5.4 Maximum Dynamic E a r t h C o e f f i c i e n t , K d y m a x ... Spring Constants for Rigid Base Resting on Elastic Half-. Space ... General Characteristics of Damping Force, D(t) and Loading ...... The gravity retaining structure used in the analysis is 20 feet high ...... IG = 0, means that the unit system used i s : FOOT, POUND,.
S E I S M I C RESPONSE OF RETAINING STRUCTURES
BY
FRANCISCO MANUEL GONCALVES ALVES B.Sc,
The T e c h n i c a l
A
University
of Lisbon
SALGADO (I.S.T.),
1972
T H E S I S SUBMITTED IN PARTIAL F U L F I L M E N T OF THE
REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D
SCIENCE
in
THE
FACULTY OF GRADUATE STUDIES
DEPARTMENT
We
accept to
THE
CJ
OF C I V I L ENGINEERING
this
t h e s i s as conforming
the required
standard
UNIVERSITY OF B R I T I S H A P R I L 1981
COLUMBIA
FRANCISCO MANUEL GONCALVES ALVES SALGADO, 1981
In p r e s e n t i n g requirements
this thesis
f o r an a d v a n c e d
of
British
it
freely available
agree that for
in partial
Columbia,
scholarly
degree a t the U n i v e r s i t y
I agree that f o r reference
permission
the L i b r a r y
shall
and s t u d y .
I
f o r extensive
p u r p o s e s may
f u l f i l m e n t of the
for
that
shall
of this
Itis thesis
n o t be a l l o w e d w i t h o u t my
permission.
Department o f
^ % U J ^ L ^ ^ ^ 7
The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5
thesis
be g r a n t e d by t h e h e a d o f my
copying or p u b l i c a t i o n
f i n a n c i a l gain
further
copying of t h i s
d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . understood
make
Columbia
written
-
A
s i m p l e method o f
forces
and
sented. bility
displacements
The and
analyses
method
of
of
both
degree of
freedom p e r f e c t
of motion
i s integrated
displacement. subjected indicate having dynamic ing
to
three
that:
the
(1)
usual
force
increases
sliding
The
on and
-
which allows
both
the
the
weight
backfill
and
elastic-plastic
to
both
retaining structures
considers
strength
ABSTRACT
yield
the
method i s a p p l i e d
the
to
of
earthquake
be
the
computed
wall
foundation
model
to a
and
is
the
soil.
i s used
time h i s t o r i e s of
and
A
the
wall
induced preflexisingle
equation
force
gravity retaining wall
and structure
d i f f e r e n t a c c e l e r a t i o n time h i s t o r i e s .
The
results
the
for
walls
dynamic
f a c t o r of the can
i s prevented
wall be from
displacements w i l l
safety
against
increases greater
as
the
than the
occurring.
-
i i -
sliding
be
small
> 1.5;
f a c t o r of
(2)
safety
the
maximum
against
Mononobe-Okabe v a l u e
when
slid-
TABLE OF CONTENTS ABSTRACT 1.
INTRODUCTION
2.
METHOD OF ANALYSIS 2.1 2.2 2.3
3.
General Incremental Equation o f Motion Governing Equations 2.3.1
General
2.3.2
Incremental
2.3.3
Step
2.3.4
Summary
Equation o f Motion
by S t e p
MODEL PARAMETERS AND RETAINING STRUCTURE 3.1 3.2
General C h o i c e o f Mass f o r E q u i v a l e n t Lumped
3.3
Choice
o f Spring Constants,
Relations 3.3.1
and E m p i r i c a l
Lateral 3.3.1.1
3.3.2
Base
3.4
Choice 3.4.1
System
U s i n g Measured
Equations.
Required
t o Reach A c t i v e
States.
Values
o f K^ a n d Kp U s e d
Different
Soil
i n the Analyses
Estimation of Foundation
Stiffness,
Kg
Poisson's Ratio, u Modulus o f E l a s t i c i t y i n Shear, G Values of Foundation S t i f f n e s s f o r D i f f e r e n t F o u n d a t i o n T y p e s a n d L/B R a t i o s
of Effective
3.5
Choice
3.6
Retaining Wall
o f Time Increment,
EARTHQUAKE DATA
and P a s s i v e
Backfills.
o f Damping f o r E q u i v a l e n t Lumped Values
Stress-Strain
Strains
Spring.
3.3.2.1 3.3.2.2 3.3.2.3
USED I N THE ANALYSES
Spring
For
4.
Integration
of Procedure
Damping U s e d A t , used
Dimensions
USED IN THE ANALYSES
-
iii
-
System i n the Analysis, C ( t )
i n the analyses.
B
5.
RESULTS 5.1 5.2
Introduction Earthquake Induced
5.3
F u n c t i o n o f Time. Maximum D i s p l a c e m e n t s V e r s u s
Displacements
and Dynamic L a t e r a l
Static
Factor
of Safety
Forces
as a
Against
Sliding.
5.4
5.3.1 E f f e c t o f F o u n d a t i o n a n d E a r t h q u a k e 5.3.2 C o m p a r i s o n w i t h Newmark's A n a l y s i s
Conditions
Maximum
Versus
of
Dynamic E a r t h Safety
5.4.1 E f f e c t 5.4.2 E f f e c t 5.4.3 6.
Against
Coefficient,
Comparison
with
y
m
a
x
Mononobe-Okabe A n a l y s i s .
BIBLIOGRAPHY - PROGRAMME
d
Static
o f F o u n d a t i o n and E a r t h q u a k e C o n d i t i o n s o f S o i l B a c k f i l l State o f Compaction
CONCLUSIONS
APPENDIX
K
Sliding.
WALLQUAKE
-
iv -
Factor
LIS
Table
I
- Soil
Table
II
-
Backfill
OF
!
TABLES
Parameters.
Spring Constants
for Rigid
B a s e R e s t i n g on
Elastic
Space Table
III
-
Poisson's
Table
IV
- Test
Ratio
Procedures
Values f o r Measuring
M o d u l u s and
Damping
Characteristics. Table
V
- Ranges o f
G
Table
VI
- Foundation
Table
VII
-
Spring Constant
Table
VIII
-
Effective
Table
IX
- N a t u r a l P e r i o d , T,
Table
X
- Earthquake
Table
XI
-
m
a
x
Parameters Values Values,
Values
G.
Kg.
Damping V a l u e s , and
to Assess
Cg.
Time
Increment,
At.
Data. Correspondent
Conditions.
