the
direction
of
the
earth
pressure
-5..
See
figure
16
for
the
point
of application
of
PA
6.
T•etrial
wedge
method
ma•
also
be
use
for
a
level
or
constantly
loping
ground surface,
in which
c se
it should
yield
the
same
result
as
that
given
by
Ran.kine s
or
Coulomb s
equations,
whichever
is
applicable.
GUR
EI
II
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I T IIR
A
L
WEDGE
COHESIONLESS
CULMANN S
METHOD
SOIL
CONSTRUCTION
FOR:
STATIC
EARTH
PRESSURE
ONLY)
Failure
Plane
D
Pressure
Surface
c
4
W
PROCEDURE
I.
Draw
line
A-G
at
an
angle
of
{o
to
the
horizontal
for
active
pressure
2.
Draw
trial
wedges
ABCDI,
ABCD2,
etc.
a
minimum
o•
four
will
usually
uffice.
3.
Calculate
the
weights
of
the
wedges
say
wl
w•,
etc.,
and
plot
these
to
a
suitable
scale
on
A-G,
each
measured from
A.
4. Through
Wl,
w
etc.,
draw
lines
at
an
angle
•,
(see
text
for
direction
f
PA
and
hence
6),
to
intersect
A-l,
A-2,
etc.,
at
H,
J,
et•.
5.
Draw
a
urve
through
A,
H,
J,
etc.
6.
PA
is
obtained
by
drawing
a
tangent
to
the
curve,
parallel
to
A-G
tO
touch
at
T.
PA
is
the
line
W-T,
to
the
sa•e
scale
as
w•,
etc.
7.
The
failure
plane
is
the
line
through
A
and
T.
, ¸
FF GURE
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TRIAL
WEDGE
METHOD SOIL
WITH
COHESION
IRREGULAR
GROUND SURFACE
surface
.on
which
pressure
is
coloulo ed..
-,x&
/
7
/
2
3
/
/
/
/
NOTES
TRIAL
WEDGES FOR
ACTIVE
PRESSURE
.PA
FORCE
POLYGON
FOR
TYPICAL
WEDGE.
yo
Depfh
of
Tension
zone
2c
tan(45o+•}
COMBINATION
OF
FORCE
POLYGONS
TO
OBTAIN
MAX.P
A
The
above example
show
Rankine•s
conditions
But
the
s me
principle
applies
for
CoUlomb's
conditions.
Adhesion
on
the
back of the
wall
ignored .
For
direction
of
PA
see
figure
15
(Rankine's
conditions)
or
figure
16
(Coulomb's
conditions .
3.
See figure
16
for point
of application.
See
figure
17 for
resultant
pressure
diagram.
5.
The
trial
wedge
method
may
be used for
a
level
or
constantly
sloping
ground
surface.
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tt J
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POINT OF APPLICATION
OF
RESULTANT
PRESSURE
AND PRESSURE
DISTRIBUTION
surcharge
B
.///
A
TRIAL
WEDGES
h
B
A
PRESSURE
ON A-B
Use
when
t•e
ground
surface is
very
irregular
or
when
a
non-uniform
surcharge
is
carried.
PROCEDURE
.1.
Subdivide
th•
l•ne
A-4 into
about 4
equal
parts h
I
below
the
depth
Yo
of
tension cracing).
Compute
the
active
earth
pressures
PI;
P
P3'
etc.
as
if
each
of
the
points
I, 2, 3,
etc.,
w r
the base
of
the
wall.
The trial
wedge
method
is
Used
for
each computation.
Determine
the
pressure
distribution
by
working
down
from
point
4.
A
linear
variation
of
pressure
may
be assumed between
the
points
where
pressure
has
been
calculated.
Determine
the elevation
of the
centroid
of
the
pressure
diagram,
•.
This
is
the approximate
elevation
of
the point,
of
application
of
the
resultant
earth
pressure
PA
FIGURE
17
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BRACED
EXCAVATION
DEFLECTED
/
/
•F ILURE
SURFACE
POSITION
PRESSURE
DISTRIE UTION;3
H
EXCAVATION
I N
CLAY
The
above
apparent
pressure
diagrams
may
b•
used
{or
determining
the
s•r,.,
oads
in
braced
excavations.
EXCAVATION
IN
SAND
Area
abcd
is
the
pressure
distribution.
acts
at
0.50
H
above
the
base.
