1. Response Spectra for Seismic Analysis and Design Bo Li
Department of Civil and Environmental Engineering 1
2. Wei-Chau Xie Outline 1. Motivation and Objective 2. Modified
Newmark Design Spectrum 3. Response Spectra for Equipment-Structure
Resonance 4. Future Research 2
3. Motivation and Objective Wei-Chau Xie Engineering Background
OliveView Hospital after 1994 Northridge earthquake (PGA of 0.82 g)
3
4. Motivation and Objective Wei-Chau Xie Engineering Background
OliveView Hospital after 1994 Northridge earthquake (PGA of 0.82 g)
4
5. Motivation and Objective Wei-Chau Xie Engineering Background
OliveView Hospital after 1994 Northridge earthquake (PGA of 0.82 g)
5
6. Motivation and Objective Wei-Chau Xie Engineering Background
No structural damage under this earthquake Hospital was inoperable
and 300 patients were evacuated 6
7. Motivation and Objective Wei-Chau Xie Engineering Background
Realize importance of facility-performance in operation of system
Emphasize performance-based seismic design (P-BSD) Find a most
economic balance between safety and economy . = Accurate failure
probability of structures and non-structures . = Reliable and
realistic responses . = Reliable and realistic design response
spectrum 7
8. Motivation and Objective Wei-Chau Xie Various design
response spectra Soil Layer 1 Soil Type 1 Soil Surface Structural
Analysis Soil Layer 2 Soil Type 2 Seismic Site Response Analysis
Soil Layer m Soil Type n Bedrock Seismic Source Seismic Wave
Propagation Design Spectrum at Bedrock Ground Motion at Bedrock
Design Spectrum under Soil Surface Ground Motion under Soil Surface
Design Spectrum at Soil Surface Ground Motion at Soil Surface Floor
Response Spectrum Structural Response Normalized Shear Modulus with
Variability Shear Wave Velocity with Variability
GroundResponseSpectrum 8
9. Motivation and Objective Wei-Chau Xie Various design
response spectra Soil Layer 1 Soil Type 1 Soil Surface Structural
Analysis Soil Layer 2 Soil Type 2 Seismic Site Response Analysis
Soil Layer m Soil Type n Bedrock Seismic Source Seismic Wave
Propagation Design Spectrum at Bedrock Ground Motion at Bedrock
Design Spectrum under Soil Surface Ground Motion under Soil Surface
Design Spectrum at Soil Surface Ground Motion at Soil Surface Floor
Response Spectrum Structural Response Normalized Shear Modulus with
VariabilityVV Shear Wave Velocity with VariabilityVV
GroundResponseSpectrumdesign response spectrum at bedrock 9
10. Motivation and Objective Wei-Chau Xie Various design
response spectra Soil Layer 1 Soil Type 1 Soil Surface Structural
Analysis Soil Layer 2 Soil Type 2 Seismic Site Response Analysis
Soil Layer m Soil Type n Bedrock Seismic Source Seismic Wave
Propagation Design Spectrum at Bedrock Ground Motion at Bedrock
Design Spectrum under Soil Surface Ground Motion under Soil Surface
Design Spectrum at Soil Surface Ground Motion at Soil Surface Floor
Response Spectrum Structural Response Normalized Shear Modulus with
VariabilityVV Shear Wave Velocity with VariabilityVV
GroundResponseSpectrumdesign response spectrum under soil surface
10
11. Motivation and Objective Wei-Chau Xie Various design
response spectra Soil Layer 1 Soil Type 1 Soil Surface Structural
Analysis Soil Layer 2 Soil Type 2 Seismic Site Response Analysis
Soil Layer m Soil Type n Bedrock Seismic Source Seismic Wave
Propagation Design Spectrum at Bedrock Ground Motion at Bedrock
Design Spectrum under Soil Surface Ground Motion under Soil Surface
Design Spectrum at Soil Surface Ground Motion at Soil Surface Floor
Response Spectrum Structural Response Normalized Shear Modulus with
VariabilityVV Shear Wave Velocity with VariabilityVV
GroundResponseSpectrumdesign response spectrum at soil surface
11
12. Motivation and Objective Wei-Chau Xie Various design
response spectra Soil Layer 1 Soil Type 1 Soil Surface Structural
Analysis Soil Layer 2 Soil Type 2 Seismic Site Response Analysis
Soil Layer m Soil Type n Bedrock Seismic Source Seismic Wave
Propagation Design Spectrum at Bedrock Ground Motion at Bedrock
Design Spectrum under Soil Surface Ground Motion under Soil Surface
Design Spectrum at Soil Surface Ground Motion at Soil Surface
Structural Response Floor Response Spectrum Normalized Shear
Modulus with VariabilityVV Shear Wave Velocity with VariabilityVV
GroundResponseSpectrumfloor response spectrum 12
13. Motivation and Objective Wei-Chau Xie Problems of design
response spectra Ground response spectrum commonly used in nuclear
industry Newmark design spectra exhibit lower amplitude at high
frequencies higher amplitude at low frequencies Uniform Hazard
Spectra (UHS) for soil sites are not realistic and reliable 13
14. Motivation and Objective Wei-Chau Xie Problems of design
response spectra Ground response spectrum commonly used in nuclear
industry Newmark design spectra exhibit lower amplitude at high
frequencies higher amplitude at low frequencies Uniform Hazard
Spectra (UHS) for soil sites are not realistic and reliable Floor
response spectrum Accurate and efficient method to generate
probabilistic floor response spectrum has not been developed
13
15. Motivation and Objective Wei-Chau Xie Problems of design
response spectra Ground response spectrum commonly used in nuclear
industry Newmark design spectra exhibit lower amplitude at high
frequencies higher amplitude at low frequencies Uniform Hazard
Spectra (UHS) for soil sites are not realistic and reliable Floor
response spectrum Accurate and efficient method to generate
probabilistic floor response spectrum has not been developedGap
between P-BSD for nuclear facilities and realistic design spectra
13
16. Motivation and Objective Wei-Chau Xie Objectives Bridge gap
between P-BSD for nuclear facilities and realistic design spectra
14
17. Motivation and Objective Wei-Chau Xie Objectives Bridge gap
between P-BSD for nuclear facilities and realistic design spectra
Construct site design spectrum coefficients = more realistic
Newmark design spectrum Propose a framework to integrate two
uncertainty sources = more realistic and reliable soil UHS
Establish statistical relationship between two types of response
spectra = probabilistic FRS by direct spectra-to-spectra method
14
18. Motivation and Objective Wei-Chau Xie Objectives Bridge gap
between P-BSD for nuclear facilities and realistic design spectra
Construct site design spectrum coefficients = more realistic
Newmark design spectrum Propose a framework to integrate two
uncertainty sources = more realistic and reliable soil UHS
Establish statistical relationship between two types of response
spectra = probabilistic FRS by direct spectra-to-spectra method
15
19. Motivation and Objective Wei-Chau Xie Objectives Bridge gap
between P-BSD for nuclear facilities and realistic design spectra
Construct site design spectrum coefficients = more realistic
Newmark design spectrum Propose a framework to integrate two
uncertainty sources = more realistic and reliable soil UHS
Establish statistical relationship between two types of response
spectra = probabilistic FRS by direct spectra-to-spectra method
16
20. Motivation and Objective Wei-Chau Xie Objectives Bridge gap
between P-BSD for nuclear facilities and realistic design spectra
Construct site design spectrum coefficients = more realistic
Newmark design spectrum Propose a framework to integrate two
uncertainty sources = more realistic and reliable soil UHS
Establish statistical relationship between two types of response
spectra = probabilistic FRS by direct spectra-to-spectra method
17
21. Motivation and Objective Wei-Chau Xie Objectives Bridge gap
between P-BSD for nuclear facilities and realistic design spectra
Construct site design spectrum coefficients = more realistic
Newmark design spectrum Propose a framework to integrate two
