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CIVIL 706 � Seismic Risk Analysis EDCE-EPFL-ENAC-SGC 2016 -1-

EDCE: Civil and Environmental Engineering CIVIL 706 - Advanced Earthquake Engineering

Seismic Risk Analysis


Content

•  Framework

•  Hazard assessment

•  Vulnerability

•  Exposure

•  Risk computation

•  Conclusions


References � Risk-OFEV project •  Karbassi A. and Lestuzzi P. (2014) Seismic risk for existing buildings

in Switzerland – development of fragility curves for masonry buildings, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, report prepared under contract to the Federal Office for the Environment (FOEN), 56 p.

•  Jamali N. and Kölz E. (2015) Seismic risk for existing buildings in Switzerland – framework for risk computation, Risk&Safety AG, Gipf-Oberfrick, Switzerland, report prepared under contract to the Federal Office for the Environment (FOEN), 82 p.


Elements of seismic risk analysis •  Risk = Hazard x Vulnerability x Consequences

31st January 2012 3

Seismic Risk for Existing BuildingsDevelopment of a framework for the probabilistic risk computation

Figure 1: Elements of risk analysis


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Seismic Risk for Existing Buildings

Framework for Risk Computation

Figure 2: Rock hazard curves for Zurich (ETH), Basel and Sion OT at 1 Hz

10-2 10-1 100 101 10210-4

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10-1Rock Hazard Curves for Zurich at 1 Hz

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10-1Rock Hazard Curves for Basel at 1 Hz

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10-1Rock Hazard Curves for Sion OT at 1 Hz

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Figure 3: Rock hazard curves for Zurich (ETH), Basel and Sion OT at 5 Hz

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10-1Rock Hazard Curves for Zurich at 5 Hz

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10-1Rock Hazard Curves for Basel at 5 Hz

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10-1Rock Hazard Curves for Sion OT at 5 Hz

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Seismic hazard assessment •  Rock hazard curves



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Figure 4: Rock hazard as a function of frequency for Zurich (ETH), Basel and Sion OT

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10-1Median Hazard Curves for Zurich at SED Rock

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10-1 Median Hazard Curves for Basel at SED Rock

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10-1 Median Hazard Curves for Sion OT at SED Rock

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Figure 5: Rock uniform hazard spectrum for a return period of 500, 2'500 and 10'000 years

0.1 1 10 1000.1

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10Rock Uniform Hazard Spectrum for an annual probability of exceedance of 2.00E-03 (500 year return period)

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Seismic hazard assessment •  Site effect

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2.4 Site effects

Probabilistic seismic hazard analysis (PSHA) has been done to compute the rock hazard. To consider site effects, for each site an amplification factor has been provided (Figure 6). Beside the aforemen-tioned three sites an amplification factor is provided for an extra location with deep unconsolidated deposits in the Rhone valley (hereafter called Sion TE).

Figure 6: Amplification factors (Camp) for frequencies between 0.1 and 10 Hz

It must be taken into consideration that the provided amplification factors are computed for low acceleration levels. Nonlinearities have not been considered in computing them. Applying a constant amplification factor over the whole range of spectral acceleration leads to an overestimation of the expected accelerations (and displacements) at the surface. To avoid unrealistic ground motions, the nonlinear response of the sites has been considered.

To this end some de-amplification factors (Cdeamp) are calculated based on [ASCE 41-06, 2007]. They are documented in Table 1. Note that two series of factors are given. For risk assessment of bench-marks with periods of vibration shorter than 1 second (short period), de-amplification factors from the upper table are used. For benchmarks with long period of vibration (larger than 1 second) the factors from the lower table are used.

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Amplification functions

Zurich

Basel

Sion OT

Sion TE


Seismic hazard assessment •  Soil spectrum

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Figure 7: Soil hazard as a function of frequency for Zurich (ETH), Basel, Sion OT and Sion TE

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10-1 Median Hazard Curves for Basel Soil (Surface)

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Seismic hazard assessment •  Soil UHS

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Figure 8: Soil uniform hazard spectrum for a return period of 500, 2'500 and 10'000 years

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Soil Uniform Hazard Spectrum for an annual probability of exceedance of 2.00E-03 (500 year return period)

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Soil Uniform Hazard Spectrum for an annual probability of exceedance of 4.00E-04 (2500 year return period)

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Seismic hazard assessment •  EMS-Intensity hazard curves

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Figure 9: EMS-I hazard curves for Zurich (SED and Faenza models), Basel (SED model), Sion OT (SED model) and Sion TE (SED and Faenza models)

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10-1EMS-I Hazard Curves for Sion OT (SED Model)

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Vulnerability in terms of EMS-Intensity •  Risk-UE LM1 - Typology 418 Bull Earthquake Eng (2006) 4:415–443

