Regional Seismic Risk Assessment of Bridge ... - Rice University
Journal of Earthquake Engineering, 14:918–933, 2010 Copyright Ó A.S. Elnashai & N.N. Ambraseys ISSN: 1363-2469 print / 1559-808X online DOI: 10.1080/13632460903447766
Regional Seismic Risk Assessment of Bridge Network in Charleston, South Carolina JAMIE E. PADGETT1, REGINALD DESROCHES2, and EMILY NILSSON3 1
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Department of Civil & Environmental Engineering, Rice University, Houston, Texas, USA 2 School of Civil & Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA 3 Datum 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 for prioritization of bridge retrofit. This study includes an inventory analysis of the approximately 375 bridges in the Charleston area, and convolution of the seismic hazard with fragility curves analytically derived for classes of bridges common to this part of the country. State-of-the-art bridge fragility curves and replacement cost estimates based on region-specific data are used to obtain economic loss estimates. The distribution of potential bridge damage and economic losses are evaluated for several scenario events in order to aid in the identification of emergency routes and assess areas for investment in retrofit. This article also evaluates the effect of uncertainty on the resulting predicted economic losses. 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 considered. Keywords Seismic Risk Assessment; Loss Estimation; Bridges; Fragility; Transportation Network; 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 identification, retrofit selection and prioritization, among other critical tasks. Methodologies for seismic risk assessment of transportation systems have been presented 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 methodologies 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]
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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.
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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 methodologies 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 deterministic 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
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J. E. Padgett, R. DesRoches, and E. Nilsson Bridge and Roadway Inventory (characteristics, location, etc.)
Earthquake Scenario
Fragility Curves for Bridge Classes
Estimation of Ground Shaking at Bridge Locations
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Replacement Cost Data
Bridge Damage State Evaluation
Bridge Repair Cost Ratios (fraction of replacement cost)
Seismic Performance and Consequence 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.
(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,
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Wisconsin to Boston, Massachusetts. Summerville, South Carolina, located to the northwest 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.
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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 MSC_Concrete MSC_Steel MSC_Slab MSC_Conc Box MSSS_Concrete MSSS_Steel MSSS_Slab MSSS_Conc Box SS_Steel SS_Concrete Other Total
Quantity
Percent
1 31 14 6 61 62 118 2 26 19 35 375
0.27% 8.27% 3.73% 1.60% 16.27% 16.53% 31.47% 0.53% 6.93% 5.07% 9.33% 100.00%
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FIGURE 3 Comparison of hazard for deterministic scenarios: (a) Mw 5.3 and (b) Mw 7.3.
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 functionality, 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
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TABLE 2 Damage state definitions [Padgett and DesRoches, 2007] and damage ratios [Basoz and Mander, 1999] Damage state definition [Padgett and DesRoches, 2007] Damage state None Slight Moderate Extensive
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Complete
Damage ratios [Basoz and Mander, 1999] Best mean damage ratio (D)
Functionality description No reduction in functionality Fully functional within a day Reduced functionality for a week Closed for a week, with partial functionality beyond 30 days Complete closure beyond 30 days
Range of damage ratio
0.005 0.03 0.08 0.25
0–0.01 0.01–0.03 0.02–0.15 0.1–0.4
1.0 (if n < 3) 2.0/n (if n 3)
0.3–1.0
n = number of spans.
framework, the damage state is determined from a mean damage ratio, mD, found as follows: D ¼
4 X
Dj P DSj ;
(1)
j¼1
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. Additionally, the mean value of the losses for the bridges in the region is found in MAEViz as: L ¼
X
Cn Dn ;
(2)
n
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 replacement 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 3 Bridge replacement cost data based on South Carolina statistics [SCDOT, 2007] in dollars per area of bridge deck Type Concrete Girder Concrete Box Girder Steel Girder Slab Other (truss, moveable, etc.)
Cost ($/ft2) 67.71 67.98 94.37 60.04 72.53
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bridge types per recent construction data [SCDOT, 2007]. Additionally the standard deviation of the losses is found as: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rX L ¼ ðCn Dn Þ2 ; (3) n
where the sD, the standard deviation of the damage ratio for each bridge is: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 4 uX 2 Dj D P DSj : D ¼ t
(4)
j¼1
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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
FIGURE 4 Spatial distribution of damaged bridges in downtown Charleston for the Mw 5.5 event.
