10-regional seismic risk assessment of bridge networks in charleston

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Regional Seismic Risk Assessment of Bridge Network in Charleston, SouthCarolinaJamie E. Padgetta; Reginald DesRochesb; Emily Nilssonc

a Department of Civil & Environmental Engineering, Rice University, Houston, Texas, USA b School ofCivil & Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA c DatumEngineers, Austin, Texas, USA

Online publication date: 08 July 2010

To cite this Article Padgett, Jamie E. , DesRoches, Reginald and Nilsson, Emily(2010) 'Regional Seismic Risk Assessment ofBridge Network in Charleston, South Carolina', Journal of Earthquake Engineering, 14: 6, 918 — 933To link to this Article: DOI: 10.1080/13632460903447766URL: http://dx.doi.org/10.1080/13632460903447766

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Journal of Earthquake Engineering, 14:918–933, 2010

Copyright � A.S. Elnashai & N.N. Ambraseys

ISSN: 1363-2469 print / 1559-808X online

DOI: 10.1080/13632460903447766

Regional Seismic Risk Assessment of BridgeNetwork in Charleston, South Carolina

JAMIE E. PADGETT1, REGINALD DESROCHES2,and EMILY NILSSON3

1Department of Civil & Environmental Engineering, Rice University, Houston,

Texas, USA2School of Civil & Environmental Engineering, Georgia Institute of Technology,

Atlanta, Georgia, USA3Datum Engineers, Austin, Texas, USA

This article presents the results of a seismic risk assessment of the bridge network in Charleston,South Carolina and the surrounding counties to support emergency planning efforts, and forprioritization of bridge retrofit. This study includes an inventory analysis of the approximately375 bridges in the Charleston area, and convolution of the seismic hazard with fragility curvesanalytically derived for classes of bridges common to this part of the country. State-of-the-artbridge fragility curves and replacement cost estimates based on region-specific data are used toobtain economic loss estimates. The distribution of potential bridge damage and economic lossesare evaluated for several scenario events in order to aid in the identification of emergency routesand assess areas for investment in retrofit. This article also evaluates the effect of uncertainty onthe resulting predicted economic losses. The findings reveal that while the risk assessment is verysensitive to both the assumed fragility curves and damage ratios, the estimate of total expectedeconomic losses is more sensitive to the vast differences in damage ratio models considered.

Keywords Seismic Risk Assessment; Loss Estimation; Bridges; Fragility; Transportation Net-work; Sensitivity Study

1. Introduction

Regional seismic risk assessments (SRAs) are becoming popular tools for evaluating the

performance of transportation networks under earthquake loading. The term seismic risk

refers to the potential for damage or losses that may be associated with a seismic event.

Such regional assessments provide a unique approach for estimating the risk to highway

infrastructure by evaluating potential bridge damage and consequences of the seismic

event, such as the estimated direct and indirect losses. This framework offers support to

decision-makers for pre-event planning and risk mitigation, emergency route identifica-

tion, retrofit selection and prioritization, among other critical tasks.

Methodologies for seismic risk assessment of transportation systems have been pre-

sented by many researchers in the field of lifeline earthquake engineering [Kiremidjian, et

al., 2007; Shinozuka et al., 1997; Luna et al., 2008; Werner et al., 2000]. These methodol-

ogies offer a potential framework for assessing likely bridge damage, direct losses due to

repair and replacement of the structures, and some extend this evaluation to include an

Received 23 March 2009; accepted 28 October 2009.

Address correspondence to Jamie E. Padgett, Department of Civil & Environmental Engineering, Rice

University, 6100 Main Street, MS 318, Houston, TX 77005, USA; E-mail: [email protected]

918

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assessment of the impact of the event on network performance and the resulting indirect

economic losses [Kircher et al., 2006; Werner et al., 1997.]

In this article, a detailed seismic risk assessment of the bridge network in Charleston,

South Carolina is conducted. The assessment is performed for a range of hazard levels,

for an inventory of approximately 375 bridges. The seismic risk assessment uses bridge

fragility curves that represent the unique characteristics of bridges in the region, as well

as state-specific bridge repair and replacement cost data. Distribution of damage and loss

estimates are tabulated for the different hazard levels. There are numerous uncertainties

associated with the seismic risk assessment process, and the resulting damage and loss

estimation. The second half of the article will assess the effect of uncertainty on the

resulting bridge damage distribution and estimated losses in Charleston, South Carolina.

