Journal of Natural Disaster Science, Volume 28, Number 2, 2006, pp61-72

Integrated Earthquake Fire Risk Evaluation Based on Single
Building Fire Probability Applicable to All Map Scales
Takaaki KATO1, Cheng HONG2, Yalkun YUSFU2, Makoto YAMAGUCHI3 and Akiko NATORI3
1
Department of Urban Engineering, the University of Tokyo
2
GLOSIS Japan, Co., Ltd.
3
Non-Life Insurance Rating Organization of Japan(Received for 26 May, 2006 and in revised from 25 Dec., 2006)

ABSTRACT
It is difficult to create a fire risk evaluation method that is applicable to different map scales from a single building to the whole region of Japan. Conventional simulation methods use city indices or mesh-data, but in the proposed method the fire destruction probability of each single building can be calculated. Thus the method reflects
the actual spatial characteristics of a city and can be used for general purposes with no margin of error. It is possible to rearrange the results in different area units and to obtain the numbers of burned out houses and areas. In
addition, the method provides appropriate information for conveying the fire risk to the public by showing themcluster data of the simulation. This cluster data is sometimes referred to as the Fatalistic Collaboration
Community Unit.

1. INTRODUCTION
The Central Disaster Prevention Council1) claims that is a highrisk of earthquake fire disasters.
Recognizing the risk of earthquake fire disasters is importantfor developing national, prefectural, and citizen's countermeasures.
Accurate comprehension of the risk provides essential data for formulating national strategies to reduce the earthquake fire risk in
6,000 ha of major densely-populated areas2) in Japan. Such information is also necessary for prefectural promotion of the publicawareness of disaster prevention, incorporating disaster control inurban planning, conducting disaster prevention urban development,
and other activities. Information on the earthquake fire risk is also
useful for making decisions at a personal level or city level to build
fire-proof houses or fire-resistant houses and to simultaneously rebuild houses in a neighborhood. For measures at any level, it isimportant to understand the balance between risk reduction andcost in making decisions. For these reasons, information isrequired on not only earthquake probability but also earthquake firedamage probability or expected earthquake fire damage.
Earthquake fire risk information is often demonstrated as an
estimating damage by assuming specific scenarios of fire breakout
locations and fire spread. It is important information for considering detailed measures against the fire disaster, and should be
acknowledged as an image of possible damage. In practice, fire
breakout is a probability event, but the fire breakout probability is
not included in the framework of the damage estimation. In theevaluation of earthquake fire risk, it is hence important to take into
account the probability of earthquake fire breakout and assess possible damage caused by the breakout and fire spread. In addition todamage estimation, the disaster risk is sometimes presented in relative risk levels in various locations, as performed in District-based

Vulnerability assessment to an earthquake in Tokyo3), which is designated by the Tokyo Metropolitan Government , although it would
be more helpful for detailed examination of measures to use, notrelative, but absolute risk levels.
Risk communication is also important at the citizen level.
Information on earthquake fire risks should be easy to understandand realistic as well as emphasizing the individual perspective ofrisk sharing.
Technology for evaluating earthquake fire risks such as thecreation of digital city maps and the power of computer processing
has greatly advanced, enabling improved evaluation methods
reflecting the times to be developed.
In the present paper, we propose a practical earthquake-firerisk evaluation method that is highly accurate and meets various
needs. The method applies to all map scale, meets national, prefectural, and citizen's needs and provides absolute fire spread risk levels by taking account of not only fire spread but also fire breakout
probability. Here, the earthquake fire risk is defined as the probability of suffering fire damage or the expected cost of fire damage.
Conventional methods use functions of explanatory variablesof district indices for simple evaluation of fire spread risk4−6), or
simulations to draw and analyze fire spread behavior7−10). The former method is versatile as it calculates the fire destruction rate
based on city indices, but is limited because it models cities as a
uniforme city image. The latter method is useful for showing temporal changes in the fire spread behavior based on city data, but it
is limited in its high dependency on the fire breakout location
because it shows fire spread damage images starting from specificfire breakout locations. Conventional methods thus have advantages and disadvantages in earthquake fire risk evaluation, depending on the development purposes. The proposed method takes
account of the techniques and advantages of the conventional

KEY WORDS: fire risk evaluation, urban disaster, fire destruction probability, urban fire-spread, earthquake, GIS.

