Earthquake Risk Assessment for Transportation Systems:
Analysis of Pre-Retrofitted System

Anne S. Kiremidjian(1), James Moore(2), Yueyue Fan(3), Ayse Hortacsu(4), Kelly Burnell(5), and Jeremiah LeGrue(4)
1 Professor, Department of Civil and Environmental Engineering, Director of the John A. Blume Earthquake Engineering Center, Stanford University, Stanford, CA 94305
2 Associate Professor of the Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA 90089
3 Graduate Student, Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA 90089
4 Graduate Student, Department of Civil and Environmental Engineering, The John A. Blume Earthquake Engineering Center, Stanford University, Stanford, CA 94305
5 Undergraduate Student, Department of Civil and Environmental Engineering, The John A. Blume Earthquake Engineering Center, Stanford University, Stanford, CA 94305

Transportation systems are spatially distributed systems whereby components of the system are exposed to different ground motions due to the same earthquake event. Consideration of the spatial dependence of individual components, connectivity, and flow through the network are key factors in the development of an earthquake risk assessment model for such systems.

Most recently, Werner et al. (1999) and Basoz and Kiremidjian (1996) considered transportation network systems subjected to earthquake events. In both of these publications, the risk to the transportation system is computed from the direct damage to the major components such as the bridges, the connectivity between a predefined origin-destination (O-D) set, and the time delays from bridge closures. The software HAZUS (1999) for regional loss estimation, developed by the National Institute for Building Standards (NIBS) for the Federal Emergency Management Agency (FEMA), considers only the direct loss to bridges in the highway transportation network. The connectivity and traffic delay problems resulting from damage to the components of the system are not included. In a paper by Chang et al. (2000) a simple risk measure for transportation systems is proposed to represent the effectiveness of retrofit strategies by considering the difference in damaged highway links before and after retrofitting. The proposed risk measure can be a useful tool but should be expanded to consider actual travel times because damaged links do not necessarily reflect the actual costs associated with travel delays, which is a function of the network redundancy.


Figure 1. Risk assessment methodology for highway network systems

In the current study a framework for risk assessment of a transportation system is postulated that considers the direct cost of damage and costs due to time delays in the damaged system. The study was conducted by PEER faculty participants Anne S. Kiremidjian and James Moore, and graduate student researchers Yueyue Fan, Ayse Hortacsu, Kelly Burnell, and Jeremiah LeGrue. The model is first formulated for a scenario event and then expanded for a suitable ensemble of earthquake events to capture the total hazard and risk to the system.

Model Formulation

For the purposes of this project, the risk to transportation network systems is defined as the expected cost of damage and loss of functionality of the system when subjected to a severe earthquake, denoted by E[Loss]. For a given earthquake event , the expected loss from the system can be estimated as
     (1)

where

 = cost of repair of individual components of the system at damage D due to intensity IM from an event , where
 = probability density of damage D due to intensity IM from an event
= probability density of hazard intensity IM from an event
= costs associated with time delays T due to detours of route closures or reduced traffic capacity per event

 

 

 

 

 

The annualized risk of loss for the transportation system from all possible events that may affect the system, occurring with rates , is
     (2)

Equations 1 and 2 are consistent with the general equation used by PEER (Cornell and Krawinkler 2000) to characterize the performance of a structure or, as in this case, a system. If we define the total cost to be the decision variable DV in the PEER equation, Equation 2 reflects the expected value of that decision variable. Similar relationships have been developed for estimating the standard deviation of the costs. Evaluation of the decision probability distribution   will require very high computational capabilities, such as those by supercomputer, to perform the large number of simulations needed for this process.

Figure 1 shows the major components of the overall methodology. Four types of hazards from earthquakes are identified in that figure — ground motion, liquefaction, landslides, and fault displacements. The hazard intensity measure IM for such a system consists of the hazard from ground shaking denoted as IM(A) and hazard due to ground deformations IM(G), such as amount of lateral spreading or settlement from liquefaction, ground displacements due to landslides, or surface ruptures from direct fault displacements or local ground fissuring. The main distinction between the hazard evaluation of a network system and a building is that the hazard has to be evaluated at the multitude of the system component locations. This process is greatly facilitated with the use of geographic information systems (GIS) that enables the storing of such information in a spatial manner that permits overlay of network system data onto the hazard information, creating a link between the hazard and the network component within the same platform.

 
Figure 2. Distribution of pre-retrofit damaged bridges in the San Francisco Bay Area for a scenario earthquake of moment magnitude 7.5 on the San Andreas Fault.