-
v
-
to the
Softer
Foundation
Half-
FIGURE INDEX -
Cantilever
Retaining
Wall
Figure
1
Figure
2
Model
Figure
3
Lateral
Figure
4
S t r a i n s Required Dense Sand
Figure
5
Base
Figure
6
Figure
7
Single
Figure
8
General C h a r a c t e r i s t i c s force, E(t).
o f Damping F o r c e ,
Figure
9
Motion
Time
Figure
10 -
Earth
Figure
11-
Spring
Figure
12 -
Illustration
Figure
13 -
Cantilever
Figure
14 -
Approximate R e l a t i o n s h i p s Rock a n d O t h e r L o c a l S i t e
Figure
15 -
Earthquake
Figure
16 -
Dynamic
Lateral
Figure
17 -
Maximum
Displacements
-
Spring t o Reach A c t i v e
and P a s s i v e
States
in a
spring
Relationship Movement.
between Base and L a t e r a l
Degree o f Freedom
o f System D u r i n g Coefficients Constant
Springs,
and W a l l
(S.D.O.F.) D ( t ) and L o a d i n g
Increment
vs. Strain.
Coefficients
f o r Rectangular
o f Shear Modulus L o c a t i o n
Retaining
Induced
Wall
Used
Assessment
i n the Analysis.
B e t w e e n Maximum Conditions.
Displacements
Force
Foundations
A c c e l e r a t i o n s on
as a F u n c t i o n
as a F u n c t i o n
o f Time.
o f Time.
vs. Static
Factor
of Safety
Against
Maximum
Displacements v s . S t a t i c
Factor
of Safety
Against
Sliding
Effect
Sliding. Figure
18 -
Figure
19 -
Comparison
Figure
20 -
Maximum of
Figure
21 -
with
o f L/B
Newmark
Dynamic E a r t h
Safety
Ratio.
Against
Displacements.
Coefficient,
K, vs. Static dymax
Factor
Sliding.
Maximum
Dynamic E a r t h
Level.
Effect
of Soil
-
Coefficient, Backfill
v i -
K
d
y
m
a
x
vs. Acceleration
Compaction.
Figure
22 -
Maximum ing
Figure
23 -
Dynamic E a r t h
Comparison
With
Coefficient,
K
, , vs. Static
d y
a;
Factor
Mononobe-Okabe
Maximum D y n a m i c E a r t h C o e f f i c i e n t , K vs. Acceleration Level. E f f e c t o f S o i l B a c k f i l l Compaction. Comparison w i t h Mononobe-Okabe R e s u l t s . d
- v i i -
y
m
a
x
ACKNOWLEDGEMENT The for
w r i t e r wishes t o acknowledge
h i s suggestions
consultations also
a n d t h e 100% s u p p o r t
throughout
by t h e N a t u r a l
study.
h i sappreciation f o rthe financial
Science
The w r i t e support
and E n g i n e e r i n g C o u n c i l o f Canada
5109).
-
viii
Byrne
shown d u r i n g t h e i n u m e r o u s
t h e development o f t h e p r e s e n t
wishes t o acknowledge
offered
h i s a p p r e c i a t i o n t o Dr. Peter
-
( G r a n t P.
JOAO and MARTA
1.
INTRODUCTION The
earthquake
commonly theory
computed
f r o m an
i n which the
represented
by
coefficient. Okabe
induced
an
f o r c e s on
extension
sufficiently
equivalent
static
Mononobe and
to
Mononobe-Okabe e q u a t i o n .
failure
of
the
considered existing seismic
induced
structural
methods t o
e x c i t a t i o n and
towards cycles
can the
concludes
take
place
backfill
of motion,
the
and
N i i g a t a 1964
w a l l m u s t be
decreases with the
the
and
i n the
studies
materials wall
wall
on
The
during
Whitman,
must
extensive
of
earth
by
due
wall
Ohara
thus
the
teh
to
method
is
at
the
base
of
the
i t s movement after
a number
of
different position.
earthquakes 1970).
of
pressures.
sliding
Therefore,
assumes a
the
be
review
retaining walls
resistance to
analysis since
o f M a t s u o and
this
cause
movements away f r o m
larger. and
for
i s generally referred
and
caused
by
yields
equation
above p s e u d o - s t a t i c
whereas the
i n c r e a s i n g magnitude of
experimental
wall
increment
considered.
w a l l moves o u t
considered
the
pressures
i s considerably
(Seed
Their
are
seismic
assumes t h e
( 1 9 7 7 ) d i d an
that
observed
a
wedge
backfill
T h e s e a d d i t i o n a l f o r c e s may
dynamic
easily
soil
by
are
sliding
cohesionless
and
the
to displacement
a l s o be
S u c h movements a h v e b e e n 1964
earth
f o r computing the
s t r u c t u r e s must
backfill
(1929),
f o r c e s on
Prakash
compute
H o w e v e r d i s t r e s s due the
designated
f o r dry
components o f
i n i t s design.
mainly used
the
t o p r o d u c e minimum a c t i v e p r e s s u r e s . earthquake
structures
Coulomb-Rankine
f o r c e s on
force
Matsuo
the
the
the
developed
computing as
of
t r a n s i e n t earthquake
T h i s m e t h o d was
(1926) and
retaining wall
i n C h i l e 1960, displacement
maximum e a r t h
displacement,
(1960).
as
Alaska of
the
pressure shown
by
2. Newmark earthquake for
(1965) p r e s e n t e d
induced
displacement
earth slopes, i s also
method e s t i m a t e s seismic
interface.
approach:
a) S l o p e s
Walls of
- Richards
b) N u c l e a r a n d Helms
respond
as a s i n g l e however,
be
desirable
cannot
backfill)
o f freedom
model based
method
from
plastic this
plastic
Sharma
(1975),
c) R e t a i n i n g
the displacement
from
the time soil to
system.
T h e f o r c e s on
method.
T h e Newmark a p p r o a c h
but not the wall forces.
method o f a n a l y s i s
allows the
I t w o u l d be
which would
allow both the
o f t h e w a l l t o be computed.
surrounding
requires that
the wall
(soil
both
would
together with
t h e f l e x i b i l i t y and
f o u n d a t i o n and s o i l
the weight
A rigorous analysis
o f t h e domain
equations
rigid
e t a l (1979),
i s computed
rigid
subjected to
a l l o w s t h e s e i s m i c f o r c e s on t h e w a l l t o
be c o n s i d e r e d t o g e t h e r w i t h
discretization resulting
i t s base
method o f a n a l y s i s
the wall i t s e l f .
(1966),
In t h i s
His
at the block-
h i s simple
- Kausel
etc.
be c o m p u t e d
t o have a s i n g l e
of the s o i l
friction
block
c o n s i d e r i n g t h e w a l l and a d j a c e n t
degree
and d i s p l a c e m e n t s
strength
simpler
along
t o be c o m p u t e d
A rational
of
(1979),
but not the displacements.
displacements
forces
Powerplants
Mononobe-Okabe e q u a t i o n
computed
b y Coulomb
developed
structures.
of a r i g i d
a n d Dams - Goodman a n d S e e d
of accelerations,
The
mass, w h i c h a l t h o u g h
appropriate for retaining
t h e w a l l due t o s l i d i n g
wall,
f o rp r e d i c t i n g the
Numerous d e s i g n e r s u s e d
history
the
of a soil
and r e s i s t e d
foundation
(1975),
method
t h e amount o f d i s p l a c e m e n t
excitations
Mineiro
a simple
and s t r u c t u r a l
require a finite
a time
o f motion.
