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Development and Calibration of an Earthquake Fatality Function

Author(s)

John M. Nichols and James E. Beavers

Corresponding author: James E. Beavers

Mailing address: Mid America Earthquake Center, NCEL, Room 1241,

UIUC, Urbana Il 61801

Phone: 217 244 6827

Fax: 217 333 3821

E-mail address:beavers@uiuc.edu

Submission date for review copies: Tuesday, 22 April 2003

Submission date for camera-ready copy:

Paper: Paper24.Doc

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Development and Calibration of an Earthquake Fatality Function

John M. Nicholsa) and James E. Beaversb), M.EERI

Structures present a risk during seismic events from partial or full collapse that can cause death and injury to the occupants. The United States Geological Survey (USGS) has collated data on deaths from and magnitudes of earthquakes. These data have not previously been analysed to establish any relationships between fatality tolls or fatality rates in different earthquakes. An investigation of the fatality catalogue establishes a bounding function for the twentieth century fatality data using the USGS assigned earthquake magnitude as the dependent variable. A simple equation was established and calibrated to relate the fatalities in earthquakes having tolls lower than the bounding function to the bounding function. This equation and the calibration data, essentially for unreinforced masonry and timber-framed buildings, provides a procedure for estimating fatality counts in future theoretical events with a specific combination of circumstances. Potential uses of the fatality function with further refinement are economic analysis of seismic mitigation alternatives for unreinforced masonry structures, Current uses of the fatality function can be for real time estimating of fatalities in earthquakes in remote locations, and estimating fatality counts in future earthquakes for planning purposes.

INTRODUCTION

This paper presents the development of a fatality estimation function that extends the mathematical theory developed by Shiono (1995, 1995a). Shiono related distance to the epicenter to the fatality rates through the collapse rate of buildings. The collapse rate function for masonry buildings was a function of the felt intensity for the 1976 Tangshan, China earthquake. Forrest (2000), in a letter to the first author , questioned the likely impact of the movement fault close to Wellington, New Zealand on an area of older unreinforced masonry dwellings. This question formed the starting point for thesis of this research into economic and social losses from earthquakes. The work initially related to older masonry dwellings in areas such as Wellington, NZ and Memphis, TN.

The objective of this research was to develop an earthquake fatality function that can be used to estimate future earthquake fatalities for a given set of earthquake and urban circumstances. This function provides theoretical data fro economic and social loss studies (OMB, 1992).A number of nineteenth and twentieth century earthquake events were identified as having characteristic features making them useful as calibration events for developing the proposed fatality function. The function was calibrated using Chinese, European, New Zealand (NZ), and United States (US) data that provided a basis for estimating death tolls in future events where the ground and building conditions were

a) Department of Construction Science, Texas A and M University, College Station, TX, 77843 b) Mid-America Earthquake Center, University of Illinois, Urbana, Illinois, 61801

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consistent with the existing calibration data. The central and eastern United States (CEUS) presents one example of the type of urban areas where this method is directly applicable.

The events selected for study were the 1886 Charleston, South Carolina ; 1915 Avezzano, Italy; 1931 Napie r, NZ; and 1976 Tangshan, China earthquakes. Each of these earthquakes had death tolls in excess of one percent of the population or was a large earthquake with high-quality point data on the destruction of an urban area. These earthquakes occurred near areas with older unreinforced masonry or timber -framed construction that were similar in construction type, age, and likely quality to the areas of original interest in Memphis, Tennessee, and Wellington, NZ. The Napier and Tangshan earthquakes had similar magnitudes providing a sound calibration point for the extension of the previous research work by Shiono. The 1886 Charleston earthquake damaged masonry and timber-framed housing on filled and natural ground providing well-documented research data for comparison to other areas of similar housing (USGS 1977). The USGS (1977, 2000) assigned magnitude was used for all earthquakes in all papers that were derived from this research. We consider that this decision provides a consistent standard for the work, and one that makes the earthquake fatality function easy to apply.

LITERATURE REVIEW

INTRODUCTION

This literature review presents details of the specific earthquakes used as calibration data for development of the fatality function. Earthquake data presented are the statistics and analysis of earthquake deaths, existing fatality functions, and commentary on the public perception of earthquake risk. Public perception presents a significant problem as the tragic consequences of earthquakes are often underestimated or ignored by the world’s inhabitants, e.g., total fatality counts not being recorded. The world’s seismic literature is replete with accounts of the devastation caused by earthquakes (Algermissen 1972, Steinbrugge 1982, Ward and Valensise 1989). An earthquake kills more than 5,000 people on average every 900 days (Nichols et al, 2000). Kunreuther (1993) commented on the common human perception that attributes a lower apparent probability to these events than is the reality with earthquake recurrence intervals. These are, however, low probability but high consequence events for which the average human is poorly prepared to understand or credit a realistic risk level to the event. The central and eastern United States is an example of one such area where this risk exists. The critical issue to the thesis is developing the ability to compare the results of the function deve lopment and calibration between different cities.

The CEUS had no significant earthquakes in the twentieth century in direct contrast to Italy, New Zealand, and China. The CEUS represents about three percent of the world’s population and area. The last significant earthquake in the CEUS occurred in 1895. The lack of earthquake activity in the CEUS during the twentieth century belies the current significant risk for an earthquake in the range of M5.5 to M7 (Nuttli 1974). This paper specifically avoids discussion on the large cyclic events in the range of M8 that appear to dominant the New Madrid Seismic Zone (NMSZ). The topic of the size of the New Madrid events is the subject of some current debate. The paleoseismological and structural geologic data would appear substantive enough to answer this minor question without further comment (Frankel et al. 2000, Tuttle et al. 2000, Wallace and Scott 1999).

Beavers (1993) conducted a conference entitled Earthquake Hazard Reduction in the Central and Eastern United States — A Time for Examination and Action. As part of

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Monograph 5, Socioeconomic Impacts, Jones et al. (1993, 19-53), summarized the methodologies used to estimate deaths in earthquakes to 1993. Jones’ paper listed the estimated fatalities and injuries from different possible earthquakes in the CEUS. Jones specifically examined and discussed the lack of epidemiologic data for earthquake casualties. The ratios of the fatalities to the injuries varied widely within this table of results. FEMA (1999, Ch 9, 47) sets out the method used to estimate deaths in earthquakes in the program HAZUS99. The function uses loss estimates based on collapse rates for three levels of structural damage. The rates can be varied in the functions. The manual clearly identifies the deficit of data that exists in this field and this limits the reliability of the estimates. FEMA (1985) estimated an earthquake fatality count for Memphis and surrounding regions at approximately 3500 persons for a major event in the NMSZ and for Charleston, SC (Table 1).

Table 1. Loss estimates in the central and eastern United States1

Reference Region Fault Deaths Injured Mann, et al., 1974

Mississippi, Arkansas, Tennessee

New Madrid 1,100 4,400

Liu, et al., 1979

New Madrid New Madrid 646 64,567

FEMA, 1985 Six Cities Study New Madrid 4,907 19,590 FEMA, 1985 Charleston, SC Woodstock/Ashley 2,143 8,574

1. Table 3 from Jones et al. (1993, 29)

Jones et al., (1993, 27) commented “Serious doubt exists as to the validity of the existing casualty estimation functions – both pre and post event. Most are based on engineering functions with little input from medicine or epidemiological studies.” The conclusion reached from the data presented in these studies is the physical separation between the Memphis population center and the known active faults should prevent the extreme death tolls such as occurred in Tangshan, but even moderate earthquakes in this region have the potential to cause fatalities in Memphis. Shannon and Pyle, (1993, 111, figure 11.1) provide details of motor vehicle deaths. This research shows 20 deaths per 100,000 people per annum for the early 1990s. The earthquake loss estimated by FEMA at 3,500 in Memphis is equivalent at current rates to about twenty-five years of motor vehicle deaths occurring at one time in this region. So while infrequent, the consequences are high for the population that experiences such an earthquake.

Nichols et al, (2000), in considering the original question raised by Forrest, estimated the likely fatality rates caused by earthquakes at two locations that had been identified as having a potential problem with older unreinforced masonry dwellings. These locations were Wellington, NZ and Memphis, TN. The fatality rates were estimated to provide information for a simple economic analysis. The economic analysis considered the cost to benefit ratios of various retrofit techniques for unreinforced masonry buildings for moderate to high seismic risk zones. Nichols and Totoev (2001) looked at the direct benefits and costs of mitigation work to show the benefits to the property owner and the potential reduction of fatalities. Peek-Asa et al, (2000) studied the deaths and injuries in the 1994 Northridge earthquake. The study showed the Modified Mercalli Intensity (MMI) provided the best indicator as the level of death and injury. The general findings presented in Peek-Asa’s study show an elliptical area containing the fatalities and a fatality rate. Peek-Asa observed the rate of fatalities and injuries decreased with decreasing MMI.