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T. KATO, C. HONG, YALKUN. Y, M. YAMAGUCHI AND A. NATORI

methods and minimizes their disadvantages.
The simulation method sets a fire breakout location anddescribes successive fire spreads starting from that location. In
contrast, the proposed method but also identifies buildings in an
entire city area that are expected to burn down finally instead treats
fire spread between buildings dynamically. The fire destruction
probability of the buildings is calculated from the probability offire breakout in the buildings. This allows us to handle single
building data, which directly reflects the spatial characteristics ofthe cities, as well as national-scale data, and to obtain useful dataof the fire destruction probability of each building, that is notdependent on fire breakout locations. Moreover, the conventional
methods treat fire breakout and fire spread in a separate manner,
while the proposed method makes logical connections between
each building's fire breakout probability and the fire destruction
probability and enables the process from fire breakout to fire
spread to be handled in an integrated manner. In the present study,
a fire that would be extinguished in fire fighting at the early stagesof the fire was incorporated into the fire breakout probability, andwe examined only fires that would not be extinguished.
In this paper, we summarize the conventional methods, andcharacterize and describe our evaluation method. Then, we use theearthquake fire risk evaluation system of nationwide building datathat was made in the present study to present an evaluation example with the proposed method and discuss the versatility andusability of the evaluation results produced. In this paper, we focus
on the development of the evaluation method, and analysis of theevaluation results such as the characteristics of the evaluation, andregional distribution of earthquake fire risk will be given elsewhere.
2. SUMMARY OF CONVENTIONAL METHODSAND NECESSARY EVALUATION METHOD(1) Summary of conventional methods
Conventional methods of evaluating the risk of earthquake
fires spreading can be classified into ones that use the functions of
explanatory variables of district indices4−6) and ones that perform
simulation 7−10). The simulation methods are further classified
according to the data used: ones that use mesh data(1) and ones thatuse single building data6，9，10). Below, we summarize the characteristics of each method and expected issues in the present evaluation.
a) Method of using functions with explanatory variables ofcity indices
Based on the relation between city indices and fire spread riskthat is obtained with the simple modeling of cities and fire spreadprocess, the method calculates the fire spread risk from the city
indices. Typical methods use the ratio of the noncombustiblearea 4) and the wooden building coverage ratio 5). For example,
in the method that uses the ratio of the noncombustible area, a city
is modeled by assuming that noncombustible areas and combustible areas are randomly distributed over 101x101 square latticesites according to the ratio (left in Fig. 1) and fire spread is modeled by assuming that fire propagates to combustible buildings
located in neighboring sites. Based on the modeling, numericalsimulation is performed to obtain the relation between the ratio of

the noncombustible area and the fire destruction rate (right in Fig.
1). This method was developed for simple treatment of urbanizedarea and the fire spread process.
In this method, the fire destruction rate can be calculated fromthe relation shown in the right graph in Fig. 1 if we know the ratioof the noncombustible area of the target area. The same ratio of
noncombustible area gives the same evaluation result. For example, in a comparison between a relatively uncrowded residential
area with wooden buildings and a relatively crowded residential
area with some large noncombustible areas including schools, thecity characteristics of both areas, and hence the fire spread risk,
may be different, although the ratio of the noncombustible area
may be the same in both areas.
Evaluation error is dependent on the evaluation unit, and anerror may be observed if a different evaluation unit is used11). For
example the ratio of a noncombustible area could change depending on whether a school located in the vicinity of the evaluation
unit boundary is included in the evaluation.
Thus a method that uses city indices is useful to simply, globally understand fire spread risk, but it also has a limitation in its
evaluation precision as it handles large areas but does not reflect
the spatial characteristics of districts.
b) Simulation method
The simulation method focuses on dynamic aspects of fire
spread. It uses city data as input data for a simulation program toobtain time series changes in the fire destruction area. Mesh data isused in traditional simulation methods, while single building data
is used in more recent simulation methods.
In the mesh data method, statistical values in the mesh area areused as basic data, and hence the mesh area is treated as a uniform
urban area. Therefore, even if there is a wide main street or large
open space, which is expected to have a fire-spread prevention
effect, in the mesh area, it is sometimes not taken into account for
fire spread behavior. Fig. 2 shows a sample mesh area with wide
main streets that have fire-spread prevention effects. The mainstreet running from south to north in the center of the figure is so
wide that it can interrupt fire spread from the left side of the street(Fig. 2 (b)-1). In the method using the mesh data, however, thearea inside the mesh is assumed to have uniform city characteristics and the main street is not effectively presented (Fig. 2 (a)-2).
As a result, the street has the effect of reducing the fire spread
speed but does not stop the fire spread over the street (Fig. 2 (b)-2).
The method that uses single building data has been widelyused in recent years with the development of digital maps and theimprovement of computer capability. High precision simulation

Fig. 1 Development of evaluation method, using city indicesINTEGRATED EARTHQUAKE FIRE RISK EVALUATION BASED ON SINGLE BUILDING FIRE PROBABILITY APPLICABLE TO ALL MAP SCALES(a)-1 Single building data(a)-2 Mesh data(b)-1 Results(b)-2 Results (image)Fig. 2 Limitations in the simulation method using mesh data(a)-1

3 hours later(a)-2

3 hours later(b)-1 6 hours later(b)-2

6 hours later

Fig. 3 Limitations of the simulation method that uses single building data(1): Different fire breakout locations have different results. The redcircle in the figure shows the fire breakout location. The red color
indicates burning buildings and the black color indicates burneddown buildings. All the figures use the same setting for the speed
and direction of the wind.

has become possible because the smallest unit of burning, i.e. abuilding, is incorporated in the simulation data. Despite theimproved computer capability, it is still difficult to simulate a widecity area due to the limitation of computational time (2), and theevaluation results are dependent on the location of fire breakout
because fire spread is highly dependent on the situation around thefire breakout location. Fig. 3 shows an example in which the evaluation results change with the fire breakout location. Different fire
spread patterns were obtained, depending on whether the fire
breakout point was set on a certain building with an open area
nearby or on a building with no road around. Figs. 3 (a) and (b)show the results of fire spread at 3 hours and 6 hours after the
breakout, respectively. In the left figure, almost the entire area isburned out, while in the right figure the road on the north side of
the fire breakout building stops the fire spread at an early stage.
Hence the areas burned out in 6 hours in both cases are very different from each other(3).
To eliminate these negative effects, it is necessary to perform
simulations for as many fire breakout patterns as possible and takethe average of the outcomes and use it as the fire spread risk of thearea12). However, performing simulations is time-consuming andcurrent technology does not allow large area simulations (Fig. 4).

