CECW-EG
Department of the Army
EM 1110-2-1902
U.S. Army Corps of Engineers Engineer Manual 1110-2-1902
Washington, DC 20314-1000
Engineering and Design Stability of Earth and Rock-Fill Dams (Inclusive of Change 1)
Distribution Restriction Statement Approved for public release; distribution is unlimited.
1 April 1970
Foreword
Experiment This manual was prepared in the U. S. Army Waterways Station under direction from the Office, Chief of Engineers. General supervision and technical guidance was provided by W. E. Johnson, Chief, Engineering Division, G. E. Bertram, Chief, Soil Mechanics Branch until 1968, and R. A. Barron, Branch Chief from 1968 to date. The manual was prepared by W. E. Strohm, Jr., Trahan, Yu-Shih Jeng, and D. P. Hanrner under direction of S. J. Johnson and J. R. Compton, the U. S. Army Waterways Experiment Station.
assisted by C. C. the innnediate of the staff at
A draft of the manual was reviewed by the Corps Advisory Board The Board consists of R. A. Barron, Chairman; for Soil Mechanics. R. B. Peck, University of A. Casagrande, Harvard University; Illinois; G. E. Bertram, Consulting Engineer; S. D. Wilson, Tippetts-Abbett-McCarthyShannon &Wilson, Inc; J. Lowe, III, and S. J. Johnson, Waterways Experiment Station. Stratton;
DEPARTMENT Office of the Washington,
ENGCW-ES
OF THE ARMY Chief of Engineers 20314 D. C.
EM
Manual No. iiiO-Z-1902
iiiO-Z-1902
1 April
ENGINEERING Stability of Earth
Table
and
AND DESIGN Rock-Fill Dams
of Contents Page
Paragraph 1.
Purpose
2.
Scope
3.
Applicability.
4.
References. a. b. c.
1
..................................
i
...................................
1
..............................
i
...............................
2
.................................
Notation.
6.
Basic
7.
Embankment Causes of Unsatisfactory ........................... Shear Failure a. .................... Excessive Deformation. b. .......................... Liquefaction C.
9.
I 1 2
......................... EM 1110-2-2300 .................... Other Engineer Manuals ...................... Selected References.
5.
8.
197-F..
Design
2
...................
Considerations.
Performance
....
f .
5
........................... Special Problems ...................... Progressive Failure. a. .......................... Problem Shales. b. ..................... Rate of Fill Placement C. Design Shear Laboratory a. Selection b.
Strengths. Tests. of Design
of Stability
....................... ........................ Shear Strengths.
Analysis.
2 7 7 7 13
............
14
...................
10.
Methods
11.
.................. Design Conditions for Analysis ................. End of Construction Case I: a. ............ Cases II and III: Sudden Drawdown. b. ..................... Partial Pool Case IV: C. Seepage with Maximum Case V: Steady d. .......................... Storage Pool Case VI: Steady Seepage with Surcharge Pool. e. ..................... Earthquake. Case VII: f. ............. At-Rest Earth Pressure Analyses. g* i
3 3 4 5
15 15 16 18
.....
19 19 19’ 20
EM iilo-Z-1902 1 April 1970 Paragraph
Page
12.
Factors
13.
Presentation
14.
Use
of Safety.
26
. . . . . . . . . . . . . . . . . . . . . . . . . .
in Design
of Electronic
Memoranda.
Computers.
26
. . . . . . . . . . . . . .
28
. . . . . . . . . . . . . . . . . , .
APPENDIX References
I
APPENDIX Notation
II
APPENDIX III Estimating the Lowering of the Seepage Line in Pervious Upstream Embankment Zones During Reservoir Draivdown APPENDIX IV Simplified Procedures for Preliminary Determination of Embankment Slopes Infinite
Slope Modified
APPENDIX Analysis for
V Cohesionless
Soils
APPENDIX VI Swedish Method of Analysis Using Slice Procedure
1.
General.
2.
Procedure
3.
Graphical
4.
End
5.
Sudden
Drawdown--Cases
6.
Partial
Pool,
7.
Steady
8.
Earthquake--Case
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . of Finite
Slices
Integration
. . . . . . . . . . . . . . . . . . . .
Procedure
of Construction--Case
Seepage,
VI-5
I . . . . . . . . . . . . . . . . . . .
VI-IO
Slope--Case
Downstream VII
. . . . . . . . . . . . . .
VI-10
IV.
VI-12
Slope--Cases
. . . . . . . . . . . V and
VI . . .
VI-13
. . . . . . . . . . . . . . . . . . . . . . .
VI-i4
PLATES
No. VI-i
Modified Water
Swedish Forces
VI-2
Modified Swedish Method, Drawdown Impervious
VI-I
. . . . . . . . . . . . . . . .
II and III.
Upstream
VI-I
Method,
Finite
Slice
Procedure,
No
Finite Slice Embankment
Procedure,
Sudden
ii
EM
IliO-Z-1902 1 April 1970
No. VI-3
Modified Steady
Swedish Seepage,
Method, Water
VI-4
Modified Swedish Method, Integration Procedure,
VI-5
Modified cedure,
Swedish Method, Graphical No Water Forces
Integration
Pro-
VI-6
Modified cedure,
Swedish Sudden
Method, Drawdown
Graphical
Integration
Pro-
VI-7
Modified cedure,
Swedish Steady
Method, Seepage,
Graphical Integration Water Forces
Pro-
VI-8
Stability Analysis, stream Slope, Slice Procedure
VI-9
Stability Analysis, Modified Swedish Procedure
VI-10
Stability Analysis, stream Slope, Slice Procedure
VI-ii
Stability Analysis, and Semipervious down, Modified Procedure
VI- 12
Stability Analysis, Case stream Slope, Modified Integration Procedure
VI- 13
Stability Analysis, Slope, Modified Procedure
Case IV - Partial Swedish Method,
Pool, Upstream Finite Slice
VI- 14
Stability Analysis, Slope, Modified tion Procedure
Case IV - Partial Swedish Method,
Pool, Graphical
Upstream Integra-
VI-15
Stability Analysis, stream Slope, Method, Finite
Case V - Steady Max Storage Pool, Slice Procedure
Seepage, Modified
DownSwedish
VI- 16
Stability Analysis, Case V - Steady Seepage, stream Slope, Max Storage Pool, Modified Method, Graphical Integration Procedure
DownSwedish
Case Modified
Finite Forces
Slice
Procedure
with
Finite Slice and Graphical Earthquake Loading
I - End of Construction, Swedish Method, Finite
Up-
Case I - End of Construction, Method, Graphical Integration
Case Modified
II
- Sudden Drawdown, UpSwedish Method, Finite
Embankment with Central Core Shell, Case II - Sudden DrawSwedish Method, Finite Slice II - Sudden Drawdown, UpSwedish Method, Graphical
...
111
EM 1110-2-190~ 1 April 1970 No. VI-17
Stability Analysis, Case VII - Earthquake, Seepage, Downstream Slope, Modified Method, Finite Slice Procedure
VI- 18
Stability Analysis, Case Construction, Modified Graphical Integration
Steady Swedish
VII - Earthquake, Swedish Method, Procedure
End
of
Page
Paragraph APPENDIX VII Wedge Analysis 1.
General.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.
Basic
Principles.
3.
Basic
Criteria
4.
End
5.
Sudden
6.
Partial
7.
Steady Seepage Pool - - Case
VII-I
. . . . . . . . . . . . . . . . . . . . . . . . . .
VII-2
Drawdown--
8.
Steady
9.
Earthquake
I. Cases
Upstream
. . . . . . . . . . . . . . . .
II and III Slope--Case
with Maximum V.........................
Seepage
with
. . . . . . . . . . . . IV
. . . . . . . . .
VII-II
Surcharge
VIIPool--Case
VI
. . . . .
12
VII-13 VII-
14
PLATES 1
Stability
Analysis,
Wedge
Method
Direction Passive
VII-3
Use
VII-4
Stability Case
Analysis of Embankment I - End of Construction,
with Wedge
Central Method
Core,
Stability Case
Analysis of Embankment I - End of Construction,
with Wedge
Inclined Method
Core,
VII-6
VII-8 -
VII-2
VII-
VII-5
Storage
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
No. VII-
. . . . . . . . . . . . . . . . . . . . . . . .
of Construction--Case
Pool,
VII-i
5
of Resultant Earth Forces and Active Sliding Planes, Wedge Method
of Conjugate
and
Stresses
Embankment Stability Analysis, and Semipervious Shell, Case down, Wedge Method
iv
with Central II - Sudden
Core Draw-
.-
EM
1110-2-1902 1 April 1970
No. ..VII-7
Stability Analysis, Embankment with Inclined and Free-Draining Shell, Case II - Sudden down, Wedge Method
VU-8
Stability Analysis, Embankment with and Free-Draining Shell, Case IV Pool, Wedge Method
VII-9
Stability Case
Analysis, V - Steady
VII-IO
Stability Case
Analysis Embankment Pool, VI - Surcharge
VII-11
for 8A vs +D Sliding Slope
VII-12
KA
9,
for
Inclined - Partial
Core
Embankment with Central Seepage, Wedge Method with Wedge
Cohesionless
Core,
Central Method
Core,
Soil,
Coulomb
Active
Active
Wedge
Beneath
Negative
Cohesionless
Soil,
Coulomb
Active
Wedge
Beneath
Plane
vs
Core Draw-
for
Sliding Plane tive Slope
for
Active
Nega-
Page
Paragraph Evaluation
APPENDIX VIII of Embankment During Construction
Stability
. . . . . . . . . . . . . . . . . . . . . .
VIII-I
Development of Pore During Construction
Water Pressure . . . . . . . . . . . . . . . . . . . . .
VIII-i
3.
Installation
of Piezometers
. . . . . . . . . . .
VIII-4
4.
Evaluation
. . . . . . . . . . . .
VIII-5
1.
Basic
2.
Consideration.
and
Uses
of Embankment
Stability
PLATES
No. VIII-1
Pore Pressures in Partially Drainage During Loading
Saturated
VIII-2
Pore Pressures of Complete. Construction
VIII-3
Pore Pressures in Partially Saturated Soils, Effect of Partial Dissipation of Pore Pressure Between Construction Seasons
in Partially Dissipation Seasons
Soils,
Saturated Soils, of Pore Pressure
V
No Effect Between
EM 1110-2-1902 1 April
1970
No. VIII-4
Pore
VIII-5
Development
VIII-6
Data
VIII-
VIII-8
7
Pressure
for
Coefficients of Excess
Estimating
A and Pore
Pore
Water
Pressures
Undrained of Q/Q3
Shear Strength for at Start of Shear
Various
Undrained Conditions
Shear
Field.
Strength
for
vi
B Pressures in
Q Test Ratios
Stress
DEPARTMENT Office of the Washington,
ENGCW-ES
OF THE ARMY Chief of Engineers D. C. 20314
EM
1110-2;1902 1 April 1970
Manual No. IliO-2-i902 ENGINEERING of Earth
Stability 1.
Purpose.
ity
of earth
2.
Scope.
This and
rock-fill
Methods
in the
methods,
but
3-777
(ref
Minimum may
and
for
dams.
4.
References.
factors and
during
all
liiO-2-2300,
tion
Considerations Other
b.
other
design
EM
and
EM
design
but
Earth
and
of the
Swedish
special
in table
and are
factors.
illustrated
method
Technical
I, page
tests
or design
to all
Corps
by
approved
slide
D of WES
given
works
functions.
highway
fills,
IiiO-2-2300.
Report
25, are
used.
analyses
that
and
must
and
reservoir
in draft
The
Manuals.
dams
of earth and
General
September following and
should
and
rock-fill
are Design
rock-
dams,
material
to provide
operation
Divi-
to stability
earth
and
be satisfied
Dams, form
as for
zoning,
that
Rock-Fill
rock-fill
as well
section,
of Engineers
It is applicable
Types
of cross
criteria
(issued Engineer
manual
is applicable
of construction
of earth
than
civil
selection
phases
EM
of safety
manual
levees,
a.
general
stabil-
to be used,
safety
described
of this
in Appendix
tests
acceptable
are
the use
given,
having
ihfluencing
the
included.
This
dikes,
fill
tion,
factors
not
Districts
analyzing
of strength
(c) minimum
methods
given
are
are
for
(a) types
stability
prohibit
(c))
requirements
analyses
and
Case
Applicability.
sions
and
The
not
1) if the
be required
3.
does
of slices,
for
embankment
appendixes.
this
procedures
presented analysis,
computing
examples
(method
are
requiring
for
establishes
AND DESIGN Rock-Fill Dams
dams.
Criteria
(b) conditions
No.
manual
and
utilizastability
described and
in
Construc-
1969). manuals
also
be referred
relate to for
to use criteria
stability:
iiiO-i-1801
This manual 27 Dee 1960.
rescinds
Geological EM
Investigations
1iiO-2-1805,
21 July
(November 1964,
and
1960) EM
1110-2-1902,
EM 1110-Z-1902 1 April 1970
EM
1110-2-1802
Geophysical
EM
I 1iO-2-
Subsurface
EM
1110-2-1901
Seepage
EM
1110-2-1904
Settlement
Analysis
EM
iiiO-2-1906
Laboratory
Soils
EM
1110-2-2902
Conduits,
Where
the
sion
above-listed
of this c.
Selected
Notation. II.
The
Committee
Basic
be evaluated situ
Symbols
used
majority
of them
Design
pertinent properties
to (1) possible borrow
compacted
densities
The
decrease
terials
values,
Other but
judgment, ments and
high
are
which
can
the
that
proA-
and
embankment and
rate
and
of granular
embankment
must
only
through
of differential foundations characteristics 2
normal
for
water methods,
and
high
ma-
dams.3 design
of engineering
settlements
where
or in narrow, the
control.
foundation
for
of
(4) climatic
contents
and
and
be given
construction
exercise
in
contents
in establishing
within
must
engineering must
water
be considered
be accounted
be evaluated
of strain
must
and
materials
selecting
(2) natural
in placement
stresses
by the
expected
consideration
materials,
in Ap-
Mechanics
utilizing
angle
on compressible
to similarly
and defined
conditions
with
located
and are
of an embankment
be expected
effect
herein
Engineers.2
must
(1) the
cited
recommended
stability
in placement
include
(2) compatibility
agree,
of the Soil
determining
variations
confining
factors
1969)
correspond
listed
materials,
in borrow
that
The
foundation
When
(5) inevitable
are
to those
operating
embankment
in friction
under b.
and
(3) variations
and
are
of Civil
a.
of the
variation
conditions,
do not
Definitions
Society
information.
materials,
1965)
(3 March
numbers
manual
and
American
of proposed
Pipes
manual
correspond
of Terms
properties
geologic
(10 May
I.
in this
construction
engineering
1953)
references
these
Considerations.
for
this
Selected
in Appendix
Division,
(January
and
1954)
4952)
Testing
and
numbers;
on Glosstiry
Foundations
(March
(February
Culverts
References.
references
pendix
Control
1948)
govern.
by superscript
numbered
6.
shall
(September
Investigations--Soils
references
manual
designated
5.
1803
Explorations
embank-
deep
embankment
valleys, and
of
EM
the
embankment
manual
assume
materials
and
seepage
bedding,
movement
existing
along The
fects
of changes
-.
validity
after
compatibility
and
operating
where stresses
for
all
to evaluate and
after
(3) the come stresses rapid 7.
of existing
consolidated are
used
drawdown Causes a.
an embankment remainder
of the
steady
and
and
(5) alter-
earthquake
for
activity,
for
comparing
material
results
where
the
ef-
properties depends
should
structures
rel-
evaluating
analyses
utilize
on the
be reviewed construction
for
pressures
construction
embankment
and have
Total
in a general
used during
available,
exist.
and,
are
(2) stability are
and
total
stresses
conditions,
foundation
stresses
and
normal
observations
pore
effective
predicted,
effective
when
be-
normal sense,
for
conditions.
A failure
mass
and
herein
Embankment
foundation
in-
(7) weathering;
foundation
seepage
no excess
earthquake
Failure.
faulting;
a means
of stability
similar
piezometer
and
and
systems;
be satisfactorily
dams
of Unsatisfactory
Shear
and
in designing
and
and
In general,
where
past
(4) structure,
to slides,
strengths,
can
pool
de-
known.
cases.
(1) partial
joint
design
described
pressures
construction
fully
are
geologic
(3) maximum
etc.),
afford
value
for
ground-
jointing.
during
shear
analyses
other
stability
analyses
procedures
water
and
tension
The
design
pore
and
construction.
experiences
closed,
(i)
and
evidence;
relating
embankment
with
The
e.
open,
sections
design
in this in all
includes
stratigraphy,
geological
in assumed
of assumed
for
from
faults,
cross
presented
simultaneously
interpretation;
evidence
of trial
analyses
be considered
geologic
(9) field
of stability
merits
mobilized
(6) joints
results
ative
are
(2) lithology,
by faulting; and
stability
should
(amount,
(8) slickensides;
and
that
and
folding
The
surfaces.
as deduced
of materials
during
sliding
conditions;
at site
d.
strengths
by borings
overburden
ation
design
information
disclosed
cluding
foundation.
assumed
Geologic
water
the
that
along
C.
tails
with
IiiO-i-1902 1 April 1970
in which
moves
is designated
Performance. a portion
by sliding as a shear 3
or
of an embankment rotation
failure.
relative A shear
or
of
to the failure
is
.b--
EM illO-2-1902 1 April 1970
represented
COnVentiOnally
in stability
analyses,
thickness.
The foundations
mately
represented
within
nearly
approximate
a thick,
compacted
wet
to develop
slightly
dry
greater
than
standard
materials.
As
given
may fill
be given
tests
show
cent
strain,
tents for
it may
design
ment
shear
may
large
foundation
strengths ment
in the
formation of fill
and can
existing
foundation and
be controlled.
more
planes
at high
and
large these
or
under are
pore
these mobilized should
water
Q and not
to be used R strength
peaked
placement
settlement
saturated.
consolidation will
at 45 per-
water
at large
may
Excessive of the
occur.
conditions
con-
Shear
strains
Surface
to detect the
occur
if the
embankespe-
deformations
where
so that
values
foundation,
and also
be installed
pressure
soils
(2) use conservative
or
settlements
pressures
attention
for
or have
in
in an em-
particular
When
slightly
develop
water
pore
curves
excessive
from
to or
placed
high
large
compacted
may
are
average
becomes
when
strains
study,
those
relatively
equal
soils
strains
of optimum,
result
require
create
design
to (1) limit
then
especially
Even
foundation.
However,
piezometers
excessive
stratum
may
and
soils,
stress-strain
in the
side
also
be high
a weak
arcs
to densities
and the
of the
differential
may
indicators
shape
strengths.
deformation where
and
when
During
dry
or thin
surface
content,
relatively
be necessary
too
cially
content
strengths
is compacted
failure
and
be approxi-
embankments
resistance.
excessively
dry
may
or where
the
water
of shear
water
on the
zoned
cohesive
of optimum
deform
shear
to slightly
soil
the
peak
embankments
deposits
involved
Some
a consequence,
and
of substantial
surfaces.
is placed.
in an embankment
is so assumed
in a zone
of interconnected
maximum,
to the
Where
deposit,
levels
of optimum
as additional should
side
occur
and
homogeneous
are
fine-grained
plane
strains
they
bedrock
a surface
fine-grained
arc.
Deformation.
on the
bankment
of thick,
a combination
Excessive
may
in relatively
by a circular
interconnected
b.
such
surface
overlying
exists
along
shearing
consisting
layers
several
although
failure
in soil
foundation
as occurring
rate
the
in
peak
move-
excessive of placement
de-
EM iiiO-2-1902 1 April 1970 Liquefaction.
C. sands,
sensitive
when
such
silts,
The
basis
than
cohesionless
age
relative
present
than
briefly
those
tion
and
shear
resistance
peak
requiring
described
in this
exhibits
peak
shear
sible
solutions are
to use
the
highly
the the
entire
manual.
to or greater
drainage
However, zones,
an aver-
embankment
adequate
potential
Some
than
shear
failure
strength. conditions
stability
investiga-
of these
problems
of nonuniform
stress
shear
of progressive
failure
minimums embankment
analyses
are
safety
in some
the
is mobilized
the
after
peak
curve stresses
and
or to use soils,
it may
are
the use
be unconservative.
factor
total simul-
stress-strain
is increased,
would
distribu-
develop
so that
stress
In certain
strengths.
may
strength
Where
in shear
of
POS-
shear
strengths
even
be necessary
strengths. are
or
heavily
characteristics
consideration
peak
surface.
the
strains
progressively,
drop
embankments plastic,
large
if the
failure
to increase peak
Because
than
in stability
are
stress-strain
bankment,
equal
comprehensive
be reached
a significant
ultimate
brittle,
be less
strengths
Where
and
relatively
may
possibility
less
(2)
zones,
will
for
the
to provide
more
laboratory
to minimize
types
(1)
Failure.
strengths
along
reached,
soil
problems
failure
taneously a soil
and
occur
on the 5 tests and
to liquefaction.
fills
and
may
b-
below.
in potential
that
of piping,
and
be evaluated
density
susceptible
saturated
or earthquake
by special
is required
Certain
Progressive
areas
for
danger
concern,
presently
a relative
to be not
of loose,
deformations
must
having
of 85 percent
discussed a.
to shear
in embankment
Problems.
unusual
tions
believed
materials
or the
Special
8.
are
is of major
supplemented
Sands
density
settlement,
clays
knowledge4
70 percent
of liquefaction
of liquefaction
judgment.
for
quick subjected
possibility
engineering
over
are
of empirical
phenomenon
and
materials
shocks.
ing
The
should required at strains
constructed
on foundations
overconsolidated significantly be given
in table
consisting
clays, different
or clay from
to (a) increasing
I (page
comparable 5
25), to those
(b) using in the
the
of
shales
those
of the
safety
factor
shear foundation,
strengths or
havem-
EM IiiO-2-1902 1 April 1970
(c)
using
ultimate
(3) from
shear
progressive
failure
longitudinal
to construction
mum
of cracking,
the
the
does
crack
in all
tan
not
exceed
should
stability
(a) clay
or
other
because
noncohering
Foundation
shales
than
been
Clay
into
two
to a few
cycles
either
have
been
encountered
water
broad
groups:
by the
weight and
by calcareous, bonding
usually
usually
along
cementation
particle
shales
as-
is expected.
produced
are
depth
with
condition
from
or in which
maxi-
resistance
consolidated
strength
subjected
shales
this
or
from
maximum
to be filled
strength
substantial
the
be divided
have
The
be estimated
Shear
assumed
significant
when
strength
are
upon
in situ
presence
of slickensides
strengths.
Prediction on results
leading,
and
clay
shales
aerial
or
with
has
slake
oc-
rapidly
of wetting
unaffected
into
and dry-
or reduced
to
ground
high
in clay of the
field
be determined reconnaissance,
may
pore
laboratory may
tests, be required.
by (a) observation (b) presence 6
containing
low,
even
may
since
develop
Existence of slide
areas
of slickensides,
unalunder
The of low
shear
not
be based
should they
of
strength
under
of clays.
shales
loss
shear
an indication
of clay
in clay
consequent The
those
is usually
behavior
tests
and
pressures
approaching
field
those
be quite
water
shales
frequently
particularly
to weathering.
shales
properties
of conventional
large-scale can
and
more
to expansion
exposure
of clay
soil
shales,
susceptible
and/or
conditions,
in load
solely
highly
modulus
increase
Clay
shales.
unloading
deformation
tered
problems
in cemented
montmorillonite,
8b(2)
that
pressure.
particles
cemented
height.
may
of deposits, and
that
where
during
pieces.