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1886 CHARLESTON EARTHQUAKE

Charleston, South Carolina experienced the 6.8mb earthquake at 9:50 pm on August 31, 1886. The recorded death tolls range from 60 (USGS 1977) to 93 (San Francisco Chronicle 1906). Stockton (1986) states "a total of 27 people were killed outright and another 49 died of injuries". The city had a population of 49,000 and an eyewitness account notes that the event occurred just after the population had returned from Sunday service. The peak-felt intensity for the earthquake has been estimated at MMI X near Summerville; although the extensive collection of photographs of the damaged buildings and subsequent analysis by the USGS (1977) suggests that Charleston experienced a peak-felt intensity of MMI IX.

The eyewitness account noted that falling walls and chimneys killed people rather than collapsing buildings. The type and level of damage to the brick houses in Charleston was reasonably constant between the filled river areas and the original solid high ground. One third of the population lived in timber-framed buildings on solid ground. These buildings suffered less than 0.5 % damage (USGS 1977). Almost 90 % of chimneys collapsed in the earthquake. Robinson and Talwani (1983) reported on building construction type, location and damage for the earthquake (Table 2).

Table 2 1886 Charleston earthquake damage (after Robinson and Talwani 1983)1

Location Brick total Brick damaged Frame total Frame damaged

Solid land 1,214 765 (63%) 2,420 12 (0.5%)

Reclaimed land 10,850 523 (69%) 2,059 294 (14%)

City wide 3,125 1,288 (66%) 4,479 306 (7%)

1. The arithmetic error in the original table has been corrected.

1915 AVEZZANO EARTHQUAKE

An earthquake with a probable recurrence interval of 1,400 to 2,600 years struck the Abruzzo region of Italy on January 13, 1915 (Ward and Valensise 1989) . In the Abruzzo region the towns of Avezzano and Ortucchio sit at either end of the Fucino Plain. Following the 1915 Avezzano earthquake the Italian authorities collected statistical data on the locations and the rates of death in the various villages scattered in the fatality area (ING-SGA 2000). This well-documented data provided point type data that were extremely useful in calibration (Figure 1).

The Fucino Plain located about 65 to 80 kilometers east of Rome is a 25 by 15 kilometer basin formed as a Quaternary tectonic depression or intermontane half-graben. The Romans used a tunnel system to drain the lake or depression to provide farmland. The tunnel system silted up in the first millennium AD. The drainage system was repaired in the late nineteenth century to recreate a sparsely settled farmland with the older existing towns situated on the higher ground around the old depression. The Avezzano earthquake occurred on the fault system adjacent to the plain for med by draining the lake. Prior movement on this fault system caused the Quaternary tectonic depression.

Ward and Valensise (1989) established a “variable slip planar fault model of the earthquake [which] reduces the uniform slip planar models variance by 82 percent and reveals a broad two-lobed slip pattern separating a central region of low moment release.” In simple terms, their analysis shows there were higher levels of energy release beneath the two

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towns at each end of the plain. Galadini and Galli (1999) noted that “this observation (regarding the recurrence interval) clearly directs future geological and paleoseismological research towards the individuation and characterization of historically ‘silent’ active faults.” This type of fault and event with a long recurrence interval and few if any smaller events to delineate this as an active fault doesn’t permit testing of local construction techniques between such catastrophic events.

Figure 1: 1915 Avezzano earthquake fatality rate contours.

Specific information about the event was available from descendants of the Abruzzo region who had migrated to the United States (Troz 2000). The death toll in Avezzano was 95 per cent of the population (ING-SGA 2000). The disaster struck during church services in the early morning. As one observer noted “the stone church in Ortucchio, as in many Abruzzo villages, collapsed upon the parishioners, killing many of them. Some entire families perished at this time” (Troz 2000). The coordinated data in the Italian records (ING-SGA 2000) were plotted in the form used by Shiono (1995) to derive a fatality rate against distance to the epicenter (Table 3). This data has a clear elliptical shape that was similar to the Californian findings of Algermissen (1972) and Peek-Asa et al, (2000).

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Table 3. Avezzano fatality rates against distance

Fatality rate %

Radius (Elliptical long axis) kilometers

Radius (Elliptical short axis) kilometers

75 to 100 5 2

33 to 75 16 5

10 to 33 25 10

0 to 10 45 21

1931 NAPIER EARTHQUAKE

New Zealand has one of the highest rates of plate movement (IGNS 2000) on the Pacific Rim, and has a legacy of existing masonry buildings of two to three story construction located within the major cities. The IGNS (2000) expects that the next major movement that might cause damage in NZ may occur in the Wellington region. This region had deaths in the late 1800s from an earthquake (Forrest 2000). The 1931 Napier, NZ earthquake killed 256 people in a population of approximately 30,000. The information on this event and the affected towns available from the NZ Ministry of Civil Defence (2000) and Massey (2000) is summarized in Table 4.

Table 4. 1931 Napier earthquake data

Location 1931 Population 1999 Population 1931 Deaths

Napier 16,025 54,000 162

Hastings 10,850 ----1 91

Havelock 3,125 ---- ----

Wairoa ---- ---- 3

Total 30,000 ---- 256

1. The population data was not supplied.

These data were useful for calibration purposes as it provided point datum at four different locations in a form that was consistent with the Chinese and Italian data. The earthquake had a magnitude of 7.9 and an epicentral distance of 15 to 20 kilometers to the town centers. Napier forms approximately eighteen percent of the Heretaunga Plains. These plains evolved by the deposition of sedimentation from surrounding rivers. They are noted as some of the highest quality soils in the country. The land use is predominantly horticultural and pastoral (NCC 2000). NCC (2000) noted “Historically Napier has developed as a distinct series of urban ‘cells’, often separated or bordered by the open drainage network which characterizes the city’s urban form. As a result of the staged ‘cell’ development of the city, most areas have developed with a distinctive period character.”

1976 TANGSHAN EARTHQUAKE

TMG (2001) noted that the hundred year old city is “situated in the central section of the Bohai Bay area. It lies against the Yanshan Mountains to the North, overlooks the Bohai Sea to the South, neighbors Qinhuangdao to the East, and Tianjin and Beijing to the West. Corn,

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wheat, rice peanuts, and vegetables are cultivated in the central plains area, which is known as ‘The Granary of East Hebei Province’”. The 1976 earthquake damage further north of the city was noted as being less than the city and farmland areas because of the thinner sedimentary layers.

Shiono (1995) showed for the city of Tangshan that a simple set of relationships and an equation could be established to relate the percentage of deaths to the percentage of buildings that collapsed, and then the distance from the epicentre could be related to the percentage of buildings that collapsed. The fatality and collapse rates for the M8.0, 1976 Tangshan earthquake data from Shiono’s data (1995) are presented in Table 5.

Table 5. Collapse and fatality rates for Tangshan (after Shiono 1995)

Seismic Intensity

Building Collapse Rate %

Area (km2)

Approximate Radius (km)

Fatality Rate %

5 0 216,000 250 0

6 1 ---1 --- ---

7 7 33,300 100 ---

8 16 7,270 50 3

9 30 1,800 20 82

10 60 370 10 15

11 90 47 4 ---

11.2+ 100 --- 0 30

1. Data not provided. 2. Interpolated.

Shiono’s theory was established from the official fatality information for the 1976 Tangshan earthquake, which included 242,000 deaths. The unofficial death toll in the 1976 Tangshan earthquake has been reported as high as 655,000 (USGS 2001). The problem of the official fatality counts being an underestimate of the real count has been informally raised for a number of twentieth century events, but this count problem is not readily resolvable. The example of the recent three-fold increase in the 1906 San Francisco toll presents evidence of the difficulty of determining a final accurate toll (Hansen and Condon 1989). The official toll was used for this research to be consistent with Shiono’s analysis (Shiono 2000). A linear regression of the injury rates in the Peek-Asa study of the 1994 Northridge Earthquake against the fatality rates for the Tangshan data for felt intensity had a regression co-efficient of 0.91. The result can be partly attributed to the the effect of improved construction in California reducing the death tolls.