Such an a n a l y s i s
on a s i n g l e
degree
o f freedom
stiffness element
step i n t e g r a t i o n i s complex, system
of the
and h e r e i n a
i s presented.
2.
METHOD OF
2.1
General
ANALYSIS
Analysis
of
determination These
soil
of a
functions
structure
set of
are
foundation
required
to
the
structure
foundation
the
ground
a location well
general, in
the
at
these
time domain
by
equivalent
as
Modal S u p e r p o s i t i o n
masses,
step
by
2.2
A n a l y t i c a l Model The
single
shown on
with
a
contained
Figure
wall.
dashplots and
A-B
i n the
the
above the
Later
equivalent
or
the
of
3.2)
effective
motions of
the
forces
foundation
structure.
at
and,
However,
dependent which p r e c l u d e s
and
to
Step
the
doing
i n the
in
analysis
free
base
base and
hence the
mass o f
this,
the
soil
be
.
replaced
methods
such
followed.
The
analysis.
1 i s modelled
with
spring with
damping C
and
wall
field
usually
present
shown i n F i g u r e
effective
the
By
are
i n t e g r a t i o n can
used
the
The
wall
functions
springs.
domain above t h e
heel
(Chapter
2.
with
wall plus
functions.
r e l a t i o n s h i p between
dependent
S t e p by
Figure
1, moves w i t h
mass o f
line
frequency
dashpot
the
(1972)).
lumped mass, c o n n e c t e d
coupled
the
frequency
requires
(or compliance)
removed from the
cantilever retaining wall
as
in
relative
i n t e g r a t i o n m e t h o d was
springs
soil
are
stiffness
establish a
the
(Whitman
In p r a c t i c e t h e s e
Step
and
functions
interaction usually
two
as
elastic-plastic
stiffness
Kg
I t i s assumed
shown a s equivalent i n the
a
the
is that
shaded
the
zone
s i n g l e mass
shaded
zone.
The
represents
the
effective
face
some c o n s i d e r a t i o n s
are
presented
regarding
mass c h o s e n
above.
is
of
the the
The developed The
force
i n the l a t e r a l
spring
a t the e f f e c t i v e face
represents
of the wall
force-deflection characteristics of this
the lateral
during spring
earth
the seismic
force
action.
a r e shown on
Figure
R O C K
FIG.2 FIG.I CANTILEVER
RETAINING WALL.
WALL
MOVEMENT,X
FIG.3 L A T E R A L S P R I N G .
MODEL.
5. This
lateral
spring
upper represents backfill
(K
( 1 9 3 4 ) and
L
) of
distinct
Passive
the
Lambe and
relationship
(after
the
two
c h a r a c t e r i s t i c s and
stiffness
strain,
has
spring Whitman
between the
i n percent, Lambe and
the
(P )
lower,
i n the
case
the
plastic
(1969).
of
On of
forces
or
correspondent
p
coefficient
f o r the
Whitman,
force
limiting
Active range
Figure earth
a dense
yield
to
force
the
on
4 i s shown a
pressure
versus
s a n d b a s e on
the
soil
(P&).
i s based
points:
The Terzaghi typical horizontal
Laboratory
data
1969). 7i
f r
-«—Ko - 5
- 1 0
0
+5
+10
Horizontal strain (%)
Fig.4
STRAINS
REQUIRED TO
REACH
AND PASSIVE STATES IN (after Lambe and Three d i f f e r e n t r e l a t i v e considered d e n s e and
i n the loose
density
analysis, correspondent
conditions.
The
A DENSE SAND
Whitman,
conditions
ACTIVE
of
the
1969) soil
respectively to
r e l a t i o n s h i p used
i n the
backfill
dense,
were
medium
analysis
6. between e a r t h presented spring
c o e f f i c i e n t s and h o r i z o n t a l
i n Chapter
i s the s t a t i c
strain
3 (Model P a r a m e t e r s ) . value
P
f o r these
Initially,
, and as t h e w a l l
three
cases are
the force
moves away
in this
from t h e
st backfill
during
Should
the wall
passive
value
The force
the earthquake,
drops t o the a c t i v e
move t o w a r d s t h e b a c k f i l l
a s shown o n F i g u r e
initial
static
correspondent
condition".
the force
These
force
the force
increases
value. towards the
3.
value,
t o , an " a t r e s t "
P s t , c a n be c o n s i d e r e d condition
two s t a r t i n g c o n d i t i o n s
either
as t h e
o r t o an " a c t i v e .
were c o n s i d e r e d
i n the
analysis. The soil
o r base
spring
r e l a t i v e to the free
limiting force
lower
frictional
represents
field
resistance
the compliance
and i t s y i e l d that
limit
can be m o b i l i z e d
deflection c h a r a c t e r i s t i c s of t h i s spring
of the foundation
represents
at the base.
a r e shown on F i g u r e
WALL MOVEMENT, X
FIG.5
BASE
SPRING.
the The 5.
Under t h e p r e - e a r t h q u a k e will P
be Q
.
opposing
st
As t h e w a l l
static
the s t a t i c
condition
force
moves away f r o m
from
the force
the l a t e r a l
the b a c k f i l l ,
in this
spring,
the force
spring
ie. Q = st
in this
spring
st may
increase
wall
t o the y i e l d
moves t o w a r d s
the b a c k f i l l
yield
on t h e n e g a t i v e
force
i s expressed
(F
s
), w h i c h
value
side
a t which time base the force
a s shown o n F i g u r e
i n terms o f t h e s t a t i c
i s defined
as
force)
from
c a n be
Base
the
static
value.
equation
(1) t h e b a s e
The s p r i n g
I f the sign
and
limiting
against
sliding
"a" Forces Forces
(1)
limiting
force
(resistance
derived:
Spring
lateral
Assuming
the analysis
Limiting
force
Force
(Q ) = F y
c a n be t a k e n
an a c t i v e v a l u e ,
performed,
correspond
to different
represents
a retaining wall
expected,
5.
change
factor of safety
spring
different
conditions
Static
s
a s an i n i t i a l
t h e above e q u a t i o n
°-v =
In
a n d may
occurs.
follows, Resistance Driving
therefore
drops
slip
F
s
P
Lateral
'active
1
or 'at r e s t '
c a n be r e w r i t t e n
as:
(3)
A
values
(2)
Force
of F
g
were c o n s i d e r e d ,
of the s t r u c t u r e
w h e r e no movement
such as the case o f a r e t a i n i n g w a l l
foundation.
in relation founded
on
which A
high
t o i t s base i s piles.
8. In o r d e r springs
and
presented during
the
to v i s u a l i z e
the
on
relative
figure
6.
the
relationship
wall displacement Points
1,2,3
and
4
between the a schematic represent
f o r c e s on diagram
possible
the
is stages
motion.