63

Fig. 4 Limitations of the simulation method that uses single building data(2): All fire breakout patterns were simulated based on the assumption that there is only one fire breakout in the area. The colors in the
figure indicate the number of burned out buildings. This simulation
was relatively time-consuming.

Fig. 5 Proposed method in relation to conventional methods

3. BASIC IDEA OF THE PROPOSED EVALUATION METHOD OF EARTHQUAKE FIRE
RISK
Conventional methods have advantages and disadvantages assummarized above. The proposed method retains the advantages
and minimizes the disadvantages (Fig. 5). The vertical axis in Fig.
5 shows the computational load. Higher points on the vertical axis
indicate the capability of calculating a wider city area, or indicate ahigher calculation speed for a fixed city area.
The proposed evaluation method: (i) Reflects city characteristics in the evaluation by using single building data, under the current situation where a digital map has been developed and GIS's
versatility has been enhanced. (ii) Calculates a wider city area than
the simulation methods can do, by using a simple fire spread
model. (iii) Retains connection with the fire breakout probability.
The proposed method uses a deterministic model of fire spread
between buildings (with fire spread limit distance d＊) and firstly
determines the buildings (referred to as a cluster ) that are
expected to be burned out (Fig. 6). If we have a probability of fire
breakout in a group of buildings, we can obtain the fire destruction
probability of each building in the group. In this study, the fire
destruction probability thus obtained is called the earthquake firerisk.
In this study, the earthquake fire risk is calculated for eachbuilding, and hence the result is not dependent on how the area unit
is selected. In other words, any area unit can be used for the calcu-

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T. KATO, C. HONG, YALKUN. Y, M. YAMAGUCHI AND A. NATORI

Fig. 6 Cluster generation: Neighboring buildings located within thefire spread limit distance d＊ belong to the same cluster.

lation of fire risk. For example, to determine the expectation valueof the number of fire destroyed buildings, we add the fire destruction probability of each building located in the area unit of interest,
e.g. mesh units, city blocks, community units, fire department control areas, etc. To determine the fire destruction probability of thearea unit, we divide the expectation value by the number of thebuildings in the area. We can also obtain the expectation value ofthe burned area by multiplying the fire destruction probability ofeach building by the total floor area. This method thus gives an
output that is highly processable and versatile for use in calculating
various other values.
This study was developed, based on the concept of CVF(Covering Volume Fraction) 13), on which macro-evaluation methods of Development of Assessment and Countermeasure
Technologies for Disaster Prevention in Town Planning 6) , theGeneral Technology Development Projects (hereafter referred to as
General Project) of the Ministry of Land, Infrastructure andTransport are based. The differences between the proposed
method and the macro-evaluation method are: (i) In the proposed
method, the speed and direction of the wind are taken into accountto set fire spread limit distance d, which is used in the macro-evaluation of the General Project. (ii) In the macro-evaluation, fire
spread limit distance d is given for fire spread from a single building, while in the proposed method it is given for fire spread frommultiple buildings. (iii) In the proposed method, the fire destruction probability is integrated with fire breakout in the cluster. (iv)
Calculation on a nation-wide scale is technologically realized in the
proposed method.
In addition, we developed a database of all the buildings overthe country (about 62.5 million polygons) and developed a systemfor calculating the fire destruction probability in only a few seconds based on the fire breakout probability using a standard area
mesh (third-level area division).
The overall flow of the evaluation method is shown in Fig. 7.
We first need to prepare polygon data with structural attributes of asingle building to make basic data. This kind of data has alreadybeen prepared for example in Tokyo. Based on the data, we assign
parameters that affect fire spread, i.e. the speed and direction of thewind, to each building, and make polygon data with not only structural attributes but also wind-speed and -direction attributes.
Next we calculate the inter-building distance and angle foreach building and compare the distance with the fire spread limit
distances of various wind speeds and directions and various build-

