The development of a synthetic fatality function for

The development of a synthetic fatality function for use in the economic analysis of the rehabilitation and repair of structures. John M. Nichols Post Doctoral Researcher, Department of Civil and Environmental Engineering, UIUC, Urbana, Illinois, USA, [email protected] Fabiana Lopes de Oliveira PhD Candidate, Departamento de Engenharia de Estruturas e Fundações, Universidade de São Paulo, Brazil, [email protected] Yuri Z. Totoev Lecturer, the Department of Civil, Surveying and Environmental Engineering, The University of Newcastle, Australia, [email protected]

ABSTRACT Construction of existing structures, such as masonry or concrete buildings, often pre-date the introduction of modern seismic codes. The quality of the construction in these types of buildings is often poor or the techniques used in the construction are now known to be unacceptable in a seismic event. In some combinations of circumstances, such as Tangshan in China, and Spitak in Armenia, this can lead to tragic loss of life and a significant expense to the world community. This loss is due to the application of an extreme environmental load, such as a seismic event. The current dilemmas in the intraplate regions of the world relate to the strategy that should be used to prepare for earthquakes. The strategy that is developed for an area must consider the funds that should be expended on retrofitting the stock of existing buildings. Then after an earthquake determining what is economic to repair and what should be demolished. Finally, how should the funds be expended to the greatest benefit of the population? The purpose of this paper is to suggest a simple model for estimating fatalities in major earthquakes based on the data collated mainly for the twentieth century. This model, which is developed for masonry study purposes, can be used to estimate the potential fatalities under a standard set of conditions. This model can then be used in the development of rehabilitation and repair strategies that provide the greatest economic and social benefit to the community.

1. INTRODUCTION A building can pass its design life without suffering significant damage from an environmental load, merely enduring the vagaries of aging materials. On the other hand, this building can be subjected to a large environmental loading. Alternatively, the building can be retrofitted, before a large environmental load occurs and then it can be damaged in an environmental loading. The damaged building may then require a structural and economic analysis to determine if the building should be repaired or demolished. This final point is predicated on the building being repairable. The issue of historic buildings is set-aside in this analysis. It is assumed each will be treated on their merits, which usually does not have a strong economic component or can involve funds that cannot be estimated before the event. A simple example is set out here to explain this point. New Zealand has one of the highest rates of plate movement (IGNS, 2000) on the Pacific Rim. New Zealand has a legacy of

existing masonry buildings of two to three storey height that are located within the major cities. The IGNS (2000) expects that the next major movement that will cause damage may occur in the Wellington region. This region had deaths in the late 1800s from an earthquake (Forrest, 2000). Buildings, which were damaged at the time or have since been constructed, present an interesting problem to the authorities. What level of retrofitting is applied as against the do nothing alternative? The two alternatives considered for this paper are Alternative 1 – Repair after the environmental event or Alternative 2 – Provide some form of remediation now and further repairs after the event. There are two components to these alternatives, the engineering cost, and the social costs. The social cost includes the fatalities, the injuries, and the lost time to the community. The fundamental question then comes to: ‘Is it better to spend money in advance or to repair the damage?’ This specific question requires an estimation of the likely fatality rates in an event that is clearly defined for the economic analysis of the alternatives. The objectives of the paper are to collate the fatality statistics for the world’s earthquakes for a representative period, to graphically analyse the results and to provide a model for estimating fatality counts in future theoretical events with a specific combination of circumstances. The set of circumstances that form the basis for this and a subsequent paper relate to a high probability of an event occurring near an area of existing two and three storey unreinforced masonry buildings in New Zealand.

