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Empirical Damage Relationships and Benefit-1 Cost Analysis for Seismic Retrofit of URM 2 Buildings 3
Brandon Paxton,a) Kenneth J. Elwood,b) M.EERI, and Jason M. Ingham,c) 4 M.EERI 5
Benefit-cost analyses for seismic retrofit of unreinforced masonry (URM) 6
buildings in downtown Victoria, British Columbia, Canada were undertaken, 7
considering the seismic hazard, building value, occupant/pedestrian exposure, a 8
variety of strengthening measures, and local construction costs. The analyses are 9
underpinned by building motion-damage relationships developed based on 10
observed damage in past earthquakes in California and New Zealand. The 11
considered upgrading measures ranged from parapet bracing to comprehensive 12
seismic upgrades consistent with local practices. Parapet bracing and other partial 13
retrofits were shown to have favorable benefit-cost ratios and thus be strong 14
candidate measures for risk mitigation programs. Full upgrades were shown to 15
have less favorable benefit-cost ratios. While applied to Victoria, the generality of 16
the methodology and the use of observed damage date from California and New 17
Zealand make the findings of this study particularly relevant for similar locations 18
throughout the Pacific Northwest and abroad. 19
INTRODUCTION 20
Victoria, Canada is located in southwestern British Columbia on Vancouver Island and its 21
seismic hazard is driven by the Cascadia Subduction Zone, with the potential for crustal, 22
subcrustal, and subduction earthquakes. As a result, Victoria’s seismic hazard is one of the 23
highest in Canada (NRC, 2010). For comparison, the seismic hazard of Victoria is similar to 24
nearby Seattle, Washington, and slightly lower than Wellington, New Zealand, as illustrated 25
in Figure 1. Despite this hazard, since the middle of the 19th century when URM building 26
construction began in Victoria, the city has not yet experienced shaking beyond MMI VI 27
intensity (Lamontagne et al., 2008). “Active” programs to identify or mitigate URM (or 28
a) Read Jones Christoffersen Ltd., 645 Tyee Road, #220, Victoria, BC, Canada V9A 6X5
b University of Auckland, Private Bag 92019, Auckland, New Zealand
c) University of Auckland, Private Bag 92019, Auckland, New Zealand
other) seismic risks in Victoria are currently lacking in comparison to other regions facing 29
similar seismic hazards (Paxton et al., 2013). Typically seismic strengthening is only required 30
when buildings undergo a change of use or substantial alteration. Furthermore, there are no 31
ordinances in place addressing falling hazards posed by parapets or other similar 32
components, as have been implemented as a minimum in many cities facing similar risks, 33
such as Los Angeles and San Francisco (Paxton et al., 2015). Tax relief programs for heritage 34
buildings undergoing retrofits as part of a change in use have resulted in comprehensive 35
seismic retrofits for a small portion of Victoria’s URM building stock, but the vast majority 36
remains entirely unretrofitted. This lack of action was the impetus for the study summarized 37
herein on benefit-cost analysis of URM seismic retrofitting using observed damage data 38
collected in past earthquakes. 39
While results focus on URM bearing wall buildings in Victoria, BC, the methodology 40
could be adapted and applied to other locations and buildings. The term “URM building” as 41
used herein refers to clay brick URM bearing wall buildings with flexible timber diaphragms 42
(similar to the model building type “URM” as described in FEMA, 2006) and that all dollar 43
figures herein represent third quarter 2014 Canadian dollars. The Canadian and American 44
dollars were approximately at parity at the time of the study, which eliminated the need for 45
conversions in many instances. 46
In subsequent discussions on retrofit types the following definitions apply: 47
"Braced-parapet": a building with tension anchorage provided at all roof-to-wall 48
interfaces and additional out-of-plane bracing provided as required for tall 49
parapets (height-to-thickness ratio greater than 1.5:1). 50
"Partially-retrofitted": in addition to the "braced-parapet" definition, tension 51
anchorage is provided at all floor-to-wall interfaces and excessively slender walls 52
(as defined, for example, in the International Existing Building Code, ICC 2012) 53
are provided with supplementary out-of-plane bracing. 54
"Fully-retrofitted": in addition to the "partially-retrofitted" definition, includes 55
shear anchorage to all diaphragms, supplementary vertical supports under major 56
gravity members, in-plane wall strengthening, and diaphragm strengthening as 57
required, for example by the International Existing Building Code (ICC 2012). 58
While it was straightforward to ensure that these definitions were reasonably reflected in 59
the subsequent cost data, such detailed information was not always available in the observed 60
damage data used to develop the relationships between shaking intensity and expected 61
building damage. For example, a building noted by field personnel as having braced parapets 62
may not have been provided with tension anchorage throughout the roof perimeter. Likewise, 63
the standard to which the upgrading work was designed and constructed was generally not 64
ascertained. Typically such lack of information will result in a conservative assessment of the 65
retrofit category (e.g. assumption of no retrofit if not detected by external inspection when 66
internal access is restricted) and the performance of each retrofit category may be 67
understated. Such are the limitations of using observed data to quantify building 68
performance. 69
Before proceeding with a discussion of the overall benefit-cost analyses, a detailed 70
description of the derivation of the building structural vulnerabilities using data from both 71
California and New Zealand is provided. Further details of the study can be found in Paxton 72
(2014). 73
QUANTIFYING BUILDING VULNERABILITY THROUGH OBSERVED DAMAGE 74
There are three well-accepted methods to quantify building vulnerability functions, 75
commonly referred to as “empirical,” “analytical,” and “expert opinion” methods (Porter et 76
al., 2012). An empirical approach was used in this study, whereby observed building 77
structural damage is expressed as a function of the estimated ground motion intensity at the 78
