EFFECTS OF MICROZONING AND FOUNDATIONS ON DAMAGE RATIOS FOR DOMESTIC PROPERTY IN THE MAGNITUDE 7.21968 INANGAHUA, NEW ZEALAND EARTHQUAKE

In a recent study the present authors examined the damage ratios for houses and household contents in the Inangahua earthquake for intensities MM5-MM10, including the effects of chimney damage. The present study continues this work by examining the effects of ground class and construction type on damage levels. Houses from six towns are considered, i.e. Inangahua, Reefton, Westport, Greymouth, Runanga and Hokitika, covering a range of intensities from MMl0.5 down to MM7.0. A range of ground classes is also considered, covering the three classes described in the New Zealand loadings standard. The structural types considered comprise two foundation types (piled vs. concrete perimeter wall footings), and number of storeys. Some complexities and difficulties of reliable microzoning are revealed and discussed.


INTRODUCTION
The Inangahua, New Zealand, earthquake which occurred at 5.24 a.m. on the 24 th May l 968, had a magnitude of M_, = 7.4 (I] and M .. = 7.2 [1].It was predominantly a thrust event with the source rupture located beneath lnangahua.Although there was some secondary surface rupture in the vicinity of lnangahua the primary rupturing plane did not extend to the surface [2].Peak ground accelerations ranging from 0.58g to O.Ol5g were recorded (3) at distances of 15 km to 304 km (Table I).The earthquake was felt over most of the country from North Cape to lnvercargill, with intensities ranging up to Modified Mercalli X (MM 10) in the lnangahua area [4], as shown in the isoseismal map (Figure I).This earthquake was New Zealand's fourth most damaging in material damage cost terms in over one hundred years [5].While it was fortunate in socio-economic terms that much of the area or strong shaking was in part of the lightly populated Southern Alps (Figure 2), the earthquake resulted in over 11,000 insurance claims (valid or invalid) being made on the New Zealand Earthquake and War Damage Commission (EWDC).About 85% of the claim documents still exist, in the care or the National Archives of New Zealand in Wellington.This is the largest database on damage costs for any event in New Zealand history, considerably greater than those of the two other significant events, the 1987 Edgecombe and 1931 Hawke's Bay earthquakes.
The damage costs for domestic property in the latter events have already been studied by two of the present authors (6 -l l ).
As in the previous studies, in the present case the authors have statistically robust sets of data for studying the degree of damage to various classes of property in terms of damage ratio, D,, defined as D = Cost of damage to an Item ' Value of that Item (I) The damage ratios are studied here as functions of intensity of ground shaking, and are related to the MM intensity isoscismals.The Value of each Item in equation (l) was first expressed in terms of the Insured Value, which in the case of houses was converted globally by intensity zone to Replacement Value, except for the MM IO zone, where the Replacement Value could be estimated directly for each house.
The present study offers an opportunity to enrich the database of damage ratios, and provide some insights into inter-event variability of damage ratios by comparing the damage ratios determined here with those from studies of other earthquakes [12 -14].The opportunity has been taken to go beyond our previous housing studies by (I) examining damage ratios over a wider range of intensities down to MM5. (2) separating out chimney damage over a range of intensities and (3) comparing one and two storey houses over a range of intensities.Also the authors have started the next phase of this study which considers microzoning effects and different classes of construction.r1, = shortest distance to surface projection of rupture (km).

DESCRIPTION OF THE HOUSES IN THE AFFECTED AREA
Within the area of stronger shaking, i.e. intensity 2: MM7.
there were very few houses of a type likely to collapse, namely brick bearing-wall houses.Most houses were timber framed with a variety of wall claddings, including weatherboard, corrugated iron, brick, artificial stone (concrete masonry), fibrous (asbestos) cement sheet, and stucco (roughcast) as illustrated in Figures 3 and 4. A small number of houses were made of (nominally) reinforced concrete blocks.In some cases ageing weatherboard had been protected from weathering by coverings of fibrous cement sheets or stucco.
While most roofs were made of corrugated iron, other materials were used including aluminium, tiles (various materials) and bituminous felt.The majority of houses were founded on unbraced timber piles, with some concrete piles and concrete strip footings also used.Nearly all houses had chimneys, most of which were of brittle materials (brick or concrete).