DISCUSSION

Sufficient observational data exists to confirm that it is reasonable to use prior fatality data for estimating fatalities in future theoretical earthquake events for specific circumstances. The initial analysis points to the potential development of a predictive function, that such a function has limitations are accepted, but such a function can be used for planning or real time estimating purposes. A number of factors affecting the level of the death toll were identified for these tragic events.

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These factors were, the timing of the events, and the time between events impacts on the death toll. The felt intensity has a causal relationship to the death toll through the rate of building collapse. The magnitude of the earthquake, the distance between each population area and the epicenter, and the distribution of energy release relative to the population’s location affected the death toll. The construction quality of the buildings and the ground conditions affected the fatality rates in the different buildings or areas. The number of people exposed to the earthquake inside buildings also affected the death toll.

The similarities between geological conditions and the soil conditions are of interest in assessing the impact of historical earthquakes that occurred in these areas. Tangshan and Napier comprise urban areas scattered among first class farming land. This farming land was sedimentary material overlying the residual rock. Charleston has been described as having part solid ground on the original riverbanks and reclaimed river land. Avezzano was partly a drained lake used as farmland and the surrounding hinterland that had been settled for many millennia. Tangshan and Napier are approximately 100 to 150 years old with typical construction for the periods of development. It would appear reasonable to conclude that this type of geological setting and the types of masonry and timber construction in Napier and Tangshan are equivalent to that which would be found in places such as Memphis located on similar types of sedimentary depositional material, where the buildings are of a similar age. These areas were developed in large part before the introduction of seismic codes and the current knowledge gained in California and Japan had been effectively disseminated. Charleston had a reasonable mixture of masonry and timber framed houses in 1886. These houses would represent typical construction in the late nineteenth century for the eastern United States. The 1915 Avezzano earthquake represented failure of church buildings. The final point that comes out in passing in this literature review, particularly Charleston and Avezzano, was the danger presented by failure of churches. These structures with their large masonry walls and heavy roofing materials and low levels of structural redundancy presented and still present a significant danger to the public if occupied at the time of the earthquake.

MEIZOSEISMAL DEFINITION

The development of this research requires clarification of the term meizoseismal that has previously been used in the description of earthquakes, associated ground movements and damage. The definition of interest to a fatality function is the term meizoseismal area. The Oxford English Dictionary (2001) attributes meizoseismal to Mallet in the year 1859 as pertaining to the points of maximum disturbance in an earthquake. Richter (1958) quotes from Kato regarding the 1891 Mino-Owari earthquake where the areas of peak meizoseismal movements were in the alluvial valleys.

The fatal meizoseismal area in the context of this paper was defined as the area of damage that can cause death. In this case we are specifically refering to areas enclosed by the line of building damage likely to cause death. Shiono’s (1995) data indicates this is about the isoseismal delineating the felt intensities five and six. The damage outside this area is economically significant but not generally fatal. The building damage within this fatal meizoseismal area can cause death, the building damage in the remaining or economic meizoseismal area should not cause significant deaths.

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EARTHQUAKE AND FATALITY DATA

Twentieth-century earthquakes that have caused significant fatality counts for the magnitude are presented in Table 6.

Table 6. World earthquake data – magnitude and fatalities

Year Fatality count

Number of people in the area

Magnitude: USGS

coding Ms NOAA -UNO 1

Percentage of total population in fatal meizoseismal area

that died %

Name Country

1976 242,500 750,000 8 30 Tangshan China

1908 58,000 282,000 7.5 20 Messina Italy

1915 32,610 195,540 7 17 Avezzano Italy

1988 24,900 550,000 2 6.8 4.5 Spitak Armenia

1972 6,000 600,000 3 6.2 1 Managua Nicaragua

1999 1,124 270,000 5.9 Ml - EERI

0.42 Armenia Columbia

1989 13 250,000 5.5 MDCNB

0.005 Newcastle Australia

1. Source http://neic.usgs.gov/neis/epic/epic_global.html

2. Armenian et al. (1997), this lower bound estimate is based on the count of the homeless and dead, p. 806.

3 U.S. Bureau of the Census (2000), This estimate is based on the U.S. Census data, International Data Base Table 001, Total Midyear Population 2000 by assuming half in capitol as for current population </www.census.gov/ftp/pub/ipc/www/idbprint.html>

Fatalities for all fatal twentieth century earthquakes were plotted against earthquake magnitude (Figure 2). One event prior to the tenth century was included in the plot. This was the 856 AD Iranian earthquake. The events in California and New Zealand causing death in the nineteenth century are also included on the graph. The figure has been divided into four regions named Regions 1, 2, 3, and 4. The fitted trivial equation for the plotted indicator lines, Plots 1 to 3, on the graph has the form shown in Equation 1. These equations are meant as bounding lines between regions in the figure and are not estimator lines for fatalities. The pre1900s data was included to depict significant world trends but they do not form part of the analysis. The data included a notation as to the year of the event and a brief two-unit descriptor for the place, for example, the notation CA refers to California, TR Turkey, CH China, AU Australia, NZ New Zealand and AL Alaska. These points were annotated to permit explanation of the initial development of the earthquake fatality function theory from this graph. M represents the earthquake magnitude, )(MFΞ represents the fatality count, and J and K variables represent the fitting points for the plotted lines. Plot A has zero slope.

KMF JeM =Ξ )( (1)

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Figure 2. Earthquake fatalities and magnitude for the twentieth century

The variables for the plotted lines are presented in Table 7.

Table 7. Plotted Line Data from Figure 2

Plotted line Name of main earthquakes on the plotted line J K

1 1976 Nicaragua-Newcastle 6*10-21 9

2 1976 Tangshan-Newcastle 5*10-09 4

3 1906 California-Newcastle 0.0052 1.4

INTERPRETATION OF THE REGIONS IN FIGURE 2

Plot 1 represents the lower bound to Region 1. No Region 1 events were reported in the last century. Region 2 has Plot 2 as the lower bound and represents the area of the greatest known fatality rates for magnitude of earthquake. Earthquakes in this region of the figure were considered unusually savage for the magnitude of the event. The plotted point for the 856 AD Iranian earthquake resulted obviously from poor adobe and stone construction. It was plotted to highlight the problem with weaker masonry. It is, however, considered an outlying point for the twentieth century data set because of the difficulty of confirming the magnitude and death toll, and because of changes in construction methods.

Plot 2 is fitted through the Newcastle to Tangshan events. This line is considered the primary indicator function between Regions 2 and 3. Fatal events that fall above Plot 2 within Region 1 or 2 are rare and unusually savage. An earthquake that falls into Region 2, which

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clearly defines the characteristics of this type of tragic failure, was the 1988 Spitak earthquake, which had significant child loss in schools (Hadjian 1992).

Region 3 typically contains events that occur in larger urban population centers such as Kobe in 1995 and China in 1920, or where the death toll can be partially attributed to a poor standard of building construction, e.g., Turkey in the period from 1939 to 1999. These earthquakes are often intraplate; involve large population centers, or the failure of large areas of unreinforced masonry and/or non-ductile concrete.

Plot 3 line separates Regions 3 and 4. Region 4 is most interesting because it demonstrates two intersecting factors in New Zealand and Californian history, hence the depiction of the earlier data. These factors are improvements in construction standards since the 1930s, and rapidly increasing population levels through the last 200 years. So while we have seen a significant increase in population, the second factor appears to have been significantly offset by changes in the first for earthquakes in these regions. The net effect was a reduction in the fatality rate for the given population levels. This standard of construction factor is simply not present in other parts of the world, except for Japan, which, nevertheless, had two unusually high fatal events in 1923 and 1995. A third factor that contributes to the relatively low counts in the three interplate regions of California, New Zealand, and Japan was the rapid attenuation rate of earthquake energy with distance from the epicenter, however this does not affect our first conclusion, related to the improvements in construction leading to a lower death toll as it was a common element in these regions of earthquakes. The elliptical shape of the felt intensity areas does provide a significant reduction in the total injuries, when compared to comparable intraplate regions struck by earthquakes.

A final critical issue is what is the upper limit in terms of death tolls for a magnitude 7.8 to 8 event? Is the Tangshan toll the upper limit, or asymptotic event, or are larger fatality counts expected in future events? The data for the 1920 Kansu, China earthquake would suggest that with a typical urban density of housing the Tangshan event is a reasonable upper limit for masonry construction for the purposes of this model development. Thus, this places the upper limit to fatalities for the twentieth century as the 242,000 who died in the 1976 Tangshan event. While this limit provides a mathematical limit on the development of the function, it does not mean larger death tolls are not possible in future events.

