1 INTRODUCTION

Performance-based wind engineering (PBWE) is a new branch of Performance-based engineering gain-ing interest in the last years, aiming at the perfor-mance assessment of structures subject to wind ac-tions. The central objective is the assessment of the adequacy of the structure through the probabilistic description of a set of decision variables (DVs). Each DV is a measurable attribute that represents a specific structural performance, which can be de-fined in terms of the interest of the users or the soci-ety. Thus, the problem of risk assessment is dis-aggregated into different elements: site and struc-ture-specific hazard analysis; structural characteriza-tion; interaction analysis; structural analysis; damage analysis; loss analysis.

Considering the last two risk assessment elements (damage and loss analysis), even though there is a great deal of literature on Performance Based Design (PBD) in earthquake engineering, but also, for ex-ample, in hurricane engineering, these elements have not been investigated thoroughly in the PBWE for non-hurricane winds. Especially with regard to the serviceability assessment of structures under wind, additional research efforts are needed in order to complete the PBWE procedure.

In a first step, appropriate criteria need to be de-fined in order to characterize the uncertainty affect-ing the response thresholds assumed for the evalua-tion of the serviceability levels. This is particularly difficult in the evaluation of the building residents comfort )Kwok et al 2009). In addition, the monetary

quantification of the loss of serviceability is re-quired. In the authors’ knowledge this aspect is, at the moment, poorly treated in literature on tall build-ing serviceability under wind action.

Aim of this paper is to investigate the role of damage and loss analysis in the PBWE. Starting from a focused literature review on the topic in other fields, and on the basis of critical analysis and syn-thesis, a conceptual framework is presented, not only for safety, but also for the serviceability assessment of structures under wind loads.

The paper is organized as follows: Section 2 pro-vides an overview of PBWE and wind related risks in general. Section 3 focuses on the damage and loss evaluation in PBD and some critical considerations for the extension to PBWE. Section 4 builds on the existing PBWE procedure, expanding it for what re-gards damage and loss evaluation, while Section 5 pro-vides indications for further research.

2 AN OVERVIEW OF PERFORMANCE-BASED WIND ENGINEERING

A procedure for PBWE is provided in Petrini (2009) and Ciampoli et al (2011) extending the approach proposed for Performance-Based Seismic Design (PBSD) by the researchers of the Pacific Earthquake Engineering Research Center (PEER) – see for ex-ample Porter (2003). In this approach, PBWE is tackled in probabilistic terms, due to the stochastic nature of both the resistance and loading parameters. The procedure for PBWE, here briefly reported,

Damage and loss evaluation in the performance-based wind engineering

F. Petrini, K. Gkoumas & F. Bontempi School of Civil and Industrial Engineering, Sapienza University of Rome, Italy

ABSTRACT: Aim of this paper is to investigate the role of damage and loss analysis in the PBWE. Starting from a comprehensive literature review on the topic in other fields, and on the basis of critical analysis and synthesis, a conceptual framework is presented, not only for safety, but also for the serviceability assessment of structures under wind loads. First, appropriate criteria need to be defined in order to characterize the uncer-tainty affecting the response thresholds assumed for the evaluation of the serviceability levels. This is particu-larly difficult in the evaluation of the building residents comfort. Second, the monetary quantification of the loss of serviceability is required. In the authors’ knowledge this aspect is, at the moment, poorly treated in the literature on tall building serviceability under wind action.

