ASTUDY OF SEISMIC RISK FOR NICARAGUA,PART 1 by Haresh C

Transcription

Department of Civil and Environmental Engineering
Stanford University
A STUDY OF SEISMIC RISK FOR NICARAGUA, PART 1
by
Haresh C. Shah,
Christian P. Mortgat,
Anne S. Kiremidjian
and
Theodore C. Zsutty
Report No. 11
January 1975
The John A. Blume Earthquake Engineering Center was established to
promote research and education in earthquake engineering. Through its
activities our understanding of earthquakes and their effects on mankind’s
facilities and structures is improving. The Center conducts research,
provides instruction, publishes reports and articles, conducts seminar and
conferences, and provides financial support for students. The Center is
named for Dr. John A. Blume, a well-known consulting engineer and
Stanford alumnus.
Address:
The John A. Blume Earthquake Engineering Center
Department of Civil and Environmental Engineering
Stanford University
Stanford CA 94305-4020
(650) 723-4150
(650) 725-9755 (fax)
earthquake @ce. stanford.edu
http://blume.stanford.edu
©1975 The John A. Blume Earthquake Engineering Center
A STUDY OF
SEISMIC RISK
FOR NICARAGUA
Part I
by
Haresh
Christian
C. Shah
P. Mortgat
Anne Kiremidjian
Theodore
The John
A.
Blume
Department
Earthquake
of
Stanford
Stanford,
This
research
Banco Central
C. Zsutty
Civil
Engineering
Center
Engineering
University
California
was partially
94305
supported
by
de Nicaragua and by NSF GI 39122
ACKNOWLEDGMENTS
The authors
of
this
Incer,
B. President
of
Banco Central
Muniz,
General
est
this
in
Manager of
project
report
would
giving
to
thank
de Nicaragua,
Banco Central
and for
like
Dr.
and Mr.
de Nicaragua,
them
their
Roberto
time
for
their
and their
The help and advice of Arq. Ivan Osorio and the personnel
cion
Urbana
to take
are
this
gratefully
opportunity
Filadelfo
Chamorro,
gave
advice,
and
them
encouragement,
risk
in
they
Foundation
model
Chapter
is
also
grant
spite
could
of
not
GI 39122
Jose Francisco
Teran
and
is
about
Mr.
Ing.
and
by
assistance
appreciated
the
development
much appreciated.
ii
their
provided
theoretical
like
busy schedule,
without
learned
acknowledged.
very
extremely
support
for
of Planificaalso
their
have
patience.
would
Truly,
The partial
gratefully
2 on geology
Arq.
and direction.
in Nicaragua.
conditions
Science
to thank
G
inter-
authors
acknowledged.
who, in
help,
The
Carlos
David
Hoexter's
the
National
of
the
help
SYMBOLSAND DEFINITIONS
= Fixed
a
A
,
A
Acceleration
= Effective
Ground
Acceleration
g
AZG
= Acceleration
c
= Subscript
for
Condemnation Threshold
Subscript
for
Structure
Subscript
for Condemnation Capacity
Zone
Condemnation
Charts
Capacity
Threshold
Spectrum
for
Structure
Deformation
Determination
D
=
Subscript
for
= Effective
= Dynamic
IYfSS
KG
Damage Threshold
Ground Displacement
Amplification
Factor for
Subscript
for
Damage Capacity
Subscript
for
Earthquake
Subscript
for
Member
=
Damage Threshold
=
Expected
=
Confidence
Spectral
Demand
Design
Spectrum
Level
for
Member
Strength
Use Group
Determination
Value
Limit
Contribution
due
to
due to structural
Kr
= Confidence
Limit
Contribution
(KG+~)a
= Confidence
Limit
above the mean DAF
t
= Structure
m
= Fixed
M
= Richter
~
Shape
Life
Richter
in years
Magnitude
Magnitude
= Body WaveMagnitude
iii
system
type
MS
= Surface
Wave Magnitude
MMI
=
Modified
Mercalli
n
=
Number
of
events
=
Number
of
earthquakes
N' (M)
= Normalized
p
=
p
= Probability
R
= Reliability-
RP
=
Return
s
=
A basic
a
ce,T)
above
Richter
Magnitude
M
N(M)
Probability
of
success
(Bernouilli
Trials)
l.-P
Period
acceleration
response
wi th damping S, and period
= Square
T
spectrum
ordinate
Root of Sum of Squared Mbdal Responses
t
=
Fixed
v
=
Lateral
v
=
Effective
g
Intensity
Period
Load
~
= Damping
~t
= Modified
BF
= Damping
due
to
Earthquake
Motion
a
Ratio
Damping Ratio
due to structure-foundation
Damping due to structural
~
= Deformation
4
= Mean Rate
~
=
Ductility
Ground
Coefficient
Normalized
=
Time
GroWld Velocity
= Regression
at
of
of Occurrence
interaction
system type
(Poisson Law)
Ratio
pt
= Modified
Ductility
Ratio
<1
= Standard
Deviation
of the na.F
iv
for
a system
TABLE OF CONTENTS
Page
ii
ACKNOWLEDGMENTS
iii
LIST OF SYMBOLSAND DEFINITIONS
Chapter
1.
Chapter 2
INTRODOCTION
1
GEOLOGICSETTING.. . . .
5
Relation
to
Plate
Tectonics.
Geology
of
Nicaragua
Geology
of
Managua
Volcanism.
Soils.
.
Water
.
.
.
Depression.
Region.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Levels:.
Paul
ting '. . . . . . . . . . . . . . . . . .
Chapter 3.
SEISMIC
22
DATA BASE ~
Introduction.
...............
Data Analysis;.
. . . . . . . . . . . . . . .
Limi tations.
. . . . . . . . . . . . . . . .
Chapter 4.
PROBABILISTIC SEISMIC LOADING:
TION MAPPING OF NICARAGUA. . .
lSO-ACCELERA-
Poisson Model of Seismic Occurrences -' /. . . .
Source Mechani sms c::~ . . . . . . . . . . . . .
Peak GroundAcceleration at a Site.
Iso-Acceleration Mapsfor Nicaragua.
Chapter S.
of
Return
Acceleration
Period
and
Zone Graphs (AZG)
.
.
.
.
.
DAMAGE
ESTIMATION. . . . . . . . . . . ..
Forecasting.
"Insurance
.
Risk"
.
.
.
.
.
.
.
or Damage Potential.
v
.
.
. . . . . . . . . . .
PROBABILISTIC INTENSITY FORECASTING--
t.f.fI
50
51
54
56
68
93
Seismic Risk Zoning",.
Chapter 6.
. . . .
. . . .
SEISMIC RISK ZONING
Concept
22
27
47
so
...............
Introduction.
S
6
10
1.1
12
.tZ
1.2
.
.
.
. .
.
.
.
. . . .
93
110
116
116
118
TABLE OF CONTENTS (Continued)
Page
Chapter 7.
THE RELATIONSHIP OF ISO-ACCELERATION
AND ACCELERATION ZONE GRAPHS (AZG)
TOSEISMIC
DESIGN
PROVISIONS.
. . . . . . . . .
Introduction.
Basic
.
Response
Response
Types
Spectrum
of
Force
Properties.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Terms
Resisting
.
.
of
139
148
155
Their
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Spectra.
Design
Construction
Chapter 8.
.
Systems.
156
.160
165
and Formulation
of Design
in Terms of Modified
Inelastic
Proposed
.
in
Spectra.
Definition
Spectra
.
Analysis.
Structures
Lateral
Design
.
Spectra.
139
.
Procedure.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
of Example Design
Spectra.
. .
165
172
174
SUMMARY, CONCLUSIONS, AND FURTHER RESEARCH ~ ..
REFERENCES
Appendix
1.
THE DECEMBER
23, 1972 EARTHQUAKE
.
Appendix 2.
MODIFIED MERCALLI INTENSITY SCALE
Appendix 3.
LISTING OF EARTfKlUAKES
Appendix 4.
COMPUTERPROGRAMLISTING.
Appendix
5.
NEWMARKAND HALL PAPER
Appendix
6.
VERTICAL
ACCELERATIONS.
. . . . . . . . . . . .
vi
A6-1
CHAPTER I
INTRODUCfION
On December 23, 1972, three
the
city
of
caused
of deaths,
and disruption
if
to
impossible
economic
However,
terms.
devastation
translate
and
far~reaching
rebuilding
Are
questions.
future
risk
translated
such
design
acceptable
design
the
for
other
icant
damaging
these
questions
future
questions
event.
is
making
ately
times,
no significant
process
after
significant
on irrational
on at
of
in
the
a notably
events
analysis.
are
slow
often
up many
What
risk
level
level
similar
relevant
be
land
after
leads
taken
to
These
answers
the
while
based
on expediency
for
engineer-
process.
to decisions
uses
a signif-
expediency,
place~
of
damage?
rate,
leads
!
events
bring
major
making
have
This
events
the
and proper understanding
decision
events
us of
earthquake
Should
political
hard
quantitative
acceptable
which
very
remind
suffered
process
optimization
earthquake
goes
the
event
amount of
is
adequate?
especially
mixture
involved
such
which
The decision
ing knowhow, socioeconomic
parameters
areas
into
major
parameters?
become
a complex
of
follow
How should
It
does
requirements
into
and numerous
when
which
acceptable?
in
overall
a catastrophe
is
be permitted
losses
consequences
efforts
existing
these
life.
struck
this
an untold
of a way of
all
tremors
magnitude,
many more injuries,
economic hardship
not
earthquake
Even though of "moderate"
Managua.
thousands
strong
of the
In
times
decision
decisions
which
immediand,
at
might
well
be considered
on the
basis
of
This
Stanford
inadequate
long-term
report
is
Science Foundation
Nicaragua
In
is
Part
result
in
I
light
of
two
is
of
rational
a seismic
by Banco Central
decisions
made
parts
associated
risk
study
conducted
at
de Nicaragua and the National
The
grant GI 39122.
done
general,
the
perspective
the
and supported
in
total
This
report
with
the
seismic
is
risk
Part
future
I
analysis
of
the
probably
of
study.
seismic
load-
ing
determination
termine
of
future
regarding
and
seismic
design
Part
I,
zoning
spectra
the
in
structures
and
of
associated
risks
in
developed,
tailed
The
to
procedures
of
loss
method.
be emphasized
a base
results
make
for
planning
provide
major
effort
with
probabilistic
is
concepts
This
seismic
is
that
risk
focused
in
all
on presenting
2
classes
analysis
loss
will
be
design procedure will
of
the more de-
approach
making
in
in
Nicaragua
future
is
intended
structures
presented
A single
analysis.
to fit
economic
regular
and decision
of
A decision
simplified
work
this
information
different
and findings
the
de-
response
of
and
equivalent
-in
loading
response.
injury
to
a continuation
exposure
professionals
today does not appear practical
Hence,
II
used
Suggestions
seismic
for a maj ori ty of ordinary
should
to
life.
be
presented
Part
structural
of
can
risk."
also
between
A simplified
spectrum
loading
are
seismic
based on the general
provide
project
country
associated
seismic
II.
to be applicable
is
the
Part
response
It
the
discussed.
is
that
and "insurance
probapilistic
of
performed
is
general
analysis,
of
how
relationships
provisions
and
and
damage potential
Similarly,
part
Nicaragua
this
report
Nicaragua
with
tools
and
recommendation
circumstances
methodology
and procedures
be
that
can be used
by participating
organizations
in
decision
making
processes
Finally,
presented
here
reliability
data
it
of
on which
criticize
any
ever,
it
is
have used
on the
results
are
the
results
work
from
best
the
if
However,
model
can
easily
in
Chapter 3.
results
of
the
future
2 deals
data.
in
detail,
future
particular.
obtain
as
and
the
data
this
time,
here
are
of
on this
the
the
on those
available,
new information
will
of
this
"best
and
be prereport
feel
available"
is
organized
the
in
geo'logic
In
eight
chapters
setting
this
of
chapter,
Chapter
and
the
geologic
3 gives
the
esti
chapter
should
be
carefully
read
of
the
available
seismic
treated
in
models
maps for
Chapter
the
based
the
5,
country
the
present
work.
on past
data.
in
concept
3
general
of
in
appendices.
general
hazards
because
data
Chapter
seismic
selected
zoning
and
their
on avail
it
points
out,
and how those
4 develops
and presents
and
and
discussion
This
shortcomings
six
Nicaragua
out.
In
organizations
forecasts
with
are
We
data.
are
topic
authors
represent
and
How-
based
data
inclusion
the
attack
various
reliable
discussion
to
reliable
and predictions
the
of
reliability.
through
more
The
information
easy
long-range
and results
reliability
very
of
work
pointed
forecasting
acceleration
base
is
view
the
are
the
shortcomings
It
of
future
At
Managua in particular.
implications
data
information
presented
The report
Chapter
to
that
as good
point
Further
sented
mind
based.
accommodate
results.
mates
the
the
the
the
are
forecasts
in
update
that
best
available
The
in
available
at
difficult
researchers.
data.
be kept
depend
very
the
should
the
iso.
cities
is
in
presented
Charts relating
period
and
risk
the
corresponding
presents
some thoughts
tionship
between
needed design
II
part
of
I
the
4 and
see
start
with
structural
should
As the
zoning,
II
of
the
group
Chapter
and use
7 should
return
presented
of
in
that
prediction
7 gives
the
structures
be viewed
and
rela-
and
the
as an introduc-
study in which further
design provision
Chapter 8 gi yes summary and conclusion
be presented.
research
are
damage potential
risk.
Chapter
of the current
of structures,
levels
on insurance
seismic
will
In
it
loading
provisions
to part
development
for
economic life
Chapter 6 deals with future
chapter.
tion
level,
project
and
introduces
to
the
reader
part
with
Chapter
study
reading
the
this
report,
forecasting
Chapter
engineer
5 to
on future
see
the
reader
seismic
seismic
can
start
loading.
zoning
of
A planner
can
country
A
the
should read Chapters 4, S, 6, and 7.
be emphasized
name implies,
a casual
that
there
a chance that nature will
this
are
is
a report
many uncertainties
have the last
4
say.
on seismic
and
In
conclusion,
risk
analysis
there
is
always
CHAPTER I I
REGIONAL GEOLOGIC SE1iING
Relation
to
lies
tectonics
of
the
lies
on the
western
new global
underridden
Plate,
to
in
the
many
plates.
sion,
and
the
to
Costa
of
also
crust,
arcs
km deep,
the
Cocos
extends
Rica,
and
runs
the
is
and
of Managua
parlance
apparently
the
the
being
Atlantic
or long,
of
of
linear
depres
intersection
of
the Nicaragua
Depres-
arc.
plate
the
of
intersections
Middle
Plate
west
west,
such a graben,
of
is
the
Plate
characteristic
a volcanic
a trench
In
and grabens,
within
characteristic
such
to
which domin-
The city
Plate.
Caribbean
Plate,
are
"Ring of Fire"
region.
Caribbean
the
Volcanic
within
of
Ocean
the
Cocos
Managua lies
depression
4-5
the
earth's
case,
is
Pacific
tectonics,
east.
Another
this
the
plate
the
on the Circumpacific
edge
by both
sions
In
Tectonics
Nicaragua
ates
the
Plate
below
the
America
the
Central
sub-parallel
to
are
Trench,
Caribbean
American
the
ocean
trenches
which
marks
The trench
Plate.
Coast
arc-shaped
from
chain
Mexico
of
andesitic
stratovolcanoes.
Marking
generally
termed
earthquakes,
interior.
zone,
the
descent
the
Benioff
extending
The
as they
1972
were
of
the
Zone.
several
earthquakes,
much shallower.
Cocos
Plate
is
a zone
of
friction.
This zone is marked by numerous
hundred
kilometers
however,
did
They
were
s
not
into
occur
probably
the Earth's
along
this
related
to
relatively
the
shallow
southwest
GeolOR:Y of
part
the
The
Nicaragua
of
or
the
feature
or the
from
Rica,
in the south (figures
placed
the
by
Mateare
began
has
at
Fonseca,
the
to
the
fault
is
or
of
regular
It
the
of
the
fault,
suggesting
less
recent
cal
movement
Pacific
fault
of
Nicaragua
by a long,
the
Depression
near
Limon,
ex-
Costa
The western boundary
Ocean,
by
others
along
Downfaulting,
zone.
about
1,000,000
(opposite
The
either
it
which
years
ago,
normal
Mateare
have
been
is
movement
Fault.
taken
moves
In
laterally
tilted
is
to
the
This fault
along
the
entire
away
from
the
or
that
it
minor,
addition,
on several~
suggests
rocks.
traceable
floor
a normal (block
locally
by volcanic
is
graben
fault,
block
buried
Mateare;
on the
at depth probably
downward)
locally
the
that
could
to
and 2-3).
although
Depression.
than
Region
the
Fault,
north,
Quaternary,
slip
is
than
length
within
present
strike
movement.
more
the
the
moves relatively
right-lateral,
right)
to
beneath
The Boundary Fault,
above the
Coastal
called
Boundary
a semi-continuous
beginning
continued
(also
2-1,2-2,
some workers
Fault,
Pacific
Bounded on the northeast
fault,
of
the
Depression
tends
is
strain
Plate.
of
Valley).
Gulf
crustal
Depression
Nicaragua
en echelon
the
to accumulating
Caribbean
Nicaragua
Central
straight,
the
outstanding
is
Graben,
adjustment
much of
sub-parallel~
the
verti-
en echelon
faults.
The Mateare
Where
prominent,
it
Fault
is
is
less
a normal
clearly
fault,
6
expressed
displaying
in
all
a scarp
is
places
with
a
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maximum
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height
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of
as evidenced
despite
easily
Latham
calculate
the
in
graben
the
eroded
as
2.4
by
sediments,
Sierras
slight
erosion
rocks
and high
vertical
adding
the
The uplift
de Carazo.
of
the
upland
along
thickness
of
surface
Matumoto
rainfall.
movement
the
western
accumulated
drop (scarp)
km) to the vertical
Depression
deeply
contains
weathered
aggregating,
The basement
rocks
nor
ejected
from
volcanoes.
are
largely
buried,
a thicker
volcanic
are
and
edge
(See
although
of
being
exposed
to
to
subsidence
in
in
of
the
this
excess
Tertiary
southwest,
part
of
the
deof
1400
by wells
volcanics
This sug-
northeast.
the
lake
flow
penetrated
hills
accumulation
greater
thickness
neither
isolated
more
alluvium,
and some volcanic
to a total
The
of
giving
graben
Geology of Managua Regi2n
The
and
city
sediments
section
though
is
of
Managua
aggregating
probably
specific
at
typical
units
sits
least
of
lense
atop
1000 meters
the
out
a succession
entire
and
are
of
in
Depression,
by other
rocks
The
thickness.
Nicaragua
replaced
volcanic
units
alelse-
where in the graben.
To a depth
of
at
least
homogeneous and predominantly
angular
posits.
of
sediments
(1 km).
accumulation
ash,
unknown,
sedimentary
evidence
a thick
as stated,
m.
further
the
11.)
The
gests
the
total
km
(1.4
by
along
volcanic
the
graben
reference
posits,
1000 meters
scoria,
These
or cinder
are
derived
200 m,
the
volcanic
deposits,
either
section
sequence
with
from
10
is
of
interbedded,
Masaya
Crater,
a relatively
lapilli-sized,
thin
ash de-
22 km distant,
or
the
line
lithified
volcanoes
are
scoria
is
thick
and
vertical
slopes if
of
the
rocks
the
rocks
common.
The
stones
features
a low
and
bulk
density
loads,
~
stable
under dynamic loading
emphasize
sedimentary
rocks,
especially
aid
in
Amore
exact
predictions
of
attenuation
of
the
of
Managua,
with
in
stands
here
seismic
in
in
near-
of
wave
general,
lava
similar
during
lake
the
nature
propagation,
and
the
effect
particular
dense
pyroclastics
occurred
determination
waves,
relatively
the
because of the greater
probably
also
static
but is
on accelerations,
damage
are
as building
and
under
undisturbed,
would
associated
Less
deposits
well-
14).
West
are
and relatively
be used
permeable,
in the sequence.
especially
mudflow
to
stability
Some authors
sediments,
Firm
west.
enough
porous,
good
(~ee reference
the
the
volcanic
firm
extremely
demonstrates
of
to
(consolidated)
These
It
of
to
1972
distance
flows
those
and vent
underlying
earthquake.
from
debris
the
but
the
this
earthquake
city
is
epicenter
14).