In summary, two critical lines have been defined from the data shown in Figure 1. Plot 1 line represents the function that defines the upper bound of Region 2 for twentieth century data. A second is the flat line (Plot A) defining the upper limit to the fatalities using the 1976 Tangshan and 1920 China events. These lines lead immediately to the concept of a bounding function to the twentieth century data that can be developed using standard curve fitting techniques (Kaplan and Lewis 1971). The earthquake fatality data and the fitted bounding line to this fatality data are shown on Figure 3.

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Figure 3. Earthquake fatalities bounding function for the twentieth century data

The bounding function is intended as a guide. The over-estimation at the M5.5, 1989 Newcastle event is not considered significant and with a larger area of sand or poor soils the death toll could have been significantly higher in the 1989 Newcastle event. The form of the fitted equation is given in Equation 2.

405.32577.0335.9))(log( 2 −−=Ξ MMMB (2)

The function has a regression coefficient of 0.95 for a fatality count of )(MBΞ and an earthquake magnitude M . This interpolation function, )(MBΞ , provides a fatality estimate for an earthquake of magnitude M that can be used to predict the future losses in human terms for specific earthquakes and conditions near or in an urban area. The lower bound is always zero deaths, which is the case for the vast majority of earthquakes.

DEVELOPMENT OF THE EARTHQUAKE FATALITY FUNCTION

The fatality data from the 1976 Tangshan and 1915 Avezzano earthquakes showed there was a relationship between the separation distance of the urban areas from the epicenter and the death tolls. The 1931 Napier earthquake showed a direct relationship between the size of the urban population and the number of deaths where consistent housing types and ground conditions exist. Damage data from the 1886 Charleston earthquake showed a distinct and statistically significant difference in the response of timber framed and masonry structures to the earthquake loading. The quality of the data collected from all of these events provides a sound basis to reach these observational conclusions. The concept of an earthquake fatality function derives from this observational data and Shiono’s earlier work. The function provides an input to the economic analysis of structural alternatives.

Let us assume that there exists a Region, R , which is divided into a number, say m homogenous regions of construction, soil type, and population density. The urban area may be subjected to a future theoretical earthquake dM (Figure 4).

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Earthquake epicenter M d

urban area (1)

urban area (2) urban area (k)

urban area (m - 1)

urban area (m)

d (k)

Earthquake d

urban area (1)

urban area (2) urban area (k)

urban area (m - 1)

urban area (m)

d (k)

Region R

Figure 4. Model urban areas subjected to an earthquake

We can therefore postulate that there is a constant kξ that can be estimated for each urban area k that relates the bounding function )(MBΞ to the estimated fatality count ),( dF MkΞ for area k as:

)(),( dBkdF MMk Ξ=Ξ ξ (3)

Which can then be summed for the m areas within the regional setting to yield a total fatality count ),( dd MRΞ for a regional area, R , and the specific theoretical earthquake dM :

),(),(1

d

mk

kFdd MkMR ∑

=

=

Ξ=Ξ (4)

Finally, we assume that a series of site specific multiplicative factors define kξ uniquely for each theoretical earthquake dM and urban area :

∏=

=

=ni

ikik

1,λξ (5)

where ki,λ represents the series of standard condition factors that reduce the estimated fatality

count from the bounding function, )(MBΞ , because of different site-specific circumstances at each location k ,. i is the index counter and n is the total number of factors. The factors will be limited to five for this paper, although there is no theoretical constraint to this number. A summation form for the regional area of the earthquake fatality function can then be established from these equations to estimate the fatality count under these known circumstances for the specific theoretical earthquake dM . This product function determined for each subregion can be summed over the m distinct homogenous areas that form a regional population center.

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)(),(1 1

, dB

mk

k

ni

ikidd MMR Ξ=Ξ ∑∏

=

=

=

=

λ (6)

where ),( dd MRΞ is the estimated death toll for the specific circumstances of the event dM for a regional area R .

Shiono (1995a) provided an equation to estimate the death toll with the form shown in Equation 7. The equation has been slightly changed in the method of expressing the population density and number of dwellers per housing type to simplify the equations use in small homogenous areas and with larger groups of small homogeneous areas.

∫ ∫ ∑∞

=π

θρ2

0 0

iiii drd))]I(f(dS([D (7)

The fatality count, D , is for a specific region, iS is the population present in each building construction type, iρ is the housing density per square kilometer for each type, id is the fatality rate per dwelling type expressed as a ratio and iA is the sub area for each homogeneous area. The assumption must be made that these four variables are constant in each sub-area. This is a slightly tighter constraint than that imposed by Shiono (1995a) in the original development of Equation 7, however it is necessary if the process is to be implemented in a computer program and to ensure that the analysis will not become unwieldy. The fatality rate per dwelling for the seismic intensity is )I(f i . The seismic intensity I is nondimensional, which is a function of the radial distance, r , in kilometers and the azimuth angle, θ , in radians. The absolute constraint is that the estimated fatality count cannot exceed the total population, )(RP , within the study area or by extension the same constraint applies to each sub-area. This regional constraint is shown in Equations 8 and 9. It was implicitly accepted in Shiono’s (1995a) paper. Nevertheless, it is stated here to confirm the symbolic meanings of the variables. There are of course pragmatic limits to the fineness of this type of calculation and the need for determining average values for each area.

ii

n

ii ASRP ρ∑

=

=1

)( (8)

)()( RRP dΞ≥ (9)

COMMENT ON THE EARTHQUAKE FATALITY FUNCTION AND SHIONO’S ESTIMATION METHODS

Only a few earthquakes each year make up the fatal set of events. There were on average five fatal earthquakes per year at the start of the twentieth century and eighteen fatal earthquakes per year at the start of the twenty-first century. Of the estimated minimum two million people who died in the twentieth century, almost half died in ten events and one quarter died in two events (Jones et al, 1993).

The fatal earthquakes are scattered across the world’s surface and usually within totally different economic, geographical and geological settings. What we do know from long experience is the higher the felt intensity in the fatal meizoseismal area the higher the death toll, the poorer the standard of construction the higher the death toll, and location of the population at the time of the earthquake can vary the death toll significantly. This last

16

statement was quite obvious in an examination of the high tolls in the 1915 Avezzano event. The 1886 Charleston earthquake demonstrated the difference in damage rates between masonry and timber frame. The interesting feature of the 1886 Charleston event was the reasonably constant rate of damage between the natural ground and the reclaimed river ground for the masonry structures, which did not carry over to losses for the timber framed dwellings.

Different standards in the data collection and presentation have occurred in the post-earthquake period. Jones et al, (1993) made a pertinent comment on this last point. The calibration earthquakes used in this paper had acceptable levels of data collection for the period in which the event occurred.

Irrespective of these problems and issues, in the development of urban infrastructure there is a need to estimate the economic losses from varying alternative engineering systems. One of the potentially significant losses in the CEUS is the loss of life in earthquake events. While it would be irresponsible to believe or state that we can, with any certainty, estimate death tolls in future earthquakes, we can provide some guidance as to the likely issues in estimation of fatalities and provide an order of magnitude estimate of fatalities for specifically defined events. As an absolute minimum these estimates are useful for planning and economic purposes (U.S. Department of Transportation 1995, U.S. Office of Management and BusinessBudget 1992).

Equations 6 and 7 approach the estimates of the fatality count from two different perspectives. In Equation 6 the earthquake fatality function uses the method of calibrating to known large death rates and reducing the estimate based on a series of factors. Equation 7 integrates the equation de rived from Shiono’s (1995a) theoretical work to estimate a limit. The answers from a practical perspective should not vary for this initial work because of the common basis for the calibration data and from a pragmatic approach, as both are limited summations rather than exact analytical functions. Nevertheless, the approach in using Equation 6 is to directly account for the difference in intensity for varying magnitude events. Equation 7 relies on the calculation of the felt intensity areas for the given magnitude event. Any analysis should use both methods to provide a confirmation that the orders of magnitude are correct. The factor that causes the greatest conceptual difficulty is determining how to deal with the ground, soil, and building conditions. To some extent, this was engineering judgement based on the authors’ personal observations of earthquake damage and an extensive review of the literature. In the case of masonry and timber dwellings, such as was common in late nineteenth and early twentieth century construction, one sees consistent death rates from building collapse rates for the U.S., Chinese, Italian, and NZ data.