considers performances related to safety or function-ality and comfort, and consists of the following steps: defining the Aeolian hazard at the site, in terms of

the parameters of a specific model of the wind ve-locity field;

defining the models of the wind-structure interac-tion phenomena and their relevant parameters;

analysing the structural response, mainly in the context of stochastic dynamics;

defining and evaluating indicators of the structur-al damage, that influences the considered perfor-mances;

defining the decision variables that are appropri-ate to quantify the performances required for the structure, mainly in terms of consequences of damage (personal damages, restoration costs, costs due to loss or out-of-service, variations of users comfort, etc.);

evaluating the structural risk on the basis of the probabilistic characterization of the decision vari-ables;

optimizing design, that is minimizing risk, by ap-propriate techniques of decision analysis. The assessment of the Aeolian hazard requires the

use of accurate models of the wind actions on a rigid or a slender structure, and the choice of a set of in-tensity parameters (IMs) that are sufficient and effi-cient to describe the site-specific hazard (Luco & Cornell 2007). Each IM must be chosen by consider-ing the characteristics of the wind actions and the relevant features of the construction site (mean ve-locity, turbulence, direction etc.), the structural properties and the interaction phenomena (wind tur-bulence, vortex shedding, aeroelastic phenomena, aerodynamic effects).

Probabilistic modelling of the wind-structure in-teraction phenomena implies the choice and proba-bilistic characterization of a set of interaction pa-rameters (IPs), that allow taking into account the relevant aspects of the interaction between the envi-ronment and the structure: proper examples of IPs are the aerodynamic coefficients and the aeroelastic derivatives.

In addition, probabilistic modelling of the struc-tural response requires the choice of the relevant random structural parameters (SPs) and engineering demand parameters (EDPs), like the inter-storey drift, the acceleration and velocity at selected points, the stresses and displacements, etc.The damage evaluation requires the choice (and probabilistic characterization) of the damage parameters (DMs) that are able to quantify the structural damage due to wind actions that influences the considered perfor-mance. The choices of any EDP and DM are strong-ly dependent on the considered structural type and performances. Different parameters can be assumed as potential DMs: they can be defined by one or a combination of relevant EDPs (e.g. the inter-storey

drift), or by other parameters, representing, for ex-ample, the damage to the partitions and claddings in a building as a function of the inter-storey drift.

The decision variables (DVs), that quantify the performance objectives, must distinguish between low and high performance levels (Augusti & Ciam-poli 2008): low performance levels imply possible consequences on structural integrity and personal safety (e.g. partial or total collapse, permanent dam-ages); high performance levels are related to the oc-cupant comfort or the structural serviceability, and, in case of buildings, to inconvenient alterations of the wind field in pedestrian areas around the con-struction (Stathopoulos 2006).

Regarding low performance levels, a significant DV is the cost necessary to restore the construction to the undamaged state (or rebuild it in case of col-lapse); accordingly, the corresponding DM is the set of damages to be restored, and the EDPs are the more significant response parameters for the specific case (peak displacement or acceleration at the build-ing top, overall action at the base, local pressures, etc.). A shortcoming of this definition is the impos-sibility of including the “intangible” losses, i.e. the losses that cannot be measured in “monetary” terms (loss of human life or cultural and architectural val-ues, etc.).With respect to high performance levels, crucial DVs are the peak displacements, velocities and accelerations at selected points, although the problem of defining proper measures of the wind-induced discomfort in a building and the surround-ing area have not yet found a satisfactory solution. Moreover, if the risk assessment is referred to the whole life-cycle of the construction, the effects of deterioration shall be considered, e.g. by varying the values of the parameters of the probability density function of the structural properties (SPs).

The structural risk is defined as the probability of exceeding a threshold level of the relevant DV:

SPIPIMSP

SPIMSP

ddddEDPDMdf

f,f,,EDPf

EDPDMfDMDVGDVG

IMIPIPIM (1)

Where: G(·) is the complementary cumulative distribution function and G(·|·) the conditional com-plementary cumulative distribution function; f(·) is the probability density function, and f(·|·) the condi-tional probability density function; DM is a proper damage measure; EDP is an engineering demand pa-rameter; the basic parameters characterizing the Ae-olian hazard, the interaction phenomena and the structural systems and non-environmental actions are described respectively by the vectors IM, IP and SP.

In Equation 1, IM and SP are assumed as uncor-related and independent on IP, while IP is depend-ent on both IM and SP.