(see reference
Volcanism
The
tially
active
derived
Crater,
historic
within
the
Depression
Managua
that
have
centered
times
underlying
Nicaragua
area.
sediments
Masaya
lies
entire
lies
been
atop
22 km distant
reference
12).
city
have
traced
been
and
the
Managua,
some of
to
this
offset
11
an active
or
pot en-
and volcanically
in
from
right-lateral
either
volcanics
deposited
(see
an apparent
is
the
recent
has
geologic
been
volcanic
same volcanoe.
of
a line
of
active
past.
in
deposits
Managua
volcanoes,
the
Cordillera
The reason
de 105 Marrabios.
for
this
offset
is
unclear.
Soils
The
soils
throughout
of
the
canic
deposits
loose
to
Managua
city
(Figures
of
well-consolidated
The
few to several
hundred
as degree
The
sites.
It
depths.
is
Water
Levels
m in
first
city
reaches
to
within
deep
to
be of
(see
references
is
are
gravels
However,
material
occurs
of
from
a
thicknesses,
even
at
reference
at
indi-
variable
sandstone,"
10-30 m below
from
cementation"
layers
variable
(see
ranging
of
well-defined
somewhat
agglomerate
mainly of vol-
degrees
or "volcanic
generally
similar
but in
17).
the
ground,
and
Near Lago de Managua (Lake Managua) it
center.
3 m of
significance
17.
various
in
"rock-like"
tuff
and
thickness.
"cantera,"
table
the
sand
occur
compaction,
a volcanic
The water
silts.
soils
relatively
They "consist
centimeters
is called
reality
19
of
whole,
2-4,2-5)
and having
17).
vidual
on the
cohesionless
(see reference
as well
are,
the
For
surface.
in
the
design.or
most
of
the
location
of
city,
it
is
too
foundations
14).
~aulting
The faults
of
faults
which
some normal,
part
of
the
east
the
or
city
which pass through Managua are members of a system
scar
much of
vertical
the
In
movement.
show movement
demonstrate
Nicaragua
the
down to
general,
the
Thus,
opposite.
12
The faults
Depression.
east,
faults
in
whereas
a shallow
show
the
western
faults
to
composite
graben
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within
extremely
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the
in
1972 earthquake
Fault,
ourselves
final
discussions
rently
downfaulted
other
to
is
the
underlying
Active
volcanics
A few
same
in
more
zones
from
as faults
light
(2)
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the
the
poorly
where
distance
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offset
defined
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relation
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total
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more
these
ad-
faults~
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of
to
fault,
and on the
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and vol-
than
1000 m in
seismic
zoning
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offset
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in
earthquake
displacement
a structure
active
thickness.
surface
relating
actual
1972
there
4 suffered
by an active
as each zone of
or
seismic
As many as 10
least
Depression
fault.
points
fracturing
to
and
and made available.
Depression
important
at
thorough
Nicaragua
cover part
because
earthquake
remarks
active
in Managua,
significance
agree-
describe
15
suffer
earthquake
should
be considered
actually
occurred
should
of
past is not of
could
a future
follow:
than a line
Whether the I'faul tll has moved in the recent
movement.
fracture
general
as an aid
One other,
1931
Wltil
city,
Managua.
2-6.2-7);
(1) Each of the 10 "faults"
either
in
bounded on one side
the
the
faults
the
completed
by a potentially
canics
in
wait
conclusion,
block,
in
was to
however,
2-8).
some general
must
underway,
In
(Figure
was offset
dress
is
study
difficult,
have been mapped (Figures
Stadium
earthquake
geologic
faulting
faults
the
1972
displacements.
pattern
zoning.
in
be placed
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the
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pre-
In a
California,
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in
located
rupture
as the
opinion
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structures
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in
although
zones,
outward
opinion
same trace
movement,
this
would
not
case.
of
on which the structure
the
material,
are
case of Managua, these
would
on
our
that
same line,
fault
occur
stations,
the
as Managua,
because
exceptions
the
San Andreas
along
saturation
the
nearly
observed
zone or individual
(3) The type of material
the
been
much wider
is
and fire
as
has
easily
from any fault
can be expected
in
within
breakage
police
100 feet
along
located
rupture
as hospitals,
major
repeatedly
are
It
debate.
of
the
nearness
be saturated
materials
fill
faired
extremely
parameters
of
seismic
and
lake
especially
rests,
and
important
are relatively
The only
activity
Structures
sediments.
poorly
in-
in
the
1972
earth-
quake.
(4) The definition
Many geologists
terion
In
40.000
the
economically
pated
tegically
valid
of
important
defined
faults
of
argument
impractical
lifetime
years
This,
of "active."
addition,
over
use
of an "active"
when
less
than
the
city
the
course,
that
is
public
is not agreed upon
last
movement
often
even
considering
100 years.
and large,
in
since
fault
difficult
10,000
structures
It
is
our
structures
of Managua, unless
18
as the
to
years,
with
opinion
should
or
cri-
determine
less,
is
an anticithat
stra-
not be located
the most conservative
(40,000
years)
10 faults
and
some buried
~y
no
definition
that
longer
"active"
zones
is
discussed
As a practical
have
~
This
used
earlier,
as well
manner for
displaced
.It
is
be found
by numerous
surface
unlikely
within
that
the
a better
Nicaragua
On a random
faults.
rupture
chance for
would
rupture
be
less,
location
movement
would require
have to locate
would
city
should
one fault
moved
in
the
where
critical
zone
or
zoning
sistance
develop
are probably
in
a future
fault
rupture
should
individual
rupture.
scheme
to
(fie.
study
cOlporate-results
and
not
design
the location
the
of
future
that
of rupture
zoning
still
are
geologic
the
and fault
study
19
such
the
chances
actual
a lesser
study,
wi thin
other
fau1 ts
faults
hazard
point
main
concern,
of
of
the
chapters
should
zones within
hazards
one
For re-
hazard.
It
of
fault
20) suggested
following
geologic
only
~
4
100 feet
requirements.
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cut
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(see reference
and zoning
is
"fau! ts"
a geologic
within
loading,
graben
site
displacement
Wallace
could
and time-consuming
that
From
be built
city
To find
and at least
likely
fault
city,
active
earthquake.
vibrational
for
and
is
the
or near-surface
2-8) based on strictly
seismic
criteria
it
the
greater.
fault-free
potentially
earthquake,
facilities
in mind that
under
the
of Managua,
and the chances for
or
in the 1931 earthquake.
1972
the
an exhaustive
surface
for
as
from
same,
an almost
be considered
ruptured
could rupture
view,
to
as possibly
the city
Depression,
the
Each of the identified
the
apply
the "White Pumice" unit
for an earthquake would be equal or greater,
which
would
active.
(5)
easily
fracture
faults.
faults
of
will
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Managua is
should
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OIAPTER I I I
SEISMIC
-
DATA
BASE
Introduction
In
also
Chapter
discussed
of
geologic
a facility
or vibration
omic
the
we discussed
general
hazards
that
One major informational
consider.
planning
2,
that
In
life.
in
this
other
words,
helps
parameters
They
used
in
seismic
in
the
planners
region
will
We
Nicaragua.
and builders
one has
zoning
literature
is
the
amount
have to undergo
to
consider
dynamic loads for which the structures
formation
of
should
parameter needed in any future
a seismic
facility
geology
of
shaking
during
the
future
its
seismic
Such in.
should be designed.
of
a region.
to
represent
There
the
econ-
are
various
seismic
loading.
are:
(1)
Richter
Magnitude
(M);
(2)
Modified
(3)
Peak
(4)
Spectral
(5)
Root Mean Square
Mercalli
ground
Intensity
acceleration
(MMI);
(PGA);
Intensity;
(RMS) acceleration,
velocity,
or
are
the Richter
displacement.
However,
the most commonly used loading
Magnitude,
eration.
the
form
the
Modified
As for
the
of
overall
Mercalli
Richter
energy
Intensity,
Magnitude,
release
parameters
of
22
and
the
the
loading
a seismic
peak
ground
information
event.
It
does
accelis
not
in
explicitly
represent
a loading
the
of
release.
source
energy
The Modified
an earthquake
a site.
at
Thus,
Mercalii
a given
for
different
distance.
Appendix
casting
of MM lntensities
as
engineering
the
used
peak
ground
ground
is
the
peak
ground
frequency
content,
veloped
for
different
parts
regarding
the following
(1)
of
intensity
help
from
effect
of
damage
various
Future
in
with
fore-
determining
the
However, for
risk.
parameter
is
at
sites
decreases
scale.
this
In
acceleration.
be used to represent
normalized
of
country
past
scale
a region,
region
the
design
not
struc-
as useful
these
in
seismic
some time
peak
frame,
In
events.
this
work,
the
seismic
spectra
will
peak
load
be de-
(See Chapter 7.)
country.
probabilistically
the
the
away
The most commonly and conveniently
(PGA) will
To estimate
represents
general,
purposes,
For
formation
in
and hence insurance
acceleration.
acceleration
throughout
event
a given
design
some distance
a subjective
In
for
level.
levels
scale
is
seismic
site
2 gives the MM Intensity
and
parameter
It
site.
intensities.
damage potential
tural
a given
Intensity
a given
experience
future
at
ground
acceleration
we need
particular,
to
get
we need
into
~~rmation:
Epicentral
locations
of
past
seismic
events;
2) Time of occurrence;
(3: Magnitude
(4)
Depth
with
each occurrence;
of hypocenter;
5) Acceleration
6)
associated
records
at different
sites;
If
information
possible,
associated
with
on how energy
23
the
above
(or
peak
occurrences
ground
get
acceleration)
to
Central
cuss
in
general
items
in
two
National
depth
Information
for
events
The
used
list
to
The
u.s.
1900 was the
the
data
total
the
base
of
Com-
obtained
from
end of
data
from
Earthquake
source
of
(see
this
that
source
was
con-
Nicaraguan
& ~ore,
this
of
obtained
National
"Catalog
the
magnitude
Department
Leeds of Dames
at
dis-
As for
were
Another
1973.
references
develop
basic
for
We will
occurrence,
Agency,
J.
release
available
chapters.
information
1900 to
by David
of
of
Center,
is
particular.
two
time
Information
before
1520-1973"
Angeles.
next
the
from
earthquakes
Earthquakes
the
in
hypocenter,
Boulder.
energy
not much data
& Atmospheric
Oceanic
all
in
of
source.
locations,
of
Center,
contained
sources
detail
Earthquake
National
the
source
and Nicaragua
on epicentral
and
from
from
5 and 6 above,
America
occurrence
suIted
away
items
these
merce,
site
As for
information
the
any
attenuates
Los
report
gives
references
other
21,22,
23, and 24).
Before
available
amount
data,
and
remain
seismic
assume
same for
events
major
the
sources
in
the
base
one
in
recorded
used
in
for
the
with
phenomenon
more.
in
years
increases
with
the
17th,
24
16th,
That
It
Nicaragua
and that
the
each
year.
and
18th
type,
research.
time.
However.
of
the
current
common shortcoming.
years
general
and analysis
be made regarding
few hundred
hundred
use
increases
seismic
the past
a few
were
should
data
have
on the
earthquakes
that
recorded
events
discussion
observations
recorded
changed
the
the
of
data
of
to
drastically
only
the
frequency
realistic
certain
reliability
All
the
we go into
is,
is very
has
it
not
will
number
Also,
centuries
of
This
gives
and
a bias
small,
are
to
the
data
recorded,
because
whereas
in
old
records
This nonhomogenei ty in data reliability
not
get
away
recorded
as
from
to
church records
information
Another
it.
time,
place
for
performance
shown in figure
problem
is
in
and magnitude,
the
but
tied
in
with
variation
the
methods
axis
deformation,
seismic
about
10% about
ever,
this
the
the
demand
to this
events.
and we can
which
conveyed
and
were
not
through
10 percent
such
on the
designed
structure
based
uncertainty
Further
in
the
Also,
torical
events
loading
parameters
substantially,
a large
collection
of
Due to
in
the
above
loading
past
data
or
does
to
mentioned
aspect
not
variations
may result
helps
in
be presented
of
the
the
Howin
overcoming
ground
accelera-
in
Chapter
some unrecorded
estimated
estimates
values
hisof
2S
the
the
are based on
with
considerations~
only
of a well
will
exclusion
could
P1 and P2.
This ability
code
can be
by DI
as peak
change
repre-
a 10 percent
such
because
begin
by
estimate
side.
parameter
inclusion
Thus,
designed
on this
axis
The performance
represented
consequence
discussion
report.
P,
on a well
the pattern
structural
the performance
in
loading
follow
the
D can be represented
variation,
variation
structures,
the vertical
loading).
value
mean performance
variation
this
events
represents
whereas
(or
mean demand
a slight
tion.
large
big
How can one incorporate
well-codified
The horizontal
say,
Corresponding
D2"
events,
of life"
only
the consequences of those performances.
sents
show
and consequences in general
3-1.
formance such as,
of
only
all
quanti tati vely?
structural
the
years,
is a "fact
or through word-of-mouth.
Fortunately,
be
recent
authors
of
this
7
C/)
~
u
Z
&AI
~
a
w
C/)
Z
0
u
C2
C1
°1
D
FIGURE3-
23
°2
SEISMIC DEMAND
report
feel
that
analysis,
the
seismic
are realistic
loading
estimates,
and representative
based
of
the
on probabilistic
future
seismic
load-
two main sources of information
were
ings
pat a Anal~s
As mentioned previously.
The NEIC-NOAAdata file
considered
to August 1973 constituted
is
referred
to hereafter
covering
the primary
as Source
from January
source of information
and
The Catalogue of Nicaraguan
1.
1520-1973, by David J
Earthquakes,
the period
is referred
Leeds,
to as Source 2.
I t was used to obtain
data
.
the
about
Cordillera
.
earthquakes
associated
de 105 Marrabi05
with
volcanic
activity
along
(1850-1973);
data about earthquakes
not reported
in the NEIC-NOAAfile
additional
about
incompletely
(1900-1973);
information
in the NEIC-NOAAfile
The
time
period
and
123 years
the
Cordillera
In
in
analysis.
judgment
from
such
(1900-1973).
data
gathering
for.earthquakes
spite
of
formation
documented
is
thus
associated
73 years
with
for
volcanic
the
whole
activity
country
along
de 105 Marrabi05.
number
the
of
events
events
of
the
complementarity
remained
of
insufficiently
Rather
than
the
two
sources,
documented
disregarding
these
to
events,
a large
be used
as
such
the missing
in-
was generated using a Monte Carlo Process supplemented by
It
is
felt
an additiona
that
the
total
analysis
input
27
benefits
more
than
suffers
The
following
remarks
No critical
.
mation
study
and
Whenever
tude
the
reliability
for
of
both
the
as basic
missing,
with
valid
was made regarding
information
were
Events
are
the
Richter
the
validity
of
the
infor-
data
as
event
sources:
epicentral
location
or
magni-
was disregarded.
Magnitude
smaller
than
contained
in
3.0
were
not
con-
sidered
Source
1
When complete,
for
a given
time
event
depth of hypocenter
one of
the
the
information
of
occurrence,
epicentral
this
location
The magnitude
(km), and magnitude.
source
is
includes
(degree)
in
terms
of
following
(1) CGSMb average (body wave magnitude)
(2)
CGS M
(3)
Richter
The acceleration
the
Richter
average
s
Magnitude
Magnitude
relationships
Hence~
Magnitude.
It
is
wave magnitude)
M.
attenuation
ated from ~ or Ms'
Richter
(surface
used in Chapter
when missing~
known that
and CGS Mb are
for
linearly
this
4 are based on
information
a given
part
of
related
such
that
was gener-
the world,
..!~1.
M=a+b~
In
order
to
was run for
total
data
determine
all
of
by substituting
the
coefficients
the earthquakes
Central
the value of
~
a and b,
of which M and
The
America
the
Richter
a regression
Mb
28
were known using the
Magnitude
in equation 3-1
analysis
was
then
obtained
Whenever data
was
assigned,
as will
From Source
are plotted
on depth
of hypocenter
be e~lained
later
1, 419 events
in Chart
were not
in
the
contained
a depth
chapter.
complete
1 and shown as a function
available,
information;
of depth
they
in Table
3-1
Source 2
When complete,
event:
given
depth,
Richter
time
is
information
of
Magnitude
The depth
event.
the
occurrence,
and
either
either
expressed
by
its
a short
expressed
In
in
epicenter
sometimes
60 km) or I (70 - 200 km).
is
contained
in
source
location
description
same way,
value
or
the
includes
(degree),
of
km or by a letter
the
numerical
this
the
seismic
symbol N
Richter
by a letter
Magnitude
symbol,
as
follows:
Through
a simulation
assigned a numerical
Hence,
from
Source
43
40
events
1 -< M -< 1.1
c-
6 < M < 6.9
DE-
5.3 -< M -< 5.9
process,
Richter
an additional
1 with
8-
partial
all
M< 5.3
the
events
Magnitude from letter
196 events
were
information),
from
events
with
shallow
obtained
(including
as
activity
deep hypocenters
63
events
no data
47
events with
with
N (0
hypocenters
I
-
60 km).
(70 - 200 km).
numerical data on depth (km).
events
follows:
and with
on depth.
29
2 were
magnitude.
distributed
associated
with
volcanic
N (0 ~ 60 km).
Source
hypocenters
events with
3
taken
shallow
Table
Data from
Source
1. Sorted
(Total
3-1
According
Events
Number of
Earthquakes
to Depth of Hypocenter
421)
Depth
Range
(kms.)
0-
8
9
9
10- 19
12
20- 29
159
30- 39
35
40- 49
32
50- 59
34
60- 69
32
70- 79
18
80- 89
14
90- 99
13
100-109
9
110-119
3
120-129
7
130-139
3
140-149
150-159
3
160-169
6
170-179
3
180-189
5
190-199
9
200-215
30
The
466
earthquakes
47 from Source
2),
plots
with
mation
together
from
5 to
gives
the
location,
a function
of
of
From
those
the
from
partial
infor-
events were assigned
to
7.7
in
in
Appendix
magnitude.
Chart
2-7
they
are
pattern
of
3
plotted
the
general
seismic
Nicaragua
regions
dipping
North
East
toward
the
Nicaraguan
This zone is marked by numerous earthquakes
whole
and
extending
range
interior.
source
of
magnitude
several
The
are
get
30 to
closer
Hence,
under
situated
on the
Benioff
for
identified
scale,
as those
these
from
Zone
and nearness
extensive
damage
and
the
are
very
(5
to
generate
31
of
life
due
deep
this
As the
and
30 km).
past
-
200 km).
such as the
2-3
areas,
get
of. earthquakes
(100
major
in
to
hypocenters
However.
populated
loss
-
earth's
coast.
sources,
are shallow
Zone.
the
hypocenters
seismic
do not
the
the
(Figures
Benioff
lowness
coast,
Managua
sources
on the
100 km away
the
30 km)
covering
increases)
into
(t
local
under
the hypocenters
kilometers
Managua
the
as depth
earthquakes
to
deeper.
In contrast,
(larger
hundred
shallow
from
epicenters
2),
value,
those
data of 615 events ranging
earthquakes;
Zone
the
ones
3.0
following
Benioff
coast.
(2)
and
charts.
into
The
the 156 remaining
Using
1 and
depth
these
can be divided
1)
depth
of depth.
magnitude
This led to a total
215 km in
419 from Source
data
as a function
epicenter
depths
listing
complete
were plotted
on depth and judgment,
appropriate
as
with
2-6,
Chapter
In magni tude
earthquakes
due
they
to
their
have
history.
such
shal-
caused
The
December
23,
(3)
The
event
Appendix
Managua.
seismic
1972
I gives
line
of
ities.
volcanoes
seismic
recorded
the
5:
Source
are
into
area
source
this
under
source
of
in
as
Rica
Pacific
coast
the
of
low
themselves
various
shallow
For
sources
this
treated
earthquakes.
one more or
between
in
have
reason
were
tectonic
one
activ-
earthquakes
activity
regions,
other
(Cordillera
seismic
eruptions.
seashore
border,
future
volcanic
30 km) seismic
the
of
by
past
volcanic
4)
Southeast
seldom
the
with
to
Lake
the
less
co-
Managua
and
Gulf
of
Fonseca
seismicity
and Seismicity
Based
divided
(f
The Atlantic
Location
and
(Chapter
with
Costa
sources
are
"associated"
(4) Two shallow
the
local
regarding
Northwest
eruptions
preceding
model
inciding
from
activity,
earthquakes
in
the
details
represents
Volcanic
been
to
activity
de 10s Marrabios)
of
was due
on the
above
13 seismic
sources.
observations,
sources:
Table
3-2
the
Ten
shows
of
these
these
total
number
are
line
13 sources,
of
events
sources
the
was
and
number
of
three
events
and the depth range of each source.
