probabilistic performance-based earthquake...

Probabilistic Performance-based Earthquake Engineering

K H A L I D M . M O S A L A M , P R O F E S S O R

S T R U C T U R A L E N G I N E E R I N G , M E C H A N I C S & M A T E R I A L S

D E P A R T M E N T O F C I V I L & E N V I R O N M E N T A L E N G I N E E R I N G

U N I V E R S I T Y O F C A L I F O R N I A , B E R K E L E Y

A C K N O W L E D G E M E N T S :

F I B T A S K G R O U P 7 . 7 : P R O B A B I L I S T I C P E R F O R M A N C E - B A S E D S E I S M I C D E S I G N

D R . S E L I M G Ü N A Y , U C - B E R K E L E Y

Probabilistic Performance-based Earthquake Engineering, Tongji University, Shanghai, China, Dec. 17-18, 2015

Course Outline 1/2

2

Part I:

1. PBEE assessment methods

Conditional probability approaches such as SAC/FEMA & PEER formulations

Unconditional probabilistic approach

Questions

2. PBEE design methods

Optimization-based methods

Non optimization-based methods

Questions

3. PEER PBEE formulation demonstrated for electric substation equipment

Introduction

Hazard analysis

Structural analysis

Damage analysis

Loss analysis

Combination of analyses

Questions


Course Outline 2/2

3

Part II:

1. Application 1: Evaluation of the effect of unreinforced masonry infill walls on reinforced concrete frames with probabilistic PBEE

Questions

2. Application 2: PEER PBEE assessment of a shearwall building located on the University of California, Berkeley campus

Questions

3. Application 3: Evaluation of the seismic response of structural insulated panels with probabilistic PBEE

Questions

4. Future extension to multi-objective performance-based sustainable design

5. Recapitulation


Outline

4

1. Application 1: Evaluation of the effect of unreinforced masonry

infill walls on reinforced concrete frames with probabilistic PBEE

2. Application 2: PEER PBEE assessment of a shearwall building

located on the University of California, Berkeley, campus

3. Application 3: Evaluation of the seismic response of structural

insulated panels with probabilistic PBEE


II-1 Application 1

KHALID M. MOSALAM, PROFESSOR

UNIVERSITY OF CALIFORNIA, BERKELEY


6

An idealized portal frame with and without infill wall

Demonstration of hazard and structural analyses

The geometry of the portal frame based on dimensions of a single story RC frame

with infill wall tested on UC-Berkeley shaking table [Hashemi & Mosalam, 2006].

Application I

Prototype structure

A1 A2

B1 B2

C1C2

A3 A4

B3 B4

C4

Development

and validation of

FE model

Verification of

hybrid simulation

with sub-

structuring

Development of generalized

hybrid simulation framework

Infill-RC

frame

interaction

Damage sequence

and collapse

mechanism

Development of

element removal

algorithms

Improvement of RC

constitutive material

& damage models

Development of

new SAT

models

Progressive collapse analysis

for RC structures with URM

infill walls

Shake-

table

tests

Pseudo-

dynamic

tests

Numerical

simulations on URM

infill walls

Reliability analysis for

performance evaluation

of RC structures with

URM infill walls

Development of

error-free

hybrid

simulation

Mixed variables

(displacement/force)

control for flexible/

stiff structures

Error

compensation in

displacement

control

1

2 3

4 5 67

8 9 10

11 12

14

15 16 1817

Development of

element removal

criteria13

Prototype structure

A1 A2

B1 B2

C1C2

A3 A4

B3 B4

C4

Development

and validation of

FE model

Verification of

hybrid simulation

with sub-

structuring

Development of generalized

hybrid simulation framework

Infill-RC

frame

interaction

Damage sequence

and collapse

mechanism

Development of

element removal

algorithms

Improvement of RC

constitutive material

& damage models

Development of

new SAT

models

Progressive collapse analysis

for RC structures with URM

infill walls

Shake-

table

tests

Shake-

table

tests

Pseudo-

dynamic

tests

Pseudo-

dynamic

tests

Numerical

simulations on URM

infill walls

Reliability analysis for

performance evaluation

of RC structures with

URM infill walls

Development of

error-free

hybrid

simulation

Mixed variables

(displacement/force)

control for flexible/

stiff structures

Error

compensation in

displacement

control

1

2 3

4 5 67

8 9 10

11 12

14

15 16 1817

Development of

element removal

criteria13


7

Application I

Hazard Analysis

UC Berkeley campus

Location of the structure: @North gate of campus (37.877˚, -122.264˚)

Site class: NEHRP D


8

Application I

Hazard Analysis

Source: USGS


9

Application I

Hazard Analysis

OpenSHAhttp://www.opensha.org

Location

Site class

IM type

Attenuation Model

Hazard CurveShear wave velocity in top 30 m of soil

(IM) years50,1(IM) (IM) TeP T


10

Application I


Removable bolt

assembly to be cut

Load cell

Lever hoist

(comealong)