Fig. 7 Flowchart of the present evaluation

ings that are defined in the building polygon data. We then determine the cluster that is formed by the buildings located within thefire spread limit distance. The cluster is a kind of fatalistic collaboration unit , inside which buildings would be burned out if thefire were to start from any single building in the cluster.
Finally, we calculate the occurrence probability of one ormore fire breakouts inside the cluster by using the fire breakout
probability of each building in the cluster. The fire destruction
probability of each building is calculated by using the fact that theprobability that buildings in the cluster are burned out is the sameas that of fire breakout in the cluster. By adding up the fire
destruction probability of each building, we can calculate the number of buildings that are expected to be burned out in the area unit.
4. DETAILS OF THE EVALUATION METHOD(1) Model of fire spread limit distancea) Conventional model of fire spread limit distance
Hamada's fire spread speed equation is a typical equation giving the fire spread limit distance. There are three types of Hamada
model equations, which are given respectively for wooden structures, fire-proof structures, and simple fire-resistant structures.
They are respectively called Hamada type14), Horiuchi type15), andMurosaki type16). When a Hamada-type fire spread limit distance is
1, that of the Horiuchi type is 1/2 and that of the Murosaki type is
1/4. The fire spread limit distance is determined according to thedirection of the propagation, i.e. whether fire propagates down
wind, up wind, or perpendicularly to the wind.
Recently, the macro-evaluation model6) of the General Projectof the Ministry of Land, Infrastructure and Transport has definedINTEGRATED EARTHQUAKE FIRE RISK EVALUATION BASED ON SINGLE BUILDING FIRE PROBABILITY APPLICABLE TO ALL MAP SCALES

fire spread limit distance d . The macro-evaluation model wasdeveloped to study the fire spread risk of a city and find dangerous
areas in a city block unit. The macro-evaluation model sets the fire
spread limit distance for each building structure and focuses onbuilding groups located close to each other within the limit distance. The buildings in the group are considered to have fire
spread risk. The fire spread limit distance in the macro-evaluation
model is defined by:① The fire spread limit distance of bare wooden structures is set to
12 m, according to the class 4 curve of fire temperature that wasused by the Building Standards Law to identify the areas that
could be burn out in fire spread.
② The fire spread limit distances of fire-proof wooden and quasifire-resistant structures are set to 6 m and 3 m respectively, in
consideration of the ratios of the Hamada-type, Horiuchi-type-,
and Murosaki-type limit distances.
③ The side length of a standard house is set to be 10 m, and theelevation surface of burning buildings is assumed to be covered
with fire. For houses with different building areas, the fire
spread limit distance is determined to have the same fire geometric factor at the heat-receiving point under the eaves on thevertical surface of a neighboring building.
Fire spread limit distance d thus defined is given by the following
equation.
d = kAr―[1]

Here, A is the side length of the building (approximated by a squareroot of building area). Coefficient k and power r are given for eachbuilding structure type. The fire spread limit distance of a fireproof structure is set to zero. Let us first consider fire spread froma single building.
b) Modeling of fire spread limit distanceIn the present study we define a new fire spread limit distanced＊, based on the concept of the fire spread limit distance d definedin the General Project Disaster Prevention in Town Planning .
Unlike the fire spread limit distance of the General Project, thefire spread limit distance of our model is derived with wind speed
to take account of local climate characteristics and is calculated forfire spread from more than one building. In other words, our fire
spread limit distance is defined by considering the condition of theburning building itself and burning of buildings nearby.
Fire spread limit distance d＊ is determined in the following
modeling steps in this study. First, we make an assumption of fireand set a radiant heat receiving point, taking account of windspeed. Next, we derive the limit distance of fire spread from a single building. To be more specific, we take into account the widthof buildings and tilting of fire to calculate the distance. Finally, we
correct the distance to obtain limit distance d＊ of fire spread frommultiple buildings. This distance d＊ is used as the fire spread limit
distance in this study.
c) Assumption of fire and setting of radiant heat receiving
point
Here, we assume that the room height of each floor in a building is 3 m and that fire can reach up to 2 m higher than the upmost
point of the outer wall (Fig. 8). In the early stages of a fire, the fireblows out from openings of the building. Then the roof starts burning and finally the fire covers the entire building. So this length is65

chosen in consideration of the mean fire height under these twoburning conditions. The heat receiving point is set to the top of asecond floor room, i.e. 6 m from the ground. The assumption thatfire reaches 2 m higher than the total room height is different fromthat in the General Project's macro-evaluation model.
In general, wind increases the fire spread limit distance. Thisis because fire tilts in a downwind direction. To take account ofwind speed, we need to define the relation between wind speed andfire tilting angle. The relation has been extensively studied forexample in Ref. 4. For convenience, we assume constant fire
length, as in Ref. 4. Reference 4 used the following equation toexpress the relation between wind speed ν and fire tilting angle θ(angle between fire and ground in the unit of radian):Ï 1
sin q = Ì
0.2
Ó(2 / v)

0£v<2
2£v

―[2]

We assume that the influence of wind on fire is taken into accountonly for the downwind direction. When considering fire spread in
the upwind direction or fire spread in a direction perpendicular to
the wind direction, we assume that fire stands perpendicularly to
the ground. Elliptic approximation is used for a direction not parallel to the downwind direction.
d) Derivation of limit distance of fire spread from a single
building
Next, we assume the inter-building distance to have the same
geometric factor (referred to as limiting geometric factor) as thefire spread limit distance in the macro-evaluation of the General
Project Disaster Prevention Town Planning . We set this distance to be fire spread limit distance d＊. In the present study, we
solved the equation for a certain fire tilting angle to calculate thedistance by increasing the side length of Building A from 4 m to23.5 m by 50 cm. The calculation results are presented in the formd = kAr, the same functional form used in the macro-evaluation of
the General Project Disaster Prevention Town Planning . The
obtained coefficient is shown in Table 2. The limiting geometricfactor is given in Table 1.
e) Derivation of limit distance d＊ of fire spread from multiple
building
Finally, we correct the fire spread limit distance to takeaccount of the influence of multiple-building fires. We use the citymodel shown in Fig. 9 where an odd number (2N + 1) of buildings
are located in a line and makes a square lattice, whose center faces
a heat-receiving building. We assume that the buildings in the line
closest to the heat-receiving building are burning.
Here we calculate, as a function of N, the minimum interbuilding distance to prevent fire spread to heat-receiving buildings,
i.e. fire spread limit distance d＊, with the building coverage being