Table 1 Proposal for aEuropean building typologyclassification

Typologies Building types

Unreinforced Masonry M1 Rubble stoneM2 Adobe (earth bricks)M3 Simple stoneM4 Massive stoneM5 U Masonry (old bricks)M6 U Masonry – r.c. floors

Reinforced/confined masonry M7 Reinforced/confined masonryReinforced Concrete RC1 Concrete Moment Frame

RC2 Concrete Shear WallsRC3 Dual System

The proposed classification system, essentially corresponds to that adopted byEMS-98 (Grunthal 1998), apart from the inclusion of reinforced concrete dual systemtypology RC3 and for the introduction of sub-typologies. In particular, the type ofhorizontal structure has been considered for masonry buildings: wood slabs, M_w,masonry vaults, M_v, composite steel and masonry slabs, M_sm, reinforced concreteslabs M_ca. Pilotis sub-typology (RC_p) has been introduced to take into consider-ation, for all RC typologies, vertical irregularity, often leading to soft-storey collapsemechanisms, while the presence of effective infill-walls has been considered onlyfor reinforced concrete frame typology (RC1_i). For all building typologies threeclasses of height have been considered (_L = Low-Rise, _M = Mid-Rise, _H = High-Rise) differently defined in terms of floor numbers for masonry (_L = 1/2, _M = 3/5,_H = ≥6) and reinforced concrete buildings (_L=1/3, _M = 4/7, _H = ≥8). For buildingsdesigned according to a seismic code the following have been considered: the levelof seismic action depending on seismicity (_I = zone I, _II = zone II, _III = zone III);the ductility class, depending on the prescription for ductility and hysteretic capac-ity (−WDC = without ductility class, −LDC = low ductility class, −MDC = mediumductility class, −HDC = high ductility class).

3 The macroseismic method

The macroseismic method allows the vulnerability assessment for a differently numer-ous set of buildings, up to the vulnerability assessment for a single building.

Vulnerability is measured in terms of a vulnerability index V and of a ductilityindex Q, both evaluated taking into account the building typology and its construc-tive features.

The hazard is described in terms of the macroseismic intensity, according to theEuropean macroseismic scale EMS-98, which is considered, in the framework ofthe macroseismic approach, as a continuous parameter evaluated with respect to arigid soil condition; possible amplification effects due to different soil conditions areaccounted for inside the vulnerability parameter V.

For physical damage to the building, the EMS-98 damage grades have been consid-ered, describing the observed damage for structural and non structural components.Five damage grades are identified Dk(k = 0/5) : D1 slight, D2 moderate, D3 heavy,D4 very heavy, D5 destruction, plus the absence of damage D0 no damage.


Vulnerability in terms of EMS-Intensity

•  Vulnerability Index (V = V(typology) + ∑ ΔV)

•  Mean damage ratio

•  Damage grade distribution (binomial function)

for the damage grades Dk (k = 0 to 5)


Vulnerability in terms of EMS-Intensity •  Vulnerability Indexes

Bull Earthquake Eng (2006) 4:415–443 423

Fig. 5 Building typologies: a EMS-98 vulnerability table for masonry building typologies, bmembership function χ(V) for M4 building typology

Table 3 Vulnerability index values for building typologies

Typologies Building type V−− V− V V+ V++

Masonry M1 Rubble stone 0.62 0.81 0.873 0.98 1.02M2 Adobe (earth bricks) 0.62 0.687 0.84 0.98 1.02M3 Simple stone 0.46 0.65 0.74 0.83 1.02M4 Massive stone 0.3 0.49 0.616 0.793 0.86M5 U Masonry (old bricks) 0.46 0.65 0.74 0.83 1.02M6 U Masonry—r.c. floors 0.3 0.49 0.616 0.79 0.86M7 Reinforced /confined masonry 0.14 0.33 0.451 0.633 0.7

Reinforced Concrete RC1 Frame in r.c. (without E.R.D) 0.3 0.49 0.644 0.8 1.02Frame in r.c. (moderate E.R.D.) 0.14 0.33 0.484 0.64 0.86Frame in r.c. (high E.R.D.) −0.02 0.17 0.324 0.48 0.7

RC2 Shear walls (without E.R.D) 0.3 0.367 0.544 0.67 0.86Shear walls (moderate E.R.D.) 0.14 0.21 0.384 0.51 0.7Shear walls (high E.R.D.) −0.02 0.047 0.224 0.35 0.54

a most likely vulnerability class plus probable and less probable range of behaviours(Fig. 5a) for each typology. These linguistic judgements have been numerically trans-lated according to the fuzzy set theory. The membership function of each building typeχ(V) has been obtained by the soft union of the membership function (Ross 1995)ascribed to the vulnerability classes, each considered with its own degree of belonging.As an example in Fig. 5b the membership function for the building typology M4 isshown. Probable V−/V+ and less probable vulnerability index ranges V−−/V + +have been identified by α-cut procedures, respectively, for cuts α = 1 and for α = 0.5.For each of the typology a representative value V of the vulnerability index has beenidentified via a centroid deffuzification procedure (Ross 1995).