(2)
and
lack
have
types
of heat
fine
whereas
small
that
slope
resulting
by drying. can
limitation
Shales
cracks occurring
caused slope,
the crack
shales)
tension
settlements
embankments
and
shales
the the
(1)
sediments
siliceous,
with
soils.
along
an infinite
and
for
start
shrinkage
0.5 times
(compaction
(b) cemented
ing,
(45 + 3
Shales.
shales
curred
or from
analyses
of overlying
may
foundation
differential
be ignored
Problem
b.
also
assuming
v
equation
sumed
of the
or transverse
subsequent depth
strengths
may
be misof problem
through (c) presence
EM
of bentonite natural
water
(3) tain
types
joints,
of the
wherever
shales
be required
are
bankments
on silt,
occurring
ment,
and
clay, and
past
(Appendix
also
may
investigation
In addition,
special such
where
material,
geologic
(1)
with
they
con-
and weak control
the
over-
is essential laboratory
as shear
Foundations.
shale
significant
tests
strength
may
and
horizontal
and
construction.
experience
are
may
movements
Analyses
excessive should
and
of such
to control
the
of em-
create
Instruments
vertical
used
Construction
foundations
deformations.
during
occur
contents
Excessive
in embankments
greater
than
and
deform
pressures dry
of pore
water
rate
rate
foundations
semipervious optimum
while
placing
soils
even
pore
pore
be in-
water
pres-
observations, of fill
judg-
placement
be necessary
in the the
outer
core
to limit
shells
slightly’
placed
can
cases
wet
movements
data
except
placement
water
contents
vertical
provide
at water
pore
at water
of embankments
material
deformations
high
and
In some
placement.
are
develop
placed
construction
and
soils
of horizontal
during
of fill
pressures
may
when
Observations
it may
material
water impervious
Some
excessively
pressures the
pore where
optimum.
of optimum.
to control
plastic
soft
pressures
properties
or clay
Embankments.
slightly
limits
VIII).
(2)
used
physical
Placement.
to measure
sures
and
encountered.
of Fill
pressures
may
A detailed
problems
with
water
plastic
pressure.
Rate
stalled
mass.
filled
pore
and
tests.
foundation
seams
excess
liquid
mineralogical
present
faults,
to determine
water
water
may
and
of Atterberg
(e) clay
of shales
defects
strength
C.
and
slickensides, Such
pore
(d) comparison
contents,
All
layers. all
layers,
11iO-2-1902 1 Aprii 1970
that
may
be
on weak,
water
contents
of
to the
dry
of
of optimum
side
water
content.
9.
Design
Shear
values
used
tests
performed
corresponding
Strengths.
in stability under to these
a.
analyses three drainage
Laboratory are
generally
conditions
determined
of test
conditions 7
(1)
Tests.
are
specimen (a)
Shear
strength
from
laboratory
drainage.
Q tests
in which
Tests the water
*-
EM IIIO-2I902 1 April 1970
content
is.kept
swelling
constant
1s allowed
kept
constant
which
full
ditions
strengths
for
Q tests
The
for
shear
quantities
apparatus
soils
to expected
maximum
compaction
effort
applied
narrow
standard
placement cores
tests
maximum
should
S shear
required
for
rel-
in a very
letters
Q,
R,
and
to various
prototype
triaxial
compression
S
used
usually
contain
are
tested
significant
in triaxial
field
in the
compres-
graphically strength
shells is less
for
of gravel important placement
sufficient. 8
content
contents.
and The
estimated
minimum
allowable
of standard
maximum
density).
water
content
and
density.
These
minimum
in- figure
‘1, are
intended
expected
placement
additional
as shown
specimens
water
water
at optimum dry
test
optimum
placement
maximum
conditions
strength
to standard
to test
estimated
soils
in preparing
result
in shear
materials
which
specimens.
illustrated
and
with
be performed
be prepared
be necessary
core
943)
in
and
design
foundation
soils,
impervious
minimum
also
are
impervious at the
is
stress.con-
R,
which
by the
be made
as 95 or 97 percent
the variation
central
Where
should
(such
which
of expected
will
correspond
should
it may
in the
on fine-grained
contents
and
to 103 percent
However,
initial
not
corresponding
tests
S tests
should
density
determine
for
content S tests
Q,
generally
designated
large-diameter
water
specimens
are
the
shear.
soil
occur
values
strength
sizes,
of cohesive
quirements,
strength
S tests
using
Molding
pacted
conditions
apparatus.
of gravel
placement
test
all
except
they
under
(c)
or
conditions.
Normally,
direct
unless
shear
drainage
apparatus
soils
and
during
consolidation
the water
stresses,
of load
However,
needed.
and
Test
increment
in which but
is permitted
are
loading
(3)
swelling
representative
limiting
(2)
of shearing
on each
provide
sion
each
R tests
conditions
be conducted
condition.
with
or
(b)
stress
application
free-draining
loose
the test,
initial
consolidation
will
atively
under
during
and also
tests
during
specimens
in figure . or rock,
1. the
in the water
For shear
stability
content
reto
conditions.
within
the
dams
having
strength analysis.
are
com-
considered
zone
of the Shear
EM
IIiO-2-1902
1 April
i
I 0 A
OPT
DRY OF OPT IMUM MOLDING
WET OF OPTIMUM
IMUM
WATER
CONTENT
LEGEND ZONE OF PLACEMENT
ESTIMATED MINIMUM ALLOWABLE DRY DENSITY IEXPRESSED AS A PERCENTAGE OF MAXIMUM DRY DENSITY)
A .
AS-COMPACTED SHEAR STRENGTH
0
Figure
EXPECTED FIELDCONDITIONS
1.
CONDITION SPECIMENS
Compaction of shear cohesive soils
9
FOR
test
specimens
of
1970
EM 1110-2-1902 1 April 1970 (4)
Strength
compacted which
is the
be used
of the
placed
in the
where
individual The and
posed
embankment
stress
making
more
compaction. or from soil
be demonstrated test
types
that
composites
and
should
&her.
not
should
the
same
will
be
be used
representative.
principal
stress
in direct
planes
and/or
field
of different
up the
be
of 85 percent,
areas
proportions,
used
on failure
for
should
used
shear
tests
comparable
foundation
in triaxial should
to those
to obviate
compression result
expected
extrapolation
in
in the
pro-
of shear
data
analysis.
(7)
When
Mohr
circles,
cles.
This
slightly
results the
in error
strength
sponding
to the
unimportant
caused
the
strength
for
compacted
should
testing,
Mohr
envelopes
pass
undisturbed
should
strength
Q and the
and
are
representing
should
stresses
are
to the
plQtted,
on Mohr
circles
corre-
The
error
ciris
is considered effect
of dis-
for
undisturbed
soils
Mohr
circles.
However,
be drawn failure
of
but
as the
to have
on the
form
plotted,
to the
presumed
envelopes
tengent
of the compensating
tangent
in the
are
Therefore,
testing.
be drawn
R tests
planes.
because
plotted
stresses
points
on failure
are
is drawn
effective
through
which
specimens, the
for
soils
by sampling
tests
customarily when
stresses
envelope
before
envelope
stresses
normal
for
compression
is correct
if total
envelope
turbance
of triaxial
procedure
strength
negligible through
plane,
disturbance points
on the
as illustrated
in
2.
(a)
water
permitted
occurs
947)(a)
The
Q test.
a constant not
are minor
normal
it can
in similar
maximum
stresses
figure
soils
samples
normal
in design
individual
density
samples
soils
density
in the borrow
unless
embankment
the
types
Composite
programs
pervious
to a relative
relative
soil
be tested.
in test
proportion
(6)
acceptable
representative
should
of free-draining
corresponding
average
All
sources
tests
specimens
to densities
(5)
not
test
content
either
in partially
shear
strength
condition.
prior saturated
resulting This
to or during samples
means shear.
as a result 10
from
a Q test
that
water
However,
corresponds
content a volume
of compression
change
to is
decrease of gas (air)
EM
1110-2-1902 1 April 1970
. :
ENVELOPE
TANGENT
TO CIffCLES
Q.
t
f
b. //
ENVELOH REPEN
SOIL
ENVELOPT DRAWN CIRCLES MP&FSEN ON FAlLURE PLANE
c. SOIL
UNDISTURBED
OffAWN TUffOUGn POINTS W CfRCLES TtNC S Th5SSES ON FAILURE CL AN?
COMPACTED
Figure
2.
SELECTION
WET
OF OPTIMUM
TU#OUGN PO/NTS TING STRESSES
ON
COMPACTED
DRY OF OPTIMUM
NORMAL
d.
SOIL
OF C AND
Construction
STRESS,
@ VALUES,
of failure
ii
U
CURVED
envelopes
ENVELOPE
EM 1110-2-1902 1 April 1970 in the voids
and While
pressure. generally
strength
low
this
low
placed
stress
envelope for
the
range. with
proximate
of design,
the
cohesion
normal
ranges
soils,
is also
applicable
rate
is
slow
soil
exists
it ir
advisable
or
shear
that
to the
fill
is unsaturated
abscissa
of the
envelope
in fig. strengths
stresses may
parallel
to the
2d).
can
Q test
be recurved
embankments.
placement
rate.
In cases
where
saturated
during
prior
to axial
specimens
apof
This
the
undisturbed
in
consisting
in which
become
are
conditions
layers
will
be
be determined
of embankments
of zoned
por-
should
envelope
angle
are
a curved
foundation
but
to saturate
friction
zones
to impervious
compared
and
(illustrated
of impervious
curved
test
soils
embankment
approximately
intercept
end-of-construction
impervious
the
under
saturated
have
of the
the
water
soils
portion
when
lines
to the
saturated
curved
pore
of fully
parallel
partially
of straight
in the
Q tests
intercept,
purposes
a series
various
for
This
cohesion
of gas
lines
for
range.
For
so that
the
envelopes
envelopes
including
solution
by horizontal
diagram,
in the
used,
increased
represented
strength tion
from
test
consolidation a foundation construction, loading
in the
Q test. (b)
R test.
by inducing
shearing; the
pore
pore
stability
place. pervious
used
subject test
high
fully reservoir
in analyzing
9d7) (b)
shearing
applies
been
to a stress
approximates zones during
the
the and
upstream
the
specimens
in the
R test
behavior,
that
are
be also in which
for
12
due
considered
set
drawdown.
to take
that and
This condition
or
of
drawdown, layers
to in
impervious
period
pool
water
consolidation
foundation
a partial
esti-
those
one
sudden
construction
during
methods,
bracket
only
under
during
to sudden
is obtained
at constant
must
time
of impervious
prior slopes
water
without
embankment
conditions
stresses
consolidated
change
R test
back-pressure
to conditions
fully
an
using
to reservoir
test
have
from
confining
developed due
that
embankment
consolidated under
soils
‘This
then
The
analysis.
are
under
pressures
pressures
semipervious stresses
and
resulting
in specimens
specimens
conditions, The
strength
saturation
these
field
content.
shear
complete
consolidating mated
The
of imhave
swell test and
is also
EM
liiO-2-1902
1 April downstream
slopes
(c)
S test.
The
consol.idating stresses
each
draining
soils
strengths
during
complete
in which
VIII,
pressures
pressures
have
in Appendix
water are
and
have
do not
been
measured
water
field
and
slope
is obtained applying
to dissipate
. to (1) free-
applicable
tend
by
shearing
(2) evaluating
that
or can
(3) evaluating
and
and
develop,
pore
measured
S test
pressures are
materials
excess
been
water
of S tests
or foundation
consolidation
cussed
shear
to increase
in
pressures
due to in-
be estimated,
as dis-
shear
strengths
failures
have
where
pore
occurred
or
impending. Selection
b. shear
should
pacted peak
the
or
(c) the
are
reached,
stress
deviator
creases
with
design
strength
selected
where
(2)
For
strengths
R or
each
S test
embankment
zone
or
other
where
between strengths
soils
and
peak
deviator
will
intermediate
shear
after as (a) stress,
resistance
foundation peak
com-
stress
be chosen
the
the
soil
can
sensitive
and foundation
such
In most cases, should
always
means that
that
soils,
undisturbed
generally
in the
and
re-
correspond
strength
laboratory
layer,
two-thirds
the
design
be greater
zones and layers being considered. than laboratory test values should tests
(b) the
for
shear
individual
or deviator
strength
strain
conditions,
be selected
values.
zones and layers
design
in shear
tests,
be intermediate
for
design
values
may
be
appropriate.
should
design
shear
selecting
foundation
shear
However,
strain.
While
Q or
drop
S direct
When
curves
undisturbed
at 15 percent
increased should
stress-strain
the design
stress
strengths.
to either
of the
a significant
in
(1)
Strengths.
Where
show
shear
molded
shape
do not
stresses peak
Shear
be considered.
soils
the
the
of Design
strengths
tests --
shear
an
stress
pore
Results
pore
from
confining
excess
increment.
in which
resulting
an initial
to permit
of embankment
volume
seepage.
strength
under
enough
loading
steady
shear
a sample slowly
under
during
1970
shear
the
lowest
However, design be used when it
shear
13
test
strength
the
results
than
of
design
shear values
for test
exceed
the various
value
strengths
for
the
lower
is shown by field
are not
consenratlve.
9b(2)
EM iliO-2-1902 1 April 1970
(3)
The
velopes
shear
on the basis
figure
3, where
between gree
strength
that
can
of the
the
in the
Q and
R tests.
since
values.
quired
to assist
in estimating is used,
construction
excess
pore
the
pressures,
by interpolating
between
of consolidation
as illustrated
is expected
Care
must
an overestimate
A careful
strength
during
degree
of consolidation
design
procedure
estimated
degree
of consolidation,
this
be estimated
consolidation
the
probable
provisions
must
of consolidation,
and
field
shear
in
the de-
in unconservative
testing
be made
rate
in estimating
result
degree
en-
to be intermediate
be used
may
the
program
will
of consolidation. .to measure
magnitude
and
be reWhere
and
evall.late
dissipation
of
strengths.
3
t
R ENVELOPE 4 = 16, C = 0.4 TON/SO
? ul $
Ff
DESIGN ENVELOPE FOR 60% CONSOLlDATlON n$ q 12.. C =O.S TON/SO FT
2
I)
0
0
I
2 NORMAL
Figure
10.
Methods
of earth simple cular
and
rock-fill
method
STRESS,
0.
4 TONS/SQ
5
FT
Estimation of strength values intermediate between Q and R strength values
of Stability
adaptations arc
3.
3
The
Analysis. embankments
of the
circular
is generally
that arc
more
methods are
and
of analyzing
outlined sliding
applicable
in the wedge
for
analyzing
the
stability
appendixes
methods.
are The
cir-
essentiall’y
14 -
EM
homogeneous
earth
rials,
whereas
dams
on firm
more
weak
to supplement
vide
a uniform
basis
circular for
is generally
more
dams
infinite
arc
or wedge
slope
the
method
is used
on the vertical
one or
to some
methods
and
may
given
sides
be suppleof the
in Appendix
of slices
ex-
pro-
at the discretion
method
..-
to rock-fill
These
procedures
mate-
containing
designs
Swedish
forces
applicable
method.
alternative
modified
of fine-grained
on foundations
the
or alternative
of the
If desired,
deposits
evaluating
methods use
on thick
to earth
In addition,
by other
optional.
and
the
The
dams
method
foundations layers.
designer.
and
the wedge
tent
mented
dams
1110-2-1902 1 April 1970
VI is
may
be
ignored. Design
11.
subjected
Conditions to shear
pool
fluctuations,
bility
analyses
(II)
sudden
way
crest
storage (VII)
(VI)
II,
Case
I:
tially
or
those
corresponding
under
the
are
III,
entirely
Q shear too
(III)
(V)
steady
sudden
to upstream
for
are and by
which
sta-
of construction,
drawdown
pool,
from
with and
upstream slopes
foundation
embankment
seepage
to both
its
cases
(I) end
surcharge
apply
apply
maximum
where and
only;
spill-
applicable
downstream
and
Cases
V and
slopes.
soils
pore
readily
during
shear
strengths
to anticipated is also
thick
to consolidate
shear
strengths
implies
tests
satisfactorily
placed
water
loading,
strength
In an embankment
of Construction.
to ultimate
applicable
pool,
with
VII
The
designated
pool,
seepage
and the
forces.
are
of impervious
imposed
compacted
earthquake
partial
IV
embankment
by the weight-of
maximum
I and
and
End
consolidate
dicated,
The
steady
to downstream
a.
mens
(IV)
Cases
Cases
or
from
elevation,
VI apply
imposed
be performed
drawdown
earthquake.
cannot
stresses
shall
An
Analysis.
seepage,
pool,
slopes;
for
the
field
approximate
pore
after
complete
consolidation
will
be induced
because
the
soil
period.
Where
this
is in-
from
Q tests
placement
during
water field
water
to impervious
significantly that
higher
determined
applicable
pressures pore
15
than
contents
construction
are
par-
at water
contents
pressure
composed
water
contents
and
foundation
construction. occurring pressures.
on specidensities. layers
that
use
of Q
The
in laboratory Except
for
EM illO-2-1902 1 April 1970
thick,
impervious
conservative,
foundation since
overconsolidated than
that
soils, on
which
should
solidation
during
performing Q and
consolidation
and
struction
excess
or
embankment,
evaluate
stability
pletion actual
change
saturated
strength
during pool
reservoir
excess
pore
water
strengths
are
sipation
based does
on the
not
(Case
minimum
LII) to the
using
saturated
submerged using Ilb
or moist
weights
saturated
below
weights
become
If subse-
water
can
on the
minimum
(fig.
In general,‘analyses
4).
assumptions
drawdown pool
and
(Case
friction above
level; the
that
II)
or
the
d.riving lowered 16
spillway
embankments
forces line
pool
should
of seepage
forces
should
elevation,
for
(1) pore
(2) the water
For
elevation.
weights
above
may
fill.
be based
resisting
this
by stage
II and III
pool the
pore
the
result.
shall
com-
to determine
forces
maximum
materials,
to re-
at the
stages.
than
in the
be used
seepage
during
from
faster
con-
to develop
caused
reservoir
re-
stage
and unbalanced
conservative
occur
For
Further,
be tested
of
construction
Embankments
high down
S envelopes
instantaneously
impervious
is drawn
in Cases
R and
must
rate would
should VIII).
Drawdown.
time
expected
to consolidation
prolonged
pressures
to be used
combined
due
Sudden
by seepage the
cases
III:
are
(Appendix samples
is to be con-
design.
observations
construction
in shear
quently
the
piezometer
foundation
Il and
pressures
the
by
between
construction
during
con-
be estimated
of the
embankment
water
stage,
Cases
b.
pore
Where
an embankment
stage
be higher
shear
intermediate
evaluation that
the
values. can
For
may
reduce
effect
strengths
economical
during
of each
When
show
in foundation
a more
where
foundation
values
may
gain
permit
using
9b.
construction.
design
its
Q strengths,
characteristics
in a significant
period
low
may
is significant,
is usually
on Q tests
in selecting
in paragraph
having
based
strength
strength
during
swelling
be considered
R as described
occur
strength
Therefore,
analyses
of Q shear
will
the average
construction
on clays
the use
consolidation
R tests.
stability
structed
sult
some
based
strength,
strata,
escape, Shear of these
pressure
surface crest
dis-
is lowered elevation
composed
of
be determined at full
pool
and
be determined saturated
weights
EM
DESIGN
ii10-2-1902 1 April 1970
ENVELOPE
0 0
1
2 NORMAL
Figure within
the
drawdown
(assuming
age
shell
of pore
only
water
a minor
analyses
drawdown
assumption
possible materials,
a flow given
den
net
which
are
the
rates
and
expected
drawdown
III,
constructing envelopes
the
the flow for
Shear
as those
in which
normal
of the
conditions. slope
of proposed materials
seepage
forces
be per-
determined
from
may
nets
determining
seepage
effects.
be the
this
may
of seepage
should
sudden
embankment
of the
analyses
or with
considering
lowering
these
drain-
and where
Approximate
and
strengths
pool
stresses. line
zone
Where
conservative,
incompressible and
drawdown
level).
of the upstream
permeabilities
rates
l.lI
the
lowering
S test
to be excessively
relatively
effective for
design
pool
with by
II and
below
defined
concurrently
5
FT
Cases
weights
represented
for
strength drawdown
minimum
appears
to evaluate
for
of the
analyses
in Appendix
a basis shear
for
extension
control
drawdown
for
submerged
are
4
TONS/SCJ
and
proceed
lag,
0.
envelope
materials,
can
time
drawdown
formed
zone,
a horizontal
of free-draining
Design
4.
3
STRESS,
criteria,
same
be used
as
The as for
sud-
analyses. 17
Ilb
EM iilo-Z-i902 1 April 1970
Case
C.
mediate has
reservoir
developed
soils
R and
and
strength
(fig.
soils
net
pool
elevations,
S test
reduction
where shear
the the
in effective
The
thus
the
R R
cohesionless moist
from
eliminating
and
the
pool
the
need several
should
be performed
for
factors
of safety
plotted
as a function
of reservoir
minimum
safety
normal
5.
line
the
than
between
by a horizontal
of
between
than
draining
demarcation
zone,
strength
is greater
of freely
seepage
midway
is less
inter-
analyses
Design
The
factor.
stresses
where
2 NORMAL
Figure
strength
shear
envelope
S strength
for
01 steady
design
S strength
impervious
1
0
The
the
envelope.
Stability
construction.
to determine
the
slope
a condition
to a strength
where
of the
that
stages.
be approximated
limit
of the upstream
assume
correspond
design
may
and
Analyses
intermediate
S envelope
be the
flow
for
should
The
5).
the downstream
stage
stages
envelopes
to the
should
submerged
Pool.
should
S test
strength
soils
Partial
at these
impervious the
IV:
analysis
pore
3
STRESS,
envelope
0.
for
TONS/SO
Cases
water
must
to for
account
pressures
4 FT
IV,
V, and
VI
18 -
EM
developed
during
dition
develop.
can
Case
d.
of steady tained
construction
V:
seepage
Steady
should
the
long
to produce
may
Shear
shear
envelope
slope need
not
mainly
using
or wedge more
methods
Case
steady
seepage
zontal
thrust
should
line
in the
in Case
XV, except may
rest
on weak
that seepage
and
for
forces
zone
through
Surcharge
Pool.
same zones
of upstream
slopes
composed
analyses
plane
is overly
on the
slopes
analyses
when
by the infinite
stability
with
net
downstream
be analyzed
foundations,
if a failure
A flow
seepage
large
be main-
throughout
be based
downstream
be supplemented
can
impervious
The
Where
A condition
stability.
