performance-based hurricane engineering and its

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

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


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


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)


HAZARD ANALYSIS

3. Modeling the full track of a hurricane from its initiation overthe ocean until final dissipation.

Source: Vickery et al. (2009)


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)


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)


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?

performance-based hurricane engineering and its

Documents