Vulnerability curves for building typologies can be drawn as a function of thevulnerability index values V provided in Table 3 and of the ductility index, Q = 2.3.

In order to achieve a validation of the proposed method, the vulnerability curves,derived for building typologies, have been compared with observed damage data (Fig.6a) and with other observed vulnerability approaches (Fig. 6b). A good agreementhas generally been observed (Giovinazzi 2005).

4 The mechanical method

The mechanical method proposed in the framework of Risk-UE project is essentiallya capacity spectrum-based method, similar to that adopted by HAZUS (FEMA1999) where the performance of a building hit by an earthquake, is identified by the


Vulnerability in terms of EMS-Intensity •  Stone masonry building (M3, IV = 0.74)

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3.6.3 Benchmark CHB30 ORG

Structural characteristics of the benchmark CHB30 ORG are already documented in Table 9. The benchmark can be best categorized in in class M5 (Unreinforced masonry with old bricks) [Lagomar-sino and Giovinazzi, 2006].

Table 21: Computation of the vulnerability index Benchmark CHB30 ORG

Building type: Simple stone (M3) [Lagomarsino and Giovinazzi, 2006]

𝑉𝐼∗: +0.74

Δ𝑉𝑚 : Number of floors +0.06 Thick walls -0.02

𝑉�𝐼 : +0.78 𝑉𝐼∗: Most probable value of the vulnerability index Δ𝑉𝑚 : Behavior modifier

𝑉�𝐼 : Total vulnerability index

Figure 36: Benchmark CHB30 ORG fragility curves of DG1 to DG5 (best estimate curves)


Vulnerability in terms of EMS-Intensity •  Brick masonry building (M6, IV = 0.616)

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3.6.1 Benchmark YVR14

Structural characteristics of the benchmark YVR14 are already documented in Table 5. The bench-mark can be best categorized in class M6 (Unreinforced masonry with RC-floors) [Lagomarsino and Giovinazzi, 2006].

Table 19: Computation of the vulnerability index Benchmark YVR14

Building type: Unreinforced masonry with RC-floors (M6) [Lagomarsino and Giovinazzi, 2006]

𝑉𝐼∗: +0.62

Δ𝑉𝑚 : Good maintenance -0.04

Number of floors +0.02

Good connection of walls -0.02

𝑉�𝐼 : +0.58 𝑉𝐼∗: Most probable value of the vulnerability index

Δ𝑉𝑚 : Behavior modifier

𝑉�𝐼 : Total vulnerability index

Figure 34: Benchmark YVR14 fragility curves of DG1 to DG5 (best estimate curves)


Vulnerability : refined investigation •  IMAC research part, studied buildings


Vulnerability : refined investigation •  Structural features of the studied buildings

Applied Computing and Mechanics Labratory Seismic Risk for Existing Buildings Ecole Polytechnique Fédérale de Lausanne Development of fragility curves using dynamic analysis

Page |3

2.1.7. Reinforced concrete building (Léopold-Robert 23, abbreviated hereafter SUVA) This is an 11-story RC structure with RC slabs in La Chaux-de-Fonds in Switzerland built in 1967 (Figure 1.e). The building is 33 m long and 15 m wide with a story height of 3 m (4m for the first two floors). The first and the fifth floors are considerably softer than their immediate upper floor.

(a) (b) (c)

(d) (e)

Figure 1: Selected studied buildings in this report (a) CHB30 (b) YVR14 (c) SECH7 (d) STD40 ORG, and (e) SUVA

Table 1 summarizes the properties for all the studied building shown in Figure 1.

Table 1: Structural characteristics of the studied buildings

CHB30 CHB30 ORG

YVR14 SECH7 STD40 ORG

STD40 SUVA

Number of stories 6 6 4 7 6 6 11

Year of construction

End of 19th cent. retrofit in 2009

End of 19th

century 1955 1960’s 1956 NA (fictive

retrofit) 1967

Structural system

Stone masonry

Stone masonry

Brick masonry

Brick masonry

Dual system

(URM+RC)

Dual system

(URM+RC) RC

Floor material RC Wood RC RC RC RC RC


Vulnerability : refined investigation •  Numerical modeling with ELS software


Vulnerability : refined investigation •  Damage grade definitions

Unreinforced Masonry Reinforced Concrete

Damage Grade Description of damages D1 First wall reaching the onset of cracking D2 First wall reaching the yield displacement D3 Slope of the capacity curve tends to zero (yielding in majority of walls) D4 Failure of the first wall D5 Drop of the capacity curve to 80% of the maximum value

Damage Grade Description of damages D1 First wall reaching the onset of cracking D2 First wall reaching the yield displacement D3 Displacement corresponding to the yield of the last RC element. D4 Failure of the first RC wall D5 Drop of the capacity curve to 80% of the maximum value


Vulnerability : refined investigation •  Damage grades : DG1






Vulnerability : refined investigation •  Ground motions database (50 recordings)


Vulnerability : refined investigation •  Spectral acceleration vs. damage


Vulnerability : refined investigation •  Fragility curves


Consequences •  Casualties

•  Direct property loss

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4 Consequences

4.1 Introduction

In this project unit casualty risk and unit property risk directly caused by structural damage are considered. Collateral or indirect damages, as for example damages because of fire, ground failure, or due to the loss of function, are not covered.