The damage to individual components of the network is expressed in terms of fragility functions, here denoted simplistically as . In general, a distinct fragility function is required for each component in the network. Furthermore, separate fragility functions are needed to estimate the damage from ground shaking and from ground deformation. Given the large number and diversity in designs of bridges, pavement segments, and tunnels that exist in a highway network, it has become customary to group these components into generic classes that capture the gross characteristics of the various components. As computational power increases and our ability to efficiently and effectively evaluate damage on a structure-by-structure basis improve, such classification and generic fragility functions will not be necessary. Currently, various researchers within PEER are developing fragility functions for different bridge classes. For the purposes of applying the methodology presented in this article, the fragility functions developed for implementation in the 1999 HAZUS software will be utilized (Basoz and Mander 1999).

The direct loss functions in equations 1 and 2 include losses due to damage from ground shaking and ground deformations, and represent the cost of repair of damaged components. For a given event , losses due to time delays arise from delays in commuter and freight traffic. The time delays result from closure of particular routes because of excessive damage to key components such as bridges, or due to reduced flow capacity (either from imposed lower speed limit or closure of a number of available traffic lanes) due to minor or moderate damage. The increase in travel times is the difference in the travel times for specified origins and destinations
(O-D) for commuter and freight traffic under normal operating conditions and travel times after an earthquake with reduced capacity or closure of certain links and nodes in the system.

Application Area Description

One of the main objectives of this project is to apply the methodology to an existing highway transportation system. During the first PEER Transportation Risk Analysis Workshop, held in 1998, the workshop participants recommended that the application area be the San Francisco Bay region. The rationale for the selection was that the region has a very complex transportation network with limited redundancy. In particular, it is very likely that the major bridges in the region will be subjected to ground motions of similar severity due to their proximity to major faults in the area. All the long-span bridges, the San Francisco-Oakland Bay Bridge, the Golden Gate, San Mateo, Dumbarton, and San Rafael, are flanked by the San Andreas fault to the west and the Hayward fault or its extension to the east.

Damage State
Hayward 7.0
# of bridges
Hayward 7.5
# of bridges
San Andreas 7.5
# of bridges
San Andreas 8.0
# of bridges
1
1732
1350
1589
1334
2
585
778
658
634
3 closed
221
280
249
413
4 closed
91
182
110
201
5 closed
21
50
35
59

Table 1. Distribution of pre-retrofit bridge damage for different scenario earthquakes

In addition to the San Andreas and Hayward faults, the Calaveras and the San Gregorio-Palo Colorado fault are also capable of significant earthquakes that can cause damage to the system. For the purposes of the demonstration project, however, only events on the San Andreas and the Hayward faults were considered. These include moment magnitude events of 7.5 and 8.0 on the San Andreas fault and 7.0 and 7.5 on the Hayward fault. The rupture length was estimated using the Wells and Coppersmith (1994) relationship for strike-slip faults, and the rupture location is assumed to be such that it flanks the entire network system. Ground motions for the region were estimated using Boore et al. (1997) attenuation function for peak ground and spectral accelerations. The ground motions reflect the local soil conditions classified as B, C, D, and E (Boore et al. 1997). Ground motions within 15 km from the fault were estimated using the Campbell (1997) attenuation function. Currently, the team is evaluating the liquefaction potential and ground deformations for the scenario events. Figure 2 shows the distribution of ground motion for the magnitude 7.5 event on the San Andreas fault. The commercial software ARC/INFO(TM) was used for the purposes of storing and displaying the ground motion information.


Figure 3. Closed Highway links for pre-retrofit bridge damage in the San Francisco Bay Area for a scenario earthquake of moment magnitude 7.5 on the San Andreas Fault.

Data on bridge locations and engineering characteristics were obtained from the California Department of Transportation (Caltrans). The data were verified and corrected by Basoz [Basoz and Kiremidjian (1997)]. A total of 2,640 bridges were included in the study. These were classified according to the NIBS (1999) scheme, which utilizes the National Bridge Inventory (NBI) physical attributes. The site ground motions for each bridge were determined by overlaying the bridge location onto the ground motion map. The expected damage state for each bridge was estimated using the NIBS fragility functions. Five damage states are defined in Basoz and Mander (1999) for highway system components. These are none, slight/minor, moderate, extensive and complete. Table 1 lists the number of pre-retrofit bridges in each damage state for the four scenario earthquake events. For the analysis of the transportation network it was assumed that if a bridge is in damage state 3 or greater, the bridge is closed to all traffic, and if the bridge is in damage state 1 or 2, it is open at full capacity. Partial closures or reduction of speed limits was not considered for this initial evaluation. These will be investigated in subsequent analyses. Figure 2 shows the distribution of pre-retrofit bridge damage with the distribution of ground motion.