site. The observed data is used to generate fragility functions, which are used to estimate 79
losses for subject URM buildings. URM damage data from the 1989 Loma Prieta, 1994 80
Northridge, and 2010/2011 Canterbury earthquakes were employed. Data from the 1987 81
Whittier Narrows earthquake were also investigated but ultimately were excluded due the 82
very limited ground motion intensity at the sites. 83
Damage data were generally in the form of ATC-13 (ATC, 1985) damage states as 84
estimated by post-earthquake reconnaissance researchers and building safety evaluators, and 85
were collected by others (Rutherford and Chekene, 1990; Rutherford and Chekene, 1997; 86
Lizundia, 1993; and Moon et al., 2012, 2015). Although the ATC-13 damage states were 87
originally developed to include both structural and nonstructural building components, it was 88
decided that the data was more representative of the damage to the structural components 89
because assessments were generally only performed from the exterior (due to safety reasons) 90
and because building safety evaluators would instinctively focus on structural damage. 91
In order to develop vulnerability functions it was necessary to select a common ground 92
motion intensity measure (IM) and method to estimate the IM at a site. ATC-13 employs 93
modified Mercalli intensity (MMI) due to a paucity of more objective data at the time of its 94
development. Lizundia (1993), Rutherford and Chekene (1997), and King et al. (2002) 95
investigated a variety of IMs including MMI, instrumental intensity (IMM), peak ground 96
acceleration/velocity (PGA/PGV), and spectral response values. Lizundia (1993) and King et 97
al. (2002) concluded that spectral acceleration correlated reasonably well with observed 98
damage, although parameters such as Arias Intensity (IA), MMI, and PGV correlated better 99
on average. Cabanas et al. (1997) investigated the use of Arias intensity (IA) and cumulative 100
absolute velocity (CAV) and concluded that both were good indicators of structural damage, 101
particularly because they directly capture duration effects. However, annual exceedance rates 102
for CAV and IA are not commonly available. Because the ultimate goal of the reported study 103
was to complete loss estimates and benefit-cost analyses, the choice of IM was based on a 104
compromise between accuracy and ease of use. Ultimately, 5% damped spectral acceleration 105
at a period of 1 second, Sa(1), was selected. A period of one second was selected for a variety 106
of reasons: Turner et al. (2010) showed that the spatial variability for Sa(1) was much less 107
than that for Sa(0.2); Penner and Elwood (2016) showed that a period of one second was 108
preferable in the assessment of out-of-plane URM walls; and Lizundia (1993) showed that 109
damage to URM buildings in the Loma Prieta earthquake was much greater for buildings on 110
soft soils, suggesting correlation of observed damage with long period spectral parameters. It 111
was also necessary to select a method to estimate the IM at each building site based on 112
nearby recorded values. A weighted interpolation method using ground motion prediction 113
equations (similar to that described by Lizundia, 1993) was used in this study. Note that the 114
use of a more advanced method employing conditional probability theory (Bradley and 115
Hughes, 2013) was considered, but that a preliminary comparison indicated that there was 116
little change in the resulting motion-damage relationships, as the binning process masked the 117
differences in intensity measurements (Paxton, 2014). 118
With each building assigned an ATC-13 damage state and a ground motion intensity, 119
damage probability matrices (DPMs) were constructed for the Canterbury data and the 120
braced-parapet data from Loma Prieta following the methodology described by King et al. 121
(2005). The remainder of the DPMs were obtained by converting published DPMs (Lizundia, 122
1993; Rutherford & Chekene, 1997) from various IMs to Sa(1) as discussed in Paxton (2014). 123
From these DPMs, the resulting mean damage factor (MDFi) as defined in ATC-13 and the 124
standard deviation of the MDF (SEi) were calculated for each intensity bin and a beta 125
cumulative probability distribution was fit to the observed Sa(1) versus MDF data using a 126
weighted-least-squares criterion. The weighting factor (WFi) for each data point was defined 127
as WFi=MDFi/SEi. Example Sa(1) versus MDF relationships as derived from the 2010/2011 128
Canterbury earthquakes database are shown in Figure 2. Relationships for unretrofitted 129
buildings, buildings with braced parapets, and fully-retrofitted buildings are included. Similar 130
relationships were derived for the 1989 Loma Prieta and 1994 Northridge earthquake data 131
(see Paxton, 2014), although the lower intensities of ground shaking in these events limit the 132
applicability of such relations. The results for the various databases were compared to one 133
another and to published sources (e.g. HAZUS). Results for unretrofitted and fully-retrofitted 134
buildings are shown in Figures 3 and 4, respectively (note: "NSCs" refers to nonstructural 135
components and their significance is discussed below). Note that the HAZUS curve 136
compared to retrofitted buildings (Figure 4) is for a low-rise reinforced masonry building 137
with wood or metal diaphragms (“RM1L” category). HAZUS does not provide fragilities for 138
retrofitted URM buildings and the HAZUS technical manual (FEMA, 2012) recommends this 139
structure category as a proxy. 140
The results of the above noted fitting method were generally quite intuitive in that 141
increased retrofitting scope corresponded to decreased damage as well as decreased variation 142
among the databases (see Figures 3 and 4). All of the relationships from published sources 143
reviewed (ATC, 1985; EERI, 1994; and FEMA, 2012) appeared to overestimate damage 144
relative to the observed data. Rutherford and Chekene (1997) came to a similar conclusion 145
about the EERI (1994) relationship based on an analysis of the 1994 Northridge database. It 146
should be noted that the curves (cumulative probability distributions) have been plotted to 147
values of intensity that extend beyond the range of the observed data and that King et al. 148
(2005) cautions against such extrapolations. The curves herein are shown to Sa(1)=2g 149