11

Application I

Hazard Analysis: Hazard Curve

Hazard is more severe for the bare frame at this particular location

10-2

10-1

100

101

10-8

10-6

10-4

10-2

100

Sa (g)

Me

an

an

nu

al fr

eq

ue

ncy o

f e

xce

ed

an

ce

Tn=0.1 sec - Infilled Frame

Tn=0.5 sec - Bare Frame


12

Application I

Structural Analysis

Analytical modeling using OpenSees [2010] Force-based beam-column elements with fiber discretized sections Material for core and cover concrete: Concrete02 Material for reinforcing bars: Steel01 Material strengths [Hashemi & Mosalam, 2006] Concrete: fcʹ beam = 37 MPa, fcʹ columns = 38 MPa Steel: fy = 458 MPa

Sections: Columns: 305305 mm square section Beam: 343267 mm rectangular section

Reinforcement: Columns: Longitudinal: eight #6, Transverse: #3@95 mm Beam: Longitudinal: three #6 bars (top and bottom), Transverse: #3@70 mm

4.88 m

3.43 m

Transverse reinforcement used to determine core concrete strength


13

Application I

Structural Analysis

Twenty ground motions [Lee & Mosalam, 2006] used in nonlinear time history

analyses (explanation later in Application II)

Ground motions scaled for each of the considered Sa(T1) value

Note: Use of unscaled ground motions should be the preferred method in a

real-life application

For demonstration purposes, only uncertainty in ground motion is considered;

material uncertainty is not taken into consideration

Total number of analyses conducted for an intensity level is twenty

Peak interstory drift ratio (IDR) & peak roof acceleration (RA) are considered

as the EDPs


14

Application I

Structural Analysis: Global collapse determination

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

IDR

IM

Vu

0.7Vu

IDRf

IDRf

p(C|IM) =

# of GMs leading to collapse/total # of GMs

GMs leading to collapse

?


15

Application I


0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Sa (g)

Pro

ba

bili

ty o

f co

llap

e a

nd

no

-co

llap

se

No-collapse: infilled frame

Collapse: infilled frame

Infilled Frame

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Sa (g)

Pro

ba

bili

ty o

f co

llap

e a

nd

no

-co

llap

se

No Collapse: bare frame

Collapse: bare frame

Bare Frame

Collapse probability is much less for the infilled frame case for all intensity levels: specific for this frameIn a multistory, three-dimensional (3D) frame:• Sudden failure of infill walls can lead to weak stories, which is usually followed by a global collapse• Shear failure can be critical for columns because of lateral component of force transferred by infill wall


0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

Structural Analysis

16

ED

Pj

IM

Outcome of Structural Analysis:

Probability of each value (index i) of each EDP (index j)

for each hazard level (index m): p(EDPji|Imm)

IMm

EDPf

ED

PjRemove, treated

separately

IMIMm


17

Application I

Outcome of Structural Analysis:Probability and POE for IDR and RA ”Only RA is shown here”

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

0.01

0.02

0.03

0.04

Pro

babili

ty

Sa=0.2g

Sa=0.6g

Sa=1.1g

Sa=1.6g

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

0.5

1

RA

Pro

babili

ty o

f E

xceedance

Sa=0.2g

Sa=0.6g

Sa=1.1g

Sa=1.6g

Lognormal distribution


Application I

18

Total probability theorem:

Given n mutually exclusive events* A1,…, An whose probabilities sum to 1.0, then the probability of an arbitrary event B:

)p(A)ABp()p(A)ABp()p(A)ABp()Bp( nn2211

i

ii )p(A)ABp()Bp(

Conditional probability of B given

the presence of Ai

Probability of Ai

*Occurrence of any one of them automatically implies the non-occurrence of the remaining n−1 events

Combination of Hazard and Structural Analyses


19

Application I


mmii IMpIMEDPPEDPP

m

mmii SapSaRAPRAP

m mm

ii SapSaRIDPIDRPm

m: index for IM i: index for EDP


20

Application I


POE of RA is larger for the infilled frame due to:

Initial periods for small RA values (acceleration response for 0.1 sec-infilled frame is greater than that for0.5 sec-bare frame)

Lateral force capacity [next slide] (larger for the infilled frame compared to the bare frame) for large Sa

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RA (g)

Pro

babili

ty o

f E

xceedance o

f R

A

Bare Frame

Infilled Frame

Bare Frame

Infilled Frame


0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RA (g)

Pro

babili

ty o

f E

xceedance o

f R

A

Bare Frame

Infilled Frame

Bare Frame

Infilled Frame

21

Application I

Combination of Hazard & Structural Analyses

Remark:

For each of the intensities in this region, RA isdominated by the lateral force capacity

However, POE of RA of the two frames getscloser to each other as RA increases

This is because probability of Sa, p(Sam), whichis a weighing factor, is smaller for the infilledframe for a large value of Sa [Hazard curve]

Benefit of combining different analyses stages:

Results of structural analysis alone would indicate larger POE of the RA response for the infilled framethan that for the bare frame for larger intensities