See
figures
5
to
8
for
K
A.
EXCAVATION
IN
CLAY
The
resultant,
PH
0.65
K
A
y
•:
Area
abcd
is
the
pressure
distribution,
The
shape
of
this
diagram
he,magnitude
of
the
pressures
depend
on
the
value
of
the
stability
umber
Ns
yH
C
PH
2<:,
N
s
•<
5
5<
N
s
.75
H
PH
87
H
O'4 /H
'TH-4
C
°25H
0
50H
-75H
50H
.4Z•H
lO<Ns<
20
20<Ns
'(1.25-
-O38Ns)Hp
H
,SH
PH
•'H- (8-
.•.N
C
qrH
O
O
(1 5-'075
N
s
)H
0
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MONONOBE-OKABE
EARTHQUAKE
EARTH
PRESSURE
COHESIONLESS
SOIL
CONSTANT
BACKFILL
SLOPE
H
A
FAI
L U RE
EARTHQUAKE
PLANE FOR
LOADI
N
G
ACTIVE EARTHQUAKE
PRESSURE
ON A B
ACTIVE
PRESSURE
PAE
½
KAE
Y
H2.
cos
2
(q-B-e)
l
(•os(a+•+0)
cos(•-•)J
e
tan
-1
CF
CF
E•L•I•-
•f
•AE-•)'=
-tan
(•+•+•-•)
•
sec
C•+•+•-•)
cos
•+•+e) sin (•+•
cos
p-•9
sin
NOTES
1.
The
above
equations
re
based
on a
resolution
of the forces
acting
on
awedge
of
soil.
The
effect
of
an
earthquake
is
represented
by.a
static horizontal
force
equal to
the
design
seismic
coefficient
times
the
weight of
the wedge.
2.
Where
the
earthquake
earth
pressure
is
calculated
on a
vertical
plane
through
the
re r
of the
heel,
B is
zero
and •
is equal
to
•.
3.
For
the determination of the point
of
application
of
PAE, the
total
active
earthquake
pressure
is divided
into
two
coEB•ents,
PA
from
static loading)
and the
dynamic
increment,
•'APAEi=
PAE
PA
PA
is
applied
at
I/3H
up
the
wall
and
•PAE
at
2/3•LG•;the-'•all.
The point of application of PAE is then calculatedby
taking
moments,
and the
pressure
diagram
is determined
accordingly.
FIGURE
19
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ACTIVE
EARTHQUAKE
EARTH
PRESSURE
COEFFICIENTS
FOR
COH[-SIONLEoS
SOIL
_1 2
UNIFORM
SLOPING
BACKFILL.
PLANE
KAE
.0-3.
-20
0 25
0-20
I
0ol5
i
O-IO
J
0
-05
IO
O
B,4CKFILL
SLOPE
• °
IO
WITH.
LT.L
2O
FIGURE
30
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ACTIVE
EARTHQUAKE
EARTH
PRESSURE
COEFFICIENTS
FOR
COHESIONLESS
SOIL
UNIFOR[VI
SLOPING
BACKFILL
•ITH
PRESSURE
ON
VERTICAL
PLANE
KAE
• 20
10
0
I0
20
30
4.0
0
BACKFILL
SLOPE
•
FIGURE
2
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ACTIVE
EARTt4QJAKE
EARTH
PRESSURE
COEFFICIENTS
FOR
COHESIONLESS
SOiL
WITH
UNIFO - IL
SLOPING
BACNFILL
PRE_• _SUR'•::
011
VERTICAL
PLANE
0o6
IO-
SLOI•E
•°
20
•0
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ACTIVE
E RTHQU KE
E RTH
PRESSURE
COEFFICIENTS
FOR
UNIFORM
SLOPING
PRESSURE
•
H
COHESIONLESS
SOIL
BAC KF
LL
ON
VERTICAL
PLANE
WITH
-I0
0
I0
BACKFILL SLOPE
.0
°
2O 30
40
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ACTIVE
EARTHQUAKE
BACK
FIL
I
EARTH
PRESSURE
..C.OEFFICIENTS
FOR
COHESIONLESS
SOIL
WITI•
UNIFORM
SLOPING
PRESSURE
ON
WALL
WITH
14°
•
=
25°
H
K
E
-I0°
0
BACKFILL
SLOPE
20
°
50
°
FIGURE
2
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.ACTIV
E RTHQU KE
E RTH
PRESSURF
COEFFICIENTS
FOR
COHESIONLESS
SOIL
FORM
SLOPING
BACK
FILl
PRESSURE.