Fig. 6
RELATIONSHIP
BETWEEN
SPRINGS AND WALL
BASE AND LATERAL
MOVEMENT
two
2.3.
Governing 2.3.1 As
the
General
mentioned
previously
present analysis.
incremental good
equal
outlined
2n,
such
of v e l o c i t y .
The
The and
end
equilibrium
o f each
time
and
initial
The
(non-linearity
displacement
response
a t t h e end
the
next
interval,
the
time
z e r o t o any
The
system
strength
and
and
taken
is
of
programme by
at
or changes i n by
is satisfied
i s established
time
increment.
the
an
inputed
at
the
range
spring
of t e h base
from
elastic
spring
remains
calculating
(C
elastic,
to
new
study
and plastic
i s equal to
an
and
a
assumes
o f the s p r i n g . )
i s o b t a i n e d by
o f one
by
In t h p r e s e n t
stiffness
with the base
the base
time
u s i n g the v e l o c i t y
interal
t h e p r o c e s s i s t o be
desired
is a
response
of p r e c i s i o n
to plastic
o c c u r s a t changes
t h e damping a s s o c i a t e d
complete
the
computer
i s controlled
condition
behave n o n - l i n e a r l y :
zero value i n the p l a s t i c
which
interval.
of the
given value while
in
A t i s , when n e e d e d , d i v i d e d
elastic
of precision
(1975),
At, g e n e r a l l y
In t h e
used
acceleration
approach,
increments
from
m e t h o d was
linear
Penzien
In t h i s
increment
a t the b e g i n n i n g o f each
springs
and
the
convenience.
time
degree
dynamic
three parameters
range)
Clough
time
as change
nonlinear nature
parameters
lateral
this
uses
i n o r d e r t o achieve a high degree
points"
The
by
of short
the w r i t e r
6,
beginning
method chosen
f o r computational
by
parameter.
a step-by-step integration
for non-linear analysis.
length
"critical sign
The
for a series
developed 4,
procedure
approach
evaluated
2,
Equations
as t h e
initial
and
conditions
continued step-by-step
from
time.
deformation properties
of both
the b a c k f i l l
for
and
10. foundation comprise be
soil
of
that
soils
constant
with or
2.3.2 The in
not
time
vice
7(a)
base
particularly
the
changing the
when t h e y
they
This
could
s p r i n g p r o p e r t i e s as
properties of
exeption
i f
material.
analysis presented the
so
herein
the
change
i t i s assumed
springs from
Equation
and
are
of
the
freedom
forces
7(b). shown
of
are
elastic
kept to
The
Motion system
a c t i n g on general
in Figure
/ / /
K
the
i n the
mass o f
analysis i s the
The
system of
characteristics
described
(see
Figure
the of
presented
are damping both
3 and
5).
B
/—JULQMMJULUi^-\ /
9
^ (a)
D(t)
a') m
1
/
2
(26)
where G K
2
- Shear
max max
modulus
- parameter
that reflects
amplitude, a'
For
clays,
Seed
and
effective
Idriss
used
G -2M Su
w h e r e Su situ
test
i s the
undrained
data
o b t a i n e d by
constant.
Its value
Ohsaki
and
empirically equation
i n f l u e n c e of void
ratio
and
strain
and
= mean p r i n c i p a l
m
the
correlating
i n terms of G
an
=
equation
of
the
form (27)
constant
s h e a r i n g s t r e n g t h o f the
clay.
Laboratory
s e v e r a l r e s e a r c h e r s were u s e d
varied
Iwasaki
stress,
from
1000
to
and
to e s t a b l i s h
equation
crosshole velocity
data
f o r s a n d s and
to
SPT
clays,
N-values.
Anderson shear
moduli
i s as f o l l o w s :
1)
The
max
N-value obtained e t a l (1978) d i d a
a t competent
methods were compared.
sites,
=
1200
d u r i n g the study
N
(28)
0 , 8
SPT.
r e g a r d i n g the
where i n s i t u ,
(or Hardin-Drnevich)
laboratory G
estimation of
l a b o r a t o r y and
T h e i r main c o n c l u s i o n s a r e
Hardin-Black
mates the
by
The
" — I
i s the
the
3000.
(1973) d e r i v e d an
G
where N
in
in
situ
empirical
as f o l l o w s :
method
a t competent
sites
field
of G
typically by
a
overesti-
factor
of
1.1
max to
1.5
and
underestimates
values
by max
1.3
to
2.5.
a
factor
of
34. 2)
The
S e e d - I d r i s s method
of
the
field
G
f o r sands p r o v i d e s
where K
max
2
a closer
i s s e l e c t e d on
max
approximation
the
b a s i s of
field
data. 3)
The
Ohsaki-Iwasaki
method o v e r p r e d i c t s the
field
G
by
25
max percent 4)
For
o r more a t
important
tests
sites
sites.
i t i s essential
( p r e f e r a b l y c r o s s h o l e ) be
Empirical too
competent
and
t h a t the
performed
in situ
to establish
l a b o r a t o r y methods i n v o l v e v a r i a t i o n s
large to
justify
their
use
f o r other
geophysical
than
modulus.
which
are
approximately
G max
or
establishing
the
general
credibility
of
G max
Equation modulus o f
the
stress-depth with
(25)
strain
was
soil
and was
strain not
b e t w e e n G and
strain
1
-
For
layer
at the 2
with
suggested on
-
i t may
of the
by
be
t h e maximum
done by
(1972
shear
to
using
Idriss
and
1976)
end
the
variation of
Instead
were u s e d
was
the
considered). application
reduce
of
the modulus
G
relationship
(1970).
r a d i u s of
of
each
the
to determine
i t i s generally reasonable
e x e r c i s e d i n the necessary
a t the
and
to the
B/2,
a n a l y s i s the
directly
Seed
equal
width,
t o use
foundation. Whitman these
G: the
(In
recommends
results.
i f there
is a
In
soft
surface.
A more d i f f i c u l t
strain.
present
account
Whitman
f o r a depth
j u d g e m e n t must be
particular,
the
c o u l d have been
based
analysis half
that
In
horizontal translation
average modulus the
as
into
a n a l y s i s to estimate
I t i s known t h a t G d e p e n d s on c o n f i n i n g
level.
taken
step
steps
i n the
foundation.
computational
following
used
Whitman
t h e modulus, by
simply
problem
suggests adopting
the
i s to account use
of
an
f o r the
r e d u c t i o n of
empirical rule
a range o f values
f o r shear
to
G
determine
modulus
and
assuming t h a t any v a l u e w i t h i n t h i s range i s p o s s i b l e . shear modulus determined a r e proposed
If
i s the
u s i n g r e l i a b l e d a t a , then t h e f o l l o w i n g ranges
(see T a b l e V ) .
TABLE V Ranges of G ( A f t e r Whitman (1972) m a x
MOTION VERTICAL AND HORIZONTAL ROCKING
LARGE EARTHQUAKE
MACHINE FOUNDATION °'
7
G
max
t
o
G
°'
5
G
max
t
o
G
°-
max
°'
max
A shear modulus v a l u e = 1/2 G was adopted max f o r i t s change with
t
o
G
max
t
o
G
G
3 3
G
max
max
1
1
to account
max
5
i n the present
analysis
strain.
