Earthquake Vulnerability of the Built Environment
6.1 Introduction
To manage and minimize risk in future earthquakes, by design, planning and retrofitting, we need to understand and evaluate the earthquake vulnerability of the built and natural environments. This is best done by developing models by studying damage in past earthquakes, and quantifying the data on damage to a much greater degree than is possible in earthquake reconnaissance reports, or is given in the excellent book by Steinbrugge (1982).
Earthquake damage to the built environment is caused by a number of factors beyond the principal cause, ground shaking - for example, landslides (as listed in Section 3.1). In this chapter, our discussion of vulnerability is restricted mainly to that relating directly to ground shaking. All other effects, such as subsidence, landslides, liquefaction and earthquake induced fires (Section 7.2.2), are supplementary phenomena.
The vulnerability of items of the built environment to damage in earthquakes varies enormously. It depends on the robustness of the item, which may be inherent or the result of its earthquake resistant design. Thus, vulnerability may be defined as the degree of damage of a given item of the built environment to a given strength of shaking. It is helpful to describe the degree of damage both qualitatively and quantitatively, as discussed below.
6.2 Qualitative Measures of Vulnerability
Vulnerability of different classes of construction has long been described in words in the subjective intensity scales. This is illustrated in Table 6.1 where the degree of damage to six classes of construction is described for six Modified Mercalli intensities (MM6-MM11). An aspect of this table that is worth noting is the speculative nature of intensity MM11.The author knows of no verified instances of intensities higher than MM10 worldwide. It appears that the upper bound on intensity is MM10, as shown
Earthquake Resistant Design and Risk Reduction D. Dowrick © 2009, John Wiley & Sons, Ltd
|
Construction classes | ||||||
|
Intensity |
Pre-code |
Post-code 'brittle' era |
Capacity design era |
Special low damage | ||
|
I2 |
II |
III |
IV |
V |
VI | |
|
MM11 |
All destroyed |
Many destroyed |
Heavily damaged, some collapse |
Damaged, some with partial collapse |
Minor^damage. a few moderate damages | |
|
MM 10 |
All destroyed |
Most destroyed |
Heavily damaged, some collapse |
Damaged, some with partial collapse |
Moderately damaged, a few with partial collapse4 |
A few instances of damage |
|
MM9 |
Many destroyed |
Heavily damaged, some collapse |
Damaged, some with partial collapse |
Damaged in some cases, some flexible frames seriously |
Damaged in some cases, some flexible frames moderately | |
|
MM8 |
Heavily damaged, some collapse |
Damaged, some with partial collapse |
Damaged in some cases |
A few instances of damage | ||
|
MM7 |
Cracked, some minor masonry falls |
A few damaged | ||||
|
MM6 |
Slight damage may occur | |||||
:MM12 deleted and changes to MM10 and MM11 shown in italics.
Construction classes paraphrased below are given in full in Appendix A. Type I. poor quality unreinforced masonry (URM), or pre-code reinforced concrete (RC) with a weak storey. Type II. average-quality URM. Type IE. pre-code reinforced masonry or concrete (subdivided here as follows): 111(1). brick walled with RC ring beams: 111(2). RC beams, columns, floors, plus brick infill. 111(3). RC walled (no weak storeys). Type IV. post-code (c. 1935-1975).
3This is speculative, on the optimistic side.
4A11ows for structures of this era not having capacity design or being 'below average'.
by Dowrick and Rhoades (2005a) from data from near-surface-rupturing New Zealand earthquakes, in their plot of intensity at the centre (I0) and the innermost isoseismal (In) against magnitude (Figure 6.1). Also, more recently it has been found using the two-dimensional source model of Dowrick and Rhoades (in preparation) that MM intensities do not exceed MM10 in the most powerful surface-rupturing earthquakes (e.g. see Figure 4.39). The possibility remains that while the while the maximum intensity for an isoseismal of substantial area is MM10, that topographical amplification within such a zone could result in a local area of MM11.
Another way of making qualitative measures of vulnerability is in terms of damage states. It is useful to compare the damage states of non-domestic buildings in the Napier/Hastings area resulting from the intensity of MM10 induced by the pre-code 1931 Hawke's Bay earthquake in New Zealand, as described by Dowrick (1998). For this purpose the buildings were divided into five subsets: (a) types I and II, (b) type III(1), (c) type III(2), (d) type III(3), and (e) timber (as defined in the footnote to Table 6.1). The
Near surface rupturing New Zealand earthquakes 0 < ht < 8 km
Figure 6.1 Plot of data for intensity at centre (I0) and innermost isoseismal (In) for near-surface-rupturing earthquakes, with upper bound line for I0 versus MW (modified from Dowrick and Rhoades, 2005a)
degree of damage to each building has been assessed according to a scale of four damage states:
(2) damaged - cracked or moderately cracked, parapets and gables fall (no volume loss);
(3) partial collapse - volume loss less than 50%;
(4) collapse - volume loss 50% or greater.