General
As in the author's previous studies [ 6 -I OJ, the approach used was to account for the total population of property of any given class in the area under consideration.For relating the data to intensity, the houses and household contents were divided into intensity zones, which were defined such that the MM7 intensity zone (for example) was the area between the MM7 and MM8 isoseismals as illustrated in Figure 2. The total number of houses in the intensity zones are given in Table 2, as derived from the counts of houses reported in the national census of I 966 [ 15] for MM5 -MM9, while the MM IO zone data were derived during this study.
A house was defined as a building containing mostly a single dwelling (occasionally two) and had either one or two storeys (Figures 3 and 4).Dwellings classed as flats in the census were excluded, as were holiday homes (or baches).
The costs of damage and the insured values were derived from the claims on the EWDC, of which about 8,000 valid claims related to houses and household contents.and which formed the starting point for the database.In a substantial number of cases the claims provided information on the nature of the damage and of the building, such as the foundation, wall and chimney materials, and a breakdown of the costs of repairs.It proved possible to split out the costs relating to chimney damage for 90% of the houses.It is_ noted that the EWDC claims represent the total cost ot damage paid out for insured property, as there was no participation by the private sector insurance companies in underwriting earthquake damage in New Zealand in 1968.In addition it is noted that the claim payments were for repairs sufficient to restore property to its pre-earthquake condition [ 16], although less than this amount was paid out in some cases mainly in the MM IO zone.All costs are in 1968 dollars.
A valuable complementary source of data on construction materials, the nature and degree of damage, and uninsured houses, was the information collected in a survey conducted by the New Zealand Geological Survey (NZGS) [ I 7] immediately after the earthquake.About 1.000 children from schools located mainly in the MM7-MM9 zones were helped by their parents or other adults to record data concerning their homes, as part of what was one of New Zealand's earliest microzoning studies relating to earthquake damage (16]. A great deal of effort was required to complete the database in relation to numbers of storeys, construction materials, addresses, and the data on undamaged houses.This phase of the work involved extensive field trips, use of the NZGS survey data sheets, the 1966 census reports, the 1969 Official Year Book [ I 8], and reference to papers on damage to houses arising from the Jnangahua earthquake reconnaissance mission of New Zealand engineers [ I 9 -21].In order to make the rather slender subset of two-storey houses as statistically robust as possible, all of the two-storey hotels of house-type construction (Figure 4(b)) in the MM6-MM IO region were included in the database (see Table 2).These hotels were restricted in size to those with Insured Value up to $40,000.The NZGS survey data sheets referred to above comprised questionnaires for 995 houses.From an extensive study of the data sheets it was found that 610 of them correlated with insurance claims in our main database and 224 related to undamaged privately owned houses.Of the remainder, 108 were for public sector houses and 53 were for uninsured privately owned houses.A breakdown of this information by MM intensity zone is given in Table 3.
These data are an essential aid to accounting for uninsured houses that must be deducted from the total populations of houses for the purpose of our damage ratio analyses.Public sector houses, i.e. those owned by central and local government, were not insured for earthquake damage at that time.Of the NZGS sample of 995 houses (Table 3), 10.9% were public sector houses which is close to the national average figure of 9.6% for 1968 as derived from the Official Year Book data for that time [18].It is also interesting to note from Table 3 that 5.3% of privately owned houses were uninsured which is somewhat less than insurance industry assumptions of about I 0%.
For household contents we have assumed that 30% of households were uninsured.This is a current insurance industry figure based on slender data, and happens to coincide with the percentage uninsured of 78 households in the Inangahua (MMI0) area.The figure of 30% was also the middle of the range suggested for use in the Edgecumbe earthquake study [7].
The above data was used to derive the estimates of the total numbers of public sector houses and uninsured private sector houses given in Table 2.This was done by assuming that in each of the intensity zones MM6 -MM9, 10.9% of the houses were in the public sector and 5.3 % were otherwise uninsured.it has been found in previous studies [8,9] that two storey buildings are more damaged than one storey buildings, it has also been found [8] for houses of a given number of storeys (i.e. one storey) that size of house is not influential on damage level for medium to large size, while small houses may have been more damaged than larger ones.
Rather than basing the damage ratios on Insured Value as discussed above, it is mostly preferable to use Replacement Value of the houses.This was done here as follows.It is known from the Official Year Book [18), that the national average cost to build a new house in 1968 was $8,165.Using the data in Comparing the mean Replacement Values (Table 5) with the mean Insured Values (Table 4), it is seen that the insured value reflects the market value rather than the replacement value.This is supported by many comments in the claims,  For houses in the MM l 0 zone, the tloor areas were estimated for each property, and the Replacement Value of the property was based on its floor area and the quality of the construction.The value per unit area was assigned individually to each house.ranging from 70% to 100% of the national average.