However, combination of the two analyses indicates that the POEs of the RA response of the bare andinfilled frames are comparable for large intensities

First comment is true if a large intensity earthquake is likely to occur, e.g. Hayward fault, Bay Area

10-2

10-1

100

101

10-8

10-6

10-4

10-2

100

Sa (g)

Me

an

an

nu

al fr

eq

ue

ncy o

f e

xce

ed

an

ce

Tn=0.1 sec - Infilled Frame

Tn=0.5 sec - Bare Frame


0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IDR (%)

Pro

babili

ty o

f E

xceedance o

f ID

R

Infilled Frame

Bare Frame

22

Application I


POE of IDR of the bare frame is muchlarger than that of the infilled frame

Significant contribution of the infillwall in reducing frame deformationresponse

Specific to the portal frame analyzedin this application and the adoptedmodeling assumptions Should not

be generalized

Bare Frame

Infilled Frame


23Probabilistic Performance-based Earthquake Engineering, Tongji University, Shanghai, China, Dec. 17-18, 2015

Questions?

[email protected]

http://www.ce.berkeley.edu/people/faculty/mosalam

mailto:[email protected]


Outline

24








II-2 Application 2




Application II

26

University of California Science (UCS) building in UC-Berkeley campus

Modern reinforced concrete shear-wall building

High technology research laboratories for organismal biology, animal facilities,

offices and related support spaces

An example for which non-structural components contribute to the PBEE

methodology due to valuable building contents, i.e. the laboratory equipment

and research activities


Application II

27

Six stories and a basement

Almost rectangular in plan with overall dimensions of ~93 m x 32 m

Gravity load resistance: RC space frame

Lateral load resistance: Coupled and perforated shearwalls

Floors consist of waffle slab systems composed of a 114 mm thick RC

slab supported on 508 mm deep joists in each direction

Foundation consists of a 965 mm thick mat


28

Application II

Hazard AnalysisLocation of the structure: close to west gate of campus

UC Berkeley campus

Site class: NEHRP C


29

Application II

Hazard Analysis: Hazard Curve

10-2

10-1

100

101

10-5

10-4

10-3

10-2

10-1

100

Sa (g)

Me

an

an

nu

al fr

eq

ue

ncy o

f e

xce

ed

an

ce

Lognormal distribution of Sa with

the mean of 0.633g and standard

deviation of 0.526g

Matches with MAF of exceedance

of Sa at periods of 0.2, 0.3 and 0.5

seconds reported by Frankel and

Leyendecker [2001]


30

Application II

Hazard Analysis: Probability and Probability of Exceedance

0 0.5 1 1.5 2 2.5 3 3.5 40

0.02

0.04

0.06

0.08

Sa, g

Pro

babili

ty o

f S

a

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

Sa (g)

Pro

babili

ty o

f E

xceedance o

f S

a

TeP (IM)1(IM)

otherwise)P(IM)P(IM)p(IM

points data IM of #mif)P(IM)p(IM

points data IM of #:1mfor

1mmm

mm


31

Application II

Structural Analysis

Two damageable groups

Structural components: EDP = Maximum peak interstory drift ratio along height (MIDR)

Non-structural components: EDP = peak roof acceleration (RA)

Twenty ground motions

Same site class as the building site and

Distance to a strike-slip fault similar to the distance of the UCS building to Hayward fault

Nonlinear time history analyses conducted for 9 scales for each ground motion

POE(%) 90 80 70 60 50 40 30 20 10

Sa (g) 0.18 0.25 0.32 0.39 0.47 0.57 0.71 0.90 1.39

Level # 1 2 3 4 5 6 7 8 9


32

Application II

Structural Analysis

For other scales, median and COV are extrapolated by curve fitting

0 1 2 3 40

0.005

0.01

0.015

Media

n M

IDR

data

linear fit

0 1 2 3 40

0.25

0.5

0.75

1

Sa (g)

CO

V M

IDR

data

quadratic fit

0 1 2 3 40

0.5

1

1.5

Media

n R

A (

g)

data

quadratic fit

0 1 2 3 40

0.25

0.5

0.75

1

Sa (g)

CO

V R

A

data

quadratic fit

Similar concept in optimization

based design example using

[Aslani & Miranda, 2005]


33

Application II


0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10M

IDR

IM

Median (m), Coefficient of variation (COV)

2

2

ln

2

2

1

2

x

f x ex

Lognormaldistribution

)mln( )COV1ln( 2

a) p(C|IM) = # of GMs leading to collapse/total # of GMs

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

MID

R

IM

MIDRf

b) p(C|IM) = shaded area

Tests of shearwall specimens: median capacity (Hwang & Jaw, 1990)


34

Application II


0 1 2 3 40

0.2

0.4

0.6

0.8

1

Sa (g)

Pro

ba

bility o

f co

lla

pse

an

d n

o-c

olla

pse

No Collapse

Collapse


35

Application II

Outcome of Structural Analysis:Probability of MIDR and RA

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450

0.05

0.1

0.15

0.2

MIDR

Pro

babili

ty o

f M

IDR

Sa=0.5 g

Sa=1.0 g

Sa=3.0 g

0 0.5 1 1.5 2 2.5 3 3.5 40

1

2

3

4x 10

-3

RA (g)