2. LITERATURE REVIEW The estimation of casualties for a particular set of events has been studied for a number of locations. The estimates for the New Madrid region for a specific event are a baseline estimate of 646 to 4907 fatalities and 4400 to 64567 casualties (Jones, et al., 1993, Monograph 5, Chapter 2, Table 3). Jones et al., (1993) clearly demonstrates the need for further studies into the deaths and casualties in earthquakes. These recommendations include the need for the collection of epidemiologic data on earthquake casualties. The interesting comment from this paper is ‘Results from more recent earthquakes in Coalinga (1983), Whittier-Narrows (1987), Loma Prieta (1989), Sierra Madre (1991), Ferndale (1992) and Landers-Big Bear (1992) indicated that these moderate to large magnitude (6.5 – 7.4) events, deaths were relatively uncommon and most injuries included only minor contusions sprains, lacerations or extremity fractures. Note that this observation pertains specifically to California events and may not be generalizable to regions such as the Central and Eastern United States. California has had few events with death tolls more than 100. The two exceptions are the 1906 (700 deaths) and the 1933 (117 deaths) earthquakes. The introduction and application of detailed seismic design and construction requirements has occurred in California since the 1933 earthquake, (Gubbins, 1992). The same statement is simply not true for all bar a few select urban areas, notably in Japan. The twentieth century suffered an earthquake that caused more than 5000 deaths on average every 900 days or 2.5 years. In that same century there has been a fourfold population increase from 1.5 billion in 1900 to 6 billion in 1999, and a corresponding increase in the use of unreinforced masonry from the hive kilns at the turn of the century (Baker, 1912) to modern plants capable of supplying one million masonry units per day. The distribution of the deaths in earthquakes through the twentieth century was far from uniform across the period. The quiescent period in the middle of the century is particularly significant. Jones et al., (1993) provides data on major casualty earthquakes for the 20th century until 1988. This data is augmented with data from the almanac (FEC, 2000) and the USGS (2000) database of world earthquakes. The results for this data are presented in Table 1.

Table 1: World Earthquake Data – Magnitude and Fatalities. Year 1976 1920 1923 856 1755 1970 1908 1990 1927 1999 1939 1950 1915 1939 1985 1935 1988 1976 1970 1972 1995 1998 1999 1990 1997 1999 1906 1999 1931 1933 1964 1969 1971 1994 1886 1812 1929 1989 1952 1855 2000 1848 1968 1857

Fatality Count 242,500 200,000 142,800 100,000 70,000 66,800 58,000 50,000 40,900 36,000 32,700 30,000 29,980 28,000 25000 25,000 24,900 23,000 15,621 6,000 5,100 5,000 2,100 2,000 1,500 1,124 700 500 256 117 117 67 65 61 60 40 17 13 12 5 5 3 2 2

Magnitude 7.8 - 8 8.5 8.3 6.5 8.75 7.8 7.5 7.7 8.3 7.5 8 Not Found 7 8.3 8.1 7.9 6.8 7.5 7.7 6.2 7.2 7.1 7.6 7.7 7.1 6 8.3 7.2 7.9 6.3 8.5 7.1 6.6 6.6 7.7 7.5 7.7 5.5 7.5 7.5+ 5.9 (GS) 7 7 8

Name Tangshan# Kansu Kanto Damghan Lisbon Ankash Messina # Caspian Sea area Tsinghai Kocaeli Erzincan Assam Avezzano # Chillan Mexico City Quetta Spitak# Guatemala City Yunnan Managua# Kobe Northern Northern Northern #

San Francisco Napier Long Beach Alaska San Francisco San Fernando San Fernando Charleston Murchison Newcastle# Kern County Wairarapa Yunnan Marlborough Inangahua

Country China China Japan Iran Portugal Peru Italy Iran China Turkey Turkey India Italy Chile Mexico Pakistan Armenia Guatemala China Nicaragua Japan Afghanistan Taiwan Philippines Iran Columbia California Turkey New Zealand California USA USA California California SC, USA California New Zealand Australia California New Zealand China New Zealand New Zealand California

Six earthquakes that have caused fatalities before 1900 are included in the data as these are relevant to the analysis of the results. The first earthquake in the 21st century to cause fatalities was at Yunnan in China. This earthquake included 1500 casualties and 31,064 houses destroyed. As a rough guide, this corresponds to a meizoseismal area of about 15 to 31 km2 at typical housing densities. These additional earthquakes are highlighted in Table 1. The term meizoseismal is adopted from the paper by Shiono (1995) and is assumed for the purposes of this paper to be the area of the main fatality and damage count. It is proposed in subsequent papers to refine this definition to provide a consistency between the studies. An intraplate earthquake of magnitude M5.5 is known to damage un-reinforced masonry. This is evident where the detailing of the masonry has not provided for specific seismic requirements (Melchers and Page, 1992). A death count starts typically at this magnitude and can rise to 1 in 3 of the population at M8 in unreinforced masonry dwellings. The Tangshan event had a meizoseismal are of 47 km2 (Shiono, 1995). There is no significant evidence that the death rates in the unreinforced masonry dwellings in interplate regions will deviate from these statistics for equivalent earthquakes. The equivalence of earthquakes between intraplate and interplate regions of the world is however affected by the subduction and cracking of the plates at the interplate boundary. This deformation causes an elliptical shaped felt area compared to the circular areas of the intraplate events (Abrams, 1997). The short axis of the ellipse is normal to the boundary. The definition of an interplate area has been established by Wysession et al. (1995) as being with in two degrees of a plate boundary. The simple statistics point to two-thirds of all earthquakes being concentrated in interplate areas. The estimated rates for world and New Zealand earthquakes are presented in Table 2 (ISGN 2000). The New Zealand data is provided because of the completeness and volume of the records. This self-contained community includes representation of all aspects of earthquake engineering for masonry. Table 2: World and New Zealand Earthquake Data Description Magnitude World Average Annually New Zealand since 1850 Great