By means of Eq. (1), the problem of risk assess-ment is disaggregated into the following tasks: site and structure-specific hazard analyses, that is,

the assessment of the probability density func-tions f(IM), f(SP) and f(IP|IM, SP);

structural analysis, aimed at assessing the proba-bility density function of the structural response f(EDP|IM, IP, SP) conditional on the parameters characterizing the wind field and the structural properties;

damage analysis that gives the damage probabil-ity density function f(DM|EDP) conditional on EDP;

finally, loss analysis, that is the assessment of G(DV|DM). The flowchart of the procedure, that is the exten-

sion to PBWE of the flowchart reported in Porter (2003) is depicted in figure 1 (Petrini & Ciampoli 2012).

Practical applications of the PBWE framework are presented in Petrini & Ciampoli (2012) for the serviceability assessment of high-rise buildings and in Petrini et al (2010) for the safety assessment of offshore wind turbines.

3 DAMAGE AND LOSS ANALYSIS IN THE PBD FOR WIND

In the classical Performance Based Design, damage analysis uses EDPs to determine damage measures from which repair or replacement costs can be esti-mated. The loss analysis involves the determination of (usually) direct financial losses to the structure and its contents. Thus, in general, costs are related to the loss of safety or performance, and commonly are divided in structural or non-structural and in indirect

or indirect. Damages are either independent or de-pendent on each other. Also, it is common to have interrelationships between damage and losses for different components (Deierlein 2004), meaning that a certain cost can be associated either to the repair of certain element or to the damage of others. Structur-al costs range from direct damage to the structural parts to psychological damage to the people. Kanda and Shah (1997) provide a list of structural failure related costs. Serviceability and Safety performance criteria are identified in Simiu (2009), together with roots for the uncertainty of wind induced losses: the uncer-tainties in the estimation of extreme wind speeds, the aerodynamic effects, and the ultimate capacities of structural and architectural engineering components, connections, and assemblies. What emerges is the difficulty to calculate wind-induced losses, due to the different loss models and the different assump-tions.

This section focuses on the (recent) literature on damage and loss analysis in the PBD for wind, con-sidering two different cases: hurricane and non-hurricane winds. As it will be further explained in the Section 4, the first case is mostly applied for safety-related performances, and the second for ser-viceability.

3.1 Hurricane wind damage and loss

Hurricane damage and loss analysis research fo-cuses on residential buildings, and is often treated in combination with other phenomena (surge, inunda-tion, etc.). Yazdani et al (2010) on the basis of a large database of inspections, identify common defi-ciencies for residential buildings in the US to storms and their principal causes.

Figure 1 Flowchart of the PBWE procedure.

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

Aerodynamicanalysis

Structural analysis Damage analysis Loss analysis

IM: intensity measures

IP: interaction parameters

EDP: engineering demand parameter

DM: damage measure

DV: decision variable

SelectO - D

O: location

D: design

Environment information

Decisional strategy

D

f(SP|D)

f(SP)

Structural system characterization

SP: structural system parameters

Structural system information

Most damage models in literature use fragility or vulnerability curves to estimate probable damage for a given hazard. Filliben et al (2002) discuss fragility curves and damage matrices for the wind induced loss estimation, for different states of dependence between damage states. Lee & Rosowsky (2004) de-velop a fragility model for assessing the response of roof sheathing for low rise wood frame structures subject to extreme wind loading, which could be used for structural and economic loss estimation. Li and Ellingwood (2006) discuss extensively the role of uncertainties in hurricane damage, and provide fragility curves for different structural and non-structural components.

Li et al (2012) present and apply a method for es-timating loss from wind and surge in hurricanes in residential buildings, using historical data for the correlation between hurricane and surge. Both struc-tural (based on the fragilities of the structural com-ponents) and non-structural losses (based on the amount of rainwater entering the building as a result of pressure on panel loss) are accounted for, and mitigations measures are considered (e.g. by raising the building elevation).

