Overview of Multi-hazard

Overview of Multi-hazard
Francesco Petrini
Department of Structural and Geotechnicl Engineering
Sapienza Università di Roma
francesco.petrini@uniroma1.it
Cagliari, September 17th
1st SHORT COURSE ON MULTIHAZARD FOR EXTREME EVENTS:
Fires, Explosions, Floods, Earthquakes,
University of Cagliari (Italy), 17th – 20th September 2019
Co-Sponsored by:

1st SHORT COURSE ON MULTIHAZARD FOR EXTREME EVENTS: Fires, Explosions, Floods, Earthquakes,
2
Lecture Sumary
1. Introduction/Motivations
2. Background concepts in structural design under single hazards
I. Definitions (hazard, damage, fragility, exposure, risk)
II. Sources of uncertainties other than hazard IM
3. Probabilistic Performance-Based Engineering (PBE) for risk assessment and
management
4. Towards Multi-Hazard
I. Primary Needs and Open issues in facing multiple hazard structural problems
II. Hazard interaction problem
III. Opposite design strategy problem
5. Concluding Remarks
Overview of Multi-hazard Cagliari, September 17th, 2019 francesco.petrini@uniroma1.it

3
Motivations

4
Great Tōhoku earthquake and Tsunami (Japan, March 11, 2011) - I
Earthquake
Tsunami
Morti accertati: 15.894
Feriti: 5.314
Dispersi: 4.647
≈100 KmPGA=2.99g

Great Tōhoku earthquake and Tsunami (Japan, March 11, 2011) - II
5Overview of Multi-hazard Cagliari, September 17th, 2019 francesco.petrini@uniroma1.it
Earthquake
Tsunami
Explosions
Fire

Hurricane Katrina (USA, August, 23-31, 2005) - I
6
Strong winds
Windborne debris
Storm Surge (flooding)
Heavy rain (flash flooding)

11/9 terrorist attack (USA, September, 11, 2001)- I
7
Impact
Explosion
Fire

Events on single structures
8
Montebello, Calif. — Foam rains down on the truck.
Tanker truck blaze closes 60 Freeway
Source: http://framework.latimes.com/2011/12/14/tanker-explosion-fire-closes-freeway/#/14
The truck driver reported the rear trailer ablaze before he came to a stop under the overpass. The fire burned so
hot that he was forced to abandon the truck before he could pull to the side of the freeway, authorities said. He
and a passenger escaped uninjured.
Impact
Explosion
Fire

Motivations
• Multi-Hazard (MH) scenarios are not currently taken into account in design practice and in State of Art
methods;
• MH catastrophic events occurred in the past, forced the research community to devote great effort in the
development of appropriate frameworks for tackling structural design under a coherent MH philosophy;
• Knowledge and probabilistic or semi-probabilistic methods are well-established and advanced in structural
design for single hazards, but there is an urgent need for an unified, general framework for coherently taking
into account the interactions between different hazards in structural design and assessment;
• Such a advanced methods are often based on interdisciplinary collaborations between different
scientists/experts (e.g. Geologists, Engineers, Insurance brokers in case of seismic design)
• The research community is today mature and ready for joining knowledges about different hazards in a single
unified framework for structural design.
9
Zaghi AE, Padgett JE, Bruneau M, Barbato M, Li Y, Mitrani-Reiser J, McBride A (2016). Establishing Common Nomenclature, Characterizing the Problem, and
Identifying Future Opportunities in Multihazard Design. J. Struct. Eng., 142(12): H2516001.

Background Concepts
in structural design under single hazards

Definitions
(hazard, damage, fragility, exposure, risk, PBD)

Basic definitions - I
12
Hazard. A hazard is a potentially damaging event, any source of potential damage, it is
any object, situation, or behaviour that has the potential to cause injury, ill health,
damage to property or the environment, social and economic disruption or
environmental degradation.
Exposure The situation of people, infrastructure, housing, production capacities and
other tangible human assets located in hazard-prone areas. Exposure is a concept
which describes factors or constraints of an economic, social, physical or geographic
nature, which reduce the ability to prepare for and cope with the impact of hazards
Vulnerability refers to the proneness of a system to suffer/experiment the damaging
effects of a hazard. There are many aspects of vulnerability, arising from various
physical, social, economic, and environmental factors. Examples may include poor
design and construction of buildings, inadequate protection of assets,. Vulnerability
varies significantly within a community and over time.
Hazard is one of the three components of RISK

Basic definitions - II - Risk definition (qualitative)
13
RISK is the probability that negative consequences may arise when hazards interact with vulnerable areas, people, property,
environment. RISK is a concept which describes a potential set of consequences that may arise from a given set of circumstances.
Risk is a combination of the interaction of hazard, exposure, and
vulnerability, which can be represented by the three sides of a triangle.
Risk can be also seen as the intersection of Hazard,
Exposure and Vulnerability