uncertainty sources = more realistic and reliable soil UHS
Establish statistical relationship between two types of response
spectra = probabilistic FRS by direct spectra-to-spectra method
18
22. Modied Newmark Design Spectrum Wei-Chau Xie Response
spectrum in tripartite 0.01 Period (sec) 0.1 1 10 100
Pseudo-Velocity(in/sec) 10 1 10 100 0.01 0.1 D isplacem ent (in) D
isplacem ent (in) PGA PGD PGV 0.1= 0.05= 0.1 1 10 100
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
(gg))gggg 1 0.1 0.01 0.1 0.01 D isplacem ent (in) D isplacem ent
(in) D isplacem ent (in) D isplacem ent (in) D isplacem ent (in)
PGA PGA 0.050.050.05= Spectral ordinates depend on in long periods
peak ground displacement in short periods peak ground acceleration
in intermediate periods peak ground velocity
23. 19
24. Modied Newmark Design Spectrum Wei-Chau Xie Response
spectrum in tripartite 0.01 Period (sec) 0.1 1 10 100
Pseudo-Velocity(in/sec) 1 10 0.1 10 100 0.01 0.1 0.01 D isplacem
ent (in) D isplacem ent (in) D isplacem ent (in) D isplacem ent
(in) D isplacem ent (in) D isplacem ent (in) PGA PGD PGV 0.1= 0.05=
0.1 1 10 100 Pseudo-Acceleration Pseudo-Acceleration (gg))gggg 1
0.01 0.1 PGVPGVPGV 0.10.1= Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Spectral ordinates depend on in long periods peak ground
displacement in short periods peak ground acceleration in
intermediate periods peak ground velocity
25. 20
26. Modied Newmark Design Spectrum Wei-Chau Xie Response
spectrum in tripartite 0.01 Period (sec) 0.1 1 10 100
Pseudo-Velocity(in/sec) 1 10 0.1 1 0.01 0.1 0.01 D isplacem ent
(in) D isplacem ent (in) D isplacem ent (in) D isplacem ent (in) D
isplacem ent (in) D isplacem ent (in) PGA PGD PGV 0.1= 0.05= 0.1 1
10 100 Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration gg))gPGD PGD 10 100
Pseudo-Acceleration Pseudo-Acceleration (gg))gggg Spectral
ordinates depend on in long periods peak ground displacement in
short periods peak ground acceleration in intermediate periods peak
ground velocity
27. 21
28. Modied Newmark Design Spectrum Wei-Chau Xie Newmark design
spectrum Construct Newmark designs spectrum requiring ground motion
parameters (v/a and ad/v2) a = peak ground acceleration (PGA) v =
peak ground velocity (PGV) d = peak ground displacement (PGD)
22
29. Modied Newmark Design Spectrum Wei-Chau Xie Newmark design
spectrum Construct Newmark designs spectrum requiring ground motion
parameters (v/a and ad/v2) a = peak ground acceleration (PGA) v =
peak ground velocity (PGV) d = peak ground displacement (PGD)
spectrum amplification factors (A, V and D) A = spectrum
amplification factor of PGA V = spectrum amplification factor of
PGV D = spectrum amplification factor of PGD 22
30. Modied Newmark Design Spectrum Wei-Chau Xie Newmark design
spectrum Newmark design spectrum was developed Using only 28 ground
motions recorded at Western U.S. Not consider earthquake magnitudes
in ground motion parameters Not consider earthquake magnitudes and
site conditions in spectrum amplification factors Newmark design
spectra exhibit lower amplitude at high frequencies higher
amplitude at low frequencies 23
31. Modied Newmark Design Spectrum Wei-Chau Xie Newmark design
spectrum Newmark design spectrum was developed Using only 28 ground
motions recorded at Western U.S. Not consider earthquake magnitudes
in ground motion parameters Not consider earthquake magnitudes and
site conditions in spectrum amplification factors Newmark design
spectra exhibit lower amplitude at high frequencies higher
amplitude at low frequencies 24
32. Modied Newmark Design Spectrum Wei-Chau Xie Newmark design
spectrum Newmark design spectrum was developed Using only 28 ground
motions recorded at Western U.S. Not consider earthquake magnitudes
in ground motion parameters Not consider earthquake magnitudes and
site conditions in spectrum amplification factors Newmark design
spectra exhibit lower amplitude at high frequencies higher
amplitude at low frequencies 25
33. Modied Newmark Design Spectrum Wei-Chau Xie Newmark design
spectrum Newmark design spectrum was developed Using only 28 ground
motions recorded at Western U.S. Not consider earthquake magnitudes
in ground motion parameters Not consider earthquake magnitudes and
site conditions in spectrum amplification factors Newmark design
spectra exhibit lower amplitude at high frequencies higher
amplitude at low frequencies 26
34. Modied Newmark Design Spectrum Wei-Chau Xie Newmark design
spectrum Newmark design spectrum was developed Using only 28 ground
motions recorded at Western U.S. Not consider earthquake magnitudes
in ground motion parameters Not consider earthquake magnitudes and
site conditions in spectrum amplification factors Newmark design
spectra exhibit lower amplitude at high frequencies higher
amplitude at low frequencies 27
35. Modied Newmark Design Spectrum Wei-Chau Xie Site design
spectrum coefcients Site design spectrum coefficients constructed
in this study Site Condition Earthquake Magnitude Coefficients cA
cV cD B Sites Small M 1.15 0.40 0.15 Large M 1.15 1.00 1.15 C Sites
Small M 1.15 0.40 0.15 Large M 1.15 0.85 0.60 D Sites Small M 1.10
0.55 0.15 Large M 1.10 1.00 0.65 28
41. Newmark spectrum is lower higher high frequencies lower
frequencies than benchmark spectrum in 33
42. Modied Newmark Design Spectrum Wei-Chau Xie Example Newmark
design spectrum Design spectrum for rock sites dominated by small
earthquakes 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.01 0.01 0.01 0.01 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
0.001 0.001 0.001 0.001 0.001 0.001 11
10101010101010101010101010101010101010101010 100 100 100 100 100
100 100 100 100 100 100 0.1 1 10 1000.01 Period (sec)
Pseudo-Velocity(m/sec) 10 1 0.1 0.01 0.001 Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration Pseudo-Acceleration Pseudo-Acceleration
Pseudo-Acceleration ((((((ggg))ggg D isplacem ent(m ) D isplacem
ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D
isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem
ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D
isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem
ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D
isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem
ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D
isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem
ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D
isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem
ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D
isplacem ent(m ) D isplacem ent(m ) D isplacem ent(m ) D isplacem
ent(m ) D isplacem ent(m ) D isplacem ent(m ) 111111111111
101010101010101010101010 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.001 0.001 0.001 0.001 0.001
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
0.001 0.001 0.001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
Newmark design spectrum Modified Newmark design spectrum
BenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmarkBenchmark
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Modified Newmark spectrum by this study well match benchmark
spectrum 34
43. Modied Newmark Design Spectrum Wei-Chau Xie Research
contributions Analyze factors affecting ground motion parameters
Establish site design spectrum coefficients to modify Newmark
design spectrum Obtain more realistic modified Newmark design
spectrum Reflecting seismic features of target sites Considering
Site conditions Earthquake magnitudes 35
44. Modied Newmark Design Spectrum Wei-Chau Xie Research
contributions Analyze factors affecting ground motion parameters
Establish site design spectrum coefficients to modify Newmark
design spectrum Obtain more realistic modified Newmark design