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TABLE 4 Distribution of bridges by damage state and bridge type for the Mw 5.5 event Damage state Type
None
Slight
Moderate
Extensive
Complete
TOTAL
0 12 1 0 23 25 25 0 6 26 30
0 0 2 1 8 1 22 2 6 0 3
1 12 11 5 30 32 71 0 7 0 2
0 7 0 0 0 4 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
1 31 14 6 61 62 118 2 19 26 35
148
45
171
11
0
375
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MSC Concrete MSC Steel MSC Slab MSC Conc Box MSSS Concrete MSSS Steel MSSS Slab MSSS Conc Box SS Concrete SS Steel Other TOTAL
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
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TABLE 5 Summary of direct losses by bridge type for the Mw 5.5 event Type
Direct losses
MSC Concrete MSC Steel MSC Slab MSC Conc Box MSSS Concrete MSSS Steel MSSS Slab MSSS Conc Box SS Concrete SS Steel Other TOTAL
$13,000 $26,000,000 $830,000 $200,000 $2,800,000 $6,000,000 $1,400,000 $60,000 $510,000 $94,000 $2,400,000 $40,307,000
less to the total direct losses. The relative contribution of bridges to the loss estimate offers one approach to help identify and prioritize bridges in need of retrofit.
5. Results: Comparison of Different Earthquake Magnitudes The seismic risk assessment was performed for three different hazards, Mw 4.0, 5.5, and 7.0 (epicenter in Summerville, South Carolina), using the MAEViz platform [MAEC, 2006]. The distribution of expected damage for the three hazard levels is shown in Fig. 5.
FIGURE 5 Distribution of damage as a function of earthquake magnitude.
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120 × 106 100 × 106
Loss ($)
80 × 106 60 × 106 40 × 106 20 × 106 0
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4.0
5.5 7.0 Earthquake Scenario (Mw)
FIGURE 6 Direct economic loss estimates for three scenario earthquakes (Mw 4.0, 5.5, and 7.0). 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,
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fragility information on the bridge vulnerability, repair cost information, among others. Different modeling assumptions and input tools may be classified as epistemic uncertainties. 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 transportation 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 performance 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
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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 presented 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, extensive, 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
0.00 0.03 0.25 0.75 1.00
0–0.01 0.01–0.05 0.05–0.5 0.5–0.8 0.8–1.0
None Slight Moderate Extensive Complete
1.0
0.8 Damage Ratio
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Basoz REDARS (for n = 3)
0.6
0.4
0.2
0.0 None
Slight
Moderate Damage state
Extensive
Complete
FIGURE 7 Comparison of Basoz and REDARS damage ratios for a three span bridge.
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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 7.3 Base Case 7.3.A 7.3.B 7.3.C 5.3 Base Case 5.3.A 5.3.B 5.3.C
Scenario 7.3, CSUS Fragilities, Basoz Damage Ratios 7.3, HAZUS Fragilities, Basoz Damage Ratios 7.3, HAZUS Fragilities, REDARS Damage Ratios 7.3, CSUS Fragilities, REDARS Damage Ratios 5.3, CSUS Fragilities, Basoz Damage Ratios 5.3, HAZUS Fragilities, Basoz Damage Ratios 5.3, HAZUS Fragilities, REDARS Damage Ratios 5.3, CSUS Fragilities, REDARS Damage Ratios
Estimated total direct losses
Standard deviation
$105,000,000
$19,900,000
$71,400,000
$17,700,000
$197,000,000
$27,500,000
$267,000,000
$41,200,000
$50,900,000
$14,700,000
$27,900,000
$11,500,000
$74,200,000
$10,700,000
$125,000,000
$24,900,000
Low Level Event (Mw 5.3)
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HAZUS Fragilities, REDARS Damage Ratios
E[Loss] stdev[Loss]
HAZUS Fragilities, Basoz Damage Ratios CSUS Fragilities, REDARS Damage Ratios
High Level Event (Mw 7.3)
HAZUS Fragilities, REDARS Damage Ratios
CSUS Fragilities, REDARS Damage Ratios
−50
0 50 100 % Variation from Base Model
150
200
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).
250
100
50
Mw = 7.3 CSUS/Basoz CSUS/REDARS HAZUS/Basoz HAZUS/REDARS
250 Number of Bridges
CSUS/Basoz CSUS/REDARS HAZUS/Basoz HAZUS/REDARS
150
0
300
Mw = 5.3
200 Number of Bridges
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−100
HAZUS Fragilities, Basoz Damage Ratios
200 150 100 50
None
Slight
Moderate Extensive Complete Damage State
(a)
0
None
Slight
Moderate Extensive Complete Damage State
(b)
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.