It is usual describing the occurrence of the LSs as a function of some parameter describing the probabilistic Intensity Measure (IM) of the
hazard- triggered loads acting on the structure (or system); the IM will be described by a probabilistic distribution or by an hazard curve
It is desirable to express the LS “i” by means of scalar threshold values (EDPi*) for opportune response parameters (Engineering
Demand Parameter - EDPi).
Under these assumptions, the mean rate of failure for structure exposed to hazard (occurrence of the risk associated to the limit sate “i”),
can be expressed as
Where 𝑃 𝐸𝐷𝑃𝑖 > 𝐸𝐷𝑃𝑖
∗
𝐼𝑀 is the conditional probability of failure given IM, which is know as the fragility function (often
referred as vulnerability function), E(IM) is the exposure (e.g. coefficient), f(IM) is the occurrence of IM values (pdf of the hazard).
NOTE: exposure often does not explicitly appear but it is “hidden” in the hazard probabilistic characterization f(IM)
The risk can be identified with the value of the occurrence G(LS) of exceeding a certain loss magnitude or a certain Limit State (LS)
during a reference period.
14
𝐺(𝐿𝑆𝑖) = න
0
∞
𝑃 𝐸𝐷𝑃𝑖 > 𝐸𝐷𝑃𝑖
∗
𝐼𝑀 ∙ 𝐸(𝐼𝑀) ∙ 𝑓 𝐼𝑀 ∙ 𝑑𝐼𝑀
IT IS A CONVOLUTION INTEGRAL!
Fragility (or vulnerability) Hazard
Probabilistic approach: Limit States, Intensity Measure (IM), Fragility Curves

15
Severity
G[●]: Complementary Cumulative Distribution Function (G=1-F,
with F : Cumulative Distribution Function);
P[●|■]: conditional probability
DM: Damage
The hazard decreases
as intensity increases
HAZARD CURVE
G(IM)
(e.g. PGA for seismic hazard)IM
1
0
Occurrence/probability
(inareferenceperiod)
Probabilistic approach: LSs, IM, Fragility Curves (quantitative)

16
Severity
DM: Damage
P(DM│IM)
Vulnerability increases as the
seismic intensityand the
consequences of damages
increase
VULNERABILITY or FRAGILITY
IM
HAZARD CURVE
G(IM)
1
0

17
Severity
IM
(e.g. value of possible monetary losses due to
occurred damage for seismic hazard in the
reference period)
RISK
Total annual losses
Risk as the convolution
of hazard and
vulnerability
f(Losses)
DM: Damage
P(DM│IM)
Vulnerability increases as the
seismic intensityand the
consequences of damages
increase
IM
HAZARD CURVE
G(IM)
1
0

18
Severity
IM
f(Losses)
DM: Damage
P(DM│IM)
IM
HAZARD CURVE
G(IM)
IM
1
0
Annual Losses
(often called Decision
Variable – DV – due to
its importance in risk
management)
G(Losses)
1
(e.g. value of possible monetary
losses due to occurred damage for
seismic hazard in the reference
period)
Risk

Examples - I: Earthquake
19
Source: http://byungminkim.unist.ac.kr/research-seismic-risk-assessment/
𝑅𝑖𝑠𝑘 = 𝑃 𝐷𝑀 =
න
0
∞
𝑃 𝐸𝐷𝑃 > 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝐼𝑀 ∙ 𝑓 𝐼𝑀 ∙ 𝑑𝐼𝑀
P(x|y) conditional probability of x with respect to y
IM Environmental action magnitude (Intensity Measure) EDP Engineering Demand Parameter describing the response
DM Damage Measure (components condition in terms of functionality requirements)
E Exposure coefficient
IM=PGA EDP=inter-storey drift DM=No of collapsed panels
DM
DM
P(DM)
Fragility Hazard

Examples - II: Wind
20
EDP = Av - DM= max (av) [m/s2]
1.0
0.8
0.6
0.4
0.2
0
G(EDP)
0 1 2 3
Failureprobability1-P(EDP)
0.07
1.1
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
EDPs
𝑅𝑖𝑠𝑘 = 𝑃 𝑐𝑙𝑜𝑠𝑢𝑟𝑒 𝑜𝑓 𝑏𝑟𝑖𝑑𝑔𝑒 𝑑𝑢𝑒 𝑡𝑜 ℎ𝑖𝑔ℎ 𝑤𝑖𝑛𝑑𝑠 =
න
0
∞
777 m
183 m
3300 m
183 m
627 m
+383 m +383 m
+53 m
+118 m
+77 m
+52 m
+63 m
S C
7.18 m
Roadway girderRailway girder
Main suspension cables (twin)
Hangers
Service
lane
Wind
barriers
8.48 m14.74 m
53.08 m
61.00 m
12.00 m
50.63 m
2.78 m
variable3.67m
2.69m
777 m
183 m
3300 m
183 m
627 m
+383 m +383 m
+53 m
+118 m
+77 m
+52 m
+63 m
S C
777 m
183 m
3300 m
183 m
627 m
+383 m +383 m
+53 m
+118 m
+77 m
+52 m
+63 m
S C
7.18 m
Hangers
Service
lane
Wind
barriers
8.48 m14.74 m
53.08 m
61.00 m
12.00 m
50.63 m
2.78 m
variable3.67m
2.69m
7.18 m
Hangers
Service
lane
Wind
barriers
8.48 m14.74 m
53.08 m
61.00 m
12.00 m
50.63 m
2.78 m
variable3.67m
2.69m
7.18 m
Hangers
Service
lane
Wind
barriers
8.48 m14.74 m
53.08 m
61.00 m
12.00 m
50.63 m
2.78 m
variable3.67m
2.69m
IM=Vm_wind EDP=max vert acc of
the deck
DM=No of days in which the
bridge is closed to train transit
No of closure days each year
G
1
Fragility Hazard