spectrum Reflecting seismic features of target sites Considering
Site conditions Earthquake magnitudes 36
45. Modied Newmark Design Spectrum Wei-Chau Xie Research
contributions Analyze factors affecting ground motion parameters
Establish site design spectrum coefficients to modify Newmark
design spectrum Obtain more realistic modified Newmark design
spectrum Reflecting seismic features of target sites Considering
Site conditions Earthquake magnitudes 37
46. Modied Newmark Design Spectrum Wei-Chau Xie Research
contributions Analyze factors affecting ground motion parameters
Establish site design spectrum coefficients to modify Newmark
design spectrum Obtain more realistic modified Newmark design
spectrum Reflecting seismic features of target sites Considering
Site conditions Earthquake magnitudes 38
47. Modied Newmark Design Spectrum Wei-Chau Xie Research
contributions Analyze factors affecting ground motion parameters
Establish site design spectrum coefficients to modify Newmark
design spectrum Obtain more realistic modified Newmark design
spectrum Reflecting seismic features of target sites Considering
Site conditions Earthquake magnitudes 39
48. Modied Newmark Design Spectrum Wei-Chau Xie Research
contributions Analyze factors affecting ground motion parameters
Establish site design spectrum coefficients to modify Newmark
design spectrum Obtain more realistic modified Newmark design
spectrum Reflecting seismic features of target sites Considering
Site conditions Earthquake magnitudes 40
49. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Objective-Part 2 Bridge gap between P-BSD for nuclear
facilities and realistic design spectra Construct site design
spectrum coefficients = more realistic Newmark design spectrum
Propose a framework to integrate two uncertainty sources = more
realistic and accurate soil UHS Establish statistical relationship
between two types of response spectra = probabilistic FRS by direct
spectra-to-spectra method 41
50. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Floor response spectrum (FRS) FRS reflects characteristics of
supporting structure under specific earthquakes Input earthquakes
contribute most to uncertainty of FRS Two methods to generate FRS
Time history method Direct spectra-to-spectra method 42
51. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum u1 u2 un uN N-DOF system
Response of Floor Floor Response SpectrumSecondary Structure 2 1 n
N ug uF(t) uF(t) un(t) un(t) SDOF Oscillator Time History Method
uF(t) t u1 u2 un uN N-NN DOF system 2 1 n N un(t) SDOF Oscillator
Direct Spectra-to-Spectra Method Ground Response Spectrum Given a
specified GRS 43
52. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum GRS-Compatible Hime History u1
u2 un uN N-DOF system Response of Floor Floor Response
SpectrumSecondary Structure 2 1 n N ug t ug(t) uF(t) uF(t) un(t)
un(t) SDOF Oscillator Time History Method uF(t) t u1 u2 un uN N-NN
DOF system 2 1 n N un(t) SDOF Oscillator Direct Spectra-to-Spectra
Method Ground Response Spectrum Generate time history
spectrum-compatible with the GRS 44
53. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum GRS-Compatible Hime History u1
u2 un uN N-DOF system Response of Floor Floor Response
SpectrumSecondary Structure 2 1 n N ug(t) ug t ug(t) uF(t) uF(t)
un(t) un(t) un(t) SDOF Oscillator Time History Method t uF(t) t u1
u2 un uN N-NN DOF system 2 1 n N un(t) SDOF Oscillator Direct
Spectra-to-Spectra Method Ground Response Spectrum Input time
history to supporting structure and do structure analysis 45
54. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum GRS-Compatible Hime History u1
u2 un uN N-DOF system Response of Floor Floor Response
SpectrumSecondary Structure 2 1 n N ug(t) ug t ug(t) uF(t) uF(t)
un(t) un(t) un(t) SDOF Oscillator Time History Method t uF(t) t u1
u2 un uN N-NN DOF system 2 1 n N un(t) SDOF Oscillator Direct
Spectra-to-Spectra Method Ground Response Spectrum Generate floor
response spectrum from response of floor 46
55. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum GRS-Compatible Hime History u1
u2 un uN N-NN DOF system Response of Floor Floor Response Spectrum
2 1 n N ug(t) t ug(t) uF(t) uF(t) un(t) un(t) SDOF Oscillator Time
History Method t uF(t) t u1 u2 un uN N-DOF system 2 1 n N SDOF
Oscillator Analytical Approaches Direct Spectra-to-Spectra Method
Ground Response Spectrum Given a specified GRS 47
56. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum GRS-Compatible Hime History u1
u2 un uN N-NN DOF system Response of Floor Floor Response
SpectrumSecondary Structure 2 1 n N ug(t) ug t ug(t) uF(t) uF(t)
un(t) un(t) un(t) SDOF Oscillator Time History Method t uF(t) t u1
u2 un uN N-DOF system 2 1 n N un(t) SDOF Oscillator Analytical
Approaches Direct Spectra-to-Spectra Method Ground Response
Spectrum Generate floor response spectrum from the GRS directly
48
57. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum Features of two methods to
generate FRS Time history: low efficiency,yielding FRS with large
variability Direct spectra-to-spectra: high efficiency, cannot
consider uncertainty from input earthquakes Proposed direct
spectra-to-spectra method possible to consider uncertainty from
input earthquakes (work by others in our group) Need statistical
relationship between t-response spectrum and GRS 49
58. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum Features of two methods to
generate FRS Time history: low efficiency,yielding FRS with large
variability Direct spectra-to-spectra: high efficiency, cannot
consider uncertainty from input earthquakes Proposed direct
spectra-to-spectra method possible to consider uncertainty from
input earthquakes (work by others in our group) Need statistical
relationship between t-response spectrum and GRS 50
59. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum Features of two methods to
generate FRS Time history: low efficiency,yielding FRS with large
variability Direct spectra-to-spectra: high efficiency, cannot
consider uncertainty from input earthquakes Proposed direct
spectra-to-spectra method possible to consider uncertainty from
input earthquakes (work by others in our group) Need statistical
relationship between t-response spectrum and GRS 51
60. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum Features of two methods to
generate FRS Time history: low efficiency,yielding FRS with large
variability Direct spectra-to-spectra: high efficiency, cannot
consider uncertainty from input earthquakes Proposed direct
spectra-to-spectra method possible to consider uncertainty from
input earthquakes (work by others in our group) Need statistical
relationship between t-response spectrum and GRS 52
61. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Generate oor response spectrum Features of two methods to
generate FRS Time history: low efficiency,yielding FRS with large
variability Direct spectra-to-spectra: high efficiency, cannot
consider uncertainty from input earthquakes Proposed direct
spectra-to-spectra method possible to consider uncertainty from
input earthquakes (work by others in our group) Need statistical
relationship between t-response spectrum and GRS 53
62. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Concept of ground response spectrum (GRS) SA(, ) = et sin t
ug(t) max Determined by max responses of SDOF oscillators stood on
ground mounted on an identical SDOF oscillator SDOF Oscillators
Ground Response Spectrum ttt Max Response f3f2f1 f3 f2 f1 f
Earthquake Input ug(t) t f f2fff1ff f3ff Response Time Histories
t-Response Spectrum f3fff2fff1ff tt t Max Response f1ff f2ff f3ff
SDOF Oscillators Perfect-Tuning, Uncoupled SDOF Structures 54
63. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Concept of t-response spectrum (tRS) St A(, ) = 1 2 2tet cos t