ON
WALL
WITH
WITH
0 1
20
°
-I0
°
BACKFI
LL
0
I0 °
SLOPE
•
°
20
°
30
o
FIGURE
26
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r
ACTIVE
EARTHQUAKE
EARTH
PRESSURE
COEFFICIENTS
FOR
COHESIONLESS
SOIL
WITH_
UNIFORM
--SSURE
SLOPING
BACKFILL_
ON
WALL
WITH
,•
-14 °
-20
°
qO
°
BACKFILL
SLOPE
I0
°
•°
50
°
[FIGUR
27
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EARTHQUAKE
LOADING
TRIAL
WEDGE
METHOD
SOIL
WITH
OR
WITHOUT
COHESION
IRREGULAR
GROUND
SURFACE
2 5
4
5
CFW
FORCES
ACTING.
ON
•
TRIAL
WEDGES
FOR
/
Z
EARTHQUAKE
•
M•X.PA
E
PAE
FORCE
POLYGON
FOR
TYPICAL
WEDGE
2
\•CFW
COMBINATION
OF
•CX
FORCE
POLYGONS
TO
OBTAIN
MAX.
PAE.
The
ab ve
example
is
drawn
for
Rankine's
conditions
but
the
principle
pplies
also
for
Coulomb's
conditions.
For
direction
of
PAE
s
figure
15
(Rankine's
conditions)
or
figure
16
Coulomb's
conditions).
For
construction
of
pressure
diagram
and
point
of
application
of
resultant
see
figure
9• also
clause
4.3.3
for
cohesive
soils.
For
cohesionless
soil
the
vector
c
x
is
omitted
from
the
force
olygons,
iFIGUR
28
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d
_
Z
Z
Z
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I 00
m
R
//
0-4.
-60H
R
0.5
.•6H
•
o.•
.Ts
.59H
0.2
0.4.
0 6
0 8.
VALUE
OF
PQ
QL
For
m
S
0.4
0.20n
PQ(
(0.16
+
n2) 2
PRESSURES
LINE
LOAD
PQ
0.55QL
For m
>
0.4
FROM
1.28m2
n
QL
pQ •L
)
(m
2
+
n2)2
0.64q
L
•__
PQ__=__
m•
+
PQ
=
KA
QL
FROM
LINE
FORCE
LOAD
QL
(approx.
method
for
low
retaining wails)
LINE
LOAD
0 5..60
.54H
0 6 -46
48H
5
1 0
1'5
H
2
VALUE
OFPQ
(•)
For
m
_ <
0.4
d
p^•
H2)
0.28n2
q'Qp
(0.16
+
n2) 3
For
m
>
0.4
H
2
1.77m2n
2
pQ •-•-•)
(m2
+
n2)
3
E m
H
SECTION
A-A
p'Q=pQ
cos
2
(l.10a)
PRESSURES
FROM
POINT
LOAD
Qp
POINT
LOAD
LATERAL
PRESSURE
DISTRIBUTION
ON
WALL
TO
POINT
AND
LINE
LOADS
DUF
IFIGURE
31
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0
.
o|
•• -
•
I,O
l .
o..
•/•o_•o
•
.0
O t
O
•:;
¢0
,•
•
0
1--
6
o
6
6
2
0
0
z
0
0
0 0
z
H
•J.,z4/n
OI.LV•I
LU
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]
Z
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TYPE
OF
WALL
GRAVITY
SEMI
GRAVITY
CANTI
.EVER
COUNTER
FORT.
LOAD
DIAGRAM
7
TOE
STABILITY
CRITERIA
FOR
RETAINING
STABILITY
CRITERIA
SLIDING
S
(W
t
+ pv
tan
6
b
+
CbB
Fs
(sliding)
S
+
p
PH
•
1.5
(static
loading)
or •
1.2
(earthquake
loading)
OVERTURNING
Moments
about
the
toe
of
the
base
Fs
(overturning)
Wt
a
+
Pv
f
PHb
•
2 0
(static
loading)
or
•
1.5
(earthquake
loading)
Also
check
overturning
at
selected
orizontal
planes
up
the
wal
for
gravity
type
walls.
