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Performance-Based Hurricane Engineering
and its Application to Tall BuildingsMichele Barbato
London (UK)November 11, 2015
Associate ProfessorLouisiana State University
OUTLINE• Introduction
• Objectives
• Performance-Based Hurricane Engineering (PBHE) Framework
• Multilayer Monte Carlo Simulation (MMCS) method
• Risk Assessment of Tall Buildings
• Conclusions
INTRODUCTION• Hurricanes cause significant economic
and societal losses
• Performance-based engineering (PBE)is a rational way of assessing andreducing risk for engineering facilitiessubject to natural/man-made hazards
• Hurricanes are characterized by severalsources of uncertainties/hazard
• A general methodology is needed toassist the decision making on costeffective risk management ofstructures subject to hurricane hazard
OBJECTIVES
• Formulate a rigorous probabilistic PBHE framework
• Develop a consistent methodology for riskassessment of tall buildings
• Identify appropriate parameters and theirprobabilistic description for all analysis components
• Reduce/control economic and societal losses fromhurricanes and strong winds
• Provide guidance for performance-based design oftall buildings
PBE APPROACHES IN CIVIL ENGINEERING
• Performance-Based Earthquake Engineering (PBEE)
• Performance-Based Blast Engineering (PBBE)o Hamburger RO, Whittaker AS. Considerations in performance-based blast resistant design of steel
structures. Proceedings of AISC-SINY Symposium on Resisting Blast and Progressive Collapse; Dec. 4-5, 2003; New York, USA
• Performance-Based Wind Engineering (PBWE)o Augusti G, Ciampoli M. First steps towards Performance-based wind engineering. Performance of Wind
Exposed Structures: Results of the PERBACCO project. Florence, Italy: Firenze University Press; 2006. p. 13-20.
o Petrini F. A probabilistic approach to Performance-Based Wind Engineering (PBWE) [PhD. dissertation]. Rome (Italy): University of Rome “La Sapienza”; 2009.
o Ciampoli M, Petrini F. Performance-based Aeolian risk assessment and reduction for tall buildings. Probabilistic Engineering Mechanics. 2012;28:75-84.
o Spence SMJ, Gioffrè M. Large scale reliability-based design optimization of wind excited tall buildings. Probabilistic Engineering Mechanics. 2012;28:206-215.
o Huang M.F., Chan CM, Lou WJ. Optimal performance-based design of wind sensitive tall buildings considering uncertainties. Probabilistic Engineering Mechanics. 2012;98-99:7-16.
• Performance-Based Fire Engineering (PBFE)o Lamont S, Rini D. Performance-based structural fire engineering for modern building design.
Structures Congress 2008. p. 1-12
• Methodology based on the total probability theorem.
• Hurricanes represent “multi-hazard” scenarios.
• The multi-hazard character of hurricanes can appear inthree different ways, namely:
• Independent hazards
• Interacting hazards
• Cascading hazards (hazard chains)
PBHE FRAMEWORK
Hazard Sources1. Wind (uncertain parameters W): aeolian hazard2. Water bodies (uncertain parameters F): flood hazard3. Sources of windborne debris (uncertain parameters D): windborne debris hazard4. High rainfall rates (uncertain parameters RA): rainfall hazard
PBHE FRAMEWORKENVIRONMENT (E)
Hurricane action
Structural system
Non environmental
actions
STRUCTURAL SYSTEM (SS)
Structure-Environment Interaction
Wind(Aeolian hazard)
Water bodies (Flood hazard)
Modified structural systemSources of
windborne debris(Windborne
debris hazard)
Rain(Rainfall hazard)
W
F
D
RA
IM S
A
SPIP
EXCHANGE ZONE (I)
= Interaction= It results
Site-specific Hazard
Hazard Sources1. Wind (uncertain parameters W): aeolian hazard2. Water bodies (uncertain parameters F): flood hazard3. Sources of windborne debris (uncertain parameters D): windborne debris hazard4. High rainfall rates (uncertain parameters RA): rainfall hazard
PBHE FRAMEWORKENVIRONMENT (E)
Hurricane action
Structural system
Non environmental
actions
STRUCTURAL SYSTEM (SS)
Structure-Environment Interaction
Wind(Aeolian hazard)
Water bodies (Flood hazard)
Modified structural systemSources of
windborne debris(Windborne
debris hazard)
Rain(Rainfall hazard)
W
F
D
RA
IM S
A
SPIP
EXCHANGE ZONE (I)
= Interaction= It results
Site-specific Hazard
PBHE FRAMEWORK( ) ( ) ( ) ( )
( ) ( ) ( ) d d d d d
G DV G DV DM f DM EDP f EDP IM,IP,SP
f IP IM,SP f IM f SP DM EDP IM IP SP
= ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
PBHE FRAMEWORK( ) ( ) ( ) ( )
( ) ( ) ( ) d d d d d
G DV G DV DM f DM EDP f EDP IM,IP,SP
f IP IM,SP f IM f SP DM EDP IM IP SP
= ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
• Component losses are not independent.