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
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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.
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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 approximately 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 disproportionately 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
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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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References ATC (Applied Technology Council) [1991] ‘‘Seismic vulnerability and impact of disruption of lifelines in the conterminous United States,’’ Report No. ATC-25. Redwood City, California. Basoz, N. and Mander, J. B. [1999] ‘‘Enhancement of the lifeline transportation module in HAZUS,’’ National Institute of Building Sciences Report, Washington, D.C. Bollinger, G. A. [1977] ‘‘Reinterpretation of the intensity data for the 1886 Charleston, South Carolina, earthquake,’’ in Studies Related to the Charleston, South Carolina, Earthquake of 1886: A Preliminary Report, ed. D. W. Rankin, U.S. Geological Survey Professional Paper, pp. 17–32. Crowley, H., Bommer, J. J., Pinho, R., and Bird, J. [2005] ‘‘The impact of epistemic uncertainty on an earthquake loss model,’’ Earthquake Engineering and Structural Dynamics 34, 1653–1685. Dutta, A. [1999] ‘‘On energy based seismic analysis and design of highway bridges,’’ PhD Dissertation, State University of New York at Buffalo, Buffalo, New York. FEMA [2005] HAZUS-MH (Hazards US Multi-Hazard) Software, Federal Emergency Management Agency, Washington D.C. FHWA [2005] National Bridge Inventory Data, Federal Highway Administration, Washington, D.C. Grossi, P. A. [2000] ‘‘Quantifying the uncertainty in seismic risk and loss estimation,’’ PhD Dissertation, University of Pennsylvania, Philadelphia, Pennsylvania. Kircher, C., Whitman, R., and Holmes, W. [2006] ‘‘HAZUS earthquake loss methodologies,’’ Natural Hazards Review 7(2), 45–60. Kiremidjian, A., Moore, J., Fan, Y. Y., Yazlali, O., Basoz, N., and Williams, M. [2007] ‘‘Seismic risk assessment of transportation networks,’’ Journal of Earthquake Engineering 11, 371–382. Luna, R., Hoffman, D., and Lawrence, W. T. [2008] ‘‘Estimation of earthquake loss due to bridge damage in the St. Louis metropolitan area. I: Direct losses,’’ Natural Hazards Review 9(1), 1–11. MAEC (Mid-America Earthquake Center) [2006] MAEViz Software: Mid-America Earthquake Center Seismic Loss Assessment System, http://mae.ce.uiuc.edu/software_and_tools/maeviz.html, Urbana, Illinois Nielson, B.G. [2005] ‘‘Analytical fragility curves for highway bridges in moderate seismic zones,’’ PhD dissertation, Georgia Institute of Technology, Atlanta, Georgia. Nielson, B. G. and DesRoches, R. [2007] ‘‘Seismic fragility curves for typical highway bridge classes in the Central and Southeastern United States,’’ Earthquake Spectra 23(3), 615–633. Padgett, J. E. and DesRoches, R. [2007] ‘‘Bridge functionality relationships for improved seismic risk assessment of transportation networks,’’ Earthquake Spectra 23(1), 115–130. Porter, K. A., Beck, J. L., and Shaikhutdinov, R. V. [2002] ‘‘Sensitivity of building loss estimates to major uncertain variables,’’ Earthquake Spectra 18(4), 719–743. SCDOT [2007] ‘‘Personal communication: South Carolina bridge construction cost data,’’ with J. Padgett and R. DesRoches. Shinozuka, M., Chang, S., Eguchi, R., Abrams, D., Hwang, H., and Rose, A. [1997] ‘‘Advanced in earthquake loss estimation and application to Memphis, TN,’’ Earthquake Spectra 13(4), 739–758. Werner, S. D., Taylor, C. E., Moore, III, J. E., Walton, J. S., and Cho, S. [2000] ‘‘A risk-based methodology for assessing the seismic performanceof highway systems,’’ Technical Report No. MCEER-00-0014, Multidisciplinary Center for Earthquake Engineering Research, State University at Buffalo, Buffalo, New York. Werner, S. D., Taylor, C. E., and Moore, J. E. [1997] ‘‘Loss estimation due to seismic risks to highway systems,’’ Earthquake Spectra 13(4), 585–604. Werner, S. D., Taylor, C. E. Cho, S., Lavoie, J. P., Huyck, C. K., Eitzel, C., Chung, H., and Eguchi, R. T. [2006] ‘‘REDARS 2 methodology and software for seismic risk analysis of highway systems,’’ Report No. MCEER-06-SP08, Buffalo, New York.