primarily for comparison with the published data. Fortunately, the results beyond Sa(1)=1.5g 150
have little impact on the benefit-cost analysis for Victoria’s seismic hazard, but should be 151
used with caution for other regions with higher seismic hazard. Another observation is that 152
the New Zealand data (from the 2010/2011 Canterbury earthquakes and denoted as “CHCH” 153
in the figures) indicates substantially more damage than do the remaining databases, all of 154
which are from earthquakes in California. This observation may be at least partly explained 155
by the following: 156
cavity wall construction was reportedly quite common in the Canterbury region 157
(Ingham and Griffith, 2011, Giaretton et al., 2016), whereas cavity wall 158
construction is reportedly rare in California (Lizundia, 1993, Rutherford and 159
Chekene, 1997); 160
two-wythe walls are reportedly common in the Canterbury region (Derakhshan, 161
2011) whereas walls are most often a minimum of three wythes in California 162
(Rutherford and Chekene, 1997); 163
the cumulative effects of the ground motions in the 2010/2011 Canterbury 164
earthquakes likely acted to increase damage (Moon et al., 2014); while the 165
cumulative effects of damage may impact the validity for certain applications, 166
severe aftershocks and triggered events are a possibility (especially for Victoria 167
which lies in a subduction zone) and thus to ignore these possible impacts would 168
also be questionable; 169
many cities in California have experienced damaging earthquakes in the past and 170
thus some of the more vulnerable buildings may have been demolished before the 171
events considered here; and 172
There is a lack of data for California buildings in the high-intensity range. 173
A comparison between the observed data and structural-only damage as specified in 174
HAZUS (FEMA 2012) is provided in Figure 5, whereas the HAZUS models in Figures 3 and 175
4 include non-structural components. The observed damage data is more consistent with the 176
structural-only damage relationships. 177
The results thus far have focused solely on the MDF (also commonly referred to as a 178
“damage ratio”). While developing the MDF vs. Sa(1) relationships based on the observed 179
data was straightforward, developing damage state fragilities presented a challenge: it was 180
desired that the fragilities be developed in terms of HAZUS damage states because this 181
procedure is now the most commonly used loss estimation methodology in North America, 182
but the observed data were in terms of ATC-13 damage states. Thus a conversion process 183
was required. Fragilities in terms of HAZUS damage states were thus developed heuristically 184
based on two criteria: 185
1. The derived fragilities should closely match the observed data in terms of their MDF 186
vs. Sa(1) relationships (i.e. the observed and predicted mean damage should match over the 187
range of practical interest); this criterion was deemed to be the most important, as the benefit-188
cost analysis was concerned only with average damage. 189
2. The damage state distributions should reasonably reflect the observed data (eg. if 40% 190
of buildings were observed to be undamaged at a given intensity, then the derived damage 191
state fragilities should indicate this). 192
Developing structural damage state fragilities in terms of HAZUS damage states was 193
advantageous because default HAZUS fragilities could be used for nonstructural components 194
and contents and combined to estimate overall losses. ATC-13 and HAZUS damage state 195
equivalencies were assumed as shown in Table 1 for the purposes of achieving criterion #2. 196
Mansouri et al. (2014) makes a slightly varied comparison, but it was decided that the 197
mapping presented here is more consistent in terms of corresponding loss values and CDFs. 198
The associated loss value for each damage state is also shown. The process was applied to 199
develop damage state fragilities for both the Canterbury data and the California (Loma Prieta 200
and Northridge) data for unretrofitted buildings, buildings with braced parapets, and “fully-201
retrofitted” buildings. Damage state fragilities were defined for “partially retrofitted” 202
buildings by taking a weighted average of the “braced-parapet” and “fully retrofitted” results 203
due to a lack of sufficient observed data, by applying a weighting of 67% on the braced-204
parapet results. The results for unretrofitted and fully retrofitted buildings for Canterbury and 205
California are shown in Figures 6 through 9. Fragility functions were in the form of 206
lognormal cumulative distributions and the parameters for each curve are given in Table 2. 207
Criterion #1 was successfully achieved, with the resulting difference between the model 208
("Model MDF") and observed ("Observed MDF") relationships typically being within 2%. It 209
is also noted in passing that the “Observed MDF” curves in Figure 6 through 9 are the same 210
as the “UNRET-CHCH” and “FULL RETROFIT-CHCH” curves from Figures 3 and 4 (i.e. 211
the solid black curves from Figures 3 and 4 have been copied to Figures 6 through 9, as 212
applicable, for comparison). Criterion #2 was generally achieved for the Canterbury data with 213
higher intensities and more severe damage states, while lower intensity motions from the 214
California events resulted in greater scatter in the observed performance and thus larger 215
discrepancies with the damage state distributions. It was concluded that the resulting 216
distributions represent an improvement of the previously available results, particularly for 217
fully-retrofitted URM buildings which were simply represented by a proxy category 218
(reinforced masonry, "RML1") per the HAZUS technical manual and for "partial retrofits" or 219
"braced-parapet" type upgrades for which no fragilities were available. 220
Table 1. Assumed ATC-13 and HAZUS Damage State Equivalencies 221
ATC-13 HAZUS
Damage State CDF* Damage State Loss Value
None 0% None 0%
Slight 0.5% Slight 2%
Light 5.5%
Moderate 10%
Moderate 20%
Heavy 45% Extensive 50%
Major 80%
Complete 100%
Destroyed 100%
*CDF (Central Damage Factor) is defined as the cost to repair damage as a
fraction of the building value and is effectively equivalent to "Loss Value" as
defined in HAZUS
222
Table 2. Fragility Function Parameters 223
Retrofit
Status
Damage
State
Canterbury California*
Median
Sa(1)
Mean
Sa(1)
Std. Dev.