8+

1

1

Major

7-7.9

18

11

Strong

6-6.9

120

2 to

Moderate

5-5.9

800

5 annually

Light

4-4.9

6200 (estimated)

100-150 felt

Minor

3-3.9

49000 (estimated)

10-15,000 recorded

This data in the table illustrates the problem faced in New Zealand. The location of the unreinforced masonry buildings near the Wellington fault zone compounds the problem.

3. FATALITY PLOT AND PLOTTED FEATURES The data from Table 1 has been plotted in Figure 1. This plot has been presented as a logarithmic – linear plot for clarity. The scattering of points is to be expected however there are clear pointers in the data to the functional form of an envelope fatality function. The data in Table 1 represents a reasonable statistical sample of the fatal earthquakes of the twentieth century. A set of indicator lines is shown on Figure 1 as Plots one to four.

1,000,000 Plot 1

Plot 2

856 IR

100,000

1999 TR

1988 AR

Fatality Count

1923 JA

1970 PE 1927 CH 1990 IR 1939 TR 1976 GC 1939 CL 1935 PA 1 9 8 5 M E 1970 CH

1915 IT

10,000 1976 NI

1920 CH

1976 CH

1908 IT

1755 PO

1976 PH

1995 JA 1999 TA 1998 AF

Plot 3

1990 PH

1997 IR

1999 CO

1,000

1999TR

1906 CA

1999 TR2 1931 NZ 1933 CA

100

1964 AL

1971; 1994CA

1886 SC 1989 CA

1812 CA 1929 NZ

1989 AU

10

1952 CA 2000 CH

1848 NZ 1968 NZ

Plot 4

1855 NZ 1857 CA

1 5.5

6

6.5

7

7.5

8

8.5

9

Earthquake Magnitude

Figure 1: Earthquake Fatalities and Magnitude. These equations for these indicator lines are of the form shown in equation 1.

y = Ie KM

(1)

The fitted constants for the four plotted lines are presented in Table 3. Table 3: Plotted Line Data from Figure 1. Plot

Name

I

K

1

Nicaragua-Newcastle

6*10-21

9

2

Tangshan-Newcastle

5*10-09

4

3

Californian

6*10-05

2

4

New Zealand

3*10-15

5

M is the assigned magnitude of the event, which is typically obtained from the USGS database. The lo west of any nominated values for the magnitudes were taken for historical events. The variable y is the estimated fatality count. The K and I represent the fitting points for the plotted lines. It will require further analysis to confirm the limits proposed with this analysis, but for the purposes of the establishment of the model, they are considered sound indicators. The first plot line, which is designated Plot 1, represents the boundary introduced by the 1974 Nicaraguan and 1999 Colombian earthquakes. The plotted point for the 856AD Iranian earthquake is obviously a product of the adobe and stone construction. It is plotted for this reason to highlight the problem with weaker masonry. It is however considered an outlying point for this data set for the usual historical reasons. This line is considered to represent the upper limit to the fatality function for the lower values of the magnitude. It of course suffers from the problem of individual building collapse often representing the bulk of causalities in events in the range of M5.5 to 6. This data set needs to be augmented in a subsequent analysis using a greater number of events in this magnitude range. The second plot line, which is designated Plot 2, represents a curve fitted through the Newcastle to Tangshan events. The Shiono’s figures (1995) for the Tangshan event have