V should
envelope.
case.
to determine
dams
same
rary
with
havior
Case of earth
The
surcharge
by the
by the
in-
circular
arc
the foundation
is
imparts
Shear
where
and an additional
should
also
strengths should should
case
hori-
be examined critical
used
should
materials
rock-
be the
be by the wedge
of impervious
for
for
be considered
a
or
as a tempoabove
the
line. Much
Earthquake.
seismic
the traditional
The
is especially
pool
no saturation
evaluating
present,
condition
V, and analyses
subjected
for
pool
cores.
dams
methods
earthquake
This
in Case
saturation VLI:
in an embankment
central
causing
seepage f.
used
with
by a surcharge
stability.
method.
condition
Seepage exists
narrow
arc
steady
Steady
condition
slope
as those
circular
VI:
is imposed
downstream
the
line
phreatic
_ __-.
con-
critical. e.
fill
this
soils
method
the
pool
Pool.
of steady slope
that
a partial
level
downstream
in Case
S strength for
storage
a condition
materials
the
be examined
slope
water
used
used
of cohesionless
finite
Storage
Maximum
phreatic
strengths
of cohesionless
method
with
to determine
conservative.
consisting
before
for
of a horizontal
strength
not dissipated
maximum
be critical
be constructed
the assumption
Seepage
from
sufficiently
an embankment
are
1110-2-1902 1 April 1970
research
to earthquake effects
approach an additional
are
is still
shocks, being
developed.
force
on the
and new
recommended.
horizontal 19
is in progress
analytical However,
This Fh
be-
acting
assumes
at that
in the ilf
EM 11lo-2-1902 Change 1 17 Fell 82 direction of potential failure. The arc or set of planes found to be critical without earthquake loading Is used with this added driving force to determine the factor of safety for Case VI. It is not necessary to study effects of earthquake loading in sudden drawdown stability The horizontal seismic force is equal to the mass involved analyses. times the horizontal acceleration, i.e.
The total weight of the sliding soil mass W should be based on saturated unit weights below the saturation line and moist unit weights above the line. Selection of the seismic coefficient $ should be based on the degree of seismic activity in the region in whioh the dam is to be built. * The seismic coefficients for the various geographical areas are shown on In areas where earthquakes are likely, or for figures 6 through 6c. locations near active faults, the safety of dams should be increased by utilization of defensive design features regardless of the method or results of the earthquake analyses. ‘The defensive design features may (a) ample freeboard to allow for the loss of crest elevation include: due to subsidence, slumping or fault displacement; (b) wide transition sections of filter materials which are less vulnerable to cracking; (c) vertical or near-vertical drainage pones in the central portion of the embankment; (d) filter materials of rounded to subrounded gravels and conducti.v%ty of ,f<er layers and vertical sands ; (e) increased hydraulic drainage zones or the inclusion of additional properly designed filter zones of higher conductivity; (f) wide impervious cores of plastic clay materials or of suitable, well-graded materials to help insure self-healing in the event cracking should occur; (g) stabilization of reservoir rim slopes to provide for dam safety against effects caused by slides into the reservoir; (h) crest details that will mLnimize erosion in the event of overtopping; (i) removal of foundation material that may embankment sections be adversely affected by ground motion; (j) flaring at abutment contacts; and (k) zoning of embankments to minimize saturation of materials. In some cases, stock-piling of filter material * may be desirable for use in emergency repairs. (1) An at-rest earth pressure g- At-Rest Earth Pressure Analyses. de as an independent check of the ( K, > analysis is sometimes stability of an embankment. b This analysis is particularly applicable to earth and rockfill*dams with narrow central cores, and is performed to check analyses of Case I (end of construction) and Case V (steady seepage ) conditions. (2) For Case I and assuming are negligible or have dissipated;
that construction the horizontal
llg(2)
20
pore water pressures earth force acting on a
Bf 1110-2-1902 1 April 1970 vertica.1
plane
through
the dowlstrcarr. using
base
an equation
the crest of the
ermilar
is compared
embankment
The
shear
!owet
would
shear
into
stresses.
Lf pore
struction,
they
i
Appendix
VIII, should
following
and/or are
he estimated
value
clay-
be required
13
Ko
is often for
(GZR.
ior for
(3)
factor
for
of I
ample
suil
.= i!
taken
normally
llg(3)
X analyses.
be modified
if a
sliding
plane
the
the
expected
to exist
methods
Case
should
by using
from
S strength
at low
at the
such
those
ss
diagram
norma!
end of condescribed
of the horizontal
pressure
with
I is given
-For Case
walghts
dre
of safety
‘4, the used
using
strengths
shown
as 0.5,
d high
overconsolidation cade
_’ u) K.
force.
developed
in This
from
the
from
similar CL+ = -i z(Y,h;
I are
than
0.S
an overconsolidation
(PI).7
the maximum
the horizontal
an equation
in table
with
greater
-4 relationehiy in figure
of 7.
used 21
to the W
force
pool and
and
submerged
checking
the
following.
tan+
+ Y’ H2Ko) for
Case
V, and
it is assumed
X
An ex-
8.
force
in computing
index
values
of i and 2 is shown
in figure water
clays
plasticity
ratios
+ u
although
consolidated
F.S.
The
the
in the computation
on a horizontal
other
equation.
The
&no
for
above
using
ph :- (zy,
ratio
used
by shifting
pressures
included
be based
..-
of safety
YmKo
as those
is obtained
water
and
the factor
along
z
in the equation
the embankment
should
resistance
CL+ Wptan+
-
same
terms
resistance
foundation
force
be the
resistance
shear
to determine
Z H strengths
the
to the following.
F.S.
The
with
that
0
:,:H 1110-2-1902 dlangc 1 I ? I',-I, 81
0
m UJ
”
%
s 0
%
E z a
1
0
I EM 1110-2-1902 C11mj.y 1 I'! I.‘C.Il r(.!
CALIFORNIA.
NEVAOA
C ARIZONA
------SCALE
22-A
-\
ZcNE
,ElWlC -
PROBABILITY DAH.ACE
.
HOHE
1
MINOR
2 3
.
4
I
PACIFIC
0
COEFF.
MODERATE MAJOR 1
GREAT
I
0 0.025 0.05 0.10 0.15
0CEA.N
SEISMIC ZONE MAP Alaska
:t
Figure
6b.
Seismic
Zone Flap of
Alaska
*
1
/
/
/
KAUAI
/
/
/ /
/
/
NIIHAU / 1
-E-P
/ /
2
/ /
/
flC N N A
I/
0-l
/
/ /
/
/
OCE
I
PN
MOLOKAI -
KAHOOLAWE IO
0
IO
20
30
40
STATUTE MILES
3
1
PROBABILITY 1-~~--SEISMIC~~~
t
3a
11
GREAT MAJOR
1
0.15 0.10 SEISYIC ZOHE YAP HaAJlr
0.9
0.S
AFTER:
I
30
i
7.
K versus
PI
and
W.
BROOKE,R
00
SO PI,
Figure
E.
PLASTICITY
overconsolidation
AND
H. 0.
IRELAND
’
70
INDEX
ratio
(Brooker
and Ireland)
7
’ i ,’
hw ,
.
SHELL N c
YlV! = 0.130 KCF
!i
1 W,,
AssuL(y srmsrn
CASE
I.
F S. =
Ko = 0.5 FROM FIGURE 7 FOR PI = I5 AN0 CASE
P,
STEADY
#=37*=35*
Ymi
= 0.140
KCF
34’ ==-.-4zkEk&J.
wcz TAN 35.
ROCK
4
40&OlAN32-+ 20,230TAN35f (0 I30)(450)~(0.5)
_ -
2540
l
14.160
I- 2,,5
65eo
OCR = I. SEEPAGE:
F.
S. =
K, = 0.65 FROM FIGURE 7 FOR PI = 15 AN0
c=O, c=o.
-
Zfrn SEAR Iv’ cm ’
EN0 OF CONSTRUCTION:
TAN 32.
4080
TAN 32.
t (0.0624)(440?
+ 18,350 TAN 35’ l
t (0 0676)(450)*(0
L1 65)
6050
15.300 + 4450
= ’ 47
OCR = 2.
Figure
8.
Examples
of at-rest
earth
pressure
analyses,
Cases
I and
V
Minimum
Case No. I II
Design End
Minimum Factor of Safety
Condition
of construction
Sudden drawdown maximum pool
III
Sudden drawdown spillway crest of gates
IV
Partial pool with steady seepage
Table I Factors
Shear
Upstream slopes
SS
and downstream
Q or
from
i*O$$
R, S
Upstream posite
slope only. Use comenvelope. See fig. 4
from or top
1*2$$
R, S
Upstream posite
slope only. Use comenvelope. See fig. 4
1.5
R+S -for 2
RCS,
S for Steady seepage with maximum storage
VI
Steady seepage with surcharge pool
VII
Earthquake IV, and seismic
(Cases V with loading)
Remarks
Strength
i.3tt
N ul V
of Safety1
R > S
Upstream slope only. termediate envelope. fig. 5
Use inSee
1.5 R+S 2
pool 1.4 I,
I 1.0 *
for
S for
I
R C S, R > S
Downstream intermediate fig. 5
Upstream siopes
slope only. envelope.
Use See
and downstream
t
Not applicable to embankments on clay shale foundations. For embankments over 50 ft high on relatively weak foundations use minimum factor of safety of 1.4. $ In zones where no excess pore water pressures are anticipated, use S strength. The safety factor should not be less than 1.5 when drawdown rate and pore water $.$ pressures developed from flow nets (Appendix III) are used in stability analyses. 5 Use shear strength for case analyzed without earthquake except that it is not necessary to analyze sudden dravdown for earthquake effects. tt
E! t-cr g: 10 I ZN .I 5;s so N
I
EM
1110-2-1902
1 April the
1970
core
from
has
an overconsolidation
moist
to submerged
An example
for
12.
Factors
pend
on the
values)
strength
tures
within
condition
design the
terials,
(g) probable
on past
experience
safety for
for
analyses
are
Methods
of stability
Swedish
(normally
The
of safety
Trial
fac.rs
reached.
in basic with
cular
arc
safety
to those
For for
until method,
example,
determined
and
soils
and
of relative factors are
by infinite
not slope
mabased
analysis,
the
damage,
and
portions
of the
of shear
tests.
are the modified method
infinite
with
slope
several method.
SD where
of limiting of safety
equilibrium is related
inclination. factors
ac-
minimum
the
strength
factor slope
final
types
the
shear
the
of struc-
foundation
I lists
surfaces)
a condition
resistance
plastic
arc
of
in establishing
conditions,
de-
(f) stress-
property
in the appendixes
method,
, comparisons
caution. method
tried
life,
applicable
on developed
slope
shearing
assumptions
made
are
infinite
frictional
wedge
is based
of safety In the
to the
the
factor-s
(h) judgment
In the
Table
design and
circular
procedures,
to human
the various
considering
alternative
and
dams.
projects.
described
7.
reliability
and
considerations
analyses
figure
(d) presence
control,
respect
required,
from
of investigations,
rock-fill
specific
changed
safety
of embankment
important
for
required
which
factor
are
of safety
factors
dam
with
of functions factors
and
K.
(b) estimated height,
of construction
earth
of a failure
impairment ceptable
with
analyzed,
compatibility
quality
for
of computed
(e) thoroughness
and
have
8.
(c) embankment
embankment,
weights
a value
values
being
values,
characteristics
consequences
in figure
Appropriate
(a) design
of 2 (since
in selecting
V is given
of Safety.
shear
strain
Case
ratio
Due
is directly
to differences
of safety
should
be
of safety
determined
by the cir-
directly
comparable
in degree
computations
for
granular
materials. 13.
Presentation
in Design
Uniformity
Memoranda. 26
in presenting
results
of
of stability
analyses
randa.
Analyses
appendixes.
the
the
condition
ration,
zones
graphical
be included
centers
of circles
with
critical
the
extent
surface of the
each
.of the
tions
will
maries
Atterberg
valuable
aids
A tabulation
d.
A brief
and
rate
pool,
a slow
and
with
Atterberg
for
to demonstrate
and
unit
weights
foundation.
for
Correla-
graphical
of foundation and similar
for
rate
as a basis that
either
to those
with
limits,
charts,
computations
of drawdown
on
sumand
borrow
correlations
are
be presented.
of the
of drawdown
be shown
in addition
presentations
should
of the
All
analyzed,
number
and
sections
should
together
embankment
on plasticity
discussion
rate
values,
the
envelopes,
to reviews
cross
surfaces
found
used,
of analyses.
radii
in sufficient
strength
strength
limits
c.
factors
of satu-
values
Separate
failure
obtained
performed.
comprising
strength
material
trial
safety
analyses
shear
of shear
the
of shear
materials
of foundation
of the
analyzed
of safety
strength
circle
in the
or lines
thoroughness and
being
construction
reactions.
of safety
be presented
stability
A tabulation
b.
and
....
data:
factor
shear
to indicate
locations and
net
memo-
given
foundation
lowest
to the
forces
factors
or wedge,
the
flow
corresponding of all
The
arc
applicable
and
of design
to those
following
embankment
as necessary
sections.
the
for
strata
delineation
circular
.-
or
the
for
review
in scope
include
surface
analyzed,
should
these
of the
failure
facilitates
conform
should
section
assumed
data
generally
analysis
A cross
showing
supporting
should
Each
a.
for
and
critical
of reservoir for
may
the
apply
sudden
rise,
arc
or wedge.
the
duration
drawdown
to an ungated
of full
computations flood
or
control
embankment. e. mediate tation
Presentation S and
of shear
support
the f.
R strength strength
selection
Proposed
instrumentation
of, design
shear
envelopes, test
data
of these
design
instrumentation should
for
be included
strength
data
and
as shown
in figures
representative shear
3 and
or inter4.
Presen-
samples
is required
Complete
information
to
strengths.
to be installed. in accordance 27
composite
with
guidance
contained
on in i3f
EM
iiiO-2-1902
1 April
1970
Civil
Works
Engineer
Letter
14.
TUse of Electronic to (a) reduce
variations
in material
must
and
be capable
solutions
must
be reviewed have
Under
some
conditions,
circle
or
The
analyses
that
and the
tions patible
with
an analysis or
set
manual
not
limited
computer
in the
design
for
a sufficient
factor circle
also
or
set
be verified
design
to ensure
found
computations
procedures by the must
can
search
of trial
must
be made for
be presented
each
in the
if desired,
planes.
28
include surfaces
design
of all
critical
to verify
Computer
the
solu-
used
herein.
to check design
areas. the location,
programs
presented
of
critical
failure
obtained.
computer
set
employed.
potential
been
or
out the
number
used
Computer
circle
should
has
program
program
more
of possible
conditions.
critical
is rec-
embankment
computer
memoranda
criteria
computer
be made,
or
that
and
the
may
of two
of planes
procedures
by manual
check
one
the
computer
programs
presented safety
that
effects
alternative
boundary
by the
in only
of planes
independent
significant
computers
(b) evaluate
investigate
(c)
to establish
been
of electronic
solutions,
of planes
critical
must
valid all
use
effort, and
of evaluating
found
radius,
computational
To obtain
planes
set
The
properties,
zoning.
9).
(ref
Computers.
ommended
sections
65-7
are
com-
Consequently, critical
condition. memoranda circles
circle The so that
or
sets
an of
EM
FOR
THE
CHIEF
8 Appendixes Appendix I Appendix II Appendix III
Appendix
IV
Appendix
V
Appendix
VI
Appendix Appendix
VII VIII
OF
1110-2-1902 1 April 1970
ENGINEERS:
RICHARD Colonel, Executive
- References - Notation - Estimating Seepage During Reservoir Drawdown - Procedures for Determination of Embankment Slopes - Infinite Slope Analysis for Cohesionless Soils - Modified Swedish Method of Analysis Using Slice Procedure - Wedge Analysis of Embank- Evaluation ment Stability During Cons true tion
29
F. McADOO Corps of Engineers
EM
APPENDIX
ii10-2-1902 1 April 1970
I
..-
References 1.
U. S. Army Engineer Waterways Experiment Station, chanics Design, Stability of Slopes and Foundations,” Apr port No. 3-777, Appendix D, Feb 1952 (reprinted Vicksburg, Miss.
CE, “Soil Technical 1967),
MeRe-
2.
“Progress Report on Glossary of Terms and Definitions ASCE, Soil Mechanics and Foundations Division, chanics,” Vol 84, Paper 1826, No. SM4, Ott 1958.
3.
in Angle of Internal Banks, D. C. and MacIver, B. N., “Variation Miscellaneous Paper S- 69 - 12, Friction with Confining Pressure,” Apr 1969, U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.
4.
Banks, D. C. and Strohm, W. E., Slides,” Potamology Investigations Engineer Waterways Experiment
5.
Seed, H. B. and Lee, K. L., “Liquefaction ” ASCE, Soil Mechanics Cyclic Loading, Journal, Vol 92, Paper 4972, No. SM6,
6.
Robeson, F. A. and Crisp, Construction Dam, ” ASCE, No. C03, Sept 1966, p 51.
7.
Brooker, E. W. and Ireland, ” Canadian to Stress History, Feb 1965, pp 1-15.
in Soil MeJournal,
“Methods of Preventing Flow Report 12-16, Ott 1965, U. S. Army Station, CE, Vicksburg, Miss.
Jr.,
R. L., Jr., Division,
of Saturated Sands During and Foundations Division, Nov 1966, pp 105-134. “Rockfill Journal,
H. O., “Earth Geotechnical
Design Vol 92,
Pressures Journal,
8.
Risk Algermissen, S. T., “Seismic ceedings, Fourth World Conference Santiago, Chile, 14 Jan 1969.
9.
“Inclusion of Proposed Office, Chief of Engineers, Embankment and Foundation Design Memoranda,” neer Letter 65-7, 2 Mar 1965, Washington, D. C.
10.
.
Studies in the on Earthquake
Schnitter, G. and Zeller, J., “SickerstrGmungen gelschwankungen in Erddammen (Seepage Flow tion or Level in Earth Dams),” Schweizerische Nr. 52, 28 Dee 1957, pp 808-814. I-l
Vol
- Carters Paper 4906,
at Rest Related 2, No. 1,
United States,” Engineerinq,
Instrumentation Civil Works
Pro-
in Engi-
als Folge von StauspieResulting from FluctuaBauzeitung, 75 Jahrgang,
EM 1110-2-1902 Appendix I 1 April 1970 II.
Terzaghi, K. and Peck, R. B., Soil P/echanics 2d cd., Wiley, New York, 1967, p 138.
I2.
Janbu, eters,” Harvard
13.
Scott, Mass.,
14.
and Passive Earth Jumikis, A. R., “Active Tables ,” Engineering Research Publication University, College of Engineering Research,
15.
Clough, G. W. and ing Construction,” Engineer Waterways
26.
Hilf, J. W., “Estimating Dams ,” Proceedings, chanics and Foundation
17.
Bruggeman, J. R., Zanger, C. N., and Brahtz. J. H. A., Technical Memorandum No. Analytic Soil Mechanics,” June 1939, U. S. Bureau of Reclamation, Denver, Colo.
18.
Factors Controlling the Pore Bishop, A. W.. “Some -Proceedings, During-the Construction of Earth Dams,” national Conference on Soil Mechanics and Foundation London, Vol 2, 1957, pp 294-300.
19.
Moran, Proctor, Mueser & Rutledge, Consulting Engineers, “Study of Deep Soil Stabilization by Vertical Sand Drains,” June 1958, Bureau of Yards and Docks, Department of the Washington, D. C.
20.
Skempton, technique, 147.
21.
Pressures Snyder, J. W., “Pore nical Report S-68-2, July 1968, periment Station, CE, Vicksburg,
22.
Gould, J. P., “Analysis at Logan International
N., “Stability Analysis Soil Mechanics Series University, Cambridge, R. F., 1963.
Principles
of Soil
in Engineering
of Slopes with Dimensionless No. 46, Jan I954 (reprinted Mass. Mechanics,
Practice,
ParamMay I959),
Addison-Wesley,
Reading,
Pressure Coefficient No. 43, 1962, Rutgers New Brunswick, N. Y.
Pore Pressures DurSnyder, J. W., “Embankment Technical Report No. 3-722, May 1966, U. S. Army Experiment Station, CE, Vicksburg, Miss. Construction Pore Pressures Second International Conference Engineering, Rotterdam, Vol
Pore-Pressure A. W., “The Institution of Civil Engineers,
Coefficients London,
in Rolled Earth on Soil Me3, 1948, p 234. “Notes on 592, p 124,
Pressure Set Up Fourth InterEngineering,
New York, NOy88812, Navy,
A and B,” Vo1.4, 1954,
in Embankment Foundations,” U. S. Army Engineer Waterways Miss.
of Pore Pressure and ” Soil Mechanics Airport, I-2
Settlement Series
Geopp 143-
TechEx-
Observations No. 34,
EM
Dee 23.
1949,
Harvard
University,
Cambridge,
iliO-a-i902 Appendix I 1 April 1970
Mass.
Lowe III, J. and Karafiath, L., “Effect of Anisotropic Consolidation on the Undrained Shear Strength of Compacted Clays,” ASCE Research Conference on Shear Strength of Cohesive Soils, University of Colorado, Boulder, Colo., June 1960, pp 837-858.
‘-
I-3
.-
EM
APPENDIX
IilO-2402 1 April
1970
Il
Notation The
1.
wherever
symbols
that
possible
follow
are
to those
used
throughout
recommended
this
by the
man.ual
American
and correspond Society
of Civil
Engineers. Term
Symbol A,
B ah b
cA ‘CB cD --
cP C
CD
Skempton’s coefficients Horizontal
experimentally seismic
determined
Cot p = cotangent horizontal
of the
embankment
cohesion
force
of active
Developed
cohesion
force
of central
block
Developed
cohesion
force
Developed
cohesion
force
of passive
wedge
per
Developed equilibrium)
unit
cohesion
per
unit
of foundation
layer
E
Earth
force
of slice
EP AEH AE AE’
FA FCB FD
on side
area
Resultant
force
of active
Resultant
force
of central
block
Resultant
force
of passive
wedge
Force
required
angle
with
the
wedge
area
Depth
ECB
slope
Developed
Cohesion
pressure
acceleration
D
EA
pore
(cohesion
required
for
wedge
to close
force
forces method:
polygon
in wedge
analysis
on left and right sides of slice Finite Slice Procedure)
Resultant (modified
of earth Swedish
Resultant unit width Graphical
forces acting on left and of earth (modified slice in units of ybase Integration Procedure)
Resultant
of normal
and
frictional
forces
of active
wedges
Resultant
of normal
and
frictional
forces
of central
block
Resultant
of developed
normal
and
frictional
right sides of the Swedish method:
forces
EM IiiO-Z-1902 Appendix II 1 April 1970 Term
Symbol Fh FP F.S.
Horizontal
seismic
force
Resultant
of normal
and
Factor
Gravitational
H
Height
of embankment
Height
of drawdown
Vertical
distance
h’
Modified
height
h
W
Piezometric mum pool
K
Ratio
KA KO
KP k L
Ns n n
e
pD % Q
obtained
from
from
the failure surface
surface;
earth
earth
pressure
slice
of base normal
Developed
Stability
surface
height
of maxi-
pressures
pressure
coefficient
of permeability
of the
Active
slope
h(y/ybase)
length Length of arc or failure surface; along which cohesive shear resistance
Total
wedge
coefficient
of at-rest earth
surface
to vertical
pressure
Coefficient
Length
NK
earth
Passive
AL
ND
to failure
level above above sliding
Coefficient
Width
of passive
constant
of horizontal
Active
L’
N
forces
of safety
g
HD h
frictional
parallel
to the
beneath passive block is assumed to develop
saturation
line
of slice force
normal earth
force
pressure
stability
number,
bcD YH
_yH
factor,
CD Porosity Effective
porosity
Dimensionless Horizontal
parameter pressure
= &
at depth
Shear test for specimen (unconsolidated-undrained) Q
shear
test
with
pore
tested pressure II-2
e z at constant
water
measurements
content
EM
-
Symbol
iiiO-2-I902 Appendix II 1 April 1970 . ..;;.