ug(t) + et sin t ug(t) max Determined by max responses of SDOF
oscillators mounted on SDOF supporting structures SDOF Oscillators
Ground Response Spectrum ttt t Max Response f3fff2ffff1ff
f3fff2fff1ff f Earthquake Input ug(t) t f f2 f1 f3 Response Time
Histories t-Response Spectrum f3f2f1 tt t Max Response f1 f2 f3
SDOF Oscillators Perfect-Tuning, Uncoupled SDOF Structures 55
64. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate t-response spectrum St A(, ) = 1 2 2tet cos t ug(t) +
et sin t ug(t) max Because t term in equation,analytical solution
cannot be obtained Different approximations have been recommended
St A(, ) 1 2 2 SA(, ) (Yasui et al.,1993) St A(, ) AF SA(, ),AF is
case dependent (EPRI,1995) St A(, ) 4 SA(, ) (Shi, 1997) These
approximations are too conservative 56
65. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate t-response spectrum St A(, ) = 1 2 2tet cos t ug(t) +
et sin t ug(t) max Because t term in equation,analytical solution
cannot be obtained Different approximations have been recommended
St A(, ) 1 2 2 SA(, ) (Yasui et al.,1993) St A(, ) AF SA(, ),AF is
case dependent (EPRI,1995) St A(, ) 4 SA(, ) (Shi, 1997) These
approximations are too conservative 57
66. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate t-response spectrum St A(, ) = 1 2 2tet cos t ug(t) +
et sin t ug(t) max Because t term in equation,analytical solution
cannot be obtained Different approximations have been recommended
St A(, ) 1 2 2 SA(, ) (Yasui et al.,1993) St A(, ) AF SA(, ),AF is
case dependent (EPRI,1995) St A(, ) 4 SA(, ) (Shi, 1997) These
approximations are too conservative 58
67. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate t-response spectrum St A(, ) = 1 2 2tet cos t ug(t) +
et sin t ug(t) max Because t term in equation,analytical solution
cannot be obtained Different approximations have been recommended
St A(, ) 1 2 2 SA(, ) (Yasui et al.,1993) St A(, ) AF SA(, ),AF is
case dependent (EPRI,1995) St A(, ) 4 SA(, ) (Shi, 1997) These
approximations are too conservative 59
68. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate t-response spectrum St A(, ) = 1 2 2tet cos t ug(t) +
et sin t ug(t) max Because t term in equation,analytical solution
cannot be obtained Different approximations have been recommended
St A(, ) 1 2 2 SA(, ) (Yasui et al.,1993) St A(, ) AF SA(, ),AF is
case dependent (EPRI,1995) St A(, ) 4 SA(, ) (Shi, 1997) These
approximations are too conservative 60
69. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate t-response spectrum St A(, ) = 1 2 2tet cos t ug(t) +
et sin t ug(t) max Because t term in equation,analytical solution
cannot be obtained Different approximations have been recommended
St A(, ) 1 2 2 SA(, ) (Yasui et al.,1993) St A(, ) AF SA(, ),AF is
case dependent (EPRI,1995) St A(, ) 4 SA(, ) (Shi, 1997) These
approximations are too conservative 61
70. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Simulation results to estimate tRS Use simulation results to
accurately and statistically estimate tRS Select worldwide ground
motions from PEER strong motion database European strong motion
database 49 ground motions recorded at B sites 154 ground motions
recorded at C sites 220 ground motions recorded at D sites 62
71. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Simulation results to estimate tRS Use simulation results to
accurately and statistically estimate tRS Select worldwide ground
motions from PEER strong motion database European strong motion
database 49 ground motions recorded at B sites 154 ground motions
recorded at C sites 220 ground motions recorded at D sites 63
72. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Simulation results to estimate tRS Use simulation results to
accurately and statistically estimate tRS Select worldwide ground
motions from PEER strong motion database European strong motion
database 49 ground motions recorded at B sites 154 ground motions
recorded at C sites 220 ground motions recorded at D sites 64
73. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Simulation results to estimate tRS Use simulation results to
accurately and statistically estimate tRS Select worldwide ground
motions from PEER strong motion database European strong motion
database 49 ground motions recorded at B sites 154 ground motions
recorded at C sites 220 ground motions recorded at D sites 65
74. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Simulation results to estimate tRS Use simulation results to
accurately and statistically estimate tRS Select worldwide ground
motions from PEER strong motion database European strong motion
database 49 ground motions recorded at B sites 154 ground motions
recorded at C sites 220 ground motions recorded at D sites 66
75. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Trend of median amplication ratios Trend of median
amplification ratios for horizontal component 0.1 10 100 1 0.1 1 10
100 Frequency (Hz) Horizontal Ground Motions 5%Damping Ratio tRS
GRS AR= Example from 49 ground motions recorded on rock sites
67
76. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Trend of median amplication ratios Trend of median
amplification ratios for horizontal component 0.1 10 100 1 0.1 1 10
100 Frequency (Hz) Median Ratio Obtained from Statistical
Calculation Horizontal Ground Motions 5%Damping Ratio tRS GRS AR=
Median amplification ratio 68
77. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Trend of median amplication ratios Trend of median
amplification ratios for horizontal component 0.1 10 100 1 0.1 1 10
100 Frequency (Hz) Median Ratio Obtained from Statistical
Calculation Horizontal Ground Motions 5%Damping Ratio tRS GRS AR=
0.5 5 Hz: amplification ratio almost remains constant 5 50 Hz:
amplification ratio decreases 50 100 Hz: amplification ratio
remains to be 1 69
78. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Trend of median amplication ratios Trend of median
amplification ratios for horizontal component 0.1 10 100 1 0.1 1 10
100 Frequency (Hz) Median Ratio Obtained from Statistical
Calculation Horizontal Ground Motions 5%Damping Ratio tRS GRS AR=
0.5 5 Hz: amplification ratio almost remains constant 5 50 Hz:
amplification ratio decreases 50 100 Hz: amplification ratio
remains to be 1 70
79. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Trend of median amplication ratios Trend of median
amplification ratios for horizontal component 0.1 10 100 1 0.1 1 10
100 Frequency (Hz) Median Ratio Obtained from Statistical
Calculation Horizontal Ground Motions 5%Damping Ratio tRS GRS AR=
0.5 5 Hz: amplification ratio almost remains constant 5 50 Hz:
amplification ratio decreases 50 100 Hz: amplification ratio
remains to be 1 71
80. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Trend of median amplication ratios Trend of median
amplification ratios for horizontal component 0.1 10 100 1 0.1 1 10
100 Frequency (Hz) Horizontal Ground Motions 5% Damping Ratio tRS
GRS AR= 0.1 1 10 100 Frequency (Hz) 1685 25 33 50 Median Ratio
Obtained from Statistical Calculation Establish horizontal
statistical relationship at critical frequencies 72
81. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Inuence of site conditions on horizontal relationship Influence
of site conditions on horizontal statistical relationship 4 5 3 2 1
0 t-SpectralAcceleration(g) 0.1 10 1001 Frequency (Hz) 50% 84.1% B
sites C sites D sitestRS of different site conditions are almost
the sameNot consider site conditions in horizontal statistical
relationship 73
82. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Establish statistical relationship To establish horizontal
statistical relationship Combine different suites of ground motions
together Regression model ln St A(, f) tRS = c1(, f ) + c2(, f ) ln
