DAMAGE RATIOS FOR DOMESTIC BUILDINGS IN THE 1987 EDGECUMBE EARTHQUAKE

This paper describes an analysis of damage costs to house and farm property in the M5 = 6. 6 Edgecumbe New Zealand earthquake of 2 March 198 7. The study investigated damage ratios for dwellings, plus their associated garages and farm buildings. The damage costs were converted to damage ratios, by dividing them by the total value of the relevant property in the intensity zones concerned. The mean values and statistical distributions of these damage ratios were then found, the lognormal distribution fitting very well. The mean damage ratio for house buildings at MM intensity IX was 0.08, and the mean damage ratios were generally smaller than previous studies had shown.


INTRODUCTION
The M 5 6. 6 Edgecumbe New Zealand earthquake of 2 March 1987 was the most damaging New Zealand earthquake since the 1931 Hawkes Bay event, with strong shaking with intensities up to Modified Mercalli IX (MM9).
The Edgecumbe earthquake has given rise to many informative studies.
In particular a complete volume of a journal [ 1) is devoted to papers discussing this event.
This paper describes the damage to domestic buildings, in relation to the intensity of shaking.It is part of a wider study (2) which included topics not treated here such as damage to household contents and vehicles.
Lowry et al (3] produced an isoseismal map on which our Figure 1 is based.
Figure 1 shows the extent of our present region of interest which extends from the epicentre out to the isoseismal for Modified Mercalli intensity VI.
The degree of damage to any class of property at risk is often expressed as a damage ratio, ie Cost of Dama~e to Property value of roperty (1) The damage ratio depends on the strength of shaking and is treated here as a function of MM intensity as given by Figure 1.
Editor's Note.For buildings the Replacement Value is usually preferred and is preferred here also.
However, the insurance data available to us were mainly in terms of Indemnity Value.Some adjustments have therefore been necessary.
Estimates of damage ratios for New Zealand houses have been made in two previous studies, namely those of Dowrick [ 4 J and Birss [5 J.
In the former study, Dowrick based his results on damage costs estimated by Cooney and Fowkes [6] from a 1981 sample of "typical" New Zealand houses in a model of intensity MM9, using damage observed in the 1931, 1942 and 1968 earthquakes.Because of differences in house construction styles and intensity scales in other parts of the world it is difficult to find directly comparable data elsewhere.Unfortunately the recommendations of the most comprehensive damage ratio study from the USA (7) were not based on real damage data, but on expert opinion.
The outcomes of the present study are compared with the results of earlier studies.

DESCRIPTION OF HOUSING IN THE AFFECTED AREA
It was necessary to obtain a description of the nature and amount of housing in the area of interest, so that the Replacement Value (RV) and relative vulnerability of the total population of houses could be evaluated for each intensity zone.This was done with the assistance of data held by Valuation New Zealand.The replacement value at the time of the earthquake was obtained by assuming that the average cost of housing was $600 per square metre.This figure is believed to be accurate to about ±5%.The relevant housing statistics for the four inner isoseismal zones are given in Table 1.Cooney [8] has described the main eras of design and construction of New Zealand housing as they influence seismic vulnerability.
The key dates for the interpretation of the age-distributions in Figures 2 and 3 are those given in Table 2.
Figures 2 and 3 show that most of the housing in both the MM9 and MMS zones has been built since 1949.
Hence most of it post-dates the introduction of the first two building regulations for houses in 1924 and 1935.
For the MM9 Zone we have also presented the age-distributions for the structures of seismically least vulnerable houses (Figure 4) comprising 31% of the total, and most vulnerable houses (Figure 5) comprising 7% of the total.
All of the latter class are of post-code construction.The subclass taken as most vulnerable were houses with heavy and brittle wall and roof cladding, ie those having roughcast, stucco, brick or stone wall cladding and tiled roofs.
Note that no houses having solid brick or stone external walls occur in this area.The subclass taken as least vulnerable comprised houses with wooden wall cladding, and roofs clad with lightweight materials, namely wood, galvanised iron, aluminium or bituminous felt (Malthoid).
Houses situated in the MMS Zone appear to be slightly more vulnerable than those in the MM9 zone.However the difference would not be great.This is illustrated by the (1) Reference (2) Reference (3) Reference ( 4) Reference i:: age-distribution for the two classes in Figures 2 and 3.The MMS Zone has less of the good 1950' s housing and more of the 1970' s jack-stud foundation construction, but there are fewer pre-code (1935) houses in the MMS Zone (3%) than in the MM9 Zone (8%).However, in both zones the most vulnerable class of houses comprises only 7% of the total.
Overall it therefore seems fair to conclude that the damage ratios for MMS and MM9 Zones will not be significantly biased by differences in vulnerability of their respective housing populations.
As described elsewhere [2), the geographical distribution of the housing was also examined.
It was found that in each intensity zone there was no significant tendency for the houses to be nearer one isoseismal than the other, eg the weighted mean intensity for the houses in the MMB zone was close to MMS.5.