Geographical distribution of houses
As the statistical properties of the damage ratios of the property under consideration is being considered according to the populations of data within different intensity zones, it is important also to take account of the geographical distribution of the data within each intensity zone.By visual inspection of the isoseismal map (Figures I and 2), we find that the centroid of the locations of the houses in the intensity area (I) (m zones MM5 to MM8 are likely to be near the centre of their respective intensity zones, as the rural houses are reasonably uniformly distributed across the intensity zones and the largest population centres are near the centre of the respective intensity zone.Thus, the mean damage ratios and statistical distributions apply at the average intensity of these four zones, e.g. at MMS.5 in the MMS intensity zones.
However, this is not the situation for the MM9 zone, as most of the population in this zone is located in Reefton which is just on the MM9 isoseismal.The only local intensity observation for Reetton township was MM9 and the peak ground acceleration recorded in Reetton was c. 0.6g [3].The centroid of the location of the MM9 houses is thus at intensity approximately MM9. l.
In the MM IO zone most houses were in or near the vi II age of Inangahua which is in the centre of the MM IO zone, where the intensity was likely to have been about MMI0.5.

DAMAGE COSTS
An attempt has been made to find the total cost of damage to insured houses and household contents in this earthquake.The total cost of damage including the insurance deductible was recorded for each claim, including those small amounts where the value of the claim was assessed as being below the deductible (which was the greater of $10 and one percent of 199 the loss).Also included were the damage costs relating to a small number of claims that were declined for technical reasons, such as being filed too late or expired insurance, but where the damage costs were evidently valid.
The total costs of damage to houses and contents used in this study are given by intensity zone .inTable 6.The grand total for these costs comes to $ l .67 million compared to the total for domestic and non-domestic property paid out by the EWDC of approximately $2.4 million.A striking feature of the costs of damage to houses is that about 78% of the total was caused by chimney damage.The damage ratios presented below were calculated in terms of Replacement Values for houses and Insured Values for contents.

Statistical distributions of damage ratios
The damage ratio The estimates of the parameters µ and er, found for the various data sets are given in Tables 7 and 8. Also tabulated are the numbers of damaged items n, and the total populations (damaged + undamaged) N.

Mean damage ratios
The mean damage ratio for all buildings in a given MM intensity zone is a useful parameter for various purposes [ I OJ, e.g. for comparing the earthquake resistance of different classes of property.Considering all N buildings (damaged and undamaged) in an MM intensity zone, we give here two principal ways of defining the Mean D,..

I, [ value of building i]
i=I where 11 is the number of damaged buildings.
Secondly ll

2)D,)
In general D,.,,, with its associated confidence limits is a more reliable and useful tool than D,.[ 7 and 8. Next we compare the vulnerability of different classes of property in terms of their statistical distributions of mean damage ratios, proportions of population damaged, and uncertainties.In the graphs of D,.,,, and 11/N that follow, the values for the MM9 zone are plotted at MM9. l for the reasons discussed in Section 3.2.

All houses and all damage
Plots of cumulative probability of damage ratios in the Inangahua earthquake are shown for all houses by MM intensity in Figure 5(a).There are six intensity zones, MM5-MM I 0, i.e. three more than were possible in our richest previous data set [6,7].The shapes of the distributions have   5 shows that the amount of damage is very small and the practical threshold of damage is at MM6 for houses, especially those with brittle chimneys.This is consistent with the definitions of the MM intensity scale [22) (see Appendix 1 ), and confirms that the outer isoseismals (Figure 1) have been appropriately located.
When considering mean damage ratios, parallel effects are observed to those discussed above in terms of damage ratio distributions.

Brittle Chimneys
When considering chimney costs, all costs attributable to chimney failure have been included, i.e. direct costs of damage to the chimneys and fireplaces, plus all indirect costs of damage caused by the chimneys to house structure and finishes, including roof, ceilings, floors and walls.
First consider the distributions of damage ratios plotted in Figure 6 5(a), where it is seen that the damage ratio distributions for MM8 and MM9 are virtually identical when all damage is considered.