ln(Sa(1))
Median
Sa(1)
Mean
Sa(1)
Std. Dev.
ln(Sa(1))
Un-
retrofitted
Slight 0.11 0.14 0.65 0.22 0.25 0.50
Moderate 0.32 0.40 0.65 0.60 0.80 0.75
Extensive 0.74 0.92 0.65 1.5 2.0 0.75
Complete 1.7 2.1 0.65 2.8 3.7 0.75
Parapets
Braced
Slight 0.14 0.18 0.67 0.31 0.35 0.50
Moderate 0.40 0.50 0.67 0.88 1.1 0.67
Extensive 1.0 1.25 0.67 1.6 2.0 0.67
Complete 2.3 2.9 0.67 3.0 3.7 0.67
Partially
Retrofitted
Slight 0.16 0.20 0.67 0.35 0.40 0.50
Moderate 0.48 0.60 0.67 0.96 1.2 0.67
Extensive 1.1 1.35 0.67 1.7 2.1 0.67
Complete 2.8 3.5 0.67 3.2 4.0 0.67
Fully
Retrofitted
Slight 0.18 0.25 0.80 0.35 0.40 0.50
Moderate 0.54 0.75 0.80 1.0 1.25 0.67
Extensive 1.6 2.2 0.80 2.0 2.5 0.67
Complete 3.7 5.1 0.80 4.4 5.5 0.67
*Refers to a combination of data from the 1989 Loma Prieta earthquake (for unretrofitted and
braced-parapet buildings) and the 1994 Northridge earthquake (for fully-retrofitted buildings)
BENEFIT-COST METHODOLOGY 224
Benefit-cost analyses for seismic retrofitting of a prototypical URM building having 225
commercial occupancy and located in downtown Victoria were completed in terms of annual 226
expected costs, where reduced expected losses represent the benefits. The losses considered 227
were: 228
Building owner losses: repair costs, lost rental income, and tenant relocation 229
expenses; 230
Public losses: occupant and pedestrian casualties (deaths and injuries). 231
The expected annual losses (EAL) for a prototypical URM building in Victoria were 232
calculated as shown in Equation 1 (see also Figures 1 and 10). 233
))1((*))1(|[(
)1(
iSPiSLVEAL a
Sa
a
, (1) 234
The example shown (see Figure 10) is for losses due to building damage (for an 235
“unretrofitted” building based on a weighted average of the Canterbury and California data 236
for Victoria as subsequently discussed), but the process is similar for other losses. Note that 237
the "loss value" (LV) reported here is the repair/replacement cost as a fraction of the building 238
replacement value, which is subsequently converted to a dollar value. 239
The process was performed for the four aforementioned strengthening statuses 240
(unretrofitted, parapets-braced, partially-retrofitted, and fully-retrofitted) and for four 241
different soils site classes (B, C, D, and E as defined in the National Building Code of 242
Canada [NRC, 2010]). The following subsections briefly describe several of the key 243
parameters including: building vulnerability, seismic hazard, building value, downtime, 244
casualty rates, and economic parameters. 245
BUILDING VULNERABILITY 246
Building vulnerability was represented through separate motion-damage relationships for 247
structural components, acceleration-sensitive nonstructural components (NSCs), drift-248
sensitive NSCs, and building contents, similar to the procedure contained in HAZUS 249
(FEMA, 2012). Structural damage was represented using damage state fragilities based on 250
the observed damage data, as discussed in the previous section. The vulnerability of 251
Victoria's buildings is expected to fall somewhere between those of California (i.e. Loma 252
Prieta and Northridge) and Canterbury, which is rationalized based on the fact that the 253
building stock is more similar to that of California in some regards (lack of cavity wall 254
construction; wall thickness; and retrofit standards) and is more similar to that of Canterbury 255
in other regards (lack of original floor anchors; lack of past seismic damage; and potential for 256
long-duration or multiple earthquakes). The lack of data in the high-intensity range for the 257
California results was also a key consideration. The fragilities for Victoria buildings were 258
defined using weighted averages as shown below: 259
Base case: 67% Canterbury, 33% California 260
Upper Bound: 100% Canterbury, 0% California 261
Lower Bound: 50% Canterbury, 50% California 262
Note that the fragilities used in this analysis were developed by first taking the weighted 263
average of the observed MDF vs. Sa(1) relationships and then generating the individual 264
structural damage state fragilities to match the resulting MDF vs. Sa(1) curve. Motion-265
damage relationships for nonstructural components and contents were based on default 266
HAZUS data (FEMA, 2012), converted to an IM of Sa(1), with modifications to account for 267
additional losses due to structural collapse following the methodology proposed by Farokhnia 268
(2013). Contents fragilities were equal to the acceleration-sensitive NSCs, except that the 269
resulting losses are reduced as it is assumed that some contents will be recovered (FEMA, 270
2012). 271
With the damage state fragilities for each component defined, the overall relationship for 272