been accepted for this paper. The meizoseismal area and the nominated fatalities seem as reasonable lower bounds in the absence of further authoritative data. This line is considered a primary indicator function. Fatal events that fall above this line are rare and unusually savage or can be blamed on the trucidation of a uniform idem inflictum edificium. Hadjian’s (1992) comments on this issue for the Armenian earthquake are particularly relevant. The upper limit to Plot 1 and 2 represent the defining line for the standard earthquake fatality function. The critical issue is the slope on the curve past a magnitude 7.8 to 8 event. Is the Tangshan an upper limit or asymptotic event or are larger fatality counts expected in future events? The data for the Kansu, China earthquake would suggest with a reasonable density of housing that this is an upper limit for masonry. The data for the commonly used 1933 Californian event plots well below this line. The third plot line, which is designated Plot 3, represents a curve fitted through the 1906 and 1989 Californian events, and the 2000 Yunnan, China event. This line is the interesting feature. It may represent the region in interplate earthquake statistics that represents the error in engineering, even to the highest standards, if there is a large population at risk. The low death rates in the Charleston, USA, and 2000 Yunnan earthquakes considering the magnitude, the type of building construction and the size of the population exposed indicates the need for a detailed review of the fatalities in both events. The fourth plot line, which is designated Plot 4, provides an upper bound to the New Zealand events that have caused fatalities. The concern in this case is a repeat of the 1931 event size or bigger in an older population centre of New Zealand. This is particularly relevant for any areas of unreinforced masonry. Figure 1 clearly shows the benefits of developing and applying a high standard of seismic construction practices. The question is then raised ‘What are the likely fatality counts in the cities that have poor seismic planning and enforcement of regulations?’ If there is sufficient population in the meizoseismal area and poor construction then the death rates are likely to lie above the Californian line. If there are Type i2 e buildings that are coupled with poor construction practices and a badly timed event then the death rate could lie above the Tangshan line. At an M8 level, there is a thousandfold difference in the death rates between the 1931 Napier event and the Tangshan event. This is not a trivial issue for intraplate regions of the world. No attempt is made in this analysis to draw conclusions about future earthquake events. This data is presented for the development of a suitable model that can be used to determine the likely hazard for an urban area for a given earthquake event. The next step in the models development is to estimate the bounding function to the data in Figure 1.

4. A SUGGESTED BOUNDING FUNCTION The bounding function provides a representation of the fatality counts under some reasonably standard conditions. The earthquakes that are used in the estimation of the bounding function are marked in Table 1 with a pound sign (#). The earthquake magnitude and fatality data are plotted on Figure 2. A trend line has been shown on the figure. The bounding function is intended as a guide. The slope at the M8 event level has been set at approximately zero. This appears to be a reasonable assumption because of the numbers of the fatalities in the 1920 and 1976 events, and the difficulty of using pre 1900’s data. The overestimation at the M5.5 event is not considered significant.

1,000,000

Fatality Count

100,000

856 IR

10,000 1976 NI

1,000

1999 CO 1999TR

1933 CA

100 10

1971;

1989 AU 2000 CH

Plot 4

1 5.5

6

6.5

Figure 2: Earthquake Fatalities Bounding Function. The form of the fitted equation is shown in equation (2). This equation has an R2 of 0.95. log( y) = 3.93M − 0.57 M 2 − 32.4

(2)

The form of this equation is not of great relevance. It can be cast as shown in equation (3) for the purposes of the subsequent analysis. y = Ξ (x )

(3)

5. A SUGGESTED ESTIMATOR FUNCTION The bounding function provides a representation of the extreme events of the 20th century. The vast bulk of earthquakes pass unnoticed, except for the blips at the recording stations and a line on the seismological sheets. Equation (3) provides a synthetic fatality function to estimate the fatality count under circumstances that are not as extreme as Armenia or Tangshan. The suggested form for the function is shown in equation (4). i= n

y = ∑ λi Ξ ( x )

(4)

i =1

where λi represents the series of factors that reduce the fatality count because of circumstances at each location, i is the index counter and n is the total number of factors. The factors will be limited to four for this paper. A more through analysis may require additional factors.

5. THE LAMBDA FACTORS The description of a few of the factors are presented in Table 5. The factors represent independnet entities. The total population is set, and is controlled by factors totally unrelated to the earthquake events or design. The meisoseismal area adjustment is for the noted difference between intraplate and interplate regions. The building and ground factors are related and have been combined at this stage, this inlcudes a frequency factor that relates the frequency of the event to the natural frequencies of the building. This is the issue of tuned buildings and bespeaks the issue of uniform trucidation of buildings. Table 5: A description of the lambda factors Lambda Factor

Description

1

Population exposed to danger.

