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Chapter 11
Post-earthquake Emergency Response
and Recovery Through City-Scale
Nonlinear Time-History Analysis
11.1 Introduction
Chapters 7,8, and 9of this monograph introduced the application of city-scale
nonlinear time-history analyses (THA) for earthquake disaster simulation and predic-
tion. Furthermore, the city-scale nonlinear THA can also be used as a reference for
emergency response and recovery after an earthquake, which is presented in this
chapter. Section 11.2 proposes a real-time earthquake damage assessment using
recorded ground motions and city-scale nonlinear THA, which can significantly
reduce the uncertainties of ground motion inputs. The proposed real-time earthquake
damage assessment method has been successfully used by the China Earthquake
Networks Center (CENC) in many earthquake events when the real-time ground
motions are available.
The city-scale nonlinear THA can not only simulate the damage of the mainshock
but also predict the regional seismic damage of buildings subjected to a sequence
of mainshock and aftershock. Consequently, Sect. 11.3 proposes a framework for
regional seismic damage prediction of buildings under the mainshock-aftershock
sequence, which provides a useful reference for earthquake emergency response and
scientific decision-making for earthquake disaster relief.
When lacking rational ground motion input, Sect. 11.4 proposes a framework for
near-real-time regional seismic loss estimation by taking advantage of the building
collapse scene of the disaster areas. The building collapse scene can be rapidly
identified through remote sensing image analysis. Consequently, the uncertainty of
ground motions can be reduced, and the loss estimation using the city-scale nonlinear
THA can be in close agreement with the actual loss.
Section 11.5 proposes a city-scale THA-driven building seismic resilience simu-
lation framework. Based on the city-scale nonlinear time–history analysis, together
with the component-level seismic damage assessment method of FEMA P-58 and the
repair simulation method of REDi, the proposed framework provides an insight into
© Science Press 2021
X. Lu and H. Guan, Earthquake Disaster Simulation of Civil Infrastructures,
https://doi.org/10.1007/978-981-15-9532-5_11
797
798 11 Post-earthquake Emergency Response and Recovery …
the community repair simulation with labor constraints. Accordingly, these can assist
with the seismic resilience evaluation of the built environment so as to ultimately
achieve a resilient community.
11.2 Real-Time Earthquake Damage Assessment Through
City-Scale Time-History Analysis
11.2.1 Research Background
An accurate and rapid assessment of seismic damage, economic loss, and post-
event repair time can provide an important reference for emergency rescue and post-
earthquake recovery. Experience gained from several major earthquakes in recent
years indicates that the assessment of building damage in an earthquake-stricken area
needs to be improved further. After an earthquake, communication in disaster areas
is delayed; the disaster site is usually chaotic, and there are not enough professionals
to evaluate building safety within a short time frame. Furthermore, rumors and fake
information on the internet may interfere with accurate seismic damage assessment.
Therefore, it is necessary to propose a scientific, objective, and timely method for
earthquake loss assessment.
To date, the near-real-time earthquake loss estimation tools primarily include
Prompt Assessment of Global Earthquakes for Response (PAGER), Global Disaster
Alert and Coordination System (GDACS), USGS-ShakeCast, the Istanbul Earth-
quake Rapid Response System, and the Rapid Response and Disaster Management
System in Yokohama, Japan, etc. (Erdik et al. 2011). These seismic loss estimation
systems generally comprise three parts: the ground motion intensity measure (IM),
building inventory and fragility, and direct economic losses and casualties. The
ground motion IM can be obtained directly from the real-time monitoring data of a
seismic network or calculated using ground motion prediction equations (GMPE).
The building inventory data can be determined using either a detailed building
database or macroscopic statistical data. The seismic damage to buildings can
be predicted using the damage probability matrix (DPM) method or the capacity
spectrum method. Economic loss and casualties are generally calculated using
empirical models.
However, the main problems existing in these systems are: (a) dynamic character-
istics of ground motions are not comprehensively considered; (b) the DPM method
is difficult to be applied in areas where historical earthquake data are lacking or
in quickly developed areas where there are large differences between the invento-
ries of current and historical buildings; (c) the capacity spectrum method cannot
easily represent the concentration of damage to different stories or the time-domain
properties of ground motions (e.g., the velocity impulse of ground motions); (d) the
earthquake loss prediction method relies on historical seismic damage data, and the
repair time cannot be provided in these systems.
11.2 Real-Time Earthquake Damage Assessment Through … 799
Consequently, this work proposes a real-time earthquake damage assessment
through city-scale time-history analysis (Lu et al. 2019). The actual ground motion
records obtained from seismic stations are input into the building models of the
earthquake-stricken area, and the nonlinear time-history analyses of these models
are subsequently performed. The seismic damage of the target region subjected
to this earthquake is evaluated according to the analysis results. An associated
program, named “Real-time Earthquake Damage Assessment through City-scale
Time-history analysis” (or “RED-ACT” for short), is developed. The application and
the advantages of the proposed method are demonstrated through actual earthquake
events.
11.2.2 Real-Time City-Scale Nonlinear Time-History
Analysis
11.2.2.1 Framework
The proposed framework to conduct a real-time city-scale time-history analysis
and loss assessment is illustrated in Fig. 11.1. The corresponding procedures are
as follows:
(1) Obtain real-time ground motion records from the seismic stations;
(2) Establish the building inventory database for the target region;
(3) Conduct a city-scale nonlinear time-history analysis to predict the seismic
damage of the target region; and
(4) Perform the regional seismic loss prediction to assess the seismic economic loss
and repair time of the target region.