Pro

babili

ty o

f R

A

Sa=0.5 g

Sa=1.0 g

Sa=3.0 g


36

Application II

Damage Analysis

Damage levels considered for structural components:

Slight

Moderate

Severe

Damage levels of non-structural components: Two levels based on the

maximum sliding displacement experienced by the scientific equipment

relative to its bench-top surface [Chaudhuri and Hutchinson, 2005]

Sliding displacement of 5 cm

Sliding displacement of 10 cm


37

Application II

Damage Analysis

Probability of a damage level given a value of the EDP, p(DMk|EDPji), is assumed

to be lognormal with defined median & logarithmic standard deviation values:

Structural components: shearwall tests reported in Hwang and Jaw [1990]

Nonstructural components: shake table tests of Chaudhuri and Hutchison [2005]

Component Damage level EDP Median Coefficient of variation

Structural

Slight MIDR 0.005 0.30

Moderate MIDR 0.010 0.30

Severe MIDR 0.015 0.30

Non-structuralDM = 5 cm PRA (g) 0.75 0.35

DM = 10 cm PRA (g) 1.10 0.28


38

Application II

Damage Analysis: Fragility Curves

0 0.01 0.02 0.03 0.04 0.050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MIDR

Pro

ba

bility o

f E

xce

ed

an

ce

of D

am

ag

e

Slight damage

Moderate damage

Severe damage

0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PRA (g)

DM = 5 cm

DM = 10 cm

Non-structuralComponents

StructuralComponents


39

Application II

Loss Analysis

Decision variable (DV): monetary loss

The total value of the scientific equipment [SE] $23 million [Comerio, 2005]

Loss functions: lognormal with median and coefficient of variation (COV):

Component Damage levelMedian Loss ($million)

[Percent of total value of SE]Coefficient of

variation

Structural

Slight 1.15 [5%] 0.4

Moderate 3.45 [15%] 0.4

Severe 6.90 [30%] 0.4

Non-structuralDM = 5 cm 6.90 [30%] 0.2

DM = 10 cm 16.10 [70%] 0.2

Larger variation due to lack of information

40

Application II

Loss Analysis: Loss Functions

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Economic Loss (million $)

Pro

ba

bility o

f E

xce

ed

an

ce

of E

co

no

mic

Lo

ss

Slight damage

Moderate damage

Severe damage

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


DM=5 cm

DM = 10 cm

Non-structuralComponents

StructuralComponents


41

Application II

Loss Analysis: Loss Function for Collapse

0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Pro

ba

bility o

f E

xce

ed

an

ce

of E

co

no

mic

Lo

ss

0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Pro

ba

bility o

f E

xce

ed

an

ce

of E

co

no

mic

Lo

ss

Slight damage

Moderate damage

Severe damage

Collapse

Median of $30 million (total

value of structural &

nonstructural components)

COV :0.2

In case that collapse occurs, the probability of monetary loss being greater than $27.6 million is 0.8

Difference between $27.6 million and $4.9 million is a clear

indication of the importance of nonstructural components

In case that structural components are severely damaged, the probability of monetary loss being greater than $4.9 million is 0.8

27.64.9


Application III

42

j

m

n

jm

n IMNC,DVPIMNC,DVP

m

n

mm

n

m

n IMCpCDVPIMNCpIMNC,DVPIMDVP

m

mm

nn IMpIMDVPDVP

k

i

jkk

n

j

i

j

n

j EDPDMpDMDVPEDPDVP

i

m

i

j

i

j

n

jm

n

j IMEDPpEDPDVPIMNC,DVP

End product: Structural Analysis:

Probability of no-collapse & of collapse

Loss Analysis: Loss function for collapse

m: index for IM

j: index for damageable groups (DG)

i: index for EDP

k: index for DM

Structural Analysis

Hazard Analysis

Loss Analysis

Damage Analysis

POE of the nth value ofthe DV of the facility

Combination of Analyses


Application II

43

Combination of Analyses

Loss Damage Structural Hazard

Single Damageable Group and no global collapse:

POE of the nth

value of the DV

Multiple Damageable Groups and no global collapse:

Multiple Damageable Groups (DGs) and global collapse:

mm

i

j

i

jkk

n

j

n IMpIMEDPpEDPDMpDMDVPDVPm j i k

mm

ii

kk

nn IMpIMEDPpEDPDMpDMDVPDVPm i k

mm

n

mm

i

j

i

jkk

n

j

n IMpIMCpCDVPIMNCpIMEDPpEDPDMpDMDVPDVPm j i k


44

Application II

Combination of Analyses: Loss Curve

0 5 10 15 20 25 30 35 400

0.005

0.01

0.015

0.02

0.025


Pro

ba

bility o

f E

xce

ed

an

ce

of E

co

no

mic

Lo

ss

Total

Collapse

Structural DG

Nonstructural DG

Total Loss Curve

Contribution of nonstructural components given that collapse does not occur

Contribution of structural components given that collapse does not occur

Contributionof collapse

Nonstructural components

significantly contribute to loss


Application II

45

Combination of Analyses: Loss Curve

“No collapse” case is more dominant on

the total loss curve for monetary losses

less than $8 million

All the loss is attributed to the “collapse”

case for monetary losses greater than

$25 million

“No collapse” plot can be interpreted as

the loss curve for a hypothetical case

where collapse is prevented for all

intensity levels

The significant reduction of economic

loss as a result of the elimination of

collapse shows the effect of the collapse

prevention mandated by the seismic

codes from an economical perspective

0 5 10 15 20 25 30 35 400

0.005

0.01

0.015

0.02

0.025


Pro

ba

bility o

f E

xce

ed

an

ce

of E

co

no

mic

Lo

ss

Total

Collapse

No collapse =Structural DG + Nonstructural DG



Questions?

[email protected]




Outline

47








II-3 Application 3

[Outline of Procedure]




Application III

49

Recall HS


Application III

• Structural Insulated Panels (SIPs) are composite panelsfor energy efficient construction

• Composed of an energy-efficient core placed in betweenfacing materials

• Their application in seismic regions is limited by unacceptableperformance as demonstrated by cyclic testing

• Limited number of tests with realistic dynamic loading

• Hybrid simulation is ideal to test SIPs with a variety ofstructural configurations and ground motion excitations


Application III

Reconfigurable Reaction Wall

Loading Steel Tube

Specimen

Gravity Loading

Actuator

Support beam


Application III

7/16” OSB Skins 3-5/8” EPS Insulating Foam


Application III

Specimen Protocol Gravity Nail spacing [in] Remarks

S1 CUREE No 6 Conventional wood panel

S2 CUREE No 6 -

S3 CUREE Yes 6 -

S4 HS Yes 6 Near-fault pulse-type GM

S5 HS Yes 3 Near-fault pulse-type GM

S6 CUREE Yes 3 -

S7 HS Yes 3 Long duration, harmonic GM

S8 HS Yes 3Near-fault GM; 3 stories computational

substructure

• A parameter related to the design and construction of panels: Nail spacing• Parameters related to loading:

Presence of gravity loading Lateral loading: CUREE protocol vs HS Type of ground motion (Pulse type vs Long duration, harmonic)

• Parameter related to HS: Presence of an analytical substructure

2.Investigate the effects of:

1.Compare the responses of conventional wood panel vs SIPs

Test Matrix


Application III

Specimens S4, S5, S7c

m

Specimen m (kip-sec2/in) ξ k (kip/in) c (kip-sec/in) T (sec)

S4 0.0325 0.05 18 0.0076 0.27

S5 0.0325 0.05 32 0.0102 0.20

S7 0.0325 0.05 32 0.0102 0.20


Hybrid Simulation

c=αmm

m

m

m

u1

Experimental DOF

u2

u3

c=αm

c=αm

c=αm

Analy

tical D

OFs

force-displacement relation from previous tests

Specimen S8


Application III

Objective: Make use of the tests for the performance

evaluation of a 3D structure using PEER PBEE methodology

PROFILE OF

DIAGONAL

BLOCKING

BETWEEN

STUDES

BOTTOM OF JOISTS (BOJ)

BOJ

FINISHED FLOOR

GARAGE CURB

SHAKE TABLE

1940’s San Francisco house-over-garage

tested at UC-Berkeley

[Mosalam et al., 2009]


Application III

Hazard Analysis Location of a house over garage in San Francisco

Site class: NEHRP D


Application III

58

Source: USGS

Hazard Analysis


Application III

Structural Analysis

59

N

Level 1 Plan View

19ʹ-6ʺ

4ʹ-10.5ʺ

13ʹ-6ʺ

6ʹ-9ʺ

4ʹ-10.5ʺ

4ʹ-10.5ʺ4ʹ-10.5ʺ

01 02

03

04 05

11 12

13

14 15

16

NORTH

SOUTH

WEST EAST


Application III

Structural Analysis

60

19ʹ-6ʺ

4ʹ-10.5ʺ

13ʹ-6ʺ

6ʹ-9ʺ

4ʹ-10.5ʺ

4ʹ-10.5ʺ4ʹ-10.5ʺ

11 12

13

14 15

21 22

23

24 25

26 16

NORTH

SOUTH

WEST

Level 2 Plan View

EAST

N


Application III

Structural Analysis

61

19ʹ-6ʺ

4ʹ-10.5ʺ

13ʹ-6ʺ

6ʹ-9ʺ

4ʹ-10.5ʺ

4ʹ-10.5ʺ4ʹ-10.5ʺ

01 02

03

04 05

11 12

13

14 15

16

Level 1 Plan View

Floors modeled as rigid diaphragms

Envelope of the force deformation relationship of the springs obtained from the tests

-5 -4 -3 -2 -1 0 1 2 3 4 5-8

-6

-4

-2

0

2

4

6

8

10

Displacement [inch]