2. Risk Assessment Framework and Input Models

The seismic risk assessment framework previously proposed by researchers varies in the

extent to which hazards, damage, and losses are treated. However, the general methodolo-

gies have common threads, as was highlighted in Werner et al. [2000]. The risk assessment

approach in this study is limited to an assessment of the bridge damage due to ground

shaking, and considers only the economic losses due to physical damage, rather than indirect

losses due to operation losses or time delay in the transportation system. While these losses

are significant considerations for evaluating the consequences of an earthquake event, the

objective of the study is to assess the sensitivity of the estimated bridge damage and repair

costs to input model variation. Seismic risk assessments are sometimes classified as deter-

ministic or probabilistic, in reference to the hazard itself. Probabilistic analysis is often

carried out by developing loss estimation for multiple simulations and scenario earthquakes,

then aggregating their results. While an SRA may be deterministic in terms of assessing a

specific scenario event, the potential uncertainty in achieving different levels of damage,

economic losses, or other consequences may still be treated probabilistically in the analysis.

The general seismic risk assessment framework used in this study is presented in Fig. 1.

As illustrated in Fig. 1, the first phase of the SRA process for bridge networks is to

initialize the process and define the problem by identifying the characteristics and locations

of the bridge inventory. The bridge inventory is obtained from the National Bridge

Inventory, with supplementary data provided by the South Carolina Department of

Transportation. Scenario earthquake events are used for the example presented herein,

where the magnitude and location of the event must be specified. During the system

analysis, fragility curves for classes of bridges common to the region are utilized. These

fragility curves depict the probability of meeting or exceeding different levels of damage

conditioned upon the ground motion intensity. Thus, the level of ground shaking at the

location of each bridge in the spatially distributed region must be estimated. This facilitates

evaluation of the expected level of damage to each bridge. The bridge damage coupled with

information on the damage ratio (or fraction of replacement cost) and replacement cost data

for different bridge types permits an assessment of the losses. The following sections detail

the different input models and scenarios which will be evaluated as a part of this study.

3. Case Study

3.1. Region of Interest

Charleston, South Carolina (Fig. 2) is located in the southeast United States. Charleston

has a history of large, but infrequent earthquakes. On August 31, 1886, a large earthquake

Risk to Charleston Bridges 919


(approximate magnitude of 7.0) struck the Charleston region. The earthquake resulted in

60 casualties, and widespread destruction of the built environment in Charleston

[Bollinger, 1977]. The earthquake was felt over a wide area, ranging from Milwaukee,

EarthquakeScenario

Bridge and RoadwayInventory

(characteristics, location, etc.)

Estimation of GroundShaking

at Bridge Locations

Fragility Curves forBridge Classes

Bridge DamageState Evaluation

Bridge Repair Cost Ratios(fraction of replacement cost)Replacement Cost Data

Seismic Performance andConsequence Assessment

(Damage Summary,Direct Losses, etc.)

FIGURE 1 General flow chart for seismic risk assessment of bridge network.

FIGURE 2 Case study region in Charleston, South Carolina.

920 J. E. Padgett, R. DesRoches, and E. Nilsson


Wisconsin to Boston, Massachusetts. Summerville, South Carolina, located to the north-

west of Charleston, was subjected to extremely large ground shaking, resulting in the

collapse of many homes and widespread foundation settlement. A repeat of the 1886

earthquake could have a devastating effect on the Charleston region, as well as the local

and global economy.

3.2. Bridge Inventory

Using the National Bridge Inventory (NBI) data for the state of South Carolina [FHWA,

2005], bridges were first filtered by county and bridge identification number to limit the

case study evaluation to the region of interest in Charleston, South Carolina. All of the

bridges in Charleston County, and a select few from Berkeley, Dorchester, and

Orangeburg counties, were filtered out using Microsoft Access. The select additions

include the bridges on the I-26 corridor, along I-26 from Charleston to the Bowman

exit, as well as bridges along US 17 from Beaufort, Colleton, Georgetown, Horry, and

Jasper counties. This yielded in a revised inventory containing 375 bridges out of the

overall 10,000 in the state.