Consequences are linked to vulnerability by the help of damage grades (Table 4) as they are defined in [EMS, 1998].

No variability has been considered for the damage grade dependant consequences. The given ratios are considered to be expected values. Such variability could be easily introduced for the damage grade dependent consequences. Because these consequences are modelled as ratios, they could be modelled as uncertain quantities by the help of discrete or continuous probability distribution with arguments in the range between zero and one. In case of the casualty rate the results are more or less linear propor-tional to the adopted values for the casualty rate.

4.2 Casualties

Numerous factors govern the casualty rate in an earthquake. In this study the focus is laid on the direct casualty risk related to the structural failure and neglect secondary hazards as for example tsunamis, earthquake-related fires and landslides. Besides, other factors affecting death toll as slowness of search, treatment and rescue program are not covered here.

From the structural point of view there are several parameters that may affect the casualty rate in a building, e.g.: – Building type – Detailing – Construction method – Workmanship

The major primary cause of death in an earthquake is total or partial building collapse. Because of this, damage grades 4 and 5 are considered to contribute to the casualty risk. Given a certain earthquake, the probability of extensive structural damage and collapse is a function of the structural behaviour, which can roughly be associated to certain building types [Jaiswal et al., 2011; Spence, 2011]. In Table 26 casualty rates of different building types are given. They can be compared with those given in Hazus (Table 27).

Table 26: Casualty rate as a function of the building type [Jaiswal et al., 2011]

Building type Casualty rate Brick masonry with lime/cement mortar 0.06 Rubble or field stone masonry 0.06 Block or dressed stone masonry 0.08 Adobe building 0.06 Mud wall building 0.06 Non-ductile concrete moment frame 0.15 Steel moment frame with concrete infill wall 0.14

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Table 27: Casualty matrix pertinent to vulnerability classes A and B based on HAZUS casualty rates for unreinforced masonry building type [Hazus, 2003]

Studies done by Jaiswal et al. seem to be more consistent with EMS definition of damage grades. A casualty rate of 2% for DG4 (extensive structural damage) and 10% for DG5 (collapse) will be applied:

𝑃(𝐶𝐶|𝑃𝐷4) = 0.02 4.1

𝑃(𝐶𝐶|𝑃𝐷5) = 0.10 4.2

However, it must be noted that generally proposing reasonable values of casualty rates (CR) condi-tioned on damage grade is a very challenging task. Particularly for damage grade 4 there are very few references to CR in the literature.

4.3 Direct property loss

To investigate the direct property loss rate of a structure in this study the expected monetary loss is related to the structural damage with empirical relationships. With this aim the damage ratio is defined as a function of damage grade as:

𝑃𝐷𝑚𝐷𝑙𝐷 𝐶𝐷𝑅𝑖𝑙 = 𝑓(𝑃𝐷𝐸𝐸𝐸) = 𝐶𝑙𝐶𝑅 𝑙𝑓 𝑟𝐷𝑟𝐷𝑖𝑟𝐶𝐷𝑟𝑙𝐷𝑅𝐷𝑚𝐷𝑅𝑅 𝑅𝑙𝐶𝑅 4.3

Ranges of damage ratios for all damage grades are given in Table 28 [ATC 13, 1985; Tyagunov, 2004]. For each range a mean damage ratio representing the range is also given.

Table 28: Mean damage ratio [Tyagunov, 2004]

Classification of damage Damage ratio [%]

Mean damage ratio [%]

Damage grade 0: No damage 0 0 Damage grade 1: Negligible to slight damage (no structural damage, slight non-structural damage) 0 – 1 0.5

Damage grade 2: Moderate damage (slight structural damage, moderate non-structural damage) 1 – 20 10

Damage grade 3: Substantial to heavy damage (moderate structural damage, heavy non-structural damage) 20 – 60 40

Damage grade 4: Very heavy damage (heavy structural damage, very heavy non-structural damage) 60 – 100 80

Damage grade 5: Destruction (very heavy structural damage) 100 100

Actually, the mean damage ratio is not only a function of damage grade, but also of several other parameters as for example economic condition of the studied region or country. In a country with a stronger economy, the social acceptance to repair a badly damaged structure is much lower in compar-ison to another country, where there are considerably fewer resources available for the replacement of damaged structures. Because of this, the SIA 269/8 working group preliminarily defined the values given in Table 29 for Switzerland:

Damage state Casualty rate Complete structural damage with collapse (URMM and URML) 0.10

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Table 29: Mean damage ratio (as suggested by working group SIA 269/8)

Classification of damage Mean damage ratio [%]

Damage grade 0: No damage 0 Damage grade 1: Negligible to slight damage (no structural damage, slight non-structural damage) 1

Damage grade 2: Moderate damage (slight structural damage, moderate non-structural damage) 40

Damage grade 3: Substantial to heavy damage (moderate structural damage, heavy non-structural damage) 80

Damage grade 4: Very heavy damage (heavy structural damage, very heavy non-structural damage) 100

Damage grade 5: Destruction (very heavy structural damage) 100


Sa-based Risk computation

•  Discretization into several events : Ri R = ∑ Ri

risk related to event i with return period Ti : Ri = Pi x Ci with c(DG) loss ratio

total loss:

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5 Risk Computation Framework

5.1 Spectral-acceleration-based Risk assessment model

The total risk of casualty and damage caused by earthquakes is a function of the seismic hazard (including site effects), vulnerability of the affected buildings and assets (fragility) and the conse-quences of their failure or destruction (loss of life and financial loss).

Risk = Hazard x Vulnerability x Consequences 5.1

All these components have been already introduced in former chapters. The same framework for risk assessment is applied for both spectral-acceleration (Sa-based) and intensity-based risk assessments. In section 5.1 relations for the Sa-based framework are given. Relations for Intensity-based framework are given in section 5.3.

For simplicity the whole range of the possible seismic actions has been discretized into several events. Each event represents a specific return period. The total seismic risk can be computed as:

𝐶 = �𝐶𝑖𝑛

𝑖=1 5.2

in which Ri is the seismic risk related to the seismic event i with a return period Ti. Ri can be computed as:

𝐶𝑖 = 𝑃𝑖𝐶𝑖 5.3

in which Pi is the probability that event i happens and Ci is the consequence of this event (including vulnerability). Pi and Ci are computed as follows:

𝑃𝑖 = 𝑃(𝑆𝐷|𝑇𝑖) = ∆𝐻(𝑆𝐷) = 𝐻(𝐶𝐷𝑖) − 𝐻(𝐶𝐷𝑖+1) = 𝑃𝑃𝑃(𝐶𝐷𝑖)(𝐶𝐷𝑖+1 − 𝐶𝐷𝑖) (Figure 41) 5.4

𝐶𝑖 = � 𝑃(𝑃𝐷 = 𝑑𝑙|𝑆𝐷(𝑇𝑖)) 𝑅(𝑃𝐷 = 𝑑𝑙)𝑑𝑑=5

𝑑𝑑=0 5.5

in which c(DG) is the loss ratio (casualty rate and damage ratio, see chapter 4). To compute Ci deter-ministic and probabilistic approaches have been used. In the deterministic approach for each event i single values for hazard and fragility have been used, e.g. mean, median or any other percentile of the variables. In probabilistic approach, however, a range of data considering the uncertainty of the variables has been used. For example in Figure 42 for the event i one may see the range of data (hazard and fragility) considered for the convolution.

Hence, the total loss is:

𝐶 = �𝑃(𝑆𝐷|𝑇𝑖) � 𝑃(𝑃𝐷 = 𝑑𝑙|𝑆𝐷(𝑇𝑖)) 𝐶(𝑃𝐷 = 𝑑𝑙)𝑑𝑑=5

𝑑𝑑=0

𝑛

𝑖 = 1 5.6

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5 Risk Computation Framework

5.1 Spectral-acceleration-based Risk assessment model

The total risk of casualty and damage caused by earthquakes is a function of the seismic hazard (including site effects), vulnerability of the affected buildings and assets (fragility) and the conse-quences of their failure or destruction (loss of life and financial loss).

Risk = Hazard x Vulnerability x Consequences 5.1

All these components have been already introduced in former chapters. The same framework for risk assessment is applied for both spectral-acceleration (Sa-based) and intensity-based risk assessments. In section 5.1 relations for the Sa-based framework are given. Relations for Intensity-based framework are given in section 5.3.

For simplicity the whole range of the possible seismic actions has been discretized into several events. Each event represents a specific return period. The total seismic risk can be computed as:

𝐶 = �𝐶𝑖𝑛

𝑖=1 5.2

in which Ri is the seismic risk related to the seismic event i with a return period Ti. Ri can be computed as:

𝐶𝑖 = 𝑃𝑖𝐶𝑖 5.3

in which Pi is the probability that event i happens and Ci is the consequence of this event (including vulnerability). Pi and Ci are computed as follows:

𝑃𝑖 = 𝑃(𝑆𝐷|𝑇𝑖) = ∆𝐻(𝑆𝐷) = 𝐻(𝐶𝐷𝑖) − 𝐻(𝐶𝐷𝑖+1) = 𝑃𝑃𝑃(𝐶𝐷𝑖)(𝐶𝐷𝑖+1 − 𝐶𝐷𝑖) (Figure 41) 5.4