0
0,02
0,04
0,06
0,08
0,1
0,12
0 5 10 15 20 25 30 35
Vm [m/s]
RotvelMAX[RAD/s]
Se1_BU-SLS thresold
Se2_BU-SLS thresold
max(vrot)[rad/s]
Vm [m/s]
0,10
threshold
threshold
0.12
0.10
0.08
0.06
0.04
0.02
0
SLS-1
SLS-2
0
0,02
0,04
0,06
0,08
0,1
0,12
0 5 10 15 20 25 30 35
Vm [m/s]
RotvelMAX[RAD/s]
Se1_BU-SLS thresold
Se2_BU-SLS thresold
max(vrot)[rad/s]
Vm [m/s]
0,10
threshold
threshold
0
0,02
0,04
0,06
0,08
0,1
0,12
0 5 10 15 20 25 30 35
Vm [m/s]
RotvelMAX[RAD/s]
Se1_BU-SLS thresold
Se2_BU-SLS thresold
max(vrot)[rad/s]
Vm [m/s]
0,10
threshold
threshold
0.12
0.10
0.08
0.06
0.04
0.02
0
SLS-1
SLS-2
Examples - II: Wind. Evaluating the fragility by MCarlo structural analysis
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
From velocities
to the action
 )()(
2
1
)(
2
tcBtVtD Da  =
 )(*)(
2
1
)(
2
tcBtVtL La  =
 )(*)(
2
1
)( 22
tcBtVtM Ma  =
Aeroelastic forces
calculation
Turbulent wind time
history generation
Structural analysis
Sampling of the
stochastic variable
Vm (N samples)
i=1
EDP “i”i=N?
no
EDP statistics
evaluation
yes
STOPSTART
i=i+1
Yi =1
IM
Y
i
1 2
3
4
5
f(IMYi=1)
IM
Yi samples
IMYi=1
samples
failure
threshold
*EDPi
EDPi
Yi =
)IMIM(P)IMY(P)IM*EDPEDP(P iY
iii
1
1 =
==
IMYi=1 is the value of IM for which results Yi =1; assuming that
IMYi=1 is a stochastic variable described by a Lognormal
distribution with median and fractional standard deviation
EDP*

Description of the hazard for accidental actions (Fire, Explosions, etc.)
22
HAZARD CURVE
G(IM)
IM
1
0
Due to the fact that they are cyclic, for natural hazards (earthquake, wnd, flood,……) the hazard curve can be reliably evaluated,
but it is a low fidelity representation for accidental hazards or for the so-called Low Probability-High Consequence (LPHC) events

Description of the hazard for accidental actions (Fire, Explosions, etc.)
23
HAZARD CURVE
G(IM)
IM
1
0
Due to the fact that they are cyclic, for natural hazards (earthquake, wnd, flood,……) the hazard curve can be reliably evaluated,
but it is a low fidelity representation for accidental hazards or for the so-called Low Probability-High Consequence (LPHC) events
Triggering event Fire ignition
1. Fire extinguished
by personnel
3. Intrusion of
fire fighters
Arson
Explosion
Short circuit
Cigarette fire
2. Fire extinguished
by sprinkler
YES (P1)
NO (1-P1)
NO (1-P2)
YES (P2)
YES (P3)
NO (1-P3)
Scenario
Other
A1
A2
A3
A4
A5
A6
4. Fire suppression
YES (P4)
NO (1-P4)
YES (P4)
NO (1-P4)
Fire location
YES (P1)
NO (1-P1)
NO (1-P2)
YES (P2)
YES (P3)
NO (1-P3)
B1
B2
B3
B4
B5
B6
YES (P4)
NO (1-P4)
YES (P4)
NO (1-P4)
YES (P1)
NO (1-P1)
NO (1-P2)
YES (P2)
YES (P3)
NO (1-P3)
C1
C2
C3
C4
C5
C6
YES (P4)
NO (1-P4)
YES (P4)
NO (1-P4)
AREA A
(PA)
AREA B
(PB)
AREA C
(PC)
PRAGMATIC
SCENARIO
ANALYSIS

0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5
P[Θ>θ|i]
i [kPa sec]
f (i)
24
Examples - III: Explosions (semi-probabilistic/scenario-based approach)
LOAD STRUCTURE RESPONSE
Truck bomb
1.8 ton TNT
A. P. M. Building
Before 19/05/95
A. P. M. Building
After 19/05/95
HAZARD
COLLAPSE RESISTENCEEXPOSURE
VULNERABILITY
Kg of TNT
P[●]: probability; P[●|■]: conditional probability
H: Hazard; LD: Local Damage; C: Collapse; i: scenario ID
∑i = P[C]P[LD|Hi]P[Hi]
LOCAL
DAMAGE
CAUSE
Ei
EXPOSURE
FACTOR
P[C|LD]
GLOBAL
DAMAGE
ROBUSTNESS
Fragility/VulnerabilityHazard

Sources of uncertainties other than hazard IM

Other kind of uncertainties in addition to the IM
Failure
threshold
= Stochastic = Deterministic
Failure
Input Output
(response r)
)q(θ1
1θ
)q(θ2
2θ
P(M1)
P(M2)
P(Mk)
)q(r1
1r
b =
)q(r2
2r
nθ
),θq(θ mn
mθ
SYSTEM
Input Output
(response r)
)q(θ1
1θ
)q(θ2
2θ
P(M1)
P(M2)
P(Mk)
)q(r1
1r
b =
)q(r2
2r
)q(r2
2r
nθ
),θq(θ mn
mθ
nθ
),θq(θ mn
mθ
SYSTEM
1)(
1
==
k
i
iMP
Der Kiureghian, A., (2008). “Analysis of structural reliability under parameter uncertainties”, Probabilistic Engineering Mechanics, 23, 351-358.
26
IM
OTHER
In addition to the hazard intensity (IM), other parameters are
affected by large uncertainties:
- Parameters of the structure (materials elastic module or
strengths, masses, geometries, ….)
- Parameters defining the interaction between the structure
and the environment (e.g. aerodynamic coefficients of a bridge
deck section)