The bridges studied in the Charleston region are classified with the methodology

used by Nielson [2005], according to material and construction type. The classifications

simply identify the bridges by both their span configuration—simply supported (SS),

multi-span simply supported (MSSS), multi-span continuous (MSC)—as well as by their

girder material type—concrete or steel. An overall distribution of the bridge classes is

shown in Table 1. The ‘‘Other’’ bridge category contains all additional bridges not falling

into one of the ten major classifications (i.e., truss, moveable, segmented box girder, and

box single/spread).

3.3. Seismic Hazard

One of the first steps in evaluating the seismic risk for any region is to assess the seismic

hazard or identify the events of interest. In this study, three deterministic scenarios are

used selected based on recommendations from SCDOT: earthquakes of magnitude Mw

4.0, 5.5, and 7.0 located at 32.9� N, 80.0� W, which is approximately 14.5 km outside of

TABLE 1 Distribution of bridge classes within the study area

Bridge type Quantity Percent

MSC_Concrete 1 0.27%

MSC_Steel 31 8.27%

MSC_Slab 14 3.73%

MSC_Conc Box 6 1.60%

MSSS_Concrete 61 16.27%

MSSS_Steel 62 16.53%

MSSS_Slab 118 31.47%

MSSS_Conc Box 2 0.53%

SS_Steel 26 6.93%

SS_Concrete 19 5.07%

Other 35 9.33%

Total 375 100.00%



the Charleston city center near Summerville, South Carolina. These hazards produce

maximum ground motion intensities of 0.28 and 0.62 g peak ground acceleration for Mw

4.0 and Mw 7.0, respectively, as shown in Fig. 3.

3.4. Input Models and Risk Assessment

Key input to the risk assessment, as previously indicated, include bridge fragility curves

and repair models. Bridge fragility curves offer the probability of meeting or exceeding a

level of damage given an intensity measure of the ground motion. For this study, the

levels of damage are qualitatively described as slight, moderate, extensive, and complete

damage. Each damage state is associated with an anticipated level of post-event function-

ality, as further discussed in Padgett and DesRoches [2007]. A brief description of the

damage states is presented in Table 2, corresponding to the fragility models incorporated.

The fragility curves adopted are those developed by Nielson and DesRoches [2007].

These fragility curves were developed specifically for nine bridge classes common to the

Central and Southeastern U.S. (CSUS) and are representative of the bridge inventory in

the Charleston region. Uncertainty in component stiffnesses, material strengths, and

geometry were propagated through the analysis. The fragility development considered

damage to multiple vulnerable components, including bearings, columns, and abutments

in the longitudinal and transverse directions. The CSUS fragility curves were developed

for evaluation of the vulnerability of general classes of bridges across a region rather than

bridge specific analysis, and are used in this study to evaluate the probability of the

bridges experiencing different levels of damage in Charleston and subsequent regional

loss estimation. Stochastic dependence between bridge failures in the spatially distributed

region is not considered in the present study. While likelihood of achieving each level of

damage is evaluated for all bridges in the region, the mean value of the damage state is

often presented graphically.

Repair cost models are also required for estimating direct losses due to repair and

replacement of the seismically damaged bridges. Bridge repair costs are assessed as a

fraction of the replacement cost using the damage ratios, D, presented by Basoz and

Mander [1999], as listed in Table 2. The normalized replacement costs for various bridge

types using historic, region specific construction data in South Carolina are show in Table 2,

as a replacement cost per area of bridge deck.

The damage and loss estimates are evaluated and aggregated for the Charleston

region using the seismic risk assessment package, MAEViz [MAEC, 2006]. Within this

FIGURE 3 Comparison of hazard for deterministic scenarios: (a) Mw 5.3 and (b) Mw 7.3.



framework, the damage state is determined from a mean damage ratio, mD, found as

follows:

�D ¼X4

j¼1

DjP DSj

� �; (1)

where j is the damage state, Dj is the damage ratio for damage state j, and P[DSj] is the

probability of damage state j from the difference in damage state exceedance probabilities

evaluated by entering the fragility curves at the site pga. Given the mean damage ratio, an

expected damage state is presented graphically for intermediate visual inspection. Addi-

tionally, the mean value of the losses for the bridges in the region is found in MAEViz as:

�L ¼X

n

Cn�Dn; (2)

where n is the number of bridges in the region, mDn is the mean damage ratio for bridge n,