Appendix
source.
using
from
the
Line
sources
regression
the
most
data
3 gives
a listing
were
located
For
analysis.
and
distant
The depth
the
radius
epicenter
of
each
of
area
the
source
earthquakes
by fitting
taken
in
the
a line
sources,
as
the
the
distance
included
through
centroid
from
in
the
each
data
was obtained
the
centroid
source
was computed
32
as an average
hypocentral
to
Seismic
T.ble
3-2
Sources
for
Nicaragua
Source
Number of
Events
1 Line
159
Benioff
Line
186
Benioff
3 Line
72
Benioff
80 - 109
4 Line
31
Benioff
119 - 159
5 Line
41
Benioff
1.60-
215
6 Line
23
"Costa Rica"
5-
39
7 Line
11
Atlantic
8 Line
12
Pacific
9 Line
57
Line
of
Volcanoes
33
10 Line
57
Line
of
Volcanoes
33
11 Area
5
Manag~a Area
12 Area
8
Gulf of Fonseca
13 Area
10
:2
Name of
Source
&
(kms. :
Costa
Rica
5-
39
40 -
79
All
Coast
Costa Rica
33
Depth
33
Line
Area
Depths
5
33
80 -
109
depth
of
all
no or
limited
the
earthquakes
depth
However,
cess
seismicity
of
obtained
by
were
N(M)
=
Number
M
=
Richter
~ is
e are
a measure
source
and
of
8 is
The
larger
the
For
many
sources,
cause
the
unreasonably
sion
lines
magnitude
of
value
determining
for
each
the
following
of
Let
value
of
where
L
proand the
source
locations
source
was
form:
M
above
magnitude
seismic
6,
of
the
line
severity
the
regression
line
beyond
the
for
data,
gave
For
length
range
(See Figures
cutoff.
to
for
for
area
source
~LT
for
line
source
of
the
line
34
source
source
severity
results
of
data
cases,
be-
indicated
two
consistent
3-2 through
regresupper
3-13.)
each source and the
In N(M) . 0.1
~
AT
seismic
erroneous
such
a given
a given
and a geologically
corresponding
=
the
the
0 for
for
smaller
occurrences.
to
was used
N'(M)
location
individual
magnitude
events
the
magnitude
point
averaging
a+8M
above
of
a single
cutoff
the
7 show the
Table 3-3 gives a summary of a' and 8 values
magnitude
this
constants.
number
negative
fitted
in
of
in
with
Magnitude
interpolation
were
events
a measure
high
=
e N(M)
regression
the
included
line
Earthquakes
source
not
relationship
a regression
111
a and
were
the
Charts 2 through
recurrence
fitting
in
considered
source.
The
and depths.
information
they
the
included
35
10__9__-
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SOURCE J.
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ANALYSIS
RISK
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1975
JANUARY.
~
3
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6
7
8
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5-
SOURCE
I I : I I
2
3_,
SEISMIC
2
RISK
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NICARAGUA
1975
JANUARY.
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3
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1975
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1975
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3
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1975
JANUARY.
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3
4
5
6
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MAGNITUDE
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4
SOURCE 7
3
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---: \
1975
JANUARY.
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2
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5
6
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SOURCE
4
9 and 10
3
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NICARAGUA
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3
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JANUARY.
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GRAPHS
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3-13
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4
SOURCE
-13
-'
3
r;-
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SEISMIC
2
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ANALYSIS
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"""""""
!
NICARAGUA
:
~I!,
1975
JANUARY,
III!~II'III~
!
!
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i
Ii!
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f
C
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4
5
rl'f:f
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6
7
8
i i I I
A =
Area
of
1 =
time
for
=
N' (M)
the
which
Normalized
for
area
source
data
was obtained
mean number
unit-time
of
(1 year)
events
above
and unit-area
magnitude
or
unit
M
length.
Then
In
Table
.
al
where
3-3
shows
scribed
previously.
degrees
of
at
+ B M
a
-
In(AT)
for
area source
a
- In(LT)
for
line
values
of
The
latitude
=
N'(M)
~
a'.
table
and
and the
gives
develop the forecasting
source.
upper
values
These
longitude.
3-4
cutoff
of
at
magnitude
andB
in
relationships
as de-
terms
will
of
be used
model in Chapter 4
Limitations
.
the
use
are
given
In
conclusion,
of
available
it
can be said
data
for
the
that
there
Nicaragua
are
limitations
These
region.
to
limitations
below.
1.
24% of
the
the depth.
ment
the
2.
or
by
depth
32% of
data
This
contain
information
correlating
the
information
the
data
Numerical
value
through
simulation
incomplete
was
have
of
was added
event
47
with
from
regarding
either
judg-
other
data
where
by
a symbol.
available.
magnitude
magnitude
information
defined
for
these
cases
was obtained
to
Table
Source
a1
,
B1
a2
3-3
,
B2
Cutoff
1.
2.58
-1.09
24.00
-4.55
6.8
2.
1.49
-0.74
62.80
-9.21
7.8
3.
-0.38
-0.42
3.60
-5.75
7.7
4.
-0.39
-0.65
26.50
-4.55
7.5
5.
0.33
-0.72
36.20
-5.27
8.5
6
0.42
-0.77
46.50
-7.82
6.9
7.
-2.13
-0.33
18.60
-3.53
7.5
8.
-0.89
-0.37
43.10
-7.57
6.8
9.
-4.71
-0.24
34.20
-5.43
7.8
10.
-4.71
-0.24
34.20
-5.43
7.8
11.
3.17
-0.74
79.15
-12.4
6.7
12.
0.14
-0.07
79.90
-13.04
6.5
13.
-0.66
-0.59
34.60
- 5.54
7.5
48
.
3.
The
reliability
of
the
Some information
total
data
was from
base
church
was not
evaluated
and historical
records.
Distribution
of
information
biased.
Populated
areas
sparsely
populated
areas.
over
have
the
better
country
is
records
than
(No population
-+- no
records.)
Epicentral
(iii)
location
a good grid
the
could
of recording
recording
network
presently
in
Nicaragua
understanding
of
attenuation
of
(See
is
others
in
record
does
felt
hypocenters
have
are
moved
become
locations,
able
to
the
modify
epicentral
sufficient
based
in
will
help
hoped
to
give
more
methodology
presented
the
accordingly.
results
locations
should
work.
the
increasing
relationships
in
and
the
the
through
evidence
the
the
Such
future.
past
in
information
this
the
events.
research
4) and
ESSO refinery
as yet.
(One exception
be emphasized
reliable
49
of
that
by
in
relocating
experimental
It
lack
Dewey.)
on Dewey's
fault.)
available
4 by
is
the work done by Dewey (see reference
the
not
earthquake-stadium
data
that
calibrating
may help
reference
It
installed
epicentrallocations
calibration
due to
the U.S.G.S. and private
organizations
accuracy
error
system.
Nicaraguan authorities,
It
be in
that
as
Hence. no
is
the
1931
additional
on epicentral
project
will
be
CHAPTER IV
PROBABILISTIC SE_ISMIC LOADING --
ISO-ACCELERATION
~PP)-~G.
OF NICARAGUA
Introduction
In
Chapter
the available
seismic
ship
of
of
respect
to
source
for
This
tionship.
tistical
the
understanding
forecasting
of
can be done
by means
models
and
us
length
the
we get
the
history
of
Based
two
for
on the
widely
of
the
past
used
events
line
of
magni-
If
rela-
quantitative
sta-
This,
In
however
developing
we need the
the
statistical
future
models.
future
forecasting
These
are:
Poisson
Markov
The Poisson
MOdel
Model
Model.
assumes
that
so
major
seismic
the
or area
source
recurrence
region.
data,
These
is normalized
each source.
Nicaragua,
relation-
period.
normalized
the
of
region.
M
for
gives
for
risk
the
time
source
formula
seismic
and
limitations
recurrence
magnitude
relationship
seismic
of
of
the
for
source
the
made in using the
mean number
a specified
source,
events.
the
a given
recurrence
on the
sources
above
area
past
seismic
to
normalized
seismic
represents
time
base,
presented
give
events
data
We also
the
M due
than
mean number
the
all
relationships
tude greater
of
with
the
and the approximations
Nicaragua.
associated
with
we discussed
information
data
recurrence
3,
events
are
spatially
for
the
Model
or
and
temporally
southern
assumes
California
memory
non-occurrence
in
of
non-occurrence
two
successive
an earthquake
an event
wi th the so-called
elastic
gives
(See reference
region.
of
events
This has been observed to be true
independent.
with
interarriva1
similar
results
next
this
the
of
effects
Even
year.
more
Poisson
the
though
it
than
Thus, occurrence
events.
year
rebound theory,
times
to
seismic
The Markov
25.)
this
occurrence
model
the
Poisson
spread
use
in
similar
to
atain
ltt>de1
Poisson
Mbdel
literature,
results
MOdel
of
10 years,
the
Markov
Seismic
events
to
in
using
follow
the
used
because
the
from
of
the
more
for
Model
References 26 and 27 are
Mbdel.
and because
arising
As mentioned
can be modeled
is
conforms
has been observed that
two good examples of using Poisson and Markov Chain MOdels.
study,
or
its
simplicity,
results
complex
it
models
In this
its
gives
wide-
are
such
as
very
the
Markov
Occurrences
the
previous
Poisson
paragraph,
probability
Poisson
Model,
the
earthquake
occurrences
For earthquake
law.
following
assumptions
must
be
valid:
(1)
Earthquakes
are
spatially
independent;
(2)
Earthquakes
are
temporally
(3)
Probability
that
independent;
two seismic
events
same place and at the same instant
will
take
place
at the
of time approaches
zero.
These assumptions
are necessary
~del.
assumption
The
first
for
the
implies
that
51
formulation
occurrence
of
or
the
Poisson
nonoccurrence
of
a seismic
event
occurrence
of
assumption
implies
A Markovian
sumption,
events
at
another
but
that
event
which
In
the
does
event
major
for
cannot
occur.
fits
the
physical
its
most
general
In
do not
memory in
this
errors
have
time
memory
non-
in
time.
may be a better
as-
assumption
for
large
The third
25).
(see reference
~t,
more than one
This is a very realistic
and good assump-
phenomenon
form,
the
Poisson
law
can be written
as
~t(~tl~
n!
=
of
=
having
4~1
n events
in
time
period
t
Number of events
Mean rate
Chapter
obtain
3,
the
we have
mean number
This
source.
of
Number
N(M)
M
A
=
=
seen
of
of
in
=
using
its
occurrences
Source
characteristic
time.
recurrence
above
relationships,
Magnitude
form
M for
can be written
a
as
4~
T)
Richter
(area
for
of data base.
52
of
above
source).
Time period
unit
general
<I> (M, A,
Magnitude.
line
how,
per
occurrences
Richter
for
T
occurrence
relationship
N(M)
where
events
or
The second
site.
a small time interval,
Probability
~ =
given
occurrence
Pn(t)
n
we can
the
some other
previously,
introduce
that
affect
at
seismic
Pn(t)
where
not
of one-step
as mentioned
assumption implies
tion
site
seismic
assumption
does not
seismic
one
area
Magnitude
source,
M.
length
As mentioned
in
assumed for
bi-linear
Chapter
all
(two
lines
Thus,
for
recurrence
relationship
a given
the
62).
61 and a2'
source,
the
two
lines
describing
0 ~ N ~ Nl
In
N'(M)
=
a21 + 62 M
Ml ::;. M ::;. M2
magnitude
(see,
the
depending
events
above
length
for
for
upper
3-3,
M for
a unit
above,
of
observing
the
probability
period
t,
based
inter-
for
a given
source
(see
value
of
for
is
M, the
area
given
mean number
source,
of
a unit-
by:
4-4
+ 6i M]
4-1
4.5
gives
lines
3-2)
area
exp [ai'
equation
in
the
and a unit-time
exp
Note that
recurrence
3)
[-
~
two
magnitude
and
N' (M)
Pn(t)
the
fig.
source
source,
exp
which
example,
Chapter
Magnitude
equation
at
cutoff
on the
line
the
are given by:
81 M
the
is
(See Table
~'+
is
is
relationship
~
Table
from
by aI'
source.
N'(M)
M2 is
Thus,
each
relationship
In
sect
Thus,
recurrence
for
described
3.)
NI
a loe-linear
Also.
sources.
of Chapter
where
3,
on the
(~i'
seismic
+ 8,
i
N)t]
A is
[exp
replaced
n events
history
S3
(ai'
of
by N'(M).
above
a given
4-5
+ 8;, M)t]n
i
magnitude
source.
Equation
M in
4-5
time
Source
Mechanisms
Three different
seismicity
of
three
any
source
pleteness,
a.
Point
They
mechanisms
only
will
the
are
point,
line,
be discussed
line
and
area
and
for
area
sources
generality
sources
were
the
and
com-
considered
for
region
Source
For
place
location.
although
Nicaragua
types of sources can be used to represent
at
this
type
of
to
In
time
Nt(M)
Substituting
all
The recurrence
one point.
respect
source,
occurrences
(past
relationship
and
future)
can be normalized
take
with
T as follows:
= at
the
+ aM
value
N'(M)
.
--- 4-3
repeated
of
N'(M)
in
~
4~
T
the
Poisson
law
of
equation
4-1,
we
get:
P
(M>
m,
t)
n
where
the
P
n
of
(M>
t.
m, t)
magnitude
For
period
[-~' (m) tJ
!XP
[N'(m) t ] ~
4-7
n!
notation
Richter
termining
.
gives
greater
engineering
the probability
This
probability
the
probability
than
purposes,
m in
time
we are
of at least
is
that
liven
there
period
usually
S4
be n events
t.
interested
one event greater
by
will
in
de-
than m in time
P (at
least
one
period
of
Richter
Magnitude
M > m in
time
t)
1
P (no earthquake
-
Hence, from equation
P (at
event
of
magnitude
M > m in
time
t)
4 -7,
least
one
event
of
Magnitude
M > m in
time
t)
1 - exp [-N' (m)t].
b.
Line
Source
For
linear
a line
it
For a line
fault.
data base for
and
source,
a time
equation
3-2
is
assumed
source
period
of
length
epicenters
L (fault
T, the recurrence
can be normalized
N' (M)
that
lie
length
relationship
along
a
L) and
of Chapter
to:
---
= ~
Equation
3-3
repeated
LT
and
Thus,
the
Poisson
law
of
a'
=
In N' (M)
8M ---
+
equation
4-1
Equation
3-4
can be written
repeated
as
n
P
(M
>
m,
exp
=
t)
[-N'
(m)t]
the
of
N'(m)
fault
at
period
for
line
and time
least
t
is
one
period
event
given
P (at
source
least
of
is
T.
(m)t]"
n!
n
where
[N'
normalized
Again,
magnitude
for
greater
with
respect
determining
than
to
the
m for
1 - p
0
earthquake
(M>
of
m, t)
ss
M > m in
time
t)
of
probability
a future
by,
one
length
time
3
= 1 - exp -N' (m)t]
is
tation
c.
a similar
of
N'(m)
expression
is
4-8 except
equation
that
the
interpre-
different.
Area Source
When the
along
a given
past
fault
earthquake
line)
but
source
should
be considered
a full
circle
or
In
to
this
case,
any
the
epicenters
are
scattered
as an area
section
of
recurrence
do not
over
where
relationship
on a line
a region~
the
(i.e
seismic
The area source could be
source.
a circle
lie
is
epicenters
are
normalized
with
scattered
respect
to
A and the time of data base T.
N' (M)
In
N'(M)
Thus,
the
above
magnitude
= a'
probability
and
this
also
has
Peak
Ground
least
a
line
describe
is
acceleration
we obtained
t
m in
repeated.
one
event
due
is
given
by:
time
similar
3 -3 repeated
to
t)
= I
to
this
- exp
equation
area
source
-N' (m) t] .
4 8 for
a point
source.
However, in each case the normalized
interpretation.
Acceleration
seismic
at
in
probability
a Site
Chapter
loading
(PGA, usually
the
3-4
least
source.
a different
the
Eq.
period
one M>
As we mentioned
to
at
time
expression
for
N'(M)
of
m in
P (at
Again.
+ 8M ---
--- Eq.
= !ioo.
AT
at
3,
the
a given
denoted by A).
of
exceeding
S6
most
site
In
commonly
is
the
a magnitude
the
used
peak
previous
level
parameter
ground
section,
in
time
t
by
using
Sq.
4 8 gives
purposes,
information
we wish
center.
know
to
probabilistic
know
the
following
Probabilistic
1.
source
Distance
3.
Attenuation
away
peak
several
at
ground
a given
design
from
other
by
the
epi-
2) peak ground
parameters
To obtain
site.
acceleration
at
a site
parameters:
information
of
a site,
and
as a function
2.
For
(MMI, see Appendix
loading
about
represented
magnitude.)
at
acceleration,
represent
the
loading
Intensity
information
to
distribution
on Richter
the
Mercalli
used
probability
only
spectral
been
we have
to
Modified
acceleration,
have
(The
ode!.
a Poisson
the
of
site
of
on Richter
future
from
peak
for
a
time
the
ground
Magnitude
source.
acceleration
from
source
to
site.
We have
tion.
tionship
already
determined
Various
the
attenuation
between
the hypo central
the
distance,
is
of
h
M
bl'
the
available
M, the
previous
which
give
epicentral
the
exp
(b2
form
given
secrela-
distance
by
M)
4-9
5.,
+
b4)
3
=
Peak Ground Acceleration
=
Hypocentral
=
Richter
distance
from
(PGA) in cm/sec
source
to site
2
(in
kms.).
Magnitude.
b2' b3' and b4 are constants
57
or
The most
=
(Rh
R
in
and the peak ground acceleration.
bl
A
are
Magnitude
commonly used relationship
where
parameter
formulae
Richter
A
first
depending on the region.
Since
not
much
that
part
there
is
information
of
are
available
has
been
the
is
for
parts
this
the
of
of
the
is
one developed
are given
b
5.000;
b3
0.8;
b4
1
-
Figure 4-
data for
with
the
The correlation
the
data
out
given
that
the
brating
the
When that
reasonable;
by Eq.
is
4-10
is
used
of
attenuation
done,
.
2.0;
40
4 -10
4-10
This
equation
different
was
in
Richter
correlated
and also
of the curve of Eq. 4-10 with
this
the
study.
attenuation
It
many new instruments
results
for
the 1972 December earthquake
relationship
the
The
by Esteva.
of Eq
consequently
installation
that
(Rh + 40)
wi th the ESSORefinery
ship
relationship
s:~oo e~,~0.8 M)
magnitudes and hypocentral distances
quite
b2' b3 and b4
becomes
shows the behavior
aftershocks.
in
by
relationship
A
Nicaragua,
accelerations
One such
world.
the
of
in
values of bl'
constants
attenuation
is
seismographs
on attenuation
work
b2
Thus,
grid
However, various
other
adopted
a close
available
world.
for
attenuation
not
for
presented
will
Nicaragua
in
this
should
in
relationbe pointed
help
the
study
in
cali-
future
can be readily
modified.
We have
Due to
each
a site
in
of
seen
these
a probabilistic
that
seismic
three
types
sources,
sense
of
the
seis.ic
peak
can be determined.
58
sources
ground
are
possible.
acceleration
at
T I
+i
zo--
~
qIn
\0
.q-
+1
"H
10_9.,8_1_6 -:'
5- .
3
2
.9
z
.8
0
.7
...
.6
.
I
.5
W
«
~
.4
0
LA..
.3
..cA.
=>z~
wcn
...z
"'0
..c...
..c
cn~
.
w
..c
>«
w
...
cn
'"
.2
i
t
Sl.Nn
a.
Point
Source
For
lowing
a point
source
shown
in
Figure
we can derive
4-2,
the
expressions:
P (M>
=
m, t)
Probability
m in
1
but N'(M)
of
time
- exp
at
least
one
event
greater
than
t.
[-N'(m)t].
= exp [a'
+ BM]
= 1 -
[-exp
Thus,
P(M>
m,
t)
To determine
celeration
exp
(a'
the probability
4-11
+ Sa)t]
distribution
on peak ground
A. we have
P [A> a]
~~~
=
p
(b2 M)
> a ]
b
(Rh + b4) 3
1
=
Using
equation
4-11
P [A > a]
P [M> In
in
4-12,
(Rh + b4)
{...!bl
1 - exp
{-e
a'
8/b2
( ..!b
(~
)
at
e
'Y
& =
and p
}
b
.2 ]
we get
1
Denoting
b3
=
~/b2
B b3
-
b.2
60
.
ob3
+ b4)
S/b3
1>2
t}
ac-
SITE
~
POINT
SOURCE
FIGURE 4-2
L
r--~l
"""""11
dl
liNE
D:
I
-.
