Proceedings of Computational Engineering Conference

JSCES

Vol. 27, 2022 June

City-scale simulation of wooden house collapse prediction
using the ASI-Gauss Code
Munkhzaya Myagmarjav1), Mitsuteru Asai2), Hideyuki Otani3),
Kahori Iiyama4), Hitoshi Morikawa5), and Daigoro Isobe6)
1) Kyushu University, School of Engineering (Fukuoka-shi, Nishi-ku, Motooka 744, E-mail: m-zaya@doc.kyushu-u.ac.jp)
2) Kyushu University, Faculty of Engineering (Fukuoka-shi, Nishi-ku, Motooka 744, E-mail: asai@doc.kyushu-u.ac.jp)
3) RIKEN Center for Computational Science (Kobe-shi, Chuo-ku, Minatojima, Minamimachi 7-1-26, E-mail: h.o-tani@riken.jp)
4) Kajima Technical Research Institute (Chofu-shi, Tobitakyu 2-19-1, E-mail: iiyama@kajima.com)
5) Tokyo Institute of Technology, School of Environment and Society (Yokohama-shi, Midori-ku, Nagatsutacho 4259, E-mail:morika@enveng.titech.ac.jp)
6) University of Tsukuba, Faculty of Engineering, Information and Systems (Tsukuba-shi, Tennodai 1-1-1, E-mail:isobe@kz.tsukuba.ac.jp)
A large number of wooden houses collapsed in the 2011 off the Pacific coast of Tohoku earthquake andTsunami and the 2016 Kumamoto Earthquake. The large amount of debris from the collapsed houses not
only blocked the roads and hindered the immediate evacuation, but also caused delays in the recovery andreconstruction due to the time and cost required to remove the debris. For example, there is a high risk ofearthquakes and tsunamis of the same or greater magnitude in the Tokai and Tonankai regions, and it isimportant to assess in advance the total amount and spread of debris that could be generated in the eventof a major earthquake, and to prepare a recovery plan for post-disaster emergencies. The ASI-Gauss Code,which is a finite element method of beam elements that can analyze the progressive collapse of aframework structure, is used to predict the damage and collapse of houses caused by earthquakes. Here,in order to demonstrate the validity of the proposed technique, we attempted to reproduce the damage inthe Furukawa area of Osaki city during the 2011 off the Pacific coast of Tohoku Earthquake and compared
the results with damaged reports.
Key Words : ASI-Gauss Code, Wooden House Model, City Model, Seismic Response Analysis

1． INTRODUCTION

advance the total amount and spread of debris that could be

A large number of wooden houses collapsed in the 2011 offgenerated in the event of a major earthquake, and to prepare a

the Pacific coast of Tohoku Earthquake and Tsunami and therecovery plan for post-disaster emergencies. Based on the above

2016 Kumamoto Earthquake. The large amount of debris frombackground, this study aims to establish a series of tools forthe collapsed houses not only blocked the roads and hindered

predicting the damage and collapse of wooden houses caused by

the immediate evacuation, but also caused delays in theearthquakes using the ASI-Gauss method, which is a kind ofrecovery and reconstruction due to the time and cost required tofinite element method for progressive collapse analysis of frame

remove the debris. In other words, this hindered an effective

structures, by modeling the entire city based on GIS data

recovery process. In the future, there is a high risk ofincluding building information.

earthquakes and tsunamis of the same or greater magnitude in

In this study, estimation of seismic ground motions in the

the Tokai and Tonankai regions, and it is important to assess insurface layer using RO model, and earthquake damage

prediction tool combined with ASI-Gauss method for wooden
house of entire urban area and are developed. Lastly, we
attempted to reconstruct the damage in the Furukawa area of
Osaki City, Miyagi Prefecture, during the 2011 off the Pacificcoast of Tohoku Earthquake and confirmed its validity bycomparing it with damage reports.

2． METHODOLOGY

Fig-1. Timber house model.