: Three plots of cumulatfre probability distributions of damage ratio as a function of MM intensity for houses in the Inangahua earthquake: (a) One storey houses considering chimney related damage only, (b) All houses excluding chimney damage, and (c) One storey houses in the MMS zone comparing cases including and excluding chimney damage. In (c), 95% confidence limits for the empirical distribution and the fitted lognormal curves for one storey houses in the MMS zone with and without chimney damage.
Regarding the degree of chimney damage found here, it is of interest to note that in the magnitude Mw 7.1 Wairarapa earthquake of 24 June 1942, it may be inferred from Luke [13] that 20-25% of the 25,000 houses in Wellington suffered chimney damage.As Wellington was on the outer fringe of the MM? intensity zone in that earthquake [23], this statistic is consistent with the value of 57% found for the whole of the MM? zone in the present study.
In Figures 6(c) the fitted lognormal curves as expressed byµ and rJ in Tables 7 and 8 lie close to the empirical cumulative probability curves, though the fit is not quite as close as in previous studies [6-1 OJ.It is noticeable that the fit at MM8 is better for the case where chimney damage is excluded than when it is included.and this was the case for the other intensity zones also.This is understandable, because chimney damage not only contributed a high proportion of the total, but was also less variable than the damage due to other causes.This means that the distribution of damage ratios including chimney damage is effectively a mixture of two distributions with different variances, which cannot be represented completely by the single variance parameter rJ of the lognormal model.
Next consider mean damage ratio as affected by brittle chimney damage.The influence of chimneys on D,.,,, is very apparent in Figure 5(b) where D,m is seen to range from 2.0 x 10• 5 (excluding chimneys) at MM5 to 0.044 (including chimneys) at MM8 and then flattening off to rise only slightly to 0.046 at MM9.This plateau was explained above as a result of chimney damage reaching a near maximum at MM8.The dominance of brittle chimneys as an indicator of vulnerability is also illustrated by the ratio of D,.,,, including chimneys with that excluding chimneys, which in round figures is 1.8, 6, 9, 9, 5 and 1.2 for MM5 to MM I 0 respectively (Figure 7).The figure of 1.2 for the MM IO zone is close to that of 1.3 obtained for the MMIO zone in Napier in 1931 [8] where all houses also had brittle chimneys, and were of similar construction (weatherboarded and piled) to those of the Inangahua area.
Finally, consider the effects of chimney damage on the percentage of houses damaged, as depicted in Figure 5(c).The ratio of the percentage damaged including chimney damage with that excluding chimney damage is 1.5, 3.2, 1.8, 1.9, 1.4 and 1.0 for MM5 to MMIO respectively (Figure 7).For Napier (MM 10 in 1931) [8], as in the Inangahua village area in 1968, nearly all houses had damage other than that caused by chimneys, th_e above ratio being 1.01.Considering the whole of the affected area (MM5 -MM I 0), the number of houses damaged would have been reduced by about 45% if no brittle chimneys had existed.

Number of Storeys
The vulnerabilities of houses of one and two storeys are compared at intensity MM7 and MM8 for the case when chimney damage is excluded.D,.,,, and percentage of houses damaged with their associated 95% confidence limits are plotted on Figure 8.It can be seen that at both MM? and MM8, the values of both parameters are substantially greater for two storey houses than for one storey houses.The numbers of two storey houses in both intensity zones are however not large and the 95% confidence limits are quite wide.Nevertheless, the statistics D,.m and percentage of two storey houses damaged are both significantly greater (p<0.01)than those of one storey houses at MM?, as are also the averages of the MM? and MM8 statistics, when chimney damage is excluded.Conversely, when chimney damage is included, the differences are not statistically significant.
The above findings are similar to those for one and two storey non-domestic buildings at intensities MM? and MM9 in the Edgecumbe earthquake [9].
It is also noted that the above difference between the D,,,, values for one and two storey houses excluding chimney damage is hidden when chimney damage is included, as shown in Table 8.

Damage ratio as a function of house value
As has been done in previous studies [8,9], the possibility that damage levels vary with building value (or size) was examined.In Figure 9 the damage ratio for each house in the MM8 Zone is plotted against its replacement value, and a robust smooth trend line for mean damage ratio is fitted using the Splus local regression function "loess".When chimney damage is included, Figure 9(a), damage ratio is insensi1ive to size for larger houses, i.e. those with replacement values larger than the mean value of $7,000 for the MM8 zone, but below that the damage ratio increases strongly with decreasing value.A similar trend was found for Napier houses at MM IO [8].However when chimney costs are excluded, Figure 9(b), it is seen that damage ratio is insensitive to value (size) of houses.This is consistent with the findings [9] for one storey non-domestic buildings in the MM9 zone of the Edgecumbe earthquake.

Effects of foundations
In the MMIO zone there were three houses with full concrete foundations and three with partial foundations (at the comers only).These two subsets of houses had D,.,,, of 0.035 and 0. I 8 respectively, which are both considerably less than the D,w of 0.35 for all the 55 houses for which D,-m is dominated by houses with unbraced pile foundations (Figure 5(b)).The effects of foundations on house vulnerability at intensities MM? -MM9 are being evaluated in an ongoing study.