The data from this assessment are plotted in histogram form in Figure 6.2. These plots show very clearly that the buildings of subset (a) are much more severely damaged than any of the other four subsets. The percentages of buildings suffering some degree of collapse (damage states 3 and 4) are 71%, 23%, 0%, 0% and 1% for building subsets (a) to (e), respectively.
As damage states 3 and 4 cause most casualties, these figures confirm the appropriateness of past and present priorities to reduce the risk of collapse of URM buildings. While this is well understood by engineers, as is the safety of timber construction (e), what has not been widely recognized is the almost collapse-free performance at MM10 of pre-code low-rise concrete buildings with walls (van de Vorstenbosch etal., 2002). This is true not only for buildings with concrete walls (d) but also, remarkably, for concrete beam and column buildings with brick infill in this data set. However, it should be borne in mind that brick infill panels are not always as reliable as they were in Hawke's Bay.
6.3 Quantitative Measures of Vulnerability
6.3.1 Introduction
For most purposes in risk assessment, it is necessary to have quantitative measures of vulnerability (also named fragility in some contexts) of the classes of property under consideration. This is conveniently done in terms of a damage ratio Dr, defined as
Cost of damage to an item
Value of that item where value is best expressed in terms of replacement value, and Dr is a function of the strength of shaking and the physical nature of the item considered. It follows that Dr would most helpfully be modelled in an attenuation function in terms of magnitude, distance and scatter. With the small number of good Dr data sets yet available, we are mostly limited to describing Dr as a function of intensity, but are able to examine the distribution (scatter) of Dr well in those terms. The population of property items for any given distribution of Dr is drawn from the area between two adjacent isoseismals, so that the MM7 intensity zone (for example) is defined as the area between the MM7 and the MM8 isoseismals (Figure 6.3).
The New Zealand studies of damage ratios referred to below, all lead by the author of this book, are of four earthquakes:
Unreinforced masonry and SSRC
Damaged
Partial collapse
Collapse
Number of storeys and damage state (a) Buildings types I & II
Conc beams & columns & brick infill
Damaged
Partial collapse
Collapse
Number of storeys and damage state (c) Buildings type III (2)
Brick walls & RC ring beams
Damaged
Partial collapse
Collapse
Number of storeys and damage state (b) Buildings type III (1)
Concrete walled
Damaged
Partial collapse
Collapse
Number of storeys and damage state (d) Buildings types III (3)
Damaged Partial collapse Collapse
Number of storeys and damage state (e) Timber (pre-code)
Figure 6.2 Damage distributions for non-domestic buildings in intensity MM10 in Napier and Hastings in the Mw = 7.8 Hawke's Bay, New Zealand earthquake of 1931. N1, N2, N3 are the numbers of buildings of 1, 2 and 3 storeys respectively in each subset. Building types are defined in the footnotes to Table 6.1 (from Dowrick, 1998)
D 60
d 60
- Figure 6.3 Map showing inner isoseismals, state highways and key place names for the 1968 Inangahua, New Zealand, earthquake. The fault rupture model dips at 45° with the top on the east side (from Dowrick et al., 2001)
In all of these studies, the robustness of the results was maximized by three procedures:
• accounting for all property items, damaged and undamaged, in each area considered;
• use of the actual repair costs in all cases (including the cost of the insurance deductible);
• use of the replacement value in all cases except household contents.
The use of these three procedures make these studies the only ones in the world (to the knowledge of the author) to have been so thoroughly conducted up to the time of writing (2009).
A typical distribution of damage ratios is that for non-domestic buildings shown in histogram form in Figure 6.4, from a study of damage ratios in the Edgecumbe earthquake by Dowrick and Rhoades (1993). This distribution fits the truncated lognormal form well,
er 200
er 200
Figure 6.4 Histogram of damage ratios for non-domestic commercial and industrial buildings with non-zero damage in the MM9 zone of the 1987 Edgecumbe, New Zealand, earthquake (from Dowrick and Rhoades, 1993)
Figure 6.4 Histogram of damage ratios for non-domestic commercial and industrial buildings with non-zero damage in the MM9 zone of the 1987 Edgecumbe, New Zealand, earthquake (from Dowrick and Rhoades, 1993)
as do all the other distributions studied by those authors (e.g. Figure 6.5(a)). The lognormal distribution has the density function
Here the parameters \ and o are estimated by the sample mean and standard deviation of the natural log of the damage ratio, example values being given in Table 6.2. From this table it is seen that the scatter within distributions varies considerably, and even for larger populations (n > 100) the normal variability parameter o lies within a wide range 0.7-1.77.