DAMAGE RATIOS FOR DOMESTIC PROPERTY Damage Ratios For House Buildings
The average damage ratios for house building damage have been found as a function of

Replacement
Value, for a range of intensities using the specific form of equation ( 1) as follows: In evaluating the numerator for equation (2), an attempt was made to find the complete cost of damage within each intensity zone.
As described in detail elsewhere [2], the total cost for domestic building damage within the MM6 isoseismal was approximately $(NZ)20.8 million of which $3.1 million was uninsured.
The Intensity Zone sub-totals are given in Table 1.(The above totals do not include the costs of fees for insurance assessors and engineers.) The denominator of equation ( 2) was found from Table 1, thus ensuring that the total population of dwellings in each zone was included, (i.e. both undamaged and damaged houses).

The resulting values of D
for house buildings are presented in rTable 3 and Figure 6.
As discussed elsewhere [2), it was found that the clusters of urban development within each intensity zone were balanced so that it would be appropriate to• plot !\ at the centre of the MM zone intervals in Figure 6.
But because there was no MMlO isoseismal (Figure 1), there was some uncertainty as to where to plot Dr for  the MM9 Zone on the horizontal axis of Figure 6.
Therefore an estimate has been made of the epicentral intensity, I 0 , at the geometric centre of the MM9 Zone. Figure 7 is an attenuation plot of the mean horizontal radii of the MM isoseismals (MM5-MM9) of the Edgecumbe earthquake, together with the mean attenuation curve for a shallow earthquake of the appropriate magnitude, i.e.M 5 = 6.6.This curve is based on a data set of New Zealand earthquakes prepared in a separate study by Dowrick ( 14]. It can be seen that the Edgecumbe data points fit the mean attenuation curve quite well.Read together, the data points and the curve suggest that the value of I 0 may well have been close to MMl0.If we assume that I 0 ~ 9.8, we then plot D, = 0.070 at I~ 9.4 on Figure 6.By extrapolation of the resulting curve on Figure 6, we find D, (complete MM9 zone) ~ 0.080 In Figure 6 the damage ratios from this study are compared with estimates made in some previous studies for similar housing stock.
It will be seen that the present estimates of D are lower than those found in the other studies.In particular we note that both earlier studies [4,5) of New Zealand houses gave a damage ratio of 0.13 for intensity MM9, as compared to c.The Damage Cost in Indemnity terms is the cost of repair to return the item to its Present Value without betterment.The damage ratios for all three classes have been found to fit reasonably well to the lognormal distribution, a typical example being the fit for the data from Figure 8 as shown in Figure 9 (the shapes of the empirical and fitted curves relative to each other are similar for all three classes).
However, since the lognormal distribution is not bounded above, the fit can be good only if the damage ratio is small on average, as it is in this study.
The lognormal distribution has the density function   Here the parametersµ and a are estimated by the sample mean and standard deviation of the natural log of the damage ratio.
The lognormal distribution has mean (4) and coefficient of variation (ratio of standard deviation to mean) (5) The estimates of the parametersµ and a (and hence "! and 6) for the three classes are given in Tables 4 and 5.As these estimates were obtained on a different mathematical basis and exclude undamaged property, the values of "! in Table 5  This ratio is ~bviously mathematically comparable to the Dr values of Table 3, but is again incomplete in that it does not include uninsured costs in the numerator or values of undamaged properties in the denominator.
The similarity of ~2 and 6 for buildings in each of the three intensity zones (Tables 4  and  5), signifies that the three distributions are of similar shape, i.e. the scatter does not change significantly with intensity.It is noted that the scatter is very large, as the coefficient of variation is 2.4 to 2.7 (Table 5).
When undamaged buildings are added to the cumulative distributions, they become as shown in Figure 10.
In this figure P; denotes the proportion of buildings in the intensity zone MM i which are undamaged.Using the properties of the ~ognormal distribution and the appropriate Dr values from Table 3, the damage ratio associated with any chosen probability of exceedence may be found.This may be appropriate when estimating the likely damage to individual or small numbers of properties in some future event.If the chosen probability of being exceeded is a, and pis the fraction of the population that is undamaged, we find that The derivation of equation ( 7) is given in Appendix I.
As noted earlier, these statistical distributions are based on indemnity value data, but for buildings we generally prefer to work in terms of Replacement Values as in equation ( 2).
In such cases a satisfactory conversion of equation ( 7) to replacement values is achieved by scaling the ratio m to equal the corresponding Replacement Value mean damage ratio, assuming that the shape of the distribution is otherwise the same, i.e.
that the a values in Table 4 ~emain  where D,(RV) is the damage ratio given in Table 3, and m is the damage ratio given in Table 5.
As an example, let us consider an earthquake for which the distribution of house building damage in its MMS Zone is similar to that represented in Figure 10, but that the mean damage ratio in RV terms is D, (RV) = o.025, and that the fraction of undamaged houses is p = 0. 55.
To find the 95 percentile (a = 0. 05) , we use equation ( 8) with m = 0.042, µ_= -3.920, a= 1.447, z 0 • 111 = 1.22, and obtain D, 0 _ 05 , 055 (RV) = 0. 07 As the sensitivity of the outcome to the value of pis of interest, let us suppose that the distribution of damage had been the same as above, but that there were no undamaged houses, ie P = 0 instead of 0.55.The corresponding 95 percentile damage ratio is found to be D,o.os,o (RV) = 0 .13 The increase in the 95 percentile from 0.07 to 0.13 demonstrates the importance of including undamaged as well as damaged property in the calculation.