Dao et al (2012) obtain the damage probability and the resulting loss due to hurricane debris impact (specifically roof sheathing panels to windows), in-cluding the location and approximate timing of the impacts.

At a system level, Dueñas-Osorio (2012) develop a framework that compares human risk perception and engineering estimates of risk, focusing on the evacuation behavior in storm-prone residential areas (in particular shadow evacuation). The risk of storm surge damage is evaluated on the basis of inundation (storm surge) damage for the single household, ac-counting also for non-structural damage.

Legg et al (2010) summarize different hurricane probabilistic loss estimation methods, and provide a new method that uses a mixed-integer linear pro-gram to select a reduced set of hurricanes from a candidate set and to determine the hazard-consistent annual occurrence probability.

Hurricane wind losses can be part of a multi-hazard assessment. Li (2012) propose a framework based on the lifecycle cost-benefit analysis for the hazard mitigation of multiple hazards (hurricane and earthquake) and apply it to a wood-frame residential construction. Garciano & Koike (2007) propose and apply a Performance Based Design for the design of wind turbines in typhoon and earthquake-prone are-as.

3.2 Non-hurricane wind damage and loss

The biggest issue for non-hurricane winds is the loss of serviceability in terms of comfort for the building occupants due to excessive vibrations. This is some-thing non rare, especially for high-rise buildings

(lack of comfort for building residents) and for sus-pension or cable-stayed bridges (temporary closure of the bridge to the users). In these cases damage and loss evaluation is not trivial and is very poorly investigated in literature. The problem arises with the difficulty of quantifying the losses since it is not easy to consider all possible loss aspects.

Just to make an example, it is possible to calcu-late the direct losses, estimating the closing hours of (usually different classes) vehicles for a long span bridge, and consequently the direct losses, however, indirect long term losses (e.g. due to bad publicity), that have a protracted effect, is something of diffi-cult assessment. The same applies for the rehabilita-tion and upgrade of an existing structure: in a cost-benefit analysis, it is not easy to consider also the indirect gains.

That said, principal literature focuses on the “loss” of comfort in high rise buildings, applying some threshold rule, without arriving at the defini-tion of a proper “loss function”.

Smith & Caracoglia (2011) calculate the perfor-mance loss probability of a tall building by means of Monte Carlo simulation, using wind data, and focus-ing on lateral drift values (maximum lateral dis-placements). Their application focuses on different cases, including human comfort/occupancy condi-tions and potential damage to secondary non-structural systems.

Huang et al (2012) focus on the damage and loss evaluation for the occupant comfort in tall buildings, in terms of lateral deflection and excessive vibra-tions, and provide a multi-step optimization algo-rithm, subject to the deterministic (drift) and proba-bilistic (occupant comfort) performance-based constraints. An application on a 60-story building is presented.

Petrini & Ciampoli (2012) assess the comfort re-quirements of a 74-story building in terms of the probability of not exceeding certain thresholds of the across-wind acceleration at the top of the building. In calculating the annual probabilities of exceeding human perception vibrations thresholds, however, no loss model that accounts for monetary losses is pro-vided.

4 CONSIDERATIONS FOR AN EXTENSION OF THE PBWE FRAMEWORK

The estimation of possible losses after a harmful event or a disaster is fundamental in the design phase of structures and infrastructures, also for fi-nancial and insurance issues. However, this calcula-tion is extremely trivial and of difficult implementa-tion. This is due to several factors: one is the scale of the problem. In fact, it is different when a single structure is considered, and when we consider an aggregate of structures. Another issue is the difficul-

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5 CONCLUSIONS

Since this study merely outlines an extension of the PBWE for what regards damage and loss analysis, no proper conclusions are reached.

The authors intend to apply findings from the lit-erature review to a high-rise building, focusing on the serviceability (comfort) under non hurricane winds, explicitly accounting for the improvement (retrofitting) costs.

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