Term R
i? S 8
sD U
(a) Radius of failure arc (b) Shear test for specimen consolidated constant water content (consolidated-undrained) R
shear
test
with
pore
Shear
strength;
Developed
s = c t u tan
shear
strength;
force
U
Pore
pressure
V
Velocity
W
Total
water
of pool weight
P
Weight frictional
X
Dimensionless
z a
Distance
-
af
P Y Y’
soil
mass
ratio
of the
Angle shear
of inclination. test results)
of failure
Angle of inclination horizontal
unit
above
(Appendix
of inclination
Moist
+D
failure
plane
subblocks above plane is assumed to develop
Angle
unit
unit
+
along
which
III)
crest
of the
saturation
line
plane
with
(based
embankment
the
horizontal
on laboratory
slope
with
the
volume
weight
Base unit weight modified Swedish
ybase
or
height beneath
Buoyant
re-
drawdown
of slice
per
at
and sheared without (consolidated-drained)
sD = cD t u tan
of passive block or shear resistance
Weight
sheared
measurements
Shear test for specimen consolidated striction of change in water content
Hydrostatic
W
pressure
then
of the
soil
used in graphical method
weight
of the
integration
procedure
of
soil
ym
Ysat
Saturated Unit
unit
weight
weight
of the
soil
of water
YW
A 8 %A
Increment Angle
or
small
part
of inclination
of the
failure
Angle of inclination horizontal
of the
base
II-3
arc of the
with active
the
horizontal
wedge
with
the
EM 1110-2-1902 Appendix II 1 Xpril 1970 .-
Term Angle of inclination horizontal
9P u Off =h Q.
1
=i
u3 5
- u3 ;fc Qff F i 7 3 T Tfc fff 4’ 9’ +D 4’
Normal,
of the
base
of the
passive
wedge
the
stress
Normal stress test specimen) Horizontal
on failure
stress
Conjugate
stress
plane
at failure
on vertical
plane
on a plane
parallel
Major
principal
stress
Minor
principal
stress
(in
to the
laboratory
outer
stress
Effective
normal
stress
on failure
plane
prior
Effective
normal
stress
on failure
plane
at failure
Effective
major
principal
stress
Effective
minor
principal
stress
Shear
stress
Shear
stress
on failure
plane
at end
Shear
stress
on failure
plane
at failure
Angle based
of internal friction on total stresses
Angle based
of internal on effective
Developed
angle coefficient,
shear
slope
Deviator
Seismic
with
to start
of test
of consolidation
(or
slope
angle
of strength
envelope)
friction (or stresses
slope
angle
of strength
envelope)
of internal ah 5
II-4
friction
(required
for
equilibrium)
EM
APPENDIX
III
Estimating the Lowering in Pervious Upstream During Reservoir General.
1.
to various for
time
use
of the
meability
and
as sands during
the
and
drawdown gravel
ratio
X
drawdown eter
lowering
which
do not
Relation.
The
of the
flow
line
flow
nets,
of seepage
seepage line can 10 Zeller that relates
and
relation
change
is valid volume
only
as the
at the
be estifill
per-
in materials
water
nets
it is nec-
of the
by Schnitter This
such
intercept
subjected
to construct
To construct’
of the
rate.
desirable
slopes
such
content
changes
drawdown.
Mathematical
2.
forces.
The
in a method
embankment
it is often
lowering core.
of the Seepage Line Embankment Zones Drawdown
of pervious
of drawdown,
impervious
as shown
analyses
seepage
to determine
mated
-
rates
in determining
essary face
In stability
iii@-2-1902 1 April 1970
(i.e.,
the
ratio
expressed
P
D
equations
of height
in percent
for
of saturation
the line
of drawdown)
and
dimensionless
height
at face
at end
the
of core
dimensionless
of
param-
are x=
HD-
mDxloo HD
where HD AI-ID=
= height
of drawdown
change
in height
k = coefficient n
wi e =Tbx
of saturation
of permeability - w2 w1
= effective
of pool
of shell porosity;
drained
to unit
rosity,
wi
is water V = velocity
line
III-i
of impervious
core
material i.e.,
volume
is saturated
content
drawdown
at face
after
the
ratio
of soil water drainage
of void
where content,
n
space is poand
w2
EM iiiO-2-1902 Appendix III 1 April 1970 All
quantities
3.
Computations.
veloped
should
for
drawdown
the
case
is to some
considering The
the
following
and
is to be drawn
The
effective
pool
velocity
elevation
they above
may
the
of the
a narrow
The
pool
is 100 ft above
500 X iOD4 water
be used
min is
and
i2
when
base
core
embankment
base
to be a sandy
a porosity
percent,
of
and after
is 3 percent. n
is
e
12 - 3 20 x = 0.15 12 100
=
e
drawdown
V
is
60 (ft) ?O X 24 X 60 (min) V = 0.00139
ft per
= 13.9 X 10
min
500 x io-4 0.15 From
the
chart,
for
a i-on-3
-= X 100
-=10 100
x 13.9
slope,
HD
-4
ft per
min
= 240
x io-4 X = 10 percent.
‘Solving
- AHD for
AHD
HD
60 - AHD or
60 III-2
AH
D
= 54 ft
by
III-i.
impervious the
de-
embankment.
is assumed
ft per
content
also
of the
central
shell
were
in plate
with
The
III-i
embankment
chart
dam
saturated
porosity
in plate
as the base
the use
of
content
of pool
level
60 ft in 30 days.
n
The
presented
pool
slope.
average
units.
drawdown,
illustrates
down
the water
curves
intermediate
a permeability The
drainage
reservoir
upstream
having
20 percent.
of full
a i05-ft-high
a i-on-3
gravel
the
example
and
in consistent
Although
intermediate
Assume
a.
be expressed
the
equation
EM
Thus,
the height
level,
or 46 ft above Assume
b. less
of saturation
pervious
the
the
soil
at the
base
same
with
core
is 54 ft below
or 6 ft above
of dam,
conditions
except
k = 5 x iOW4
ft per
that
original
the lowered the
min
the
and
IiiO-2-1902 Appendix III 1 Apri 1 1970
shell
pool
pool.
is constructed
the water
of
content
after
is 9 percent.
drainage
n
12-
=
e
20 = 0.05 100
9,
12
5 x io-4 pD
A value for
of
X
a i-on-3
equal
=Fo5 .
to 51 percent
slope.
Solving
for
70.6
the height
ft above
the
4.
Limitations.
for
determining
of seepage
at the
in determining and
k.
selecting complete, must
face
Information
virtually
approach
in plate
of central velocity
30.6
the
of shell
core
In order e’ instantaneous
curve
in
plate
III-i
pool
or
pervious
= 29.4 ft
Yt below
give
the the
only
material
embankments.’
of drawdown,
for
D
ft above
III-1
by Terzaghi
of n
a highly
or
of drainage
given
from
AH
is 29.4
dam,
curves
rate
probable
values
of the
The the
or
60
of saturation
base
obtained
AI-ID
100
case,
is
= 7*2
60 - AI-I~
AL In this
x 13 9 x 10-4 .
and values
drainage condition.
III-3
original
lowered
pool.
approximate and
criteria
lowering
Judgment
the
must
line
be used
and reasonable values of ne Ii may be used as a guide in Peck of X to approach of the
shell
material),
0 percent the
(i.e. shell
1 April
LII-4
EM
APPENDIX
iiiO-2-3902 1 April 1970
IV
Simplified Procedures for Preliminary Determination of Embankment Slopes
1. using for
Two
General. design
charts
determining
analyses
a rigid
as shown
yses
and
assume
The
on shallow that
failure
cases of the
VIII.
and
foundations
in plate
methods
to homogeneous
Homogeneous a.
because
The
neous
they
design
The
1.
crown
width
through
thickness
charts and
5, the
of foundation slopes
These
in the
methods
Due
presented,
on 2 horizontal to shear +D
no restrictions
and strength for
the
Foundation
to the
overlying
slopes
are
stability D
embankment
as to developed
assumed
soil
and
to those The
conserva-
a Rigid case
crests. Boundary.
of a homogeas shown
H
ratios
between
between
between
0 and critical
of
0 and 1 vertical
factor angles
The
and
for
stability
in
In plates
of developed
of cohesion. IV-i
more
height.
height
foundation
values
as those
is presented
plates
by values
such
boundary
embankment
on 4 horizontal.
of
to be symmetrical,
Ns = g
in these
differences
or wide
general
to embankment
limited
of the
the
a rigid
the
factor
horizontal
founda-
of anal-
comparisons
Overlying
for
to one-eighth
1 vertical
having
developed
foundation
layer are
and
are
embankment is equal
IV-
Embankment
to slopes
Embankment
embankment IV-
apply
a rigid
surfaces
no seepage.
first
a ci.rcular
overlying
plane
IV-6.
The
along
is applicable
aiong
useful
detailed
and
occurs
foundations
occurs
two
failure
method
involving
VII,
slopes
are
to more
embankments
clay
as shown
for
VI,
s that
second
prior
methods
should be made with caution. Other charts 12 13 by Janbu may also be used; they yield or Scott
2.
friction
1.
assumptions
results
lated
IV-
embankment
tive
IV-2
clay
and
The
slopes
to homogeneous
embankment
of safety
prepared
the
appendix.
embankment
boundary
applicable
in the basic
plate
in this
approximate
in Appendixes
assumes
in the
are
factors
presented
embankments
boundary and
determining
outlined
in plate
cohesionless
tion
methods
is applicable
overlying arc
are
for
approximate
by the
method
methods
is reof internal
25 deg, arc
with
1.
EM 1110-2-1902 Appendix IV 1 April 1970 originates
on the slope
beyond
opposite
that under
the toe of the embankment,
impervious section
embankment is not suitable
The following Example structed
on a clay
weight
and foundation illustrates
of the foundation
bankment shear
are
foundation should
of
and the unit
be used
condition?
as a basis
The values
method
given
of the
in this
foundations.)
underlain
weight
Results
120 ft high,
of
What
slope
estimated
for a detailed
indicate
that
em-
a design
may be used for the
a factor
analysis
The unit
for the compacted
Q tests
having
is to be con-
by bedrock.
c = 950 lb per sq ft, tan + = 0.165
and embankment.
thickness
on clay
embankment,
40 ft thick,
110 lb per cu ft.
strength
(The
embankments
earth
foundation,
on the relative
layer.
at or
and emerges
the use of the charts.
A homogeneous
:
depending
for cohesionless
example
investigation
of safety
of 1.3
of the end-of-construction
to be used in the appropriate
design
charts
are as
follows. -D = - 40 = 0.33 H 120 - 950 - 731 lb per
‘D
1.3
0.165 =i .3
tan +D
_ - 0.127
sq ft
and
+J~ = 7.2 deg Stability From
plate
IV-4,
to a stability from
plate
1 on 3.55. for D/H mole 2a
the stability
factor IV-3,
detailed
N
chart
s
the stability Thus,
chart
_ YH = 110 x 120 = 18 731 cm
for D/H
of 18 and a tan 0,
By interpolation, = 0.33.
factor
of 0.12i
for D/H
an embankment
an embankment
= 0.25,
slope
analysis. IV- 2
the slope
is approximately
= 0.50, slope
the slope
corresponding 1 on 3.30; is found
to be
of 1 on 3.38 is indicated
of 1 on 3.5 may be chosen
for
EM
b.
The
foundation
design soils
weighted
charts
have
averages
are
limited
similar
are
unit
a refinement
is not
more
appropriately
used
and
of a symmetrical
utilizes
can
of the
2 in plate
and
negative
A design
slope
2 of plate
trial
value bcD
of
from
earth
IV-7
values
gives
for
KA
in figure
value
number of
bility
A number
bility
chart
soil to the
cohesion is taken ample
is Q
into illustrates
Example strength
The
shear
strength
shear
the use :
corresponding
weight
of 120 lb per
having
a shear
changes
A few
to small
is expressed
embankment, of internal
cu ft is to be constructed of 1200
KA
thickness
failure
sta-
The
sta-
soil
corre-
of an equivalent
plane
coefficient.
the
of plastic
foundation in terms
as the
in the
The
embankment
following
ex-
chart.
to an angle
strength
.
of the
of the
adequate,
in
the
to detera revised
changes
strength
pressure
and
and
shear
the
are
this
be used
angles
that
fig-
number
in slope
assumes
along
from
substituting
then
trials
IV-7
and
KA
stability
can
surface
of embankment).
2, if necessary,
small
earth
A homogeneous
figure 1.
resistance
by the
slope
ratio
dam.
ground
and
of the
figure
insensitive
1 of plate
account
from
for
small.
The
c .
This
of the
in
chart
to the
of
slope
a value
as shown This
side
a value
embankment
KA
from
relatively
in figure
foundation sponds
is
on opposite
be
material
IV-7.
center
can
Boundary.
boundary,
a horizontal
by determining
slope.
slowly
for
slope
involved
corresponding
at the
KA
1 to obtain
slope
changes
K
of
an assumed
and
KA
.
be selected.
a Rigid
i in plate
pressures
be estimated
IV-7
figure
reverse
(i.e.
and a corresponding NK=yH mine a second trial value of stability
effort
a rigid
coefficient
to vertical
can
the
and
Otherwise,
of cohesionless
overlying
pressure
slopes
must
Overlying
embankment
foundation
earth
horizontal
for
Foundations
be approximated
Figure
ure
clay
an active
arc
analyses.
outer
IV-6,
failure
stability
Clay
embankment
strengths.
in detailed
The
plate
a trial
the
shear
since
on Shallow
on a shallow
and
justified
Embankment
resting
where
considered
3.
slopes
weights
required
Such
to cases
iiio-2-1902 Appendix IV 1 April 1970
lb per
sq ft.
IV-3
100 ft high, friction
a shear
of 28 deg and a unit
on a layer What
having
of clay,
approximate
10 ft thick, slope
should
EM 1110-2-1902 Appendix IV 1 April 1970 be used
in an analysis
The developed
angle
0.532 tan C$J~= 13 . (
assuming
KA.
IV-7
for
Solving
D/H for
of internal
= 0.409
1200 = 923 lb per 1.3 of
of the stability
)
.
sq ft. a slope
= 0.1
and
of the dam for a factor
friction
The developed The ratio
of
of 1 on 4-l/2, KA = 0.40,
3
of the foundation
As a first
is 0.40.
or
of 1 on 4 may of
KA
b=
From number
figure
trial,
are unnecessary.
IV-4
for
1 of plate
NK is 0.300.
NK yH CD
detailed
analysis;
is
the Value
x 120 x 100 = 3 9 . 923
be selected
of 1.3?
is 22 deg
b in the equation
a slope values
cD
is 0.1.
the stability
b = 0.300
trial
of the embankment
cohesion D/H
NK=yH bcD
Thus,
+,,
of safety
additional
HOMOGENEOUS
0
HOMOGENEOUS
I
EMBANKMENT
FOUNDATION
+ RIGID
I4 = HEIGHT D = DEPTn = STABILITY
Ns
EMBANKMENT FOUNDATION FACTOR
= DEVELOPED
%
y = WEIGHT MATERIAL TAN
OF OF
&,
= TANGENT
b
BASE
LAYER =yll/C,
COHESION OF
PER
EMBANKMENT PER OF
UNIT DEVELOPEQ
INTERNAL
FRICTION
= COTANGENT
OF
SLOPE
UNIT
AND OF
OF
VOLUME
CROSS
ANGLE ANGLE
AREA
FOUNDATION OF B
SECTION AND SYMBOLS STABILITY CHARTS
(SEE PLATES
I%?
THROUGH
FOR m-5)
EM 1110-2-1902 Appendix IV 1 April 197( 200
a0
200
loo a0 m 70 00 80
40
20
20
10 0 (I 7 6 0
0.1
0.2
0.2 TAN
NOTE:
8Ct
PLATE=-1
DtPlNITIONS
0.4
40
FOR OP
SYMBOLI.
STABILITY CHART FOR HOMOGENEOUS EMBANKMENT AND FOUNDATIONa FDUNDATION HEIGHT
Plate
IV-2
Iv-6
DEPTH-EMBANKMENT RATIO, D/H = 1.0
0.8
I
EM
0
0.1
0.2
0.8 TAN
NOTE:
SEC l LAtEsl DLFlNltlONI
OF
iilO-2-1902 Appendix IV 1 April 1970
0.4
0.1
&,
FOR SYYDOLS.
STABILITY CHART FOR HOMOGENEOUS EMBANKMENT AND FOUNDATION FOUNDATION HEIGHT
DEPTH-EMBANKMENT RATIO, D/H = 0.50
Plate
IV- 7
IV-:
I
EM IIIO-21902 Appendix IV 1 April 1970
0.1
0.2
0.1 TAN
NOTL:
SLL PLATE DtFlNlTlONS
0.4
4.
COR
Ip;l OF
SYMbOLI.
STABILITY CHART FOR HOMOGENEOUS EMBANKMENT AND FOUNDATION FOUNDATION HEIGHT
slate IV-4
IV-8
DEPTH-EMBANKMENT RATIO, O/H = 0.25
0.1
EM
1liO-2-1902 Appendix IV 1 April 1970
mo
20
NOTE:
SEE PLATEI% DEFINITIONS
OF
FOR SYMBOLS.
STABILITY CHART FOR HOMOGENEOUS EMBANKMENT AND FOUNDATION FOUNDATION HEIGHT
DEPTH-EMBANKMENT f’:ATIO. D/H = 0
Plate
IV- 9
IV- 5
msmv~
SLOPE
&
NEGATIVE OPPOSITE
COl4ESlONLESS
SLOPE WllW RESPECT UImJwMENT SLOPE
To
EMBANKMENT
v CLAY RIGID
l4 = HElGt4T
OF
D = THICKNESS = RATIO
K.
EARTH
b
y = WEIGHT
CLAY
OF OF
BASE
FOUNOATION
HORIZONTAL
PRESSURES,
= COTANGENT
0
EMBANKMENT OF
OF
/ FOUNDATION /
TO ACTIVE
SLOPE
CASE
ANGLE,
EMBANKMENT
AND
MATERIAL
PER
UNIT
OF
C = COHESION
PER
UNIT
AREA
LAYER
VERTICAL /3 FOUNDATION
VOLUME OF
FOUNDATION
SOIL
CROSS
SECTION AND SYMBOLS STABILITY CHART (SEE
PLATE
IS&71
FOR
I
EM
E _ DEPTb4 n-
FIGURE
OF
FOUNDATION
HEIGHT
OF
EMBANKMENT
1. N,
VERSUS
K,
AND
g
i
FIGURE
2.
dr,
VERSUS
b AND K4
1110;2-1902 Appendix IV 1 April 1970
EM
APPENDIX Infinite 1.
Infinite
tions
applicable
stability
flow
that
the
General
Analysis
Computations.
slope
is neither
flow
The
may
parallel
where
nor
to obtain seepage
throughout
factor
for
horizontal
the
to the
Soils
materials
be used
is uniform
safety
Cohesionless
cohesionless
of an embankment
seepage
Case.
slope
V for
For
to an infinite
of the
sumed 2.
Slope
Slope
i110-2:1902 1 April 1970
an estimate
is involved.
the
general outer
(c = 0))
soil
mass.
case
where
slope
equaof the
It is as-
seepage
is
y’ - (VW9) F.S.
=
’
cotptan+
Y sat where y1 = submerged = unit
YW
p = angle
of inclination
= saturated
the
unit
of internal
Parallel
Seepage
of soil
of water
between
+ = angie
with
weight
weight
(Y = angle
Y sat 3.
unit
seepage
slope
F.S.
line
and
of embankment
weight
embankment slope
with
slope horizontal
(cot
p = b)
of soil
friction For
to Slope.
embankment
flow
seepage
((Y = 0) , the
= y’ Ysat
cot
flow
safety
j3 tan
parallel
factor
Y’ + =Ysat
to and coincident
becomes
b tan
(p
where b = cot 4.
Horizontal
of safety
p Seepage.
Where
seepage
flow
is horizontal
(a = p) , the
is YW
F.S.
Y’ - 2 ‘Ot = Y sat
p (cot
/3 tan
bzy’ by +) =
- y w (tan sat
V-l
4-4
factor
EM iilO-Z-1902 Appendix V 1 April 1970 5.
Where
No Seepage.
factor
of safety
no seepage
Earthquake
to all
of the
term
b’
7.
i.e.
for
a dry
slope,
the
The
. previous
effects
= s
= b tan
of an earthquake
equations
for
factor
+I
loading
of safety
can
be applied
by replacing
b
with
the
where
Example.
on the
exist,
is F.S.
6.
forces
factor
4 = seismic
coefficient
An
of the influence
example
of safety
is illustrated
(see
in the Factor
As sumed design values
Seepage parallel to outer slope
fig.
6, main
text)
of the direction following of safety Horizontal seepage
of seepage
tabulation. .-
for No seepage
b = 3.5 Ysat = 2Yw tan + = 0.7 qJ = 0.1
1.23t
I.137
2.45t
0.88tt
0.74tt
1.76tt
b’ = 2.52 t tt
Without earthquake loading. With earthquake loading.
v-2
flow
EM iilO-2-1902 1 April 1970 APPENDIX Modified
1.
General.
making
slope
stability
a circular
arc
simplicity
of presentation,
arc.
or along
In the modified
of either
finite
sliding
feature
the slices
are
parallel
forces
are
solve
whether based most
because
shown trial
to illustrate Procedure
The sliding shown
relative
of Finite mass
in figure
reasonable
is divided 1 of plate
accuracy,
critical.
Since
to obtain using
An be as-
the side
a solution.
a digital
or graphical procedures
This
computer
to
integration While
to homogeneous
or the wedge
in the
dams
The decision
embankments.
method
of the soil
appendix
to
are described
and clarity.
applicable zoned
of
or the use of graphical
simplicity
since a.
should
mass.
be
The
are not necessarily
the examples
have
the
been developed
and procedures. Embankment
into
a number
VI- 1.
Generally,
depending
is most
or arbitrary
should
of this
methods
Slices.
arcs
slices
forces
of stratification
surfaces,
into
of the side
method
in the examples
the various
is divided
circular
on the sides
graphical
Swedish
a trial
and
acting
polygons
for analyzing
failure
along
along
forces
be balanced
is particularly
or lack
uniformity
failure
by iteration
force
of their used
For
mass
procedures
The
on the stratification arcs
must
forces.
to use the modified
critical
only
for
they
shape.
of the embankment.
equations
method
it is also
circular
slope
occur
which
earth
The direction
composite
earth
Swedish
and dikes,
is that
for use in
would
of trial
to determine
are
failure
to occur
the sliding
the use of analytical
internal
appendix
is assumed
method
forces,
appendix
of any arbitrary
and a number
to the average
involving
modified
2.
width,
a set of simultaneous
this
assuming
method,
considered.
either
balance
analyses
failure
of this
internal
procedures
in this
are investigated
important sumed
presented
a surface
Swedish
or unit
surfaces
requires
Swedish Method of Analysis Using Slice Procedure
The procedures
detailed
VI
Without
of slices
VI-1
of convenient
six to twelve
on the embankment
Seepage slices
zonation
Forces. width
are and
as
sufficient
EM ii10-2-1902 Appendix VI 1 April 1970 foundation figure
conditions.
