Seismic Hazards and
Response Spectrum
Fundamentals
Derrell Manceaux
S
Senior
S
Structural Engineer
FHWA Resource Center
Learning
g Outcomes
Topic Applicability
Force Displ. Retro
9
9
9
Identify Upper & Lower Level EQ hazards
Explain how seismic hazard maps are used
Determine Seismic Design Category (Zone)
Define a response spectrum and factors that
effect the spectrum shape
ƒ Describe how a “three point” response spectrum
is constructed
ƒ
ƒ
ƒ
ƒ
Upper
pp & Lower Seismic Hazards
Topic Applicability
Force Displ. Retro
9
9
9
ƒ Lower Seismic Hazard
Hazard-100
100 year recurrence
‰ Retrofit
ƒ Upper Seismic Hazard-1000 year recurrence
‰ Retrofit
‰ Guide Specification
‰ LRFD 2008 Interims
ƒ Upper Seismic HazardHazard 500 year recurrence
‰ Old AASHTO
Upper
pp & Lower Seismic Hazards
Recurrence Time
Period
((years))
(years)
100
75
500
50
500
75
1000
75
Probability of Exceedence
Probability of
Exceedence
75%
10%
15%
7%
≈
Time
Return Period
Topic Applicability
Force Displ. Retro
9
9
9
Upper
pp & Lower Seismic Hazards
AASHTO
Ground Acceleratiion (g)
Retrofit
USGS
100
500
1000 1500
Return Period
2000 2500
Topic Applicability
Force Displ. Retro
9
9
9
Seismic Hazard Maps
p
Topic Applicability
Force Displ. Retro
9
9
9
ƒ Seismic Hazard Maps display earthquake
ground accelerations for various
probability levels
‰
‰
‰
100 year return period (Retrofit)
1000 year return period (LRFD & GS)
Used to Determine:
¾
¾
Acc of structure (3 Points) on Rock
Seismic Design Category (Zones)
Seismic Hazard Maps
(PGA 1 sec & 0
(PGA,1
0.2
2 sec
sec-1000
1000 year)
Topic Applicability
Force Displ. Retro
9
9
Seismic Hazard Maps
p
Topic Applicability
Force Displ. Retro
9
9
9
2500 year recurrence
500 year recurrence
Seismic Hazard Maps
p
S2/50
Ln(S2/50)
Si
Ln(Si)
S10/50
Ln(S10/50)
475 P
2475
R t
Return
P
Period
i d
Topic Applicability
Force Displ. Retro
9
9
9
Ln(475) Ln(P) Ln(2475)
N t lL
Natural
Log(Return
(R t
P
Period)
i d)
Linear Interpolation (ASCE 41-06)
Ln( S 20 / 50) − Ln
L
L ( S 10 / 50)
Ln( Si ) =
× ( Ln( P ) − Ln( 475))
Ln( 2475) − Ln( 475)
Seismic Hazard Maps
p
Topic Applicability
Force Displ. Retro
9
9
9
Seismic Hazard Maps
(PGA 500 year)
(PGA-500
PGA Map
Topic Applicability
Force Displ. Retro
9
9
Acc Coefficient
Seismic
Zone
(PGA)
A ≤ 0.09
1
0.09 < A ≤ 0.19
2
0.19 < A ≤ 0.29
3
0 29 < A
0.29
4
K=∞
rock
Seismic Hazard Maps
PGA 0
PGA,
0.2
2 sec & 1
1.0
0 sec (1000 year)
Topic Applicability
Force Displ. Retro
9
9
9
T=1-second
T=0.2 second
PGA
rock
rock
rock
Seismic Hazard Maps
PGA 1 sec & 0
PGA,1
0.2
2 sec (1000 year)
Topic Applicability
Force Displ. Retro
9
9
9
Struct a
acc
Structure Acceleration on Rock
PGA
rock
0.2 second
1-second
rock
rock
Seismic Hazard Maps
PGA 0
PGA,
0.2
2 sec & 1
1.0
0 sec (1000 year)
Topic Applicability
Force Displ. Retro
9
9
9
0 2 second
0.2
d
PGA
1-second
Structure Acc
on Rock
Seismic Hazard Maps
p
Topic Applicability
Force Displ. Retro
9
9
9
Structure Acc on Rock
Rock
Seismic Hazard Maps
p
Topic Applicability
Force Displ. Retro
9
9
9
Seismic Hazard
Structure
S
uc u e acc o
on So
Soil
Rock
Seismic Hazard Maps
p
SD1 =S1xFv
Topic Applicability
Force Displ. Retro
9
9
9
POF
Seismic Hazard Maps
p
Topic Applicability
Force Displ. Retro
9
9
9
ƒ How are Seismic Hazard Maps used?