Other kind of uncertainties in addition to the IM
Failure
threshold
= Stochastic = Deterministic
Failure
Input Output
(response r)
)q(θ1
1θ
)q(θ2
2θ
P(M1)
P(M2)
P(Mk)
)q(r1
1r
b =
)q(r2
2r
nθ
),θq(θ mn
mθ
SYSTEM
Input Output
(response r)
)q(θ1
1θ
)q(θ2
2θ
P(M1)
P(M2)
P(Mk)
)q(r1
1r
b =
)q(r2
2r
)q(r2
2r
nθ
),θq(θ mn
mθ
nθ
),θq(θ mn
mθ
SYSTEM
1)(
1
==
k
i
iMP
Der Kiureghian, A., (2008). “Analysis of structural reliability under parameter uncertainties”, Probabilistic Engineering Mechanics, 23, 351-358.
27
ProbabilisticdistributionsMustbe
identifiedonaphysicalbasis
In addition to the hazard intensity (IM), other parameters are
affected by large uncertainties:
- Parameters of the structure (materials elastic module or
strengths, masses, geometries, ….)
- Parameters defining the interaction between the structure
and the environment (e.g. aerodynamic coefficients of a bridge
deck section)
- These uncertainties should be also taken into account by
assigning to the pertinent the parameters, some appropriate
probabilistic distributions
- The different parameters can be correlated each other, then
being characterized by joint or conditional distributions
- The above-mentioned correlations or conditional dependence
must be identified on a physical basis

Other kind of uncertainties: the example of wind
Campoli M, Petrini F., Augusti G., (2011). “Performance-Based Wind Engineering: towards a general procedure”, Structural Safety (IF=2.086), 33 (6), 367-378.
28
Types of uncertainties
ENVIRONMENT
Wind action
Structural
systems
Non
environmental
actions
EXCHANGE ZONE
1. Aleatory
2. Epistemic
3. Model
Interaction
parameters
Structural parameters
Site-specific
Wind
Aerodynamic and
aeroelastic phenomena
Wind site basic
parameters
Intensity measure
1. Aleatory
2. Epistemic
3. Model
1. Aleatory
2. Epistemic
3. Model
Environmental
effects (e.g.
waves)
Structural
system as modified by
service loads
( )IM ( )IP ( )SP
STRUCTURAL SYSTEM
( ) ( ) ( ) ( )SPPIMPSP,IMIPPSP,IP,IMP =
Vm
Mean wind velocity profile
Vm+ v(t)
Turbulent wind velocity profile
river
Vm
Mean wind velocity profile
Vm+ v(t)
Turbulent wind velocity profile
river
river
ENVIRONMENT EXCHANGE ZONE

29
ENVIRONMENT
Wind action
Structural
systems
Non
environmental
actions
EXCHANGE ZONE
1. Aleatory
2. Epistemic
3. Model
Interaction
parameters
Site-specific
Wind
Aerodynamic and
Wind site basic
parameters
Intensity measure
1. Aleatory
2. Epistemic
3. Model
1. Aleatory
2. Epistemic
3. Model
Environmental
effects (e.g.
waves)
Structural
service loads
( )IM ( )IP ( )SP
STRUCTURAL SYSTEM

30
ENVIRONMENT
Wind action
Structural
systems
Non
environmental
actions
EXCHANGE ZONE
1. Aleatory
2. Epistemic
3. Model
Interaction
parameters
Site-specific
Wind
Aerodynamic and
Wind site basic
parameters
Intensity measure
1. Aleatory
2. Epistemic
3. Model
1. Aleatory
2. Epistemic
3. Model
Environmental
effects (e.g.
waves)
Structural
service loads
( )IM ( )IP ( )SP
STRUCTURAL SYSTEM

31
ENVIRONMENT
Wind action
Structural
systems
Non
environmental
actions
EXCHANGE ZONE
1. Aleatory
2. Epistemic
3. Model
Interaction
parameters
Site-specific
Wind
Aerodynamic and
Wind site basic
parameters
Intensity measure
1. Aleatory
2. Epistemic
3. Model
1. Aleatory
2. Epistemic
3. Model
Environmental
effects (e.g.
waves)
Structural
service loads
( )IM ( )IP ( )SP
STRUCTURAL SYSTEM
𝑅𝑖𝑠𝑘 =
න
0
∞
Fragility Hazard
𝑅𝑖𝑠𝑘 =
න
0
∞
න
0
∞
න
0
∞
𝑃 𝐸𝐷𝑃 > 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝐼𝑀, 𝐼𝑃, 𝑆𝑃 ∙ 𝑓 𝐼𝑃 𝐼𝑀, 𝑆𝑃 ∙ 𝑓 𝑆𝑃 ∙ 𝑓 𝐼𝑀 ∙ 𝑑𝐼𝑃 ∙ 𝑑𝑆𝑃 ∙ 𝑑𝐼𝑀
Fragility Hazard
Coupled systems-
variability
The consideration of additional uncertainties other than IM, has two effects on the Risk assessment procedure:
- The dimension of the convolution integral increases (the number of dimensions will be equal to the number of conditioning
parameters/variables)
- The functions inside the integral increase in number (we will have as many functions as twice of the number of added
uncertain parameters)
Other kind of uncertainties: changes in the convoluton integral
Struct system-
variability