Regional Seismic Risk Assessment of Bridge Network in Charleston, South Carolina JAMIE E. PADGETT1, REGINALD DESROCHES2, and EMILY NILSSON3 1
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Department of Civil & Environmental Engineering, Rice University, Houston, Texas, USA 2 School of Civil & Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA 3 Datum 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 for prioritization of bridge retrofit. This study includes an inventory analysis of the approximately 375 bridges in the Charleston area, and convolution of the seismic hazard with fragility curves analytically derived for classes of bridges common to this part of the country. State-of-the-art bridge fragility curves and replacement cost estimates based on region-specific data are used to obtain economic loss estimates. The distribution of potential bridge damage and economic losses are evaluated for several scenario events in order to aid in the identification of emergency routes and assess areas for investment in retrofit. This article also evaluates the effect of uncertainty on the resulting predicted economic losses. 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 considered. Keywords Seismic Risk Assessment; Loss Estimation; Bridges; Fragility; Transportation Network; 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 identification, retrofit selection and prioritization, among other critical tasks. Methodologies for seismic risk assessment of transportation systems have been presented 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 methodologies 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]
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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.
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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 methodologies 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 deterministic 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
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Earthquake Scenario
Fragility Curves for Bridge Classes
Estimation of Ground Shaking at Bridge Locations
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Replacement Cost Data
Bridge Damage State Evaluation
Bridge Repair Cost Ratios (fraction of replacement cost)
Seismic Performance and Consequence 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.
(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,
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Wisconsin to Boston, Massachusetts. Summerville, South Carolina, located to the northwest 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.
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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 MSC_Concrete MSC_Steel MSC_Slab MSC_Conc Box MSSS_Concrete MSSS_Steel MSSS_Slab MSSS_Conc Box SS_Steel SS_Concrete Other Total
Quantity
Percent
1 31 14 6 61 62 118 2 26 19 35 375
0.27% 8.27% 3.73% 1.60% 16.27% 16.53% 31.47% 0.53% 6.93% 5.07% 9.33% 100.00%
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FIGURE 3 Comparison of hazard for deterministic scenarios: (a) Mw 5.3 and (b) Mw 7.3.
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 functionality, 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
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TABLE 2 Damage state definitions [Padgett and DesRoches, 2007] and damage ratios [Basoz and Mander, 1999] Damage state definition [Padgett and DesRoches, 2007] Damage state None Slight Moderate Extensive
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Complete
Damage ratios [Basoz and Mander, 1999] Best mean damage ratio (D)
Functionality description No reduction in functionality Fully functional within a day Reduced functionality for a week Closed for a week, with partial functionality beyond 30 days Complete closure beyond 30 days
Range of damage ratio
0.005 0.03 0.08 0.25
0–0.01 0.01–0.03 0.02–0.15 0.1–0.4
1.0 (if n < 3) 2.0/n (if n 3)
0.3–1.0
n = number of spans.
framework, the damage state is determined from a mean damage ratio, mD, found as follows: D ¼
4 X
Dj P DSj ;
(1)
j¼1
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. Additionally, the mean value of the losses for the bridges in the region is found in MAEViz as: L ¼
X
Cn Dn ;
(2)
n
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 replacement 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 3 Bridge replacement cost data based on South Carolina statistics [SCDOT, 2007] in dollars per area of bridge deck Type Concrete Girder Concrete Box Girder Steel Girder Slab Other (truss, moveable, etc.)
Cost ($/ft2) 67.71 67.98 94.37 60.04 72.53
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bridge types per recent construction data [SCDOT, 2007]. Additionally the standard deviation of the losses is found as: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rX L ¼ ðCn Dn Þ2 ; (3) n
where the sD, the standard deviation of the damage ratio for each bridge is: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 4 uX 2 Dj D P DSj : D ¼ t
(4)
j¼1
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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
FIGURE 4 Spatial distribution of damaged bridges in downtown Charleston for the Mw 5.5 event.