Cn is the cost to repair the bridge computed as a function of the deck area and replace-

ment cost shown in Table 3. The replacement cost data shown in Table 3, given in dollars

per deck area, reflects the average cost of new construction in South Carolina for different

TABLE 2 Damage state definitions [Padgett and DesRoches, 2007] and damage ratios

[Basoz and Mander, 1999]

Damage

state

Damage state definition

[Padgett and DesRoches, 2007] Damage ratios [Basoz and Mander, 1999]

Functionality description

Best mean damage

ratio (D)

Range of damage

ratio

None No reduction in functionality 0.005 0–0.01

Slight Fully functional within a day 0.03 0.01–0.03

Moderate Reduced functionality for a week 0.08 0.02–0.15

Extensive Closed for a week, with partial

functionality beyond 30 days

0.25 0.1–0.4

Complete Complete closure beyond 30 days 1.0 (if n < 3) 0.3–1.0

2.0/n (if n � 3)

n = number of spans.

TABLE 3 Bridge replacement cost data based on South Carolina

statistics [SCDOT, 2007] in dollars per area of bridge deck

Type Cost ($/ft2)

Concrete Girder 67.71

Concrete Box Girder 67.98

Steel Girder 94.37

Slab 60.04

Other (truss, moveable, etc.) 72.53



bridge types per recent construction data [SCDOT, 2007]. Additionally the standard

deviation of the losses is found as:

�L ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX

n

Cn�Dnð Þ2r

; (3)

where the sD, the standard deviation of the damage ratio for each bridge is:

�D ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX4

j¼1

Dj � �D

� �2P DSj

� �vuut : (4)

The input models and loss estimate approach presented above are subsequently used in

the case study risk assessment of the 375-bridge network in Charleston.

4. Results: Magnitute 5.5 Earthquake Event

4.1. Bridge Damage

The risk assessment is conducted for the Charleston case study to evaluate expected

damage and total direct losses for different scenario events. Figure 4 illustrates the

distribution of bridge damage in the downtown Charleston region due to the Mw 5.5

earthquake event. These types of maps of the anticipated spatial distribution of bridge

damage can be beneficial not only for assessing economic losses, as emphasized in this

Damage States

None Slight Moderate Extensive Complete

Damage States

None Slight Moderate Extensive Complete

FIGURE 4 Spatial distribution of damaged bridges in downtown Charleston for the Mw

5.5 event.



article, but can support the identification of viable emergency response routes and

identification of bridges in need of potential retrofit. While a majority of the damaged

bridges in this region may be expected to experience moderate damage, a limited number

of bridges are in the extensive damage state. A summary of the bridges by type and

damage state is shown in Table 4. The anticipated level of damage is a function of the

ground motion at the bridge site, as well as the relative vulnerability of the bridge. For

example, the MSC and MSSS Steel bridges have fragility models that reveal they are

among the most vulnerable bridge types in the region, and the results of the risk

assessment also indicate that the extensively damaged bridges are of these types. It is

also clear that there are a larger number of bridges in the higher damage state in the

location closer to the epicenter of the earthquake.

4.2. Economic Losses

The calculation of expected economic losses is based on the potential damage states and the

repair and construction data from the state of South Carolina, as described in the previous

section. For the Mw 5.5 event, the direct economic losses are approximately $40 million

(Table 5). It is interesting to note that one bridge type alone (MSC steel girder bridge)

accounts for over 64% of the total direct economic losses. This is due to several factors.

Although the MSC Steel girder bridge only accounts for less than 10% of the bridges, it

accounts for 63% of the bridges in the extensive damage state. The economic losses

associated with the extensive damage state are considerably higher than those in the

lower damage states. A bridge in the extensive damage state would have a repair cost

ratio that is three times as high as the moderate damage state, and eight times as high as the

slight damage state. The other reason for the large losses in the MSC steel bridge are due to

the fact that this bridge type tends to have longer bridge lengths and widths as compared to

the other bridge types, as well as the fact that the normalized cost to repair or replace the

steel bridges tends to be higher than other bridge classes. Since the total loss is proportional

to the area, this bridge type tends to have higher loss values. It is also observed that the

bridges that are more robust (i.e., SS steel, SS concrete, MSC concrete box) also contribute

TABLE 4 Distribution of bridges by damage state and bridge type for the Mw 5.5 event