~
SITE
TO P
VIEW
61
SOURCE
we get
.
P {A >a]
b.
Line
of
located
around
centers
falling
The line
the
1 - exp { ~y
the
the
one of
~)}.
of
a peak
ground
source
of
fault
all
such
gives
a point
can be treated
[A
<
the
the
the
4-14
world
usual
so-called
segments
+ 0,
gives
a value
we have
seen
of
are
case
of
line
source
length
source.
the
a due to
generally
Summing
probability
a fault
a]
p
t1
6
exp f-yCl-)
1
(Rh+ b4)
i
source,
we have
~
p
+ b4)
of
the
line
~
=
(Rh.
i
ti}
dR.. t .}
i
Fig.
(d2 + 82
Rh
1 is
the
distance
~
~
of
element
2 1/2
+ h )
under
62
consideration
epj-
dl
that
(Rh + b4)
1.
where
t}
as a point
as dl
A exceeding
source,
an element
P.
From
p
L
P [A < a:
for
to
K small
P [A > a] =
Thus,
Thus,
rise
into
segments,
acceleration
around
systems.
a line
segments
length
For
major
epicenters
can be divided
these
effects
earthquake
along
source
then
(Rh + b4)
Source
Most
Each
"
~
from
the
of
line
perpendicular
on the
line
source.
Thus,
0
P1' [A < a] = exp {- y(~a
'bl'
From
rences,
the
basic
assumption
of
spatial
independence
of
occur-
we get
K
P [A < a]
=
lim
n
i=l
P.
[A<a].
1
dR..-+o
1.
~~~
lim
6K
1/2
I [Cd2+ R..2+h2)
dR..+o exp {- YCf-)
1 i=l
1.
J.
K+-
a
12
t
=
P [A < a]
4-15
[(d2+t2+b2)1!2
f
1}
Alternatively,
a
J
12
t
p
+ b:'4]
[(d2+12+h2)1!2
4-16
d1}
11
Expressions
4-15 and 4-16 provide
acceleration
whose
the
seismicity
attenuation
A due to a line
is
available
relationship
the probabilities
source
in
of
located
terms
the
fora
63
of
of peak ground
some distance
a'
of
and
Eq.
B
and
4-9
is
also
away and
for
available
which
c.
Area Source
Peak
be obtained
parts
of
in
the
the
case,
scatter
be used
to
to
located
or
are
the
for
alona
the
of
where'point
or
less
than
m in
the
time
t
probability
is
given
Summing the
= exp [ -e
effect
P [A < a,
of all
t]
=
at
a site.
crisslocations
may not
area
fit
source
Figure
should
4-4
shows
With this
elemental
J.
Richter
Magnitude
M will
be
dAit]
+
8m) tR.dR.de.]
1. 1. 1.
a' a SIb2
(/;;-:-" "h2
P.
areas,
(A
1.
dR.-+O
1
de Q
1
Hence,
64
<
a,
. Sb3
-
+ b4) b2
(b )
1
elemental
lim
the
J.
by
[-exp (a.'
or
P.[A<a,t]
1
faults
sources
cases,
J.
that
P. [M < m, t] = exp -N'(m)
1.
= exp
allover
epicentral
= R.dR.d0..
area dA.
J.
as a source.
where the
scattered
such
loadings
In many
numerous
line
can
geometry.
Consider an elemental
area
are
estimating
For
a site
are regions
existence
in
at
source.
but
places
source
line
a line
errors
probabilistic
source
there
locations.
area
an area
that
due to
epicentral
determine
to
Nicaragua,
may be due to
there
schematically
similar
only
region
of
due
including
not
This
region.
any
a manner
are
crossing
In
acceleration
the world,
epicenters
the
ground
we get
t)
tR.dR.d0.
1 1 1
TOP VIEW
AREA
SOURSE
FIGURE
65
4-4
e0
P [A < a,
t]
i-.
+<1'
= exp
<f:)
1
Bb3
R2
~/b2 t
1
-b
~3
= exp
{-eCl'
8/b2
(~)
1
2 RdR}
Rl
y = e0'
Let
<5 =
S/b2
~ . ~3
as before
~
and
= /R2:h2
Rh
Then
P (A < a,
t]
= exp {
-
a 4
Y(bi)
te
R2
4.17
f
Rl
and
R2
P [A > &, t]
;4
= 1 - exp { - y ~)a
te
1
Equations
ground
4~7
and
acceleration
4-18
provide
A at
a site
the
probability
due
to
fRl
distribution
a generalized
of
area
peak
source
shown
in Figure 4-4.
In
general,
a site
is
usually
66
surrounded
by any
or
all
of
the
above
three
ing
due to
Let
there
sources
such
be
a case
given
in
this
section.
can be obtained
NP
point
NL
line
sources
NA
area
sources
The probability
then
discussed
by
The probabilistic
the
following
load-
expression.
sources
distribution
of
peak
ground
acceleration
at
a site
is
by
~
NP
P [A > a,
t]
= 1 - exp
{ -
>::
i=l
Yi
(a)
J.
[(d.2,
J
tf
hi
j
+ b4)
p.1.
R.2j
0.
J
y
t (~.
(b)
1
NL
r
j=l
i
a
R.lj
R
0
Yk (~) k
b.1
NA
L
Jc:=l
In
j
equation
is
4-19,
for
all
line
As we have
three
area
sources
based on past data.
sources,
depending
summation
sources,
over
is
and over
seen
in
that
we have
Chapter
Any part
upon
i
the
of
all
proximity
there
67
all
the
sources,
area
are
for
country
of
point
for
formulated
the
4-19
RdR}
for
k is
3,
Pt
ten
the
is
site
over
sources.
line
sources
Nicaragua
affected
to
that
the
by
and
region,
these
source
location
Iso-Acceleration
Maps for Nicaragua
Equation
bution
function
For
~pace.
with
at
at
a given
site,
If
that
the
peak
we take
the
country
different
locations
for
probability
tions.
determine
These
of
lines
of
ground
equal
the "exposure
we can
obtain
lines
accelerationsfor
The maps representing
iso-acce!eration
seismic
maps.
zoning
maps.
From
risk,
one can determine
tion)
for
the
describing
sented
the
in
a time
defined
period
7 of
this
of
a given
are
a form
structural
of
or
the
accelera-
methodology
design
in
the
reliability
Detailed
and also
called
(peak ground
a structure.
report
accelera-
"Iso-Acceleration"
parameter
maps for
and
probability
maps are
during
under
In
13 show
of 50 years
maps are
as the
be exceeded
facility
these
8 through
iso-acceleration
is
of
equal
time)
will
Part
II
be prereport
of
study
Charts
for
use
design
of
iso-acceleration
loading
accelerations
a specific
for
some
(exposure
lines
maps,
the greater
exceed
iso-acceleration
these
the
seismic
Chapter
the total
These
t
a increases
time,"
will
period
of non-exceed ence and exposure time are called
lines.
A>
and determine
time
distri-
of time and
of
acceleration
a specific
probability
probability
as a whole
A < a,
the
as a function
the
In other words, the longer
a.
specific
to
of peak ground acceleration
probability
level
can be used
example,
time.
the
4-19
the
for
three
that
exposure
iso-acceleration
and 20 years.
drawn
probability
the
the
time
For
risk
peak
(or
maps for
each
time
levels.
ground
economic
Nicaragua
period
the
The risk
acceleration
lifetime)
level
will
of
the
consideration
addition
to
the
iso-acceleration
68
maps for
the
whole
country.
the
following
cities
are
1.
Managua
2.
Leon
3.
Granada
4.
Masaya
s.
Chinandega
6.
Matagalpa
7.
Esteli
8.
San
9.
Rivas
Juigalpa
11.
81uefields.
4-5
the
peak
are
presented
through
ground
4-~6
for
ground
the
for
0.20
g in
years.
The
ponding
acceleration
in
4-8).
the
ceeding
celeration
method
for
see
each
of,representing
time
is
of
of
21\.
the
will
the
relative
In
seismic
the
it
seismicity
is
69
goes
in
it
up to
and
plots
terms
of
can be said
by means
not
of
the
exceed
a SO year ex-
in Chapters
distribution
conclusion,
will
probability
values
be discussed
Thus
53% chance that
time
of
results
50 years.
value for
probability
risk
Again,
and
exposure
Thus,
cumulative
function
cities.
20 years
47%~ whereas
these
values
city.
of
is approximately
is
of
the
each
distribution
The corresponding
20 years
implications
we can
detail.
cumulative
20 years
same city
When we compare
cities.
for
exposure
acceleration
time
the
Leon, there
0.20 g (see Figure
posure
show
acceleration
as an example, for
peak
in
Carlos
10.
Figures
studied
the
of
ex-
19% in
50
the
corres-
5,6,
for
peak
that
and 7.
different
ground
one
iso-acceleration
ac-
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ri
maps and
the
cumulative
method
distribution
The
sented
other
in
next
should
zone
logical
macro
incorporated
this
risk
of
Figures
4-5 through
of
these
should
is
results
also
The macrozoning
characteristics.
with
region.
features
It
chapters.
seismic
by means
of
4-~.
will
be pre-
be pointed
out
that
maps and any zoning based on such maps' only
be modified
a given
plots
interpretation
three
the iso-acceleration
represent
representing
function
engineering
the
of
(such
together
site-specific
In that
case,
as those
with
micro
the
discussed
92
the
characteristics
local
in
geotechnical
Chapter
the macro characteristics
chapter.
of
country
to
micro-
and geo-
2) should
be
presented
in
CHAPTER V
SEISMIC RISK ZONING
Concept of ~!~~eriod
Zone Graphs(~G)
In
function
time
deriving
of
Poisson.
tion
This
Using
this
city,
the
for
cumulative
5-1
acceleration
acceleration
of
not
are
of
site
as a
is
process
independent
an appropriate
in
att-enuation
maps for
cumulative
the
country.
distribution
A, as mentioned
in
func-
Chapter
4
20 years.
=
in
4-5.)
(See Figure
51~
0.73
in
0.20g
will
be exceeded
the
during
following
way:
the next 20 years,
be exceeded
is a 27% chance that
there
will
and
the
a given
forecasting
iso-acceleration
developed
time
at
events
acceleration
Thus,
the
can be interpreted
"For Managua, there
ground
the
assumption
P20 (A > O.20g)
Equation
that
distribution
an exposure
Then
loading
that
the
we, also
the peak ground
Managua
peak
implies
we developed
a given
Consider
probabilistic
we have assumed
process
and space.
of
the
time,
relationship,
For
and Accele!ation
at
least
the
once."
for Managua, O.20g peak ground
a single
time.
O.20g in
20 years)
Hence"
P
(Zero
exceedence
Binomial
Probability
From
the
with
probability
of
success
of
Law,
p at
we know
each
93
trial,
that
the
for
=
0.21~
independent
probability
trials
ofr
successes
in
n trials
is
given
by
5-2
where
r = 0, 1. . . . n;
n = r,
r+l,
r+2,
and
Let
the
level
event
of
when
is
the
trial
peak
the
Thus,
0.2g.
years
each
the
be a one-year
duration
acceleration.
Let
us
for
a given
ground
peak
nl
r)(n-r)!
=
CD
r)
ground
acceleration
probability
same as the
of
zero
for
define
of
0 successes
we are
success
trial
in
observing
a~ that
(year)
level
of
exceedence
probability
which
0.2g
20 trials.
exceeds
in
20
Hence
from Eq. 5-2:
(20)
0
P20(O)
P20(O)
p
0
=
(}) -p 20
=
0.27
(1-p)20
However,
P20(O)
.
(1-p)20
or
Thus,
ground
p
for
Managua,
there
acceleration
However,
0.063.
is a 6.3% chance that
of 0.20g will
the
return
period
in any given
be exceeded.
is
94
defined
as
year,
a peak
Return
~US,
the return
period
~
O~20g is -~
I
O~
It
should
cQrrespondi;ng
function
if
example,
RP in Managua for a peak ground acceleration
be pointed
of
we use
out
fQr
PGA A at
the
that
this
by using
Managua
for
exposure
Pso
Pso
the
to
time,
0.963
(A
=
0..037
=
.037
< 0.20g)
Thus,
using
the
£Or
in
period.
the
period
CDFs for
RP ~
using
the
(1)
The
considered.
concept
all
the
following
period:
A return
period
the
an event
of
is
interest.
mean
Thus,
between 2 events producing
years.
95
,
time
exposure
does
time.
not
For
4-27),
cities
in
Nicaragua
considered
of return
16
distribution
16 years
Table 5-1 is a general. table
cities
16 years
0.063
in Chapter 4, we can develop a table
return
of
exposure
50 year
=
Return
and
cumulative
(A > O.20g)
p =
gives
period
(see Figure
O:r
which
return
a 20 year
CDF corresponding
~ 50 year
H~nce,
of
years.
ito O.2g,obtained
(CDF)
change
16
-p1
=
RP
=
Period
giving
statements
(or
the
average
average
this
and
relationship
should
waiting
(waiting)
be understood
time
for
time
O.20g in Managua is approximately
cO
:>
1
I'/)
0
~
I'/)
N
~
(:()
~
0
U
(:()
...
0
0
N
\0
N
~
~
t"-.
~
~
..
~
cO
t/)
!/)
~
cO
~
>-
~
1
~
~
Cl.
0
0
t"-.
N
\0
~
N
N
~
N
0
0
0
\0
N
0
~
\0
~
~
cO...
1
~
~
0
~
~
!/)
W
.
cO
bO
cO.qo
~
.0
cO
E-o
1
~
~
~
~
0
I
0
(:()
N
~
!/)
0
~
~
cO
~
t"-.
I'/)
~
cO
~
cO
bO
~
~
~
;j
~~
~
~
~
0
0
0
0
0
0
I'/)
t"-.
N
\0
N
t"-.
~
0
~
(:()
.qo
~
\0
~
cO
~
I
~
U
cO
>.
cO
0
0
0
0
0
0
0
0
cO
!/)
N
\0
0
0
N
.qo
.qo
0
~
N
t"-.
~
~
~
t"-.
t"-.
I'/)
'""
0
N
0
~
0
t"-.
0
0
0
\0
~
I'/)
~
~
.qo
~
N
~
~
0
0
0
I'/)
~
N
I'/)
\0
.qo
~
NON
0
I,f)
~
~
cO
~
cO
cO
~
0
I'/)
0
t"-.
~
to:)
~
0
0
~
...J
Nt"-.
0
.
0
. .
0
0
I'/)
\0
.
~
cO
;j
bO
~
0
0
0
0
0
0
0
0
0
~
cO
~
~
~
\0
~
\0
0
t"-.
t"-.
~
~
I'/)
~
~
~
.qo
N
(:()
\0
t"-.
~
N
0
~
cO
~
~
1
<x:~
!/)
~
1
<x: ;j
~
0
0
~
0
~
0
~
~
~
N
N
I'/)
I'/).qo.qo
to:) bO
Cl.
0
~
.
96
,
I
(2)
The probability
that
period RP will
Thus,
an event
corresponding
to
a return
occur in any given year is given by p = iff
probability
a.20g in Managua in any
of exceeding
- 0.063 (same as Eq.S..S).
(3)
The probability
occur
in RP years
base.
will
be a single
not
Thus,
one
16 years,
be
is
of
probability
that
event
of
e
e
producing
the
RP type
= 2. 718,
in
the
16 years,
a peak
in
35 years,
For
in
RP years
acceleration
seismic
zoning
will
there
ground
there
acceler-
will
be at
Consider
be exceeded.
purposes,
through
period
corresponding
the
following
statements
is
16 years,
in
Leon
Masaya
is
20 years,
in
Chinandega
Thus, for
81 years.
acceleration
5-12
show
these
Figure
acceleration
for
the
all
event
period
(say,
is
32 years,
.It
100 years),
Granada
106 years
a graph relating
refer
5-1 shows return
cities.
is
in
to
can be seen that
Bluefields
has
graphs
vs.
for
the
lowest
of
(.34g).
these
acceleration
two
limits.
Qualitatively,
97
The
values
it
can
for
other
be said
as
a given
(~. OSg) and Managua has the highest
ground
5-1
peak ground
peak
in
the peak
these
period
is
and
Figures
can be plotted.
We will
graphs.
Zones.
period
each city,
and return
Acceleration
return
to a peak ground acceleration
Managua
in
is
ground
between
will
made
0.20g
Rivas
1 where
For Managua. there
RP type.
The return
of
event
by
given
64% chance that
O.20g peak ground
again Table 5..1..
can
Thus,
a single
of O.20g in Managua is given by ~ - 0.36
there
event
not
is
Naperian
ation
least
that
value
value
cities
that
lie
for
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Esteli
ments
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above
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finally,
help
or
In
peak
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able
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is
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of
a structure,
zoning
Granada,
Managua.
for
a given
San
require-
Chinandega,
come next;
This
class
return
type
of
graph
and use
of
and
can
a structure
7.)
and
Nicaragua.
in
selecting
of
the
in
any
the
risk
one
the
trials,
with
probability
a given
zoning
(or
to
life.
of
p of
for
r
by
accept-
procedure,
exposure)
take,
economic
The probability
period
for
seismic
between
relationships
period
willing
and
return
these
economic
is
risk
distribution.
relationship
corresponding
a return
step,
with
seen
However,
between
level
consistent
given
the
of
a relationship
the
we have
The next
Bernoulli
is
requirement;
requirements,
for
section,
help
Binomial
independent
trial,
Chapter
risk.
period
the
is
a 200 year
similar
Rivas,
zoning
a country
cities
do not
again
similar
zoning
have
level;
acceleration
themselves
return
and Juigalpa
previous
major
level
seismic
to
Zoning
ground
different
corresponding
lowest
level
(See
Risk
the
having
macro zoning
Seismic
loading
Bluefields
highest
facility.
the
the
Leon,
the
in
a design
life
and the
Consider
successes
success
at
in
n
each
by
p (r)
n
=
()n
r
Pr (l-p) n-r
Eq. 5-2 repeated
Thus
PIO
(0)
10
= (0)
(p)
= (l-p)lO
0
(l-p)
10
= probability
ten
trials
of
zero
success
in
(years).
110
I
liIr8,
I
II
= (l-p)lO
Let p(O)
no occurrence
be equal to 0.90.
(or success) of a certain
Then the probability
level
of loading
of
in ten years
is given by 0.90.
or
(l-p) 10
=
0.90
p
=
.01048
Hence
or return
RP = 95 years.
period
Thus, for
a structure
able risk
level
whose economic life
is 90% of not exceeding the specified
(i.e.,
10% of exceeding),
return
period
acceptable
return
risk
level,
is 50 years,
period
corresponding
If
economic life
risk
level
is 80% for
If
this
having the same economic life
(80%), the two consistent
different
level,
risk
economic life
independent
whose econto a
level
is to be built
0.39g.
in
level
should be
and use of structure,
and same acceptable
risk
values of peak ground accelerations
in
Figure
This is the concept of
region
to another region
5-13 shows the graph relating
and the return
of any region
for
is in Managua, the
a given class
design from one seismic
seismicity.
If,
is approximately
(50 years)
period.
and gives return
a
between
level
Managua and Matagalpa are 0.39g and 0.12g.
consistent
period.
peak ground acceleration
Thus, for
level
should correspond
structure
the same risk
the corresponding
0.12g.
loading
a structure
level
approximately
the accept-
should be designed for
and return
then the loading
for
if
Table 5-2 gives the relationship
of 225 years.
the same facility
Matagalpa,
then the structure
of 95 years.
example, the acceptable
omic life
is ten years,
the risk
This particular
periods
of
graph is
only as functions
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life.
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level
for
graphs
a given
given class and use of a structure,
immediately
obtained
return
period
5-12),
the
concept
Graphs
Figure
Ys. peak ground
loading
of
from
at
risk,
a site
economic
can
life,
that
this
cities.
exposure
to
The
is
selected
based
return
on the
(similar
be determined.
a
period
graph
is
of
5-1 to
us describe
Let
period
for
to Figures
this
and Acceleration
which
a seismic
facility
is
economic
in
5-13,
life
and
Now let
5-2).
us
peak
Managua,
the
7 for
Leon,
Zone
risk
each
and
Esteli
the
Similarly,
Leon,
acceleration
return
period
are
peak
ground
acceleration
O.llg
in
of
SO
level
three
must
for
different
Assume
risk
is
that
remain
for
functional
corresponding
to
we will
life
of
accept
the
corresponding
a 20\
chance
structure.