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TABLE 4 Distribution of bridges by damage state and bridge type for the Mw 5.5 event Damage state Type
None
Slight
Moderate
Extensive
Complete
TOTAL
0 12 1 0 23 25 25 0 6 26 30
0 0 2 1 8 1 22 2 6 0 3
1 12 11 5 30 32 71 0 7 0 2
0 7 0 0 0 4 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
1 31 14 6 61 62 118 2 19 26 35
148
45
171
11
0
375
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MSC Concrete MSC Steel MSC Slab MSC Conc Box MSSS Concrete MSSS Steel MSSS Slab MSSS Conc Box SS Concrete SS Steel Other TOTAL
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
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TABLE 5 Summary of direct losses by bridge type for the Mw 5.5 event Type
Direct losses
MSC Concrete MSC Steel MSC Slab MSC Conc Box MSSS Concrete MSSS Steel MSSS Slab MSSS Conc Box SS Concrete SS Steel Other TOTAL
$13,000 $26,000,000 $830,000 $200,000 $2,800,000 $6,000,000 $1,400,000 $60,000 $510,000 $94,000 $2,400,000 $40,307,000
less to the total direct losses. The relative contribution of bridges to the loss estimate offers one approach to help identify and prioritize bridges in need of retrofit.
5. Results: Comparison of Different Earthquake Magnitudes The seismic risk assessment was performed for three different hazards, Mw 4.0, 5.5, and 7.0 (epicenter in Summerville, South Carolina), using the MAEViz platform [MAEC, 2006]. The distribution of expected damage for the three hazard levels is shown in Fig. 5.
FIGURE 5 Distribution of damage as a function of earthquake magnitude.
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120 × 106 100 × 106
Loss ($)
80 × 106 60 × 106 40 × 106 20 × 106 0
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4.0
5.5 7.0 Earthquake Scenario (Mw)
FIGURE 6 Direct economic loss estimates for three scenario earthquakes (Mw 4.0, 5.5, and 7.0). 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,
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fragility information on the bridge vulnerability, repair cost information, among others. Different modeling assumptions and input tools may be classified as epistemic uncertainties. 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 transportation 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 performance 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
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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 presented 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, extensive, 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
0.00 0.03 0.25 0.75 1.00
0–0.01 0.01–0.05 0.05–0.5 0.5–0.8 0.8–1.0
None Slight Moderate Extensive Complete
1.0
0.8 Damage Ratio
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Basoz REDARS (for n = 3)
0.6
0.4
0.2
0.0 None
Slight
Moderate Damage state
Extensive
Complete
FIGURE 7 Comparison of Basoz and REDARS damage ratios for a three span bridge.
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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 7.3 Base Case 7.3.A 7.3.B 7.3.C 5.3 Base Case 5.3.A 5.3.B 5.3.C
Scenario 7.3, CSUS Fragilities, Basoz Damage Ratios 7.3, HAZUS Fragilities, Basoz Damage Ratios 7.3, HAZUS Fragilities, REDARS Damage Ratios 7.3, CSUS Fragilities, REDARS Damage Ratios 5.3, CSUS Fragilities, Basoz Damage Ratios 5.3, HAZUS Fragilities, Basoz Damage Ratios 5.3, HAZUS Fragilities, REDARS Damage Ratios 5.3, CSUS Fragilities, REDARS Damage Ratios
Estimated total direct losses
Standard deviation
$105,000,000
$19,900,000
$71,400,000
$17,700,000
$197,000,000
$27,500,000
$267,000,000
$41,200,000
$50,900,000
$14,700,000
$27,900,000
$11,500,000
$74,200,000
$10,700,000
$125,000,000
$24,900,000
Low Level Event (Mw 5.3)
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HAZUS Fragilities, REDARS Damage Ratios
E[Loss] stdev[Loss]
HAZUS Fragilities, Basoz Damage Ratios CSUS Fragilities, REDARS Damage Ratios
High Level Event (Mw 7.3)
HAZUS Fragilities, REDARS Damage Ratios
CSUS Fragilities, REDARS Damage Ratios
−50
0 50 100 % Variation from Base Model
150
200
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).
250
100
50
Mw = 7.3 CSUS/Basoz CSUS/REDARS HAZUS/Basoz HAZUS/REDARS
250 Number of Bridges
CSUS/Basoz CSUS/REDARS HAZUS/Basoz HAZUS/REDARS
150
0
300
Mw = 5.3
200 Number of Bridges
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−100
HAZUS Fragilities, Basoz Damage Ratios
200 150 100 50
None
Slight
Moderate Extensive Complete Damage State
(a)
0
None
Slight
Moderate Extensive Complete Damage State
(b)
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.
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
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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.
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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 approximately 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 disproportionately 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
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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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