building damage losses (similar to that shown in Figure 10) can be calculated as the weighted 273
average of the four components, based on their relative contributions to the overall building 274
replacement value. The value of the structural components, acceleration-sensitive NSCs, 275
drift-sensitive NSCs, and contents were assumed to be 22.1%, 32.3%, 20.6%, and 25.0% of 276
the building value, respectively, as specified by HAZUS for a commercial ("COM1") 277
occupancy building. The building replacement value was taken as $260/sq.ft. (≈$24/m2) as 278
recommended by Thibert (2008) for URM buildings in British Columbia. In passing it is 279
noted that the notion of a “replacement value” for a URM building is somewhat flawed in 280
that URM building construction is prohibited in many locations of significant seismicity, 281
including Victoria, and even if URM construction was permitted one could not truly recreate 282
a century-old building and its associated heritage value. Finally, an "economic critical loss 283
ratio" (ECLR) was employed. The ECLR is the (overall) damage ratio at which a building is 284
assumed to be uneconomical to repair and is instead replaced. Rutherford and Chekene 285
(1990) suggested using an ECLR of 40% for unretrofitted URM buildings and 50% for 286
retrofitted URM buildings. EERI (1989) suggested an ECLR of up to 65%. It is 287
acknowledged that demolition decisions are governed by many factors in addition to building 288
damage, and there is potential for widespread demolitions to more lightly damaged buildings 289
as was observed in the 2010/2011 Canterbury earthquakes (Marquis et al., 2015). An ECLR 290
of 50% was used for all cases herein. 291
DOWNTIME 292
From a building owner's perspective the relevant downtime is the time to assess and 293
repair the building to a state such that it could be re-occupied and resume generating rental 294
income (i.e. “loss of function” time as defined in HAZUS). This is a complex issue 295
dependent upon many factors (Comerio, 2006), but the methodology and default data for 296
calculating loss of function time from HAZUS (FEMA 2012) were used. Additionally, a 297
modification to account for increased downtime due to concentrated severe damage in a 298
community of many URM buildings (as was observed in the 2010/2011 Canterbury 299
earthquakes) and the possible implementation of a cordon was employed wherein the 300
building's downtime is a function of both its damage state and the fraction of all buildings 301
experiencing "Extensive" or "Complete" damage. The downtime relationships employed are 302
shown in Figure 11. This modification was found to have a minor impact on the resulting 303
benefit-cost analyses for URM buildings as the additional downtime occurs for low-304
probability ground motions and downtime itself was a relatively small component of the 305
overall expected losses. The impact of a possible cordon would be more significant for a 306
building stock including less vulnerable buildings. Downtime losses were monetized by 307
assuming a rental rate of $0.07/sq.ft/day ($0.0065/m2), which is typical for URM buildings in 308
desirable downtown Victoria locations. 309
CASUALTIES 310
The key parameters required to estimate casualties are the exposure (i.e. number of 311
pedestrians/occupants) and the casualty rates. The occupant and pedestrian densities used in 312
this study were 0.0036 persons/sq.ft. (0.00033 persons/m2) of floor area and 313
30 persons/1000 ft of sidewalk, which represent time-averaged values from Rutherford and 314
Chekene (1990). Several different densities are provided by Rutherford and Chekene (1990) 315
for various districts within San Francisco, California, and the aforementioned values were 316
judgmentally selected as being representative of present-day Victoria. 317
The occupant and pedestrian fatality rates used in this study are shown in Table 3. The 318
occupant fatality rates are those specified by HAZUS (FEMA, 2012) for URM buildings. The 319
pedestrian fatality rates from HAZUS were considered too low (a maximum of 0.6% percent 320
for buildings in the "complete" damage state) considering experience in Christchurch 321
(Canterbury Earthquakes Royal Commission, 2012). Pedestrian fatality rates shown were 322
adapted from Rutherford and Chekene (1990) by converting from ATC-13 to HAZUS 323
structural damage states based on a comparison of the ATC-13 central damage ratio to the 324
overall MDF of our model. "Hospitalized injuries" were also accounted for and were taken as 325
four times the number of deaths, similar to assumptions by Rutherford and Chekene (1990). 326