Fo

rce

[kip

]

Full-History

Envelope

Parameters used to define the hysteretic relationship are calibrated in the analysis (next slide)


Application III

Structural Analysis

62

0 20 40 60 80-4

-2

0

2

4

Time (sec)

Dis

pla

cem

ent (inch)

0 20 40 60 80-20

-10

0

10

20

Time (sec)

Forc

e (

kip

s)

0 20 40 60 80-40

-20

0

20

40

Time (sec)

Velo

city

(in

ch/s

ec)

0 20 40 60 80-2

-1

0

1

2

Time (sec)

Accele

ratio

n (

g)

analysis

test


Application III

Structural Analysis

63

3182 ground motions from the used version of PEER NGA database

http://peer.berkeley.edu/peer_ground_motion_database/

Unscaled ground motions

Ground motions seperated into bins based on Sa(T1)

T1 is the period in the north south direction which is the critical mode

because of torsional coupling

Nonlinear time history analyses using the

3182 ground motions for each analytical

model corresponding to a specimen

EDP: Maximum Interstory Drift (MIDR)

N

19ʹ-6ʺ

4ʹ-10.5ʺ

13ʹ-6ʺ

6ʹ-9ʺ

4ʹ-10.5ʺ

4ʹ-10.5ʺ4ʹ-10.5ʺ

01 02

03

04 05

11 12

13

14 15

16

N

open


http://peer.berkeley.edu/peer_ground_motion_database/

Application III

Damage Analysis

64

Forc

e

Displacement

Light

Moderate Severe

Collapse

Conduct pushover analysis for each analytical model corresponding

to a different specimen

Determine the damage levels on each pushover curve

Obtain MIDR values at the pushover steps corresponding to the

determined damage levels for each analytical model

Determine the median and coefficient of variation of MIDR for each

damage level from the values obtained from each analytical model


Application III

Loss Analysis

65

Determine the median value of loss corresponding to each damage

level as a percentage of total value of the building

Determine the corresponding coefficient of variation

Obtain the loss curves from a probabilistic PBEE



Questions?

[email protected]




Course Outline 2/2

67

Part II:

1. Application 1: Evaluation of the effect of unreinforced masonry infill walls on reinforced concrete frames with probabilistic PBEE

Questions

2. Application 2: PEER PBEE assessment of a shearwall building located on the University of California, Berkeley campus

Questions

3. Application 3: Evaluation of the seismic response of structural insulated panels with probabilistic PBEE

Questions

4. Future extension to multi-objective performance-based sustainable design

5. Recapitulation


II-4 Future Extension

& II-5 Recapitulation




Introduction

69

Basic


Introduction

70

PEER

PBEE

Resiliency &

Sustainability

Establish safety

and move to the

upper levels

Required to guarantee

the fulfillment of the

basic needs of the

future generations


Introduction

71

Basic Needs: Safety Objective PEER PBEE Probabilistic Formulation

Upper Level Needs for sustainability: Environmental safety and human

comfort objectives Uncertain and probabilistic by nature

Motivation for an inherent extension of PEER methodology to a generalized

probabilistic multi-objective framework

ObjectiveRequired Analysis Type

Hazard Structural Damage Climate Energy Sustainability Life Cycle Cost

Structural Safety √ √ √ √Environmental

Responsibility √ √ √ √

Human Comfort √ √ √ √

Analogy to Hierarchy of Needs (Maslow, 1963)


72

Structural Safety Objective:

dDMdEDPdIMIMpIMEDPpEDPDMpDMDVPDVP

Extended Framework: Safety Objective


Extended Framework: Environmental Responsibility Objective (ERO): Sustainability

73

P(S

DV

)

Sust. Dec. Variable (SDV) (EDV)

P(S

DV

EMi)

Sust. Dec. Variable (SDV)

p(C

V)

in t

ye

ars

Climate Variable (CV)

p (

EM|C

Vi)

Energy measure (EM)

For each CV value

Climate Analysis

Energy Analysis Sustainability Analysis

For each EM value

dCVdEMCVpCVEMpEMSDVPSDVP

EROSustainabilityCurve


Extended Framework: Environmental Responsibility Objective (ERO): Sustainability

74


Sustainability Analysis

Energy Analysis

Climate Analysis

SDV : Sustainability Decision Variable, e.g. Carbon or ecological footprint

EM : Energy measure, e.g. Building energy

CV : Climate Variable, e.g. Temperature change


Extended Framework: Environmental Responsibility Objective (ERO): Life Cycle Cost

75

P(C

SV)

Cost Variable (CSV)

P(C

SV

EMi)

Cost Variable (CSV)

p(C

V)

in t

ye

ars


p (

EM|C

Vi)

Energy measure (EM)

For each CV value

Climate Analysis

Energy Analysis Lifecycle Cost Analysis

For each EM value

dCVdEMCVpCVEMpEMCSVPCSVP

ERO Cost Curve


Extended Framework: Environmental Responsibility Objective (ERO): Life Cycle Cost