SA(, f) GRS +ln St A Regression analysis = c1,c2 and ln St A
74
83. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Valid coverage of statistical relationship Valid coverage:
restrict statistical relationship to certain intervals Example for
5% damping ratio Min of Predictor Varible Mean Max of Predictor
Varible NUREG/CR-0098, Soil USNRC R.G. 1.60 50% 5%Damping 84.1% 0 1
2 0.1 10 1001 Frequency (Hz) SpectralAcceleration(g)Valid to
estimate tRS of any GRS falling inside coverage 75
84. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Valid coverage of statistical relationship Valid coverage:
restrict statistical relationship to certain intervals Example for
5% damping ratio Min of Predictor Varible Mean Max of Predictor
Varible NUREG/CR-0098 USNRC R.G. 1.60 50% 5%Damping 84.1% 0 1 2 0.1
10 1001 Frequency (Hz) SpectralAcceleration(g)Design spectra from
NUREG/CR-0098 fall inside coverage 76
85. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Valid coverage of statistical relationship Valid coverage:
restrict statistical relationship to certain intervals Example for
5% damping ratio Min of Predictor Varible Mean Max of Predictor
Varible NUREG/CR-0098 USNRC R.G. 1.60 50% 5%Damping 84.1% 0 1 2 0.1
10 1001 Frequency (Hz) SpectralAcceleration(g)Design spectra from
USNRC R.G. 1.60 fall inside coverage 77
86. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by statistical relationship Estimate tRS for given
GRS falling inside coverage 78
87. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by statistical relationship Estimate tRS for given
GRS falling inside coverage Use statistical relationship to
estimate tRS 78
88. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by statistical relationship Estimate tRS for given
GRS falling inside coverage Use statistical relationship to
estimate tRS For a given GRS, estimate tRS with any probability p
ln St,p A (, f ) tRS =c1(, f )+c2(, f ) ln SA(, f ) given GRS +ln
St A (, f ) 1 (p) 78
89. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by amplication ratio method Estimate tRS for given
GRS falling outside coverage 79
90. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by amplication ratio method Estimate tRS for given
GRS falling outside coverage Propose amplification ratio method to
estimate tRS 79
91. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by amplication ratio method Estimate tRS for given
GRS falling outside coverage Propose amplification ratio method to
estimate tRS f 50 Hz: use a constant amplification ratio St,p A (,
f) = GRS SA(, f) amplification ratio ARp (, fh) At 100 Hz: St,p A
(, f) = SA(, f) 50 f 100: use linear interpolation in log-log scale
of frequency 79
92. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by amplication ratio method Estimate tRS for given
GRS falling outside coverage Propose amplification ratio method to
estimate tRS f 50 Hz: use a constant amplification ratio St,p A (,
f) = GRS SA(, f) amplification ratio ARp (, fh) At 100 Hz: St,p A
(, f) = SA(, f) 50 f 100: use linear interpolation in log-log scale
of frequency 80
93. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by amplication ratio method Estimate tRS for given
GRS falling outside coverage Propose amplification ratio method to
estimate tRS f 50 Hz: use a constant amplification ratio St,p A (,
f) = GRS SA(, f) amplification ratio ARp (, fh) At 100 Hz: St,p A
(, f) = SA(, f) 50 f 100: use linear interpolation in log-log scale
of frequency 81
94. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by amplication ratio method Determine ARp(, fh)
0.1 10 100 1 0.1 1 10 100 Frequency (Hz) Median Ratio Obtained from
Statistical Calculation tRS GRS AR= fh = 5.0 Hz ARp (, fh)= St,p A
(, fh) Smean A (, fh) 82
95. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Estimate tRS by amplication ratio method Determine Smean A (,
fh) for various damping ratios 0 5 10 15 20 1.5 1.0 0.5 0 Damping
Ratio (%) MeanPredictorVariable(g) Smean A (, fh)=0.02[ln(100)] 2
0.28 ln(100) + 1.14 83
96. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Example of estimating tRS Example 1: use horizontal statistical
relationship to estimate tRS 0 0.5 1.0 1.5 SpectralAcceleration(g)
Target Horizontal GRS 0.2 1 10 100 Frequency (Hz) 0 2 4 6 8 10
t-SpectralAcceleration(g)gg tRS from Statistical Relationship
Directly 50% 84.1% 0.2 1 10 100 Frequency (Hz) Specify GRS
statistical relationship Estimated tRS 84
97. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Example of estimating tRS Example 1: use horizontal statistical
relationship to estimate tRS 0 0.5 1.0 1.5 SpectralAcceleration(g)
Target Horizontal GRS 0.2 1 10 100 Frequency (Hz) 0 2 4 6 8 10
t-SpectralAcceleration(g) tRS from Statistical Relationship
Directly 50% 84.1% 0.2 1 10 100 Frequency (Hz) Specify GRS
statistical relationship Estimated tRS 85
98. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Example of estimating tRS Example 1: use horizontal statistical
relationship to estimate tRS 0 0.5 1.0 1.5 SpectralAcceleration(g)
Target Horizontal GRS Mean of 30 Time Histories +30% 10% 0.2 1 10
100 Frequency (Hz) 0 2 4 6 8 10 t-SpectralAcceleration(g)gg tRS
from Statistical Relationship Directly 50% 84.1% 0.2 1 10 100
Frequency (Hz) Generate 30 time histories spectrum-compatible with
GRS 86
99. Response Spectra for Equipment-Structure Resonance Wei-Chau
Xie Example of estimating tRS Example 1: use horizontal statistical
relationship to estimate tRS 0 0.5 1.0 1.5 SpectralAcceleration(g)
Target Horizontal GRS Mean of 30 Time Histories +30% 10% 0.2 1 10
100 Frequency (Hz) 0 2 4 6 8 10 t-SpectralAcceleration(g) tRS from
Statistical Relationship Directly tRS from 30 tRS of TH Analysis
5050%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 84.1% 0.2 1 10 100 Frequency
(Hz) Calculate tRS of 30 time histories 87
100. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Example of estimating tRS Example 1: use horizontal
statistical relationship to estimate tRS 0 0.5 1.0 1.5
SpectralAcceleration(g) Target Horizontal GRS Mean of 30 Time
Histories +30% 10% 0.2 1 10 100 Frequency (Hz) 0 2 4 6 8 10
t-SpectralAcceleration(g) tRS from Statistical Relationship
Directly Benchmark tRS from 30 tRS of TH Analysis 50% 84.1% 0.2 1
10 100 Frequency (Hz) Estimated tRS match benchmark tRS well
88
101. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Example of estimating tRS Example 2: use amplification
ratio method to estimate tRS 0 0.5 1.0 1.5 2.0
SpectralAcceleration(g) Target Horizontal UHS 0.1 1 10 100
Frequency (Hz) 84.1% 50%%50%%%%%%%505050%% 84.184.184.184.184.184.1
%%%5050%%%%%5050%5050%%%%%50%505050%%%%%50%%50505050%% 84.184.1
50505050505050505050%%5050%%50%%50%%5050505050 84.1 505050%% 84.1
%%50%%%50%%%%5050%%50 84.1 %%%5050%%%%50%50%%%50%5050%%5050%%%%
84.1 %%%%%%50% 84.1 50%%% 0.1 1 10 100 Frequency (Hz) 0 2 1 4 3 6 5
t-SpectralAcceleration(g)gg Amplification Factor Method 30 tRS of
TH Analysis %% Specify UHS amplification ratio method Estimated tRS
89
102. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Example of estimating tRS Example 2: use amplification
ratio method to estimate tRS 0 0.5 1.0 1.5 2.0
SpectralAcceleration(g) Target Horizontal UHS Coverage for
Horizontal Statistical Relationship 0.1 1 10 100 Frequency (Hz)
84.1% 50%%50%%%%%%%505050%% 84.184.184.184.184.184.1
%%%5050%%%%%5050%5050%%%%%50%505050%%%%%50%%50505050%% 84.184.1
50505050505050505050%%5050%%50%%50%%5050505050 84.1 505050%% 84.1
%%50%%%50%%%%5050%%50 84.1 %%%5050%%%%50%50%%%50%5050%%5050%%%%
84.1 %%%%%%50% 84.1 50%%% 0.1 1 10 100 Frequency (Hz) 0 2 1 4 3 6 5
t-SpectralAcceleration(g)gg Amplification Factor Method 30 tRS of
TH Analysis %% Check valid coverage with respect to UHS 90
103. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Example of estimating tRS Example 2: use amplification
ratio method to estimate tRS 0 0.5 1.0 1.5 2.0
SpectralAcceleration(g) Target Horizontal UHS 0.1 1 10 100
Frequency (Hz) 84.1% 50% 0.1 1 10 100 Frequency (Hz) 0 2 1 4 3 6 5
t-SpectralAcceleration(g) Estimated tRS Specify UHS amplification
ratio method Estimated tRS 91
104. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Example of estimating tRS Example 2: use amplification
ratio method to estimate tRS 0 0.5 1.0 1.5 2.0
SpectralAcceleration(g) Target Horizontal UHS Mean of 30 Time
Histories 10% +10% 0.1 1 10 100 Frequency (Hz) 84.1% 50% 0.1 1 10
100 Frequency (Hz) 0 2 1 4 3 6 5 t-SpectralAcceleration(g)gg
Estimated tRS Generate 30 time histories spectrum-compatible with
UHS 92
105. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Example of estimating tRS Example 2: use amplification
ratio method to estimate tRS 0 0.5 1.0 1.5 2.0
SpectralAcceleration(g) Target Horizontal UHS Mean of 30 Time
Histories 10% +10% 0.1 1 10 100 Frequency (Hz) 84.1% 50% 0.1 1 10
100 Frequency (Hz) 0 2 1 4 3 6 5 t-SpectralAcceleration(g)
Estimated tRS Calculate tRS of 30 time histories 93
106. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Example of estimating tRS Example 2: use amplification
ratio method to estimate tRS 0 0.5 1.0 1.5 2.0
SpectralAcceleration(g) Target Horizontal UHS Mean of 30 Time
Histories 10% +10% 0.1 1 10 100 Frequency (Hz) 84.1%
50%%50%%%%%%%505050%% 84.184.184.184.184.184.1
%%%5050%%%%%5050%5050%%%%%50%505050%%%%%50%%50505050%% 84.184.1
50505050505050505050%%5050%%50%%50%%5050505050 84.1 505050%% 84.1
%%50%%%50%%%%5050%%50 84.1 %%%5050%%%50%50%%%50%50%%5050%%%% 84.1
%%%%%50%% 84.1 50%%% 0.1 1 10 100 Frequency (Hz) 0 2 1 4 3 6 5
t-SpectralAcceleration(g) Estimated tRS Benchmar tRS from 30 tRS of
TH Analysis %% Estimated tRS match benchmark tRS well 94
107. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Research contributions Analyze influence of site
conditions on statistical relationship Develop statistical
relationship to estimate tRS Applicable to GRS falling inside valid
coverage Develop amplification ratio method to estimate tRS
Applicable to GRS falling outside valid coverage 95
108. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Research contributions Analyze influence of site
conditions on statistical relationship Develop statistical
relationship to estimate tRS Applicable to GRS falling inside valid
coverage Develop amplification ratio method to estimate tRS
Applicable to GRS falling outside valid coverage 96
109. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Research contributions Analyze influence of site
conditions on statistical relationship Develop statistical
relationship to estimate tRS Applicable to GRS falling inside valid
coverage Develop amplification ratio method to estimate tRS
Applicable to GRS falling outside valid coverage 97
110. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Research contributions Analyze influence of site
conditions on statistical relationship Develop statistical
relationship to estimate tRS Applicable to GRS falling inside valid
coverage Develop amplification ratio method to estimate tRS
Applicable to GRS falling outside valid coverage 98
111. Response Spectra for Equipment-Structure Resonance
Wei-Chau Xie Research contributions Analyze influence of site
conditions on statistical relationship Develop statistical
relationship to estimate tRS Applicable to GRS falling inside valid
coverage Develop amplification ratio method to estimate tRS
Applicable to GRS falling outside valid coverage 99
112. Future Research Wei-Chau Xie Other works Propose a
probabilistic framework to obtain realistic soil UHS 100
113. Future Research Wei-Chau Xie Other works Propose a
probabilistic framework to obtain realistic soil UHS Develop
methods to generate time histories compatible with GRS and FRS
100
114. Future Research Wei-Chau Xie Future research Combine PSHA
to generate probabilistic floor response spectrum for
performance-based seismic design 101
115. Future Research Wei-Chau Xie Future research Combine PSHA
to generate probabilistic floor response spectrum for
performance-based seismic design Develop probabilistic design
response spectrum under soil surface for soil- structure
interaction analysis 101
116. Design Earthquake for Nuclear Power Plants Considering
Nonlinear Site Effects Bo Li Department of Civil and Environmental
Engineering 1
117. Design Earthquake for Nuclear Power Plants Considering
Nonlinear Site Effects Wei-Chau Xie Outline of Presentation
Engineering Background Probabilistic Seismic Hazard Analysis
Probabilistic Site Response Analysis Design Earthquake for Soil
Sites Summary and Research Plan 2
118. Design Earthquake for Nuclear Power Plants Considering
Nonlinear Site Effects Wei-Chau Xie 1. Engineering Background 1985
Mexico Earthquake Mexico city is 350 km away from epicenter Lake
zone of the city suffered major damages Other zones of the city
suffered minimal or negligible damages. Lake zone deep deposit of
soft soils compact deposit of dense soils thin deposit of stiff
soil Major Damage Minimal Damage Negligible Damage Foothill zone
Transition zone 3
119. 1. Engineering Background Wei-Chau Xie Eight-story frame
structure with brick infill walls broken in two and foundation came
off Collapsed and damaged of Ministry of Telecommunications
building Soft soils underneath Lake zone = enormous amplication of
ground motion (PGA amplied by 5 times) = major damages 4
120. 1. Engineering Background Wei-Chau Xie Objective of
Research Soil Layer 1 Soil Surface Structural Analysis Soil Layer 2
Seismic Site Response Analysis Soil Layer m n Bedrock Seismic
Source Seismic Wave Propagation Ground Motion at Bedrock Design
Spectrum at Soil Surface Ground Motion at Soil Surface Structural
Response Design Spectrum at Bedrock Construct Uniform Hazard
Spectra and Vector-valued Uniform Hazard Spectra on soil
sites,considering local site effects in detail. 5
121. Design Earthquake for Nuclear Power Plants Considering
Nonlinear Site Effects Wei-Chau Xie 2. Probabilistic Seismic Hazard
Analysis Three factors affecting ground motions Source effect:
earthquake magnitudes, fault types Path effect: rock media
modifying seismic waves Local site effect: local site soils and
topography modifying seismic waves Local soil Source Effect
Earthquake magnitude M Mean rate of occurence v Local Site Effect
Soil properties topographyPath Effect Source-to-site distance R
Wave propagation by GMPEs Fault Seismic Wave Propagation 6
122. 2. Probabilistic Seismic Hazard Analysis Wei-Chau Xie
Scalar Probabilistic Seismic Hazard Analysis (PSHA) sj = NS i=1 i r
m P Sa(Tj)sj m, r fM(m) fR(r)dm dr i = Seismic Hazard Curve
Spectral acceleration (g) 0.01 0.1 1 104 103 102 101
Annualprobabilityofexceedance Period 0.1 sec Period 1 sec 7
123. 2. Probabilistic Seismic Hazard Analysis Wei-Chau Xie
Ground Motion Prediction Equations (GMPEs) GMPEs correlate ground
motion intensities with important factors General form ln Y=C1 +
C2M + C3 ln(R+C4) + C5R + C6 f1(source) + C7 f2(soil), GMPEs for
rock sites give rigorous results. However,GMPEs for soil sites
usually yield results in much less rigor due to generic soils used
in GMPEs. 8
124. 2. Probabilistic Seismic Hazard Analysis Wei-Chau Xie
Uniform Hazard Spectra 0.01 0.1 0.2 1 Period (sec) 0.001 1 0.0 0.1
SpectralAcceleration(g) 101 103 4104 105 107 109 1011 UHS ( )4104
2% probability of exceedance in 50 years Seismic Hazard Curves
Annual Probability of Exceedance 0.2 sec 1.0 sec Each point on a
UHS has the same annual probability of exceedence. 9
125. 2. Probabilistic Seismic Hazard Analysis Wei-Chau Xie PSHA
for Soil Sites GMPEs for soil sites cannot give rigorous results.