ASI-Gauss method used in this study is a type of Finite
Element Method that uses Timoshenko beam elements for finite
deformation elastoplastic analysis. By adaptively shifting
numerical integration point during elastoplastic analysis, asingle member can be divided into two elements andelastoplastic analysis can be performed with high accuracy aswell as reducing the computational cost. Also, by modeling withbeam members, we can easily do member fracture and member

Fig-2. Unit

contact analysis. Plasticity is determined by substituting the

As shown in Fig-3, the skeleton curve is simplified as a three-cross-sectional forces at both ends of the element into the yield

linear model with two break points, and the inter-layer

function. In this study, Mx, My, N are bending moment of x, ydeformation angle shows elastic behavior up to 1/120 rad, withaxes and axial force respectively and defined as the yield

1/30 rad considered to be the fracture initiation point. All non-function shown in the following equation.

rigid floor elements, i.e. columns and brace elements, were2

𝑀𝑀𝑦𝑦
𝑀𝑀𝑥𝑥 2
𝑁𝑁 2
𝑓𝑓𝑦𝑦 = �� +�� +� � =1
𝑀𝑀𝑥𝑥0
𝑀𝑀𝑦𝑦0
𝑁𝑁0

assumed to be fully elastoplastic.
For setting the weight of each component, the weight per floor

Here, sub 0 indicates the total cross-sectional plasticity value

area for each representative construction age was referred towhen each cross-sectional force component acts alone on thefrom the "Japanese Building Disaster Prevention Association,member cross-section. In case of members that are considered

Seismic Retrofitting Support Centre designated by the Minister

as fractured, stiffness is set as 0, and the cross-sectional forcesof Land, Infrastructure, Transport and Tourism, 2012 Revised

stored in the element are instantly released in the next step. This

Edition of Seismic Diagnosis and Reinforcement Methods forallows the analysis of collapse phenomena.

Wooden Houses" shown in Table-1. The weight of eachcomponent (columns, beams, walls, and floors) was determined

3． ANALYSIS MODEL PREPARATION

by distributing the roof weight on the second floor between the

Fig-1 shows an example of modelling a wooden house. To

beam and floor components and the external and internal wall

simplify the modelling of houses of arbitrary shape, automaticweight between the column and wall components. Similarly, onmodelling was carried out by using the cube-shaped units shown

the ground floor, the floor weight and load carrying capacity

in Fig. 2. The unit consists of four elements - columns, walls,

were allocated to the beam and floor members, and the externalbeams, and floors - and each element was assigned an

and internal wall weight to the column and wall members.

appropriate physical property value. Here, the face members
such as walls and floors were modelled using beam elements,
and braces were installed to provide shear stiffness. The
stiffness and bearing capacity of each element is fitted toskeleton curve (see Fig-3), which shows the relationshipbetween layer shear forces and interlaminar deformation angles
based on the building standard for each construction age.

Building
Roof
Outer wall
Inner wall

Very heavy
2.40
1.20
0.45

Heavy
1.30
1.20
0.20

Light
0.95
0.75
0.20

Floor
Loading weight
Building standard year

0.60
0.60
1959

0.60
0.60
1981

0.60
0.60
2000

Table 1. Simplified weight table for houses (per floor area, kN/m2)

4.

SEISMIC MOTION INPUT

The input seismic motions were estimated by applying themethod of Morikawa et al. This method is one of the methods
for estimating the acceleration time history (incident waves) thatshould be input to the engineering base when the surface
acceleration time history at a certain point and the surfaceⒸ 2021 Google

ground properties immediately below the engineering base are
Fig-4. Aerial view of the Furukawa model

known.
The distribution of the maximum response acceleration of the
input earthquake motion is shown in Fig-3. The seismic motions

Area: 1.86 km x 1.69 km, number of buildings: 4,405, number

were evaluated at 451 sites and the house model was given theof elements: 2,172,546, number of nodes: 1,165,744. The entire

seismic motions evaluated at the nearest neighbor sites. As

city can be analyzed as a whole, but if contact between buildings

shown in the Fig-3, the maximum response acceleration tends

is not considered, the buildings are defined as independent

to be dominated by the NS component compared to the EW

problems, so the scale of area can be divided into approximately

component over the entire domain. Furthermore, the North-East

equivalent smaller areas that can be analyzed. In this study, it isand South-West regions show a tendency to have particularlyclassified into four sub-domains to improve the computationallarge NS components of acceleration, while the North-West is aefficiency. The computational environment used was the Kyoto

region where both acceleration components are small. The fact

University supercomputer system Camphor2, 1 node, 64 threads,

that damage to houses tended to be concentrated in the south-

with a real time of 20 s (number of analysis steps: 10,000). The

west and scattered even in the north-west, where the maximum

average time required for the four compartments was 65.91

acceleration is relatively small, suggests that the assessment ofhours, which means that a large-scale analysis of the entire city

earthquake damage to houses cannot be measured only by theis possible to be carried out within a few days.