Johnson et al. (2014) reports 161 medically-treated injuries due to “masonry” in the February 327
2011 Christchurch earthquake, which is approximately four times the 39 deaths attributed to 328
unreinforced masonry (Canterbury Earthquakes Royal Commission, 2012). Casualties were 329
monetized using the "value of a statistical life" (VSL) as specified by United States 330
Department of Transportation (2013) guidance, which specifies a best estimate value of $9.1 331
million as well as upper and lower bound values of $12.9 million and $5.2 million, which are 332
considered in the sensitivity analyses. At the time of the study, (and the USDoT publication), 333
the Canadian and American dollars were approximately at parity, so no conversion was 334
applied. Note that the VSL and its method of determination have been controversial topics 335
for decades, with highly variable recommendations on the appropriate value (FEMA, 1992, 336
1994, Miller 2000, Viscusi, 2002). 337
Table 3. Fatality Rates 338
Structural Damage State Occupant Fatality Rate
(deaths/person)
Pedestrian Fatality Rate
(deaths/person)
None 0% 0%
Slight 0% 0.02%
Moderate 0.001% 0.30%
Extensive 0.002% 12%
Complete* (no collapse) 0.02% 15%
Complete* (collapse) 10% 15%
*HAZUS assumes that 15% of buildings in the "complete" damage state will collapse
339
ECONOMIC PARAMETERS 340
The key economic parameters for the benefit-cost analyses are the time horizon (the 341
future duration over which the annual expected benefits are calculated) and the discount rates 342
(which reduce the present value of future benefits/losses). FEMA 227 (FEMA, 1992) 343
recommends discount rates of 3-6% for use in benefit-cost analyses for seismic rehabilitation. 344
FEMA 255 (FEMA, 1994), which focuses on benefit-cost analysis for seismic rehabilitation 345
of federally-owned buildings in the U.S.A., recommends a discount rate of 4%. Additionally, 346
the United States Office of Management and Budget (OMB, 2003) notes that lower discount 347
rates of 1-3% are appropriate for intergenerational benefits. For the baseline case considered, 348
a discount rate of 5% was applied to owner benefits (i.e. damage and downtime) and a rate of 349
3% was applied to public benefits (i.e. reduced casualties). A time horizon of 50 years was 350
used for the analyses. Alternative values were considered in the sensitivity analysis 351
subsequently discussed. 352
RETROFIT COSTS 353
The only costs considered in the analyses were the construction cost of the seismic 354
upgrade work as well as the related design fees, permit fees, and taxes. Architectural costs 355
associated with a substantial remodelling were not considered. A variety of additional costs 356
could be incurred depending upon building authorities and owner decisions. Lizundia et al. 357
(1993) provide a list of possible costs. Benefits associated with a resulting increase in market 358
value or rental rates were also not accounted for, which is considered appropriate in Victoria 359
where seismic risk in buildings generally does not impact the rental rates or property market; 360
however, substantial value may be seen in other communities such as New Zealand where 361
property values have reportedly been impacted by the earthquake-prone building policy 362
(Chapman, 2012; Tarrant, 2012). Sources for construction costs included detailed estimates 363
for sample buildings in Victoria and actual costs from 19 local seismic upgrade projects. 364
Published unit rates (FEMA, 1988; FEMA, 1994b; Rutherford and Chekene, 1990; 365
Rutherford and Chekene, 1997) were also considered for partial retrofitting, although 366
preference was given to up-to-date local construction costs. The costs used in the study are 367
shown in Table 4, evaluated for a prototypical two-storey building with a gross floor area of 368
8000 sq.ft. (note that the unit cost for "parapet bracing" is in terms of a roof area of 369
4000sq.ft., while the costs for partial retrofits and full retrofits are in terms of gross floor 370
area). Alternative values are considered in the sensitivity analysis subsequently discussed. 371
Table 4.Unit Costs for Seismic Retrofitting 372
Retrofit Type Cost
$
Unit Cost
$/sq.ft. [$/m2]
Parapet Bracing 24,000 6 (0.54)
Partial Retrofit 80,000 10 (0.93)
Full Retrofit 264,000 33 (3.1)
BENEFIT-COST RESULTS 373
The overall benefit-cost results include both owner benefits (reduced damage and 374
downtime) as well as public benefits (reduced casualties). Benefits (B), Costs (C), and 375
Benefit/Cost Ratios (BCR) were calculated for a hypothetical two-storey building in 376
downtown Victoria, with a gross floor area of 8000 sq.ft. (744 m2) and 30 ft (9.1 m) of 377