BEARING
PRESSURE
Point
where
R
w
intersects
base,
rom
toe,
d
Wt
a
+
Pv
f
PHb
Wt
+
Pv
assuming
pp
0
For
soil
foundation
material,
d
should
be
within
middle
third
of
the
base
(static
loading)
or
middle
hal#
(earthquake
loading).
For
a
rock
foundation,
d
should
be
ithin
middle
half
for
both
static
and
earthquake
loading.
Fs
(bearing)
•
3.0
(static
loading)
r •
2.0
(earthquake
loading).
See
section
7.4
for
calculation
of
actor
of•safety
for
bearing.
W
t
total
•eight
of
the
wall
in-
cluding
soil
on
toe
plus
soil
bove
heel
(for
cantilever
and
counterfort
walls
only)
v
vertical
component
of PA
H
horizontal
component
of
PA
w
resultant
of
W
t
and
PA
IWALLS
36
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SHAPE
FACTORS
s
c
+
0.2 N@
B/L
Sq)=
1.00 for
@
0
sy)
I
+
0.1
N@
B/L
for
For
continuous
strip
footi.ng
s
c
=.Sq
sy
1.0
DEPTH FACTORS
for
D/B
<
d
c
+
0.2•
D/B
dq)
ii.00
for
•
0
dy)
I
+
0.1
N•r•@
D/B,
fob
@
>
10
o
t•O•: Ny=O
for
•=0
5 I0 15 20
25
50
55
40
ANGLE
OF
INTERNAL
FRICTION,
•,
DEGREES
N@ =
tan
2
45
°
+
3
L FOOTING
LENGTH
D
| •
=•D
ASSUMED
CONDITIONS
i.
2.
3.
5.
D
•
B
Soil
is
uniform to
a
depth
do
>
B
Water
level
is
lower than
d
o
below
the base
of
the
footing
The
applied
load is vertical
and concentric
Friction
and
on
the vertical
sides
of the
footi,ng
are
neglected
ULTIF•TE
BEARING
CAPACITY
qult
E-Q--=BL
cNc
sc
dc
+
•
Nq
Sq
dq.
+
½
X
B Ny
sy
dy
BEARING
CAPACITY
OF SHALLOW
FOOTINGS
WITH CONCENTRIC LOADS
FIGURE
57
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INCLI
20•
Z
<
I00
'
I0
20
•-0
60
80
NATION
OF
LOA__D
•
DEGREES
Q=
total
inclined
load
•B
HORIZONTAL
BASETINCtclNED
ECCENTRIC
LOAD
NOTES
]
Calculate
effective
base
width
B
=
B-2e
;2
Obtain
Nyq
and
from
chart
above.
Ncq
3.
Vertical
component
of ultimate
bearing
capacity
quit v)
CNcq
+
½yB
NTq
4.
Bearing
pressure
from
vertical
component
of
applied
loading
qCv)
B
qblt(v)
s
•(v)
BEARING
CAPACITY
6
0
20
40
60
80
INCLI______NATION
OF__FOOTING
@
DEGREE•
q=
normal
pressure(load/area)
INCLINED
BASE
WITH
NORMAL
LOAD.
NOTES
1.
Obtain
and
from
chart
bove.
Nyq
Nc
q
2.
Ultimate
bearing
capacity
qult
-=
CNcq
+.½yB
Ny•
3.
Fs
qul•t
q
FOR
AN
INCLINED
LOAD
HIGHER Q
ULT.
IS
OBTAINED
WITH
AN
INCLINED
BASE,
A
FOR.
INCLINED
LOADS
FIGURE
38
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roundel/on
depth/width
3 B=O
Linear
interpolation
lot
termed[ale depth•
4O
0
tO 20
30
40
50
Incliner;on of •lope
e•
FOUNDATION ON
FACE
OF
SLOPE
In
general
qult
cNcq
+
½yBNyq F
S
qult
q
for
0
quit
CNcq
+'YD
BEARING
DIB
lactarNs
I
0
2
3
4
5
D•slonce
of
[oundel•on
from
edge
of Slope
9/B=I
•
Linear
interpolation
0
Dislance
of
[oundat•on
[ram
edge
of
FOUNDATION ON
TOP
OF
SLOPE
@OEE: The
charts
given
are
for
vertical loading.
The base
Ns
xH
wldth
is
reduced
for
eccentric
c
loads.