• Computation of G(DV) requires the joint PDF of thecomponent losses, which is very difficult to obtain.
• A Multilayer Monte Carlo Simulation (MMCS)approach is used to estimate the loss curve.
• MMCS incorporates the uncertainties in all randomvariables involved in loss analysis (i.e., IMs, SPs, IPs,EDPs, DMs and DVs)
MULTILAYER MONTE CARLO SIMULATION (MMCS)
For each hurricane
No. ofhurricanes
per yearIM
SP
Hazard models
IP
IA parameters
EDP
SA parameters
DM
Chain effects
DA parameters
DV
LA parameters
DV per year
MULTILAYER MONTE CARLO SIMULATION (MMCS)
Sample generation (stochastic simulation) Analysis step (e.g., FE analysis, windborne debris trajectory analysis)
IA: interaction analysis; SA: structural analysis; DA: damage analysis; LA: loss analysis
Specialization for Tall Buildings
MULTILAYER MONTE CARLO SIMULATION (MMCS)
HAZARD ANALYSIS
1. Statistical description of wind velocity, V, at the location forappropriate averaging times.
Hurricane Wind Field
NOTE: used also fornon-hurricane wind
HAZARD ANALYSIS
2. Site specific statistics of fundamental hurricane parameters.
Source: Vickery and Twisdale (1995)
Hurricane Wind Field
HAZARD ANALYSIS
3. Modeling the full track of a hurricane from its initiation overthe ocean until final dissipation.
Source: Vickery et al. (2009)
Hurricane Wind Field
HAZARD ANALYSIS
( ) ( ) ( )( ) ( )( ) ( )
mx j j j
y j j
z j j
V z V z u z
V z v z
V z w z
= +
=
=
( )m 10 10j
j
zV z V
α
= ⋅
zj = quote from ground of j-th floorVm(zj) = mean wind speed at floor jV10 = wind speed at z = 10 m (10 min average)
Hurricane Wind Field
HAZARD ANALYSIS
( ) ( )( )
5232
, , 6.868
1 10.302
u u
u
v v j j u j
vu j
n S n z z n z
n zσ⋅
= +
( ) ( )( )
5232
, , 9.434
1 14.15
v v
v
v v j j v j
vv j
n S n z z n z
n zσ⋅
= +
Along wind velocity (auto-spectra)
Across wind velocity (auto-spectra)
( ){ }2 20 *6 1.1arctan ln 1.75
0.75
u
v
u
v
v
v
z uσ
σσ
= − + ⋅
=
n = current wind frequency (Hz)nu, nv = non-dimensional
height-dependent frequencies
z0 = roughness length (m)u* = shear velocity (m/s)
Cross-spectra
( ) ( ) ( ) ( ) ( ), , , , , , exp , , ,l l l l l lv v j k v v j j v v k k j kS n z z S n z z S n z z f n z z l u v = ⋅ ⋅ − =
( ) ( ) ( )m m
, , z j kj k
j k
n C z zf n z z
V z V z
⋅ ⋅ −=
+
Carassale and Solari (2006)
Di Paola (1998)
Hurricane Wind Field
1. Geometrical properties (deterministic)• Position and dimensions of openings • Dimensions of the building
2. Mechanical properties (random) • Natural period • Damping
3. Intensity of the wind effects (random) • External and internal pressure coefficients • Gust effect factor
STRUCTURAL CHARACTERIZATION
Experimental model for wind tunnel test Source: Spence et al. (2008)
Obtained either from existing literature orwind tunnel tests.
Directly measured for existing structures andcharacterized by small variability.
Obtained from vibration measures or estimatedfrom finite element models.
Turbulent Component of Wind Force( ) ( ) ( ) ( ) ( )
( ) ( ) ( )m
, , , , , 1, 2,..., ; ,
F F l ll l j k j v v j k k f
j D j j
S n z z A z S n z z A z j k N l u v
A z C Ar z V zρ
= ⋅ ⋅ = =
= ⋅ ⋅ ⋅
INTERACTION ANALYSIS
z1
z2
zn
.
.
.
.