Type

Damage state

TOTALNone Slight Moderate Extensive Complete

MSC Concrete 0 0 1 0 0 1

MSC Steel 12 0 12 7 0 31

MSC Slab 1 2 11 0 0 14

MSC Conc Box 0 1 5 0 0 6

MSSS Concrete 23 8 30 0 0 61

MSSS Steel 25 1 32 4 0 62

MSSS Slab 25 22 71 0 0 118

MSSS Conc Box 0 2 0 0 0 2

SS Concrete 6 6 7 0 0 19

SS Steel 26 0 0 0 0 26

Other 30 3 2 0 0 35

TOTAL 148 45 171 11 0 375



less to the total direct losses. The relative contribution of bridges to the loss estimate offers

one approach to help identify and prioritize bridges in need of retrofit.

5. Results: Comparison of Different Earthquake Magnitudes

The seismic risk assessment was performed for three different hazards, Mw 4.0, 5.5, and

7.0 (epicenter in Summerville, South Carolina), using the MAEViz platform [MAEC,

2006]. The distribution of expected damage for the three hazard levels is shown in Fig. 5.

TABLE 5 Summary of direct losses by bridge type for the

Mw 5.5 event

Type Direct losses

MSC Concrete $13,000

MSC Steel $26,000,000

MSC Slab $830,000

MSC Conc Box $200,000

MSSS Concrete $2,800,000

MSSS Steel $6,000,000

MSSS Slab $1,400,000

MSSS Conc Box $60,000

SS Concrete $510,000

SS Steel $94,000

Other $2,400,000

TOTAL $40,307,000

FIGURE 5 Distribution of damage as a function of earthquake magnitude.



The results show that for the Mw 7.0 event, over 85% of the bridges are damaged, with

73% of the bridges having moderate to complete damage. For the Mw 5.5 event,

approximately 60% of the bridges are damaged, with nearly 50% of the bridges having

moderate to complete damage. Finally, the Mw 4.0 earthquake results in only 17% of the

bridges having damage, and less than 9% have moderate or greater damage.

It is interesting to note that a Mw 4.0 scenario results in expected damage states of

only slight or moderate damage to 65 bridges, with the remaining bridges having no

damage. This is an indication that for pre-event planning purposes the Mw 4.0 earthquake

might be a viable threshold upon which inspection teams are mobilized following an

earthquake event. However, this would depend on the location of the epicenter for the

particular earthquake. It is also important to note that as previously highlighted in the

input model and risk assessment section, while expected damage states are presented

graphically there is probability of achieving each damage state even at the lower level

events, which is further propagated through the loss estimation.

As shown in Fig. 6, for a Mw 4.0 seismic event, direct economic losses are estimated

to be close to $6.3 million. In contrast, the more severe earthquake scenario, Mw 7.0,

produces direct losses of approximately $90 million. As the earthquake scenarios increase

in intensity, the direct economic losses increase exponentially, and the error about that

estimate increases as well. While outside of the scope of the current study, indirect losses

in a transportation network due to bridge damage are often orders of magnitude greater

than the repair and replacement costs alone. For example, past studies have shown that

the indirect losses due to rerouting may be roughly 7–20 times direct losses [ATC, 1991],

revealing that for an increase of 13 times, the total losses in the Charleston region may be

on the order of $90 million to over $1 billion for the Mw 4.0 and 7.0, respectively.

Refined total loss estimates would require transportation modeling, which is outside of

the scope of this study.

6. Uncertainties and Sensitivity Study

While there have been many studies that propose and illustrate the viability of the risk

assessment framework, the results may depend heavily on the availability and reliability

of utilized tools and input models. These include such items as ground motion models,

4.00

20 × 106

40 × 106

60 × 106

80 × 106

100 × 106

120 × 106

5.5Earthquake Scenario (Mw)

Los

s ($

)

7.0

FIGURE 6 Direct economic loss estimates for three scenario earthquakes (Mw 4.0, 5.5,

and 7.0).



fragility information on the bridge vulnerability, repair cost information, among others.

Different modeling assumptions and input tools may be classified as epistemic uncertain-

ties. An epistemic uncertainty is often defined a knowledge-based uncertainty, which

stems from incomplete data, ignorance, or modeling assumptions. The adoption of

different input models in the SRA framework could potentially have a significant effect

on the overall results and conclusions of the study.