DEVELOPMENT OF THE STANDARD CONDITIONS

In the design of a building a load-event, or amalgam of load-events, needs to be synthesised to use for the theoretical environmental loading. This theoretical event provides standard conditions used for the structural analysis as typically presented in loading standards (AS 1170.4 1993) or derived from a sample-building document (FEMA 1997). As for building design, the development of a earthquake fatality function requires the enumeration of a standard set of urban conditions. These conditions provide the comparison points for using the earthquake function in other locations for theoretical earthquake events. The standard condition factors, iλ , that have been identified from the review of the fatality counts relate to the population characteristics, the location in an intraplate or interplate region, the building type(s), and the fault distance. These standard conditions factors, which are termed lambda

17

factors for brevity, have been estimated from the data for the Charleston, Napier, Avezzano, and Tangshan events.

The first lambda factor, oneλ , is a population factor to allow for differences in population densities between an event that defines a point on the bounding function )(MB? and the characteristics of the urban area that is to be modelled. One method to deal with this condition is to introduce a factor that adjusts for the ratio of the total populations within a given radius or population density. Table 6 showed the population and fatality count statistics for seven significant earthquakes. There is an evident relationship between the magnitude of the event and the percentage that died in each event. oneλ is based on the assumption that if the population density is doubled the fatality percentages will remain constant and the total death toll will double. In comparing the Napier and the Tangshan earthquakes that had a similar earthquake magnitude, oneλ was determined from the ratio of the populations that were within the fatal meizoseismal area, immediately prior to the earthquake.

This second lambda factor, twoλ , is a building and ground factor that is site dependent. The building and ground factors are related and have been combined at this stage; this includes a frequency factor that relates the frequency of the event to the natural frequenc ies of the building. This is the issue of tuned buildings problem resulting in significant damage to the buildings. The 1886 Charleston earthquake, which occurred in a mixed area of masonry and timber frame houses, included damage on both natural ground and land reclaimed from the river. This damage provided a method to check CEUS construction that predated seismic standards subjected to an mb 6.8 earthquake. The significant quantity of damage data collected on this earthquake provides the base data that permits this detailed analysis. These data provided the closest available calibration data for the CEUS.

One must use caution in extrapolating engineering judgements from limited data. The obvious errors that can occur are firstly; the housing construction standards may have been different in Charleston in 1886, China in 1976, Italy in 1915, and New Zealand in 1931 when compared to a comparison area in the year 2001. Secondly, the ground conditions may be distinct as in Mexico City (Jacob 1997). Thirdly, the population densities may vary. Accepting that these are valid criticisms of any factor developed from limited data; the solution to mitigate these issues is to examine the data and determine whether it reaches a reasonable conclusion and does it supply an acceptable estimate for analysis purposes. The building collapse rate was consistent enough between the calibration earthquakes to make the entirely reasonable assumption that urban areas that have had a similar background of construction practices will suffer a similar building loss for damage caused by an earthquake of a given felt intensity and for a specific regional ground type.

The third lambda factor, threeλ , is an attenuation factor that relates the difference in the areas of the equivalent felt intensity between intraplate and interplate regions. This factor relates the area of a constant intensity in the study event to the base event. It should be assessed for each regional area. The intraplate area typically has more circular isoseismals and the interplate area typically has more elliptical. The elliptical fatality curves for Avezzano shown on Figure 1 suggest a 2 to 1 ratio. The Californian data suggests a ratio between 5 to 1 and 8 to 1 (Algermissen 1972 Part 1 Isoseismal Studies, Hanks and Johnston 1992, Peek-Asa et al 2002). There are site-specific constraints that will affect this value. The factor for this paper was calculated as a ratio of 3 to 1, or the equivalent threeλ factor of 0.33 for the NZ study site, which is between the Italian and the American data points. This factor

18

will require adjustment to unity in a computer analysis that divides the fatal meizoseismal area into sub-areas and the threeλ factor reduces to the unity value for intraplate regions.

The fourth standard condition factor, fourλ , relates the seismic intensity to a building collapse rate, and then fatality rate for each building type. Shiono (1995) compared the Tangshan data to published twentieth century European data and found a direct correlation between the Chinese and the European data for the twentieth century. The building collapse rates at Tangshan are assumed upper bounds for masonry construction. The provision of improved construction may reduce these rates. The dominant wall material in Tangshan was listed as stone or brick. The adobe damage was not counted in the analysis, because of its limited use in the Tangshan area. fourλ uses the functional relationship between the distance to the epicentre and the centroid of each isoseismal population area to allow for the percentage of deaths in the exposed population.

The fifth lambda factor, fiveλ , is an aleatory uncertainty factor that essentially allows for the number of people who are inside or on structures that may collapse and cause death, when compared to the relative safety of the outside ground. fiveλ is assumed one for the eight earthquakes on the fitted line (Figure 3), because these are the deadliest earthquakes in the twentieth century. The factor was also assumed one for the 1931 Napier, NZ, event. Estimates of this factor have been determined for the difference between a day and night event for Memphis where the estimated ratio is ten to one (FEMA 1985). The aleatory factor cannot be ignored in the field of earthquake engineering and analysis. If the 1989 Newcastle earthquake had occurred 30 minutes later the death toll in the Workers Club would have been higher with the elderly playing bingo. If the 1933 Long Beach earthquake had occurred when schools were occupied, the toll would have been significantly higher. If the 1988 Armenian earthquake had occurred at 11:59 a.m. instead of 11:43 a.m., a whole generation of school children may have been spared. If the 1915 Avezzano earthquake had occurred on a late warm summer day, when many people would have been outside, the nearly one hundred percent tolls that occurred in church collapses may have been avoided. One can of course develop a mathematical formalism for what is essentially a probability function with a number of system states. However, the authors do not consider fiveλ as truly random. It has distinct values depending upon the types of buildings, time of day, time of week and month of the year.

CALIBRATION EVENTS

The 1931 Napier, NZ, earthquake provides a calibration event at the magnitude of the Tangshan earthquake. The analysis method used Equations 3 to 6 to estimate the lambda factors that calibrated this event to the )8(MBΞ . The population factor , oneλ , was determined by comparison of the Napier to the Tangshan data for the total population sizes. The base population data are presented in Table 6, column 3 for the earthquakes that define the bounding function.

The building and ground factor, twoλ , was the variable used for fitting the equation to the data. A twoλ factor of one was assumed for Tangshan and was fitted as one at Napier. As discussed above, the Tangshan and Napier building and ground were similar and the determination of a similar numerical value for the fitted factor between disparate earthquakes suggests that a comparison can be made between these spatially separated urban areas.

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The Napier earthquake occurred in an interplate area and the nominal interplate area adjustment factor, 0.33, was used for this threeλ calibration. This number is generally consistent with the Italian data as discussed above. The fatality rate fourλ was determined from the results in Table 5 for a twenty-kilometer separation from the epicenter to the towns. The aleatory factor fiveλ was assumed at one, as a one percent death rate was considered high for such an area. The five estimated standard condition factors for the Napier earthquake established by comparison to the Tangshan event are presented in Table 8.

Table 8. Napier earthquake standard condition factors, the estimated values, and derivation

Factor Numerical Value

Derivation

1 0.04 30,000/750,000

2 1.00 Frequency, building and ground factor

3 0.33 Elliptical area factor assumed as it is interplate

4 0.08 Shiono’s data for Tangshan fatalities (1995) for 15 to 20 kilometers

5 1.00 Assumed as a first guess

Using Equation 7 and the lambda values above, the expected death toll for Napier is 255. The actual death rate was 256, or 0.001 times the fatality count of the Tangshan earthquake. This result indicates that the Tangshan and the Napier deathrates using the earthquake fatality function are comparable even given the significant difference in populations and location and period.

The 1886 Charleston earthquake occurred in an area of masonry and timber-framed housing. The data collected for the earthquake damage provides sufficient information to establish the lambda values for the masonry and the timber framed dwellings. The assumption that was required for the analysis was that the occupant number was constant for the different housing types.

The five-estimated standard condition factors, for the Charleston earthquake are presented in Table 9. The derivation of these factors follows the same procedure as established for the Napier analysis. The Spitak earthquake information for deaths taken from Table 6 was used for calibration of the lambda one factor for the Charleston earthquake. Charleston has areas of masonry and areas of essentially timber construction. The lambda factors were estimated separately for the timber area and the masonry area. The final result was calibrated using the second lambda factor for timber as the unknown variable. The second lambda factor for masonry was assumed to be unity, which is consistent with the results established from previous results.