‰
‰
To get 3 points to build the “rock” response
spectrum (“Struct
( Struct. acc on rock
rock”))
To determine Seismic Design Category
(Zone),SD1, using acc,S1, modified with Site (soil)
factor, Fv
Seismic Design
g Category
g y (Zone)
(
)
Topic Applicability
Force Displ. Retro
9
9
9
ƒ Calculate associated soil factors
‰
L
Long
P
Period,
i d Fv
Site
Class
Mapped Spectral Acc at 1.0 s
S1 ≤ 0.1
S1 = 0.2
S1 = 0.3
S1 = 0.4
S1 ≥ 0.5
B
1.0
1.0
1.0
1.0
1.0
C
17
1.7
16
1.6
15
1.5
14
1.4
13
1.3
D
2.4
2.0
1.8
1.6
1.5
E
3.5
3.2
2.8
2.4
2.4
Seismic Design
g Category
g y (zone)
(
)
ƒ New Seismic Zones (SDC)
ƒ
500 year
2007 4th Edition LRFD
Topic Applicability
Force Displ. Retro
9
9
1000 year
2008 Interims & Guide Specs
Acceleration
A
l ti
Coefficient
S i i Z
Seismic
Zone
Acceleration
A
l ti
Coefficient
Seismic
S
i i Z
Zone
(SDC)
A ≤ 0.09
1
SD1 ≤ 0.15
1
0.09 < A ≤ 0.19
2
0.15 < SD1 ≤ 0.30 2
0.19 < A ≤ 0.29
3
0.30 < SD1 ≤ 0.50 3
0.29 < A
4
0.50 < SD1
A=PGA
4
SD1 =Structure acceleration=S1xFv
Seismic Design
g Category
g y (Zone)
(
)
1 Second Rock Acceleration Coefficient (S1)
2008 Interims & Guide Specs (1000 year)
Soil Site B
Soil Site C
Topic Applicability
Force Displ. Retro
9
9
PGA
2007 4th Edition
(500 year)
Soil Site D Soil Site E Seismic
Acceleration
Z
Zone
Coefficient
1
APGA < 0.09
0.09 < 0.20 0.07 < .15 0.04 < .09
2
0.09<APGA ≤ 0.19
0.30 < 0.50
0.20 < 0.35 0.15 < .27 0.09 < .15
3
0.19<APGA ≤ 0.29
0.50 < S1
0.35 < S1
4
0.30 < APGA
S1 < 0.15
S1 < 0.09
0.15 < 0.30
S1 < 0.07
0.27 < S1
S1 < 0.04
0.15 < S1
Topic Applicability
Force Displ. Retro
9
9
Seismic Design
g Category
g y
Seismic Zones vs Acceleration,S1
1.2
1
0.8
S1 (g)
Zone 4
Zone 3
Zone 2
Zone 1
0.6
04
0.4
0.2
0
B
C
Soil Type
D
E
Seismic Design
g Category
g y
ƒ SDC-Zones
Zone 1-SDC “A”
Zone 2-SDC “B”
Zone 3-SDC “C”
Z
Zone
4-SDC
4 SDC “D”
ƒ Soil ((Site)) Class
‰
‰
‰
‰
“B” (Rock)
“C” (N> 50 blows/ft)
“D” (15<N<50 blows/ft)
“E” (N<15 blows/ft)
Topic Applicability
Force Displ. Retro
9
9
Seismic Design
g Category
g y
Topic Applicability
Force Displ. Retro
9
9
Seismic Design Category (zone)
(500 year Return Period)
Zone 1-SDC “A”
Zone 2-SDC “B”
Zone 3-SDC “C”
Zone 4-SDC “D”
Topic Applicability
Force Displ. Retro
9
9
Seismic Design Category (zone)
(1000 Year Return Period)
Zone 1-SDC “A”
Zone 2-SDC “B”
B
Zone 3-SDC “C”
Zone 4-SDC “D”
SITE CLASS “B”
Topic Applicability
Force Displ. Retro
9
9
Seismic Design Category (zone)
(1000 Year Return Period)
Zone 1-SDC “A”
Zone 2-SDC “B”
B
Zone 3-SDC “C”
Zone 4-SDC “D”
SITE CLASS “C”
Topic Applicability
Force Displ. Retro
9
9
Seismic Design Category (zone)
(1000 Year Return Period)
Zone 1-SDC “A”
Zone 2-SDC “B”
Zone 3-SDC “C”
Zone 4-SDC “D”
SITE CLASS “D”
Topic Applicability
Force Displ. Retro
9
9
Seismic Design Category (zone)
(1000 Year Return Period)
Zone 1
1-SDC
SDC “A”
A
Zone 2-SDC “B”
Zone 3-SDC “C”
Zone 4-SDC “D”
SITE CLASS “E”
Topic Applicability
Force Displ. Retro
9
9
Seismic Design Category (zone)
(1000 Year Return Period)
Topic Applicability
Force Displ. Retro
9
9
ƒ How to Calculate Seismic Design Category
(zone)?