The o n l y s t e p n o t f o l l o w e d by t h e w r i t e r t o Whitman's i n t h e c a l c u l a t i o n o f mean p r i n c i p a l
effective stress
s u g g e s t i o n s was
(o' ). m
Whitman
recommends t o i n c l u d e the e f f e c t o f t h e weight o f t h e s t r u c t u r e when e s t i m a t i n g a'
m
.
However i n t h e p r e s e n t a n l y s i s t h e weight o f t h e
r e t a i n i n q w a l l and b a c k f i l l were not taken i n t o account 3
evaluation.
f o r the a' m
The r e a s o n i n g f o l l o w e d i s t h a t although t h e column o f s o i l
36. directly
beneath the block
of
the r e t a i n i n g wall
to
that
soil
Figure
and s o i l
column o f s o i l
that
will
react
f o u n d a t i o n becomes " s t i f f e r " backfill,
the surrounding
horizontal
force.
weight
foundation
does n o t g e t a f f e c t e d and i t i s t h i s
t o any d e v e l o p e d
12 i l l u s t r a t e s
due t o t h e
The
soil
surrounding following
the above.
R-stiff pile 'soil (b)
Fig. 12
Figure
12(b)
considerations, Figure
ILLUSTRATION OF SHEAR MODULUS LOCATION ASSESSMENT
illustrates
i n a more r e a l i s t i c
manner
t h e above
where t h e c o l u m n o f s o i l
with
shear
1 2 ( a ) , c a n be v i s u a l i z e d a s s t i f f
pile
when c o m p a r e d
with the
.
The d e f o r m a t i o n
of the
surroundinq
soil
with
shear
modulus, G
modulus, G
shown i n
stiff
soil pile
t o any d e v e l o p e d
modulus
horizontal
of the surrounding
soil
force G
... soil
F will
be c o n t r o l l e d b y t h e s h e a r
37. b.2 To
estimate
foundation (Goodman (or
silstone
G
1979).
A typical
3.3.2.3
Values
correspondent
f o r rock
max
type
and K
range
from
Used
10 x 1 0 6
6
type
were
used
t o 400 x 1 0 p s f 6
p s f correspondent
to
i n the Analyses
of foundation
t h e assumed s o i l
using equation
13
t o a rock
i n the literature
v a l u e o f G = 16 x 1 0
of G
the different
VI p r e s e n t s
constnat
of G enocuntered
G values
chosen.
max
Foundation
the spring
was
For
for
Rock
the values
higher).
Table
-
c o n d i t i o n s used
parameters
required
(26) a n d t h e c o r r e s p o n d e n t
i n the analysis,
to assess
values
values
obtained,
TABLE V I Foundation FOUNATION CONDITION
Cohesionless Soil Soft
Clay
Rock
VOID RATIO, e
Parameters Values OVER CONSOLIDATION RATIO (O.C.R.)
t o Assess
G
UNIT
SHEAR MODULUS
WEIGHT
G
Y( L b / c f )
max
u u
E a> o
o-—oAlameda Deep Soft Foundation scaled to 0.27g
a
to
L / B = 10
E E x o
1.0
1.2
1.4
1.5
1.6
IB
2.0
Static Factor of Safety Against Sliding
Fig. 17 MAXIMUM DISPLACEMENTS VS. STATIC FACTOR OF SAFETY AGAINST SLIDING (MOTION DURATION =IOsec.) For
a l l three
for
F
and
was o b t a i n e d
soft
s
> 1.5.
The maximum using
clay foundation
markedly the
records
i t may be s e e n displacement
conditions.
record.
the displacements
f o r F =1.5 was e q u a l s
the earthquake record
and a r e c o n s i d e r a b l y
Alameda Park
that
correspondent
are small
t o 0.49
feet
t o t h e deep
F o r F < 1.3 t h e d i s p l a c e m e n t s s
l a r g e r f o r the l a r g e r predominant
increase
period of
In o r d e r it L/B
to illustrate
i s shown t h e r e s u l t s
obtained
ratio
u s i n g t h e Alameda
i n Figure
18 b e l o w
record for different
ratios.
Static
Fig. 18
As i t may same. and
t h e i n f l u e n c e o f L/B
Similar
Factor of Safety Against Sliding
MAXIMUM DISPLACEMENTS VS. STATIC FACTOR OF S A F E T Y AGAINST SLIDING (MOTION DURATION =IOsec.) EFFECT OF L / B RATIO
be
seen
results
the response were
foundation conditions.
obtained
t o L/B
equal
t o 1 a n d 10
f o r the remaining
i s almost
earthquake
the
records
51. 5.3.2 The
Comparison maximum
(1965) i n F i g u r e predicts rigid
W i t h Newmark's A n a l y s i s
displacements
19, a n d i t may be s e e n
displacements
plastic
a r e compared w i t h
that
a r e i n good
that
these
o b t a i n e d b y Newmark
the analysis
agreement w i t h
presented
the simpler
herein Newmark
model.
0.05 O.I V A L U E S OF
A
=
MAXRESISTANCE
CQEFF.
MAX.EARTHQUAKE ACC.
FIG.I9 COMPARISON WITH NEWMARK D I S P L A C E M E N T S .
For maximum
this
comparison
acceleration
the E l Centro
(1940) r e c o r d was s c a l e d
o f 0.5g a n d t h e t i m e
scale
maximum v e l o c i t y
o f 30 i n c h e s / s e c o n d .
seconds
c o n s i d e r e d and z e r o damping assumed.
was a l s o
acceleration,
N was c o m p u t e d
A total
altered
as f o l l o w s :
to a
t o produce
d u r a t i o n o f motion The
yield
a o f 30
52. "N" was d e f i n e d multiplied
b y Newmark a s b e i n g
by g ( a c c e l e r a t i o n
acceleration
value,
acting
overcome t h e r e s i s t a n c e
a c o e f f i c i e n t that
of gravity)
i n the proper
to sliding
wil£> p r o d u c e direction that
when
t h e minimum would
just
of the element,
hence: P
where
equation
P„ = a c t i v e A
force
F
factor
s
= static
A
F
S
= A P
+
of safety
N
= Newmark's c o e f f i c i e n t
g
= gravity
M
- mass
N
^
(33)
M
against
sliding
acceleration
( 3 0 ) c a n be r e w r i t t e n
as
follows:
N W =
P (F -D A
(34)
S
where w = w e i g h t
N
= 4
< sF
X )
(35)
53. 5.4
Maximum L'ynamic E a r t h Safety 5.4.1 The
safety
Effect
maximum
against
Coefficient,
o f Foundation earth
and Earthquake
coefficient,
sliding,
K, Versus dymax
s
Factor o f
Conditions.