20

Table 9. Charleston earthquake standard condition factors, the estimated values, and derivation

Component Numerical Value Masonry

Numerical Value Timber

Framed

Unit Derivation

Population 14,942 34,508 49,000 7.6 persons per house

Percent Damaged

66 7 6,444 Total houses

Earthquake 6.8

)8.6(BΞ 24,690 Estimated bounding function value

Lambda 1 0.027 0.061 Spitak population 550,000 used for comparison purpose

Lambda 2 1.00 0.70 Building factor, masonry lambda factor was set to 1.00

Lambda 3 1.00 1.00 Intraplate

Lambda 4 0.075 0.02 Shiono’s data for Tangshan fatalities (1995) for 20 kilometers, based on level of damage for timber framed

stuctures

Lambda 5 1.00 1.00 Assumed as a first guess

Deaths per house

(percentage)

1.55% 0.65% with the building factor for masonry set to 1

The Charleston earthquake of 1886 provided a wealth of data on the performance of masonry and timber framed buildings in a major earthquake of mb 6.8. The masonry buildings showed similar level of damage whether they were located on filled or natural ground. These results are considered to be directly transferable to Memphis and provide calibration data that can be used in similar areas of the CEUS. An assumption of 1.00 for the masonry dwellings yields a lambda two value for the timber structures of 0.70.

The difficulty in the interpretation of the Tangshan data for use in deriving the Charleston factors was in determining the fatality rate for the level of damage, as the damage for Charleston was essentially fallen gables, walls, and chimneys. The fatalities often occurred as people ran from their homes and were struck by falling masonry. About ninety-five percent of chimneys collapsed or suffered severe damage (USGS 1977). This is similar to the fatality types in the Newcastle earthquake that included fallen fronts on shops. We have used a literal translation so that seven percent building overall damage was treated as equivalent to Shiono’s seven percent data.

Shiono’s concept of distance being the greatest factor in the rate of deaths in masonry building collapses was supported strongly by the significant element of damage to masonry buildings in both the reclaimed and solid ground in the 1886 Charleston event. The same conclusion cannot be drawn for the timber-framed structures in Charleston. A nominal design value of 0.70 is considered reasonable for this type of timber framed houses, provided that the fourth lambda value reflects the lower damage levels in timber structures at given distances compared to masonry structures. The effective death rates for a single masonry dwelling and a single timber framed dwelling could be higher than two to one for Charleston. This ratio was significantly affected by the rate of failure differences in timber dwelling between reclaimed and solid ground. The aleatory factor was set to one for all calibration and bounding function events as the events that form the bounding function are all noted as being savage events of the twentieth century. The high fatality rates in the building collapses in the

21

1915 Italian and 1988 Armenian events are of significant concern. The 1976 Chinese earthquake has unofficial tolls up to three times the official count. This places a significant constraint on reducing this factor. While the death toll could have been higher in the 1886 Charleston earthquake it is considered that this would have been due to people still being in church so that when the fourth factor would have been adjusted rather than the aleatory factor. The aleatory factor represents the death toll due to the timing of the event and the location of the population. The research findings indicate that certain times are likely to cause a higher percentage death toll for some circumstances, such as during a time of high-church attendance or evening compared to very early morning when people are asleep. The location of the population either inside or outside is an element in this factor and its value. The factor should be set to one for planning purposes.

THE CHARLESTON, MISSOURI 1895 EARTHQUAKE

Charleston, Missouri (pop. 5,000) is located about 20 kilometers southwest of the junction of the Ohio and Mississippi rivers in Mississippi County. Mississippi County had a total population in 1900 of 11,000 and in 2000 of 14,400. An earthquake with a magnitude of M 6.6 ± 0.3 occurred on 31 October 1895. The epicenter was located about 10 kilometers NNW of Charleston near the small village of Anniston. The earthquake had an observed maximum felt intensity VIII to IX (Johnston 1996) (Figure 5). The earthquake had no recorded deaths so that we are unable to use this earthquake for calibration purposes. The earthquake occurred at about 4 am, and the records of damage are extensive in Charleston, MO and Cairo, IL (USGS 2000, Stover and Coffman 1993). Richter (1958, 137) provides a full statement of the Modified Mercalli Scale, which details the damage to masonry due to different felt intensity. The masonry in Mississippi County in Missouri in 1895 would be classified as Masonry C or D as it would not contain reinforcement.

Figure 5. 1895 Charleston, Missouri earthquake Isoseismals (after SLU, 2002)

Figure 5 shows the NE-SW directional nature of the VIII to IX felt area. The damage descriptions for Charleston and Cairo suggest that both areas were at intensity VIII as no

22

building collapse occurred. A similar observation can be made about the limited collapse rates in some villages in the Abruzzo region that were within the meizoseismal area. The villages that are out of the direct line of the observed movement can have significantly lower fatality rates. It can only be concluded that the timing of the event in the small hours of the morning, that the buildings were badly cracked, but had not collapsed, and the relatively low farming population at 11,000 in the Mississippi County prevented fatalities. The 1895 earthquake occurred at 4 a.m. The common cause of death in this intensity of event is residents fleeing the house and being struck by falling chimneys as in the 1886 Charleston earthquake. The additional time required to get out of bed at 4 a.m. , and flee the house is probably the main contributory to the zero death toll when compared to the 1886 Charleston earthquake that occurred at 9:50 pm.

The felt intensity of IX that traverses along the Ohio River basin provides sufficient information to calculate a theoretical fatality count for the current population of Charleston, Missouri, and Cairo, Illinois for a daytime event. This sample calculation has been prepared for these towns only and not the surrounding environs or other areas that could be affected by an earthquake in the New Madrid seismic zone. Thus these results specifically represents two sub-area calculations and not the overall fatality count for such an event. This calculation, which is presented in Table 10, demonstrates the procedure outlined in the paper.

Table 10. Estimated fatalities in Charleston and Cairo for a repeat of the 1895 Charleston earthquake

Description Mississippi County (Charleston, MO)

Alexander County (Cairo, IL)

Unit Comment

Population 14,442 10, 626 Residents

Distance to epicenter 12 30 Kilometers Mean

)6.6(BΞ 11,800 11,800 Fatalities

Lambda One 0.0268 0.0193 550,000 base count Spitak, Armenia

Lambda Two 1.00 1.00 Assume as for Napier and masonry at

Charleston.

Building component

Lambda Three 1.00 1.00 Shape factor Intraplate

Lambda Four 0.075 0.03 Shiono felt intensity VIII to IX

Lambda Five 1.00 1.00 Aleatory Assume worst, i.e. it occurs during the day

not at night

Estimated Fatalities

)(RdΞ

24 (0.2%) 8 (0.06%) People Total 32

The earthquake was assumed to have the same magnitude as the 1895 event and at the same epicenter. The current populations have been established and the Shiono fatality rate was adopted for the towns based on the radial distance to the epicentre. We have assumed a factor of one for the building component in line with the masonry results for Napier, NZ, and Charleston, SC. The 1988 Spitak Armenia base count has been used to estimate oneλ , because it the closest bounding earthquake in terms of magnitude .

The exposed population is low and the epicentral distance places these two towns on the edge of intensity VIII. The death toll is consistent with collapse of individual buildings in each town such as a church or a shop front on a busy day. The death rate of 0.2 % of the

23

population in Charleston, MO was the same as the overall death rate in the 1886 Charleston, SC earthquake. The placement of such an event beneath a major urban area such as Memphis or St Louis would cause a significant increase in the fatality rate.

RETROFIT, FATALITY PLANNING AND COST ISSUES

Two purposes have been identified for the use of the function. The first use of this function was in informally estimating the likely fatalities in earthquakes. The function provides a basis to allow the real time estimating of potential earthquake losses for planning purposes. The development of this type of modelling will require establishment of a data-base of the world’s population distribution with the common housing types identified for each region. The calibration of this data using the twentieth century earthquake and fatality data provides a first step in this implementation. The second use is in considering the level of retrofit that needs to be applied to structures in va rious areas of varying seismicity. As for standard transportation studies the study of proposals on retrofitting may include alternatives. The information determined from this study of a fatality model provides input to this economic analysis.

Buildings damaged at the time of a previous earthquake or that have since been constructed present an interesting problem to authorities in seismic regions. An existing building may require an economic analysis to determine the appropriate level of retrofitting before a potential seismic event. A damaged building may require a structural and economic analysis to determine if the building should be repaired or demolished after a seismic event. This final point is predicated on the building being repairable. The issue of historic buildings is set-aside in this analysis. It is assumed that historic buildings will be treated on both their heritage and economic merits, which can involve external fund sources that cannot be allowed for before the event. The issue of the fabric of the historic building is also often a contentious issue that affects the ability to change the structural capacity of a historic building, as in the case of the National Civil Rights Museum in Memphis, TN, (Howe 2000) or St Andrews Presbyterian Church after the 1989 Newcastle, Australia, earthquake (Nichols 1999).