2

Meizoseismal area adjustment.

3

Radius from epicenter to the population centre and the fatality rate.

4

Building and ground type factor

6. THE NAPIER 1931 EARTHQUAKE AND ITS LAMBDA FACTORS The Napier, NZ earthquake of 1931 killed 256 people in a population of approximately 30,000. The earthquake had a magnitude of 7.9 and an epicentral distance of 15 to 20 kilometres. The information on this event and the towns, which is available from the NZ Ministry of Civil Defence (2000) and Massey (2000), is summarized in Table 6. Table 6: Napier Earthquake 1931 data Location

1931 Population

1999 Population

1931 Deaths

Napier

16,025

54,000

162

Hastings

10,850

Havelock

3,125

91

Wairoa

3

Total

30,000

256

The estimated lambda factors for the Napier earthquake established by comparison to the Tangshan event are presented in Table 7. Table 7: Napier earthquake lambda factors Lambda Factor Numerical Value

Derivation

1

0.04

30,000/750,000

2

0.30

Elliptical factor assumed as it is interplate

3

0.20

Shiono’s data for Tangshan fatalities (1995)

4

0.44

Frequency, building and ground factor (fitted)

The Napier event had 0.001 times the fatality count of the Tangshan earthquake. The final lambda factor is used to fit the model. The model will require detailed calibration, which will require the collation of existing data on fatal events. An example of the models use is presented in Table 8. Although these results are for a sample city from any intraplate zone, they support the types of estimates provided by Jones, et al., (1993) for Memphis. Allowance has to be made for the greater epicentral distance to a Marked Tree event and the population of Memphis. It is evident from the results presented in Table 7 that a combination of high lambda factors produces significant fatalities. It is expected that this conclusion will hold for injuries and damage functions. Table 8: Sample data set Description

Unit

Population

Number

100,000

Earthquake

Magnitude

7 intraplate

Epicentral Distance

kilometres

25

Lambda 1

Exposed population

2.5

Lambda 2

Type of event

1.0

Lambda 3

Likely collapse rate

0.07

Lambda 4

Building and ground factor

0.5

Ξ ( x)

Number

40,000

Fatalities

Number

3,500

7. CONCLUSIONS

The purpose of this paper is to develop a model that is capable of being used to estimate earthquake fatalities for theoretical events. The proposed model is based on the major earthquake disasters of the 20th century that has been augmented with additional events from the 19th and 21st centuries. In order for an earthquake to cause fatalities, people have to be living or occupying the meizoseismal area. This limit on the area that is affected by each earthquake provides the main barrier that limits the loss of life in earthquakes. The rapidly expanding population of the world and the increased use of masonry present a real difficulty in limiting the deaths in earthquakes in this century. A function has been estimated that provides under reasonably standard conditions the estimated loss of life in extreme events. This function is a bounding function that matches the primary source data from the twentieth centuries. The bounding function is determined by using the plotted line for the Nicaraguan and Columbian events as a tangent. The historic records for Tangshan and Kansu in China are used as a guide to the upper limit. These limits clearly define the use of the function. It is not contended in this paper that the bound is a strict upper bound for all future events. It is however a reasonable estimate for masonry buildings of two to three storeys height in an urbanized setting, because of the automatic limit on the population density that this assumption implies for the analysis. A model is then proposed to relate the function to the fatalities in real earthquakes. A preliminary set of lambda factors are derived for the Napier NZ, 1931 earthquake. These lambda factors enumerate the independent variables that determine the true fatality count for the calibrated events from the bounding function. It is a considerable exercise in data collection and statistical analysis to determine representative domains for the lambda factors and to determine whether the fourth factor can be further divided into frequency, and building and ground components. The Napier calibration demonstrates that the two events can be related given the difference in fatalities. A sample exercise has estimated the fatalities for a theoretical town of 100,000 people. The results provide an estimate of 3,500 fatalities for the nominated conditions. This result is considered consistent with the results for Memphis derived in the earthquake monograph of 1993. It is simply to early in the stages of the development of the model to provide error estimates for this data. The synthetic fatality function has been derived to estimate losses in an earthquake under standard conditions. The function can be used in an economic analysis to compare alternatives. The main alternatives that are able to be compared are the do nothing option compared to the rehabilitate in advance of an event, thus potentially limiting the damage and the overall cost to the community.

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