𝐶𝑖 = � 𝑃(𝑃𝐷 = 𝑑𝑙|𝑆𝐷(𝑇𝑖)) 𝑅(𝑃𝐷 = 𝑑𝑙)𝑑𝑑=5

𝑑𝑑=0 5.5

in which c(DG) is the loss ratio (casualty rate and damage ratio, see chapter 4). To compute Ci deter-ministic and probabilistic approaches have been used. In the deterministic approach for each event i single values for hazard and fragility have been used, e.g. mean, median or any other percentile of the variables. In probabilistic approach, however, a range of data considering the uncertainty of the variables has been used. For example in Figure 42 for the event i one may see the range of data (hazard and fragility) considered for the convolution.

Hence, the total loss is:

𝐶 = �𝑃(𝑆𝐷|𝑇𝑖) � 𝑃(𝑃𝐷 = 𝑑𝑙|𝑆𝐷(𝑇𝑖)) 𝐶(𝑃𝐷 = 𝑑𝑙)𝑑𝑑=5

𝑑𝑑=0

𝑛

𝑖 = 1 5.6



•  Probabilistic approach : combination seismic hazard - fragility curve

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(a) (b) (c)

Figure 41: (a) Hazard, (b) cumulative distribution function and (c) probability density function of the seismic hazard for a site

Figure 42: Median seismic hazard and its 10th and 90th percentiles of a site in combination with a fragility curve

1.E-04

1.E-03

1.E-02

1.E-01

0 1 2 3 4 5

Sa [m/s2]

Hazard

0.90

0.92

0.94

0.96

0.98

1.00

0 1 2 3 4 5

Sa [m/s2]

CDF

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5

Sa [m/s2]

PDF



•  Hazard curve : basic data event with 475 y. return period, Pi = 1x10-4 = 1/475 � 1/500

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5.2 Numerical application of the Sa-based framework

To show how the model works, the seismic risk value is computed for a benchmark. The studied benchmark is similar to the benchmark STD40 ORG (introduced in section 3.5.6). Note that there are some minor differences to the benchmark STD40 ORG. Both deterministic and probabilistic ap-proaches are used to compute the casualty risk. In deterministic approach the median hazard and fragility curves will be used. In probabilistic approach the seismic hazard is considered on the whole range and truncated at 90th percentile value. For fragility, however, only the median curves are used.

Risk assessment is done in the following steps: – The whole range of the possible seismic actions has been discretized into 400 events with return

periods from 25 years to 10'000 years. Percentile hazard curves for Sion OT at surface at 1 Hz (1st mode of the building) are demonstrated in Figure 43. Median Hazard, CDF and PDF are demonstrated in Figure 44. Probability of occurrence (Pi) of events is demonstrated in Figure 45. For example the Pi for the event with a return period of 475 years is 1x10-4 (1/475 - 1/500).

Figure 43: Hazard curve for Sion OT at surface at 1 Hz

(a) (b) (c)

Figure 44: (a) Hazard, (b) cumulative distribution function and (c) probability density function of the seismic hazard at surface for Sion OT at 1 Hz

10-2 10-1 100 101 10210-4

10-3

10-2

10-1Soil Hazard Curves for Sion OT at 1.0 Hz

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10%20%30%40%50%60%70%80%90%

1.E-04

1.E-03

1.E-02

1.E-01

0 1 2 3

Sa [m/s2]

Hazard

0.90

0.92

0.94

0.96

0.98

1.00

0 1 2 3

Sa [m/s2]

CDF

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3

Sa [m/s2]

PDF



•  Median hazard, CDF and PDF: probability of occurrence (Pi) of events

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Figure 45: Probability of occurrence (Pi) of events

– To compute the consequences in deterministic approach for each event the median value of the spectral acceleration of the event is read. Then the fragilities (probabilities) of relevant damage grades at this spectral acceleration are read. For example for the event with a return period of 475 years the median spectral acceleration at surface is about 0.6 m/s2. For loss of life only damage grades 4 and 5 are relevant. Probabilities that at spectral acceleration 0.6 m/s2 damage grades 4 and 5 happen are 2x10-18 and 4x10-23, respectively. Noting that loss ratios (in this case casualty rates) are 0.02 and 0.10 for damage grades 4 and 5, respectively, Ci will be 4x10-20. Multiplying this with the probability of occurrence of this event the casualty risk for this event will be 4 x10-24. Ri values are given in Figure 46a.