The fundamental question that derives directly from Forrest’s question is “what level of retrofitting should be applied to buildings to protect the inhabitants from seismic damage within accepted economic bounds?” In developing an economic model to determine a measured response to this specific question, it is necessary to consider “what alternatives need to be established for the study?” Economic models compare specific events or scenarios. These models are based on historic data, which permits a rational choice between a set of alternatives. The final cost of an alternative will differ from the historic estimate; nevertheless, this does not negate the use of the economic models in comparing the alternatives. But, they are not open-ended predicative models but tools to provide a comparative analysis between alternatives. An engineer selects an alternative and then implements it.

There are as a minimum two basic engineering alternatives: Alternative 1 — Repair after the environmental event: Alternative 2 — Provide some remediation now and further repairs after the event. There are three components to these alternatives, engineering and economic costs, and social costs. Engineering costs can be established from previous repairs of similar nature. Social costs include fatalities, injuries. Economic costs include lost wages, loss of business, and all other indirect costs. Fatality costs have two components. The first component is the cost to the community for a fatality. This cost has been investigated for US

24

motor vehicle accidents and was presented in the work by Rollins and McFarland (1986) and the U.S. Department of Transportation Memorandum (1995). Rollins and McFarland (1986) provided an estimated total cost to the community per fatality of about $850,000 ($1.2 million in today’s dollars). The U.S. Department of Transportation recommended an averted fatality should have a value of $2.7 million. The second fatality cost component is estimating a reasonable base number for the number of fatalities for the nominated events. FEMA (1985, 7-28), provide a simple illustrative calculation for 3,500 deaths from an earthquake near Memphis, TN. In this case, the fatality cost is a loss of over $3 billion based on the work of Rollins and McFarland. This loss does not include other losses or building damage costs.

The fundamental question for this analysis in terms of human loss then reduces to a more specific focus: “Is it better to spend money in advance or to wait and only repair the damage?” This question requires a solution method that provides an estimation of the likely fatality rates in an event that is clearly defined for the economic analysis of the alternatives. The economic methodology required for U.S. federal government work was presented in an OMB Bulletin (U.S. Office of Management and Budget, 1992). This bulletin requires inclusion of the societal losses such as fatality costs in any economic analysis of seismic mitigation works. This bulletin and its methods are commonly used in transportation engineering, extending the method to structural engineering problems presents no ethical issues (ASCE 2001, Fundamental Canon 1). The caveat is that no one has yet successfully predicted earthquakes and this model is not designed to predict but to provide a planning tool.

COMMENTS ON THE USE AND LIMITATION OF THE PROCEDURE

This paper does not imply that larger fatality counts than those listed here will not occur in some future earthquakes. However, this issue of an extreme fatality count would require a large magnitude event, striking an ill prepared population. The development of this fatality function quite clearly allows for larger death tolls than the bounding function points, if an area has a greater population density than the base events then the fatality count could be higher. There is no constraint on the value of the first lambda factor. However, the population density in such an ill prepared area would have to be greater than the 1,300 persons pe r square kilometer used in the post 1976 Tangshan fatality analysis (Shiono 1995). The earthquake’s meizoseismal area would need to coincide with the population center. Analysis of the probability of this occurrence was not possible with this fatality function.

The definition of the fatal meizoseismal circle in the context of this paper is limited to the area of building collapse or damage causing or potentially causing fatality. If these circumstances occurred in an area that had an active fault, which had given little or no warning, or the silent active fault that was not known to exist, then the death toll could be a multiple of the Tangshan event. The combination of joint low probability environmental events that are infrequent earthquakes on a silent active fault and dense population has, however, occurred in the past records of earthquakes. This is clearly the case in the Avezzano earthquake, pointing to the need to clarify the probability of silent active faults as a cause of death in earthquakes. Galadini and Galli (1999, 143) noted that the 2,000-year Italian record does not cover the seismic cycle of the active Apennines fault, showing that even a near complete record can be a poor indicator of future events in specific sites.

There are a number of major cities in the world that would be ill prepared for such an event and where the population density is greater than the Tangshan average. The chance of an undocumented active fault, which generated this magnitude event, occurring in such an ill

25

prepared urban area is low, but not zero. This event is probably beyond that level of probability that is normally planned for by the human population, which is typically a 500-year earthquake event. It has only been recently, in the US, that seismic design provisions specifically consider earthquakes having a 2500-year recurrence interval (Frankel et al, 2000, Leyendecker et al, 2000). This point is worth further study.

CONCLUSIONS

An old adage is that we learn from failures. The failure in Tangshan teaches us tha t earthquakes can and do kill large portions of urban populations. The failure in Avezzano teaches us that the fatality rates can approach one hundred percent in towns. The failure in Napier New Zealand , and Charleston South Carolina, teaches us that the fatality rates can be related for different events by a series of simple factors and a bounding function. The luck in 1895 in Charleston, Missouri suggests that an earthquake in the early morning hours may reduce the death toll from falling chimneys, but this may not occur in future events at the same location, where the next event is at a different hour of the day. The masonry and timber failures on different ground types at Charleston South Carolina, teaches us that we still have a long way to go in understanding the causes for deaths from masonry buildings in earthquakes. The eye witness accounts point to the failure of chimneys, parapets, and end gables as leading to deaths as people ran from all types of buildings. This type of death appears to represent masonry failures in areas subjected to MMI IX intensity or less. A similar problem was observed in the 1989 Newcastle earthquake. Building collapse becomes the primary mechanism of death in felt intensity areas greater than MMI X. The Avezzano, Italy and Charleston, South Carolina, events showed the problem of damage levels in churches. The Avezzano event demonstrated the very high death rates that occur in such buildings that have limited redundancy and heavy masonry walls.

Shiono (1995) has established an equation to estimate fatalities in earthquakes based on the 1976 Tangshan earthquake data. This paper has extended this work by Shiono and developed a procedure to estimate the probable death rates in some earthquake events for a given set of circumstances. A function has been established that relates the earthquake magnitude to the high fatality count events of the twentieth century. The function has been calibrated using a number of earthquake events. The calibration data provide a tool for estimating fatalities for specific earthquake events, where there is a large area of unreinforced masonry. As with all such models, there is significant room for further work and we suggest that a detailed look at the Californian fatality and building data would add to the uses of the fatality function.

The fatality function has a number of potential uses in the planning, disaster recovery and engineering fields. The fatality function could be used to estimate fatalities for planning purposes. An example would be est imating the fatality count in St Louis for an event on the New Madrid fault. The fatality function could be used for the economic analysis of engineering alternatives. The use is here is considered to be conceptual related to the types or elements of struc tures that will require special detailing in an area, rather than for specific buildings. This type of analysis requires a specific event to be established for the region. The fatality function has shown itself to be useful for approximately estimating the losses in larger events in areas outside the continental United States. This use provides a potential real time system to establish initial estimates of deaths in remote regions when communications are poor or early in the response recovery period.

26

ACKNOWLEDGEMENTS

This study is supported by the Mid-America Earthquake Center under National Science Foundation Grant EEC-9701785. We would like to thank the many people who provided information for this study.

REFERENCES CITED Algermissen, S. T., 1972. A study of earthquake losses in the San Francisco Bay Area: Data and

analysis, U.S. Dept of Commerce, NOAA: SF, (Algermissen, S.T.; PInvest), p. 220. Applied Technology Council (ATC), 1997. NEHRP Guidelines for the Seismic Rehabilitation of

Buildings, prepared for the Building Seismic Safety Council, published by the Federal Emergancy Management Agency, Washington DC.

Armenian, H. K., Melkonian, A., Noji, E. K., and Hovanesian, A. P., 1997. Deaths and injuries due to the earthquake in Armenia: A cohort approach, International Journal of Epidemiology 26 (4), 806-13.

AS 1170.4-1993/Amdt 1-1994. Minimum design loads on structures (known as the SAA Loading Code) - Earthquake loads, Standards Australia: Sydney.

ASCE, 2001. Code of Ethics, http://www.asce.org/about/codeofethics.cfm#note1, accessed 6 October 2001.

Beavers, J. E., 1993. Conference Chair, Earthquake Hazard Reduction in the Central and Eastern United States—A Time for Examination and Actions, Proceedings, Central United States Earthquake Consortium, Memphis, Tennessee, May 2-5.