Then,
to the 50 year
225 years
in Managua is 0.39g.
year
system
Thus, whether the planned
AZG corresponding
The peak ground acceleration
the peak ground
the
of
that
Leon,
period
is
to
for
details).
or
of
facility.
acceleration
level
economic
the return
refer
ground
acceptable
SO years
life
facility
Managua,
20\
economic
a critical
Esteli,
the
or
be designed
(see Chapter
during
from Figure
is
event,
20\
damage
are
a design of a hospital
the
should
cities
hospital.
Figure
Then,
return
time
determine
facility
damage is
of
the
We are
years
after
life
the corresponding
5-13.
Once
be codified.
(AZG).
Assume
the
economic
acceleration
As an example, consider
which
can easily
and
the
referring
values
0.27g.
three
114
for
to
Managua
a 225 year return
to the AZG for
corresponding
Thus
different
(see
these
cities
Esteli
to the
three
are
period
and
225
values
consistent
of
with
the
given
acceptable
risk
As an alternate
structures
life
warehouse
of
with
30 years
a ten
Referring
school
should
have
year
to
consider
in Managua.
to be built
economic
level.
situation,
Let
be designed
5-13,
is
life
the
return
5-2),
are
0.36g
and
the
same two
ing
peak
0.21g
advantage
sistent
risk
for
of
level
and
method
from
one
acceptable
at a loading
application
7 of
level
of
this
the
report
of
would
region
to
risk
levels
through
AZG to
and
in
is
from
Juigalpa,
and
one
can
be accounted
period
design
of
for
the
Managua
values
If
the
correspond-
0.07g.
The
will
total
keep
in
for
a conthe
in
transformation.
be presented
study.
a
which
the
can
Variations
II
and
respectively.
another.
structural
115
period
acceleration
that
the return
Part
which
return
be O.llg
zoning
for
Again
in
20%,
the
ground
be located
of
period
and warehouse,
values
this
arriving
Chapter
to
level
an
risk
and the
peak
school
acceleration
life
in
the
were
economic
Further
corresponding
facilities
ground
major
the
with
of
a 40% acceptable
the warehouse should be designed is 20 years.
AZG (Figure
classes
building
risk
have
135 years,
separate
a school
an acceptable
economic
Figure
two
CHAPTER VI
-- DAMAGE
ESTIMATION
PROBABILISTIC
INTENSITY
FORECASTING
*I
Forecasting
zoning or seismic
Seismic
the
previous
tive
section,
cities
or by acceleration
in
the
ferent
of
and useful
form
of
types
and
a seismic
work
in
references
the
ready
obtained
ground
of
masonary
the
a given
the
region.
In
probabilistic
is
tinuous.
To obtain
Various
intensity
at
a Monte Carlo
discrete,
this
different
simulation
behavior
structures
due
to
empirical
discrete
of
process
the
a site
was used.
116
event.
(See
is usually
the
we have
form
of
a1-
peak
are available
t.t.f! Scale.
acceleration
country
as follows:
in
dif-
amount
a seismic
relationships
probability
the
of
at
chapters,
level
to the
whereas
parts
previous
loading
The MMcr Scale
the
Appendix
has been a considerable
observed
dif-
seismic
MMI (see
This damage correlation
and 37.)
for
there
damage
Scale
frame
for
Another very
future
describes
and
cumula-
accelerations
(AZG)
Intensity
as shown in
maps or
representing
scale
Recently,
acceleration.
to convert
described
classes
correlating
MMI level
for
Mercalli
intensity
event.
iso-acceleration
zone graphs
parameter
This
35.36.
of
can be presented,
(CDF) of peak ground
Modified
definition).
due
form
functions
informative
for
the
distribution
ferent
is
in
risk
scale
mass
for
function
20 years
The: procedure
is
conof
the
MM
and 50 years,
can be
'I
(1)
(2)
Obtain
the CDF for
region
under
Select
an empirical
celeration
this
peak ground
study.
(See Figures
equation
to MMI.
report
(see reference
a is
I
Thus,
is
the
is
for
the
MM
the
(4)
This
6 1
in
peak
cm/sec2
ground
acceleration
at
a site
=
I has to be VII
random
of
the
acceleration
generated
Repeat
step
for
(3)
I.
7.5.
of
probability
mass
function
process
was repeated
for
all
VIII.
6-1
of
peak
PGA. Substitute
the
and obtain
a histogram
frequency
of
=
a value
equation
and draw
, the
I
pick
CDF for
PGA in
n times
As n~
we pick
generation,
by using
value
0.5
-
or VIII,
number
981.46
98.146.
= 3I
I
Through
chart
ac-
used in
0.5
-
10 x
O.lOg = TOO
=
or
this
peak ground
intensity.
9.-ogl0 98.146
ground
convert
38) is
=
(3)
the
then
a
Since
to
acceleration
example,
O.lOg,
I
"3
=
A for
4-5 to 4-26.)
The relationship
9.-cglO(a)
where
acceleration
I will
of
I.
frequency
approach
the
I.
eleven
cities
mentioned
in
117
I
II
I
,
A time
Chapter S.
Figures
convenience.
tions
period
for
all
explained
the
of
6-1
20 years
through
The
cities.
(see
6-11
was selected
mass func-
show the probability
interpretation
of
these
for
graphs
can be
by means of an example.
the next 20 years, probability
For Managua, during
max~~
and 50 years
Modified
Figure
Mercalli
Intensity
I will
be VIII
is
that the
given
by 0.39
6-1).
Thus,
P [Maximum MMI in 20 years will
Similar
Iso-seismal
whole
very
statements
maps based
It
country.
much
a function
evaluation
of
these
on such
should
of
are
based
damage
seismic
event.
such
in
present
a given
From the
Intensity-Damage
intensity
soil
for
coWltry.
for
of
the
shaking
For
conditions.
site-specific
study
The values
is
proper
and
presented
the damage data for Nicaragua with
This
study
class
of
will
in part
can be made by observing
structures
1972 earthquake
correlation
be presented
due
can be obtained.
a given region
118
to
in Managua,
a methodology of using such information
surance risk"
the
be generated
are needed.
Such correlation
study.
centage
site
of
Dama2ePotential
observed past intensities.
current
and
parts
study.
We have not correlated
the
that
a detailed
of the
"Insurance !i!!~'or
can
out
geologic
parameters.
on macro
other
forecasting
be pointed
local
micro-characterization
here
can be made for
= 0.39.
be VIII}
II
past
information
However,
of
the per
an observed
the
the
we will
to est.imate the "in-
on
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',_.c.
t"!f.i
'".
of p.f.i intensity
A study
and dollar
damage
was
conducted
after
the Long Beach, the Kern County, and the San Fernando earthquakes.
Figure 6-12 shows a graph of Median Loss in percent
MMI for
these
in
different
values
are
Nicaragua
will
types
built
exhibit
numerical
tensity
forecast
conclusions
similar
is
for
If,
as wood
ical
values
to
is
insurance
to
behavior
the
Southern
Figure
of
6-12.
hand,
structures
region
The purpose
The
three
classes
(1)
All
(2)
Pre-1940
(3)
Light
to
potential
should
to repeat
tilt-up
can be used
in
structures
once
of this
or light
Southern
structures.
with
be
However, appropriate
houses
those
pre-
No
be used in Part II
residential
and
of
damage
of
and in-
methodology.
methodology.
similar
here
the
of
that
California
The purpose,
values.
dwellings
presented
show
or
values will
constructed
frame
to
risk
demonstrate
on the other
such
in
similar
numerical
are
Nicaragua,
those
numerical
strictly
buildings
to
Nicaragua
these
and applicable
to
we realize
examples wi th damage data from California
regarding
made by using
study.
applicable
though
Even
structures.
relationships
senting
again,
not
of
as a function
industrial
California
then
the
numer-
some caution
considered
in
the
example
are:
one-
and two-story
residential
industrial
wooden
homes;
frame
buildings.
to any MM intensity
level
are
in
The losses corres-
percentages.
example, due to MM[ of V, damage to a wood frame dwelling
0.1\.
The
corresponding
houses;
and
Using Figure 6-12, Table 6-1 can be constructed.
ponding
residential
loss
to
pre-1940
130
design
dwellings
Thus,
for
would be
would
be
Table
Median
All
Intensity
Dwellings
Losses
Due to
6-1
Different
Pre-1940
Construction
v
0.1
0. 2
VI
0.2
0.4
VII
0.6
0.9
VIII
1.4
2.1
IX
3.3
5.0
x
1.7
12.0
XI
18.0
29.0
132
MM[ Levels
Light
Industrial
Buildings
131
4
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FIGURE6-12
i~e
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...
---
~
X
~
~
ME DIAN
-
LOSS
IN
--
~
AS A FUNCTION
--
~_lli!~:~~
~
--
PER
CENT
OF
MMJ
-~
SEISMIC
RISK
A N A LV S I S
NICARAGUA
JANUARY,
VIII
lx
x
1975
XI
MMI
0.2%,
and to
termine
of
light
the
expected
any MMI level
that
level.
loss
in
industrial
percentage
a twenty
to
for
for
year
any
over
that
period
class
at
of
by
all
example,
it
class
be multiplied
summation
Consider,
for
loss
must
The
buildings,
would
structure,
the
the
loss
will
give
probability
mass
function
(see
6-4):
of
Masaya
to
expected
structure.
Figure
of
VII
VIII
IX
X
Probability
.01
.47
.51
.01
0.6
1.4
3.3
7.7
MMI
%
All
Dwellings
The
expected
median
E [Damage]
Thus,
due
the
Intensity
Damage
To de-
probability
corresponding
intensities
the
be 0.75%.
for
damage
=
(.01)
=
2.424%
a $1,000
in
(.6)
20 years
(.47)
+
valuation,
the
for
"all
(1.4)
dwellings"
+ (.51)
expected
is
(3.3)
damage in
given
+ (.01)
20 years
by
(7.7)
is
given
by
Expected
Similar
considered
results.
20 and
Table
of
twenty
years
= 2.424
100
x
=
per
$24.24
calculations
for
chance
Damage
6-3
exceedance.
a light
can be
50 years.
shows
1,000
industrial
carried
Table
similar
Thus,
$1,000
in
valuation
out
6-2
expected
shows
loss
Managua,
there
building
will
133
for
in
all
these
20 years.
eleven
loss
cities
calculation
calculations
for
a 20%
is
a 20% chance
that
in
have
an expected
loss
of
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However,
$321.00.
the
median
(expected)
loss
for
the
same time
be $128.40.
in Managua for
the same class of structure
will
6-13
behavior
as a function
shows
the
class
of
economic
It
per
the
year
time
$1~000
ing
over
for
a 20 year
it
this
per
would
was
Thus,
time.
gives
economic
be cheaper
it
that
as opposed
to
buying
buying
of
insurance,
for
our
$128.4
per
$1,000
buying,
or $638.8
in
valuation
per
these
$1,000
simple
cities
the
would
valuation
"insurance
risk"
a light
it
Managua
2.
Masaya
or
for
all
over
cost
year
$31.84
over
the
valuation
per
$1,000
decreasing
3. Granada
136
of
6-2
order
and
and 6-3
of
then
long
at
the
range,
would
be
For a
life.
valuation
per
Of
course,
span.
money
averag-
facility
years
cost
economic
a twenty-year
value
the
a
s $1.31
building),
In
of
valuation
a given
twenty
is
life
$26.2/20
$1,000
insure
and
one year
$1,000
industrial
a twenty
is:
1.
loss
averaged
per
problem,
From Tables
in
per
loss
year-by-year.
numerical
the
account.
to
insurance
for
calculations
are not taken into
that
it
of
time
a 20 year
loss
$5.84
possible
(say,
buy
$26.20
mean rate
to
in
over
expected
of
expected
region
Figure
This is the concept of risk
were
life
to
is
compared
same time
year-to-year
that
considered.
if
the
Managua
loss
less
year
that
However,
median
example
period
one year
the
valuation.
valuation
when only
for
expected
from
losses
can be seen
risk
thousand-dollar
be seen
twenty
expected
It
insurance)
structure,
can
of
structure.
(or
per
$5.84
the
the
period
the
it
magnitude
interest
year
rate
can be seen
in
different
100-9__8-_6__7
5__4
3__2__-
.
~
I
~
1-1
M
tj
1-1
~
0
...
:"'7.
9...~
8~;.::
.7
6__-
5_4
!;;.;;.
tj
~
2_-
98_T:
6-13
--ECONOKIj;:_L:tF~
VS~SS
FIGURE
00;:;;
6-
5-
-
4~
-
MANAGUA
3-
SEISMIC
2-
RISK
ANALYSIS
NICARAGUA
JANUARY.
.1975
1-,
SO
100
MEDIAN LOSS/$l,OOO VALUATION
150
DOLLARS
Leon
s.
Chinandega
6.
Rivas
7
Juigalpa
8.
Esteli
9.
San
Matagalpa
11.
Bluefields.
Granada
and
risks.
Similarly,
very
similar
Bluefields
the
is
California
economic
the
here
gation
is
in
In
conclusion,
expected
II
should
of
of
If
risks
it
will
damages
the
current
seismic
problem
these
cities
that
in
from
substantially.
a closer
study
question.
138
will
at
even though
the
are
Nicaragua,
the
methodology
levels
look
seismic
Nicaragua
not
that
risk
their
in
change
1n-
were from Southern
data
intensity
needs
out
or
and Matagalpa
insurance
conditions
can be said
the probable
economic
San Carlos
be pointed
proper
economic
expected
Esteli,
The
order
valid.
their
determining
Part
It
the
appropriate
determining
equal
used in the numerical
cities
for
almost
risks.
small.
risks
with
have
Juigalpa,
earthquakes,
sidered
of
Leon
insurance
very
damage data
and
Carlos
10.
surance
have
4.
go deeper
further
into
ordering
presented
and their
and
con-
use in
investi-
that
CHAPTER VI I
mE RELAT19~SHIP OF ISQ-~C~ELERATION AND ACgLERATION ZONE
!Q SEISMIC DESI~ PROVISIONS
GRAPHS (AZG)
Introduction
From
the
information
ground acceleration
These
location.
during
ceeded
chapter
is
load
tion
values
must
economic
total
sideration
for
structure
against
of
acceptance
structure
building
design
be converted
building
life,
owner
life
acceleration
seismic
for
preceding
for
chapter,
a given
probabilities
structure
to
these
P of
structure
are
load
levels,
being
to
accelera-
information,
will
such
have
and a much higher
condemnation or incipient
ex-
be inco~orated
Basically.
provisions.
load
not
The purpose of this
L.
values
seismic
Ro of damage protection
While
tection
selected
economic
as designed
the
g
have
for
in
may be established
A
show how these
criteria
structures,
against
values
a given
to
into
liability
values
as developed
that
a desired
RC
reliability
collapse
re-
during
the
life.
at first
both
the
thought
the hazards
complete
of
a building
some level
set
of
owner may desire
of damage and condemnation,
of
his
objectives
For
risk.
and Use Group or Function,
are:
139
a given
these
will
show
site
full
pro-
a conthe
necessity
location,
objectives
of the
Low construction
.
Low operating
.
Functional
configuration
.
Attractive
configuration
.
Damage protection
.
Condemnation
and
possible
damage
to
and
the
determination
the
For
Graphs
structure
life
the
operation
Group
hospitals;
and
building's
the
Peak
use
groups
penal
Critical
and mental
life,
PD'
of
PD'
PC'
which
the
probability
structural
L.
Owners,
L for
the
in
and hence
first
of
contherefore,
given
Chapter
can
6
result
in
values.
and
L,
the
Acceleration
Acceleration
values
Pc probabilities
or
of
presented
risk
is
and in
of
PC'
probability
Ground
site
damage protection
A:
level
of
demands
a moderate
for
objectives
fulfillment
Graphs
appropriate
these
probability
building.
a given
the
of
values
on the
of
earthquake
economic
of
values
all
Practical
a small
PD and small
example,
and
the
the
L at
following
in
acceptance
set
given
provide
moderate
the
decide
of
these
For
into
owner
(AZG)
the
the
Use GToup of
help
of
uncertainties
l-RD)
a definite
can
have
to
Pc during
agree
fulfillment
and behavior.
requires
PD (equal
demnation
value,
the
capacities
objectives
must
protection.
certain
due to
structural
four
cost
.
Perfect
not
cost
of
Zone
AD and AC which
exceedence
during
the
location.
function
of
depend
on the
in
event
the
facilities
structures
necessary
institutions;
gas,
may be organized
desired
of
reliabilities
a large
for
life
water,
of
earthquake.
care
electric,
and
safety;
and waste
140
I
!
II
1
water
treatment
departments;
facilities;
and disaster
Gr~~
:
entertainment
dustrial
control
Multi-family
structures;
structures
churches
Facilities
An example
of
such
and
normal
which
are
Example
in
values
Managua
and
7-2, 7-3, and 7-4.
would
of
the
Leon.
peak
are
hotels;
schools;
for
facilities
police
and fire
centers
commerce and where damage will
normal
facilities;
residences;
necessary
Group C:
sites
communications
recreational
commercial
and
in.
commerce
relatively
not
non-essential
create
a life
for
safety
hazard
be warehouses
ground
given
in
accelerations
the
AD arid AC.
following
These are based on structure
Tables:
at
7-1.
Ii yes of 20 and 50
years, and on reasonable values for Po and Pc corresponding to the
structure
for
Use GIOup.
demonstrating
engineers
same
at
the
this
facility
The values
concepts,
time.
and risk
Leon
the
objectives
of
Provide
Provide
that
the
motions
a structure
no significant
deformation
a level
a lower
tables
are strictly
meant to be used by
from
these
demands
represented
seismic
structural
with
four
designer
sufficient
structural
caused
by AD.
141
are
rigidity
damage
of a level
with
demand
sufficient
non-structural
quake ground
.
and are not
has
a structure
significant
these
tables,
in Leon and Managuarequires different
Obviously.
.
in
As can be seen
Ac values.
primary
given
will
represented
to
due
to
no
earth-
by An.
strength
by earthquake
Managua.
such that
occur
damage will
than
~ and
capacity
occur
ground
such
due to
motions
of
Table 7-.1
20 Year
Economic
Life,
Managua
Region
P
D
RPo
AD
Pc.
RPc
At
A
20\
90
.33g
10\
190
.38g
B
sO%
30
.24g
20\
90
.33g
c
70\
.17
.20g
50%
30
.24g
Group
Table 7-2
20 Year
Group
Economic
Life,
P1>
RPo
AD
A
20%
90
B
50\
c
70\
Leon
Region
p
c
RPc
AC
O.24g
1°'
190
O.26g
30
O.20g
20%
90
O.24g
17
O.17g
50%
30
0.171.
142
Table 7-3
SO Year Economic
Group
Po
Life,
Managua Region
RPo
AD
Pc
RPc
AC
A
20\
225
0.40g
10%
475
0.44g
B
50%
72
O.32g
20\
225
O.40g
'C
70%
42
0.27g
50\
n
0.32&
RPc
AC
Table
SO Year
Economic
7-4
Life,
~
Leon
Region
Group
Pn
A
20%
225
O.26g
10\
475
O.30g
B
50%
72
O.23g
20\
225
0.26g
c
70%
42
O.21g
50%
72
0.23g
RPD
Pc
143
.
Provide
a structure
deformation
will
not
of
a level
. While
capacity
result
the
PC'
serious
injury
safety
objecti'fe
are
types
integrity
to
of
and
of
neither
at
the
and
structure
ground
of
motions
to
at
small
prob-
be made to
prevent
Th:Ls life
details
of
and
complete
the
both
injurious
are
of
occupants.
the
struc-
struc-
system
collapse
last
which
admissible
possibility
represented
this
deformations
is
the
structural
a level
systems
stability
the
nor
consequence
structural
building
that
debris,
motions
the
elements,
such
falling
is
that
the
with
effort
of
requires
system
and
admissible
death
tural
damage
PO'
prudent
and non-structural
of
earthquake
significant
is
tural
The practical
of
probability
or
stability,
condemnation
effects
of
every
ground
that
strength,
by AC'
condemnation
ability
from
the
possibility
injurious
those
from
moderate
building
sufficient
such
represented
the
with
with
failures,
will
result
that
only
by AC'
objective
capable
is
of
retaining
and beyond
the
their
AC level
are
be used.