76


Lifecycle CostAnalysis

Energy Analysis

Climate Analysis

CSV: Cost/Saving Variable, e.g. Ratio initial cost/savings during lifecycle

EM: Energy measure, e.g. Energy consumption

CV: Climate Variable, e.g. Temperature change


Extended Framework: Human Comfort Objective (HCO): Sustainability

77

P(S

DV

)


P(S

DV

EMi)

Sust. Dec. Variable (SDV)

p(C

V)

in t

ye

ars


p (

EM|C

Vi)

Energy measure (EM)

For each CV value

Climate Analysis

Energy Analysis



For each EM value

HCOSustainabilityCurve


Extended Framework: Human Comfort Objective (HCO): Sustainability

78



Energy Analysis

Climate Analysis

SDV : Sustainability Decision Variable, e.g. Human productivity

EM : Energy measure, e.g. Energy consumption



Extended Framework: Human Comfort Objective (HCO):Life Cycle Cost

79

P(C

SV)

Cost Variable (CSV)P

(CSV

EMi)

Cost Variable (CSV)

HCO CostCurve

p(C

V)

in t

ye

ars


p (

EM|C

Vi)

Energy measure (EM)

For each CV value

Climate Analysis

Energy Analysis Lifecycle CostAnalysis

For each EM value



Extended Framework: Human Comfort Objective (HCO):Life Cycle Cost

80


Lifecycle CostAnalysis

Energy Analysis

Climate Analysis

CSV : Cost/Saving Variable, e.g. Ratio initial cost/savings during lifecycle

EM : Energy measure, e.g. Energy consumption



Extended Framework: Multi-objective Life Cycle Cost

81

P(C

SV)

Cost Variable (CSV)

P(C

SV)

Cost Variable (CSV)

Safety

Environmental Resp.Human Comfort

Lifecycle cost curves Multi-objectiveLifecycle cost curve

Σ


Extended Framework: Decision Tools

82

P(S

DV

)

Sust. Dec. Variable (SDV) P

(CSV

)

Cost Variable (CSV)

P(S

DV

)


EROSustainabilityCurve in termsof e.g. CarbonFootprint

Multi-objectiveLifecycle costcurve

HCOSustainabilityCurve interms of e.g.Productivity


Framework for Performance-based Engineering (PBE) Approach to the Holistic Best Design Decision

83

→MAUT/MAVT (Multi-Attribute Utility/Value Theory)

Steps: Tree Construction

Value Function

Weight Assignment

Selection Amongst Alternatives

Multi-Criteria Decision-Making:

Compared to other daily products,

– The life cycle of a building/structure is long;

– The number of stakeholders/users is large;

– The requirements and circumstances related to the building/structure are unpredictable.


Extended Framework: Systematic Decision

84

MIVES: Decision-Making Process

Tree Construction

San José and Garrucho (2010); Pons (2011) Objectives Relevance Difference-making for each one of the alternativesMinimal number of items

Iyengar (2012) Cut: Use 3 levels of unfolded branches, and every branch to have 5 sub-

branches or less in the successive unfolding steps; Concretize: Use indicators that experts and stakeholders can understand; Categorize: Use more categories and fewer choices; and Gradually increase the complexity.


Integrated Value Model for Sustainable Assessment (Modelo

Integrado de. Valor para una Evaluación Sostenible – MIVES)


85

MIVES: Decision-making Process

Value Functions

Number of new patents used in building design Annoyance to neighbours (noise) during construction

Examples

Non-negative increasing/decreasing functions, Linear, concave, convex, S-shaped, etc. Presence of value functions allows for consideration of a broad range

of indicators and allows the use of indicators with different units.

0 1i i

kV X



86


Weight Assignment

Requirement Wreq % Criteria Wcrit % i Indicator Wind % Unit

Functional 10.0

Quality

perception30.0

1 User 75.0 0-5

2 Visitor 25.0 0-5

Adaptability to

changes70.0 3 Modularity 100.0 %

Economic 50.0

Construction

cost50.0

4 Direct cost 80.0 $

5 Deviation 20.0 %

Life cost 50.0

6 Utilization 40.0 $

7 Maintenance 30.0 $

8 Losses 30.0 $

Social 20.0

Integration of

science10.0 9 New patents 100.0 #

⁞ ⁞ ⁞ ⁞ ⁞ ⁞

Environmental 20.0

Construction 20.0

15 Water consumption 10.0 m3

16 CO2 emission 40.0 Kg

17 Energy consumption 10.0 MJ

18 Raw materials 20.0 Kg

19 Solid waste 20.0 Kg

Utilization 40.0

20 Noise, dust, smell 10.0 0-5

21 Energy consumption 45.0 MJ/year

22 CO2 emission 45.0 kg/year

⁞ ⁞ ⁞ ⁞ ⁞ ⁞



87


Selection Amongst Alternatives

1

indNi i i i i

k req crit ind k

i

V W W W V X

Value functionWeights

Integration of values of every indicator ofany alternative k

The value of each alternative is determined The alternative

that has the highest value, i.e. closest to 1.0, becomes the most suitable alternative, i.e. the “best” solution.