2 of plate
resisting
A typical
VI- 1.
cohesive
and
is equal
FD
acting
fective
force
to chord
ing
a trial
AB
the
composite
force
factor
force
CD
at an angle
normal
venient
The
+D
of safety,
with
the
base
and
polygon and
the
scale
(1)
Draw
the
weight
(2)
Draw
the
developed
(3)
Draw
a line
acting
total
weight
to act
normal
to
shown
following
steps
cohesion
AB
is the
3 of plate
cohesion
VI-I,
slice CD
vector
are
2)
of the
ef-
Assum-
combined
using
into
a con-
below:
(slice
parallel
(fig.
The-force
force.
5 as outlined
of the uppermost
AB
resultant
slice
in The
CT;, .
frictional
1 through
slice.
to chord
on each
in figure
of the
unit
the developed acting
on it is shown
parallel
developed
forces
vector
forces
is the
is assumed
the
force
with
W
times
at the
force
slice
1).
to the base
of the
slice.
weight
Construct
tablishes
the
frictional
forces
(5)
structed,
using
results,
errors
can
trial
points 2a
of the
head
of the average
closing
the
slice
from
the upper
end
of the
force
vector be drawn
they
cumulative-type
of the
composite in figure
effect
external are
polygon
force are
of the
esand
to determine polygon.
the
of safety
The versus
A smooth
force
the
resultant
the magnitude
the
are
slice
as a base.
polygons
the
factor
factors
to zero
ac-
safety
different
of closure
drawn
con-
small
for
safety
trial
then
to ensure
To obtain
errors
of
slice
in which
what
curve
corresponding VI-2
earth
scale
diagrams
force
VI- 1.
side
to a large
composite
plotted
the
previous
of closure.
4 of plate factor
This
of the normal
subsequent
error
constructed
composite force
on the
forces,
line.
establishes
on each
since
are
normal
to intersect
This
must
of safety
establishes
forces
draw slope
polygon.
The
the
resultant
vector,
embankment
earth
a large
from
slice.
polygons
have
factors
side
4,
cohesion
force
FD .
of
force
of balanced
as shown
base
the
composite
in closure
on the
vector
curate
trial
of the
FD , the
vector
to the
thereby
developed
at an angle of the
the
parallel
vector,
factor
a line
direction
From
vector
The
to the base
vector.
(4)
the
normal
through error
for
results each
of safety, the
plotted
ofclosure.
EM iiio-24902 Appendix VI 1 April 1970 Sudden
b.
Drawdown.
for impervious before
embankments
drawdown
analyses
TWO
subject
to determine
the developed
normal
illustrated
in plate
A typical
ing before
drawdown
composite
force
In this pore
are
it is assumed
pressures
acting
in soil
weight
from
of the developed
drawdown
analysis
and is used
in developed
sidered
for an impervious
above
the upper
moist
unit
force
determined
weight
drawdown before
pool
are
drawdown
balanced lines
upper
pool
level
embankment
as shown
for
the weight
for that
portion
is conservatively
to the trial
down
is based
rated
weight
pool,
and submerged
sliding
on the saturated between
weight
below
before
of the slice
below
assumed
to extend
pool
a base located
the lowered
from
pool.
polygon VI-i.
of closure) from
by con-
the tail
of the
2(a) of plate
are
indicated
drawdown,
VI-2.
in figsubmerged
pool level.
of the slice the upper
extension
The
the before-
horizontally
above
and horizontal
force
the upper
The weight weight
having
3 of plate
in figure polygon
is con-
in the after-
error lines
one slice
of the slice
or moist
the upper
force
no
of the side earth
is used
(zero
since
of material
is determined
force
surface.
with
in figure
polygons
the before-
state
the composite
shown
the after-drawdown
In determining are used
analysis
the zone.
polygon,
the magnitude
in constructing
force
reflect
from
force
is composed
drawdown),
VI-2.
in the drawdown
any slice
to the normal
vectors
drawdown
is determined
For
forces
of the
and that the
the before-drawdown
slice
normal
perpendicular
in constructing
weights
ND
over
as those
composite
friction
2(b).
Steps
the same
of the developed
ure
and after
polygon.
magnitude
Steps
force
the entire
before
drawdown
developed
force
embankment.
(i.e.,
after
act-
sections
has occurred
to saturated
in the before-drawdown
force
structing
no seepage
is
forces
2(a) and 2(b) of plate
in the after-drawdown
normal
with
1, and corresponding
submerged
draw-
The procedure
in an embankment
of the slices
normal
and one after
drawdown.
in figures
that
on the bases
The value increase
shown
arc are made
one for conditions
forces
before
slice
failure
drawdown,
normal
forces in figure
show-n
polygons
procedure
increase
is
each trial
to sudden
developed
down using
VI-2.
for
The
through after pool,
the
drawsatu-
of the lowered
When the trial
failure 2b
.--:
EM iiio-z-i902 Appendix VI I April 1970 surface
is a circular
puted
as indicated
cessity ure
arc,
by the equation
of constructing
Z(b),
plate
pervious given
zones
in figure
with
They
linearly
below
figure
2 of plate
VI-3.
gon, the resultant
R
plate error oil,
This
flow
for
can be com-
eliminates force
drawdown
the ne-
polygon
net for
this
type
from
construction
of the weight
in fig-
semi-
of analysis
for
are
for determining as that
shown
in the direction
Fh
graph
i if of the main
text.
This
for each
to vary
are
shown
force
slice
3 of plate
having
The 4 of
the factor
of safety
for
failure
is computed
zero
VI-i.
in a stability
an additional
analy-
horizontal
as discussed from
a
VI-3.
in figure
effects
in
poly-
is shown 4 of plate
as
must
of safety
imparts
force
slices
in figure
in figure
of potential
or assumed
of the composite
earthquake
that the earthquake
nets
forces
factor
seepage
on each slice
on typical
as shown
one trial
of steady
acting flow
and water
To consider
Earthquake.
forces
To simplify
is the same
acting
the water
is determined,
force
In the case
The forces
The procedure
it is assumed
Seep=
line.
polygon
of closure d.
drawdown
composite
can be determined
surface
force
VI-3.
VI-3,
the saturation
water
composite
VI-2.
and the procedures
Steady
i of plate
be determined.
sloping
after
VI- 1 i.
Embankment
shown
in plate
The use of a sudden
embankment
C.
of safety
the after-drawdown
VI-2.
in plate
the factor
in para-
the equation
Fh = +W where W = weight += The weight and moist water a guide computed 2d
assumed W
unit
above
weight
mass
seismic
is based
on
above
coefficient saturated this
the embankment
in selecting for
of sliding
each
the seismic slice
line,
slope.
unit
below
the saturation
and does not include Figure
coefficient.
and included
weight
6 of the main The horizontal
in the force VI-4
polygon
line
the weight text
of any
can be used as
force
Fh
as shown
in
is
EM iiio-2-1902 Appendix VI 1 April 1970 figure
i(a),
with
plate
the weight
plate
VI-4,
VI-4. and water
and the resultant
drawdown posite
and steady
strength normal
quently,
the applicable
as the composite down,
the
if the
analyses
(including
polygon
R
The
divided
by
R envel-apes
Graphical
stability factor are
of shear
analyses of safety
taken
to balance for
arc
sultant
of the side
each unit ber
balanced
at appropriate
failure
or surface
width
of unit
AE’ , which
width
the internal
earth
slice slices
external
of sliding.
using
the trial
is plotted must
is the resultant
to form be used
an area to define
of the earth VI-5
forces
seepage
must
+D
also
be
normal
force
at the intercept
of the
S and
or the than
S strength
one type
gov-
of soil,
ap-
slice. forces
Vertical
the cross
determined
force
to
developed
earth
along AE’
the steady
integration
intervals forces
R envelopes
por-
for each
forces.
is compared
in the first
more
side
is
for
Graphical
Procedure.
AL
S and
strength
are used
by
polygon
Z(a) of
stress
through
force
in figure
with
strength
nor-
illustrated
and the resulting
passes
and error
and the developed
normal
as a basis
normal RtS the 2
by trial
draw-
For
polygon,
arc
Integratinn
of the
to the procedure
when
the failure
values
plicable:
3.
to determine
Where
erns.
force
Cons@-
sudden
divided
governs.
is assumed
is compared
AL
ND
the developed
similar
S strength
of the composite
force
on the de-
forces. for
as the composite
S strength pool),
earth
+D
sudden
the use of com-
In analysis for
diagram. for
depends
be determined
at the intercept
or the
plate
VI-2.
normal
value
in a manner
slice
analyses
strength
,,..-.:
i(b),
force
require
by the side
as a basis
for each
partial
pool)
shear
must
in figure
Stability
is constructed.
is assumed
determined tion
strength
can be combined
in the composite
partial
shear
stress
determine
(including
Fh
as shown
Envelopes.
is influenced
The developed
the normal
seepage,
slice
The applicable
is determined
constructed.
each
which
force
S strength
force
for
Strength
seepage
force,
of steady
R can be used
envelopes.
veloped
with
forces
Use of Composite
e.
mal
In the case
from diagram, accurately acting
in
and determine
slices
section factor
may be used of unit
above
the repolygon
A sufficient the area on the left
width
the trial
of safety, the force
the
for num-
diagram. and right
EM 1110-2-1902 Appendix VI 1 April 1970
’
sides
width
of the unit
bankment area
slope
of the
ternal
being
AE’
forces respect
into
an equivalent
of feet)
1 of plate
is equal
soil
includes
obtained its unit
weight
is often
of one of the soil feet)
is constructed
plate
VI-5
using
Construct
(2)
Draw
This
times
of ex-
having
may be transformed
as a base.
or zones
may be used.
for
each unit
width
weights,
ybase
more
at any a
h’
is
type times weight
the unit
weight
polygon
as illustrated
(in units
in figure
1 of
steps:
h’ .
1
X-
Ybase
(4)
Construct
a resultant
line
1 CO8 8
from
friction
at the base of the width
the head of
C;> .
and normal
force
vector
slice
h’
at an angle
the normal.
Construct
from
AE’
the top of the unit
width
slice
h’
to intersect
vector.
(6)
The magnitude
(7)
Construct
to the normal.
of
a line This
FD from
is defined
by step
the intersection
step defines
of
the developed
5. FD
and
normal
AE’ force
perpendicND
and
l
section
must
be drawn VI-6
to a large
scale
of
. The unit
convenient
The force
weight
Where
of each soil
weight
strata
h’
of the unit
unit
poly-
is illustrated
section
different
base unit
force
procedure
used
height
slice
is not homogeneous
the ratio
weight
but where
a normal
+D)
mass
for use in obtaining
as the base,
C ’ =&x D
The embankment 3a
used
Construct
the friction
Nl;(tan
types
by a selected
(3)
from
slice
the net
for a balance
the arc
slices.
the incremental
the following
(1)
Of 9, (5)
ular
together
above
to the unit soil
of safety
of the equivalent
of a unit
in the slice
divided
width
for which
em-
analyzed.
density
The height
two or more
by adding
of water
for the unit
to the average
of safety
If the soil
section
of uniform
to the height
embankment
being
Seepage.
the cross
VI-5.
factor
is the factor
surface
Without section
to act parallel
The trial
is zero
to density,
gons (in units
slice
diagram
for the sliding
with
in figure
is assumed
analyzed.
Embankment
a.
point
slice,
so that
the force
of
EM IilO-2.-i902 Appendix VI 1 April 1970 polygons for
for each unit
each unit in either
toward
the crest
diagram
in figure
responding
factor
corresponding lower
equal,
by planimeter
which
is the net area
shown
in figure
balanced
3 of plate less
time
for the sudden
utilized
to reduce
viders
(or a slide
b. for
AE’ Sudden
sudden
the trial
can be used
when
failure
arc
drawdown
requires
For
VI-6.
weights
are used
below
this
level.
figure
2(a) of plate
The cross
transformed
above VI-6.
before
the upper
The unit
into
slice
of
C AE’
of safety
, as
of safety requires
slice
procedure
techniques
can be
proportional
the equivalent Dividers
disection
can be used
for an impervious section
after
to
force
level
The developed VI-7
normal
embankment,
section
moist
or
before stress,
above
for conditions
as shown
and submerged
polygon
procedure
of the embankment
drawdown
drawdown,
pool
integration
an equivalent
for conditions
conditions
any arbitrary
diagram.
two analyses
procedure. i5
VI-5.
a
and decreases
the factor
example,
The use of the graphical
and also
of plate
1 of plate
analyzed,
procedure
constructing
When
that using
A plot
than the finite For
being
factors
and various
required.
Drawdown, slice
analysis),
area
and the cor-
using
integration
manually
to the area
drawdown
as in the finite before
vectors
area
to determine
The graphical
in figure
zero
rule.
acts
obtained.
to note
trial
AE’
and toward-the
surface
-AE’
versus
the time
shown
equals
.:
vector
in the
are
can be measured,
can be used
drawdown
rule)
AE’
by Simpson’s
to complete
further
density
transfer
VI-5,
areas
of the
diagram,
area
section
AE’
It should
so that
It is useful
the size
forces.
(except
of uniform
forces.
VI-5.
Consequently, pius
of
The areas
of the
direction
and
of
are continuous
for the sliding
or approximated
internal
substantially
internal
area.
units,
for
is correct
increases
+AE’
slice
section.
minus
A plot
2 of plate
of the embankment
the summation
of safety
of safety
of the
part VI-5,
to balanced
factor
the size
are
in figure
for each unit
of the embankment 2 of plate
two areas
accurately.
or counterclockwise
in the upper
the bottom
as shown
polygons
a clockwise
toe near these
can be constructed
is then made
that the force
be noted
plots
slice
slice
saturated weights
drawdown using
in figure unit are used
is shown 9,
i
based
in on 3b
EM 1110-2-1902 Appendix VI 1 April 1970 the
S
strength,
of the
must
S and
R
envelopes
The
developed
normal
mal
force
Nb
versus
for
trial
the
magnitude
of
ment
between
oped
normal = 0)
as shown with
safety
for
upper
force
Nb
used
C AE’
slice
cedure
simplifies with
Therefore, cancel
each side
in figure
slice.
can
be determined
termine 3c(l)
slice l(a),
Although
the
and
Note
of the
l(d), the
1 and in any
that
and the
it is not
the
(where drawdown
balanced
side
the factor
of
analyses
must
to min-
be performed for
forces necessary
VI-7.
UR
this
type
of
sides
and
base
- Ul - U1
to compute
U ; however, VI-8
and
to that
this
alone
following
as shown
presl(a)). and of the
to it, of the
acting
pro-
slice(fig.
portion
portion
of
of these
opposite
parallel
forces
base
of water
equal
to a line
water
the
of the
remaining
U2
but
sides
applies
line
to the
and
, are
on the
influence
variation
on both
U of all U1
The
The
saturation
force
manner,
same UR
on the
normal
2 of plate
and
applies
resultant
force
the
Consequently,
two
forces
effective
appropriate
force
U1
for
procedures
Water
required.
UI,
from
from
resultant
the
to be the
forces,
The
to
embank-
after
than
the
used
of the devel-
drawdown
procedure
(1)
computations
is assumed
other.
for
C AE’
12.
influence
for
values
drawdown.
be used
nor-
drawdown, in the
of safety
after
of are
After
be greater
investigated.
in figures
total
= 0
VI-5
conditions
factor will
developed
a plot
of water
for
gov.erns.
the
before
above-described
Seepage.
width
the
the
The
should
VI-
with
be accounted
depth
VI-6.
diagrams
surface
as shown
polygons
intersection
strength
and
The
condition
C AE’
S
forces.
pool.
force
with
in plate
the
at the
in plate
the weight
drawdown
The
of unit
can
l(c),
before
and
given
forces
shown
= 0
Embankment
slice,
right
of plate
failure
are
of each
sure
2(b)
shown side
drawdown
in the unit
or
diagram
to that
from
R
An area
balanced
and
stress
by multiplying
to include
found
forces
8’.
similar
pool
errors.
trial
c.
the
the
possible
analysis
cos
is increased
sections
each
ybase
for
normal
if the
is determined
h’
are
the
stress
of safety
balanced
separate
for
factor
with
to determine
of safety
in figure
forces
imize
by
factors
determine
C AE’
be compared
on the
in figures
these
forces
separately
can
be done
if desired.
as side
of
slice l(b), to de-
EM iiiO-Z-1902 Appendix VI 1 April 1970 (2)
It can be shown
direction
that
perpendicular
use the simple without
both
determining
force
to the saturation
graphical
for determining
the resultant
procedure U1
U2.
friction
base
of the slice
ND , and (c) the resultant
AE’
are illustrated weight
procedure. shown
Details
in figure
as shown to
of water
CAE’= (3)
2(b).
This
required
side
VI-4
VI-7.
The
to obtain
in a
it possible
to
2(a) of plate
VI-7
force
normal
earth
of
force
on the
force
on the slice
is valid
only when
weight
in the unit
slice
the validity
of this
procedure
forces
plotted
and summed
AE’
the correct
are
safety
factor,
-.~
U
determination
construction
for verifying
acts
of the resultant
is used as the base unit
1 of plate
in plate
in figure
FD , (b) the developed
in figure
U/y,)
makes
The graphical
(a) the developed
the unit
(i.e.
This
and direction
or
force
line.
illustrated
the magnitude either
1J’
which
are
corresponds
0. In analyses
graphical
for
integration
steady
seepage
(including
partial
the developed
procedure,
normal
pool) force
using
the
multiplied
to the normal stress at the intersection bY YW cos 0 must be compared R+S strength the S and R envelopes to determine when the S and 2 When the trial
governs.
the appropriate
sliding
composite
surface
strength
passes
envelope
through
should
different
be used
of
materials,
for
each
material. quake
imparts
potential graph
Note that
weight effective
Fh
polygons height
above
low the saturation
force
Fh Ilf
weight
text
for each unit
as shown
Fh = JI h’ (total),
in the direction
of the main
be computed slices
acting
that the earth-
in figure
the term of the soil
mass
and in para-
slice 2, plate
h1 (total)
of
and added VI-4.
is equal
in the unit
to
slice
unit
the water
equivalent
should
for the total
on the saturated
case it is assumed
in paragraph
of the unit
in the equation
the equivalent
horizontal
as discussed
The force
2d.
the earthquake
an additional
failure
to the force
based
For
Earthquake.
d.
weight below the water table and moist unit This equivalent height is not the same as the table.
height line
based
h’ (effective)
and moist
unit
weight VI-9
on submerged
above
unit
weight
be-
it. 3d
EM 1110-2-1902 Appendix VI 1 April 1970 End
4.
of Construction--Case
analyzing
this
condition
construction
analysis
procedure
the
tion
using
record
samples
further
discussed
-Sudden strengths,
design
developed
during
at the
for
Finite
a trial
case
time
arc
fore
are
drawdown
after
and
drawdown
Submerged
unit
drawdown”
condition;
merged
unit
drawdown”
weights
safety
are
assumed,
safety
for
approximate
the
t
zero
Case
error
one
designations
the
VI-8
consfruc-
of tests
on
This
weights,
is
shear
drawdown
In some
excess
pore
shows
an example
analyses
extreme
pore
using
cases
water
pressures
reduction
water
forces the
saturated
For
the
in
pressures
ex-
weights
the
before-drawdown of closure
those
constructed
described VI- 10
used
for
are
3).
as shown
arc
of the
beslope
analysis. “before-
zone
used
two
develop
the
drawdown
in paragraph
trial
that
first
for
and
the
sub-
“after-
trial
factors
until
a factor
of
force
polygon
for
in figure
4, and
ii
main
determined (fig.
each
in the are
level
drawdown
of safety
analysis, are
is found
sudden
forces
in the
pool
of computations
For
factor
pool
minimum
is then
the
determined
the
closure
for
normal
maximum
unit
errors zero
the
to determine
normal
below
width material.
to deterrnine
below
are
text.
of impervious
second
of closure
in sudden
an appropriate
of finite
and
in plates
during
unit
dissipated,
slices
condition.
of slice
measured.
before
using
weights
of
finite
and
is possible
VI-IO
the
in
drawdown.
dam
using
main
Plate
required,
the
given
Appropriate
(1)
of a homogeneous
analyses
are be made
Slices.
failure
of the
condition
of rapid
using
are
end
Examples
be made
pressures
to be used
lib
should
text.
measurements
water
assumptions
construction
stresses
at the
are
should
II and III.
drawdown
expected
used
VU.
paragraph
in
a rapid
a.
pore
strengths
main
procedure
instrumentation
high
shear
condition
analyses
in Appendix
and
9 of the
integration
of field
and
to those
of construction
Additional
where
described
pected
end
Drawdown--Cases
5.
effective
correspond
graphical
results
weights
in paragraph
the
respectively.
-9,
where
for
and
and
are
should
as discussed
stability
Unit
1.t
The
of the
of
the
test.
EM iilO-2-1902 Appendix VI 1 April 1970 normal
forces
from
this
force
safety
for
the after-drawdown
plate
VI-10.
The factor
equation
shown
(2)
in plate
The effect
of upstream
forces
on the aides
stresses
The resultant VI-ii)
weights
are used
sider
the water
the weight
below
near
the lowered
pool
the embankment,
slope
Graphical
for a trial
den drawdown analyses
arc
case
are
required
The developed
normal
to construct trial
strength,
in plate
of the the base
depending
of
in from
the
forces
cases,
(fig.
Saturated
unit
failure
critical through
arcs
emerging
Such analyses
to. con-
way,
arcs
net.
4,
both
on the sides
a more
by failure
may be desirable.
slice
In this
forces
may create for
the flow
and it is necessary
and the water
analyses
from 5).
of the slice.
ef-
The water
for each
level,
flow
to determine
VI-ii.
(fig.
analyses
a drawdown
weights
polygon
as part
forces
in stability
are determined
pool
of the condition
the top of
should
part
consider
way the
material. using for
the graphical
ND
as in the finite
polygons. steps:
Trial
factors
diagram
of each
slice
slice
(Z AE’ ) was determined of unit
on the effective
normal VI-ii
width
4a, plate corresponds
stress
Two
procedure.
condition
of safety
C AEf = 0 was found(fig.
for the sud-
material.
The factor
the following
computations
procedure
for before-drawdown
Analysis. LIE’
integration
arc,
force
using
VI- 12 shows
dam of impervious
each trial
forces
for
Plate
Procedure.
of a homogeneous
of safety
along
as shown
than is shown
Before-Drawdown
a factor
sistance R
level
the after-drawdown
and the net area until
Seepage
arc was determined (1)
unit
slopes
Integration
failure
saturated
the force
the slice
as a free-draining
b.
In these
and water
and additional
up the upstream
soils.
the minimum
above
can be evaluated.
form
is determined
be considered
of each slice
on the outer
of water
the factor
in,tabular
drawdown must
and forces
to construct
slice
riprap
with
of the weight
is used
as shown
after
forces
and base
R
for computing
VI-2.
in conjunction
normal
plate
of safety
of semipervious
fective
are used
condition,
of seepage
slopes
net can be used
polygon
are used
of safety were
for the
assumed
for each trial VI-12).
Shear
to the
(ND COB 9)
re-
S or
on the base 5b(i)
EM 1110-2-1902 Appendix VI 1 April 1970 of the slice. plotting
The shear
the developed
S strength,
strength normal
as shown
developed
along
stresses,
in figure
the arc
was determined
Nb COB 8 , determined
2a, plate
VI-i2.