The mean damage ratio for all buildings in a given MM intensity zone is a useful parameter for various purposes, e.g. for comparing the earthquake resistance of different classes of property. Considering all N items (damaged and undamaged) in an MM intensity zone, we give here two principal ways of defining the mean Dr: first,
where n is the number of damaged items; secondly,
In general, Drm with its associated confidence limits is a more reliable and useful tool than I), . If derived from large, homogeneous populations, I), and Drm tend to be similar in value, while for more inhomogeneous populations (with large ranges of replacement values and vulnerabilities) I), and Drm may differ widely. The values of I), and Drm for the various classes of property are presented in Table 6.2.
It has been found that the damage ratio is sometimes related to property value (Rhoades and Dowrick, 1999). If it is, I), and Drm tend to differ quite markedly. For example, if higher-valued properties tend to have higher damage ratios, then Dr tends to exceed Drm. In some studies (Dowrick el al„ 1995, 2001) the tendency is for I), for houses to be less than Drm, 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 underestimation of the replacement values of low-valued properties, and/or by the costs associated with some of the main types of damage being independent of replacement value.
In general, Drm is a much more robust statistic than Dr, and is therefore preferred for modelling future events. This is illustrated in Figure 6.6, where values of Drm and I), are plotted for subsets of the data, together with their associated uncertainty intervals. The uncertainty intervals were determined by resampling many times from the empirical distribution of damage ratios and property values (Rhoades and Dowrick, 1999). They represent the variability that can be expected if similar populations of property are subjected to the same level of shaking in future earthquakes. It is seen that the uncertainty intervals for Drm are much narrower than for Dr, and that the location of I), within its uncertainty interval is erratic, being highly asymmetrically placed in the 1935-1964 data set. The relationship between Drm and I), is similarly erratic as seen by comparing the values presented for Drm and I), for a wide range of property items in Table 6.2. These effects arise because of the wide range of property values within a single data set. I), is sensitive to damage ratios for high-value property items.
Plots of cumulative probability of damage ratios in the Inangahua earthquake are shown for all houses by MM intensity in Figure 6.5(a). While very small amounts of damage occur at MM5, with a near-zero probability of damage occurring (Figure 6.5(c)), Figure 6.6 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 (Dowrick et al., 2008) - see Appendix A - and confirms that the outer isoseismals of Figure 6.3 have been appropriately located.
When considering mean damage ratios, parallel effects are observed to those discussed above in terms of damage ratio distributions. Figure 6.5(b) shows plots of Drm for six intensity zones. The values of Drm (including all damage) for the Inangahua earthquake range up to 0.34 at MM10.
Next, consider mean damage ratio as affected by brittle chimney damage. The influence of chimneys on Drm is very apparent in Figure 6.5(b), where Drm is seen to range from 2.0 x 10-5 (excluding chimneys) at MM5 to 0.048 (including chimneys) at MM8, and then flattening off to rise only slightly to 0.050 at MM9. This plateau is 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 Drm including chimneys with that excluding chimneys, which in round figures is 1.8, 6, 9, 9, 5 and 1.2 for MM5 to MM10, respectively. The figure of 1.2 for the MM10 zone is close to that of 1.3 obtained
Table 6.2 Basic statistics of the distribution of damage ratio for some subclasses of property in the intensity MM9 zones of two New Zealand earthquakes
Property class
Houses
All 1- and 2-storeys1 one-storey, incl. chimney costs2 one-storey, excl. chimney costs2 Household contents Edgecumbe earthquake1 Inangahua earthquake2
One-storey non-domestic buildings3
Code era built: 1935-1964
1965-1969/79 1969/79-1987
Equipment4
Vulnerability class:
Stock4
Vulnerability class:
Robust
Medium
Fragile
Robust
Medium
Fragile
2040 368 268
2210 280
72 60 57
80 116 11
23 35 62
2800 455 455
2800 321
154 118
197 247 16
82 53 77
0.091 0.050 0.0096
0.092 0.020
0.063 0.054 0.033
0.070 0.036 0.0071
0.079 0.022
0.034 0.085 0.063
Notes:
^owrick (1991). 2Dowrick et al. (2001). 3Dowrick and Rhoades (1997b). 4Dowrick and Rhoades (1995).