Household contents
Plots of cumulative probability of damage ratio in the Inangahua earthquake are shown in Figure IO(a) for household contents for six intensity zones (MM5 -MMlO), twice those (MM?-MM9) that were possible in the studies [6,7] of Edgecumbe earthquake.While very small amounts of damage do occur to contents at MM5 and MM6, Figure I O(a) shows that the practical threshold of damage is at intensity MM? for contents.This is one intensity unit higher than that observed for houses (Section 5.3).I/_ A_ ',,

Influence ofchinmeys 011 damage to houses as a function ofi11te11sity in the Inangahua earthquake. The D,,,, ratio is the ratio of D,.111 including chimney damage to D,111 excluding chimney damage_ The II ratio is the ratio of 11/N including chimney damage to 11/N excluding chimney damage.
Some caution is needed when considering the mean damage ratio for MM I 0, as it comes from only one earthquake, is from a small population of only 53 households, and depends on the level of insured value in relation to the "present value'' or other appropriate insured value for contents.However the mean damage ratio estimates appear to be reasonably robust in that all households are known to have suffered contents at MM6 to 74%, 88% and 100% at MM8 -MMI0 respectively.

COMPARISONS WITH OTHER STUDIES
In order to gain some understanding of inter-event variability of estimates of vulnerability for domestic property, comparisons are now made with the results of studies of other New Zealand earthquakes.The following comments are additional to some comparisons already made above.Of particular interest are the results of studies of the Edgecumbe earthquake [6,7].for which purpose the values of the statistical parameters are tabulated here in Appendix 2.
Comparisons are made graphically in Figure 11 of mean damage ratio D,111, and percentage damaged, together with their 95% confidence limits, for both houses and contents.
Here the values for the MM9 zone are plotted at MM9. l for the lnangahua earthquake (as discussed in Sections 3.2 and 5.2). while those for the MM9 zone of the Edgecumbe earthquake are plotted at MM9.4 for similar reasons as discussed elsewhere [6,7]. (1J :::,

Figure 8: Two measures of the vulnerability of one and two storey houses in the MM7 and MM8 intensity zones of the Inangahua earthquake: (a) D,111 and its 95% confidence limits, and (b) Percentage of houses damaged and its 95% confidence limits. Note that there were not enough 2-storey houses ill the MM9 and MMl Ozones for similar comparisons to be made there.
As noted in Section 3.1.in the lnangahua earthquake the damage costs paid for houses were for repairs sufficient to return the building to its pre-earthquake condition (albeit somewhat meanly in some cases at MM I 0), with no participation by private sector insurers.In the Edgecumbe earthquake the EWDC' s obligations were similar, being formally limited to repairs to "Indemnity Value", but the private insurers were widely underwriting the extra amount for full replacement cover.In practice however the private insurers' payouts were quite small, being 0.7%.3.4% and 6.4% of the total losses at MM7. MMS and MM9 respectively, as used in determining the mean damage ratios [7].Regarding household contents, the authors consider the insurance assessment regimes to be the same for both earthquakes; private sector insurers were not involved in either case.Thus in insurance terms the damage ratios from these two earthquakes are derived from very similar cost data.• .

Figure 9: Plots of damage ratio versus insured value for one storey weatherboard houses in the MM8 intensity zone of the lnangahua earthquake, including a robust smooth trend line: (a) Including chimney damage, and (b) excluding chimney damage.
First, considering houses, it is noted that those affected by the Edgecumbe earthquake had fewer and generally more robust chimneys than was the case in the Inangahua earthquake.So it might be expected that D,.,,, and n/N for the Edgecumbe event would lie between the Inangahua results which exclude and include chimney damage.As seen on Figure 11 (a) this is so for D,,,, at MM7 and MMS, but probably not at MM9, while for percentage of houses damaged (Figure 11 (c)) this is true at MMS and MM9 but not at MM7.
--0-----<!k> - Although the houses in the two locations were physically quite similar (mostly timber framed with weatherboards and unbraced piles), there was a wide discrepancy between D,,,, for houses at MM 10 in I 968 for lnangahua (D,.,,, = 0.35) and in 1931 in Napier (D,.,,, = 0.09).This difference is considered to be partly a result of the very different financial circumstances prevailing in 1931 when there was no earthquake insurance and there was a severe economic depression.The two principal features of heavy damage in both places were severe chimney damage and many houses displaced from their piles.It is remarkable how cheaply repairs were macle in Napier for foundation failure.whereas in lnangahua similar damage was relatively very expensive to repair or was considered to be not worth making good.