(In this
using
example
by the
problem,
the S strength was used when the value of Nb cos 8 was less than 4.150 kips per sq ft = 5, ft ) 0.073 kips per cu ft (2) Using the factor o; safety found in paragraph 5b(i) above for = 0,
Z AE’ were
corresponding
constructed
(3)
force
for after safety
radius
4b, plate
VI-12).
the critical surface
The radii this
is shown
above
pool
velopes
slope Subsequent
the surface
below
the center
arcs
trials
until
and
a factor
pool elevation
for various
arc,
circular
A stability
in plate
VI- 13.
Moist
and submerged
unit
level
A composite
A number
is
pool levels.
of the pool of the arc
are varied
of
until
If
should for the
the critical
should
be made with
the pool above
for
Case IV using
slices
in computing
ess repeated
for
trial
the graphical section
pool
are used design
strength should
level
for the material; for materials shear
along
below
strength
the assumed
be analyzed
and factor
of finite
enfailure
for each trial
of safety,
arc
and the proc-
arcs.
Integration integration and trial
are used
weights RtS S and 2
pool levels
critical
Graphical
weights
the shear
of different other
analysis
of the
the most
the same
directly
of the trial
to determine
using
surfaces
is a circular
of safety
each trial
The critical
IV.
failure
Slit e s .
is used
b.
-Case
factors
of safety
level.
Finite
width
arc.
Slope-
The factor
trial
(fig.
failure
pool level.
by assuming
Z AE 1 = 0 was found Upstream
then used to con-
analysis. for
is determined.
a.
were
diagram
the embankment
and below
5b(2) above
AE’
Pool,
trial.
paragraph
conditions
determined.
of the
the assumed first
were
was determined
by determining
intersect
Nl!,
for before-drawdown
for the after-drawdown
the net area
Partial
polygons
of
from
Nb
drawdown
for
found
of
polygons
determining 6.
and values
Values
struct
force
arc
Procedure.
A stability
procedure
is illustrated
as in plate
VI-i3.
VI- 12
analysis in plate
In figure
for Case IV VI-14,
1, the section
using
iiio-24902
EM
Appendix VI 1 April 1970 above
the trial
density
Qsing
weight.
arc
is converted
the submerged
The correct
values
of
factors
weight
ehear
between
mainly
embankment
of the foundation’soil used
in figure
plates
to small
an equivalent
strength
Nb COB 8 as shown
of safety
tributed
into
differences
There
are
and - 14.
---
as the base unit
can be determined 2,
VI-13
of uniform by plotting
slight
These
differences
differences
in measurements
in
are at-
of the small-scale
diagrams. Steady
7.
Seepage,
conservative
Downstream
assumption
often
zometric
pressures
However,
it may be desirra.ble
closely
along
the failure
analysis
in plate
VI- 15.
graph
2c of thie linearly
In this
appendix.
below
the saturation
seepage
pool
pool
be added
to those
must
determining
shear
in paragraph
and trial
of the soil
above
Case
V using
forces
of water
upon which
it acts.
composite
of finite on a
in paraare assumed
a surcharge
the weight using
slices
as discussed
the water
Where
more
the forces
pool
exists
to above
due to the surcharge The procedure strength
A stability
procedure
is illustrated
as in plate
VI-15.
In figure
is converted
into
arc
the failure
a unit
weight
equal
width
slices
are
pressures.
Unit
boundary
conditions
occur.
and -i6
VI-15
ments
of the small-scale accordingly
arc
to water selected
The slight
is attributed
plates creased
example,
line.
arc.
Procedure.
integration
section having
forces
Integration
the graphical
material
slices
net to determine
forces
of pie-
the saturation
of computing
water
line.
VI),
with
the curve
and
for
envelopes
is
2~.
Graphical
height
(Case
resisting
for
A simplifying
is that
the failure
The method
as that using
the steady
the same
a flow
A stability
is the same
analysis
to construct
Slices.
slice
V and VI.
coincides
Finite
finite
using
arc along
is shown
b.
in this
pressures
width
given
made
the piezometric
a.
vary
Slope--Cases
diagrams.
for those
at intervals
equivalent where
differences
In Case VI the equivalent
,u.nit slices VI-13
that
VI-16
i, plate
in factors
to small
for Case V
in plate
for convenience
difference
mainly
analysis
pass through
using
VI-16,
the
height
of
in handling change8 of safety
water in between
in measureheight
is in-
the surcharge
pool.
EM 1110-2-1902 Appendix VI 1 April 1970 8.
Earthquake9
Case IV,
-Case
or Case
made
by using
used
to compute Finite
a.
VII.
V with
either
seismic
effective
Slices. in plate
analyzed
under
earthquake
graphical
Case I (end of construction) only
difference
is that Moiet
in this
the horizontal and saturated
submerged
unit
for
but only
Fh
is analyzed
weights
are
force
the finite seepage)
of analysis in plate
slice is
is baeic-
VI-15
except
is added. analysis in plate with
for Case VII using VI-18.
in computing
in computing
VI- 14
The
in plate
to the force
polygon.
Fi,
moiet
the equivalent
the
example,
loading.
of Case I given
J?i, is added
are used
In this
an earthquake
and the example
are used
..-
can be
Case V (steady
The procedure
is presented
weights
total
Case VII using
example,
An example
earthquake
weights
this
force
example
unit
The analysis
in the Case V example
method
of Case I,
Fh.
c onditione.
Integration.
integration
In
of an analysis
included.
analysis
VI-17.
earthquake
Graphical
consists stresses,
force
as that followed
that the horizontal b.
or total
A stability
is shown
the same
case loadings
the earthquake
method ally
This
while height
h1 .
VI-9 and
I
EM IliO-i-1902 Appendix VI 1 April 1970
ASSUME0 TRIAL FAILURE ARC
FIGURE
I. EMBANKMENT
SECTION (1) THROUGH ARE STEPS CONSTRUCTION
(5) IN
‘-
*ALL E FORCES ARE PARALLEL TOAVERAGE OUTER SLOPE BEING ANALYZED.
FIGURE
2. SLICE
WITH
2
0
2 G )jii
FORCES
0
% FD6
ti ii W
OF
SLICE
IS!= EARTH
FORCE
N = NORMAL
TO
AL = CO
LENGTH
OF
ACROSS
= DEVELOPED
SIDE
ON BASE
OF SLICE
SLICE
BASE
OF
COHESION
SLICE
FORCE
FO
= RESULTANT VELOPED
OF NORMAL AND FRICTION FORCE
90’
= DEVELOPED FRICTION
OF
ANGLE SOIL
= ARC
-10 1.2
1.4 TRIAL
LEGEND W = WEIGHT
50
TAN
OF
DE-
1.6
1.1B
E
F.S.
FIGURE 4. TRIAL F. S. VERSUS ERROR OF CLOSURE
36
: ERROR OF CLOSURE
FIGURE 3. COMPOSITE FORCE POLYGON FOR ONE TRIAL F. S.
INTERNAL
TAN # F.S.
MODIFIED SWEDISH METHOD FINITE SLICE PROCEDURE NO WATER FORCES Plate
VI-
I
EM iilO-Z-1902 Appendix VI 1 April 1970 .POOL
F
DS N
n FIGURE I. EMBANKMENT SECTION AND FORCES ON TYPICAL SLICE BEFORE
SUDDEN
BEFORE
LEVEL
+o
DRAWDOWN
W,Cl,‘~ (SATURATED WEIGHT ABOVE + SUBMERGED WEIGHT BELOW DRAWDOWN POOLi
Ws iUBMERGE0 EIGHT)
l
USING F.S. REQUIRED FOR CLOSURE.
P. BEFORE
XND F.S.
=
F.S. AFTER PROCEDURE TAN
4
ZW
SIN
=DEVELOPEDNORMAL
NO W = WEIGHT c AND SHEAR
Plate
OF
PORTION
SLICE
(UFING
TRIAL
b. AFTER OF COMPOSITE
FORCE
F.S.)
STEPS
IN CONSTRUCTION.
DRAWDOWN
POLYGONS
DRAWDOWN TO 2b)
+ XChL 6 FORCEBEFOREDD
AFTER
$!B AREFORTOTALAVAILABLE STRENGTH
VI-2
2.
b
l
DRAWDOWN
FIGURE EQUATION FOR (ALTERNATIVE
C .,(2)
DO
MODIFIED SWEDISH METHOD FINITE SLICE PROCEDURE SUDDEN DRAWDOWN IMPERVIOUS EMBANKMENT
EM iiiO-Z-1902 Appendix VI 1 April 1970 i FIGURE
I\\ FAILURE
I--_
I
I
1. EMBANKMENT SECTION
\
TAILWATER
_
ARC
BLANKET
\/I,
\-
,W,
I TOTAL)
U
&I-)
SLICE WATER
R3
lb)
WITH SLOPING SURFACE
FIGURE
2.
FORCES
ACTING
FIGURE
SLICE WITH HORIZONTAL WATER SURFACE
ON TYPICAL
SLICES
3. RESULTANT OF WEIGHT AND WATER FORCES
FIGURE 4. COMPOSITE FORCE POLYGON FOR ONE TRIAL F.S.
LEGEND
UF4= UL = uEl =
WATER
FORCE
ON
RIGHT
SIDE
WATER
FORCE
ON
LEFT
SIDE
WATER
FORCE
ON
BASE
OF
OF OF
MODIFIED SWEDISH METHOD FINITE SLICE PROCEDURE WITH STEADY SEEPAGE WATER FORCES
SLICE SLICE
SLICE
Plate VI-17
VI-
EM 1110-2-1902 Appendix VI 1 April 1970 DIRECTION
I
POTENTIAL
OF FAILURE DIRECTION
\ \
POTENTIAL
Of FAILURE
l
\
w3 (TOTAL) W6 (EFFECTIVE)
C
06
YF,,~
= J, W5 (TOTAL)
Fh3 ~~~
lb)
j 0 ) NO SEEPAGE FORCES (SEE FIG. 3. PLATE~-I) FIGURE
1.
FINITE
WITH ‘SEE
SLICE
SEEPAGE FIG.
Wj (TOTAL) = 4 wj FORCES
3. PLATE=-3)
PR_OCEDURE
DIRECTION POTENTIAL
OF FAILURE
r; (EFFECTIVE)
(TOTAL) cl DIRECTION 4POTENTIAL
e/
OF
/
FAlLURE
/ 2 e-F;
(0) (SEE
NO
SEEPAGE FIG.
=$h
(TOTAL)
(b)
FORCES
1. PLATE=-5) FIGURE
WITH
(SEE 2.
GRAPHICAL
INTEGRATION
SEEPAGE
FIG.
FORCES
zb, PLATE=-7)
PROCEDURE
MODIFIED SWEDISH METHOD FINITE SLICE AND GRAPHICAL INTEGRATION PROCEDURE EARTHQUAKE LOADING Plate
VI-4 VI-18
.-
EM :iiO-2-1902 Appendix VI 1 April 1970 (+I ii 40 W (-)
TRIAL
FIGURE
4
F. S.
3.
VERSUS
EAE’
TRIAL
F.S.
(+I
$0
t-1
WHEN: +hE’AREA = -AE’AREA TRIAL F.S. FOR WHICH XAE’ BALANCE OF INTERNAL SIDE
1
FIGURE
l
STEPS
2. AE’AREA
IN CONSTRUCTION
(-)AE’
(5)
UN IITS) FOR
DIAGRAM
WAE’, .
\,
(ARBITRARY IS F.S. FORCES
=0
CURVE DEVELOPED BY PLOTTING h’ AT SELECTED INTERVALS
0
IYl\ k”
--
TRIAL
FIGURE 4OTE:
ALL
COMPONENTS
ARE
IN
UNITS
OF OF
FEET
UNIT
SLICE
FORCE
I.
EMBANKMENT
FAILURE
SECTION
POLYGON
ha = h x - Y YBASE
SINCE
LEGEND h’
= HEIGHT
OF
rE’
= INCREMENT TO BALANCE WIDTH SLICE
%
= DEVELOPED
N;J
=DEVELOPED
= RESULTANT FRICTIONAL $ D = DEVELOPED
Fb
UNIT
WIDTH
SLICE
OF EARTH FORCE FORCE POLYGON
=
h XL YBASE
REQUIRED FOR UNIT ,
COHESION NORMAL
FORCE FORCE
OF DEVELOPED NORMAL AND FORCES ANGLE OF INTERNAL FRICTION
8 = ANGLE OF INCLINATION ARC WITH HORIZONTAL
OF
1
= cI F. S.
TRIAL
FAILURE
MODIFIED SWEDISH METHOD , . ,-RATION GRAPHICAL INTFC PROCEC XJRE -----NO WATER FORCES Plate
VI-19
VI-5
EM 1110-2-I Appendix VI 1 April 1970
902 CURVE DEVELOPED BY PLOTTING h’ AT SELECTED INTERVALS: BEFORE DRAWDOW LAFTER 0RAWcmw
,/P,
POOL LEVEL BEFORE DRAWDOWN
(00)
\
POOL LEVEL AFTER
1.Yr.s
AFTER
YSAT
DO
I/
In8 BEFORE
DCJ
h" = th, t h,, y' YBASE
AFTER
DD
h hl
IY
’ + h2
YSAT
q
Yt3ASE
FIGURE
I. EMBANKMENT
SECTION
-
40 R CD FOR
ZA ,E’
\ = 0
Nb 1 XYe*sEXCOs
a. BE FORE
FIG.
1
FROM 2a
h’ BEFORE
b. AFTER
DRAWDOWN FIGURE
2. UNIT
SLICE
FORCE
h’ AFTER
POLYGON
DO
DRAWDOWN
AT A
MODIFIED SWEDISH METHOD GRAPHICAL INTEGRATION PROCEDURE, SUDDEN DRAWDOWN ‘late
VI-6
VI-20
EM iiiO-Z-1902 Appendix VI 1 April 1970 OUTER SLOPE EMBANKMWT
OF
AL=~
cos 8 AL’=-!--
TANGENT TO Lit&Q SATURATION
COS
a
u2=h,ywA~ SATURATION
LINE U
PlEZOMETRlC LEVEL ABOVE FAlLURE ARC
SIN
(90
U2
- 8) = SIN
(90
t al
“we,&
U coS=
COS
a
hwy,,,A~-A~@ u= - a)
AL u =hwywA~'
.a)
SATURATION
L/NE
FIGURE
TANGWT
/ -
I. RESULTANT
TO SATURATION
PIEZOMETRIC ABOVE TRIAL
U FORCE
LINE
LEVEL FAILURE
h
I TRIAL
FAILURE
(0)
FIGURE
2. GRAPHICAL
DETERMINATION
OF U’ AND N’D
MODIFIED SWEDISH METHOD GRAPHICAL INTEGRATION PROCEDURE, STEADY SEEPAGE WATER FORCES Plate m-2 i
VI
EM
APPENDIX Wedge 1.
General.
failure
The
may
occur
proximated
termed
larly
applicable
and
a relatively
to a zoned
materials. of the
with
or
gravel core
with
shells
defining
the
are
not
amples
are
presented
only
Principles.
In the
into
three
segments
: an active
central
the
each
segment
plate
VII-
1.
along
the
failure
safety,
F.S.,
1 of plate block
are The
and
surfaces
sliding
most
critical
values are
and
controlled
and
cores location
of
imper-
embankments. are
shown
The in the
since
the
ex-
ex-
involved. mass
block,
as shown
the
embankments
planes,
soil
passive
foun-
inclined
and
boundaries
of cohesion
is usually
divided
a passive
wedge,
are
wedges.
The
in figures angle
by the assumed
assumed
be-
forces
on
2 through
of internal trial
4 of friction
factor
of
so that
‘D
tan 9, Consequently,
the
Vertical
separately
that
procedures
a central
active
for
of the
failure
method,
wedge,
of the
with
mass
the
VII-i.
considered developed
of the
stratified
impervious
given
portions
wedge
the
are
shells
emphasize
influence
embankments
to illustrate
Basic
tween
for
upstream
the
2.
in figure
and
the
necessarily
as shown
Examples
is particuouter
or
having
the
apof what
method
appendix
shear
a surface
cohesionless
in this
demonstrate
that
variations
This
to embankments
stability.
are
homogeneous
presented
boundaries
amples
on either
assume along
procedures
containing
and
within
foundation
embankment
cores,
located
its
of analysis.
method
impervious
cores
planes
rock
and
appendix
method
analyses
wedge
.,.
in this
These
resting
on embankment
central
vious
core The
application
the
the wedge
thin
VII
presented
of planes.
1902 1970
Analysis
in an embankment
by a series
is generally
dation
procedures
IilO-2.1 April
the
magnitudes
of the
- c/F.S. = (tan resultant VII-i
+)/F.S. earth
forces
EA
and
Ep
also
EM iiiO-2-1902 AppendixVII 1 April 1970 depend
on the
vertica;
trial
boundaries
constructing m-i,
block
(fig.
required.
VII-I)
tally
and
made
quired
earth
settlement subsoQ
only
trolledby vious
core,
near
the
Iayer a.
EA
from
surface
been
Active
Iies slope
force
be assumed
for
selecting in plate
of the
such
as a foundation
VII-2.
sliding
is
5, plate
This
factor
surface
being
wedges
of the
However,
are
re-
shown
layer
in plate
planes and/or
discussions
VII-2
the
center
is often
sliding
that
imperwill
follow,
of
con-
an inclined
In general,
by trial.
criteria
a variable
beneath
sliding
and
foundation
or from
occur
active these
differential
layers
will
critical
In the
layer.
zero.
and passive
criteria
settlement
be determined
A plot
in figure
_ is
the
where
The
location
of a weak
for
of soft
desirable.
to act horizon-
of safety.
the direction
be modified
maximum
must
factor
4,
factor.
consolidation
this
zones,
and
is
safety
should
bottom
has
minimum
and
weak
forces
of the active
only
The
the
locations
illustrated
embankment.
(fig.
AIf&
are
the
polygon
at which
Criteria
where
the
is assumed
trial
on are
of safety
to balance
makes
the
--
central
factors
factor
the
resulting
with
the
safety
as shown
forces
profile
apply
vary
As
for
not be obtained
to close
force
at the
3, respectively,
polygon
different
necessary
The
sign
force
of safety,
trial
Criteria.
AEH.
2 and
generaliy
with
acting
determu~ed.by
factors
required
to determine
force
are
the trial the
illustrative
are
trial
and
Various
passive
verse
magnitude
is that
Basic
3.
of
as
will
analyses
the
forces
wedges
in the
of equilibrium trial
earth
in figures
incorporated
analysis,
to determine
analyzed.
then
versus
resultant
as illustrated
is denoted AG
of safety
and active
and several
its
of
VII-i,
the
are
In each
plate
passive
A condition
trial
first
The
polygons,
and 4).
factor.
of the
force
of plate
the
safety
occur
a thin
weak
assumed. Earth
shown
in the
tabulation
in cohesive (plate
polygons equal
m-21, using
in figure
materials the
A general
(4)
Forces.
various
to 45O + (4b/2).
value
values When VII-2
for
1 of plate
or includes
maximum
rule
of the
selecting
VII-2.
a portion of CIA. sliding
EA
When
of the must
crest
direction
the
sliding or re-
be determined
As a first plane
the
trial,
is located
BA within
by can a
1110-2-1902
EM
Append& 1 April thin
inclined
slidin
core,
the
slope
of the
value
of
will
generally
govern
corresponding
value
the angle
of the
plane. (2)
The
maximum
determined when
using
(a) the
tire
active
(fig.
l(b),
active
plate
force
cient
KA
sumed
the
strengths
of the
dams
and
for
other
structures,
45O + +/2
active active
for
earth
force
of the active
of levees,
material.
For
earth
zone
through
which
the
rection
of the
accordance of the
forces
the
general
ac
are
necessary
plane
final
can
design
E rule
depend
on the
shear
embankments,
of dams
until
by the
and
the
and
de-
each
soil
maximum
total
the
value force,
earth
polygon.
to determine
at
for
active
the
force
and
within
resultant
l(c)
for
to be inclined
be varied
of the
analyses
l(c),
analyses
The
and E A ire assumed Al ’ EA2 ’ given in plate VU-2. Other trial
in all
the as-
(fig.
design’
passes
as shown
and
materials
analyses
in figure
active coeffi-
+D
be assumed
should
slope
friction.
in preliminary
surface
outer
The
of
of wall
VI,.l-3 en-
pressure
miscellaneous
as shown
resultant
with
angle
the magnitude
determined
earth
surfaces
surface
boundary
present.
be
(b) the
to the
the value
sliding
sliding
active
the
can
in plate
of different
9A
is found. To determine A the wedge must be subdivided at each
not
structures,
E
force
are
channels,
each critical
forces
However,
sliding
of more
parallel
is composed
active
sign
acts
as the
eA
materials,
EA
by obtaining 14 tables using
involved.
the
(c)
of
illustrated
is in cohesionless
(d) seepage
wedge
soils
design
procedure
slope,
pressure
the angles
V-U-2),
the
be computed
earth
and
stress
surface
and
also
of the
When
plate
sliding
VII-2),
from
EA
conjugate
is under
may
angle
(3)
the
wedge
earth
of
core
VII 1970
di-
to be in locations lowest
factor
of safety. Central
b. block
passes
passes cause the terial
through
through of changing
central type
block (or
(1)
Block. more
a single
than
should
(e.g.
be broken
failure
material
but
stress
strength)
the
one
material
normal
shear
Where
a different using
up into
as described
VII- 3
‘plane
beneath
or where
the
shear a composite
its
component previously
the failure
strength S and parts for
the
central plane
is used
be-
R envelope), based
on ma-
active
wedge.
WI)
..
EM 1110-2-1902 AppenGx VII 1 April 1970 Resultant sumed and
forces
to be inclined E
latter
but
P’ assumption,
overburden The
stratum
easily
strength
failure
plane
be as-
inclination
is equal
E
of
With
and
partially
stresses,
may
A
this
to the
of
vertical
Ep
to determine
Where
the
boundary resultant
to occur
the
is at the passive
between
the
lowest
is located
of the soil
the
in figure
a weak
plane
than
the is slid-
in the
effective
clay
normal
“switch”
occurs
at which
passive
the
of safety,
E
P
can
= 1/2
y h2Kp
1 t sin
+D
= 1 - sin
$D
VII-4
passive and central
VII-2,
trial
be determined
the will
usually
locations
block
are
in figure and 2(a),
toe
in which
wedge
material A in fig.
the
foundation,
as illustrated
in cohesionless (wedge
and
is near
plate the
block,
wedge
wedge
2(a), within
by a central
in which KP
because
stress
The
equation Ep
occurs
this
passive
shown
embankment
resistance
a case,
intersect. When
factor
a clay
sliding
high
at which
to be horizontal. wedge
wedge toe
case
active
the
point
example,
resistance
under
sur-
be when
this
the normal
(1)
along
is assumed
passive
The
materials
Forces.
boundary
quired
two
as in the
from
shear
whereas
be true.
the
Earth
is assumed
less
failure
In such
may
other;
by computing
for
surface
in the
offer
(for
material).
failure
may
normal
embankment,
the
this
a horizontal
materials
cohesionless
layer
reverse
Passive
be separated
3c(l)
the
can
to be horizontal.
where
different
along
be determined
direction
from
on the
be considered
between
material
envelopes
C.
the
“subblocks”
between
assumed
stress
also
resistance
the
sliding
these
intermediate
or underlying
effective
stresses
the
should
cohesionless
low
of the
normal
a boundary
in one
under
value
between
conveniently
the
case
shear
in the
can
more
overlying
partially ing
at any
are
parallels
lowest
on boundaries
stress.