Fig. 8 Assumption of fire and setting of radiant heat receiving point

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T. KATO, C. HONG, YALKUN. Y, M. YAMAGUCHI AND A. NATORI

Table 1. Coefficients and powers of fire spread limit distance forvarious building structures(a) Fire-proof wooden structure

Table 2. Coefficient of fire spread limit distance for various building
structures and various fire tilting angles(b) Quasi-fire-resistant eooden structure
Fig. 10 Ratio of limit distance d＊ of fire spread from multiple buildings tothat of fire spread from a single building: The horizontal axis presents N and the vertical axis represents the ratio of the limit distance of fire spread from multiple buildings to that of fire spreadfrom a single building.
Table 3. Structure percentages in Tokyo Housing and Land Survey 1996

Fig. 9 Assumption on multiple-building fire in city

ｍ%. The side length of a building is assumed to be the squareroot of the mean building area 83 m2 of residential houses, which is
given in the Housing and Land Survey18). Fig. 10 shows the calculated ratio of the limit distance of fire spread from multiple buildings to that of fire spread from a single building as a function of N,
where 2N+1 is the number of burning buildings on a line that face
the heat-receiving building.
The figure shows that the burning buildings close to the heatreceiving building have a large influence, but the burning buildings
located further from the heat-receiving building have smaller influence. This is because the geometric factor, which is used to calculate radiant heat to the heat-receiving building, rapidly decreases as
the location of burning buildings becomes further from the heatreceiving building. When the burning buildings are located on the

fourth line (N=4 in the horizontal axis) or further location, the ratioof the limit distance of fire spread from multiple buildings to thatof fire spread from a single building does not increase and remains
almost constant. The ratio changes with the building coverage or
structure, and is about 1.5-2.2, 1.2-1.5, and 1.1-1.2 for wooden,
fire-proof and quasi-fire-resistant structures, respectively.
We then calculated the mean value of the fire spread limit distance with the weight of the proportion of wooden, fire-proof
wooden and quasi-fire-resistant structures to average all the building structures. Since we did not have the proportion data of quasifire-resistant structures for the whole country, we assumed the percentage of wooden, fire-proof wooden and quasi-fire-proof structures to be 15%, 70%, and 15%, respectively, based on the fireresistant structure study of the Tokyo Housing and Land Survey(1996) as shown in Table 3. Using these percentages as theweight, we calculated the weighted mean of the fire spread limit
distance from the ratio derived for each structure in Fig. 10. Table
4. summarizes the results for various building coverages. The
mean value slightly changes with the coverage, but we assumed
that the limit distance d＊ of fire spread from multiple buildings was
1.5 times as long as that of fire spread from a single building.

INTEGRATED EARTHQUAKE FIRE RISK EVALUATION BASED ON SINGLE BUILDING FIRE PROBABILITY APPLICABLE TO ALL MAP SCALES

Table 4. Weighted mean ratio of the limit distance d＊ of fire spread frommultiple buildings to that of fire spread from a single building(2) Determination of fire spread to neighboring buildings, calculation of inter-building distance, and generation of clusters
Before making a cluster, we need to specify neighboringbuildings that can be burned out in the fire spread and calculate theinter-building distance and angle. We then build a database of theresults. This is performed to shorten the calculation time for making a cluster. This calculation consumes most of the computation
time. Considering the balance between calculation time and precision, we employ the following calculation algorithm:
Step 1-1: Dividing the study area into a 50 m mesh. The buildings
in a 5 x 5 mesh area centering on the target building aredefined as possibly neighboring buildings. However, buildings with a median point 200 m or more distant from the target building are excluded(4) from the neighboring building
group.
Step 1-2: Drawing lines between the target building and the possibly neighboring buildings. We draw lines between the median points of building polygons and between the nearest pointsof the polygons. If a line connecting the median points of thetarget building polygon and a possibly neighboring building
polygon does not run through other building polygons, or if aline connecting the nearest points of the target building polygon and the possibly neighboring building polygon does not
run through other building polygons, we consider the possibly
neighboring building to be a neighboring building. If the distance between the nearest apexes of the building polygons isshorter than 3 m, the buildings are unconditionally considered
to be neighboring buildings.
Step 2-1: Measurement of the direction of the neighboring buildings. The direction is defined by a line between the medianpoint of the target building and that of a neighboring building.
Step 2-2: Calculation of inter-building distance. The distance ismeasured between the target building and a neighboringbuilding. Depending on the mutual positional relationship,
the distance may be given by the shortest length between
apexes or by the shortest length between the apex and theside.
To define clusters, we compare the inter-building distance andfire spread limit distance d＊, and if the former is shorter than thelatter the neighboring buildings belong to the same cluster. If theneighboring buildings have different structures, fire spread limit
distance d＊ is given by the average of the limit distances of both
structures.
(3) Assignment of fire breakout probability
In the present study, we assumed that the fire breakout proba-