‰
‰
Multiply Rock Spectrum (S1) x Site Class (Fv)
Amplification Factor @ 1.0 sec
SD1 =Structure acceleration=S1xFv
ƒ SDC is variable at any single location
‰
N single
No
i l seismic
i i map can d
determine
t
i SDC
Response Spectrum
Topic Applicability
Force Displ. Retro
9
9
9
ƒ What is the Response Spectrum?
‰
The response spectrum
Th
t
provides
id th
the
maximum acceleration a single degree
off freedom
f d
structure
t t
will
ill experience
i
when it is subjected to a ground motion.
Response
p
Spectrum
p
El Centro (1942)
ƒ How is it created?
Topic Applicability
Force Displ. Retro
9
9
9
Response
p
Spectrum
p
Topic Applicability
Force Displ. Retro
9
9
9
ƒ Actual Spectra vs. Smoothed Spectra
Range one structure may experience
for a variety of ground motions
motions.
Amplification zone
Response
p
Spectrum
p
“Dynamics of Structures”
by Anil K Chopra
Topic Applicability
Force Displ. Retro
9
9
9
Topic Applicability
Force Displ. Retro
9
9
9
Response Spectrum
ƒ 2007 Design Response Spectrum
Three Point Response Spectrum
ƒ Determine Rock Accelerations
‰
‰
‰
Ss = Rock Acceleration @ 0.2 s
S1 = Rock Acceleration @ 1.0 s
SPGA =Rock Acceleration @ 0.0 s
Topic Applicability
Force Displ. Retro
9
9
9
Three Point Response
p
Spectrum
p
Topic Applicability
Force Displ. Retro
9
9
9
ƒ Determine Soil (Site) Coefficients
‰
‰
Site
Class
Fa = Site Coefficient @ 0.2
02s
FPGA = Site Coefficient @ 0.0 s
Mapped PGA and Spectral Acc at 0.2 s (Fa, FPGA)
PGA ≤ 0.1 PGA = 0.2
Ss ≤ 0
0.25
25 Ss = 0
0.50
50
PGA = 0.3
Ss = 0.75
0 75
PGA = 0.4
Ss = 1.00
1 00
PGA ≥ 0.5
Ss ≥ 1
1.25
25
B
1.0
1.0
1.0
1.0
1.0
C
1.2
1.2
1.1
1.0
1.0
D
1.6
1.4
1.2
1.1
1.0
E
2.5
1.7
1.2
0.9
0.9
Three Point Response
p
Spectrum
p
Topic Applicability
Force Displ. Retro
9
9
9
ƒ Determine Soil (Site) Coefficients
‰
Site
Class
Fv = Site Coefficient @ 1
1.0
0s
Mapped Spectral Acc at 1.0 s
S1 ≤ 0.1
S1 = 0.2
S1 = 0.3
S1 = 0.4
S1 ≥ 0.5
B
1.0
1.0
1.0
1.0
1.0
C
1.7
1.6
1.5
1.4
1.3
D
2.4
2.0
1.8
1.6
1.5
E
3.5
3.2
2.8
2.4
2.4
FPPGA PGA
Three Point Response Spectrum
Topic Applicability
Force Displ. Retro
9
9
9
Three Point Response Spectrum
South West Indiana
Topic Applicability
Force Displ. Retro
9
9
9
ƒ Ss = Acceleration @ 0.2 s= 0.5 g
s 0.13 g
ƒ S1 = Acceleration @ 1.0 s=
X
0.2 second spectral
p
response
p
(5% damp)
X
p
response
p
((5% damp)
p)
1 second spectral
Three Point Response Spectrum
Ss=0.5g
0.5g
Site
Fa = 1.7
S1=0.13g
0.13g
Spectral Acc at SS
(0 2 sec))
(0.2
SS <
SS =
SS =
SS =
SS >
.25g
g
.50g
g
.75g
g
1.0g
g
1.3g
g
A
0.8
0.8
0.8
0.8
0.8
B
1.0
1.0
1.0
1.0
C
12
1.2
12
1.2
11
1.1
D
1.6
1.4
E
2.5
1.7
Site
Topic Applicability
Force Displ. Retro