Information on the highway transportation network for District 4 in California, which corresponds to the San Francisco Bay Area, was obtained from the Metropolitan Transportation Commission (MTC). A significant effort was devoted to importing the highway network information within the ARC/INFO(TM) GIS. The bridge data were then linked to the highway network and corrected to match bridge locations with network locations. Baseline analysis was conducted on the transportation network pre-earthquake scenario. The post-earthquake scenario for a magnitude 7.5 event on the San Andreas fault was modeled in EMME/2, a transportation systems network analysis software. Based on this initial analysis closed links within the system were identified, shown in Figure 3. Table 2a summarizes the number of links, the link and lane lengths, and the number of vehicles affected by the closures. These results should be considered as preliminary because most of the work is still in progress. Table 2b presents the results for the number of vehicle miles, average speed, average commuter traffic volume, and the maximum volume effects of the earthquake. The baseline calculations correspond to the pre-event conditions and demands. The postevent analysis results are listed under the SA (San Andreas) 7.5 column.


Table 2a. Effect of pre-retrofit bridge closure on the highway transportation system in District 4, California
Notes: Link Type 1 = freeway to freeway ramp, Link Type 2 = freeway, Link Type 3 = expressway, Link Type 4 = collector, Link Type 5 = on or off ramp, Link Type 6 = centroid connector (a virtual link connecting travel demand to physical links in the vicinity of a traffic analysis zone), Link Type 7 = major road, Link Type 8 = metered ramp, and Link Type 9 = Golden Gate Bridge


Table 2b. Effect of pre-retrofit bridge closure on the highway transportation system in District 4, California

At present, a preliminary estimate on the cost of replacing and repairing the bridges in the Bay Area in the event of an earthquake has been obtained. For that purpose an estimate of the total square foot area of each damaged bridge has been computed using basic information available in the bridge database and using California repair costs per square foot. Table 3 lists the total repair or replacement cost for each scenario event. These numbers are very preliminary and should be used only for illustrative purposes rather than as absolute terms. They are based on generic regional replacement costs and do not reflect bridge specific repair and replacement costs.

Scenario
# of Damaged Bridges
Total Repair/Replacement Costs
Hayward 7.0
974
$168,234,741
Hayward 7.0
1321
$273,477,856
San Andreas 7.5
1045
$201,759,360
San Andreas 8.0
1277
$299,843,314

Table 3. Preliminary scenario pre-retrofit bridge repair/replacement cost totals

The research team is currently obtaining more realistic cost estimates as provided by Caltrans engineers. Furthermore, the retrofitted strength of bridges has not been taken into consideration. The bridge database is currently being augmented to reflect the bridges that have been retrofitted over the past ten years. The effect of this information will be that bridge damage will be reduced, and as a result repair costs will decrease. In addition, the network performance will change, reducing the difference in pre- and post-event numbers listed in Tables 2a and 2b. Costs due to traffic delays are still under investigation.

References

Basoz, N., and A. Kiremidjian. 1996. Risk assessment for highway transportation systems. Stanford, Calif.: J. A. Blume Earthquake Engineering Center, Dept. Civil Eng., Stanford University. Report No. 118.
Basoz, N., and J. Mander. 1998. Enhancement of the highway transportation module in HAZUS. Report to National Institute of Building Sciences. Washington, D.C.: [National Institute of Building Sciences].
Boore, D., W. Joyner, and T. Fumal. 1997. Equations for estimating horizontal response spectra and peak acceleration from North American earthquakes: A summary of recent work. Seismological Research Letters 68(1): 128–53.
Campbell, K. W. 1997. Empirical near-source attenuation relationships for horizontal and vertical components of peak ground acceleration, peak ground velocity, and pseudo-absolute acceleration response spectra. Seismological Research Letters 68(1): 154–79.
Chang, S., M. Shinozuka, and J. Moore. 2000. Probabilistic earthquake scenarios: extending risk analysis methodologies to spatially distributed systems. Earthquake Spectra 16(3): 557–72.
Cornell, A., and H. Krawinkler. 2000. Progress and challenges in seismic performance assessment. PEER Center News 3(2): 1–3.
Federal Emergency Management Agency. 1997. Earthquake loss estimation methodology: HAZUS technical manual. Prepared by National Institute of Building Sciences. Washington, D.C.: Federal Emergency Management Agency.
HAZUS. 1999. Earthquake loss estimation. Technical manual. Washington, D.C.: National Institute of Building Sciences.
Wells, D., and K. Coppersmith. 1994. New empirical relationships among magnitude, rupture length, rupture width, rupture area and surface displacement. Bull. Seism. Soc. Am. 84(4): 974–1002.
Werner, S., C. Taylor, J. Moore, and J. Walton. 1999. Seismic risk analysis of highway systems: New developments and future Directions. “Optimizing Post-Earthquake Lifeline Systems Reliability,” Proc. 5th US Conf. Lifeline Earthq. Eng., ASCE/TCLEE, Monograph 16, 11–20.