– To compute the consequences in probabilistic approach for each event a distribution function is fitted for the hazard curve. At 90% probability the distribution function is truncated. Distribution functions for two events with return periods 475 and 2500 years are given in Figure 47. Perform-ing a convolution of hazard and fragility for both damage grades 4 and 5, P(DG = dg | Sa(Ti)) are 4x10-8 and 2x10-11, respectively. Multiplying these values with loss ratios and summing them, the consequence Ci of this event will be 8x10-10 (several orders of magnitude larger than the value computed with the median hazard). Multiplying this with the probability of occurrence of this event the casualty risk for this event will be 8x10-14. Ri values are given in Figure 46b. Comparing Figure 46a with b, it is clear that in this case considering only median hazard value (ignoring un-certainty of hazard data) has led to underestimation of the total casualty risk.

– In both last two steps only median fragility curves have been used to compute the casualty risk. To demonstrate how model uncertainty affects the risk value, 16th and 84th percentile fragility curves have been used to compute again the casualty risk (only with probabilistic approach). Ri values are illustrated in Figure 48.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 1 2 3Sa [m/s2]

Pi

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5.2 Numerical application of the Sa-based framework

To show how the model works, the seismic risk value is computed for a benchmark. The studied benchmark is similar to the benchmark STD40 ORG (introduced in section 3.5.6). Note that there are some minor differences to the benchmark STD40 ORG. Both deterministic and probabilistic ap-proaches are used to compute the casualty risk. In deterministic approach the median hazard and fragility curves will be used. In probabilistic approach the seismic hazard is considered on the whole range and truncated at 90th percentile value. For fragility, however, only the median curves are used.


periods from 25 years to 10'000 years. Percentile hazard curves for Sion OT at surface at 1 Hz (1st mode of the building) are demonstrated in Figure 43. Median Hazard, CDF and PDF are demonstrated in Figure 44. Probability of occurrence (Pi) of events is demonstrated in Figure 45. For example the Pi for the event with a return period of 475 years is 1x10-4 (1/475 - 1/500).

Figure 43: Hazard curve for Sion OT at surface at 1 Hz

(a) (b) (c)

Figure 44: (a) Hazard, (b) cumulative distribution function and (c) probability density function of the seismic hazard at surface for Sion OT at 1 Hz

10-2 10-1 100 101 10210-4

10-3

10-2

10-1Soil Hazard Curves for Sion OT at 1.0 Hz

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10%20%30%40%50%60%70%80%90%

1.E-04

1.E-03

1.E-02

1.E-01

0 1 2 3

Sa [m/s2]

Hazard

0.90

0.92

0.94

0.96

0.98

1.00

0 1 2 3

Sa [m/s2]

CDF

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3

Sa [m/s2]

PDF



•  Deterministic approach : median values event i with 475 years return period, Sa = 0.6 m/s2 Loss of life, DG4 and DG5 only : fragility curve (Sa = 0.6 m/s2), DG4 probability 2x10-18

DG5 probability 4x10-23

casualty rate, 0.02 for DG4 and 0.10 for DG5 Ci = 0.02 x 2x10-18 + 0.10 x 4x10-23 = 4x10-20 Ri = 4x10-20 x 1x10-4 = 4x10-24



•  Deterministic approach: Ri values

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(a)

(b)

Figure 46: Ri values (a) using median hazard values only, (b) considering hazard distribution trunca-tion at 90th percentile for the studied benchmark in Sion OT



•  Probabilistic approach: fitted distribution function of hazard curve for each event

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(a)

(b)

Figure 47: Probability distributions of events with return periods of (a) 475 years and (b) 2'500 years in terms of spectral acceleration for Sion OT at f = 1 Hz (Ticks on X-axis are giving 10th to 90th percentiles according to SED model).



•  Probabilistic approach: Ri values

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(a)

(b)

Figure 46: Ri values (a) using median hazard values only, (b) considering hazard distribution trunca-tion at 90th percentile for the studied benchmark in Sion OT



•  Impact of uncertainties (seismic hazard)

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Figure 48: Ri values using 16th, 50th (median) and 84th percentile fragility curves for the studied benchmark in Sion OT

5.3 EMS-based risk assessment

The same framework introduced in 5.1 has been applied for EMS-based approach. In EMS-based approach hazard and fragility curves are given as a function of EMS-Intensity. In equations 5.4 to 5.6 spectral acceleration (Sa) is substituted with EMS-Intensity (I):

𝑃𝑖 = 𝑃(𝐼|𝑇𝑖) = ∆𝐻(𝐼) = 𝐻(𝐼𝑖) − 𝐻(𝐼𝑖+1) = 𝑃𝑃𝑃(𝐼𝑖)(𝐼𝑖+1 − 𝐼𝑖) 5.7

𝐶𝑖 = � 𝑃(𝑃𝐷 = 𝑑𝑙|𝐼(𝑇𝑖)) 𝑅(𝑃𝐷 = 𝑑𝑙)𝑑𝑑=5

𝑑𝑑=0 5.8

𝐶 = �𝑃(𝐼|𝑇𝑖) � 𝑃(𝑃𝐷 = 𝑑𝑙|𝐼(𝑇𝑖)) 𝐶(𝑃𝐷 = 𝑑𝑙)𝑑𝑑=5

𝑑𝑑=0

𝑛

𝑖 = 1

5.9

5.4 Numerical application of the EMS-based framework

Benchmark STD40 ORG (introduced in section 3.6.6) located in the site Sion OT is selected to show how the model works. Only deterministic approach is used to compute the casualty risk.