Federal Emergency Management Agency, 1985. An assessment of damage and casualties for six cities in the central United States resulting from earthquakes in the New Madrid Seismic Zone, Prepared under Contract #EMK-C-0057 (CUSEPP), Washington, DC.

Federal Emergency Management Agency, 1999,. Hazus99 Manual, Washington, DC. Forrest, E. J., 2000. Letter dated 20 January 2000 to the first author, New Zealand. Frankel, A. D., Mueller, C. S., Barnard, T. P., Leyendecker, E. V., Wesson, R. L., Harmsen, S. C.,

Klein, F. W., Perkins, D. M., Dickman, N. C., Hanson, S.L., and Hopper, M. G., 2000, USGS national seismic hazard maps, Earthquake Spectra 16 (1), 1-19.

Galadini, F., and Galli, P., 1999. The Holocene paleoearthquakes on the 1915 Avezzano earthquake faults (Central Italy): Implications for active tectonics in the central Apennines, Tectonophysics 308, 143-170.

Hadjian, A. H., 1992. The Spitak, Armenia earthquake Why so much damage? Proceedings of the Tenth World Conference on Earthquake Engineering 1, 5-10, Madrid, Spain 19 -24 July 1992.

Hansen, G., and Condon, E., 1989. Denial of Disaster, Cameron and Company, San Francisco. Hopper, M. G., and Algermissen, S. T., 1980. An evaluation of the effects of the October 31, 1895,

Charleston, Missouri, earthquake, USGS Open File Report 80-778, p. 43 Howe, R. W., 2000. Letter dated 24 July 2000 to the second author, EQE, Memphis. Institute of Geological and Nuclear Sciences (IGNS), 2000, Frequently asked questions on

earthquakes, New Zealand, 7pp. ING-SGA, 2000. Catalogue of Strong Italian earthquakes from 461 BC to 1990 AD,

http://www.ingrm.it/homingl.htm Jacob, K., 1997. Letter to the author, and synthetic digital earthquake traces for Marked Tree, AR. Jones, N. P., Noji, E. K., Smith, G. S., and Wagner, R. M., 1993. Casualty in Earthquakes, 1993

National Earthquake Conference, Central United States Earthquake Consortium, Memphis, TN, May 2-5, Monograph 5 Socioeconomic Impacts, Chapter 5, 19-53.

Kaplan, W., and Lewis, D. J., 1971. Calculus and Linear Algebra, John Wiley and Sons: New York.

27

Kunreuther, H., 1993. Earthquake insurance as a hazard reduction strategy: The case of the homeowner, Proceedings of the 1993 National Earthquake Conference, Memphis 5, 191-208.

Leyendecker, E.V., Hunt, J.R., Frankel, A.D., and Rukstales, K.S., 2000. Development of maximum considered earthquake ground motion maps, Earthquake Spectra 16 (1) 21-40.

Massey, R., 2000. Letter dated 21 January 2000 to the first author, Napier City Council, New Zealand.

Ministry of Civil Defence, 2000. New Zealand Disasters, The Napier Earthquake, 1931, New Zealand, 2 pp.

Napier City Council, 2000, Proposed City of Napier Residential Plan, Napier, New Zealand. Nichols, J.M., Lopes De Oliveira, F., And Totoev, Y.Z., 2000. The development of a synthetic fatality

function for use in the economic analysis of the rehabilitation and repair of structures, StrucDam Conference, June 2000, Brazil, Proceedings.

Nichols, J.M., and Totoev, Y.Z., 2001, Issues associated with retrofitting and repairing typical un-reinforced masonry buildings of Two-Storey or Three-Storey Height in areas of potential Seismic Activity, Sixth Australian Masonry Conference, July 2001, Adelaide, Australia, Proceedings, 315-24.

Nichols, J.M., 1999. Assessment and repair of certain masonry buildings after the Newcastle Earthquake, Masonry International, 13 (1), 11-12.

Nuttli, O. W., 1974. Magnitude -recurrence relation for central Mississippi Valley earth-quakes, Bulletin of the Seismological Society of America, 64 (4), 1189-207.

Oxford English Dictionary, 2000. Oxford: OUP, <http://www.uiuc.edu/cgi-bin/oed> Peek-Asa C, Ramirez M. R, Shoaf K, Seligson H, Kraus J., 2000. GIS mapping of earthquake-related

deaths and hospital admissions from the 1994 Northridge, California, earthquake. Annals of Epidemiology

Richter, C.F., 1958. Elementary Seismology, San Francisco: Freeman, viii+758. Robinson, A., and Talwani, P., 1983, Building damage at Charleston, South Carolina, associated with

the 1886 earthquake, Bulletin of the Seismological Society of America, 73 (2), 633-52. Rollins, J. B., and McFarland, W. F., 1986. Costs of motor vehicle accidents and injuries,

Transportation Road Research Record, 1068, 1-7. Saint Louis University Earthquake Center (SLU), 2002. Earthquake Intensity Shaking Map, New

Madrid Seismic Zone,1895 Charleston MO earthquake http://www.eas.slu.edu/ Earthquake_Center/EQInfo/Flyers/CUS/1895Intensities.htm, accessed 1 October 2002.

San Francisco Chronicle, 1906,. Interview with an eye witness to the 1886 Charleston earthquake, April 19, 1906.

Shannon, G. W., and Pyle, G. F., 1993. Disease and Medical Care in the United States, A medical atlas of the Twentieth Century, Macmillan, New York.

Shiono, K., 2000, Letter to the first author, Japan. Shiono, K., 1995. Interpreta tion of published data of the 1976 Tangshan, China Earthquake for the

determination of a fatality rate function, Japan Society of Civil Engineers Structural Engineering / Earthquake Engineering, 11 (4), 155s-163s.

Shiono, K., 1995a. Lessons learned from reconstruction following a disaster enhancement of regional seismic safety attained after the 1976 Tangshan, China Earthquake, Japan Society of Civil Engineers Structural Engineering/Earthquake Engineering, 12 (1), 1-7.

Steinbrugge, K. V., 1982. Earthquake, Volcanoes, and Tsunamis—An Anatomy of Hazards, Skandia America Group, New York.

Stockton, R. P., 1986, The Great Shock: The effects of the 1886 earthquake on the built environment of Charleston, South Carolina, Southern Historical Press, Inc: Easly, SC.

28

Stover, C. W., and Coffman, J. L., 1993. Seismicity of the United States, 1568-1989, USGS Professional Paper 1527, U.S. Geological Survey: Reston, VA.

Tangshan Municipal Government (TMG), 2001. Tangshan Introduction, www.investchina.net accessed on 22 April 2001.

Troz, M., 2000. Letter to the first author on the effects of the Avezzano earthquake of January 1915. Tuttle, M. P., Sims, J. D., Dyer-Williams, K., Lafferty, III, R. H., and Schweig, III, E. S.,

2000,.Dating of liquefaction features in the New Madrid seismic zone, U.S. Nuclear Regulatory Commission, NUREG/GR-0018, 42p.

U.S. Census Office (USCO), 2000. U.S. Census Data, International Data Base Table 001, Total Midyear Population 2000, </www.census.gov/ftp/pub/ipc/www/idbprint.html>

U.S. Department of Transportation, 1995. Update of Value of Life and Injuries for Use in Preparing Economic Evaluations, Memorandum Office of the Secretary of Transportation March 15, 1995.

U.S. Geological Survey (USGS), 1977. Charleston Report U.S. Geological Survey (USGS), 2000a. World Earthquake Catalog, Central Region, Goldon, CO. U.S. Geological Survey (USGS), 2000a,2000b. World Earthquake Fatality Catalog, Central Region,

Golden, CO. U.S. Geological Survey (USGS), 2001,. World Earthquake Facts, http://neic.usgs.gov/neis/eqlists/

eqsmosde.html, accessed 5 October 2001. U.S. Office of Management and Budget (OMB), 1992, Guidelines and Discount Rates for Benefit-

Cost Analysis of Federal Programs, OMB Circular No. A-94, October 29, 1992 http://www.whitehouse.gov/omb/circulars/a094/a094.html , accessed Sept 5, 2001.

Wallace, R. E and Scott, S., 1999. Connection: The EERI Oral History Series, Robert E. Wallace, OHS-6, Earthquake Engineering Research Institute: Oakland, CA.

Ward, S. N., And Valensise, G. R., 1989. Fault parameters and slip distribution of the 1915 Avezzano, Italy, earthquake derived from geodetic observations, Bulletin of the Seismological Society of America, 79 (3), 690-710.