streetfront sidewalk exposure (Table 5). Results are provided for site classes B, C, D, and E. 378
As aforementioned, all costs and benefits are in terms of third quarter 2014 Canadian dollars 379
and no conversion from USD to CAD was performed. Benefits were rounded to the nearest 380
hundred dollars. Based on these results, parapet-bracing appears to be a viable investment for 381
most buildings, while “partial retrofits” may be a viable investment for buildings on soft 382
soils. It is acknowledged that the likely costs also vary with the site soils, particularly for 383
“full” retrofits. Because full retrofits did not exhibit favourable (>1.0) BCRs, such a 384
refinement was not pursued. It should be noted that the losses were impacted heavily by site 385
class because the long-period soils foundation factor (Fv) varies highly as compared to the 386
short-period foundation factor (Fa). Observed damage to URM buildings has been shown to 387
be highly correlated with soil type (USGS, 1989), supporting the correlation of BCRs with 388
site class as seen in Table 5. 389
Table 5. Overall Benefit-Cost Results (favourable BCRs shaded green, borderline values shaded 390
yellow, non-favourable values shaded red) 391
Braced Parapets Partially-Retrofitted Fully-Retrofitted
Site
Class
B
[$]
C
[$] BCR B
[$]
C
[$] BCR B
[$] C [$] BCR
B 19,000 24,000 0.79 26,200 80,000 0.33 34,000 264,000 0.13
C 32,900 24,000 1.37 47,400 80,000 0.59 62,100 264,000 0.24
D 48,700 24,000 2.03 69,900 80,000 0.87 92,600 264,000 0.35
E 96,600 24,000 4.03 135,400 80,000 1.69 180,700 264,000 0.68
392
In many cases owners are expected to bear the costs of seismic retrofits alone. Thus 393
analyses were also completed considering only the owner benefits (Table 6), ignoring 394
benefits from avoiding all casualties. It can be seen that, in general, even limited upgrades 395
such as parapet bracing are often not economically justifiable from an owner’s perspective, 396
which provides strong evidence for cost-sharing between building owners and the public. 397
Table 6. Owner-Only Benefit-Cost Results (favourable BCRs shaded green, borderline values shaded 398
yellow, non-favourable values shaded red) 399
Braced Parapets Partially-Retrofitted Fully-Retrofitted
Site
Class
B
[$]
C
[$] BCR B
[$]
C
[$] BCR B
[$] C [$] BCR
B 7,700 24,000 0.32 12,700 80,000 0.16 19,300 264,000 0.07
C 13,500 24,000 0.56 23,900 80,000 0.30 36,400 264,000 0.14
D 18,900 24,000 0.79 34,200 80,000 0.43 53,800 264,000 0.20
E 31,600 24,000 1.32 55,500 80,000 0.69 91,700 264,000 0.34
400
SENSITIVITY ANALYSIS RESULTS 401
The foregoing results were based on average or typical values for all parameters, but very 402
few buildings/locations will match exactly the assumed conditions. Thus a sensitivity 403
analysis was performed to gain an improved understanding of which parameters are most 404
critical and over what range of values the conclusions would remain unchanged. The 405
following parameters were investigated: building replacement value; cost of ugprades; 406
discount rates; time horizon; structural vulnerability; length of streetfront exposure; and value 407
of a statistical life. "High" and "low" values of each were assigned as noted in Table 7 below 408
(note that the terms "high" and "low" refer to the resulting BCR, not the value of the 409
parameter in question).The high and low values of structural vulnerability were represented 410
through varied weighting on the California and Canterbury damage data as previously 411
discussed. Note that the sensitivity analysis was only performed for Site Class C results. 412
The parameters were varied one at a time and the resulting BCRs are summarized in 413
Figure 12. Examining the results for parapet bracing reveals that the BCR drops significantly 414
below 1.0 in only one case (for a high cost of upgrades of $12/sq.ft. of roof area). For partial 415
retrofits, the resulting BCR approached 1.0 for a low cost of upgrades ($6/sq.ft., which is 416
highly unlikely) and a high value of streetfront exposure of 90 ft, which is plausible. For full 417
retrofits, none of the variations resulted in BCRs approaching 1.0. In general, it can be seen 418
that the greatest changes were associated with changes to the retrofit costs (which is the 419
denominator in the BCR), discount rates, and length of streetfront exposure. 420
Table 7. Sensitivity Analysis Parameter Inputs 421
Parameter Low Base High
Building Replacement Value $225/sq.ft. $260/sq.ft. $300/sq.ft.
Cost of Upgrades
(Parapet Bracing) $4/sq.ft. $6/sq.ft. $12/sq.ft.
Cost of Upgrades
(Partial Retrofit) $14/sq.ft. $10/sq.ft. $6/sq.ft.
Cost of Upgrades
(Full Retrofit) $50/sq.ft. $33/sq.ft. $17/sq.ft.