67

bility to be an external parameter given for individual buildings.
There are different methods of estimating fire breakout probability and results are obtained in various forms (e.g. number of fire
breakouts) for different area units. In this study, however, the calculations give fire breakout probabilities of individual buildings,
and therefore we can rearrange the results in any format for any
area unit. For example, when calculation gives the number of fire
breakouts on a standard regional mesh (the third-level area division), we can obtain the fire breakout probability of individual
buildings by dividing the number of fire breakouts by the total
number of buildings on the mesh, assuming uniform fire breakout
probability of the buildings.
(4) Calculation of fire destruction probability and expectation
value of the number of fire destroyed buildings in adefined area unit
The fire destruction probability of a building is equivalent to
the probability that one or more fire breakouts occur in the cluster
to which the building belongs. Fire destruction probability P of abuilding is given by the following equation where n is the numberof buildings in the cluster and pi is the fire breakout probability ofbuilding i in the cluster:n

P = 1 - P (1 - pi )
i =1

―[3]

Expectation value χ of the number of fire destroyed buildingsin the area unit should be equal to the summation of the fire
destruction probability of the buildings in the area unit and hence
given by the following equation.

c = Â Pk―[4]

We can calculate the probability and the expectation value forany area unit, if we can identify the buildings in the area unit, i.e.
administrative area unit, community unit, mesh, etc.,
To save computation time, we use an approximation form of
P. The fire destruction probability can be calculated for all buildings if we perform the same calculation for every cluster. The
approximation form is given by_

P = 1 - exp( - n p)

―[5]

where
is the fire breakout probability in the area unit.
The fire destruction probability of buildings is calculated by
Eq. [3] or [5] under the following conditions, and the precision of
the approximation can be examined by comparing the results.
・ Assuming that each cluster can have four different fire breakout
probabilities.
・ Assuming that fire breakout probability pi is given by a random
number between 0.00001 and 0.0001 and the number of buildings by a random number between 1 and 1000.
Fig. 11 shows the results of 10,000 calculations. We see fromthe figure that the exact value and the approximate value almost
coincide with each other, which indicates the validity of theapproximation.

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T. KATO, C. HONG, YALKUN. Y, M. YAMAGUCHI AND A. NATORI

Fig. 11 Analysis of approximation precision of fire destruction probability

5. DEVELOPMENT OF A CALCULATION SYSTEM FOR EARTHQUAKE FIRE RISK OVER
THE COUNTRY(1) Data used
In the calculations, we used DAIKEI's Telemap, a commercial
digital map, because of its comprehensive features, i.e. a variety ofbuilding attribute data, data conversion functions, and distinguished operability. The map data covers almost the entire country. Namely, it covers 3,052 out of all the 3,204 cities, towns andvillages in Japan as of July 2003 and the coverage rate is 95.7%.
We also referred to climate information database AMEDASof the Japan Meteorological Business Support Center for windspeed and direction data. The database contains climate data fromthe past 29 years (1976-2004). At total of 976 observation sites
provided both wind speed and wind direction data, including sitesthat had already been eliminated. As wind data we obtained dailymean wind speed, daily mean wind direction and daily maximum
wind speed.
(2) Assignment of structure
DAIKEI's Telemap provides building attributes such as building type (building/apartment, residential house, office house,
unknown) and the number of floors (for buildings of three or morestories), but not structural attributes. For simplicity we estimatedthe type of building structure (Fig. 12) by using two building
attributes provided by the Telemap and comparing the structureswith known data(5). Herein, we refer to buildings, apartments, andoffice houses as non-residential buildings.
In the calculations, due to the restriction on data, we assumed
that all wooden buildings had a fire-proof structure.
① Buildings of four or more stories are assigned as fire-resistantbuildings.
② 0%, 80%, and 20% of residential houses of three stories are
assigned as fire-proof wooden, quasi-fire-resistant, and fireresistant buildings, respectively.
③ 0%, 60%, and 40% of non-residential houses of three stories are
assigned as fire-proof wooden, quasi-fire-resistant, and fireresistant buildings, respectively.
④ 0%, 70%, and 30% of other unclassified buildings of three stories are assigned as fire-proof wooden, quasi-fire-resistant, andfire-resistant buildings, respectively.
⑤ The percentages q1i and q2i of buildings of one or two stories
assigned to fire-resistant and quasi-fire-resistant buildings(a) Structure assignment of buildings of three or more stories(b) Structure assignment of one- or two-story buildings
Fig. 12 Flowchart of building structure assignment

Table 5. Assumption on the percentages of structures for the assignmentof one- or two-story residential houses(5)respectively are given for various building areas in Table 5.
The number of buildings for various building areas, n i, is
extracted from the Daikei Telemap data. Regional coefficient k
is calculated by the following equation using the proportion of
non-wooden buildings Q among residential houses (including
those of three or more stories) given in the prefectural data18) of
the Housing and Land Survey:
Regional coefficient k =( Sni )Q
Sni (q1i + q2i )―[6]