Within
these
systems,
the
structural
elements
must
tie
themselves
must
not
have
brittle
systems
of
Multiple
wall
ing
quake
or
vertical
systems
frames,
bracing
such
deformation
that
the
or
must
vertical
demands
at
details
connections
structure
together,
or
buckling
sudden
back-up
provide
load
and
o£ the
systems
a series
capacity
reasonably
is
between
and the
modes
in
the
of
lateral
of
form
the
failure.
of
force
maintained
beyond
elements
for
shear
resistearth-
AC level.
144
'I.
'
,
I
The
complete
Since
Figure
7-1.
linear
structural
thresholds
of
deformation
L.
tion
capacity
design
signed
such
not
its
the
highly
demnation
of
structure
level
the
method
AZG values
of
analysis
and ~C on a given
structure.
will
such
necessary
system
structure
during
a
which
satisfies
the
has been de-
equal
to
or
condemnation
of
greater
threshold
exceedence
and the
earthquake
PC'
not
the
constant
does
structure
level
reasonably
insures
exceed
load-
for
even
exceed
the
the
PD
those
con
stability
of
collapse.
AD and AC to
be developed
structure
deforma-
~DAM'
characteristic
design
V versus
are
might
non-
load
Further,
~CON.
which
of
in
create
coordinate
probability
a reasonably
latter
terms
structure
and
shown
critical
probability
level
AC with
deformations
against
damage
Ao with
level
maintains
This
the
capacity
The purpose of this
spectrum
the
level
damage
capacity
level.
structure
capacities
at
the
line
the
is
motions
on a given
Specifically,
condemnation
improbable
solid
indicates
a given
demands
curve
~C in
may occur
of
ground
indicates
The
deformation
the
condemnation
figure
system
earthquake
exceed
deformation
the
line
objectives
earthquake
forces.
objectives.
The
having
than
design
condemnation
~DEM which
that
of
this
~D and
earthquake
levels.
structural
demands
~CAP curve
stated
the
damage
The dotted
the
of
behavior,
Demands
life
does
the
~ rather
formation
than
set
that
design requirements
chapter
will
be described
their
as the
corresponding
Second,
the
First
is two-fold.
the
resulting
the
means
earthquake
complete
design
structure
will
of
relating
demands
~
procedure
have
of ~DAM~ ~D and ~CON~ ~C'
145
response
In
the
addition,
the
types
safety
of
requirement
analysis
forth
structural
and
in
systems
of
design
reference
collapse
procedures
28.
and details
prevention
will
The order
necessary
will
follow
the
the
subjects
of
for
the
be defined.
general
to
The
concepts
be treated
follows:
.
Basic
Response Spectra:
Definition
of an earthquake
response
spectrum
for
an ideal
elastic
single-degree-of-freedom
system;
Effective
ground
acceleration
as a working
measure
of spectral
size
or level;
Spectral
shape in terms
of
(DAF),
its mean and
the dynamic
amplification
factor
standard
deviation
(cr) value;
the effect
of the damping ratio
(S);
the effect
of inelastic
behavior
as
represented
by the ductility
ratio
(~);
site
or soilcolumn response
effects
on the average
ground motion
values.
. Response
Spectrum
Analysis:
of freedom
systems
as
the squared
response
of
each mode to a given spectrum (SRSS response);
use of
the SRSS response
to an inelastic
response
spectrum
as an approximation
of inelastic
system
response.
the
Response
of multi-degree
square
root
of the sum of
. Types and Characteristics
Force-Resisting
Systems
frames;
choice
in
of Lateral
Buildings:
Ductile
frames;
shear walls;
walls
and ductile
walls
and ordinary
frames;
the effect
of the
of system
type on the accomplishment
of the
design
. Design
objectives.
Spectra:
Definition
and purpose of design spectra
for the
damage and collapse
threshold
earthquakes;
spectral
level
established
by the effective
ground acceleration
A for a given structure
use group and life
L; spectral
confidence
limits
Kcr for structural
system types;
147
life
as set
are
as
",'.,.,
structure-foundation
assignment
of~,
types;
formulation
~ Proposed
interaction
and KG for
of a set of
S,
Design
effects;
subjective
given
structural
system
example
design
spectra.
Method:
Earthquake
loading
as provided
by the SRSS response
to the Design
Spectra;
structure
modeling
for
dynamic
modal analysis;
Dead, Live,
and earthquake
Load combination;
design
on an ultimate
strength
basis;
calculation
of inelastic
deformation-demands
and comparison
with
allowable
ductility
limits,
and stability
limits.
It
and
is
important
corresponding
descriptive
design
form
design
is
within
the
fective
such
in
Response
The
by which
tural
load
detail
the
and proportions
basic
or
of
basic
still
the
spectrum
in
practice
in
a state
represent,
Part
a general
seismic
of
development
the
objectives
II
of
to
provide
analysis
of
however,
design
shape,
response
load
design
going
characteristics
confidence
spectrum
is
is
AD and AC are
most
ef-
and are
this
to
values,
in
turn,
procedure
to
provide
elements
into
design
spectrum
of
structural
Before
spectral
response
These
as structural
level,
are
proposed
AZG values
an appropriate
termed
response
be presented
current
achieving
the
to
The
They
in
the
to
study.
Spectra
values.
objectives.
methods
of
earthquake
model
within
these
means
in
that
are
report.
profession.
practical
~asic
emphasize
procedures
this
that
design
be developed
to
the
spectra,
method
it
of
is
limit,
shown in
damping,
Figure
to
necessary
satisfy
formulating
necessary
the
what
to
These
and ductility.
7-2.)
to
struc-
be employed
the
to
and parameters.
analytical
be related
are
required
the
design
may be
describe
include:
sizes
the
size
(A typical
--
,
148
,
I
I
Definition
motion,
(shown
felt
For
a given
the
ordinate
in
by
S
ratio
of
Figure
tion
period
Response
purpose
5 of
7-3
.
Three
of
and
7-4
of
29,
a damping
straight
lines
The
V
displacement
the
are
from
level
response
of
D
g
the
are
A
AZG,
g
the
employed
for
of
for
is
either
g
deviations
(2 cr) from
ground
peak
steps:
motion
effective
AC.
the
ground
to
g
following
AD or
and
A , V , D
the
acceleration,
the
In the Newmark method these
two standard
the
the
a given
g
in
is
proportional
for
spectral
construc-
spectrum;
spectrum
by multiplying
used
basic
spectrum
constant
leg
the
of
of
consists
acceleration
set
and
representing
and displacement
type
on special
and as extracted
method
it
DAF values.
having
plotted
the
reference
Basically,
values
about
in
spectra
represent
report.
formed
response
T.
practice
acceleration
is
ground
spectrum
acceleration
system,
current
. The basic
earthquake
response
effective
The Newmark
ground
and
of
acceleration
vibration
They
report.
line.
g
value.
history
show response
by Newmark
velocity,
base
the
maximum
paper.
this
this
of
time
Spectra:
representative
of
the
or
Spectrum:
single-degree-of-freedom
as proposed
is
is
logrithmic
Appendix
T)
a
and natural
three-way
shape
S (S,
7-2)
Figures
Response
accelerogram
an elastic
Basic
an Earthquake
These
velocity
this
given
A
damping
value
S
curve
values
DAF values
Ag
g
by
are at
the mean DAF shape.
~~
I
150
I
1
'r
1000.0
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DAMAGETHRESHOLDLEVEL
o.
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PERIOD - SEC
FIGURE 7.3
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CONDEMNATION THRESHOLD LEVEL
0.01
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.1
1.0
10.0
PERIOD - SEC
FIGURE
7.4
152
D
I
-.
I"
viA
I
Inelastic
Response
When the
plastic
system
inelastic
is
force
and
the
given
in
If
the
ideal
level
equal
total
inelastic
the
Displacement
the
in
terms
inelastic
system
to
deformation
known
inelastic
rules
Spectra:
are
developed
Force
at
the
of
of
ductility
are
were
to
ideal
then
the
may be obtained
by
represented
have
its
in
system
is
strength
line,
given
by
7-5.
Figure
yield
Inelastic-Acceleration
the
elasto-
factor~,
spectra
these
T)
the
deformation
the
then
the
Non-Elastic
line.
to
be introduced
in
the
Part
~
.
and
period
Some improvements
which
of
deformation
method
(with
response
The ground
sible
to
. The
are
the
Local
I
this
report,
Newmark
and
method
subsequently
values
and the
represent
the
three
principal
Systems,
resulting
envelope
sources
Volcanic
shape
of
of
pos-
major
Activity,
and
Zone.
DAF in
terms
of
a must
representative
of
type
its
for
Nicaragua;
study.
will
be prescribed
for
this
report.
for
statistical
be evaluated
of
. The rules
to
Fault
to
as follows:
base line
from
Benioff
this
Part
be modified
effects
deviation
for
this
report,
motion
earthquakes:
the
in
II
-
may need
and modifications
forming
see,
A similar
the
the
Nicaragua
inelastic
mean value
and
a macro-region
for
example,
study
standard
which
reference
as reference
region
in
is
part
acceleration
30
30
II
of
and
153
I
~
I
'
Ii'
1
I
1
v
/
~
~
m
C/)
m
~
<
m
0
)I.
n
n
m
rm
~
)I.
-4
0
Z
...
~
)I.
z
(/)
...
0
z
THE
-a
~
m
(J)
m
~
<
)I-t
m
Z
m
~
0
-<
0
z
"V
~
m
(/)
m
~
<
m
0
c
(/)
~
r)I..
n
m
~
m
Z
-.
NEWMARK- HAll
FIGURE
154
7.5
METHOD
inelastic
the
actual
given
the
displacement
might
region
be better
elastic
ture
must
in
acceleration
elastic
with
the
. Depending
on the
local
soil
column
base
column
line
A , V , D
g
be applied
structures
region
this
because
inelastic
lines
for
either
to
forces
of
the
spectrum
or
close
a real
the
are
to
strucforces,
equal
to
structure
(rather
the
particular,
acceleration
the
remains
than
the
response
of
~
value.
the
may be significantly
must
g
is
conditions,
factors
than
In
equal
elastic
motion
represent
displacement
these
ground
g
behavior.
and hence
site
to
rather
a curve
displacement
adjustment
basic
the
corresponding
inelastic)
be modified
inelastic
by
forces
magnified
average
the
for
period
elastic
underlying
of
spectrum;
be designed
low
of
system
represented
response
this
must
behavior
elastic-plastic
period
the
but
inelastic
ideal
low
spectra
different
values.
spectrum.
shallow-stiff
from
Therefore,
be evaluated
sites
soi1-
to
modify
These
factors
or
the
for
the
would
deep-soft
sites.
Response
Spectrum
Referring
to
have
Analysis
back
to
some analytical
~D and ~C'
reference
The method
31.
.
lated,
method
to
Briefly,
A linear
the
7-1,
of
consists
dynamic
it
is
computing
be employed
this
elastic
and
Figure
the
is
modal
of
the
model of
characteristic
necessary
for
earthquake
analysis
following
the
the
demands
as described
of
in
steps:
structure
mode shapes
designer
is
formu-
and frequencies
';li?
,~-
155
c
i
I
I
are
. For
evaluated.
any
given
response
square
This
of
. Design
linear
of
the
termed
that:
the
to
demand
Threshold
the
squared
be formulated
~D'
to
and
Spectrum
assumption
specially
by
the
that
the
of
the
in
part
in
Terms of
Systems
Before
proceeding
define
and
of
by
each
the
elastic
II
to
consider
of
this
the
mode.
~C'
it
dynamic
Spectrum
the
condemna-
Since
is
both
necessary
to
deformations
model
design
of
section)
response
spectra.
this
assumption
Design
Spectra,
to
A
will
be
report.
Their
formulate
the
demand
to
structure
inelastic
validity
a following
SRSS response
provides
formulated
study
Types of Structures
Lateral
Force-Resisting
be given
Damage Threshold
inelastic
presented
displacement
response
the
employ
the
and
to
(in
deformations,
detailed
structural
assumed
are
force
~D and ~C may be inelastic
the
to
model
SRSS response
may be predicted
sary
the
sum of
are
the
provides
Spectrum,
as SRSS response.
spectra
such
tion
the
root
is
Response
the
inelastic
behavior
of
it
the
is
neces-
following
systems:
.
Ductile
Moment Resisting
Uniform
Building
Frames:
(the
K:O.67
system
of
the
Code).
156
.'
"';'1;
~~$;;
h
,1
"
I
Symbol
Description
O.67M
O.67P
Complete
Ductile
Width
the
of
Ductile
and Bearing
Walls:
1.33B
building
each Bay
plan.
Frames around the plan
perimeter,
. Shear
Frames for
with
in
the plan
(the
K=1.33
non-ductile
interior
columns
areas.
System of the UBC).
A box system
of walls
with
few
openings.
1.33P
A box system of walls
ings
that
system
1.33C
form
of
an equivalent
piers
Cantilever
with many openframe
and spandrels.
walls
or towers with
walls
or towers with
alignment
of openings
few
openings.
1.33S
Cantilever
vertical
form
. Ductile
sets
Frames and Shear Walls:
.O80M
of
(the
coupling
spandrels.
K=O.80 System of the
Same as O.67M, but
which
UBC).
with
several
shear
with
few shear
walls.
.O80P
Same as O.67P,
walls
. Ordinary
(the
Frames
K=l.OO
1.OOM
with
System
Semi-Ductile
of
the
or
but
towers.
Details
and Shear
Walls:
UBC).
Same as O.80M, but
with
ordinary
frames.
157
I
i
I
I.OOP
Same as O.80P,
but
with
ordinary
but
with
vertical
frames.
1.00MX
I.OOMP
Same as
I.OOM,
bracing
in
Same as
l.OOP,
place
of
but
walls.
with
vertical
bracing.
All
sure
and
the
systems
ductility
and
Figure
a given
the
system;
ductile
load
are best
exemplified
strength
classes
or
of
walls;
transfer
level
include:
chords,
in
frames;
drag,
systems
is
the
behavior
for
and shear
construction
references
general
in-
steel
details
through
the
rigidity
to
semi-ductile
shear
diaphram
and
required
these
and
for
bracing;
stiffness
details
32 and 33
inelastic
shown
in
is
be-
Figure
as in
7-7.
of
required
tural
the
horizontal
general
a given
necessary
reinforcing
constant
various
for
advantage
In
for
or
Clearly,
systems
details
to
For
of
of
systems;
walls
the
integrity
bracing
These details
havior
have
and collector
connection
joints.
to
concrete
grid,
vertical
7-6,
and
reinforced
chord,
are
from
large
ductility~
rigidity
have
addition
for
the
to
these
All
of
7-6
and
7-7
but
-for
some cases
damage control;
desired
damping ratio
formance.
Figures
rigidity,
properties,
65'
these
the
and,
but
each
and subjective
suffer
system
systems
they
may not
alternatively,
the
from
has
reputation
characteristics--rigidity.
158
K=O.67
a lack
its
of
have
have
the
K=l.33
ductility.
particular
of dependable
ductility.
the
struc-
perdamping,
V
.67
K=0.80
A
FIGURE
7.6
V
K = 1.33
00
-0.80
K=0.67
lI.
FIGURE
I
7.7
159
":
~'i~"""~~~"'.~:;;'£i";'t:~~e
~L~1:!'r1",
,~:
and dependability--must
as given
lation,
This
in
it
is
the
is
the
enter
next
well
section.
to
adoption
given
structure
sider
the
Figure
of
section
this
system
be most
Design
of
of
in
of
section
into
aspect
of
structural
earthquake
a K=O.67M
K=O.80M
the
system
original
this
formu-
seismic
system
demand
spectra
design.
for
the
conditions.
Con-
Frame
with
~DAM < ~D
is
preferable
to
the
in-
frame.
of a K=1.33 Box System with ~CON < ~C
case
(1.33
a Kl=l.OOM
sizes
would
in
be the
PC) of
essential
for
the
system
structure,
collapse
is
original
preferable
design.
consideration
wall
of
where
to
Even
a type
of
a strong
the
more
general
dramatic
brittle
pre-cast
back-up
frame
would
safety.
Spectra
the
section
on Basic
characteristics
column
response
factor;
as the
mean and
standard
Use Group
of
this
such
were
motion
purpose
and
Ductility
ground
The
appropriate
the
sizes
formation
of
In
spectral
important
going
design
7-9).
The
in
before
of
7-8).
Figure
increase
the
Rigidity
Insufficient
(see
formulation
cases:
The adoption
crease
a very
configuration
following
the
However,
treat
of
Insufficient
(see
into
of
as the
discussed:
A , V , D
g
and
g
g
those
is
has
to
base
dealing
deviation
a structure
section
Response
of
the
already
relate
the
160
Spectra,
two
groups
of
those
dealing
mainly
lines
and
site
the
with
the
DAF,
damping,
been
actual
related
elastic
structural
soilsystem
and
to
with
ductility.
A , and
g
such
the
character-
v
/
-~---~
-1
---
I
'"
--""-
'"
INCREASE
SECTION
SIZES
! -1-
FRAME
1---1=
USE K= O.80M
ORIGI NAL
DESIGN
ADEM
AC
AD
ACAP
ADAM
4CON
FIGURE
1V
7.8
~
/
INCREASE
SECTION SIZES
---
!--
ADD BACK- UP
FRAME TO FORM
A K=1.00M SYSTEM
ORIGINAL
K-1.33C
AD
AC
SYSTEM
ADEM
~CAP
4CON
t-IGURE
161
7.9
,I
;:1
istics
to
spectral
system.
characteristics
confidence
level
the
mean DAF is
Group
and
the
is
to
. Ductility
be related
to
structural
to
be related
details,
to
and number
Confidence
Limit
for
the
DAF:
The
choice
of
spectral
record
of
a structural
reliability
spectrum
random
(or
ideal
elastic
and standard
paper
2 are
such
This
level.
confidence
level
If
the
Ka
structure
the
back-up
of
structural
Use
type
of
It
confidence
should
in
5),
it
there
would
is
is
only
proposed
proven
that
roughly
here,
for
to
with
that
different
be reliable
of
the
the
in
the
amplified
the
DAF values
their
7-10.
average
In the
DAF values
chance
the
or
explained
that
Figure
stated
indetermine-
reputation
of
terms
a 10 percent
coincide
may be different
has
is
or
on the
be realized
can be described
con-
system.
limits
(Appendix
a system
struc-
ductility,
may be best
as shown in
It
and
frames
based
(a)
that
damping
member
deviation
level
confidence
deviations
of
of
system
or
DAF).
which
the
DAF levels
levels
variables
Newmark-Hall
to
dependability
type
response
standard
or
the
the
of
be related
in
of
ceeded.
to
contained
performance
systems.
the
interaction.
is
nection
acies
number
reputation
ture-foundation
Table
with
system.
. Damping
value
or
above
structural
are
deal
Specifically,
. The
terms
which
of
upper
of
from
past
ex-
(two-a)
appropriate
types
being
in
DAF
structural
experience,
162
)
I
1
I
I
FIGURE
7.10
163
and
can
tolerate
should
its
to
merit
design
then
a low
chance
This
other
or
well
as would
not
is
a need
~ of
for
level
total
the
confidence
has
for
the
also
ability
for
or
the
design
without
protection
against
2a exceedence
level.
level
will
if
back-up
upon
it
is
system,
chance
each type of structural
for
failure.
new and untried,
no reliable
confidence
level)
can be depended
level
is
showing
collapse--then
(one-a)
system
has
excess
demands
system~ an appropriate
be assigned
the purpose of providing
facilities,
will
according
be assigned
mean DAF.
It
according
for
a given
to
the
the
group
acceleration
from
level
component
be recalled
should
the ground
assigned
a desired
an additional
level
limit,
the
the
before
to prevent
(say
a system
that
confidence
been
of
the
systems
because
if
displacements
to
the
record.
critical
fidence
above
for
by
performance
Also,
The
of
level
connected,
Therefore~
tion
hand,
be provided
component
is
exceedences
On the
there
system
range
confidence
spectrum.
resist
b.rittle
wide
damage, and has back-up
significant
it
a fairly
that
type
the
is
to
of exceedance as governed by the building
A
the
con-
Use Group.
(KG+~)a
in addition
base line
AZG according
KG of
structure
and
of protec-
g
to this
for
the
accepted
spectrum
prob-
use group.
Damping:
Damping
and will
due to
be assigned
new and additional
the
type
according
component
structure-£oundationinteraction~
of
to
structural
the
general
of damping occurs
This.will
164
system
is
material
termed
behavior.
due to the
be termed
as
effects
as SF and
~S'
A
of
T
will
be evaluated
Total
damping
in
for
accordance
a design
with
spectrum
the
is
methods
therefore
in
reference
S'
= Ss
+
34.