Use site amplication to modify bedrock GMPEs to make them suitable
for soil sites Site Amplication= SA at soil surface SA at bedrock
10
126. 2. Probabilistic Seismic Hazard Analysis Wei-Chau Xie PSHA
for Soil Sites GMPEs for soil sites cannot give rigorous results.
Use site amplication to modify bedrock GMPEs to make them suitable
for soil sites Site Amplication= SA at soil surface SA at bedrock
Three important issues proposed in this modication Soil parameters
variability: one of uncertainty sources in PSHA for soil sites Soil
nonlinearity: special dynamic behavior Proper site response
analysis method: rigorous estimation of site amplication 10
127. 2. Probabilistic Seismic Hazard Analysis Wei-Chau Xie
Previous Research on PSHA for Soil Sites Tsai (2000) focused on
soil nonlinearity,ignoring soil parameters variability. Cramer
(2003) focused on soil parameters variability,ignoring soil
nonlinear- ity,and using improper site response analysis method.
Bazzurro (2004) focused on soil nonlinearity, ignoring soil
parameters variability,and using improper site response analysis
method. Soil parameters variability, soil nonlinearity, and proper
site response analysis method should be completely integrated into
PSHA for soil sites. 11
128. 2. Probabilistic Seismic Hazard Analysis Wei-Chau Xie
Vector-valued Probabilistic Seismic Hazard Analysis Scalar PSHA
uses one ground motion parameter to estimate responses of
structures. sj = NS i=1 i r m P Sa(Tj)sj m, r fM,R(m, r)dm dr i One
parameter cannot represent all important characters of ground
motions. Non-single-mode-dominant structures 12
129. 2. Probabilistic Seismic Hazard Analysis Wei-Chau Xie
Vector-valued Probabilistic Seismic Hazard Analysis Scalar PSHA
uses one ground motion parameter to estimate responses of
structures. sj = NS i=1 i r m P Sa(Tj)sj m, r fM,R(m, r)dm dr i One
parameter cannot represent all important characters of ground
motions. Non-single-mode-dominant structures Vector-valued PSHA use
multiple parameters to improve accuracy of scalar PSHA. s1sn = NS
i=1 i r m P Sa(T1)s1, . . . , Sa(Tn)sn m, r fM,R(m, r)dm dr i
12
130. Design Earthquake for Nuclear Power Plants Considering
Nonlinear Site Effects Wei-Chau Xie 3. Probabilistic Site Response
Analysis Topography and local soil conditions profoundly inuence
amplitude, frequency content,and duration of ground motions.
One-dimensional site response analysis is appropriate for most
sites in practice. Soil damping ratio, shear wave velocity, and
normalized shear modulus greatly affect seismic site responses.
13
131. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Uncertainties of Soil Properties Uncertainties of soil properties
are classied as: Aleatory uncertainty represents natural randomness
of soil properties,due to continual geological process modifying
properties of soil in situ. Epistemic uncertainty represents
uncertainty caused by lack of knowledge and measurement errors.
14
132. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Uncertainties of Soil Properties Uncertainties of soil properties
are classied as: Aleatory uncertainty represents natural randomness
of soil properties,due to continual geological process modifying
properties of soil in situ. Epistemic uncertainty represents
uncertainty caused by lack of knowledge and measurement errors.
Normalized shear modulus and shear wave velocity are modeled by
normal distribution or lognormal distribution. 14
133. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Uncertainties of Soil Properties Uncertainties of soil properties
are classied as: Aleatory uncertainty represents natural randomness
of soil properties,due to continual geological process modifying
properties of soil in situ. Epistemic uncertainty represents
uncertainty caused by lack of knowledge and measurement errors.
Normalized shear modulus and shear wave velocity are modeled by
normal distribution or lognormal distribution. A completely
probabilistic seismic hazard analysis for soil sites includes two
uncertainties. Seismic sources Soil parameters 14
134. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Probabilistic Site Response Analysis (PSRA) Scalar PSRA: use one
input motion parameters to predict site responses P(gk)= P gk im
fIm im dim 15
135. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Probabilistic Site Response Analysis (PSRA) Scalar PSRA: use one
input motion parameters to predict site responses P(gk)= P gk im
fIm im dim Vector-valued PSRA: use multiple input motion parameters
to predict site responses P(gk)= P gk im1, im2, . . . , imn
fIm1Im2Imn im1, im2, . . . , imn dim1dim2 dimn 15
136. 3. Probabilistic Site Response Analysis Wei-Chau Xie Site
Amplication Regression Analysis Selection of predictor variables
Predictor variables are selected from input motion intensities.
All-possible-regressions is used to select good subset of predictor
variables. 16
137. 3. Probabilistic Site Response Analysis Wei-Chau Xie Site
Amplication Regression Analysis Selection of predictor variables
Predictor variables are selected from input motion intensities.
All-possible-regressions is used to select good subset of predictor
variables. Selection of functional form for regression relations
Use Linear or quadratic regression functions Refer to a functional
form provided by previous research 16
139. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Correlation of Site Amplication at Multiple Periods Correlation
between spectral accelerations (SA) at multiple periods exists.
site amplication acting as a bridge between SA at bedrock and at
soil surface = correlation of site amplication at multiple periods
Vector-valued PSHA for soil sites requires correlations of site
amplications. 18
140. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Numerical Application Soil Site in South Carolina Randomized shear
wave velocity 80 100 60 40 20 0 100 200 300 400 500 600 700 800
Shear Wave Velocity (m/sec) Depth(m) Base Case Random Case
Randomized normalized shear modulus for selected soil layer 104 103
10 2 101 100 10 0 0.2 0.4 0.6 0.8 1 Shear Strain (%)
NormalizedShearModulus Base Case Random Case 19
141. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Numerical Application Site Amplication Site amplication calculated
from results of site response analysis 0.01 0.1 1 5 0 2 4 6 8
Period (sec) SiteAmplification AVG AVG 2STD AVG+ 2STD Site
amplication is period-dependent. Two resonant period ranges of soil
deposit,0.60.8 sec and 0.20.4 sec 20
142. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Numerical Application Predictor Variables Four potential predictor
variables: spectral accelerations of input motions at zero period,
PGA at target period,X averaged over 1st resonant period range
(0.60.8 sec), Z1 averaged over 2nd resonant period range (0.20.4
sec),Z2 Rp 2 0 1 2 3 4 5 0.7 0.8 p X,PGA,Z2 X,PGA Z1 best subset
for 1 PV best subset for 2 PVs best subset for 3 PVs
all-possible-regression for 0.2 sec All-possible-regression One
predictor variable = lower value of R2 p = larger variance 21
143. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Numerical Application Regression Model Regression model for 14
selected periods: ln A = c0 + c1 ln X + c2 ln PGA + c3 ln Z2 +
c4(ln X)2 + c5(ln PGA)2 + c6(ln Z2)2 102 101 101 100 101 102 100101
100 101SiteAmplification SA corresponding to 0.2 sec (g) PGA (g) .