.
zj
B
h Ar(zj)
CD = coefficient of dragρ = density of airAr(zj) = exposed wind tributary area for the j-th floor
Mean of aerodynamic drag (CD) and lift (CL) coefficients vs. θSource: Ciampoli and Petrini (2012)
INTERACTION ANALYSISAcross Wind Force due to Vortex Shedding
( ) ( )( )
( )( )
22 0.50 3
1 22 22 2 2 2
1 2
( ), , 11 1.56 1
v v
jF F j j
z H C n C nS n z z A An n C n n C n
σ ′ = + −
− + − +
2 2
0.118 0.358 0.214 0.066 0.26 0.894H D D D DAB B B BS
= ⋅ − + − + − +
( )jzσ
B = width of the building
= root mean square of the across wind force at floor j
D = length of the building S = area of cross sectionH = height of the buildingδ = function of aspect ratio Source: Liang et al. (2002)
( ) ( ) ( )2
, , , , , , expv v v v v vF F j k F F j j F F k kS n z z S n z z S n z z
δ Δ ′ ′ ′= ⋅ ⋅ −
j kz zB−
Δ =
INTERACTION ANALYSISWind Pressure on Cladding
( ) ( ) ( )w j j p pip z q z GC GC= ⋅ −
( ) ( ) 23 sec
12j j ztq z K z K Vρ −= ⋅ ⋅ ⋅
Cp = external pressure coefficientCpi =internal pressure coefficientV3-sec = 3-second gust wind speedKzt = topographic factorα, β = parameters depending on the type of terrain at the building location
( )2
0
jj
zK z
z
αβ
=
Displacement and Acceleration Cross-Power Spectral Density Functions
( ) ( ) ( ){ }( ) ( ) ( ){ }
* T T
1 1
4 * T T
1 1
( ) ( ) ( ) ( , )
( ) ( ) ( ) ( , )
l l l l
l l l l
N N
D D q p q q F F p pp q
N N
A A q p q q F F p pp q
S n H n H n S n l u v
S n n H n H n S n l u v
′ ′
= =
′ ′
= =
= ⋅ ⋅ Φ ⋅Φ ⋅ ⋅ Φ ⋅Φ =
= ⋅ ⋅ Φ ⋅Φ ⋅ ⋅ Φ ⋅Φ =
EDPs commonly selected for engineered buildings1. Interstory drifts in the along wind and across wind directions 2. Floor accelerations in the along wind and across wind directions
STRUCTURAL ANALYSIS
2 2 2
1 1( )4 2q
q q q
H nn n i n nπ ξ
= ⋅ − + ⋅ ⋅ ⋅
Φq = mode shape for q-th mode of vibration
STRUCTURAL ANALYSIS
( ) ( ) ( ) ( ) ( ) ( ) ( )1
2 2,p m m 1 12 cov ,
u u j u ju j j j I u j u jD z D z
I z D z D z g D z D zσ σ−
− − = − + ⋅ + − ⋅
Peak interstory drift along wind direction
( ) ( ) ( ) ( ) ( )1
2 2,p 12 cov ,
v v j v jv j I v j v jD z D z
I z g D z D zσ σ−
− = ⋅ + − ⋅
Peak interstory drift across wind direction
( ) ( ),p ( , )l l j
l j A A zA z g l u vσ= ⋅ =
Peak floor acceleration
( )( )
( )
windwind
wind
0.5772ln2ln
12ln
r
r
g
g
TT
T
μ ηη
πση
= ⋅ +⋅
=⋅
Peak factor Davenport (1983)
Building Loss Estimation Approaches(1) Component-based loss estimation
• Building-specific damage and loss estimation proceduresdeveloped at the component level
• Each building component is assigned a fragility function
• Time consuming and computationally expensive
(2) Story-based loss estimation
• Components of each floor of the building are categorized
I. Structural drift-sensitive components
II. Non-structural drift-sensitive components
III. Non-structural acceleration-sensitive components
IV. Pressure-sensitive cladding
DAMAGE ANALYSIS
Serviceability Limit States(1) No generally accepted international standards for comfort
criteria in tall building design.
(2) Motion perception based on acceleration amplitude and thepredominant natural frequency of the building.
DAMAGE ANALYSIS
Comparison of occupant comfort serviceability criteria for a one-year wind storm
return period (source: Kwok et al. 2009)
Evaluation curves for wind-induced vibrations in building in horizontal direction for one-year return
period in ISO 10137.