APPLICATION OF THE RESULTS IN FUTURE STUDIES
The damage ratios determined in this study are applicable directly to studies where the housing stock and insurance regime are similar to those prevailing in 1968 in the affected regions.For valid application to loss estimates for future earthquakes, the differences between the conditions outlined here and those of any other event will obviously need to be addressed, largely speculative as this process must necessarily be.The main factors to be taken into account are: (i) The nature of the insurance policies in force.For example open-ended full replacement style policies seem likely to result in higher claims settlements than arose from the fixed sum insured policies that were prevalent in 1968 New Zealand.This difference is likely to occur mainly in cases with heavy damage.(ii) The levels of insurance deductible that are likely to be in place.The damage costs adopted in this study include the deductible subtracted from the damage cost.(iii) The possible inflationary effects of earthquakes causing very large total losses and leading to shortage of repair resources.The total direct damage cost for the Inangahua earthquake was about $(NZ) 41 million in year 2000 values, and hence was too small to cause such an effect.(iv) The nature of the housing construction, i.e. incidence of brittle chimneys and nature of foundations.Further insights into the latter effect are being sought of an ongoing study due for completion in 2001.

CONCLUSIONS
Arising from this study the following conclusions have been made: Houses /nwstlv timber framed) I. The vulnerability of domestic property has been determined in terms of probability distributions of damage ratio, mean damage ratio and percentage of property items damaged.This has been done over a range of six Modified Mercalli intensity zones (MM5 -MM 10) which is greater than in any previous study worldwide.
2. As in previous New Zealand studies the damage ratios were found to be modeled well by the lognormal distribution.
3. The total cost of damage to houses was $(NZ) 1,503,000 in 1968 values ($ I 8,000,000 in year 2000 values).
Nearly all houses had brittle chimneys, and it has been found that 7891, of the above cost was due to chimney related damage.
4. The mean damage ratio including all costs exceeds that excluding chimney costs by factors of 6, 9 and 9 at intensities MM7, MM8 and MM9 respectively.
5. The total number of houses damaged excluding chimney damage was 57% of that including chimney damage.
6.When chimney damage is included there is a plateau between MM8 and MM9 in the plots of D,.m and percentage of houses damaged, D,.,,, being 0.044 and 0.046 at MM8 and MM9 respectively.This is caused mainly by the dominance of chimney damage coupled with the near saturation of chimney damage at MM8.

7.
The mean damage ratio is insensitive to house size when chimney damage is excluded, but when chimney damage is included the mean damage ratio is larger for small houses than for medium-sized or large houses.
8. When chimney damage was excluded, two storey houses were found to be significantly more vulnerable than one storey houses at intensity MM7, as previously found for non-domestic buildings in the Edgecumbe earthquake at MM7 and MM9.11.Although the houses in the two locations were physically quite similar, there was a wide discrepancy between D,.,,, for houses at MM 10 in 1968 for lnangahua (D,,,, = 0.35) and in 1931 in Napier (D,,,, = 0.09).This difference is considered to be partly a result of the very different financial circumstances prevailing in 1931 when there was no earthquake insurance and there was a severe economic depression.
12. When the lower incidence of brittle chimneys in the Edgecumbe earthquake is allowed for, D,,,, and 11 IN for houses as found for that event and the lnangahua earthquake are consistent at most intensities.

Household contents
13.The effective threshold for damage to household contents was found to be at intensity MM7, while that for New Zealand houses was at MM6.These findings are consistent with the definitions of those intensities in the MM scale.
14.For household contents, the mean damage ratio plotted as a function of intensity is markedly non-linear between MM9 and MM I 0, D,,,, rising sharply to about 0.3 at MM I 0. This behaviour is akin to that of brittle structures, and household contents of course are mostly not designed to resist earthquakes.15.In terms of mean damage ratio.the results for contents of this study and that of the Edgecumbe earthquake are very similar at intensities :S MM8, but at MM9 the D,,.. values seem to be consistent for the two events when the geographical distribution of houses within the two MM9 intensity zones are taken into account.

APPENDIX 1:
Extracts from the New Zealand 1996 Modified Mercalli intensity scale relating to pre-1969 property (22].Criteria for MM5 -MMI0 relating to fittings (contents) and structures, (essentially the same as the New Zealand 1966 MM intensity scale).

MM5 Fiuings
Small unstable objects arc displaced or upset.Some glassware and crockery may be broken.S1ructures Some windows Type I cracked.
A few earthenware toilet fixtures cracked.

MM6 Fillings
Objects fall from she! ves.Pictures fall from walls.Glassware and crockery broken.Very unstable furniture overturned.

Structures
Slight damage to Buildings Type I.
Some stucco or cement plaster falls.
Windows Type I broken.Damage to a few weak domestic chimneys, some may fall.