The regional coefficient k, which is determined by the proportion of non-wooden buildings Q of all the prefectures, is used tocorrect the percentages of fire-resistant or quasi-fire-resistantbuildings in various districts. The corrected percentages of fireresistant and quasi-fire-resistant buildings of various buildingINTEGRATED EARTHQUAKE FIRE RISK EVALUATION BASED ON SINGLE BUILDING FIRE PROBABILITY APPLICABLE TO ALL MAP SCALES

areas are given respectively by kq1i and kq2i where k is the regional coefficient. We assign the structure of buildings by using
computer-generated random numbers according to the structure
percentages thus obtained.
⑥ Non-residential houses of one or two stories are assigned
according to the percentages of fire-resistant and quasi-fireresistant buildings to various building areas as shown in Table
6.
⑦ Data analysis indicated that other unclassified buildings of one
or two stories had various intermediate features between one- or
two-story residential houses and one- or two-story non-residential houses. We thus assume that the structure percentages ofother unclassified buildings of one or two stories are given by
the average of those for the residential houses and those for thenon-residential houses.
The structure assignment needs to be refined. No structural
estimation is necessary if we have structural attribute data such as
GIS, the city planning of Tokyo.
(3) Assignment of the speed and direction of the windTo each building, we assigned wind data of speed and direction at the nearest observation point. With the present system, we
can calculate earthquake fire risk at arbitrary wind speeds anddirections. It is also possible to calculate earthquake fire risk by
taking account of the occurrence probability of wind speed anddirection, unless computational time is limited. In our calculation,
we used data obtained at 826 observation sites that had a total of 15
months or longer observation history, and converted it to windspeed at 10 m height from the ground(6).
(4) Calculation time
We reduced the calculation time on PC by improving the algorithm, etc. The calculation of fire spread from a single neighboringbuilding required about one week to cover approximately 62.5 million buildings. The calculation of cluster buildings took about 12
hours in total. In the calculation of earthquake fire risk on the standard regional mesh (the third-level area division) over the country,
the time required to calculate the fire destruction probability with acertain data set of wind speed and direction could be reduced fromten minutes to several tens of seconds(7). These results show thatthe proposed method is practical.

69

wind speed and the most frequently observed wind direction in theyear as the basic data on the speed and direction of the wind.
Fig. 13 shows the results of test calculations with an assumption that the fire breakout probability in each building is constantover the country. In the calculation, we set the fire breakout probability of a residential house on a winter evening to be 0.00048 at
1,000 gal, following Ref. 19). The standard regional mesh of thethird-level area division was used for the area unit. From the calculation, we see regional characteristics in each city. Fig. 14 is thetest calculation result on the fire destruction probability with thefire breakout probability being set to the estimated value(8) for
Tokai-HigashiNankai-Nankai Earthquake. The fire destruction
probability distribution receives relatively little influence from theseismic center, in comparison with the fire breakout probability
distribution. This kind of analysis can be performed within a few
minutes.
Fig. 15 shows the calculation results for Tokyo with mesh,buildings, and close-up views. As shown in the figure, the results
can be arranged for arbitrary area units such as city blocks, community units, or fire department control areas, if polygon data of
the area unit is provided.
7. ENABLING RISK INFORMATION TO BE
CONVEYED TO CITIZENS AND CITIZENS TOSHARE THE RISKTo reduce earthquake fire risk, it is necessary to make morebuildings fire-proof or fire-resistant and improve methods of preventing fire spread for example by developing roads. This cannot
be done by individual people, so cooperation in local communities
and towns is essential. However, cooperation is not necessarily
required for reducing the risk of building collapse.
Here we describe the response when we showed our evaluation results to some citizens to convey risk information to them andto let them share the risk(9). There are two important factors in conveying risk information and encouraging people to share the risk.

6. EXAMPLE OF CALCULATION
Here we show the calculation results in every scale anddescribe the results.
In our test calculations of earthquake fire risk, we used mean

Table 6. Assumption on the percentages of structures for the assignmentof one- or two-story non-residential houses(5)Fig. 13 Earthquake fire risk over the country on standard regionalmesh (the third-level area division) with the fire breakout
probability being assumed to be constant70

T. KATO, C. HONG, YALKUN. Y, M. YAMAGUCHI AND A. NATORI(a) Fire breakout probability (%)(b) Fire destruction probability (%)

Fig. 14 Trial calculation of earthquake fire risk in Tokai-HigashiNankai-Nankai Earthquake: Standard area mesh (The third-level area division)(a) Fire destruction probability (%): Standard area mesh
(The third-level area division)(b) Fire destrucion probability: For individual buildings(10)Fig. 15 Evaluation results for Tokyo (In-land earthquake in Tokyo)(a) Fatalistic collaboration unit against fire spread(Cluster)(b) Fire destruction probability