periods from 25 years to 10'000 years. Percentile hazard curves for Sion OT are demonstrated in Figure 49. Median Hazard, CDF and PDF are demonstrated in Figure 50. Probability of occurrence (Pi) of events is demonstrated in Figure 51. For example the Pi for the event with a return period of 475 years is 1x10-4.


Intensity-based Risk computation

•  Discretization into several events : Ri R = ∑ Ri

risk related to event i with return period Ti : Ri = Pi x Ci with c(DG) loss ratio

total loss:

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𝑑𝑑=0 5.8


𝑑𝑑=0

𝑛

𝑖 = 1

5.9





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𝑑𝑑=0 5.8


𝑑𝑑=0

𝑛

𝑖 = 1

5.9







•  Hazard curve : basic data event with 475 y. return period, Pi = 1x10-4 = 1/475 � 1/500

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Figure 49: Hazard curve for Sion OT as a function of EMS-Intensity

(a) (b) (c)

Figure 50: (a) Hazard, (b) cumulative distribution function and (c) probability density function of the seismic hazard for Sion OT


– To compute the consequence in deterministic approach for each event the median value of the EMS-Intensity of the event is read. Then the fragilities (probabilities) of relevant damage grades at

2 4 6 8 1010-4

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10-2


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EMS Intensity [-]

10%20%30%40%50%60%70%80%90%

1.E-04

1.E-03

1.E-02

1.E-01

0 2 4 6 8 10

EMS [-]

Hazard

0.90

0.92

0.94

0.96

0.98

1.00

0 2 4 6 8 10

EMS [-]

CDF

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 2 4 6 8 10

EMS [-]

PDF

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 1 2 3 4 5 6 7 8 9 10EMS [-]

Pi



•  Median hazard, CDF and PDF: probability of occurrence (Pi) of events

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(a) (b) (c)




2 4 6 8 1010-4

10-3

10-2


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EMS Intensity [-]

10%20%30%40%50%60%70%80%90%

1.E-04

1.E-03

1.E-02

1.E-01

0 2 4 6 8 10

EMS [-]

Hazard

0.90

0.92

0.94

0.96

0.98

1.00

0 2 4 6 8 10

EMS [-]

CDF

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 2 4 6 8 10

EMS [-]

PDF

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 1 2 3 4 5 6 7 8 9 10EMS [-]

Pi

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(a) (b) (c)




2 4 6 8 1010-4

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10-2


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EMS Intensity [-]

10%20%30%40%50%60%70%80%90%

1.E-04

1.E-03

1.E-02

1.E-01

0 2 4 6 8 10

EMS [-]

Hazard

0.90

0.92

0.94

0.96

0.98

1.00

0 2 4 6 8 10

EMS [-]

CDF

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 2 4 6 8 10

EMS [-]

PDF

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 1 2 3 4 5 6 7 8 9 10EMS [-]

Pi



•  Deterministic approach : median values event i with 475 years return period, IEMS = 7.3 Loss of life, DG4 and DG5 only : fragility curve (IEMS = 7.3), DG4 probability 0.034

DG5 probability 0.003

casualty rate, 0.02 for DG4 and 0.10 for DG5 Ci = 0.02 x 0.034 + 0.10 x 0.003 = 9.8x10-4 Ri = 9.8x10-4 x 1x10-4 = 9.8x10-8



•  Deterministic approach: Ri values

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this EMS-Intensity are read. For example for the event with a return period of 475 years the medi-an EMS-Intensity is about 7.3. For loss of life only damage grades 4 and 5 are relevant. Probabili-ties that at EMS-Intensity 7.3 damage grades 4 and 5 happen, are 0.034 and 0.003, respectively. Noting that loss ratios (in this case casualty rates) are 0.02 and 0.10 for damage grades 4 and 5, respectively, Ci will be 9.8x10-4. Multiplying this with the probability of occurrence of this event the casualty risk for this event will be 9.8x10-8. Ri values are given in Figure 52.

Figure 52: Ri values using median hazard values only for benchmark STD40 ORG in Sion OT


Conclusions

•  Probabilistic Seismic Hazard Assessment

•  Return periods up to 10’000 years at least

•  Definition and interpretation of DG are crucial issues by vulnerability assessment

•  Uncertainties govern the results

•  Results of Sa-based and Intensity-based risk assessment are reasonably comparable

slide12 seismic risk - epfl · civil 706 seismic risk analysis edce-epfl-enac-sgc 2016 -3-...

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