(2) face
acting
of re2(a).
the vertical
plate graphically
VII-2)) or
EM 1110-2-1902 Appendix 1 April When of
the vertical
8
must
P
value
of
zones,
in figure
2(b),
as that
of
outer
slope.
The
trial and
plane of
the
with
parallel may
to the be used
(3) forces
fur End
to occur
of safety.
slope
core
in paragraphs
strengths
are
consolidation
Case
cases, Q
are
and
it may R .
embankment,
designations
for
for
be necessary Additional
The
described
force
to the
polygons
material
In this
stress
for
is cohesion-
are
trial
procedures
handling
following
paragraphs.
cohesive
main
Unit
text.
embankment
clay
complete
at the
to use
a design should
in Appendix
in paragraph 5
analysis,
foundation
end
and
foundation
strata
as
materials The
foundation
of construction.
be made
shear
S shear
soils.
in the
strength
during
In
construction
VIII.
main
R
when
intermediate
11 of the
is
embankments
of construction,
In the
or
of an core
weights
end
and
core
thin
for
at the
water
stability
examples presented.
VII-.3)
of safety.
for
in the
acts
(plate
factor
and impervious
of the
Ep
procedure
each
expected
VII-
case,
end-of-construction
shell
analyses
as discussed
are
VII-2).
impervious
be essentially
from
parallel
an angle
described
relatively
acts
and make
and
free-draining used
be used
Ila
Ep
t-o be the
embankment
Accordingly,
9 and
is assumed
of the
above
to those
as
sliding
for
cores
surface
a passive
Ep
1.t
inclined
for
will
Ep
applies.
embankment,
conjugate
are
location.
discussed
may
of
3a(3)
soil
the
plate
of a granular
correspond
7
and
cases
should
of the
8
design
strengths
tween
the
of the
and
some
2(c),
and P criteria
central
strengths
toe
several
ground
embankment
than
the (fig.
composed
strengths
the
---
values
a minimum
includes
along
the
trial
until
in paragraph
inclination
When
is stronger
to determine
used
wedge
If a central block is present, A’ is determined magnitude of Ep
outer
by the
both
Q
the
of Construction--Case
influenced
and
VII-2,
horizontal
various
embankment
with
is assumed
embankment,
of safety
passive
the criteria
to intersect
Examples
the
of the
factor
and
foundation
the
trial
When
plate
factors
is assumed
8p
4.
E
at the toe
each
be varied
sliding
same
less
-
should
Where
various
for
is obtained.
P
BP
shown
is not
be assumed
E
(2)
boundary
VII 1970
text.
be-
EM IliO-2-i902 Appendix VII 1 April 1970 Embankment
a. is equal
to or
flanking
a narrow
infinite
greater
slope
(2) than
illustrated
the
wedge,
lected
for
plane
to the
conjugate
be parallel determining
face
earth of the
force contained mined
is that
within from
(3)
force
Using
can
polygon
does
not
of safety
close
is used AE
cations
of the
active
safety
fat tor .
b. condition.will 4b(l)
plate
H
or passive
above
by the
force
to various
VII-4.
the
according
The
for
direction
passive
types E
to
the upper
passive
of material can
A
sur-
pressure
of the
and
of the
procedure
Because
Ep
is se-
is assumed
stress
several
i
factor EA
is
an
BA
safety
computation
wedges,
for
is
zero
force
by trial
and
AEH.
in figure and
passive
a portion
EA
as shown
as shown
and
When
is determined l(c),
When
figure.
be constructed
when
EA ure
active
trial
2 of plate
The
point
inclination
the
is horizontal, 2.
into
and
to be horizontal.
in figure
in this
the values
block
of safety
given
is divided
conjugate
example
is weaker condition
corresponding
earth
in figure
This
A trial
the
are
be deter-
diagrams.
central
tors
shown
in the
given the
is
the
using
that
wedges
each
A simplified
is assumed
wedge
is also
Ep
OA
by trial.
wedge.
for
shell
V.
a layer
mass
EA
since
slope.
Ep
Kp
force
strength
be estimated
in Appendix
failure
of active
earth
foundation embankment
contains
a passive
procedure,
and
passive
and
the
can
be found
be determined
outer
force
coefficient
The
stress
KA
must
of a series
can
to the
foundation
assumed
block, end
factor
, as discussed
the
The
Where
of a cohesionless
safety
of safety
of safety.
sliding
the
= 8
VII-4.
(I)
strength
where
the upper
active
of the
F.S.
a central
factors
the
Core.
core,
factor
in plate
active
trial
central
conditions
shell,
Central
than
equation
For
the
with
the
force
wedges of the
active
by constructing
Ep,
a force
in figure A plot 4, plate
3 of plate of
AEH
VII-4,
polygon should
a force
trial the
Other to find
fac-
factor
trial
the
through
polygon
the The
versus
closes.
passes
for
VII-4.
to obtain
be used
plane
polygon
IO-
minimum
the core,
as shown
in fig-
VII-2.
Embankment normally
with
Inclined
be located
Core. in the VII-6
(1) lower
The
failure
strength
surface core
material.
for
this While
iiio-2-1902
EM
Appendix J April the
zone
cause
of minimum
consolidation
takes
the
failure
surface
ary
where
the
strong
will
(2)
wedge
are
Ep
cussed
wedge
base
plane
should so that
the
shown
stream
gravel
normal
stresses,
the
in plate filter but
the
are
the
points.
FA(Q)
the
two
the
using
strength
used
in the
vector
A similar
shear
selected,
the
strengths
and
the
core
and
result
S
strength
in the
the two
same VII-7
S
intersections locates of
EA
low min-
surface
of locating trial
the
wedge
to
with
the
of the
gravel
intersection the
through
E
A these
of
EA
the
point
(point
at
material;
The
is
locations
strength
VII-5.
curves
under
sliding
of each
A(S) is drawn
value
In
is constructed
F
curve
through of the
developed
shear
in down-
core
active
polygon
strength
sur-
therefore
Several of the
in plate
a smooth
is drawn
intersection
the
example
developed and
shear
active
sliding
of the
of the
VII-5.
VII-5,
is obtained.
A method
A force
as dis-
of the material
the weight
developed
of the
polygon,
The
1 of plate
earth
developed
loads;
of The
2, plate
lower
higher
toe
dam.
of the
trial
force
VII-5.
5, the
of the
the
strength
core.
failure-
of the
plane
the
portion
is in the
VII-
in figure
strength
upper
is determined.
case
curve
the
is as
assumption,
earth
under
bound-
in plate
toe
zones,
shear
outer
trial
magnitude
having
shear Q
the
sliding
active
S
outer
as shown
trial
is true
when
of the
for
each
the
the
portion
1) are
location
vectors.
than
in figure
location
for
the
reverse
lower
of each
friction
is located
VII-5,
is obtained
C in fig.
Q
When
of the
stress
and
resultant
is less
is illustrated
filter
of 1.5.
maximum
point
developed
appendix
faces,
1, plate
the
conjugate
material
break
trial
the
at the
is illustrated
and
in the
and
each
from
wedge
be-
foundation
portion
with
be located
filter
right
to coincide passive
If the
.:,
of the core,
the downstream
in figure
embankment
in the
the
shown
than
along
case
of two
resistance
B, and
This
boundary
imum
(A,
shell.
section
factor the
strength case
in the
middle
here
is obtained. the lower
3c of this
safety
to lie
shell,
of the
the
rate
the
determined
is along
assumed
is assumed
in paragraph
a trial
face
than
near
at a slower
force
embankment
of the
force
place
driving
be entirely
passive
inclination
for
largest
In the
is probably
is normally
as or stronger
surface
the
strength
VII 1970
of vector
and where
D in fig.
1). 4b(2)
EM 1110-2-1902 Appendix VII 1 April 1970 From
this
drawn
to the
plate
point,
VII-
sliding
5).
which
the
which
sliding
wedge
and
a line
occur block
forces
AEH
required
plotted
versus
trial
(3)
If the
shell, 5.
the
are
are
semipervious.
central
shell
described
required
when
in the
can
portion
foundation
layer,
embankment
having
semipervious
the
into shell
drawdown of the
a passive material flow
boundaries
net
block, it may
semipervious,
to evaluate between
The
the
seepage
the wedges
8
the
a relatively
infinite
is not will
1, plate
slope are of low
as strong pass
VII-6,
failure
an active
central
genand a
or gravels
be necessary
the
is not
analyses
surface
forces.
and VII-
and
materials
of free-draining
that
potential
the
materials
Stability
layer
shear
method,
unless
of sands
sliding
to
analyses
when
factor
in figure
shells.
weights,
shell
using
a thin
are
embankment
drawdown
detailed
trial
the
forces
Sudden
is composed
block of safety
In the wedge
safety
The
to be 1.62.
be analyzed
However,
a central
wedge, is
not The
of the
active
drawdown
free-draining
as illustrated
the weaker
vided
(1)
contains
of
foundation.
in sudden text.
factor
unit
be approximated
shell
foundation
the
by seepage
need
V.
upstream
horizontal
main
foundation.
in Appendix
If the the
case
the
is 1 of
of
left
central
than
Appropriate
having
this
the
shown
strength
Core.
to the for
the
is
through
influenced
materials
the
permeability. shell,
and
is present
method
of the
Central
for
5, where
to be used
embankments
core,
cohesionless
the
with
for
polygons
pass
and
right
3 and 4, respectively.
shear
will
A(S) E in fig.
to the
polygcns
analyzed
a lower
Ilb
shell
layer
surfaces
are
force
in figure
assumptions
in the
critical
force
II and III.
in paragraph
Embankment
The
in figures
the
surface
forces
weak
shown
factors
passive
narrow
core.
to close
and
erally
in the are
active
a.
filter
in the
F
vector
D to point
gravel
has
described
point
lie
foundation
design
from
would
sliding
and
line
friction
surface,
Drawdown--Cases
strengths,
strength
sliding
the
failure
S
E on the
safety
for
trial
Sudden
point
of sliding
central
forces
(dashed
locates
would
balance
to the
surface
This
plane
parallel
through for
mass
wedge.
block
trial and
an is di-
Because
to construct
Various
as
a
locations various
EM 1110-2-1902 Appendix 1 April inclinations
of the In the
(2; wedge
and
The
planes
block
doing (4)
of the
safety
factors
versus
trial
are
tried
factor flow
for
safety
of 1.12.
safety
for
bankment riprap
on the
ation
in the b.
clined
core,
outer
outer
the
is
trial
V, results
in a factor
outer
surface
the
approxi-
procedure
slope, of the
central of 1.3.
VII-6
the
from
for
outer
to a failure
for
of 1.28;
has
hor-
the
horizontal factor
a low
surface
should
re-
equation
for
AEH trial
lower
of
factor
through
is an appreciable
of riprap
the are
an average slope
of
of the
1.07
are
Various
A plot
of safety
with
block
locations
using
ranges
If there
the
A check
slope,
weight
point
The
obtained.
of safety.
slope
for
4 of plate Other
as compared
slope,
inflection
2 with
of safety
embankment
foundation.
the
sliding
planes.
and
in figure
factor
the
drawdown
failure
factor
wedges.
to the
Therefore,
trial
passive
location
trial
at the
in figure
of forces
is shown passive
the
stress
wedge
a balance
parallel
the
thickness
be taken
into
of em-
of
consider-
analysis. with
is assumed
because
be checked assuming
Inclined
the
shear
forces
prior
with that
the the
(1)
Core.
to be located
by seepage
of the
a trial
flow
not
also
for
l-on-3
shell
should
Vu-6
the upper
the upstream increased
active
for
Embankment core
embankment;
of the
the
VII-6.
the
in Appendix
the weak
the
.,
toe
shown
for
and
of the
sudden and
be assumed. between
along
normal
envelopes
the minimum
given
to 1.17
the
in plate
until
active
portion
of safety
must
boundary
strengths
along
of safety
to determine
flow
shear
stresses
3 of plate
of the
izontal
S
strength
polygons
factor
(1 on 3.5)
the
to be at the
by comparing
force
in figure
quired
or
is demonstrated
shown
locations
R
normal
The
VII-6,
in plate
is assumed
shear
this
planes
are shown directly below figure 1. A trial P deg is assumed for the active sliding plane,
use
effective
sliding
E
composite
mate
passive
shown
is established
of the
for
for
BA = 33.5 (3)
and
example
central
computations with
active
VII 1970
along
of this
to drawdown. surface
along
VII- 9
sliding
the boundary
strength
sliding core
The
the
surface between
portion
in the the core
of the
However,
surface
and is
stability
a.t the downstream sliding
core
in-
boundary
is fully
5b(l)
EM 1110-2-1902 Appendix VII 1 April 1970 consolidated
under
When
the
sists
of an active
inciding The
foundation
with
are
the
The
with
the
passive
pool
level
for
of the
base
upstream
slope
passive
trial
or below
slightly
higher
(2)
the
than
is based
and
WA2)
fill
and
(WA3)
above
the
shell
moist.
It is assumed but
does
The
induced
and
submerged This
uA force
not
(3)
weights need Figure
in figure
for
the
sliding
the
case (4)
will
5b(4)
shell
Curves
sented
that
EA weight
increment
of
created
Ep
and
by the
the
resultant
contribute EA
a major
for
various
A condition
VII-7. analyzed
exists
trial
a factor
will
from
filter of the the up-
submerged
induces
pore in the
between
polygon
be
frictional
weight
strength
to pres-
core. the
in figure
moist
4 by
as can
be seen
from
of
and
change
in
are
pre-
UA
portion
of
factors
of equality
for
level
drawdown,
difference
force
computed,
that
sudden
of shear
and
pool
and
the moist
of weight
the
active
7), the
fill
in weight
in the
be explicitly
kips)
surface
gain
is represented
(492
5, plate
immediate
lowered
of safety
VII-
rock
During
added
4 shows
level.
level. changes
force
pool
leve 1 and
is obtained
drawdown
4, plate
in fig-
critical
the
co-
force
to intersect
factor
pool
level
the
the
of the
pool this
thus
con-
VII-7.
passive
of safety
actual
(fig.
plate
the
between
lowered
force
wedge
be located
level,
this
any
not
and
above
pressure
force
of the
critical
submerged
low
cause
pore
polygon.
weight
the
passive
as shown
factor
estimated
b e 1ow the maximum
filter
trial
pool
mass
I,
and
forces.
failure
assunlption
boundary
of the
of the
BP
should
lowered
for
on the
stream
sure,
each
of the vertical
the active
FA
for
seepage
in figure
wedge stress
by
the
toe
as shown
of safety
critical
the
submerged,
location
that
In evaluating
force
top
If the
with
conjugate
factor
and
embankment,
passive
completely
at the
wedges.
is above
of the
condition
wedge
the
wedge,
the
critical
material
embankment
using
each
than
a passive of the
most
of overlying
stronger
toe
determined
3.
(wA1 rock
is and
inclination
EP ure
the weight
the
the
E
A of safety
between
of safety
Ep equal
and to 1.23
EA in
illustrated. If the
be in the
shell
is
foundation
stronger and
than full
the
foundation,
drawdown VII-
should 10
the
passive
be considered.
sliding If high
plane
illo-
EM
2-.1902
Appendix 1 April tailwater
conditions
downskream
toe
Partial
6.
stability
for
Pool,
passive
sudden
mined
pool
by trial.
scribed a.
elevation
with
in paragraph
Either
on the
magnitude
S or of the
effective
the
Embankment
embankment 8.
with
with
an inclined
The
embankment
inclination
of the
passive
for
a trial
factor
of safety
the
sudden
drawdown
of safety the
is obtained
lowered
intersect
pool
and
pool
elevation (2)
passive
(3) ure
in figure The
shown
Core.
slope
moist
passive
each
(1)
is
plane
to the
right
core
is used,
to
A stability
analysis
of the depending
in figure
for in
1 of the
plate.
The
force
E
critical
each
condition
for
completely
should
of the vertical weights
earth
2.
trial
and
be located
boundary
are
used
As
thus to
between
below
the
P in
factor
submerged,
of safety
an
is shown
in figure
top
weights
level
and the passive P determined as shown
Submerged unit
de-
a horizontal
8
factor
at the
are
is similar
trial
foundation
shown
wedge
trial
that
at the
of the
on a strong
most
be deter-
case
used
except
the
partial
above. of.figure
1, plate
W-I-8,
on the computing normal stresses R + S strengths. Composite of S or 2
for use
4, plate
safety,
for
Computations
determining
the
wedges.
and
procedure
shown
level
the upstream
active
fied
with
the
above
stress.
section
case,
must this
the
resistance
elevation
for
procedure
strength
of 1.5 are
a pool
strengths
The
normal
sliding
and
elevation
embankment
shear
core
reduces
in weight
critical
appendix,
the
Inclined
reservoir
cases,
shear
Core.
within
RtS 2
.L
of the
text.
4a of this
is assumed
pool.
this
main
Central
A static
In many
and
a check
be made+
of reduction
is critical;
of the
operations,
IV.
because
assumptions
Embankment
VII-
should
to buoyancy.
Ilc
line
b.
drawdown Slope--Case
due
in paragraph
saturation
spillway
slope
Basic
discussed
during
Upstream
wedge
conservation
plate
exist
of the upstream
of the
that
will
VLI 1970
illustrate
trial
a simpli-
failure
strength
planes
for
envelopes
are
3.
value VII-g.
of
E
The
in figure
A
is determined
from
comparison
of
EA
5, indicates
that
the
VII-
11
a force and factor
Ep
pal:-gon
as shown
versus
trial
of safety
for
factor the
sliding
in figof
EM IliO-2-1902 Appendix VII 1 April 1970 surfaces
analyzed
(4)
This
case
at the
downstream
check
for
core
is
1.51.
should face
a more
pool
the
the
The
pool
the
level
analyses
overlying
is weaker
be in the
foundation,
and
block
Steady
reduces
in a manner
Seepage
with
the weight and
the water
thus
active
sliding
at several
should
weights
in the
are
discussed
slopes
plane
locations
assume
corresponding
bility
of the
hesionless
the
to
that
the
to the
criti-
shell,
and
the
draining,
the
factor
If the
on a strong
F.S.
line
a
seepage
by hydrostatic
At the
shear
core
same
the
time,
impervious
strength
to use
with
only
shell
surface
be expressed
= b tan
is narrow
foundation, If the
sliding
can
Steady
against
be examined.
of safety
V.
saturation
(1)
critical
using
VII-6.
-Case
and
plane
text.
Core.
need
in plate
horizontally
main
sliding
is determined
criteria
rests
passive
is reduced.
act
of the
Central
shell
the
Basic
embankment
downstream free
pool
Iid
the
Pool-
below
direction.
with
shown
resistance
reservoir
in paragraph
and
mass
shell,
resistance
Storage
shearing
of the
and
passive
Maximum soil
downstream
steep
the
the
to that
frictional
Embankment
a.
than
similar
of the
forces
core
outer
under
foundation
uplift,
with
condition.
If the
central 7.
core
assuming
elevation.
(5) will
be analyzed
of the
critical
is consolidated
cal
also
the
material
is the
slope
stais co-
of the
as
+
where b = cotangent + = angle Where
cores
critical trial.
Where
shell
material,
shell
just
of internal
are
sliding
of the
wide
or
surfaces the
above
shear
the the
downstream friction
embankment of the
foundations may
pass
strength
weakest foundation,
shell
are
weaker
through
these
of the
horizontal slightly
VII-12
within
material than
foundation sliding
slope
the
zones
and
is less surface the
shell,
may
foundation
the
must
than
most
be found
that
by
of the
be either
in the
layer,
or at the
EM
bottom
of the
strengths. block
foundation
An example
are
divided
strength
2, and
should
be used
(2)
into
is not
the
entirely-
E Al
must
change.
are
the trial
above
the
for
spectively, The
assumed varied
(for
factors
from
figure
6 that
dation.
Conditions
a.
are Steady
a condition reservoir change
factors
where
the
shear
shown
in
central
strength
based
However,
0 Al
example,
and
using
the
is shown are
EP
eA1 only
a value
of
of the
active
completely
chart
in plate
in figure
shown
of varies
portion (or
force
on the weight
Values
that
shell,
resultant
submerged
forces and
active
of safety.
When
be computed
= 50 deg)
is
BA2
EA
for
the
of the
of steady quickly seepage
value
1, and
in figures
for
lowest
the
Inclined with
pattern
factor
active
wedge
eA2
A plot
of
EA.
6, plate factor
VII-12. the
4 and
cases
has to the takes
at the
5, re-
for
such
place VII-13
EA
must
and
EP
is 60 deg.
steady
seepage core
the be versus
be noted
case
is not
on a strong
of construction
or
foun-
sudden
draw-
applies
after
a design. VI.
established
surcharge
which
of safety
Pool--Case been
with
It should
upstream end
varies
VII-9.
The
an inclined
Surcharge
rises
safety
Cores.
either
seepage
trial
of
in figure
critical with
each
shown
with
Seepage
in the
and
cohesionless
VII-9)
in the
is completely
hydrostatic
existing
usually
used
of safety.
can
in the
or by trial.
of safety
an embankment
pool
VII-11
maximum
of safety
for
each
of the base the
critical
.... . .
shear
wedge
are RtS 7
or
of the
factor
of
Embankment
b.
and
VII-9.
inclination
trial
down
BA2
value
trial
EAl
magnitude
to obtain
S
, located
for
material
of plate
(3)
the
3, plate
trial
of the
Al
maximum
plate
line)
determination EA
where
(fig.
factors all
seepage
of
active
diagrams
graphically F Al
from
in cohesionless
loads
at boundaries strength
portion
the
of
wedge
values
wedge
be determined
is used
normal
The
sections
to determine
active
65 deg
VII-9.
Composite
submerged,
for
the
given.
and direction WAl can be determined slightly
upon
in plate
intermediate
computations
Since
depending
is given
parameters
figure
The
layer,
iiiO-2-.I902 Appendix VII 1 April 1970
pool because
This
case
at a given
pool
level,
level,
and
no appreciable
of the
short
duration
the
at the
EM iliO-2-1902 Appendix VII 1 April
1970
higher
level.
narrow
This
central
used
for
in the charge
case
that
portion
the
storage
analysis
of the pool
steady
9.