maximum response acceleration.
(2) Construction ageb

In wooden houses, the construction age has a strong
correlation with the bearing capacity. In this study, model
bearing capacities according to three construction dates (1959,
1981 and 2000) are considered, and it is necessary to assign acorresponding bearing capacity to each model. However, it isoften difficult to obtain information on the date of construction,a(a) NS component

so some method of estimation had to be used. For this reason,(b) EW component

this study used GSI aerial photographs (taken between 1947 and2006) to estimate the approximate date of house completion by

Fig-3 Distribution of maximum response accelerationcomparing the condition of houses from several eras.
The procedure is outlined as follows: 1) the building center

5.

ANALYSIS CONDITION

coordinates, shape, area and number of floors are obtained from

(1) Target area and analysis environmentthe 2010 residential map data; 2) the building location is

The target city for this study is Furukawa, Osaki City, Miyagi

obtained from GSI aerial photograph data taken at five different

Prefecture. The area was the site of the 2011 Tohoku earthquake,times (1947, 1961, 1975, 1993 and 2006) and given thewhich caused damage to many wooden houses. The analysis

coordinates; 3) the building information from the older

model composed of beam elements (hereafter referred to as thephotographs is used as a reference and the new buildings

Furukawa model) is shown in Fig. 4.

obtained from the next photograph are assumed to have been
completed during that year of photography.

classification of the damage level into five levels (total
destruction, major partial destruction, partial destruction, partial
damage and no damage) was investigated according to theanalysis results of the ASI-Gauss method. For this purpose, thepercentage of damage was quantified from the ratio of thenumber of components judged to have yielded or fractured tothe total number of components
damage ratio =Blue: year 1959 Yellow: year 1981
Red: year 2000

Grey: Non-wooden houses

Fig-5. Estimated building standard date
For example, building that is absent from an aerial photographtaken in year X and present in a subsequent aerial photographtaken in year Y is judged to have been completed between X and
Y. The results of the estimation of the construction age given by
the above procedure are shown in Fig-5. Color in the diagram
indicates the date of building standard dates. However, models
with a large number of nodes and floor area larger than that of atypical wooden house are classified as non-wooden houses andgiven a robust load-bearing capacity. In terms of the distributionof construction ages, it is observed that there are many models
complying with the 1959 standards in the central part of theanalysis area, whereas there are many models complying with
the newer standards in the outer part of the analysis area.

Σ initial point = 2𝑁𝑁 + 1𝑛𝑛∑deduction = 1𝑁𝑁𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 + 2𝑁𝑁𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 + 0.5𝑛𝑛𝑦𝑦𝑦𝑦𝑦𝑦𝑙𝑙𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑+ 1𝑛𝑛𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

Here, the total number of columns is N and the total number ofbracing members is n. Based on the idea that the columns are
the most important members to make the house self-supporting
and the braces are the equivalent elements of the walls, which
are mainly expected to provide shear stiffness, the weight of thecolumns was set as twice that of the braces and initial point anddeduction were given. The deduction for fracture was set as
twice the yield, as the member releases all internal forces after
fracture, whereas it can retain the yield stress as a fully
elastoplastic state after yielding. Based on the above definitions,the damage ratio was set to 100% when all components had
broken, with higher ratios indicating more severe damage to thehouse. The level of damage to houses was determined into fivelevels: totally destroyed, majorly destroyed, partially destroyed,
partially damaged and undamaged.

6.

CITY-SCALE HOUSE COLLAPSE(3) Seismic setup
In this study, the acceleration waveforms created by themethod described in Chapter 4 were converted into
displacements and subjected to seismic analysis as forced
displacements at the base of the ground floor members.