Past studies have evaluated the sensitivity of loss estimates to input model variation

in other systems, particularly buildings. Crowley et al. [2005] assessed the impact of a

number of uncertain parameters, including ground motion modeling, structural demand,

and capacity estimates, on regional building damage. Porter et al. [2002] evaluated the

sensitivity of loss estimates for a single concrete moment-frame building and found, like

Crowley observed for regional damage, that the building capacity (limit at which damage

is expected) was the most important uncertain parameter followed by ground motion

characteristics. In a study assessing the average annual losses to a regional inventory of

low-rise wood framed buildings, Grossi [2000] compared using default models in

HAZUS to ‘‘updated’’ input models for the seismic hazard as well as the inventory

square footage and fragility. She found that models defining the seismic hazard, such

as the recurrence model for the earthquake and attenuation relationship were the most

critical updates, followed by the square footage and fragility.

While the studies listed have offered insight on the relative importance of different

loss modeling parameters for building inventories, few have assessed the impact on the

regional seismic risk to transportation networks. The relative sensitivity of the highway

bridge damage and loss estimates to different input models are evaluated as a follow-up

phase of the study in Charleston. This helps to identify critical components of the risk

assessment framework that significantly impact the overall results of a regional transpor-

tation network assessment, including bridge damage and direct economic losses due to

repair and replacement. This study emphasizes the difference due to assumed input

models, rather than variation about the estimate due to uncertainty modeled by a

particular input model. The Charleston region previously presented is used as an example

to gain insight on the effect of different input fragility curves for evaluating the perfor-

mance of bridges common to the region, as well as different estimates of the damage ratio

for repair cost modeling and loss estimation.

7. Input Parameters

Two different scenario earthquake events are considered as a part of the sensitivity study.

This permits an evaluation of whether or not the conclusions of the study are dependent

upon the level of the hazard. The characteristic scenario events assessed for Charleston

are moment magnitude 5.3 and 7.3 located 14.5 km outside of the city center near

Summerville. In order to estimate the level of ground shaking at the location of each

bridge, a weighted average of different attenuation functions is used [MAEC, 2006]. This

is to acknowledge the findings of past work which has indicated the importance of

considering the epistemic uncertainty in ground motion models, particularly attenuation

of ground motion for spatially distributed systems. Thus, the ground motions models

themselves are not a focus of this study and the epistemic uncertainty associated with

them is captured and treated explicitly in each scenario, rather than evaluating the

sensitivity of the results to different models.

The two input models that are considered in this study are change in fragility model

and in repair cost model (specifically due to change in damage ratio). The fragility

models considered in the sensitivity study for bridge classes common to the Charleston



region include the Nielson and DesRoches [2007] fragility curves developed for the

CSUS region as previously discussed in the case study, as well as those adopted in

HAZUS-MH [FEMA, 2005]. The bridge fragility curves currently used in HAZUS-MH

were developed using a nonlinear static approach in past work by Basoz and Mander

[1999] and Dutta [1999]. These sets of fragility models are subsequently termed CSUS

and HAZUS fragilities, respectively. A detailed discussion of the difference in the two

models is presented in Nielson and DesRoches [2007], which illustrated that for some

bridge types (i.e., multi-span simply supported steel or concrete girder bridges) the CSUS

fragility curves exhibit lower vulnerability than originally anticipated in the HAZUS

curves, while for other bridge types (i.e., multi-span continuous steel and concrete girder

bridges) the CSUS fragility curves indicate a much higher vulnerability than depicted in

the HAZUS curves.

The two damage ratios considered in the sensitivity study are those formerly pre-

sented in the case study [Basoz and Mander, 1999] termed Basoz, as well as the damage

ratios presented in REDARS [Werner et al., 2006] as shown in Table 6. Figure 7 shows a

comparison of the damage ratios for an example bridge with three spans, noting that the

Basoz damage ratios are a function of the number of spans, while the REDARS damage

ratios do not change depending upon number of spans. As illustrated in the plot, the

REDARS damage ratios imply a larger anticipated repair cost for the moderate, exten-

sive, and complete damage states in particular. Moreover, they indicate a more linearly

increasing damage ratio than exhibited in the Basoz damage ratios.