MM7 Fillings
Substantial damage to fragile contents of buildings.Structures Unreinforced stone and brick was cracked.Buildings Type I cracked some with minor masonry falls.
A few instances of damage to Buildings Type 11.
Unbraced parapets, unbraced brick gables, and architectural ornaments fall.Roofing tiles, especially ridge tiles may be dislodged.Many unreinforced domestic chimneys damaged, often falling from roof-line.
Water tanks Type I burst.
A few instances of damage to brick veneers and plaster or cement-based linings.Unrestrained water cylinders (Water Tanks Type II) may move and leak.Some windows Type II cracked.Suspended ceilings damaged.

MM8 Structures
Buildings Type I, heavily damaged, some collapse.Buildings Type II damaged, some with partial collapse.Buildings Type III damaged in some cases.
A few instances of damage to Structures Type IV.Monuments and pre-1976 elevated tanks and factory stacks twisted or brought down.Some pre-l 965 infill masonry panels damaged.Decayed timber piles of houses damaged.
Houses not secured to foundations may move.Most unreinforced domestic chimneys damaged, some below roof-line, many brought down.

MM9 Structures
Many Buildings Type I destroyed.Buildings Type II heavily damaged, some collapse.Buildings Type III damaged, some with partial collapse.
Structures Type IV damaged in some cases, some with flexible frames seriously damaged.
Houses not secured to foundations shifted off.Brick veneers fall and expose frames.

MMJO Structures
Most Buildings Type I destroyed.Many Buildings Type II destroyed.Buildings Type III heavily damaged, some collapse.Structures Type IV damaged, some with partial collapse.Some well-built timber buildings moderately damaged (excluding damage from falling chimneys).

Construction Types:
Buildings

APPENDIX 2:
Basic statistics of damage ratio for houses and household contents in the 1987 Edgecumbe earthquake.
In the study of damage to domestic property in the Edgecumbe earthquake [6,7), Dr was estimated, but Dr111 has not been estimated till now.The full list of basic statistics including both definitions of mean damage ratio are therefore tabulated below.
& Nuclear Sciences, Lower Hult, New Zealand.-Fellow Member BULLETIN OF THE NEW ZEALAND SOCIETY FOR EARTHQUAKE ENGINEERING, Vol.34, No. 3, September 2001

Figure J(
Figure J(a): The most common type of pre-1968 West Coast house, one storey with a corrugated iron roof weatherboard wall cladding and piled foundations.

Figure
Figure J(b ): A pre-1968 one storey West Coast house with tiled roof, stucco veneer walls and concrete strip foundations.

Figure 4 (
Figure 4(a): A pre-1968 two storey West Coast house with a tiled roof, stucco veneer walls and concrete strip.foundation.

Figure 4 (
Figure 4(b ): A typical pre-1968 two storey hotel of house style co11structio11, with a corrugated iron roof, weatherboard wall cladding and piled fou11datio11.

Figure 5 (
b) shows plots of D,.,,, for six intensity zones.The values of D,.111 (including all damage) for the Inangahua earthquake range up to 0.35 at MM I 0.The remaining key parameter in evaluating damage levels is the percentage of houses damaged, which is plotted against intensity in Figure5(c) with values ranging up to 100% at MM l 0. When chimney damage is included, there is a plateau of 81 % between MM8 and MM9.These percentages are calculated as n/N from Tables 8, where n is the number of damaged houses including all claims with non-zero costs, where n = 617,832, 2961, 2146, 372 and 55 for MM5-MM10 respectively.When claims below the insurance deductible are excluded the counts of 11 become 575,707, 2930, 2133, 371 and 55.Special features of Figure5are discussed below in Section 5.4.