Serviceability loss due to non-hurricane winds1. Examine whether yearly maximum wind caused exceedance of
human discomfort threshold
2. Assume linear relation between wind velocity and peak flooracceleration
3. Calculate minimum threshold velocity that causes humandiscomfort by scaling down the yearly maximum wind velocity
4. Generate the mean value of daily maximum wind velocities fromthe joint probability distribution of yearly maximum wind velocityand mean daily maximum wind velocity
5. Generate randomly daily maximum wind velocities for specific one-year simulation using a lognormal distribution truncated at theupper tail in correspondence to the yearly maximum wind velocity
DAMAGE ANALYSIS
6. Estimate the number of days during which the daily maximum windvelocity is higher than the minimum threshold velocity
7. Assume that business on a particular floor is interrupted for a day ifthe daily acceleration response is greater than the humandiscomfort threshold value
8. Estimate annual loss due to business interruption for each floorbased on number of days of closure
9. Calculate total loss due to non-hurricane winds by adding up all thefloor losses due to damage of different components and to businessinterruption
DAMAGE ANALYSISServiceability loss due to non-hurricane winds
NOTE: for hurricane winds, the serviceability losses are estimated byassuming that the entire building is closed when storm-level winds areactive at the location of the building
• DV is commonly chosen as the repair cost or the total cost of thestructural system during its design lifetime.
• Losses are broadly classified into “direct” or “indirect” losses.
• Direct losses
o Losses due to damaged components.
o Losses related to serviceability limit state.
o Losses related to work disruption or to the discomfort ofbuilding occupants due to wind-induced vibrations.
• Indirect losses
o Losses due to negative publicity and perception of lack of safetyfor the building which has shown excessive vibrations.
LOSS ANALYSIS
Structure Height H = 305 m Lengths D = B = 50 m Floors = 74 Total value: $329M
Finite element model of the target building: (a) 3D frame on the external perimeter; (b) bracing system; and (c) central core.
CASE STUDY
Location : Miami, Florida Exposure Type : B
Modeled using STAAD.Pro v8i
Hazard Analysis
CASE STUDY
• Hurricane wind
• Non-hurricane wind
Daily maximum 3-second wind speeds at thebuilding location obtained from the (IowaEnvironmental Mesonet (IEM) database for the1962-2013 period.
Historical hurricane tracks that passed within a250 miles radius from the site during the same1962-2013 period from the National Oceanicand Atmospheric Administration (NOAA)database and used to separate the non-hurricane wind speeds from the hurricanewind speeds
• Wind velocity (V)• Roughness length (d) : Lognormal distribution with mean value
of 0.1m and COV of 0.03
CASE STUDY
Number of hurricanes per year was simulated using a Poisson occurrence model(occurrence rate from IEM).
Recorded yearly maximum non-hurricane 10-minute wind speedswere fitted to a log-normaldistribution, with a mean of 19.3m/s and standard deviation of1.15 m/s.
Hazard Analysis
CASE STUDY
Mode Frequency (Hz)First 0.185
Second 0.587
Third 1.082
Fourth 2.057
Fifth 2.652Sixth 3.293
Structural Characterization• Structural damping (ξ)
Lognormal distribution with mean value of 0.02 and COV of 0.4
Interaction Analysis• Along wind force • Across wind force
1. Mean wind force2. Turbulence effect
1. Turbulence effect2. Vortex shedding
PSD function for wind forces: (a) along wind direction, and (b) across wind direction.
(a) (b)
CASE STUDY
Structural Analysis
2 2 20 0
1 1( )4 2dj
j j j
H ff f i f fπ ξ
= ⋅ − + ⋅ ⋅
f0j = undamped frequency for j-th mode
f = wind frequency
PSD function for floor displacements: (a) along wind direction, and (b) across wind direction.
(a) (b)
CASE STUDY
2
2 20 0
( )2aj
j j j
fH ff f i f fξ
−= − + ⋅ ⋅
f0j = undamped frequency for j-th mode
f = wind frequency
PSD function for floor acceleration: (a) along wind direction, and (b) across wind direction.
(a) (b)
CASE STUDY
Structural Analysis
CASE STUDY
Structural Analysis
Damage Analysis
Fragility curves for different component groups: (a) structural drift-sensitive, (b) non-structural drift-sensitive , and (c) non-structural acceleration-sensitive.
(a)
(b) (c)
CASE STUDY
Loss Analysis
CASE STUDY
CONCLUSIONS• A PBHE framework based on the Total Probability
Theorem is proposed.
• PBHE is built on methodologies already developed andused in other civil engineering subfields.
• This methodology can be used to evaluate thestructural risk for facilities in hurricane prone regions.
• The PBHE framework is illustrated for tall buildings.
• For the example presented, serviceability losses andlosses for acceleration-sensitive components arepredominant.
Thank you!
Questions?