Discount Rates
(Owner Benefits) 7% 5% 3%
Discount Rates
(Public Benefits) 5% 3% 1%
Time Horizon 25 years 50 years 75 years
Length of Streetfront Exposure 0 ft 30 ft 90 ft
Value of a Statistical Life $5.2M $9.1M $12.9M
422
CONCLUSIONS 423
The collected damage data from Canterbury and California were consistent with 424
expectations in that increased retrofitting resulted in decreased damage and decreased scatter 425
in performance data. New Zealand buildings appeared to be more vulnerable than their North 426
American counterparts, and isolating and quantifying the causes of the apparent differences 427
in vulnerability is an area for future research. It was also noted that an important distinction 428
between structural damage and overall building damage perhaps has not been well addressed 429
in the damage data collected to date. Future damage surveys should more clearly distinguish 430
between types of damage (or be appropriately limited to specific components) and should 431
examine potential differences in nonstructural damage patterns in URM buildings as 432
compared to more modern buildings. It would also be useful to collect future damage data in 433
terms of HAZUS damage states instead of ATC-13 damage states, as HAZUS is now the 434
most commonly used loss-estimation tool in North America. Nonetheless, the above reported 435
study provides new fragility curves based on some of the most recently collected data 436
worldwide for clay brick unreinforced masonry bearing wall buildings with flexible timber 437
diaphragms and represents an important improvement over fragility curves currently used in 438
HAZUS for retrofitted and unretrofitted URM buildings. 439
When both owner and public benefits are considered, parapet bracing appears to be 440
economically justified (BCR > 1.0) for many buildings in Victoria. Favorable results (BCR > 441
1.0) were also obtained for partial retrofits of buildings on soft soils. When only owner 442
benefits were considered, even parapet bracing was generally not economically justifiable, 443
except perhaps for buildings on soft soils. It is emphasized that the results are specific to the 444
seismic hazard for Victoria, BC, and that regions with higher seismic hazard will see greater 445
benefits due to higher EAL. Costs also increase with seismic hazard, but likely not at the 446
same rate as the costs of nonstructural work, and the labour cost for structural work is not 447
heavily affected by increased design demands (for example, increasing the size of a steel 448
brace or a floor anchor changes the overall scope of the work very little). 449
All of the aforementioned results were based on expected costs but risk-averseness and 450
political factors can significantly influence decision-making, and future research should seek 451
to incorporate these effects in a holistic assessment of the benefits and costs of seismic risk 452
mitigation. Some benefits such as historic preservation and overall community resiliency are 453
somewhat intangible and were not accounted for herein. Many decisions about the built 454
environment are not based solely on expected cost; to do so for seismic retrofitting may put 455
seismic safety at a disadvantage. One possible remedy for this issue is to combine expected 456
cost with other goals in a multi-objective optimization-based approach (eg. minimize 457
expected costs while limiting the number of deaths or demolitions for a given level of 458
shaking). Haimes (2004) discusses such a methodology. In many regions, a large proportion 459
of the public may also not be aware of the increased seismic risk of URM buildings relative 460
to other building types or do not consider this risk when entering or walking next to a URM 461
building. Notably, URM buildings provide low-cost housing in many communities, and 462
hence many vulnerable populations may not be able to avoid frequent exposure to such 463
buildings. The seismic risks posed by URM buildings must be addressed in conjunction with 464
addressing the challenges of affordable housing. Finally, the values assigned to many of the 465
aforementioned parameters were highly uncertain and required significant assumptions. The 466
results should be considered as a general indication only and there is much potential for 467
refinement, particularly in the areas of nonstructural damage, downtime considering regional 468
impacts, and demolition vs. repair decision-making. 469
ACKNOWLEDGEMENTS 470
The damage data that underpinned this study was collected as part of past research 471
efforts. Data for the Loma Prieta and Northridge earthquakes were collected and compiled 472
primarily by Bret Lizundia of Rutherford and Chekene; assistance and advice from Mr. 473
Lizundia in this research is greatly appreciated. Funding for data collection for the Loma 474
Prieta earthquake was provided by the California Seismic Safety Commission and the USGS. 475
Funding for the Northridge Earthquake was provided by the US National Institute of 476
Standards and Technology. Data collection from the 2010/2011 Canterbury earthquakes was 477
funded by the New Zealand Natural Hazards Research Platform. The work presented herein 478
was funded jointly by The Victoria Civic Heritage Trust and the Natural Sciences and 479
Engineering Research Council of Canada through an Industrial Postgraduate Scholarship. 480
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Throughout The World. Cambridge, MA, USA: Harvard Law School. 594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
Figure 1. Hazard curves for Victoria (Paxton, 2014), Seattle (http://geohazards.usgs.gov/
614
hazardtool/), and Wellington, New Zealand (Stirling et al 2012) showing example incremental
615
probability of occurrence calculation (see Equation 1)
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
Figure 2. Sa(1) versus MDF relationships for the Canterbury data (number of buildings for each data
638
point is also indicated)
639
640
641
642
P(S
a
[1] = 0.5g) = Δλ = λ
2
-λ
1
= 0.0004/year
λ
2
= 0.001
λ
1
= 0.0006
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
Figure 3. Comparison of observed data across databases and to published sources for Unretrofitted 665
buildings 666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
Figure 4. Comparison of observed data across databases and to published sources for Fully-retrofitted 688
buildings 689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
Figure 5. Comparison of observed data to structural-only damage relationships from HAZUS 711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
Figure 6. Derived structural fragilities for Unretrofitted buildings based on the Canterbury data 733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
Figure 7. Derived structural fragilities for Fully-Retrofitted buildings based on the Canterbury data 757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
Figure 8. Derived structural fragilities for Unretrofitted buildings based on the California data 780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
Figure 9. Derived structural fragilities for Fully-Retrofitted buildings based on the California data 803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
Figure 10. Conditional loss curve for Unretrofitted building showing example conditional loss value 824
(see Equation 1) 825
826
LV
(
Sa
[
1
]
= 0.5
g)
32%
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
Figure 11. Building recovery time functions 846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
Figure 12. Sensitivity Analysis Results 870
871
872
873
874