SF'
Ductility:
Ductility
to
the
material,
statistical
Each
its
varies
with
member
the
and
indeterminacies
structural
type
particular
will
type
of
structural
system
connection
details,
and
or
systems
within
back-up
be assigned
a ductility
the
according
number
the
value
of
structure.
~'according
to
description.
Properties
The
types
of
complete
structural
The values
general,
agreement
with
level
the
for
values
past
final
~ef~nition~andF~rmulation
in Terms of Modified
While
collapse
it
is
threshold
structural
behavior
concept
that
motions
representative
cept
based
at
story
.
attainment
of
for
are
on the
deformations
design
values.
of
Inelastic
generally
in
the
of
fact
earthquake
inelastic
behavior
the
that
somewhat
yield
with
different
in
Table
7-5.
a Use Group B.
judgment
behavior,
and
to
In
~--
provide
a reasonable
Design
Spectra
Spectr~
recognized
of
the
shown
by professional
reported
load
as
systems
experience,
level
for
may be organized
assigned
,
of first
properties
some example
some inelastic
.
spectral
systems
are given
the
is
set
damage
the
that
the
motions
must
range,
this
may be
tolerated
threshold
than
,~
or design strength
-"'--:-t6S'
~
'-
report
by
advances
while
damage
the
or
be resisted
earthquake.
structural
greater
condemnation
resisting
This
threshold
deformation
the
conoccurs
at
the
~-"-
at the member section
,
,
Table 7-5
Given
Use Group B~ KG = 1.0
DamageThreshold
Type
Collapse
Threshold
p'
~
0.05
1..5
1.00
0.05
4.00
1.20
0.05
1.5
1.10
0.07
3.00
1.50
0.05
1.5
1.20
0.07
2.00
~
BS
O.67M
1.00
I.OOM
1.33C
-~
-166
8S
p'
having
the
strength
highest
design,
The
stress
damage
following
and reasoning
ratio.
Figure
threshold,
and
discussion
employed
for
7-11
the
condemnation
presents
the
shows
the
formation
of
states
of
threshold.
definitions,
methods,
modified
inelastic
design
strength
determination
spectra:
the
.
Damage Threshold
(DTSS),
the
.
for
Spectrum
setting
the
Damage Threshold
(DTSD),
for
the
for
design
strength
Spectrum
evaluation
for
of
of
members,
Deformation
P-Delta
and
determination
effects
on design
strength.
. the
Condemnation
termination
demand,
Threshold
(CTSD),
and
for
Spectrum
the
for
evaluation
detection
of
inelastic
response,
Deformation
of
instability
member
problems
deductility
due to
P-Delta
effects.
The modified,
by
and
the
use
Sf.
may be termed
factors
the
inelastic
with
particular
where
what
These
to obtain
sistent
of
performance
motions.
used
of
lateral
of similar
systems
system
to Figure
having
7-12,
by test
undergone
the
factor
values
capabilities
of
a given
results
Fo'r~-iheDamage
Threshold--E-arthquake
~-'".-
;
I
.
16 - 7
._~,
'
the
structure;
and past
earthquake
are:
(DTEQ)
conof
,
1)
~'
by judgment,
strong
objectives
formed
factors
damping
and damping
as evidenced
are
modification
and
force-resisting
are
spectra
They are selected
ductility
capabilities
Referring
spectral
as ductility
spectra.
the respective
type
these
are
as
design
the
factors
ground
'
WALLS
ADAM
FRAMES
DESIGN
AT
LEVEL
UL TrMATE
x
DAMAGE 0
TRESHOlD
CONDEMNATION
TRESHOLD
STRENGTH BASIS
FIGURE 7-11
168
D
~
Vc
DUE TO CTSD
LINEAR ELASTIC
MODEL
vh
.Q.UL
T..Q.-WD-
---
VCON
3
VDAM
,
VDES
QjJ.E_T
0- W L
1
c
V]
...
u
0
..
AOES
ADES
v' =
ADAM
STORY
SHEAR ON ELASTIC MODE l
V = STORY SHEAR ON INELASTIC MODEL
DE5 = MEMBER DESIGN lEVEL
FIGURE
6.DEM
AC
AD
7.12
16!)
ACON
ACAP
~',
are
S'
D
D
Figure
the
to
produce
7-13)
(DTSS)
ultimate
an inelastic
such
strength
accordance
with
basis
the
dead load
.
code specified
.
DTSS Acceleration
Extra
story
when members
for
design
.
.
that
acceleration
forces
procedure
(non-load
shear
due
given
spectrum
are
designed
to:
(this
in
the
factored)
live
due to P-De1ta
effect
(see
on
is
next
in
section)
load
at DTSD
deformation
then
it
is
assumed
formation
able
of
capacity
level
the
assumed
2)
threshold
that
the
measure,
to
allow
study
threshold
and
For
the
~~,
Sc are
CTEQ.
is
and
~o and
the
demand
drift
it
is
the
~D
further
provided
So
an upper
deformation
an accept-
by
the
magnitude
values
be
acceptable
level
confidence
limit).
assumption
limitations
or
would
for
control
the
factors
damage.
to
produce
(CTSD)
greater
Local
If
is
de-
demands
that
having
of
with
(DTEQ).
important
the
threshold
deformation
demand
to
formulation
Condemnation
7-14)
larger,
the
DTSD values
non-structural
reliably
it
(corresponding
damage
or
threshold
shape,
provide
damage
earthquake
damage
the
structural
than
then
reliability
Figure
be equal
damage
This
of
will
reliability,
selected
of
the
of
DTSD deformation,
size
that
or
member
Threshold
Earthquake
an inelastic
that
will
equal
ductility
to
deformation
provide
the
(CTEQ)
deformation
deformation
demands
spectrum
and
values
demand
story
(see
~C of
the
stability
170
Ii.
I
I
I
,
II
MOdified
Damage Threshold
Spectra
FIGURE
FIGURE
171
7.13
1.14
with
.
,
~D and flD (Group B, Managua)
checks
(involving
formations
the
For
this
able,
tion
of
the
reliably
large
an
design
of
members,
conservative
(low)
evaluated
be upper
confidence
~C value
of
for
crSD de-
limits
spectrum,
of
then
deformation
a large
force
a more
realistic
produce
for
demand.
If
of
it
(CTSS) for
of
a reasonFor
value
would
the
forma-
~C provides
were
desired
the strength
course
provide
non-
A proposed change to the
demand values.
of
to
a large
spectrum
~C value
construction
is
CTEQ deformations.
acceleration
for
may provide
the
estimate
values
inelastic
method
of
deformation
(large)
to employ
Newmark
therefore
purpose
an inelastic
conservative
This
will
effects)
CTEQ demands.
report,
but
P-Delta
the
CTSD is
indicated
estimate
of
actual
that
the
DTSS is
design
of
in
Figure
structure
7-14
deforma-
tion.
It
CTSS and
of
the
assumed
therefore
design
chapter,
cedure
is
in
Proposed
this
controls
spectra
after
the
the
next
Design
in
report
the
strength
DTSS and CTSD will
presentation
of
.
the
complete
Examples
later
proposed
the
in
Design
this
Pro-
Procedure
procedure:
Given
Use Group,
Life,
from
Part
II
cr values
of
are to be employed in the
and Site:
AD' AC' KG' and site
The mean DAF and
able
than
section.
design
Obtain
members.
be constructed
The DTSS and CTSDdesign spectra
following
larger
this
soil-column
are
known.
response
(These will
factor.
be avail-
study.)
172
~
I
.
Given
Structure
Obtain
Ss,
Type and Foundatio~:
SF'
~,
KT at
both
Damage D and
condemnation
C
levels.
. Construct
Desig!!
DTSS for
Member
Spectra:
Section
Design,
with
~o'
So
=
Ss
+
SF'
(KG + ~)a.
CTSD for
Ductibility
with
Sc
~C'
Evaluation
= Ss
+ SF'
Member
Force
2)
Member
Deformation
Load
2)
DTSS Force
Factored
Seismic
3)
plus
P-Delta
the
Structure
-
DTSS;
to
the
CTSD.
on a~
Dead and
Vertical
Live
Dead and
Load;
Live
Load,
and
Effects;
plus
celeration
effects).
two-thirds
Dead Load
(See Appendix
(for
6 for
vertical
vertical
local
Analysis
member
due
ductility
to
CTSD Response:
demands
and
compare
established allowable values (to be determined in
Part
II
ac-
effects.)
Deformation
Evaluate
the
of
~ombinations
for:
Vertical
acceleration
1)
to
Response
DTSS Force
. Perform
Model
Response
. Design
Members f~r_Lo~d
Ultimate
Strength
Basis
1)
Analysis,
(KG + KT)a.
. ~ri~'"~I~~~S~Ss-v~l~e-~f~
Formulate
a Linear
Elastic
1)
and Stability
of
this
report).
173
with
I
2)
Investigate
Construction
of
Given
type,
such
termined
basic
that
both
the
spectra
Appendix
5.
The
a structure
use
.
can be de-
known
shown
in
with
Figures
values,
procedure
Managua
7-3
the
according
is
and
the
given
the
The
Ka,
Then,
design
Newmark
in
A,
7-4.)
inelastic
to
and
with
spectra
method
in
following
example
region.
B.
Life
System:
=
L
soil-column
S
=
ground
structural
0.67M.
20 years.
conditions
are average
such that
the
site
1.00.
Interaction
acceleration
AD
. The
and ~')
system
these
. Structure-Foundation
. The
B',
structural
Managua.
. Economic
factor
Ka,
and
may be constructed
. Type of Structural
. Site
(A,
L,
Earthquakes.
Use Group:
Region:
life
Level
complete
. Structure
system.
Damage and Condemnation
are
the
structural
group,
values
constructed
in
of
Spectra
~D and ~C ductility
DTSS and CTSD are
for
Design
spectral
(Examples
given
stability
structure
the
elastic
B'values.
the
Example
the
for
the
=
base
0.24g,
system
are
BF = 0.05.
found
from
Table
7-1.
0.33g
are
found
from
Table
7-5.
= 1.0,
DTSS
BS = 0.05,
For
KT = 1.00,
=
properties
For
1.00,
lines
AC
KG
~=
Damping
~D = 1.5
CTSD
BS = 0.05,
~C = 4.00
174
~
II I
I
I
I
I
I
The Spectral
.
Properties
are:
For
Sb
= SF
K = KG
= 0.10,
+ Ss
KT
+
=
DTSS
~b = 1.5
2.0,
Ka
For
Sc = SF +
. The
Basic
Elastic
constructed
It
is
interesting
compare with
consider
a 10 story,
and the resulting
factors
(or
Load forces
shear
from
for
these
Figures
7-3
Spectra
Figure
the
for
weights),
W
the
ultimate
values
Building
building
from
Code.
with
acceleration
this
Let us
first
mode
S = 0.14g,
a
0.112 W
the multi-mode
and W is
strength
7-4.
be about
=
VI would be combined
and
are
DTSS and CTSD are
load
frame
would
(0.8)
properties
7-15.
Uniform
7-15,
value
(0.14)
allows
equivalent
Member forces
from
base shear
0.8 factor
for
to see how design
loads
=
in
Design
From Figure
VI
where the
Spectra
Type 0.67M steel
of. 1 second.
= 4.00
~c
as shown
and shown in
spectrum
period
0.10,
inelastic
constructed
2a
CTSD
Response
and are
The modified
.
=
Ss
=
the
with
design.
response
structure
participation
weight.
Dead and un-factored
The corresponding
Live
UBC base
is
V2
= UKCW= 1.4 (0.67)
V2
=
(~)
W
If
0.047
W
175
I
i
I
I
I
,
I
I
1000.0
cO)
"Q
°0'0
/~
0
~<>"'«"O~
L-«; ~
~
~-,;IO-";
~
to~'j «; «..~
c.,v
100
,0)
?()
~O)
"0
~O
1'>«';
:(
/-1,..
()/ ...,~
i.S'A/J..~
i.S' :( ,.
Q', "'/
U
w
U)
/1- (' «'
. -1t
-:0
z
'>
«'1J'
10
U)
>-'
~O)
C~
~
"0
U
0
-'
w
'0
/-1,.
.
>
w
U)
Z
0
DU)
~
1.
C'~
9
w
>
.-
'0
~
.
/-1,.
W
~
0
c
~
w
U)
D-
o
0)
DESIGNSPECTRAFOR K=0.67M
0'
~c
."
DDTS HAS ~o
=
1.5,
So
= 10%
CTSDHAS ~C
= 4.0,
Sc
= 10%
/~
= 2a
0.0
.
.
1.0
PERIOD- SEC
FIGURE 7.15
176
II
I
10.0
Member
1.4
forces
times
from
the
Therefore,
Dead and
although
member
designs
will
amount
because
of
Load
Live
Load
the
VI
not
differ
the
should
is
different
These
to
Structural
be realized
The
example only.
order
be combined
with
forces,
2.4
for
times
from
a load-factored
ultimate
the
the
VI
method
of
V2 value,
designs
value
strength
the
of
design
resulting
VI
by as much as this
factoring
the
Dead and
Live
effects.
It
mate.
V2 would
values
provide
assigned
are
consistent
to
that
these
spectral
property
be refined
Design
resulting
in
Spectra
Types.
177
spectra
values
Part
for
II
of
all
are
this
are
very
study
Use Groups
for
approxiin
and
-I!!
CHAPTER VIII
SUMMARY, CONCLUSIONS AND FURTHER RESEARCH
Summary
In
topics
are
1.
Part
I
of
the
Geological
setting
Data
area
base
in
for
Limitations
3.
risk
study
for
Nicaragua,
the
following
presented:
Managua
2.
seismic
for
seismic
the
data
Seismic
recurrence
sources
was developed.
Based
on the
seismic
tude
derived.
Using
cess.
Cumulative
Nicaragua
accelerations
shown
ten
line
of
the
for
to
was
and the
Poisson
time
for
were
20 and
area
of
different
different
in
functions
SO years
three
occurrence
were
considered
be one way of
and
discussed.
magni-
regions
relationship,
country
distribution
studied.
were
exceeding
attenuation
the
extensively
sources
of
of
Esteva's
maps for
in
general
approximations
probabilities
cities
was
for
as functions
acceleration
in
events
and
assumption
events,
levels
country
particular.
past
of
the
were
presenting
iso-
constructed.
this
Eleven
mapping
of
peak
proground
established.
seismic
was
risk
This
for
Nicaragua.
4.
Based
on iso-acceleration
maps,
the
Acceleration
Zone
178
I
Graphs
(AZG)
method
of
the
whole
5.
of
risk
charts
Ground
the
such
the
for
and
cities.
A
consistent
risk
suggested.
as AZG be used
in
MMI scale,
in
the
in
probabilistic
U.S.A.,
It
for
for
was
seismic
understanding
sense.
a method
of
seismic
Based
on the
determining
insur-
was presented.
acceleration
level
of
prevention
ology
levels
eleven
Nicaragua.
data
risk
the
was discussed
was presented
ance
for
load
parameter,
damage
6.
determining
that
Another
developed
country
proposed
zoning
were
values
the
and
design
from
the
AZG were
spectra
condemnation
was proposed
resulting
from
for
structural
control.
based
on ultimate
above
inelastic
employed
set
damage
A design
method-
strength
design
to
and
loads
spectra.
Conclusions
It
lytical
methods
acceptable
easy
to
zoning
or
use
the
provide
country
amenable
current
study,
significantly
to
it
are
sufficient
seismic
zoning
The methods
to
presented
structural
of
zoning
availability
can be
from
clearly
region
plots
from
of
presented
of
to
that
region.
and ana-
information
are
on an
simple,
procedures.
The
iso-acceleration
peak
ground
here
is
additional
seen
data
here
design
can be interpreted
distribution
The method
there
adequate
transferable
cumulative
AZG.
that
criterion.
and
pletely
varies
to
risk
of
from
from
.can be concluded
accelerations
general
future
the
maps
and
data.
seismicity
The Managua
of
or
is
com-
From
the
Nicaragua
region
and
179
..
1
the
region
the
central
lowest
surrounding
or
AZGs,
this
report
Looking
obvious
to
Further
economic
risk
in
different
presented
in
this
report.
region,
it
purchase
is
short-term
various
parts
economic
Further
of
of
parts
seismic
Bluefields
region
has
has
the
iso-acceleration
loading
than
the
highest
maps and
as presented
information
facility
of
Again,
the
it
to
on acceptdesign
insurance
based
can be seen
that
on this
this
structural
regarding
can be compared
a seismic
the
seismic
in
based
country
long-range
Based
country
to
the
the
coverage.
due
Managua
methodologies
the
buy
much more
example,
can be obtained
to
the
impact
on the
for
insurance
method
a given
insurance
for
and
than
risk
future
to
concept,
probable
event.
Research
In
their
cheaper
at
that
life
insight
the
is
obvious.
convert
and economic
process.
For
and
becomes
also
volcanoes
region.
level.
can be used
risk
of
level
information
is
line
eastern
loading
loading
It
able
the
probable
probable
the
order
general
complished
in
.
to
form
in
Part
II:
Refined
risk
implement
this
seismic
levels
A detailed
their
effect
. The
concept
for
look
and use
report,
zoning
on cost
of
the
micro
the
procedures
following
of the
different
at
the
acceptable
and general
zoning
tasks
country
classes
a given
presented
are
to
in
be ac-
based on acceptable
and uses
of
probability
structures.
levels
and
economy.
region
in
the
country.
180
.
i
1
.
Mapping
information
values
V
as
in
the
predicted
form
in
terms
of
effective
ground
of
historical
data
velocity
and
g
geological
characteristics.
. Inclusion
the
of
the
evaluation
of
g
of
in
the
. Evaluation
of
the
nition
of
either
Groups
a more
ranging
and
establishment
ance
probability
from
or
the
to
the
corresponding
of
values
P for
the
SF and
the
with
Zone,
g
g
of
the
the
and
values.
g
Structure
non-essential
typical
of
Volcanic,
A , V , D
mean
recog-
predominance
listing
critical
a and
region,
the
(Benioff
precise
in
damping
values
a given
affect
location.
Use
facilities;
acceptable
exceed-
structure
life
L.
. Assignment
of
the
DAF confidence
. Elastic
element
use
modeling
by response
forces
. Improvements
contribution
techniques
spectrum
and inelastic
in
the
displacement
. Categorization
Group
KG to
the
spectrum
allow
reliable
level.
structure
prediction
and
sources
in
vibration.
deviation
averaging
as they
of
structure
structural
of
DAF for
the
earthquake
. Formulation
times
standard
factor
interaction
of
period
spectral
Faulting)
response
at a given
g
component
the
values
Local
g
structure
of
possible
soil-column)
foundation-structure
an additive
change
(or
of A , V ,D
. Representation
form
site
method
response
of
the
to
analysis
of
structural
deformations.
of
forming
the
inelastic
force
spectra.
types
181
of
structural
lateral
force-
resisting
systems
ductility
~,
to
the
and
damping
spectrum
of
essential
details
all
limits
the
to
that
simplified
the
design
of
analysis
would
figuration
and
. With
damage
and
economic
and
limb
economic
risk
will
allowable
the
systems.
dynamic
to
for
Building
Code.
to
response
those
and/or
analysis,
a procedure
be applicable
detailed
stability
ductility
and
Uniform
only
design
of
and
analysis,
costly,
structural
and
of
would
The
critical,
damage
member
materials
by the
be required
extremely
the
ductility
spectrum,
procedure
structures.
both
specification
the
stability
employed
design
majority
for
acceptable
and
~
contribution
strength
materials;
all
deformation
similar
for
and establishment
of
corresponding
type
ultimate
acceptable
for
the
spectra.
necessary
. Simplification
life
level,
collapse;
demand
are
DAF confidence
appropriate
for
of
structure
threshold
equations
against
~S'
assignment
and
condemnation
. Formulation
and
and the
This
the
spectrum
structures
unique
in
which
their
con-
systems.
data
analysis
is
be treated
from
Nicaragua,
an insurance
to
be accomplished.
in
Part
II
of
this
Risk
to
study.
182
,I,
I
I
REFERENCES
Note:
All sources listed as "Managua Conference Proceedings" from,
Managua, Nicara2ua Earthquake of December 23,1972,
Conference
Proceedings, November 29-30. 1973, Earthquake Engineering
Research Institute.
1.
Anon., "The Geology of Western Nicaragua," Final Technical Report,
Vol. IV, Tax Improvement and Natural Resources Inventory Project,
Nicaragua, 1972.