CONCLUSIONS
The main conclusions that may be drawn from this study are as follows:- 5 The house populations in the MMS and MM9 zones were found to be sufficiently similar in seismic vulnerability terms to preclude any significant bias from such differences in the damage ratios obtained for these zones.6 The statistical descriptions obtained of the housing mix in the affected area will give a basis for comparison with housing in other parts of New Zealand when forecasting earthquake losses elsewhere.7 The geographical centroid of the houses within the intensity zones was effectively centrally placed within each zone, so that the random pattern of urban development did not introdyce undue biases into the estimates of D,. 8 Based on substantial sets of data, the damage ratio for buildings in each zone fits well to a lognormal distribution.The shape of the distribution is similar for intensities MM7, MMS and MM9.

9
A method has been presented for forecasting D for an individual property at any desired probability of exceedance, taking account of the number of undamaged properties in the population in a given intensity zone.10 Most of the data on insured damage came from a single source, namely the Earthquake and War Damage Commission (EQC).This so greatly facilitated the task of data collection, that it is clear that in the absence of the EQC the task of attempting to collect such a comprehensive data set would have been prohibitively expensive, and the quality of the data would not have been so good.Recent moves by the insurance companies in New Zealand to improve and co-ordinate their post-earthquake data retrieval systems are greatly to be encouraged.Let Y be the random variable which represents the damage ratio associated with a particular building for a given MM intensity.

As described graphically in
FIGURE 1 MAP OF INNER ISOSEISMALS OF THE 1987 EDGECOMBE EARTHQUAKE (DERIVED FROM LOWRY ET AL [3]).

~
Cost of Damage to House Buildings ~ Replacement Value of Houses in chosen MMI Zone (2) FIGURE 7 ATTENUATION OF MM INTENSITY IN THE 1987 EDGECUMBE EARTHQUAKE.
FIGURE 10 valid.Thus if the mean damage ratio D,(RV) = m• is different from m, then in equation (7

Table 1 :
Housing statistics in the inner intensity zone

Table 3 :
Hean Damage Ratios for Total Population of House Buildings