PREDICTION SIMULATION
Using the analytical modelling procedures and methods
described up to this point, simulations were carried out topredict house collapses across the city.
1400

acceleration time histories using the linear acceleration method,

1200

The baseline was adjusted so that the velocity at the end of theduration was zero for the given acceleration time history to
avoid a monotonic increase in residual displacement after theseismic motion was applied.

損傷家屋の棟数

Displacement time histories were prepared by integrating theand velocity and displacement time histories were calculated.

Σ deduction× 100
Σ initial point

1000
800
600
400
200
0

1

1.1

1.2

1.25

1.3

1.4

1.5

1.6

実被害

モデル強度の増加割合(4) Calculation of the level of damage
In post-earthquake damage surveys, house damage levels areassessed using visual assessment criteria. In this study, in orderto objectively assess the damage to a house as much as possiblein accordance with the damage criteria in the field, an automatic

半壊

大規模半壊

全壊

Fig-6. Percentage increase in model strength andnumber of damaged housesprediction of house collapses in a city is proposed by combining
the ASI-Gauss method. The proposed simulation tool showed
good results in collapse analysis of various types of buildings.
The estimation of material properties was partly based onskeleton curves estimated from the results of destruction test on
houses consisting only of structural members, and there areconcerns that the model has lower stiffness than the actual
wooden houses, which includes cosmetic walls and finishes.
Accordingly, although the natural period of the wooden housemodel consisting of simple units was somewhat longer than thatof a typical wooden house, it was confirmed that the natural
period of each building standard model was sufficiently within
Fig-7. Analysis results with uniform waveform input

the practical range of values. Using the house models describedabove, an analysis model for the Furukawa area of Osaki City

The relationship between the percentage increase in material

was automatically generated from GIS data, and seismic

strength and the level of house damage is summarized in Fig-6.

analyses were carried out for each house with the earthquake

Although an increase in strength by a factor of about 1.50

ground motions of the Great East Japan Earthquake estimatedshowed good agreement when focusing on the number of allby the RO model. Models with stiffness and material strength

damaged houses, an increase in strength by a factor of about

identified from skeleton curves resulted in greater damage than

1.25 was equivalent to the actual damage when focusing only

actual damage. Therefore, by increasing only the materialon the number of houses that were totally destroyed. An increase

strength by a factor of 1.25 to 1.50, a realistic damage estimationof 1.25-1.50 times is also considered reasonable as a parameter

was achieved, demonstrating the potential of the developed tool.

for a real wooden house, including cosmetic walls and finishes.

Further comparisons with actual damage survey reports andOn the other hand, there is still room for improvement,

aerial photo data will be carried out to improve the accuracy ofespecially in simplified models for automatic house modelling,

the analysis and develop the tool into a more reliable tool.

which do not reflect detailed information about the house anddo not consider the effects of wall mass, finishes, post-

ACKNOWLEDGEMENTS: This work was supported byconstruction renovation and reinforcement, among others.

JSPS Grant number 20H02418, Joint Usage/Research Center

Next, in order to check the effects of different input seismic

for Interdisciplinary Large-scale Information Infrastructurescharacteristics, a simulation was also carried out in which the(jh210020-NAH, jh210037-NAH). In addition, part of thisobserved waveforms at JMA Furukawa were applied to all

research was supported by the general use of the researchhouses. The results are shown in Fig-7. There was almost no

computing system of the Research and Development Centre fordamage in the South-Central to South-West area, and damage

Information Infrastructure, Kyushu University, and by theoccurred almost exclusively to older houses of the construction

supercomputer at the Academic Media Centre, Kyoto University.

age. These results support the idea that the proper assessment of
surface ground motions amplified by the engineering bedrock isimportant for the prediction of house damage and that theseismic modelling procedure presented in Chapter 4 waseffective.

7.

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Structures - Numerical Codes and Applications, Elsevier,eBook ISBN:9780128130421, Paperback

CONCLUSION

In this study, seismic motion estimation in surface ground

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using the RO model is combined with the ASI-Gauss method to

戸建て住宅の DOD と 推定風速の概要－，平成 27 年度日

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soils using the RO model has so far been validated and gives

センター：2012 年改訂版 木造住宅の耐震診断と補 強方

reliable ground motions. A series of tools for simulating the法．
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Surface, Journal of Earthquake and Tsunami, 2021.
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