All houses including chimney damage /
Inangahua earthquake // ^
MM9 J
MM7-
Damage ratio (a)
Inangahua earthquake houses
All houses o Including chimney damage A Excluding chimney damage Houses with concrete foundations + Excluding chimney damage
MM isoseismal (b)
Inangahua earthquake all houses
Including chimney damage A Excluding chimney damage
MM isoseismal (c)
Figure 6.5 Three measures of vulnerability plotted as functions of MM intensity for all houses in the Inangahua earthquake: (a) cumulative probability distributions of damage ratio; (b) Drm and its 95% confidence limits; (c) percentage of houses damaged with 95% confidence limits (from Dowrick et al., 2001)
1935-64 1965-69/79 1970/80-87 (154) (118) (133)
Construction era
Figure 6.6 Drm. Dr and the 95th percentile of Dr for non-domestic buildings of different code eras in the MM9 zone of the Edgecumbe earthquake. The uncertainty limits are the 2.5% and 97.5% quantiles of the distributions of Drm and Dr determined by resampling (from Dowrick and Rhoades, 1997a)
for the MM10 zone in Napier in 1931 (Dowrick et al., 1995) where all houses also had brittle chimneys, and were of similar construction (weatherboarded and piled) to those of the Inangahua area.
In addition to distributions of damage ratios and mean damage ratios, a third measure of vulnerability is the percentage of property items that are damaged. This is derived from the fraction n/N, examples of which are given in Table 6.2, and as plotted in Figure 6.5(c). From the latter, it is seen that at most intensities a much greater percentage of houses with brittle chimneys are damaged than those without chimneys.
6.3.2 Vulnerability of different classes of buildings
In Figure 6.6, it can be seen that non-domestic buildings built in New Zealand's first two earthquake code eras had much the same vulnerability, but buildings built in the most recent era for which data are available (1970-1987) were found to be statistically significantly better than pre-1970 buildings, and the maximum damage levels as reflected in the 95th percentile had decreased. This improvement is attributed to the influence of greater ductility requirements of the codes of that era.
The difference in vulnerability of different construction eras is more dramatically shown in Figure 6.7, where the performance of pure brick buildings at intensity MM8 is compared with that of three other classes of building:
• non-domestic buildings of reinforced masonry from the code era 1935-1979;
• houses with brittle chimneys;
• houses excluding chimney damage.
Considering only one-storey buildings, Dowrick and Rhoades (2002) found that the mean damage ratio for the pure brick Wairarapa buildings was (1) approximately three times that for timber framed houses with brittle chimneys in the Inangahua earthquake; (2) seven times that for 1935-1979 concrete masonry buildings in the Edgecumbe earthquake; and (3) 28 times that for timber framed houses excluding chimney damage in the Inangahua earthquake.
As well as considering the code era and materials of construction, the vulnerability of buildings needs to be measured according to the number of storeys. For example, in the study of pure brick buildings in the Wairarapa earthquake (Dowrick and Rhoades, 2002), the mean damage ratio for two-storey pure brick buildings, at 0.22, was 57% greater than that for one-storey buildings. The difference between the Drm values for these two subsets fell just short of statistical significance (p = 0.057), but is consistent with the differences between one- and two-storey buildings found in studies of the Edgecumbe earthquake at intensity MM7 and MM9 (Figure 6.8) and the Inangahua earthquake at MM7 and MM8.
Why are two-storey buildings more vulnerable than those of one storey? This effect is presumed to arise from the fact that single-storey buildings generally have relatively more of their mass located above base level compared to buildings of two or more storeys. So what about buildings of more than two storeys? Unfortunately, the author has had only rather small subsets of data on buildings of three or more storeys (and none more than six storeys), but the data which do exist suggest that such buildings are about as vulnerable as those of two storeys. This may be largely the result of the fact that taller buildings have relatively more engineering design input than do two-storey buildings.
Another very basic feature of buildings that may influence their vulnerability is their size, and this factor has been examined in a number of cases (Dowrick and Rhoades, 1997b, 2002; Dowrick et al., 1995). In the study of the Wairarapa earthquake, the mean damage ratio for both one- and two-storey brick buildings was found to reduce substantially with increasing floor area (Figure 6.9). Such a trend was not seen elsewhere, except in houses with chimney damage, and the reason for it is not evident. However, this trend explains why I), (at 0.12) is so much smaller than Drm (at 0.17) for the brick buildings (Dowrick and Rhoades, 2002).
Further information on the vulnerability of different classes of buildings is given later in relation to Figure 10.54 (Section 10.5.1).
6.3.3 Vulnerability of contents of buildings
The contents of buildings considered here comprise a wide range of property items: contents of houses, and plant, equipment and stock of a non-domestic nature.
One storey
Wairarapa pure brick Edgecumbe non-domestic masonry Inangahua houses, with chimneys Inangahua houses, without chimneys
MM isoseismal (a)
100-
Figure 6.7 Two vulnerability measures for pure brick Wairarapa, New Zealand, non-domestic buildings compared with those for three other building classes from the Inangahua and Edgecumbe earthquakes: (a) Drm with its 95% confidence limits; (b) percentage of buildings damaged with 95% confidence limits. The houses are timber framed (from Dowrick and Rhoades, 2002)
One storey u
Continue reading here: Effects of microzoning on damage to houses as a function of MM intensity
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