K, , versus dymax
F , i s shown i n F i g u r e
Static
the s t a t i c
factor of
20 f o r a l l 3 e a r t h q u a k e
records.
.736 LEGEND • - S . F e r n a n d o , I97I
I.5I9 o X
- Alameda, I962
0.22g 0.2lg
L / B = 10
o £
"O
0.5g
- El Centro , I940
TABLE
1.302
K x l 0 l b / f t . 0g 6
b
0)
5= o o O o IxJ u
IX
L/B =
I.085
Ib.At/sec.
0.038
440
0.I00
743
0.570
I700
1.500
2700
16.200 43.200
9000 I4700
0.868
E
o c
>» Q
E
0.65I
3
E X
o
0.434
0.2I7 I.O 1.5 ^0 3.0 4.0 5.0 Static Factor of Safety Against Sliding
Fig. 2 0
I0.0
MAXIMUM DYNAMIC EARTH C O E F F I C I E N T , K VS. STATIC FACTOR OF SAFETY AGAINST SLIDING
dymQX
Two
different
analysed
foundation
f o r a l l 3 r e c o r d s as
K, increases with dymax and of
foundation the
F
and
(effective
v a l u e s were d e r i v e d from
i s presented
1
Fernando
record
San
the
wide
shown
20.
the
foundation
and
a brief
foundation
=
10)
As
VII
i t may
20,
seen
record
in this
to each
same (spring
curve.
These
3).
the - For
characteristics
be
understanding
parameters
(Chapter
discussion of
were
earhtquake
in Figure
(1971) - Rock F o u n d a t i o n
range of
L/B
t o have a b e t t e r
damping) c o r r e s p o n d e n t
T a b l e s VI
Following -
results IX
1 and
considerably with
In o r d e r
i n Table
=
i n above F i g u r e
varies
of the
i t i s presented
constant)
shown
characteristics.
interpretation
Figure
and
s
c o n d i t i o n s (L/B
results: this
used
particular
(K
varies
from
B 16.2
x
10
t o 43.2
6
x
10
(Lb/ft)
6
and
C
varies
from
9000 t o
14700
B Lb/ft/sec)
d i d not
0.239(1.1 K
A
foundation
) and
affect
0.224(1.03 K
conditions.
on
a very
stiff
is
almost
inegliqible.
close
to F 2
of
the
-
L/B=10.
) f o r the
higher
K, values dymax and
lower
T h e s e maximum K
motion dymax
towards the
values
were
flexible
t h a t when a r e t a i n i n g
i t s relative
which
wall soil
developed
is
found
backfill
at or
very
1.0.
E l Centro
E l Centro
noticable. and
=
A
This reflects
foundation
3
s
t h e maximum d e v e l o p e d
( 1 9 4 0 ) - Deep C o h e s i o n l e s s
r e c o r d the
A maximum v a l u e For
the
stiffer
i n f l u e n c e of of K
Foundation
foundation
- For
the
characteristics
= 0.582(2.68 K ) o c c u r s dy A c a s e o f L / B = l a maximum K = dy
case is
for F
> 3.0 s 0.312(1.44 K
) A
was
obtained.
foundation retaining 3
s
>3
Alameda
occurs are
r e g a r d i n g the
( 1 9 6 2 ) - Deep S o f t
influence
obtained
as
i t i s important
to select
structural
the
right
design
of
the
structure.
tremendous
F
shows t h a t
design parameters,
-
values
This
was
f o r the f o r the
of
the
case
K =0.038 x 1 0
6
foundation
obtained.
E l Centro
Clay Foundation
In
and
C
correspondent
= 440
on
this
the
case
a
maximum
K
t h e maximum K, values dy
A maximum v a l u e
L/B=10 where t h e Lb/ft
characteristics
general
record.
- For
Lb/ft/sec.
occur
dy for
o f K, = 1 . 1 8 7 ( 5 . 4 7 K ) dy A foundation Again
the
parameters
importance
of
B B choosing The their
the
appropriate foundation
above K
order
dymax
maximum v a l u e s , t h e
of magnitude
coefficients,
K
are
P
parameters
compared
with the
shown i n T a b l e
EARTHQUAKE RECORD San
Fernando (1971)
El Centro (1940)
Alameda
Park
(1962)
Correspondent
FOUNDATION CONDITION Rock
Deep Cohesionless Soil
Deep
Soft
Clay
K
to the
dy< s F
dy
values
for F
passive earth
s
=1.5
and
pressure
XI.
TABLE K, Values dy
K
i s emphasized.
= 1
-
XI Softer
5 )
Foundation
^(F =1.5) s
Conditions
dymax dymax
K
p
0.23g
0.05
0.23g
0.05
0.0356
0.08
0.582
0.13
0.540
0.12
1.187
0.26
Table
X shows t h e e f f e c t
developed to
0.543
value.
K
values.
dy
(soft
clay)
Reqarding
of foundation
For a F
s
= 1.5 K, values dy
correspondent
maximum K
c o n d i t i o n s on t h e r e s p o n s e range
from
0.239
t o 0.05 t o 0.12 o f t h e maximum
values
t h e range
i s wider
and v a r i e s
of (rock) passive from
dy 0.239
(rock)
passive
t o 1.187 ( s o f t
values
developed
(K ) . P
occurs
approximately
c l a y ) o r from
I t i s also
f o r the soft
a 1/4 o f K^.
seen
clay
0.05 t o 0.26 i n t e r m s o f maximum
t h a t t h e maximum h o r i z o n t a l
type
of foundation
and e q u a l s
force
5 7. 5.4.2 So
Effect
of
f a r a dense
sidered.
To
study
Soil soil
the
t h e maximum d e v e l o p e d Table
I
(page
23)
Backfill backfill
effect lateral
were u s e d
of
State of with
the
( 1 9 4 0 ) and
Alameda
foundation
conditions corresponding
soft of
clay
(1962) r e c o r d s .
respectively
safety against
and
sliding,
a zero
soil
f o r c e the
i n the
Compaction
backfill
three
analysis
soil
of
con-
compaction
backfills with
been
on
presented
the
El
deep c o h e s i o n l e s s s o i l flexibility
F
considered
was
state
has
in
Centro
r e c o r d s were a p p l i e d f o r
a foundation =1.5
angle
together
T h e s e two to a
slope
o f L/B
and
=10.
A
f o r a l l cases
a
deep
factor
which
s means t h a t t h r e e states
of
different
compaction,
as
masses were used
shown i n T a b l e
I.
f o r the
three
soil
backfill
In F i g u r e K
dy
soil
versus
21
i s shown
the v a r i a t i o n
acceleration level
b a c k f i l l states of
o f t h e maximum e a r t h
f o r t h e two f o u n d a t i o n
coefficient,
c o n d i t i o n s and
three
compaction.
x o
0
\ I 0.0
Fig. 21
. O.I
1
0.2
1
0.3
1
0.4
0.5 x Gravity
MAXIMUM DYNAMIC EARTH COEFFICIENT, Kdymax VS. ACCELERATION LEVEL EFFECT OF SOIL BACKFILL COMPACTION
59. As
expected
increasing backfill.
the
maximum d e v e l o p e d
acceleration
level
and
horizontal
decreasing
forces
relative
increase
density
of
with soil
60.