Large spectral accelerations . = nonlinear response of soils . =
large shear strain (great than 0.1%) . = great soil damping ratio .
= reduce intensity of ground vibrations . = small site amplication
22
144. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Numerical Application Regression Model Normal probability plot of
residuals 4 3 2 1 0 1 2 3 4 1.5 1.0 0.5 0 -0.5 -1.0 -1.5 Standard
Normal Variate Residual(0.2sec) R = 0.99272 . Large value of R2 . =
residuals of ln A follow normal distribution . = ln A follows
normal distribution . = site amplication A follows lognormal
distribution 23
145. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Numerical Application Two Cases Two cases for Probabilistic Seismic
Hazard Analysis for soil sites Base case: deterministic
parameters,include uncertainty in seismic sources Random case:
uncertain parameters, include uncertainties in seismic sources and
soil parameters 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.01 0.1 1.20.2 1.0
Period (sec) lnA ln A ln A due to the uncertainty of seismic
sources due to the uncertainties of seismic sources and soil
parameters Contributions of soil parameters variability greater in
period 0.21.2 sec 24
146. 3. Probabilistic Site Response Analysis Wei-Chau Xie
Conclusion Soil parameters variability cannot be ignored.
Vector-valued site amplication regression model should be used to
modify bedrock GMPEs. Site amplication follows lognormal
distributions. Nonlinear responses of soils reduce intensity of
ground vibrations. 25
147. Design Earthquake for Nuclear Power Plants Considering
Nonlinear Site Effects Wei-Chau Xie 4. Design Earthquake for Soil
Sites Soil Layer 1 Soil Surface Soil Layer 2 Seismic Site Response
Analysis Soil Layer m n Bedrock Seismic Source Seismic Wave
Propagation Ground Motion at Bedrock Modified GMPEs Normalized
Shear Modulus with Variability Shear Wave Velocity with Variability
Design Spectrum at Soil Surface Ground Motion at Soil Surface
Design Spectrum at Bedrock 26
148. 4. Design Earthquake for Soil Sites Wei-Chau Xie Scalar
and Vector-valued PSHA for Soil Sites Scalar Probabilistic Seismic
Hazard Analysis for soil sites: sk = 0 0 0 site amplication
regression model P Ak sk/xk xk, pga, z2 NS i=1 i 0 0 f xk, pga, z2
m, r bedrock GMPEs fMR(m, r)dm dr i dxk d(pga) dz2 = Uniform Hazard
Spectra for soil sites (soil UHS) 27
149. 4. Design Earthquake for Soil Sites Wei-Chau Xie Scalar
and Vector-valued PSHA for Soil Sites Scalar Probabilistic Seismic
Hazard Analysis for soil sites: sk = 0 0 0 site amplication
regression model P Ak sk/xk xk, pga, z2 NS i=1 i 0 0 f xk, pga, z2
m, r bedrock GMPEs fMR(m, r)dm dr i dxk d(pga) dz2 = Uniform Hazard
Spectra for soil sites (soil UHS) Vector-valued Probabilistic
Seismic Hazard Analysis for soil sites: s1sn = 0 0 0 site
amplication regression model P A1 s1/x1, . . . , An sn/xn x1, . . .
, xn, pga, z2 NS i=1 i 0 0 f x1, . . . , xn, pga, z2 m, r bedrock
GMPEs fMR(m, r)dm dr i dx1 dxnd(pga)dz2 = Vector-valued Uniform
Hazard Spectra for soil sites (soilVUHS) 27
150. 4. Design Earthquake for Soil Sites Wei-Chau Xie Soil UHS
and Soil VUHS Soil UHS: same probability of exceedance at each
period independent occurrence of spectral acceleration at multiple
periods Soil VUHS: same probability of exceedance at each period
simultaneous occurrence of spectral acceleration at multiple
periods Both soil UHS and soilVUHS reect characteristics of soil
site. 28
151. 4. Design Earthquake for Soil Sites Wei-Chau Xie Numerical
Application Soil UHS Soil UHS by GMPEs (base case)y GMPEs (base
case) Soil UHS by Modified GMPEs (rabdom case) Soil UHS by Modified
GMPEs (base case) Rock UHS PE =2% in 50 years 0.01 0.1 1.0 10
Period (sec) 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 SpectralAcceleration(g)
Soil UHS and rock UHS are different spectral shapes spectral
amplitudes 29
152. 4. Design Earthquake for Soil Sites Wei-Chau Xie Numerical
Application Soil UHS Soil UHS by GMPEs (base case) Soil UHS by
Modified GMPEs (rabdom case) Soil UHS by Modified GMPEs (base case)
Rock UHS PE =2% in 50 years 0.01 0.1 1.0 10 Period (sec) 1.4 1.2
1.0 0.8 0.6 0.4 0.2 0 SpectralAcceleration(g) Soil UHS by GMPEs are
less rigorous because of generic soils used in GMPEs. 30
153. 4. Design Earthquake for Soil Sites Wei-Chau Xie Numerical
Application Soil UHS Soil UHS by GMPEs (base case)y GMPEs (base
case) Soil UHS by Modified GMPEs (rabdom case) Soil UHS by Modified
GMPEs (base case) Rock UHS PE =2% in 50 years 0.01 0.1 1.0 10
Period (sec) 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 SpectralAcceleration(g)
Soil UHS for critical structures should consider soil parameters
variability. 31
154. 4. Design Earthquake for Soil Sites Wei-Chau Xie Numerical
Application Soil VUHS 0.01 0.001 0.01 0.1 0.1 1 1 10 Period (sec)
SpectralAcceleration(g) Soil VUHS Rock VUHS 0.01 0.1 1 10 Period
(sec) Soil VUHS RockVUHS PE = 2% in 50 years PE = 10% in 50 years
Max difference between soil and rockVUHS occurs in period 0.10.8
sec Lower PE = Smaller differences between soilVUHS and rockVUHS .
Lower probability level of exceedance . = high spectral
accelerations . = nonlinear responses of soils . = large shear
strain . = great damping ratio . = reduce intensity of ground
vibrations 32
155. 4. Design Earthquake for Soil Sites Wei-Chau Xie Numerical
Application Relation between PE of UHS and VUHS 105 104 103 102 10
8 107 106 105 104 103 Probability of Exceedance (UHS)
ProbabilityofExceedance(VUHS) CalculationPoints Linear Relationship
Linear relationship between probabilities of exceedance of UHS
andVUHS Simplify construction of VUHS by linear relationship
33
156. 4. Design Earthquake for Soil Sites Wei-Chau Xie
Conclusions Soil nonlinearity affects spectral shapes and spectral
amplitudes of UHS and VUHS. Soil parameters variability affects
spectral shapes and spectral amplitudes of UHS andVUHS. GMPEs are
not suitable to generate soil UHS and VUHS because of generic
soils. There is a linear relationship between probabilities of
exceedance of UHS andVUHS. 34
157. Design Earthquake for Nuclear Power Plants Considering
Nonlinear Site Effects Wei-Chau Xie 5. Summary and Research Plan
Research Contribution Completed Probabilistic site response
analysis to modify bedrock GMPEs: Inuence of soil parameters
variability on uncertainty of site amplications Vector-value
probabilistic site response analysis method Site amplication
regression models Lognormal distribution of site amplications
35