Probabilistic
Performance-Based Engineering (PBE)
for risk assessment and management

General framework for PBE
33
G(DV) = ∫…∫ G(DVDM) · f(DMEDP) · f(EDPIM, IP, SP) · f(IPIM,SP) · f(IM) · f(SP) · dDM · dEDP · dIP · dIM · dSP
Interaction
Parameters
Structural
Parameters
Intensity
measure IM IPSP
Engineering
Demand
Parameters
EDP
Damage
Measure DM
Decision
Variable DV
- The risk is identified with the occurrence during a reference period (e.g. 1 year) of the values assumed by an appropriate
decision variable DV (e.g. economic losses due to the damage caused by an hazard)
- All the pertinent uncertainties are taken into account as affecting the involved problem variables
- Risk analysis is disaggregated into its elementary components: a number of analyses that can be carried out in
sequence in order to assess the risk. Each analysis has the goal to assess the (conditional) probability distribution of a
certain (or of a number of) variables affecting the risk
Based on the total
probability theorem
REMARKS:

34
G(DV) = ∫…∫ G(DVDM) · f(DMEDP) · f(EDPIM, IP, SP) · f(IPIM,SP) · f(IM) · f(SP) · dDM · dEDP · dIP · dIM · dSP
Interaction
Parameters
Structural
Parameters
Intensity
measure IM IPSP
Engineering
Demand
Parameters
EDP
Damage
Measure DM
Decision
Variable DV
G(·|·) is a conditional
complementary cumulative
distribution function
f(·|·) is a conditional
probability density function
Based on the total
probability theorem
1a. Hazard analysis f(IM)
3. Structural analysis
4. Damage analysis f(DM|EDP)
5. Loss analysis G(DV|DM)
Risk
analysis
1b. Structural characterization
2. Interaction analysis
f(SP)
f(IP│IM,SP)
f(EDP│IM,IP, SP)
- Risk analysis is disaggregated into its elementary components: a number of analyses that can be carried out in sequence in
order to assess the risk. Each analysis has the goal to assess the (conditional) probability distribution of a certain (or of a number
of) variables affecting the risk

35
O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
Structural analysis Damage analysis Loss analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
G(·|·) is a conditional
complementary cumulative
distribution function
f(·|·) is a conditional
probability density function
Based on the total
probability theoremG(DV) = ∫…∫ G(DVDM) · f(DMEDP) · f(EDPIM, IP, SP) · f(IPIM,SP) · f(IM) · f(SP) · dDM · dEDP · dIP · dIM · dSP
Interaction
Parameters
Structural
Parameters
Intensity
measure IM IPSP
Engineering
Demand
Parameters
EDP
Damage
Measure DM
Decision
Variable DV
- The different analyses can be conducted by different experts. For example: the seismic hazard analysis can
be conducted by the geologists, while the structural analysis can be conducted by the structural engineers

O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
36
Hazard Example of IM Type Comment/description
Earthquake PGA, Sa(T1),… Hazard curve Poisson distrib
Wind Mean wind V and direction, terrain
roughness
Hazard surface Weibull distrib, Lognormal
distrib
Flood Water surface elevation,… Hazard curve Poisson
Fire Max ambient temperature,…. Pragmatic scenarios
approach
Strongly dependent from
struct typology/use
Explosions Max pressure,. … Pragmatic scenarios
approach
Different IM between
detonation and gas explos
Hazard analysis
Evaluation of f(IM) (probability density function) or
of G(IM) (complementary cumulative distribution
function)

O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
37
Hazard/structural typo/LS Uncertain parameters Comment/description
Earthquake/ RC frames/ULS Ec, fcc, fy (steel rebar), damping
Earthquake/steel frames/ULS Ey, fy, damping, geometry (imperfections)
Wind/steel build-bridges /SLS Damping, mass Damping is crucial
Wind/wood build /ULS Connections strength, mass
Flood/ … / ULS Permeability, mat. strength
Fire/steel/ULS Material decay, elements thickness, protective
paints, human behaviour (e.g. opening windows)
Protective paints have
strongly influence
Explosions/…./ULS High speed deformation behavior
Structural characterization
Evaluation of f(SP) (probability density function)
or of G(SP) (complementary cumulative
distribution function)

O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
38
Hazard Example of IP Exchange zone Comment/description
Earthquake Terrain inertial proprieties Foundations Soil-Structure interaction
Wind Aerodynamic coefficients,
peak factor
Near-structure air
region
Fluid-Structure
Interaction
Flood Flood pressure coefficients Before-structure
terrain morphology
Flood protection of down
flood elements
Fire Temperature conductivity,
Fire revitalization or speed
Compartment Combustible or
ventilation controlled
Explosions Reflected wave pressure
parameters
Inner-blasting
distance region
Blast amplification
Interaction analysis
Evaluation of f(IP|IM,SP) (conditional probability
density function) or of G(IP|IM,SP) (conditional
complementary cumulative distribution function).
Note: de-conditioning (if needed is made by convolution)

O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
39
Hazard/structural typo/LS EDP parameters DM parameters
Earthquake/ RC frames/ULS Interstorey drift, beams rotation No of ruptures (e.g. panels)
Earthquake/steel frames/ULS Interstorey drift, ductility demand No of ruptures (e.g. braces)
Wind/steel build-bridges /SLS Peak acceleration (occupant’ comfort) No of people feeling disease
Wind/wood build /ULS Max stress, impact energy % of envelope failure
Flood/ … / ULS Max stress, max curvature, max drag % of envelope failure
Fire/steel/ULS Max plastic deflection No of yielded elements
Explosions/…./ULS Max plastic deflection, ductility demand Amount of failed parts
Structural and damage analysis
Evaluation of f(EDP|IM,SP,IP) and f(DM|EDP)
(conditional probability density functions) or of
G(EDP|IM,SP,IP) and G(DM|EDP) (conditional
complementary cumulative distribution functions).