5.4.3 The for
Comparison
maximum
maximum
W i t h Mononobe-Okabe
lateral
Analysis
f o r c e s p r e d i c t e d from
t h e Mononobe-Okabe
a c c e l e r a t i o n s o f 0.33g a n d 0.27g a r e shown
with
equation
arrows i n
F i g u r e 22.
1.736 LEGEND • - S.Fernando,l97l
.519
- E I C e n t r o , 1940 O
- Alameda, 1962
X
L/B
o
-
E
S
0.5g 0.22g 0.2lg
= 10
L/B =
1.302
c O
1.085 o O o LU o
0.868
E
o c
>s Q E 3 E
0.651
'x o 0.434
Mononobe Okabe
0.33g
Mononobe Okabe 0.27g -* c —
0.217 1.0 1.5 2.0 3.0 4.0 5.0 Static Factor of Safety Against Sliding
Fig. 22
10.0
MAXIMUM DYNAMIC EARTH C O E F F I C I E N T , K VS. STATIC FACTOR OF SAFETY AGAINST SLIDING COMPARISON WITH MONONOBE OKABE RESULTS dymQX
They
s h o u l d be c o m p a r e d
results. effect
with
T h e Mononobe-Okabe
o f base
sliding
sliding.
or r o t a t i o n
soil
occurs
significant
analysis To
different
illustrate
Mononobe-Okabe
of the E l Centro
obtained
from
fairly
u s i n g t h e same well with
record, although
values
t h e 0.1g a c c e l e r a t i o n
differ
The
approximately
fact
amount o f b a s e Whitman
sliding,
(1978).
level
23 a n d
input data.
lower,
data,
The f o r the
but f o r t h e case
are considerably
ranging
dynamic p r e s s u r e s
a s shown
i n Figure
record.
lower,
( F i g u r e 23) t h e Mononobe-Okabe
of a factor
that the l a t e r a l
the present
the present
slightly
However
the l a t e r a l
f o r 0.27g maximum
A l a m e d a r e c o r d t h e Mononobe-Okabe r e s u l t s
following
with
agree
record.
c o n d i t i o n s f o t h e Alameda Park
results
f o r the
equation
t h e a b o v e F i g u r e s 21 i s r e - s h o w n
results
In F i g u r e
analysis
t o the E l Centro
the r e s u l t s
base
t h e Mononobe-Okabe
i s o b t a i n e d when c o m p a r i n g
foundation
t h e Mononobe-Okabe
consider the
conditions.
f o r c e s p r e d i c t e d from
t h e Mononobe-Okabe with
record
involved i s that sufficient
to mobilize the a c t i v e
i n results
acceleration
f o r the s o i l
presents
the
does n o t d i r e c t l y
conditions corresponding
p r e d i c t e d from
horizontal
case
and Alameda Park
l i e w i t h i n the range p r e d i c t e d i n the p r e s e n t
foundation
forces
equation
The a s s u m p t i o n
22 i s shown t h a t t h e l a t e r a l equation
the E l Centro
from
1.7
should
t o 2.0. vary
with the
i n F i g u r e s 20 a n d 22, i s i n a g r e e m e n t
of
62.
Loose backfill (0= 3 0 ° ) L / B = 10 •
0.0
1
0.1
1
0.2
1
0.3
i
0.4
I
0.5 x Gravity
Fig. 23 MAXIMUM DYNAMIC EARTH COEFFICIENT, Kdymax VS. ACCELERATION LEVEL EFFECT OF SOIL BACKFILL COMPACTION COMPARISON WITH MONONOBE OKABE RESULTS
63. who
considered
that
t h e dynamic p r e s s u r e s
the
underlying
soil
should
predicted (1979)
abutments from
be c o n s i d e r a b l y g r e a t e r
b y t h e Mononobe-Okabe
estimated i n New
equation.
t h a t t h e dynamic Zealand
t h e Mononobe-Okabe
on w a l l s
lateral
were a b o u t equation.
1.4
t h a t moved than
rigidly
the pressures
In a d d i t i o n , Rowland f o r c e s on damaged
t o 1.8
times
with
and Elms
bridge
the values
predicted
64. 7.
CONCLUSIONS
A
s i m p l e method
forces
of analysis
and d i s p l a c e m e n t s
presented.
The method
flexibility
and s t r e n g t h
of
a n a l y s i s was a p p l i e d
three
different
foundation The
the b a c k f i l l
of strength
loss
t o a 20 f e e t h i g h
induced
t o be c o m p u t e d i s of the wall
and t h e
and f o u n d a t i o n
i s not considered. cantilever wall
excitations representing
displacements of the wall
factor of safety
2)
wall
that
against
soft
soil. The method
subjected
to
t o hard
sliding,
decrease
F s , and w i l l
with
increasing
be l o w f o r t h e
h a s F s > 1.5.
T h e Newmark m e t h o d
gives
a good e s t i m a t e
o f earthquake
induced
displacements. 3)
factor
T h e maximum of. s a f e t y
predicted from
the weight
the earthquake
conditions.
The dynamic
conventional
wall
both
r e s u l t s indicate the following:
1) static
both
o f both
earthquake
soil
allows
of retaining structures
considers
However, t h e p o s s i b i l i t y
which
from
dynamic
against
horizontal force
sliding,
increases
with
the static
F s , a n d may be g r e a t e r
than
the values
t h e Mononobe-Okabe e q u a t i o n
f o rwalls
that
are prevented
sliding. 4)
The i n i t i a l
rest"
or active
force
on t h e w a l l .
somewhat h i g h e r
pre-earthquake
condition
has o n l y
However, h i g h e r
displacements.
static
a small
pressure effect
pre-earthquake
whether
i t be " a t
on t h e maximum static
forces
dynamic cause
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369. Hardin,
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B l a c k , W.L.,
1969
Consolidated Clays",
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1979, " S e i s m i c a l l y I n d u c e d S l i d i n g o f M a s s i v e S t r u c t u r e s " , J o u n r a l o f the G e o t e c h n i c a l E n g . D i v . ASCE. V o l . 1 0 5 , No. G T 1 2 , D e c . 1 9 7 9 . Lambe, T.W. Wiley Lorenz,
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P r o c e e d i n g s 2 n d WCEE, V o l . 1, p p .
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Philosophy,
de s o l o s
Frageis
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Mononobe, N., a n d M a t s u o , M., 1 9 2 9 , "On t h e D e t e r m i n a t i o n o f E a r t h P r e s s u r e During Earthquakes," Proceedings, World E n g i n e e r i n g C o n g r e s s , T o k y o , J a p a n , V o l . 9, 1 9 2 9 . Newmark, N.M., 1 9 6 5 , " E f f e c t s o f E a r t h q u a k e s o n Dams a n d Embankments", G e o t e c h n i q u e , L o n d o n , E n g l a n d , V o l . XV, No. 2, 1 9 2 6 . Okabe,
S., 1 9 2 6 , " G e n e r a l T h e o r y
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of C i v i l
E n g i n e e r s , V o l . 12, No. 1, 1 9 2 6 .