9
9
9
Fv = 3.3
Spectral S1
(1 0 sec))
(1.0
S1 <
S1 =
S1 =
S1 =
S1 >
.1g
1g
.2g
2g
.3g
3g
.4g
4g
.5g
5g
A
0.8
0.8
0.8
0.8
0.8
1.0
B
1.0
1.0
1.0
1.0
1.0
10
1.0
10
1.0
C
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
D
2.4
2.0
1.8
1.6
1.5
1.2
0.9
0.9
E
3.5
3.2
2.8
2.4
2.4
SD1=0.13*3.3 =0.43>0.3 Zone “3”
Topic Applicability
Force Displ. Retro
9
9
9
Three Point Response Spectrum
South Indiana (1000 vs 500 year return period)
1000 EQ vs 500 EQ
0.8
Spec Accc (Fraction of g)
Acc1000 year / Φ (.9)
S il “C”
Soil
Acc500 year / Φ (.9)
( 9)
0.6
0.4
0.2
0
Acc500 year / Φ (.75)
Acc1000 year / Φ (.9)
0
1
2
3
P i d (Sec)
Period
(S )
Soil type“E” – Zone “3”
4
5
Three Point Response Spectrum
Topic Applicability
Force Displ. Retro
9
9
9
West Tennessee (1000 vs 500 year return period)
1000 EQ vs 500 EQ
1000 EQ vs 500 EQ
2
2
Acc1000 year / Φ (.9)
1.5
Acc500 year / Φ (.5)
1
Speec Acc (Fraction of g)
Speec Acc (Fraction of g)
1.5
1
0.5
0.5
Acc500 year / Φ (.9)
0
0
0
0.5
1
1.5
Period (Sec)
Soil=“B”
2
2.5
3
0
0.5
1
1.5
Period (Sec)
Soil=“E”
2
2.5
3
Three Point Response Spectrum
East Idaho (1000 vs 500 year return period)
1000 EQ vs 500 EQ
Topic Applicability
Force Displ. Retro
9
9
9
1000 EQ vs 500 EQ
2
2
Acc500 year / Φ (.5)
1.5
Spec Acc (Fraction of g)
Spec Acc (Fraction of g)
1.5
1
Acc1000 year / Φ (.9)
1
0.5
0.5
0
0
0
0.5
1
1.5
Period (Sec)
Soil=“B”
2
2.5
3
Acc500 year / Φ (.9)
( 9)
0
0.5
1
1.5
Period (Sec)
Soil=“E”
2
2.5
3
Three Point Response Spectrum
North New Jersey (1000 vs 500 year return period)
1000 EQ vs 500 EQ
Topic Applicability
Force Displ. Retro
9
9
9
1000 EQ vs 500 EQ
Acc500 year / Φ (.75)
0.5
Acc500 year / Φ (.9)
0.4
Spec Acc (Fraction of g))
Sppec Acc (Fraction of gg)
0.5
0.3
02
0.2
Acc1000 year / Φ (.9)
0.1
0
04
0.4
0.3
02
0.2
0.1
0
0.5
1
1.5
Period (Sec)
Soil=“B”
2
2.5
3
0
0
0.5
1
1.5
Period (Sec)
Soil=“E”
2
2.5
3
Three Point Response Spectrum
ƒ Determine Rock Accelerations
‰
‰
‰
Ss = Rock Acceleration @ 0.2 s
S1 = Rock Acceleration @ 1.0 s
SPGA =Rock Acceleration @ 0.0 s
FPGAA PGA
ƒ Determine Soil (Site) Coefficients
ƒ Calculate Ratios SD1/SDS
ƒ Plot Response Spectrum
Topic Applicability
Force Displ. Retro
9
9
9
Conclusion
ƒ New recurrence period from 500 to 1000
year does not:
‰
‰
double the demand
necessarily increase population of seismic
bridges
ƒ Seismic Design Categories (Zones) are:
‰
‰
IImpacted
t d by
b Soil
S il (Site)
(Sit ) Coefficients
C ffi i t
Determined by structural acceleration on soil
Conclusion
ƒ New Response Spectrum is:
‰
Less conservative in long period range
0.8
1/ T
0.6
T
0.4
1/ T 2/3
0.2
0
0
10
20
30
40
50
What questions do you have?