O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
40
Hazard/structural typo/LS DM parameters Comment/description
Earthquake/ RC frames/ULS No of ruptures (e.g. panels) Indirect and non-struct losses are critical
Earthquake/steel frames/ULS No of ruptures (e.g. braces) Indirect and non-struct losses are critical
Wind/steel build-bridges /SLS No of people feeling disease Very difficult to compute
Wind/wood build /ULS % of envelope failure ----
Flood/ … / ULS % of envelope failure ------
Fire/steel/ULS No of yielded elements Progressive collapse susceptibility
Explosions/…./ULS Amount of failed parts Amount of failed parts
Loss analysis
Evaluation of f(DV|DM) (conditional probability
density function) or of G(DV|DM) (conditional
complementary cumulative distribution function).

O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
41
O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
Common simplified version

Performance-Based Engineering (PBE): examples
dIMIMEDPEDPPLS 
+
=
0
)*()()( IMEDPPfunctionfragility =
EDP=interstorey drift (IDR)
IM
Lange D, Devaney S, Usmani A (2014). An application of the PEER performance based earthquake engineering framework to structures in fire. Engineering
Structures, 66:100–115
42
Hazard curve G(IM) Risk curve
EDP=max deflection
Jalayer, F., Franchin, P. and Pinto, P.E. (2007). A scalar damage measure for seismic reliability analysis of RC frames. Earthqk Eng. & Struct. Dyn., 36: 2059-2079.
RC frame under
Earthquake
Composite beam under Fire
IDR
G(IDR)
G(LS)
G(EDP)

Toward Multi-Hazard

44
Primary Needs and Open issues in facing multiple hazard structural problems
Zaghi EA, Padgett JE, Bruneau M, Barbato M, Li Y, Mitrani-Reiser J, McBride A (2016). “Establishing Common Nomenclature, Characterizing the Problem, and
Identifying Future Opportunities in Multihazard Design”. Forum Paper J. Struct. Eng., 2016, 142(12): H2516001.
PRIMARY NEEDS:
• Need for establishing a common nomenclature;
• Need for establishing a common framework for multi-hazard assessment and design;

45
OPEN ISSUES:
• Joining knowledge problem: the level of knowledge reached in different fields has to be joined into a unified framework of risk
assessment;
• Hazards interaction problem: interactions between different hazards are intrinsically difficult to model, both for lack or raw data
and unavailability of concurrent hazards models;
• Uniform risk problem: consists in balancing the design in order to furnish similar safety levels to different multi-hazard scenarios;
• Coherency with present: design results from the new approach should improve the current practices but not contradicting them;
• Opposite design strategy problem: design philosophies for different hazards lead very often to opposites strategies for
structural design, e.g. either reducing or increasing the flexibility and/or the redundancy.
• Hazard distribution in complex systems : in complex systems, different hazards can strike different components.
Petrini F., Palmeri A. (2012). “Performance-Based Design of bridge structures subjected to multiple hazards: a review”. Proceedings of the six International
Conference on Bridge Maintenance, Safety and Management (IABMAS2012). Stresa, Lake Maggiore, Italy, July 8-12, 2012.
PRIMARY NEEDS:

OPEN ISSUES:
assessment;
• Hazards interaction problem: interactions between different hazards are intrinsically difficult to model, both for lack or raw data
• Coherency with present: design results from the new approach should improve the current practice but not contradicting them;
• Opposite design strategy problem: design philosophies for different hazards lead very often to opposites strategies for bridge
structures, e.g. either reducing or increasing the flexibility and/or the redundancy.
46
PRIMARY NEEDS:

47
Hazards interaction problem (Hazard interaction Levels)
Interactions between different hazards are intrinsically difficult to model, both for lack or raw data and unavailability of concurrent
hazards models;
.
Hazard
interaction
levels
Level I (Nature)
Hazard Triggering
Second Hazard Altering

48
Hazards interaction problem (Hazard interaction Levels)
Interactions between different hazards are intrinsically difficult to model, both for lack or raw data and unavailability of concurrent
hazards models;
.
Hazard
interaction
levels
Level I (Nature)
Level II (Effect)
Hazard Triggering
Second Hazard Altering
Changing vulnerability
(Hazard chain)

49
Hazards interaction problem (Hazard interaction typologies)
We can have the following interaction typologies in term of actions (Level I) and effects (Level II)
1. (almost) Independently Occurring Hazards. This is the case where different hazards strike the structure, but they can be
considered as independent.
2. Concurrently Interacting Hazards. This is the case where different hazards striking the structure cannot be considered as
mutually independent due to the fact that intensity levels or effects for different hazards are strictly correlated.
3. Hazard Triggering or Chains. The third case is where different hazards strike the structure in sequence. In this situation, each
hazard produces loads acting on the structure. The second hazard can be triggered by the previous one, or the first set of
actions may damage the system, so that the structural performance is modified when the second set of actions strike.