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R., 1 9 7 3 , "On D y n a m i c
Deposits", Soils
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and F o u n d a t i o n s
Moduli
and P o i s s o n ' s
( J a p a n ) , V o l . 13, No.
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P r a k a s h , S., 1 9 7 7 , " S o i l D y n a m i c s a n d i t s A p p l i c a t i o n t o F o u n d a t o i n E n g i n e e r i n g - S e i s m i c R e s p o n s e o f S o i l D e p o s i t s , Embankments, Dams a n d S t r u c t u r e s " , P r o c e e d i n g s 9 t h I n t e r n a t i o n a l C o n f e r e n c e on S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , Tokyo, 1977, p p . 624-630. Peck,
R.B., H a n s o n , W.E., a n d T h o r n b u r n , T.H., 1 9 7 4 , " F o u n d a t i o n Engineering". P u b l i s h e d b y J o h n W i l e y a n d S o n s , I n c . , p p . 415-416.
Reissner,
E., and S a g o r i ,
Elastic
H.F., 1944, " F o r c e d T o r s i o n a l
Half-Space", Journal of Applied
Physics,
Oscillations
o f an
V o l . 15, p p . 6 5 2 -
662. Richards,
R., a n d E l m s ,
Walls,"
D., 1979, " S e i s m i c B e h a v i o u r
J o u r n a l o f Geot.
of Gravity Retaining
E n g . D i v . , ASCE, V o l . 1 0 5 , No. GT4, A p r i l
1979. R i c h a r t , F . E . , J r . , H a l l , J.R., J r . , a n d Woods, R.D., 1 9 7 0 , " V i b r a t i o n s o f S o i l s and F o u n d a t i o n s , " P r e n t i c e - H a l l , I n c . , Englewood C l i f f s , N.J.
6 7 .
Seed,
H.B.
and
Dynamic
Idriss,
H.B., ships and
1970,
"Soil
Moduli
Response A n a l y s e s " , Earthquake
Berkeley, Seed,
I.M.,
C a l . , Rep.
Murarka,
R.,
No.
EERC
Bulletin
site
L y s m e r , J . , and
conditions
of the
Eng.
Res.
Cen.,
Idriss,
I.M.,
U.
1976,
Maximum V e l o c i t y ,
f o r Moderately
Seismological
Damping F a c t o r s f o r of C a l .
70-10.
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"Relation-
D i s t a n c e from
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Earthquakes.
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1976. Seed,
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Sharma, S.K., 1975, " S e i m s i c S t a b i l i t y o f E a r t h Dams and G e o t e c h n i q u e , V o l . 25, No. 4, D e c . 1975. Terzaghi,
K.,
1934,
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Timoshenko, Hill Whitman,
S.P.,
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1972,
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1951,
Theory
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I n c . , New
D y n a m i c a l l y Loaded Foudnations
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Embankments",
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M.I.T., P.
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Motion", Specialty Pasadena,
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1976, Walls
International
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V o l . 1. p p .
817-829.
to Earthquake
Ground
P r o c e e d i n g s o f t h e ASCE G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n Conference 1978.
- E a r t h q u a k e . E n g i n e e r i n g and
Soil
Dynamics,
APPENDIX PROGRAMME WALLQUAKE
69. APPENDIX -
PROGRAMME
A.
Data
Input The
programme w a l l q u a k e
Statements, 1st
descriminized
reads
EKP,
RH0,
SK,
WM,
f a c t o r of
EKA
Active
earth
(7F
10.3)
safety against
coefficient
friction
angle
EKP
=
Passive
RH.0
=
0.5yH , q u a n t i t y
earth
coefficient,
of
=
3 READ
Input
the
parameters
are:
sliding
( 1 - S i n cf>)/(1+Sin $)
soil
backfill)
coefficient =
1/EKA
t h a t when m u l t i p l i e d b y
2
(Y =
through
C
Static
( =
parameters,
a FORMAT
SAFETY = =
17
below.
READ STATEMENT - U s i n g
SAFETY, EKA, where:
WALLQUAKE
K,
gives
u n i t weight
of
the
soil
correspondent backfill
and
an
earth
earth H =
force.
height
of
the
wall). SK
=
Base
spring
stiffness
constant,
K
as
defined
in
B (3.3.2.2). WM C
2nd TI,
READ STATEMENT - U s i n g
S C A L E 1,
where:
= Mass o f t h e w a l l p l u s s o i l b a c k f i l l a s d e f i n e d = E f f e c t i v e damping, C , as d e f i n e d i n ( 3 . 4 ) . B
T0
a FORMAT
(4F
10.3)
the
in
parameters
(3.2).
are:
T0,
TURN. =
Time
interval
record.
Most o f
acceleration intervals, records. data
used
the
data
s u c h as The
i n 0.01
i n the
earthquake a c c e l e r a t i o n
earthquake
presented the
San
Alameda Park seconds time
records,
i n 0.02
have i t s
seconds
time
F e r n a n d o and
the
record
exception
as
intervals.
an
El
Centro has
its
70. This
parameter
i s used
w i t h two
a) S u b d i v i d e t h e e a r t h q u a k e
objectives:
data.
I f T I = T0
subdivision
of earthquake
acceleration
If
T0
of the earthquake
T I = 0.5
obtained an
the double
f o r t h e same r e c o r d
appropriate
b) To i n p u t
array
duration
for later
the desired
no
data i s performed. data i s
and i s s t o r a g e d i n
use.
initial
time
increment,
At. (see
(3.5) ) . This
parameter
scale
i s used
the earthquake
0.5
that
means t h a t
the
record
will
be
t o determine
acceleration
values.
the earthquake scaled
t h e "SCALE" u s e d
t o 0.5g
to
I f SCALE 1 =
acceleration
v a l u e s of
(g = a c c e l e r a t i o n
of
gravity) Example SCALE
1 g
SCALE = MAX. For
t h e C a s e o f San F e r n a n d o
acceleration SCALE SCALE :
ACCELERATION
v a l u e = 3462,
1 = 0.5, =
a n d g = 32.2 9
3462
=
Parameter
used
"critical
points".
VALUE
OF
Record
RECORD
( 1 9 7 1 ) t h e maximum
assuming feet/sec
0.004650
to limit
t h e number
of s u b i t e r a t i o n s
at
71. "Critical from
points"
elastic
are points
to plastic)
velocity).
At these
the
inputed
to
initial obtain
The
rules
Point
used
points
Until tial ler
this time
i s only
those
"points".
follows:
permitted
to turn
when
the
TI, i s subdivided
i s only |X
permitted |