TABLE 6 REDARS repair cost ratios [Werner et al., 2006]

Damage state Best mean damage ratio (D) Range of damage ratio

None 0.00 0–0.01

Slight 0.03 0.01–0.05

Moderate 0.25 0.05–0.5

Extensive 0.75 0.5–0.8

Complete 1.00 0.8–1.0

None0.0

0.2

0.4

0.6

0.8

1.0

Slight

BasozREDARS(for n = 3)

ModerateDamage state

Dam

age

Rat

io

Extensive Complete

FIGURE 7 Comparison of Basoz and REDARS damage ratios for a three span bridge.



8. Results

The sensitivity study is performed by conducting the regional risk assessment for

Charleston with different input models. The experiment conducted is a full factorial

design with each factor (fragility curves and damage ratios) having two categorical levels

(22), and a replication to consider two different levels of earthquake (2 x 22), for a total of

8 runs. Table 7 lists the risk assessment runs (scenarios) for the magnitude 5.3 and 7.3

events. The total estimated direct losses and standard deviation of the losses are compared

in the Table, indicating a potential range in estimated direct losses between $71,400,000

and $267,000,000 for the upper level event, and between $27,900,000 and $125,000,000

for the lower level event for different input model combinations. Similarly, the standard

deviation about those loss estimates varies for each scenario.

Figure 8 shows the percent difference in the mean value and standard deviation of the

losses relative to the base case (CSUS fragility curves and Basoz damage ratios). It is

noted that the base case uses the same input models considered in the Charleston case

study previously presented. This figure reveals that regardless of event magnitude, the use

of the REDARS damage ratios results in larger economic losses, as anticipated, due to the

increase in damage ratio and repair cost estimate for each damage state. The expected

value of total losses increases by nearly 150% for each earthquake level when the same

fragility curves are used as the base case (CSUS). In fact, the change in damage ratios

results in the largest impact on the loss estimate and standard deviation about that

estimate.

The use of HAZUS fragility curves results in a decrease in expected direct economic

losses for a given damage ratio. This finding is potentially counter-intuitive given the

total number of bridges expected in each damage state shown for each run in Fig. 9 for

Mw 5.3 and 7.3. As these figures reveal, the use of the HAZUS fragility curves as

opposed to the CSUS fragilities for the same damage ratio (Basoz) result in a larger

TABLE 7 SRA runs for sensitivity study and results

Run number Scenario

Estimated total

direct losses

Standard

deviation

7.3 Base Case 7.3, CSUS Fragilities,

Basoz Damage Ratios

$105,000,000 $19,900,000

7.3.A 7.3, HAZUS Fragilities,

Basoz Damage Ratios

$71,400,000 $17,700,000

7.3.B 7.3, HAZUS Fragilities,

REDARS Damage Ratios

$197,000,000 $27,500,000

7.3.C 7.3, CSUS Fragilities,


$267,000,000 $41,200,000

5.3 Base Case 5.3, CSUS Fragilities,

Basoz Damage Ratios

$50,900,000 $14,700,000

5.3.A 5.3, HAZUS Fragilities,

Basoz Damage Ratios

$27,900,000 $11,500,000

5.3.B 5.3, HAZUS Fragilities,


$74,200,000 $10,700,000

5.3.C 5.3, CSUS Fragilities,


$125,000,000 $24,900,000



number of bridges in the extensive and complete damage states; however, the expected

value of the losses is lower for the HAZUS fragility curves. This can be attributed to the

fact that: (1) The HAZUS fragility curves have been shown to underestimate the damage

of MSC bridges [Nielson and DesRoches, 2007], which are among the costliest bridges to

repair and replace and the bridges contributing the most to the economic losses (i.e.,

Tables 2 and 4); and (2) Damage to other bridge types, such as the MSSS concrete girder,

slab, and steel girder bridges, may be overestimated by using the HAZUS fragilities,

yielding more total bridges in the upper damage states, yet with insignificant net effect on

the direct losses relative to the contribution of other bridges.