2.
Anstead,
Leroy E., "A Study of Seismic Damage Patterns
interpretation,
By Photo-
Managua, Nicaragua, 23 December, 1972," Managua
Conference Proceedings,
pp. 265-270.
'5.
Caldera~ Humberto Porta, "Geodetic and Gravity Survey of Managua
and its Surroundings~" Managua Conference Proceedings, pp. 143172.
4.
Dewey, J. W., et a1., '~he Managua Earthquake of 23 December,
1972: Location, Focal Mechanism, Aftershocks,
and Relationship
to
Recent Seismicity
of Nicaragua," Managua Earthquake Proceedings,
pp.66-88.
s.
Faccioli,
Ezio, et al., "Microzonation
Criteria
and Seismic Response Studies for the City of Managua," Managua Conference
Proceedings, pp. 271-291.
6.
Hansen, Francisco, and Chavez, Victor,
Managua December 23, 1972 Earthquake,"
ceedings, pp. 104-114.
7.
Hodgson. John H.. 1964. Earthquakes and Earth Structure.
wood Cliffs,
New Jersey:
Prentice-Hall,
Inc., p. 59.
8.
Kelleher,
J., et al.,
1973, "Possible
Criteria
for Predicting
Earthquake
Locations
and Their Applications
to Major Plate Boundaries of the Pacific
and the Caribbean,"
Journal
of Geophysical
Rese~ch,
Vol. 78, no. 14, pp. 2547-2585.
9.
Knudson, Charles F., and Hansen, Francisco A., "Accelerograph and
Seismoscope Records from Managua, Nicaragua Earthquakes," Managua
Conference Proceedings, pp. 180-205.
183
"Isoseisma1 Maps of the
Managua Conference 'ProEngle-
10.
Leeds, David J., "Destructive
pp.
Earthquakes
26-51.
of Nicaragua,"
Managua
11.
Matumoto, Tosimatu,
and Latham, Gary, "Aftershock
of the Managua Earthquake
of 23 December, 1972,"
ence Proceedings,
pp. 97-103.
12.
McBirney,
Alexander
R., and Williams,
Howel, 1965, "Volcanic
History
of Nicaragua,"
University
of California
Publications
Geological
Sciences,
Vol. 55, pp. 1-73.
and Intensity
Managua Confer-
-
13.
Morgan,
Nature,
14.
Plafker,
George, and Brown, R. D., Jr.,
"Surface
fects of the Managua Earthquake
of December 23,
pp. 115-142.
15.
Saint-Armand,
Pierre,
"The Seismicity
and Geologic Structure
the Managua,
Nicaragua Area," Managua
Conference
Proceedings,
pp.
8-25.
-
16.
Santos, Carlos,
the Earthquakes
pp. 52-65.
17.
Valera,
Julio
E., "Soil
Conditions
and Local Soil Effects
During
the Managua Earthquake
of December 23, 1972," Managua Conference
Proceedings,
pp. 232-264.
18.
Ward, Peter L., et al.,
"Location
of the Main Fault that Slipped
During the Managua Earthquake
as Determined
from Locations
of
Some Aftershocks,"
Managua Conference
Proceedings,
pp. 89-96.
19.
Wilson,
1963.
20.
Wallace,
R. E., "Plan for Zoning Managua, Nicaragua,
To Reduce
Hazards of Surface Faulting,"
Managua Conference Proceedings,
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21.
Leeds,
Los
William
J., 1971,
Vol. 230, p. 43.
J.
Plumes in the
Lower Mantle,"
Geological
Ef1972," Ma?agua
"Hydro-Geological
Factors
in the Occurrence
of Managua," Managua Conference Proceedings,
T.,
"Continental
David J.,
Angeles:
"Convection
in
"Catalog
Dames
Drift,"
Scientific
of Nicaraguan
American,
Earthquakes
of
of
April,
1520-1973."
& Moore.
22.
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National
Earthquake
Information
Center,
U.S.
Department of Commerce, National
Oceanic & Atmospheric
Agency,
Boulder,
Colorado.
23.
Seismological
Society
of America (1951), Seismological
Nicaragua,
August 3-6, 1951.
Bull.
Seis. Soc. Amer.,
No.4,
p. 399.
Notes-Vol. 41,
184
ill
,
24.
Rothe)
J. P. (1969) "Seismici ty of the Earth,
1953-1965,"
Paris:
UNESCO.
25.
Gardner, J. K., and Kuopoff, L., "Recorded Earthquakes in Southern
California,"
Bull. Seis. Soc~ Amer., 1974.
26.
Dalal,
J. S., "Probabilistic
Seismic Exposure and Structural
Risk Evaluation."
Technical
Report #169, Department of Civil
Engineering,
Stanford
University,
February,
1973.
27.
Vagliente,
V. N., "Forecasting
the Risk Inherent
in EarthquakeResistant
Design."
Technical
Report #174, Department of Civil
Engineering,
Stanford
University,
June, 1973.
28.
"An Evaluation
of Buildings."
of a Response
Spectrum
Approach
to Seismic
Design
Applied
Technology
Council~
171 Second Street~
San Francisco~
California
29.
94105.
"Procedures
and Criteria
for Earthquake
Resistant
Design,"
Proceedings
of Building
Practices
for Disaster
Mitigation
Workshop,
National
Bureau of Standards,
Building
Science
Series
46, February,
1973.
(Order
by SD Catalog
No.. C 13.29/2:46,
Superintendent
of Documents,
U..S. Government
Printing
Office,
Washington,
D.C. 20402.)
Blume, J., Sharpe,R.,
and Dalal,
J.
"RecoDDDendations for Shape of
Response Spectra."
John A. Blume and Associates,
Engineers,
San Francisco,
California.
USAEC Contract
#AT(49-S)-30ll,
Feb., 1973.
Biggs, J. M., Introduction
McGraw-Hill, 1964.
32.
33.
Seismic
Design
for
Buildings,
the Army, Navy,
and the Air
RecommendedLateral
Committee
Structural
171 Second Street,
to -Structural
Army
Force.
Dynamics. New York:
TM 5-809-10,
Departments
April,
1973.
of
Force Requirements
and Commentary, Seismology
Engineers
Association
of California,
1973.
San Francisco,
California
94105.
34.
Seismic Interaction
of Structures
on Hysteretic
Foundations;
Veletsos,
A. S., and Nair,
V. V. Journal
of the Structural
Division
ASCE" Vol. 101, No. ST1, January,
1975.
35.
Benjamin, J. R., "Probabilistic
Decision Analysis Applied to
Earthquake DamageSurveys. EERI report.
Unpublished, July,
1974.
36.
Whitman, R. V. "Damage Probability
Matrices
for
ings."
NIT Technical
Report R73-57.
Department
Engineering,
November, 1973.
Prototype
of Civil
Build-
185
- I
Whitman, R. V., S. Hong and J. W. Reed,
"Damage Statistics
for
High Rise Buildings
in the Vicinity
of the San Fernando Earthquake."
MIT Technical
Report R73-24.
Department of Civil
Engineering.
April,
1973.
38.
Whitman, R. V., Biggs, J. M., Brennan, J., Cornell,
C. A., de
Neufville,
R., and Vanmarcke, E. H., "Seismic
Design Decision
Analysis--Methodology
and Pilot
Applications."
MIT Report #CER74-1S.
July,
1974.
Algermissen,
S. T. and Perkins,
Zoning:
General Considerations
of the International
Conference
struction.
Seattle,
D. M., "A Technique for Seismic
and Parameters."
Proceedings
on Microzonation
for Safer Con-
Washington,
1972.
40.
Cornell~
C. A.~ "Engineering
of the Seismological
Society
pp. 1583-1606.
Seismic Risk Analysis."
Bulletin
ofAmerica~
Vol. 54~ No. 5~-19-68~
41.
Algermissen, S. T., "Seismic Risk Studies in the United States,"
Proceedin s of the 4th World Con£e~nce on Earth uake En ineerin
Santiago, Chile, 1969.
42.
Anderson, J. C. and Bertero,
V. V., "Effects
of Gravity
Loads
and Vertical
Ground Acceleration
on the Seismic Response of
Multistory
Frames," Proceedings,
Fifth
World Conference
on Earthquake Engineering,
Rome, Italy,
Vol. 2, pp. 2914-2923.
43.
Housner, G. W., "Earthquake Ground lvbtion," ASCE-IABSE International Conference on Planning and Design of Tall Buildings,
Vol. lb.
Bethlehem, Pennsylvania,
1972.
44.
Iyengar,
R. N.,
and Shinozuka, M., "Effect
of Self-Weight
and
Vertical
Acceleration
on the Behavior
of Tall
Structures
During
Earthquakes,"
Journal
of Earthquake
Engineering
and Structural
Dynamics,
Vol.
1, No.1,
July-September,
1972, pp. 69-78.
Jennings, P. C., "Engineering Features of the San Fernando Earthquake, February 9, 1971," Report No. EERL71-02, California
Institute of Technology, 1971.
Kost,
E. G., et al.,
Progress
Report
of the 1969
Response
of Structures
to Vertical
Accelerations~
mology
Committee,
1969.
Subcommittee
SEAONC Seis-
Larson, M. A., et al.,
Annual Report of the Vertical
Subcommittee,
SEAOMCSeismology Committee,
1970.
186
on
Accelerations
,
48
Mohraz, S.,
49.
Newmark, N. M., and Hall,
Nuclear Reactor Facilities,"
on Earthquake
Engineering,
Hall,
W. J., and Newmark, N. M., "A Study of Vertical
and Horizontal
Earthquake
Spectra,"
Report to the Division
of
Reactor Standards,
u.S. Atomic Energy Commission, October,
1972.
W. J., "Seismic
Design
Proceedings,
Fourth
Santiago,
Chile,
Vol.
Criteria
for
World c.onferen~e
2, 8-4,pp.
37-50.
so.
Rosenblueth~ E.~ "The Six Components of Earthquakes~"
Australian
and New Zealand Conference
on the Plannin
of TallBuildings~
Sidney, Australia,
August,
1973.
51.
Sharpe, R. L., Kost, E. G., and Lord, J., "Behavior of Structural
Systems under Dynamic Loads," Bui1~ing Practices for Disaster
Mitigations,
Bldg. Science Series 46, U.S. Dept. of Commerce,
National Bureau of Standards, February, 1973, pp. 352-394.
52.
Newmark, N. M., and Hall,
W. J., "Procedures
and Criteria
for
Earthquake
Resistant
Design,"
Building
Science Series 46, Building
Practices
for Disaster
Mitigation.
U.S. Department of Commerce,
National
Bureau of Standards,
pp. 209-236.
187
Proceedings~
APPENDIX 1
THE DECEMBER23.
1972 EARTHQUAKE
Al-l
APPENDIX 1
I~~duction
The Managua Earthquake actually
The major
of 6.2
two
shock,
registered
a surface
and a body wave magnitude
major
aftershocks
The
ively.
major
which
within
quakes
were
earthquakes
(e.g.
tensive
damage because
rupture
occurred,
and
adobe or taquezal
consisted
relatively
with
(1)
(3)
the
in
1906,
epicenters
many buildings
5.6,
and
size,
M=8.3),
by
5.2,
respect-
compared
to
but
other
caused ex-
were shallow,
were
(Ms, NOAA)
was followed
Mb=5.0
moderate
San Francisco,
tremors
wave magnitude
(Mb, NOAA) of
one hour,
of three
(2)
constructed
surface
with
an
type of construction
!!!~~sity
The maximum
ing
the
Modified
Mercalli
commonthroughout
well-designed
pipes
off
frame
The
(reference
shaking
Scale,
structures
(Figures
was X along
considerable
foundations.
broken. II
of
most of the city
"Damage
as follows:
shifted
intensity
center.
in
GroWld
the
out
cracked
AI-2),
lakeshore,
(An intensity
specially
thrown
AI-!,
of
.
with
VII-IX
is
defined
IX
designed
plumb.
employ-
structures;
.
conspicuously.
. Buildings
Underground
(Reference 7~ p. 59.)
intensity
15. p. 18)
decreased
Near
radially
the
epicenter,
A}...2
outward
from
however,
the
city
intensity
center
contours
~
...
.r
NICARAG
...
..,
UA
ISOSEISMAL MA~ Of' THE
DECEMIER, ZS.I.TZ
ItSI
MOOI'IEO
SCALE.ltSI
HONOURAS
UR,THOUAU
ME~CALLI INTINSITY
VI~SION
./
~CAIUAI
n-U
-..'
148.
c'
_°_1--.
,
I
..
.r
D
III-IV
~
~
~
~
~
~
~
.,...
~
~
III-IV
~
,
11-111 /
Coo)
"
~
...
0('\
~
"'"",
0
..
"c-.
~-
~
~
~c-.c
0
COST~ RICA
FOR MI~
IN~lmEs.
lEI
M~~~
1_r:I'~
MAR
tilE
CADASTER AND NATURAL
...
...
...
Figure AI": l Isoseismal
After
RESOURCES
..
Map of Nicaragua
Hansen and Chavez, 1973
Al-3
.
-o'C:c
\
\.
=
\
.
] 1
j:
N
r...
0\
.-.
...
=
\
>
~
N
\
Cj.f
0
> \
-
W) .
~~
Q),
-
cdr...
~O\
.ca
.;..
.~
E
G~
DD
-D-
...
~U~
~
~
.
.-o.
..
D&.-
\
~
-0-
~..
J
/
.c-
...
Q)
.0
a
Q)
u
Q)
Q
.-
i
-
~
c
... W)
cd ...
Q) Q)
.c
cd...
~ 0
co
cd~
~ ~
cd cd
.x
~
.~
~O
cd ...
a=
.-.a
cd 0
a ...
W)Cj.f
.POI
Q) W)
W) Q)
0 U
II) cd
...
:.
~
N
D>
-8
-
"K
=
~
Al-4
I"'"
~.-.
<
~
G cd
...Cj.f
~
COG
~cd
.
~
r~
r-t
~
~
, ~
Q)
:a
!
Jot
Q)
~
'tot
<
parallel
the
the
active
This
faults.
rather
faults,
than
to
whereas
suggests
the
release
southwest
southwest
of
of
the
energy
near
4,
p. 70J.
(reference
city
the
they
city
cross
center,
Shaking
"Duration
of
the
earthquake
in
vertical
shakes,
vertical
'drop.'"
recorded
7 kIn west
followed
of the
city
destructive
shaking
center,
phase
was about
was described
by horizontal
p. 18.)
15,
(Reference
its
The
,reference 3, P 143).
7 seconds"
series
of
Peak
motion,
ground
was 0.39
as "a
then
a
acceleration.
g (reference
15, p.
18)
Damage
Damage occurred
buildings
of
high
was expressed
western
si tuated
density,
two broad
.
by
lanes
of heavily
a stretch
wherein
damaged
heavy
damage
random
pattern."
(Reference 2, p. 267.)
was bordered
by the
1931
trace;
between the. Tiscapa Fault
H~center
fault
the
eastern
and the "secondary
trace
The
was
400 m to the
2, p. 267).
(reference
Location
The
original
hypocenter
was by NOAA. The location,
erroneous
for
two reasons:
America,
and (2)
for
area.
this
recorded
center
.
separated
(Chico Pelon Fault)
east"
.
a loose,
in
lane
as I'
at
of
the
27 km northeast
(1)
standard
The "correct"
a nearby
the
calculation,
city,
refinery,
at
a depth
a poor
based
of
seismic
P-wave trend-time
determination,
placed
the
no greater
Al-S
on P-wave
the
city
net
exists
tables
arrivals
center,
for
was
Central
are incorrect
based on an accelerogram
hypocenter
than
8 km.
beneath
This
the
placement
has
led
to
relocating
velocity
a better
location
previous
earthquake
data,
data
to
substantiate
the
accelerogram
(reference
is
8-10
zones
are
in
Figures
consistent
with
fault
traces
zone,
striking
width,
two
trend
of
the
Pelon
the
faults
are
at
from
and the
the
Customs
most
le£t-lateral
movement,
reference
Nature
and Amount
Movement
though
local
occur.
The
of
Fault
faults
they
and
the
The
activity
major
4, pp.
14, pp.
115,
82°
surface
major
E,
seismic
with
the
meters
roughly
zone
passes
1500 m of
data
observed
66,
the
are
a 1 km
Tiscapa
observations
Aftershock
portion
mapped
traces,
display
within
distances,
W to
hundred
The
is
on the
of
the
that
apart,
equal
they
amounts
through
nearly
also
Laguna
all
of
suggest
The
ground.
seismic
71; reference
energy
11, p.
97;
127).
Movement
sinistral,
(right-lateral)
are
although
the
by the
a few
tremors.
was predominantly
dextral
supported
the
18,p.
74°
2 fault
for
reference
95;
that
same as that
(reference
by
Aftershock
7.SJ
of
probable
the
15 km long
America
erroneous
location,
to
of Managua.
was about
70,
teleseismic
from
only
House,
66,
parallel
into
and
1972
damaged part
responsible
is
surface
the
the severely
zone
It
is
on the
zones
at
movement
an intersection,
displacement
fault
recorded
This
Faults.
Central
Al.S.
E and dipping
near
pp.
show three
to
in
based
hypocentral
Al-3
city.
N 30-40~
Zone
4,
and
plane
within
towards
Tiscapa
km,
motions,
fault
bifurcates
and Chico
the
first
Benioff
hypocenters,
south
indicated
P-wave
the
the
depth
shown
of
manifested
or
and normal,
in
Al-6
unconsolidated
left-lateral,
or
vertical
sediments
a1slip,
and
did
86-.S'
~.P.a:
Lake
Managua
Lake
12815'
'l
"
0,
...\~.
.;;;;..
'~
1-"
~~
..
Lake
D
'C.
Asososca
Nejapa:'1
\
12810'-
.
.
.
Lake
'.
Lab
.
*
,
,
Tiscapa
.
.
I
.
*
\..V
~12.05'
*
86-20'
FigureAl-3Locations
of 171 aftershocks.
The polygons
represent
the error
in
location
assuming
a possible
error
in reading
arrival
times
at each station
of 0.1 second.
Station
locations
are designated
by stars.
The wide solid
line
in Managua represents
faults
B and C mapped at the surface
(Plate
1, Brown
and others.
1973).
.
After
Ward,
.et. al,
-
1973
Al- 7
.
MAN~GU~E~RTHQU~KE
L~KE M~N~GU~
/
.
+.
+
0
+
Fig.A1-~
Intensity
map for
the main shock and epicenters
cated
by data
from a 5-station
seismic
array.
At least
the aftershock
activity
are suggested,
as indicated
by
After
Matumoto and Latham, 1973
Al-8
5 KM
of 300 aftershocks
two linear
trends
the dashed
lines.
loin
.
~
z
-.
M
~
0=
...
-
I
..
".
~
N=
,,~
W
0\
0
c
=
~
"S!
~
z
~
~
,..
\.
J .«
...I
t
".&;1
~ ~ ~
~~.
11
2. c of
c
)1
,"
I.i
~
-
.c: .
e
c
--I
-
yo,
~..
.
\."",0
CD
-
G) G)
c.c
~
~
~l:...
.- . =
CU
~c
..~
!
=.c
0"-'
.c
+oJ""~
-
~"
-.
G)O\
~'-'
=
oo~
~ ""
= G)
~.c
~+oJ
0
-,
.~ , '-
G)
~-G).
.c~
+oJ=
-~
~C
ci
..
C
...
~
on
z
u~
~~:.::
?,
-a
44
~O
?~
~
a
G)
..
Q.
~
U~
~,
~"..
. ,-'"
...
=
u
~
Q
-
->.
G»
~~
~ G)
,
~
.Q'"
-=
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Q
~
...
! __1
"" G)
G) =
.oo.-t
~~
N~
..
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~
; ~
=
~
;1
I!!-Ii:
~
~
2
~
~
4
~
0
c
..
'0..
..:.
c..
~c;
~z
.,
~
;Q
!~
a
CD
..,==r\
~o.-tr-
°
~~O ""
U =
0
.ce.c
~
~o~-+>
CU Q)
"" ""
G)~~
..,
Z
...
"
~
r-.
~
G)r-t
~
~
~ ..,
>.
<Q).cG)
L/lUbO:a
ICUo.-t!
.-
~; J4"'"
<..,,-,J4
co-.
u
-~
"""""""'"
=
,,<
bO=O\
0" CU"'"
~~'-'
Al-9
t)

ASTUDY OF SEISMIC RISK FOR NICARAGUA,PART 1 by Haresh C

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