50
Example (LEVEL I), the occurrences of Wind and Earthquake can be evaluated separately (i.e. no mutual interactions between the intensity
or directions of the two hazards that occur individually).
Example (LEVEL II), the effects of wind and earthquake can be evaluated separately (i.e. wind can cause damage on non-structural elements
of roof, which pratically does not influences earthquake-induced effects.

51
Example (LEVEL I): interaction between Wind and Waves for bridges with piers located in the sea. The intensity and direction of one hazard
influences the other one.
Example (LEVEL II). Earthquake and Snow loads can sumup their effects on columns

52
Example (LEVEL I): interaction between Wind and Waves for bridges with piers located in the sea. The intensity and direction of one hazard
influences the other one.
Example (LEVEL II). Earthquake and Snow loads can sumup their effects on columns
Example (LEVEL I): Earthquake-induced Avalanches.
Example (LEVEL II). In hurricanes Debris can impact the envelope of a structure, then changing its aerodynamics with respect to Winds

53
O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
Hazard interaction problem. PBE for multiple hazards (MH-PBE)

54
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
(Considering
concurrence
between hazards) Interaction
analysis
Structural analysis Damage
analysis
Loss analysis
IM: intensity
measures
IP: interaction
parameters
EDP: engineering
demand parameters
DM: damage
measures
DV: decision
variables
Select
O, De
O: location
De: design
Environment
info Decision-
making
De
f(SP|De)
f(SP)
Structural
characterization
SP: structural
parameters
Structural
system
info
De(DM)
In case of hazards chain
Hazard analysis
(considering
concurrence and
triggering between
hazards)

55
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
(Considering
concurrence
analysis
analysis
Loss analysis
IM: intensity
measures
IP: interaction
parameters
EDP: engineering
demand parameters
DM: damage
measures
DV: decision
variables
Select
O, De
O: location
De: design
Environment
info Decision-
making
De
f(SP|De)
f(SP)
Structural
characterization
SP: structural
parameters
Structural
system
info
De(DM)
Hazard analysis
(considering
concurrence and
triggering between
hazards)
1.Independently Occurring Hazards.
Example: wind and earthquake.
2.Concurrently Interacting Hazards.
Example: wind and waves for bridges with piers located in the sea.
3.Hazard Chains.
Example: earthquake-damaged structures subjected to earthquake-induced fires.
Type of Hazard interactions

56
1.Independently Occurring Hazards.
Example: wind and earthquake.
2.Concurrently Interacting Hazards.
Example: wind and waves for bridges with piers located in the sea.
3.Hazard Chains.
Example: earthquake-damaged structures subjected to earthquake-induced fires.
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
(Considering
concurrence
analysis
analysis
Loss analysis
IM: intensity
measures
IP: interaction
parameters
EDP: engineering
demand parameters
DM: damage
measures
DV: decision
variables
Select
O, De
O: location
De: design
Environment
info Decision-
making
De
f(SP|De)
f(SP)
Structural
characterization
SP: structural
parameters
Structural
system
info
De(DM)
Hazard analysis
(considering
concurrence and
triggering between
hazards)
ENVIRONMENT
Hurricane
action
Original
structure
Non
environmental
actions
STRUCTURAL SYSTEM
Structure-
Environment
Interaction
Wind
(Aeolian hazard)
Water bodies
(Flood hazard)
Modified
structural
systemSources of
windbornedebris
(Windborne
debris hazard)
Rain
(Rainfall hazard)
W
F
D
RA
IM S
A
SPIP
EXCHANGE ZONE
= Interaction= It results
Site-specific
Hazard
= Uncertaintypropagation
Developed in collaboratio
Michele Barbato, Louisiana State UniW, F, D, RA = Intensity Measure vectors for individual hazards,
S, A = vector of stochastic parameters describing the structural system
Hazard interaction problem. PBE for multiple hazards (MH-PBE), Hurricanes

Barbato, M., Petrini, F., Ciampoli, M. 2011. A preliminary proposal for a probabilistic Performance-Based Hurricane Engineering framework. Proceedings of the 2011 Struc-tures Congress, Las
Vegas, USA, 14-16 April 2011.
Chained Windborne debris
and Wind hazards

Loss Analysis (MCS)
PBHE– with or without hazard chain effect
Description of Benchmark Structure
Analysis methodology
Residential development with 201 wood gable roof
structures
Roof cover is considered as debris sources &
windows and glass doors are considered debris
impact vulnerable components.
58

OPEN ISSUES:
assessment;
• Hazards interaction problem: interactions between different hazards are intrinsically difficult to model, both for lack of raw data
• Coherency with present: design results from the new approach should improve the current practice but not contradicting them;
• Opposite design strategy problem: design philosophies for different hazards lead very often to opposites strategies for
structural design, e.g. either reducing or increasing the flexibility and/or the redundancy.
59
PRIMARY NEEDS:

Opposite design strategy problem: Wind Vs Earthquake
Nakai M, Hirakawa K, Yamanaka M, Okuda H, Konishi A (2013). Performance Based wind resistant Design for Tall Buildings in Japan. CTBUH research paper.
International Journal of High Rise buildings, 2(3). Available at http://global.ctbuh.org/resources/papers/download/2279-performance-based-wind-resistant-design-for-high-rise-structures-in-japan.pdf
An effective design
strategy for wind is the
adoption of a TMD at
the top of the building