Figure 8 also indicates the interaction effects of changing both the fragility curves

and damage ratios for a given earthquake scenario. The reduction in expected value of

losses due to using HAZUS fragility curves is countered and dominated by the increase in

% Variation from Base Model−100 −50 0 50 100 150 200

E[Loss] stdev[Loss]

CSUS Fragilities, REDARS Damage Ratios

HAZUS Fragilities, REDARS Damage Ratios

CSUS Fragilities, REDARS Damage Ratios

HAZUS Fragilities, Basoz Damage Ratios

HAZUS Fragilities, REDARS Damage Ratios

HAZUS Fragilities, Basoz Damage Ratios

Hig

h L

evel

Eve

nt(M

w 7

.3)

Low

Lev

el E

vent

(Mw

5.3

)

FIGURE 8 Comparison of the change in expected value of losses and standard deviation

of losses relative to the base case (CSUS fragilities, Basoz damage ratios).

(a)

None0

50

100

150

200

250

Slight Moderate

Damage State

Num

ber

of B

ridg

es

Extensive Complete

Mw = 5.3

CSUS/BasozCSUS/REDARSHAZUS/BasozHAZUS/REDARS

Mw = 7.3

CSUS/BasozCSUS/REDARSHAZUS/BasozHAZUS/REDARS

(b)

None0

50

100

200

150

250

300

Slight Moderate

Damage State

Num

ber

of B

ridg

es

Extensive Complete

FIGURE 9 Number of bridges by expected damage state for each sensitivity study

simulation at the (a) Mw 5.3 event and the (b) Mw 7.3 event.



losses due to using REDARS damage ratios, yielding a net increase in economic losses of

46% and 88% for the Mw 5.3 and 7.3 events, respectively. The findings reveal that while

the risk assessment is very sensitive to both the assumed fragility curves and damage

ratios, the estimate of total expected economic losses is more sensitive to the vast

differences in damage ratio models.

9. Conclusions

In this article, the risk assessment framework for evaluating bridge damage and economic

losses due to earthquake events is presented for application to a case study in Charleston,

South Carolina. The bridge network for the case study consists of 375 bridges of varying

types, and the risk assessment conducted for three different scenario events utilizes region

specific bridge fragility curves and construction cost data for damage and loss estimation.

The case study reveals expected damage states of moderate, extensive, or complete

damage for over 85% of the Charleston bridges due to a Mw 7.0 event located approxi-

mately 14.5 km outside of the city center, near Summerville, South Carolina.

Additionally, while noting the potential for achieving each damage state is assessed

using the fragility curves and propagated through the loss estimation, the mean damage

state alone indicates that nearly 20% of the bridges may suffer some level of damage for a

Mw 4.0 event. Hence, this low level event may still warrant immediate deployment of

inspection teams. The expected value of direct economic losses due to bridge repair alone

are on the order of $40 million for the Mw 5.5 event, with both the loss estimate and

standard deviation about the estimate increasing exponentially with increasing event

magnitude. For the regional inventory in Charleston, the more vulnerable bridge types,

such as the multi-span continuous steel girder bridges, are expected to contribute dis-

proportionately to the economic losses, despite their relatively small percentage of the

overall bridge inventory. These results indicate that such bridge types may be critical

priorities for retrofit.

A sensitivity study is conducted to evaluate the impact of assumed SRA input models

on the resulting loss estimates, assessing the effect of fragility models and damage ratios

for upper and lower level events. In a full factorial design, both the CSUS specific bridge

fragility curves relative to current HAZUS fragilities, as well as REDARS versus Basoz

(currently implemented in HAZUS) damage ratios are considered. The findings reveal a

strong sensitivity of the resulting loss estimates, and variability about the estimate, to

assumed fragility models and damage ratios. The expected value of losses differ on the

order of 150% for both the upper and lower level events considered in the sensitivity

study (Mw 5.3 and 7.3). The roughly linearly increasing damage ratio and repair cost

estimate for the REDARS model, as opposed to roughly exponential increase with the

Basoz ratios, yields the greatest impact on increasing the loss estimate. For the case study

inventory and cost figures considered, the use of the HAZUS fragility curves resulted in

lower loss estimates. However, this was found to be a function of the type of bridges

found in the region and relative contribution of different bridge types to total losses, since

for some bridges HAZUS fragilities indicate an increase in vulnerability relative to the

CSUS specific models, while for other bridge types they depict a lower fragility.

Acknowledgments

This study has been supported by the Earthquake Engineering Research Centers program

of the National Science Foundation under Award Number EEC-9701785 (Mid-America



Earthquake Center). The South Carolina Department of Transportation (SCDOT) is

gratefully acknowledged for their input and data sharing throughout the research project.

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