88

PBE approach: PBE-MIVES

Multiple Indicators in a Direct Probabilistic Manner

2 2 , ,CO CO E E ST STf DV a A f DV b B f DV c C

2 2 2, , CO E ST CO CO E E ST STV a b c V a V b V c w u a w u b w u c

2, , 2

2 2 2 22 2,

, , , ,

,

CO E ST CO E ST

CO CO E CO ST CO EE CO ST CO E

f a b c f DV a DV b DV c

f DV a f DV b DV a f DV c DV a DV b

n n

DVa

P DV a p DV DV a f DV d DV

where P(DVn) is the POE of nth value of DV, and p(DV > DVn = a) is the probability of DV exceeding a, nth value of DV.

Assume 3 indicators DVCO2, DVE and DVST are considered and corresponding PDFs are:

For weights wCO2, wE and wST, the overall value for the indicators is:

If DVCO2, DVE and DVST (with value functions uCO2, uE, and uST) are mutually independent, the joint PDF is:

else,

Therefore, the conditional probability distribution should be defined.



89


Application to the UCS Building

Two alternatives with different fuel consumption (in Btu) ratios

Electricity : Natural gas = 5 : 2 (Plan 1), Electricity only (Plan 2)

Bivariate lognormal distribution assumed for energy expenditure and CO2

emission for 50 years (building life span).

Each mean value estimated based on data for office buildings in the West-Pacific region (by DOE, EIA, & EPA).

Standard deviation assumed as 30% of the corresponding mean value.

Coefficient of correlation was assumed as 0.8.

50100

150

510

1520

2530

0

1

2

3

4

x1 (1000 kips)x2 ($million)

f(x1,x

2)

0

0.5

1

1.5

2

2.5

3

x1 (1000 kips)

x2 (

$m

illio

n)

25 50 75 100 125 1505

10

15

20

25

30

0.5

1

1.5

2

2.5

PDF of energy expenditure (x1) and CO2 emission (x2) for Plan 1



90

Requirement Wr [%] Criteria i Indicator Wi [%] Unit

Environmental 25.0 Utilization 1 CO2 emissions 100.0 1000 kips

Economic 75.0 Life cost2 Energy expenditures 60.0 $million

3 Losses 40.0 $million


Application to the UCS Building

Contours of Vf of energy expenditures (x1) and CO2 emissions (x2) for Plans 1 and 2 of the UCS example building

[Monetary loss due to structural damages x3 = 0]

x1 (1000 kips)

x2 (

$m

illio

n)

25 50 75 100 125 1505

10

15

20

25

30

35

0.2

0.4

0.6

0.8

x1 (1000 kips)

x2 (

$m

illio

n)

25 50 75 100 125 1505

10

15

20

25

30

35

0.2

0.4

0.6

0.8

Plan 1 Plan 2

probV Vfd

Linearly decreasing value functions

The following was computed to compare Plans 1 and 2:

1.0

1.0 ( ) ( )

0.0

a

a b a a b

b

u x if x x

x x x x if x x x

if x x

Expected value of an alternative rank different alternatives

If no loss, i.e. x3 = 0Case 1: 0 ≤ x1 ≤ 80, 0 ≤ x2 ≤ 15

Plan 1: Vprob = 309.52Plan 2: Vprob = 223.56

Case 2: 0 ≤ x1 ≤ 80, 0 ≤ x2 ≤ 20Plan 1: Vprob = 393.95

Plan 2: Vprob = 449.61



91


The probabilistic nature of the indicators can be considered in MCDA either indirectly by the calculation of the value of each indicator in a probabilistic manner or directly by formulating the value determination equation in a probabilistic framework.

The correlation between the different indicators is taken into account in the direct formulation and it is the preferred method when there is significant interdependency between indicators.

As shown in the comparison of Vprob in the UCS example building, considered range of indicators can change the value of the alternatives and affect the final decision. Therefore, attention should be paid to the selection of the proper range of indicators.

Matlab code for PBE-MIVES


RECAP: Framework for PBE for “Best” Decision of Energy-efficient & Sustainable Building Design

92

Framework

Various interests

Uncertainties

Life cycle

Multicriteria

Probabilistic

LCA

+

+Energy-efficient

Sustainable

Safe

Economical

...

Holistic design

A B C ... ?Alternatives

Comparison

Overall value of A

Overall value of B

Overall value of C

Decision A B C ...

“Best”

Various levels ofhazard and

environmental demands

PBE Approach

Systemperformances

Probabilisticevaluation

Realistic and reliable

analysis/design

CVpCVEMpEMSDVPSDVP ||

Climate Variable (CV) Energy Measure (EM) Sustainability Decision Variable (SDV)

PBE for Sustainability

value 1, weight 1

value 2, weight 2

value 3, weight 3

...

Ind1

Ind2

Ind3



Questions?

[email protected]




probabilistic performance-based earthquake...

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