Figure 5 :
Figure 5: Three measures of vulnerability plotted as Junctions of MM intensity for all houses in the Inangahua earthquake:(a) Cumulative probability distributions of damage ratio, (b) D,,,, and its 95% confidence limits, and (c) Percentage of houses damaged with its 95% confidence limits.
Figure I O(b), D,.,,, ranges gradually from 2 x l 0• 0 at MM5 to 0.026 at MM9 before suddenly rising to 0.29 at MM I 0. This acute non-linearity of D,.111 with respect to intensity is akin to that of brittle structures.It appears that at MM IO a much greater proportion of household contents is overturned, or is damaged by parts of the buildings, than at MM9.
Figure 7: damage and the values of D1111 and D,. at MM IO are very similar at 0.285 and 0.271 respectively.In addition these values arc supported by a mean damage ratio of 0.21 for contents estimated from a sample of 57 European style houses near the centre of the 1995 Kobe earthquake.This information comes from proprietary insurance data (B.Shephard and D. Spurr, pers.comm.).Finally the vulnerability of household contents is considered in terms of the percentage of contents parcels damaged.as plotted in Figure I 0( e ).It is seen that the percentage damaged for the lnangahua earthquake rises from very small Second, considering contents, for D,m it is seen in Figure 11 (b) that the lnangahua and Edgecumbe values are very similar at MM6 -MMS.The Edgecumbe MM9 value is considerably greater than that of Inangahua (D,.., = 0.092 vs. 0.026), but this large difference seems to be largely explained by the strong non-linearity of the D,.'" vs. MMI function by plotting the Edgecumbe and lnangahua D,.111 values at MM9.4 and MM9.l respectively.In contrast the percentages of contents parcels damaged (Figure 11 (d)) are consistently lower for Edgecumbe at intensities ~ MM7, the Inangahua values being nearly twice those for Edgecumbe at MM7 and MMS but only I. I times the Edgecumbe value at MM9.

Figure I 0 :
Figure I 0: Three measures of vulnerability plotted as functions of MM intensity for household contents in the Inangahuaearthquake: (a) Cumulative probability distributions of damage ratio, (b) D,111 and its 95% confidence limits, and ( c) Percentage of co11te11ts parcels damaged with its 95% confidence limits.

Figure 11 :
Figure 11: Vulnerability measures for domestic property from the lnangahua earthquake compared with those from other earthquakes: (a) D,,,,for houses, (b) DrnJor co11te11ts, (c) Percentage of houses damaged, and (d) Percentage of contents parcels damaged.

9 .
In the MM IO zone the majority of houses were founded on unbraced piles and many fell off them suffering heavy damage, with D,.,,, = 0.35.This accounts for the marked nonlinearity of D,.,,, vs. intensity between MM9 and MMI0.I 0. In the MM 10 zone the three houses on concrete foundations suffered far less damage, with D,m = 0.035, while the three houses on partial concrete foundation had D,,,, = 0.18.

Table 4 : Statistics of insured values of private sector houses.
[ 16]sityNumber of Houses and also by the loss adjuster, Bird, who stated[ 16]that many buildings [in the West Coast area] were sub-standard and poorly maintained, and that property values were generally depressed with the consequences that in many cases the amounts of insurance were considerably less than the reinstatement costs.
NR = Not reliable, based on one house only•Not found in the present study.

Table 6 : Summary of material damage costs ($NZ000) for private sector domestic property in the Inangahua earthquake.
IO].If derived from large, homogeneous populations, Dr and D,.,,, tend to be similar in value, while for more inhomogeneous populations (with large ranges of replacement values and vulnerabilities) D,. and D,,,, may differ widely.The values of Dr and D,-m for the various classes of domestic property considered in this study are presented in Tables

Table 7 : Basic statistics of the distribution of damage ratios for household contents in the Inangahua earthquake
It has been found in previous studies that the damage ratio is sometimes related to property value [I 1].If it is, D,. and D,,,, tend to differ.For example, if higher valued properties tend to have higher damage ratios, then D,. tends to exceed D,.m.In the present study, as in the Napier earthquake study, the tendency is for Dr for houses to be less than D,.111, for most subsets.This indicates that lower valued houses tend to have higher damage ratios.Such a trend could arise from a number of causes, including under-estimation of the replacement values of low-valued properties, or by the costs associated with some of the main types of damage being independent of replacement value.Both elements may be present in this study.First, under-valuation of low-valued properties is likely to arise because replacement values are mostly derived from insured values.Secondly, the damage to brittle chimneys was an important contributor to repair costs for housing, and the cost of repairing chimney damage is not necessarily related to the replacement value of the whole building.

Table 8 : Basic statistics of the distribution of damage ratios for various classes of houses in the Inangahua earthquake.
T_11,e I ( Masonry D in the NZ I 966 MM scale)Buildings with low standard of workmanship, poor mortar, or constructed of weak materials like mud brick or rammed earth.Soft storey structures (e.g.shops) made of masonry, weak reinforced concrete, or composite materials (e.g.some walls timber, some brick) not well tied together.Buildings Tvpe II (Masonry C in the NZ 1966 MM scale)Buildings of ordinary workmanship, with mortar of average quality.No extreme weakness, such as inadequate bonding of the comers, but neither designed nor reinforced to resist lateral forces.Buildings Tvpe Ill (Masonry Bin the NZ 1966 MM scale)Reinforced masonry or concrete buildings of good workmanship and with sound mortar, but not formally designed to resist earthquake forces.