CAPACITY FOR
FOUNDATIONS ON
SLOPES
FIGURE
•B
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TOE
MOMENT
EFFECT
ON
HEEL
The
toe
support
moment
produces
a
oading
on
the
heel.
If
it
is
assumed
that
no
moment
is
trans-
i.tted
into
the
stem,
an
equivalent
arabolic
heel
loading
is
as
shown
elow,
with
the
maximum
ordinate
iven
by
Pt
2.4
MT/a2
where
M
T
is
the
toe
support
moment.
WEIGHT
OF
BACKFILL
BOVE
HEEL
SELF
WEIGHT
OF
HEEL
LOADING
FROM
TOE
MOMENT
SSUMED
FOUNDATION
BE RING
PRESSURES
VE
RESULTANT
LOADING
ON
HEEl_
May
be
fully
positive)
Note:
Pressure
diagrams
not
to
scale.
D__ESIGN
LOADING
ON
HEEL SLAB
FIGURE
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SSUMED
45
°
CRACK
LINE
FROM
B.
ASSUMED
a,5•
CRACK
LINE
F•
A.
ANCHORAGE
LENGTH
EQUIVALENT
jd
FOR
B
AT
B.
45
o
A
MOMENT
EQUIVALENT
jd
FOR
MOMENT
AT
A.
MAIN
TENSILE
STEEL
'IN
COUNTERFORT.
Point
of maximum
mor•nt (maximum
allowable
stress
in
all
main
tenslle
rein
forcement).
B Section
of
lesser
moment
than
at
Ao
If
some
of
the
reinforcing
bars
of
the
main
tensile
steel
were
eliminated
then
there
would
be
maximum
allowable
stress
in
the
remainin
9
bars.
The
Icut
off
position
for
some
of
the
bars
of
the
main
tensile
reinforcement
is
to
be
the
greater
of:
a)
Anchorage
I-•h• •
the-•ssumed
45
°
crackline
from
A.
b)
12"
past the
assumed 45
°
cracked
li•e
from
8.
'jd'
c n
be
taken
as
the
perpendicular
distance
from
the
centroid
of
the
steel
to the
midpoipt
of
the
stem
slab.
'CUT
OFF'
POSITIONS
OF
MAIN
TEN,SIL_F•
STEEL
IN
COUNTERFORT
FIGURE.
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SINGLE
W LL
DOUBLE W LL
TRIPLE W LL
25
ASSUMPTIONS
Soil Properties
•
30
°
c O
y
125
Ib/ft
3
Wall
Properties 8 20
°
W
w
=
I00
Ib/ft
3
Wall Slope
B
14
°
I
in 4)
Water
table below
base of
wall
Live
load
surcharge
equal
to
2
ft.
F
s
sliding)
1.5 min
I0
0
5
i0
15
20
BACKFILL SLOPE
•°
FIGURE
4-:5
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CRIBWALL
DESIGN
CURVES
NORM L
LOADING
=40
°
see
figure43for
diagrams
ASSUMPTIONS
Soil
PropePfies
•
40
°
c=O
T
125Ib/ft
3
Wall
•roperties
6
26.6
°
W
w
100
Ib/ft
3
Wall
Slope
•
-14° I
in
4)
Water
table
below
base
of
wall
Live
load
surcharge
equal
to
2
ft
f
soil
included
Fs
sliding)
1.5
min
Fs
°verturning)
2.0
min
5
I
15
BACKFILL
SLOPE,•°
2O
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SINGLE
WALl-.
DOUBLE
W LL TRIPLE WALL
ASSUMPTIONS
15
I0
Soil Properties
{
30
°
•
125
Ib/ft
3
Wall Properties 6
20
°
W
w
100
Ib/ft
3
Wall
Slope
•
-14
°
I
in
4
Water
table
below base
of
wall
F
s
sliding) 1.2 min
F
s
overturning)
1.5
min
15 20
SLOPE
•0
°
|FIGUR
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CRIBWALL
DESIGN
CURVE£
_EARTHQUAKE
LOADING
SEISMIC
COEFFICIENT
0•20
See
figure
4.5
for
diagroms)
ASSUMPTIONS
•oil
Properties
Wall
Properties
•
40
°
c
0
y
125 Ib/ft
3
6
26 6
°
W
w
I00 Ib/ft
3
Wall
Slope
•
-14
°
I
in
4)
Water
table
below
base
of
wall
Fs
slidi.ng)
1.2
min
Fs
Overturning)
1.5
min