Fig. 16 Typical city area downtown Tokyo(10)The first factor is whether they can intuitively acknowledge therisk as their own problem. The other factor is whether they canrecognize the need to cooperate within cities or local communities.
The proposed method enables people to find their houses on
the map and recognize how earthquake fire risks affect them personally. They can recognize the likelihood of having fire damage
from the fire destruction probability of their houses and they only
need to estimate the occurrence probability of an earthquake.
In addition, showing clusters on the map will promote cooperative activities in cities and local communities. Figs. 16 (a) and 17(a) show the clusters with colors. When explaining to the public,

we use the expression fatalistic collaboration unit against fire
spread to refer to the cluster. From the cluster map, people would
not think I just need to make my house fire-resistant or I'm safein my house because it is fire-proof (or quasi-fire-resistant) , theywould instantly recognize the importance of disaster prevention of
the entire city or entire local community. They would also understand the directionality of the measures that are required such as
fire breakout prevention in a cluster or further division of clusters.
When we showed our results to some people, they found that thecluster extended over several local communities. They said, We
need to collaborate not only within our community but also with

INTEGRATED EARTHQUAKE FIRE RISK EVALUATION BASED ON SINGLE BUILDING FIRE PROBABILITY APPLICABLE TO ALL MAP SCALES(a) Fatalistic collaboration unit against fire spread(Cluster)71(b) Fire destruction probability

Fig. 17 Residential area uptown Tokyo(10)neighboring communities! . This clearly indicates the effectiveness of the proposed method.
8. SUMMARY AND PROBLEMS
The proposed method has the following main characteristics:
・ This is an integrated method that can handle from a single
building to nation-wide scale.
・ Unlike conventional methods using city indices or simulation
methods using mesh data, this method uses single building digital map data and can reflect the spatial characteristics of a city.
・ This method is appropriate for fire risk evaluation as it gives anabsolute value of fire destruction probability based on the fire
breakout probability.
・ Fire destruction probability is calculated for each building.
Hence the data is highly versatile and the results can bearranged for arbitrary area units such as administrative blockareas, meshes, city blocks, fire department control areas, etc.
No errors are expected in the data arrangement. Also, the data
can be easily converted to the number of fire destroyed buildings, burned areas, and others.
・ This method is effective for conveying risk information to citizens or of sharing risk among citizens if in clusters, the intermediate data created in the calculation process, are presented tothem as fatalistic collaboration units against fire spread .
The proposed method has the same advantages of conventional methods but minimizes the disadvantages and is feasible under
the current technological environment.
Due to the limited capacity of PCs, we used the same fire
spread limit distance of multiple-building fire to make clusters.
However, as computational power and memory increase, calculation accuracy will improve and enable us to define two-level clusters, i.e. the cluster defined for the process by which a single-building fire grows to a multiple-building fire and the cluster for theprocess after the multiple-building fire begins.
In the proposed method, caution may be required when making an interannual comparison of the earthquake fire risk. As thefire spread process is described with the fire spread limit distancemodel and evaluation results are affected by position errors ofbuilding polygons in digital maps, it is necessary to pay attention to
the continuity of the polygon data between new and old digitalmaps to be used for interannual comparison. In the map that weused in our system, buildings that are actually changed are added tothe map when it is revised. However, some maps, such as city
planning base maps prepared by the administration, are completely
revised once every few years. In these maps, building shapes are
sometimes modified in the revision even if the buildings are notactually changed. This may cause a change in the evaluation
results. When studying the risk over several years, it is hence necessary to make quantitative examination of the affect that errors
contained in maps have on the evaluation results.
ACKNOWLEDGMENT
We are grateful to M. Kamogawa at Glosis Japan, R.
Yoshizawa at Tokyo Fire Department (temporary researcher at the
Department of Engineering, University of Tokyo, around that time)
for their support of the research. We are also grateful to H.
Kamiya at MANU Institute for Urban Design and Architecture forprovision of information.
NOTE(1) There are many references, such as Refs. 7) and 8). (2)For example, even the simple algorithm that we developed requires
about 10 minutes for a single fire spread simulation of 100,000
buildings. (3) This is the case of the system described in Ref. 23).
(4) When this distance is too short, neighboring buildings may not
be included in the calculation, and when it is too long calculation is
too time-consuming. We looked for the most efficient setting bychanging the distance. (5) This is based on the data of Arakawaku, Tokyo in 1996. (6) The actual wind speed at the observation
point is converted by the following equation to the speed at 10 mheight from the ground:Vh Ê h ˆ=Á ˜
Vh0 Ë h0 ¯pHere, Vh and Vh0 represent the wind speed at the height h and h0 (m)respectively. We set h0 to 0 and the constant p to 1/7.
(7) This is based on calculation using a machine equipped with
3GHz Pentium4 and 1Gb Memory. (8) This is based on a trial calculation by the Non-Life Insurance Rating Organization of Japan.
(9) This was presented to a local community by Professor K.
Takano at Tohoku University of Art and Design, H. Kamiya at
MANU Institute for Urban Design and Architecture, and others.

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T. KATO, C. HONG, YALKUN. Y, M. YAMAGUCHI AND A. NATORIThe data used here is local government data. (10) Permission number Z06A-2601 of Zenrin Co., Ltd. (11) This study was part of theresearch (2002-2003, 2005) conducted by the Non-Life Insurance
Rating Organization of Japan. (Earthquake insurance research 6,
http://www.nliro.or.jp/disclosure/q_kenkyu/index.html)
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