An effective design
On the other side, classical TMDs are known of not
being very effective for earthquake performances
due to their excessive activation time

An effective design
On the other side, classical TMDs are known of not
being very effective for earthquake performances
due to their excessive activation time
Then in multi-hazard
design situations, other
(more expensive) design
solutions are preferable

63
There are fundamental differences between design methods for wind and earthquake loading. Wind-loading design is concerned with safety, but occupant
comfort and serviceability is a dominant concern. “…..”
Taranath SB (2012). Structural Analysis and Design of Tall Buildings. Steel and Composite Construction. CRC Press, Taylor & Francis Group Boca Raton , FL, USA

64
There are fundamental differences between design methods for wind and earthquake loading. Wind-loading design is concerned with safety, but occupant
comfort and serviceability is a dominant concern. “…..”
Taranath SB (2012). Structural Analysis and Design of Tall Buildings. Steel and Composite Construction. CRC Press, Taylor & Francis Group Boca Raton , FL, USA

Nikellis A., Sett K., Whittaker S. (2019). Multihazard Design and Cost-Benefit Analysis of Buildings with Special Moment–Resisting Steel Frames. J. Struct. Eng.,
2019, 145(5): 04019031
30-storey
40-storey
50-storey

Nikellis A., Sett K., Whittaker S. (2019). Multi-hazard Design and Cost-Benefit Analysis of Buildings with Special Moment–Resisting Steel Frames. J. Struct. Eng.,
2019, 145(5): 04019031
Stiff, low
fragility
Flexible, high
fragility
Flexible and stiff have
comparable fragility
Seismic fragility Wind fragility

2019, 145(5): 04019031
In order to have a reliable parameter for choosing the best design solution, we need to operate the convolution of the
fragility with the Site-specific hazard

2019, 145(5): 04019031
Expected losses + Structural construction costs during the life-cycle
Stiff design Flexible design
Charleston
Stiff is always better than flexible

2019, 145(5): 04019031
Expected losses + Structural construction costs during the life-cycle
Stiff design Flexible design
LosAngeles
Flexible is better than stiffStiff is better than flexible

70
PRIMARY NEEDS:

71
SingleHazard
Effect (site or physical impact)

72
SingleHazard

73
SingleHazard
ULSs

74
SingleHazard
Potential
interaction

Concluding Remarks
• Multi-Hazard (MH) analysis and design are complex matters, especially for the interactions between
hazards;
• Performance-Based Engineering is a promising approach for dealing with multi-hazard. It has proven
to work properly with a range of single-hazard problems, and necessary modifications to the general
procedure to take into account of the different interactions between hazard have been already
conceived;
• Extensive tests have to be conducted on different applications of the MH-PBE procedure in order to
check the reliability and coherency of the obtained results in terms of total and partial risk for a given
design solution;
• Accumulation of historical data and measures in a statistical database for the
characterization/modelling of hazard interactions is still needed
• New approaches for coherently including in the framework accidental hazards like fire and
explosions are needed

Sapienza University group references
1. Zaghi AE, Padgett JE, Bruneau M, Barbato M, Li Y, Mitrani-Reiser J, McBride A (2016). Establishing Common Nomenclature, Characterizing the
Problem, and Identifying Future Opportunities in Multihazard Design. J. Struct. Eng., 142(12): H2516001.
2. Campoli M, Petrini F., Augusti G., (2011). Performance-Based Wind Engineering: towards a general procedure. Structural Safety, 33 (6), 367-378.
3. Jalayer, F., Franchin, P. and Pinto, P.E. (2007). A scalar damage measure for seismic reliability analysis of RC frames. Earthqk Eng. & Struct. Dyn., 36:
2059-2079.
4. Lange D, Devaney S, Usmani A (2014). An application of the PEER performance based earthquake engineering framework to structures in fire.
Engineering Structures, 66:100–115
5. Petrini F., Palmeri A. (2012). “Performance-Based Design of bridge structures subjected to multiple hazards: a review”. Proceedings of the six
International Conference on Bridge Maintenance, Safety and Management (IABMAS2012). Stresa, Lake Maggiore, Italy, July 8-12, 2012.
6. Barbato, M., Petrini, F., Ciampoli, M. 2011. A preliminary proposal for a probabilistic Performance-Based Hurricane Engineering framework.
Proceedings of the 2011 Struc-tures Congress, Las Vegas, USA, 14-16 April 2011.
7. Petrini F, Olmati P, Bontempi F (2019). Coupling effects between wind and train transit induced fatigue damage in suspension bridges. Structural
Engineering and Mechanics, 70 (3): 311-324;
8. Olmati P, Trasborg P, Naito C, Bontempi F (2015).Blast resistant design of precast reinforced concrete walls for strategic infrastructures under
uncertainty. International Journal of Critical Infrastructures, 11(3):197-212;
9. Sgambi L, Garavaglia E, Basso N, Bontempi F (2014).Blast resistant design of precast reinforced concrete walls for strategic infrastructures under
uncertainty. Engineering Structures, 78:100-111
10. Olmati P, Petrini F, Bontempi F (2013). Numerical analyses for the structural assessment of steel buildings under explosions. Structural Engineering
and Mechanics, 45 (6): 803-819;
11. Gentili F, Giuliani L, Bontempi F (2013). Structural response of steel high rise buildings to fire: System characteristics and failure mechanisms.
Journal of Structural Fire Engineering, 4(1):9-26

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