Earthquake.
in the
cient
4,.
moist
unit
water
above
forces
are
the
central
The
VII-10
weight the
above
embankment
computed block,
individually and
potential
included
mass
W
on the
saturation
In the for
in the
the
times
wedge
unit does
weight pool
respective
force
of this applied
main
text,
it is as-
force
weight
not
Fh
seismic
acting
is equal
below
passive
and
the weight
horizontal
polygons.
to
coeffi-
include
the
of
and
been
analysis, wedge,
14
sur-
has
This the
active
VII-
the unit
force
mass.
but
the
AA example pool
saturated
line,
from
horizontal
failure
criteria difference
surcharge
of the
an additional
slope.
the
a surcharge
iif
is based
thrust and
having
strength
V; the only
of moist.
in paragraph
soil
Case
between
dams
shear
polygon
VII-9.
sliding
the
force
in plate
of the
W
and for
instead
shown
to rock-fill
horizontal
zone
imparts
of the
weight
the
where
discussed
of sliding
given
wedge
submerged
example
weight
VI
active
earthquake
direction
Case
upstream
in plate
As
the
to the total
to the
of analysis
to those
in
pervious
seepage
that
identical
becomes
is given
applicable
procedure
is that
is added
the
is especially
The
are
analyses
pool
sumed
cores.
this
two
analysis
of
seismic wedge,
and
EM
I
’
I
I
’
&,,
6, = &, t ARC=
t
FRDM
TABLE
4TAN
A-73,
JUYIKIS
EARTH
0.6
0.7
’
I
‘40
PRE6SURE
0.6 J
OS J
1.0 I
4s
40
36
30
26
20
i-
0.5
0.4
0.3 I
iiiO-2-i9b2 Appendix 1 April
DECREES
t 8, [TAN
COEFFICIENT
14,
+ B, + CDT
TABLES
4,1)+ (196Zl.‘4
eA VS 4D FOR COHESIONLESS SOIL, COULOMBACTIVE SLIDIN PLANE E FOR ACTIVE WEDGEBENEATHNEGATlVESLOP1 Plate
VII-
35
VII-
ii
VU 1970
EM
APPENDIX Evaluation
1.
Basic
fected
Considerations.
primarily
When
induced
generally
not
bility
the
to:
age
construction
(a) provide
placement,
or
such
are
(c)
or
temporarily
pore
water
may
pressure
and
should
be regarded
as an integral
design
expectations
and
and
foundation
2.
Development a.
tion
in either
of Pore
Water
The
development
the
foundation
properties
and
struction.
Piezometer
during
Pressure
the
The
rate
of fill drain-
interpretation during
design with
sta-
be neces-
Emergency
of stability
of
construction
to assure
actual
that
embankment
observations
Construction.
water
pressures
embankment
of drainage
predicted
During
of pore
or in the
the amount
with
depends
or consolidation made
magnitudes
during
during
to assess
upon
the
occurring
construction
construcsoil
during should
in a general
way
conbe
stability
construction. Embankment
b. developed depend
primarily
Factors
saturated
(f) number
embankment
characteristics
(d) internal of construction
in pore
pressure
(1)
Pressures.
compressibility,
sections,
involved
Water
on (a) fill and
impervious
struction,
Pore
in partially
permeability, or
it may
operations.
consistent
is
properties.
General.
compared
and
of embankment are
in either
the
evaluation
placed.
of embankment
be considered.
assumptions
of fill
(b) decrease
fill
part
is af-
construction
measured
be made,
slopes,
also
during
analyses
should
discontinue
as electroosmosis
measured
pressures
flatten
construction
by the weight
stability
additional
period
berms
low,
water
high,
during
induced
are
If pore
Stability
stability
pressures
pressures
a problem. or foundation
during
of Embankment During Construction
water
water
embankment
sary
-
pore
VIII
Embankment
by pore
li10-2-1902 1 April 1970
Pore
materials
water during
such
as water
(b) embankment
height,
drainage seasons, development VIII
-1
provisions, and
pressures construction
content,
density,
(c) size (e) rate
(g) climatic
in embankments
of core of con-
conditions. and
means
EM 1110-2-1902 Appendix VIII 1 April 1970 for
estimating
Corps
construction
of Engineers
(2)
pore water pressures are 15 and are reviewed briefly
report
As additional
fill
is placed
above
following
effects
can
pressed,
thereby
reducing
its
solution
of air
in the pore
water
pressures
are
causes
additional
decrease;
(c) pore
stresses
are
increased
caused
by compression
weight
of overlying
and
partially and
pressures.
air
The
by loading
shown
in plate
(3) more
tigated,
are
may
Where
stability
under
construction
periods
an example.
strength
is taken
into
water.
higher
than
pore
equal,
pore
water
and water laws
taking
when
increase ness
in effective
of the
fill
placement
that
otherwise
2b(3)
no fill
soil
(i.e. is
is placed
results
consolidation
stress.
Bishop
decreases
resumed,
would
have
the
pointed
the coefficient induced
developed.
pore
out
pore
this
pressures
are and
and into
inves-
occurring
between
pressures
volume increases
of compressibility)
A procedure VIII-2
that
or
occur
is being
in soil
is
is taken
conditions
in a decrease
place
may
be estimated from procedures originally developed by the Bureau 17 18 Dissipation of pore pressures and extended by Bishop. mation periods
are
or in two
water
embankment
for
pressures
in stages,
consolidation
soil
are
air
pore
of pore
the
in the
and Henry’s
slowly,
unless
Thus,
assumed,
drainage
construction
account,
volume
decrease
pressures
without
drainage
from
pressure
stresses
evaluating
with
stage
pore
of Boyle’s for
is com-
(d) intergranular
is ignored,
be too high
air
It is generally
soil
in shear
soil
and water
constructed
soil
to the volume
somewhat
significant
pressures
gain
actually
are
and
by effective
saturated
1, together
seasons,
the
air
procedure
pore
and
pore
pore
the
and an additional
in the
during construction 16,17 from application
embankments
water,
pressures.
that
a partially
construction
account.
and air
Brahtz-Hilf
VIII-
When
estimated
partially
water
increased
corresponding
is supported
material,
compacted
increased;
of air
in a recent
below.
saturated
in the
(b) the
and solution
pressures
estimated
conservative. caused
fill
If drainage
pressures
volume;
conservatism,
pore
(a) the air
by an amount
by pore
simplicity although
be observed:
partially
discussed
may
of Recladuring and an the
stiff-
and when lower
an example
than are
those shown
iiio-2-1902
EM
Appendix 1 April in plate
VIII-2
complete plate
for
dissipation
VIII-3 (4)
large
for
The
solution, and
air
not
constant
partial
is relatively
slow
out
saturated
soils
has
Foundation developed
nificant
The
for
suggested
Pore
Water
in foundation
to the
following
not
stages
when
change
in rate
Pressures.
equation,
fill
A .and
which
are
dations the
stress
are
experimentally
illustrated
are
ratio
B
assumed
of induced
VIII-4
saturated
and
pore
water
for the
value
pore
coefficient of partially
water
presthat
sig-
can be estimated 20
pressure
conditions. of
B
to the
can
coefficients,
In general, be taken
increase
foun-
as one,
in major
so
principal
becomes
A43
A=At(i-A)= A”i
The
to the
- Au,)]
failure
pressure
therefore,
assuming
by Skempton
determined
in plate
is,
pore
is placed,
developed
Au = B [Au3 + A(Acri where
Excess
embankments,
as the
.
decrease
of consolidation
(1)
beneath
into
pressures
to apply
in
19
by Gould.
occur
forced
of consolidation factor’*
and
is relatively
and pore
with.
interval.
soils
is compressed
soils
seasons
in this
saturated
A “gas
soils
does
construction
coefficient
the
saturated
pressures
air
in later
been
consolidation
according
when
assumed.
to account
between
of pore
of solution.
as is often
in partially
of partially
period,
of consolidation
C.
dissipation
loading
comes
pressures
pressures
of consolidation
the
and
pore
of pore
rate
during
sures
evaluating
VIII 1970
value
of
A
should
correspond
1
to the
field
value
for
A=3 F,
the
ratio
of
1 lateral can
to vertical be taken
overlying
fill
total
stresses,
as approximately since
impervious
but equal
this to the
materials VIII-3
is seldom stress are
done. imposed
usually
The
value
of
by the weight
restricted
to the
Au1 of central 2c(i)
.-.-
EM 1110-2-1902 Appendix VIII 1 April 1970 part
of embankments
dependence the a
soil B
of excess
(2)
in a recent
Corps
approach
pressures
procedures
The
3.
tests
that
and
are
may
b. the
and
and
the
observations
also
assuming
were
for
later
overconsolidated
provide
the
Undisturbed should
samples
be taken
large
testing
of three
or four
soil
samples
at other
elevations
and
depths
should
piezometric
data
in stability
may
to estimate
be used field
values
studied
one-dimensional for
for
estimating
vertical
values
be compared was
were and
as-
predicting the
compression
combined
analyses.
construction
as a basis for
be selected
field
may
during
Procedures
extended
be made
materials.
or highly
are,installed
loading
loading.
must
foundation
stability.
if consolidation
with
pore
alternative
Piezometers
a.
These
of consolidation.
of consolidation
con-
field developed
radial
19 Plots pore
partially
increases
of
in unknown.
locations
in using
fill
hard
Additional
depth.
variation
such
compression
Piezometer
future
for
tips
triaxial
in design
suitable recourse
having
shales
piezometer
a common
their under
drainage.
are
the
assumed
by Gould“
dicting
VIII-5,
underestimate but
embankment
to permit
coefficient
coefficient
C.
plate
stress
in foundations of earth dams 21 Data presented in it sug-
foundations,
of Piezometers.
extrapolation
solidation
and
substantially
be true
as clay
be desirable.
values
sumed,
The
preconsolidation
Consequently,
also
controlling
Piezometer
may
at sites
may
Uses
for
from
to minimize
above
developed.
classed
in diameter
also
with
this
in which
specimens
report.
in shale
been
and
soils
of Engineers
measurements
not
means
enough
for
not
Installation
of the
VIII-4,
observed
given
to which
principal
plate
pressures
developed
have
extent
clays
ia,
on the
correct.
of 1.0.
the
to field
is reasonably
pressures
by figure
of pore
that
approximation
water
A summary
is given
water
this
pore
is illustrated
value
gest
where
of induced pressure saturated,
as loading
pore under the
continues
pressure
versus
increased ratio
fill
of induced until
all VIII-4
pore
fill
heights. pore air
load
can
be used
However,
where
soils
to applied
load
pressure is dissolved;
for
thereafter,
pre-
iiio-24902
EM
Appendix I April the
additional
pore
water
Therefore,
weight.
tions
would
would
not
pressure
linear account
extrapolation for
this
Evaluation
(4)
The all
such
items
of fill
early
relation
and
toes,
evidence
foundation,
the
added
,,.;;
fill
piezometer
prior
fill,
bridges tifying
and
observa-
to saturation
and
(e) horizontal to outlet
abnormal
behavior
(2) construction
consist
of stability
lated
to pore
water
such
analyses,
in current tant
use
factors
such
mate
strengths
it may
from
embankment
tailed
procedures b.
dure, natural
Method undisturbed moisture of back
be obtained pressures
only
be desirable
in the
lower
loading, only A:
along
peak
content
Shear are and
density
embankment been
zones
and
The
measured. VIII-
5
making
procedures ignore
impor-
surfaces,
ulti-
of stresses
make
even
the
most
de-
conditions. (1)
In this
construction Q
in situ
re-
procedure
failure
Procedure.
under
one
redistribution
during
to determine
pressure,
than
for
All
to actual
obtained
or indirectly
paragraphs.
that
show
during
procedures
potential
iden-
occurring.
stability
several
aspects
Strength
will
Therefore,
values,
similar
approximations
samples
have
than
and
In Situ
from
strain
for
are
directly
more
following
of
criteria
in behavior
various
to use
embedded
observations
are
is questionable.
as nonuniform are
are
embankment
specific
embankment that
(c) ver-
of foundations
changes
assessing
movements
in conduits
repeated
analyses
described
that
Although
There
stability
are
towers. be given,
for
pressures.
embankment
movements
the
con-
pressures,
indicators,
beyond
of joints
or anomolous means
where
at and
slope
vertical
cannot
should
to piezometric
with
movements
control
principal
and
construction
(b) horizontal
observed
of ground
and
deformations
The
Considerations.
during
in addition
as those
horizontal
leading
if continuing
stability
movements and
Basic
of settlement’plates,
such
horizontal
a.
including,
as (a) movements
(d) vertical
in the
Stability.
of embankment
relevant
and
tical
pore
of a few
nonlinear
of Embankment
evaluation
sider
cation
equals
be unconservative.
4.
-
approximately
VIII 1970
test shear
tested
at
conditions,
without
appli-
strength.
Samples
need
foundation
shear
and
proce-
strength
strata
in which
envelope
should
high be
EM 1110-2-1902 Appendix VIII 1 April 1970 determined
from
text.
The
soil
zone.
Each the
in the
samples
sample
manner
should
shown
be obtained
be tested
estimated
vertical
stress
content
and density
at various
at a single
apply
in figure
2 of the depths
confining
main
in each
pressure
under
the
in situ
condition,
only
to the
depth
at which
of
since the
its
sample
obtained. (2)
Stability
design
for
along
the
the
sliding
to the weight and
sides
are
construction
trial
total
forces
analyses
the
according the
results
should
water
was
test
undisturbed
0.8 times natural
the
surface
of the
resistance need
above.
in each
be taken
the
to those
shearing resistances
These
analyses
into
determined
the
surfaces.
account
only
driving
Water
since
in
consider
in computing
sliding
made
resistance
shear
slice
the
similar
.that
on the
along not
are
except
described
and water
slices
that
is based
procedure
shear
made
condition,
of soil
the
then
they
forces
are
on
internal
forces. (3) time
The
analyses
described
the undisturbed
height
samples
of embankment
performed
at the
consolidation
compares
values
implicit design
of
Q
required,
the
since
be
overburden
any
subsequent
(1)
Pressures. during
strengths
for
pressures
are
field
evidence
for
construction
This
pro-
construction
the
with
construction less
of embankment
other
should
is ignored.
Pore
pore
at the
an increased
tests
0.8 times
measured
shear
unless
for
Q-type
equal
period
evaluation
embankment
is conservative
pressures
additional
is not
additional
This
If measured
analyses.
as sumed,
struction
use
to the
If analyses
and Design
water
in the
obtained.
placement
Measured pore
onIy
pressures
height. fill
apply
desired,
confining
the
B:
were
also
fill
during
cedure
plicitly
the
higher
Method
C.
tion
are
in which
stresses
above
than
stability fails
condithose
im-
during
con-
to support
these
observations. (2) plies the
that
use
both
embankment
Q-type 4c(2)
The
laboratory
of Q-type
negative and
test
and foundation.
tests
can
results
positive
pore The
pore
be approximated
vm-6
water
condition
pressures
water from
are
pressures Q
and
design developed
inherent S
envelopes
imin
in the
I
EM iiio-2~1902 Appendix 1 April and
plotted
versus
plate
VIII-6.
can
be simply
installed
compared
As
to the
However,
since
tive
pressures,
of the S
with
pore
formed
can
are
time
consuming,
a
values
will
dixes forces used
on the only
where not
(2) segment
and
can
.;;
pr.essures
piezometers plane
are
for
the
the
tests
construction
for
type
test
field
method
forces
be interpolated
measuring
nega-
expectations
strengths
are
such
as method
A,
may
be
portions
higher
than
should
be
clay
analyses slice
foundation shale
from
embankments
the VIII
and
bottom
piezometer -7
test
re-
the
test
and
not
often
in both
the
labo-
pressures
of IOW
Water
in Appen-
earth segment
not
spec-
are
described
are
be per-
Considering
have
tests
complicated
pore
Method
a
of the
more
be used
or.wedge
materials
sides
ends
including
investigations
Q
tests
analyses
on procedures
of each
on the
are
should
Wedge
the
and
condition
or
laboratory and
center
so that
of
by performing that
procedures
detailed
bottom
by use
laboratory
stone
is based
It requires
for
for
shear
requires
piezometers
Swedish
soils
to be realized.
in those
at the
of porous
Modified
be used water
This
Because
and
oc-
are
measured
implied
in the
C:
field
unreliable
must
are
pressures
pressures
and
pressures
construction.
errors.
sides
water
of design
methods,
comparable
VII.
embankment
The
detailed
the
This
where
generally
in
water
failure
expectations
Q
pore
same
pore
are
where
measurements.
a
have
VI and
pore
critical
pressures
directly
so that
(1)
pore
be measured
tests
Forces.
as shown
provided
confirmation
pore
LIethod
d.
if design
of computing
The
ratory
stress
during
equalized.
performed.
assumed
piezometers
more
pressure
imen
of the
foundation
stability
slowly
expectations,
negative
If high or
In lieu they
plane,
measured
design
satisfactory
strengths,
(4)
failure
field
VIII-6,
conventional
to check
sults,
plate normal
embankment
used
location
to obtain.
shear
on the
is prepared,
with
from
of low
impossible
stress
condition.
seen
in areas
pore
normal
a plot
construction
(3) cur
If such
close
design
total
VIII 1970
been
and
water
and
should
extensive
unusual.
be and
It should
or foundations. of each
slice
observations.
or wedge For
stable 442)
EM ii10-2-1902 Appendix VIII 1 April 1970 embankments,
the
corresponding
to an effective
shear,
which
segment,
bankment
section A near
vertical
water
lying
fill.
VII
for
analysis
stability
cedure
consists
dicted
according
normal
stress
by the
of the
a decrease
with
to that
field
pore
to -5.
this
by at least
one
other pore
Modified
Swedish
E3 Stresses. shear resistance
This
method
is generally
tive
stresses 23 The tions. (1) ure
at the
tests.
shearing
start
following
A plot
plane
sion
at the
This phase
soil
of shear start
of a a
of shear
of shear
i?
versus
appendix
be supple-
This
method
doe5
Considering
to Method
strength
F1
C, except
estimated
effective
normal
for
and
that
corresponding
to those
is prepared
test
Next, construct see plate VIII-7. the effective normal stress rfc ’ drained shear, for various values and
it should
pre-
from
(after
Taylor)
corresponds lines
to the
failure
T1/T3
or that
of undrained
on the of
F
R
field
stress
condi-
start
shear
plane
prior
as shown
on the
triaxial
any
fail-
compres-
point
in the
of another strength to start
in plates
test; versus of un-
VIII-7
-8. (2)
sponding
4f(2)
Assume
a trial
shear
strength
value
of (01/G3),
parameters
c
, and
VIII - 8
such +
as 2, from
and
plate
determine VIII-8.
the
to effec-
involved:
by assuming or
2 of this
Method
similar
equal
are
strength
is done
or Wedge
is the undrained
steps
values
pro-
pressures.
E:
of the
seepage. This
with
methods.
over-
VI and
of steady
pressures
evaluation
or
by the
Procedure.
is used,
be
may
in Appendixes
in paragraph
em-
or by measured
a condition
water
method
Method
f.
under
slice
horizontal
imposed
of Reclamation
VIII-i
shear-induced
time
stress
described
slope
discussed
consider
the
the
strength
show
Bureau
of the
S
by measured
approaching
Where
the
of each
When
be defined
downstream
of comparing
analysis.
failure,
R strength
of undrained
might
similar
Modified --
D:
as the
on the base
stability
to be near
to procedures
and plates mented
effective
are
is
to start
prior
do not
that
be taken
stress,
condition that
should
normal
is considered
pressures
Method -
resistance
as determined
failure
The
e.
not
to the
movements
pore
shearing
is equal
or wedge
used.
soil
corre-
EM
(3)
Assume
the
mczdified
the
sides (4)
on the and
and
base
revise
through
5.
4f(5)
method,
bottom
of each
of each F,/?
Compare
essary,
safety
Swedish
Determine
compute (5)
trial
value
factors
and
using
field
closure
measured
pore
of force
polygons
water
pressures
for on
slice.
shear
stress
slice.
Plot
and
corresponding
as shown
3 for
each
slice.
a i /u-3
for
each
of
obtain
1110-2-1902 Appendix VIII 1 April 1970
slice
in plate
with
assumed
VIII-9
value in Step
effective VIII-8
to obtain
assumed i and
normal
stress aI
in Step repeat
Steps
and
1.
03 ,
If nec2
..
EM
.-
a.
PORE-PRESSURE COEFFICIENT
COEFFICIENT MEASURED
A VERSUS AT FAILURE,
OVERCONSOLIDATION StRESS INCREASING
iiiO-2-i902 Appendix VIII 1 April 1970
RATIO;
1 .o 0.9 0.9 0.4
od
0.2
JI
70 75 DEGREE
b.
so 85 So 95 OF SATURATION.
loo X
PORE-PRESSURE COEFFICIENT B VERSUS DEGREE OF SATURATION; COEFFICIENT MEASURED AT FAILURE, STRESS INCREASING. CURVE APPLIES TO ONE SOIL ONLY, UNDER PARTICULAR CONDITIONS OF TEST
PORE PRESSURE COEFFICIENTS A AND B Plate VIII-17
VIII-4
EM iiiO-2-1902 AppendixVIU -
Au = tltAO,+AlAO,
(FER SICEYFTOII)
Ar,Jl
= ~~cur~~ro POREWATERFRZIURC IN MINOR PRINCIPAL STRESS Au, = INCREASE IN MAJOR PRINCIPAL STRESS A01 = INCREASE Au
WHEUL
l
2 I.0
FCR
SATURATED
A = FACTOR
SOILS
DEPENDENT
ON
AU
-=A+(1 AOI
THEN
-A)-
OVERCOWSOL.IOATIOW
RATIO
A@B Au1
Ol -=1 5
1.0
-T----0,s
0.6
0.7
0.6 =
a la
o0.8
0.4
0.)
0.2
I
0.1
k
NORAULLY
CmnoLIDAYrD
IQLS
0 0
1
2
s
4
l
6
OCR-OVERCONSOLlOAflON
7
8
m
1P
RATIO
DEVELOPMENT PORE WATER Plate
VIII-5 VIII-18
OF EXCESS PRESSURES
EM
EYt3ANKXENT
IiiO-2-1902 Appendix VIII I! 970 I April
FILL ,
/ccs
ENVCLOPE
OI TOTAL
PORE
NORMAL
PRESSURES IMPLIED WHEN USED FOR CONSTRUCTION
STRESS-O
Q SHEAR STRENGTHS CONDITION DESIGN
ARE
a IS
-
TOTAL
PORE
NORMAL
STRESS
PRESSURE VS TOTAL NORMAL 9N FAILURE PLANE
ENVELOPE
HDWZONTAL
PoRe PRessURC IYPLlQfLr ASSUMED FOR fan DESIW
ON FAILURE
PLANE
5
STRESS
DATA FOR ESTIMATINO POR:NPqR:;zyRES
Plate
VIII-
19
VIII-~
EM 1110-2-1902 Appendix VIII 1 April 1970
5 ENVELOPE LINES OF UNDRAINED SHEAR STRENGTH VS rk ,THE EFFECTIVE NORMAL STRESS ON Te FAILURE PLANE PRIOR TO START OF IHORAINED SHEAR DRAINED
NORMAL
STRESS
UNDRA1NE.D SHEAR STRE_NCT_H FOR VARIOUS RATIOS OF 01/cT3 AT START OF SHEAR Plate
VIII-
7
VIII-20
EM
IS VALUE
AT
=’
START
AT
OF
START
EFFECTIVE
OF
NORMAL AT
1110-2-1902. Appendix VILI 1 April 1970
START
STRESS OF
ON
UNDRAINED
FAILURE
PLANE
SHEAR
if
= EFFECTIVE URE PLANE
NORMAL
STRESS
ON
FAIL-
xf,
= EFFECTIVE URE PLANE SHEAR
NORMAL AT START
STRESS ON FAILOF UNDRAINED
$4$fq
5 WVELOPE
---mm--
--
‘4
;,A
f
;;f
UNDRAINED SHEAR FOR FIELD STRESS
STRENGTH CONDITIONS Plate
vm-2i i?u.S.
GOVERNMENT
PRINTING
OFFICE:
1994 - 521.947/81206
VIII-~