Fig. 11.1 Framework for real-time city-scale time-history analysis and loss assessment
800 11 Post-earthquake Emergency Response and Recovery …
11.2.2.2 Real-Time Recorded Ground Motions
The ground motion records can fully describe the features of the ground motions
with no information loss. The densely distributed seismic stations and communica-
tion networks make it possible to obtain real-time ground motion records. After an
earthquake, the ground motion record near the epicenter can be quickly obtained
through the seismic stations and communication network, and information such as
the station’s latitude, longitude, and recording time can be collected simultaneously.
With the development of monitoring and data-transforming technology, the densely
distributed strong motion network will cover more regions, and the ground motion
data will be easier to access in a timely manner after an earthquake.
11.2.2.3 Building Inventory Database
Based on the Sixth National Population Census of China, this work constructs a
virtual building inventory database of cities in the mainland of China. Specifically,
according to the Sixth National Population Census, the number of buildings in the
target region classified by the number of stories, the structural type, and the year of
construction can be obtained. The buildings are divided into 33 categories according
to the number of stories, structural type, and year built, and the proportions of the 33
building types can be determined by solving the indefinite equations that describe
this problem. The building inventory database of each region can then be established
to serve the subsequent seismic damage prediction. Note that if the statistical data of
each building can be obtained for the target region, then these data can be directly
used to establish the analysis model. In addition to the cities in the mainland of China,
other building inventorydatabases for other regions (e.g., Japan and the United States)
are under construction. As a result, the proposed method can be further applied to
different regions once the corresponding ground motions and building inventory
become available.
11.2.2.4 City-Scale Nonlinear Time-History Analysis
The city-scale nonlinear time-history analysis (THA) method introduced in Chap. 7is
used to perform the seismic damage simulation for the target region. With outstanding
computational efficiency, this method can be used effectively for post-earthquake
emergency response. There exists an inherent uncertainty in the seismic performance
of buildings, which has been considered in this method by incorporating the para-
metric uncertainty of the building backbone curve (Lu et al. 2017b). Consequently,
the proposed method can provide not only the building responses using the median
value of the inter-story backbone curve parameters but also the responses with the
median value ±one standard deviation to account for the parametric uncertainty,
which is crucial for scientific decision-making.
11.2 Real-Time Earthquake Damage Assessment Through … 801
The nonlinear THA of the buildings in the target area is implemented using the
ground motions obtained from the seismic network. Subsequently, the time histories
of the seismic response of each story in every building can be obtained. According to
the engineering demand parameters (EDPs) and the damage criteria, the damage state
of each building in the region is determined, based on which the destructive power
of the ground motion to the target area is evaluated. To make full use of the real-time
earthquake ground motions obtained from the densely distributed seismic stations,
the destructive powers of ground motions obtained from different seismic stations can
be evaluated by inputting the ground motions one-by-one into the building models of
the target region. The distribution of building damage ratios under different station
records can be given subsequently, which provides an essential reference for post-
earthquake rescue work. For example, the destructive power of ground motions of
the August 13, 2018 M5.0 Yunnan Tonghai earthquake can be illustrated intuitively,
as shown in Fig. 11.2.
The human sensation of floor acceleration is highly important in the resilience
assessment of communities under moderate seismic actions. Based on the comfort
criteria (Simiu and Scanlan 1996) and floor acceleration computed by the nonlinear
THA, the human sensation of different ground motions can be obtained. The distri-
bution of human sensation under the ground motions of the November 26, 2018
Fig. 11.2 Destructive power of ground motions of the August 13, 2018 M5.0 Yunnan Tonghai
earthquake
802 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.3 Distribution of human sensation under the ground motions of the November 26, 2018
M6.2 Taiwan Strait earthquake
M6.2 Taiwan Strait earthquake is shown in Fig. 11.3. Although the damage ratio of
buildings under this earthquake is very low, the ratio of human uncomfortableness
is still fairly high.
11.2.2.5 Regional Seismic Loss Prediction and Resilience Assessment
Based on the damage state of each building, the seismic loss and even the repair time
can be predicted using the building-level or component-level seismic loss assessment
method (see Chap. 8of this monograph).
To facilitate the demand of real-time THA, cloud computing introduced in
Sect. 9.7 is adopted. By renting sufficient virtual computers from the cloud computing
platform, real-time analysis of a number of ground motions becomes technologically
and economically feasible.
11.2.3 Applications in Earthquake Emergency Response
11.2.3.1 Overview of the Applications
When an earthquake occurs, its ground motion will be collected in a timely manner
from the strong ground motion network. The real-time city-scale THA will be
conducted for the target region, and the analysis results will be fed back to the
11.2 Real-Time Earthquake Damage Assessment Through … 803
decision-makers and reported on the internet in a short time. A program is developed
named “Real-time Earthquake Damage Assessment using City-scale Time-history
analysis” (“RED-ACT” for short) to automatically implement the above workflow.
To date, the RED-ACT system has been applied to several earthquakes in China and
other countries around the world, as listed in Table 11.1.
11.2.3.2 M7.0 Jiuzhaigou Earthquake
The seismic damage assessment of the 2017 Jiuzhaigou earthquake is a typical appli-
cation case (Lu et al. 2017a). After the earthquake, several sets of ground motion
records were obtained from the seismic network, and the seismic damage prediction
of the target region was completed in 2 h (including the time for data checking and
report editing/publishing) by using the method proposed. Note that this assessment
was performed at the early stage of the “RED-ACT” system. Currently, with the
improvement of the software and hardware platform, the time required to perform a
similar assessment is reduced to a few minutes. The predicted damage of a typical
town and county in the Aba region under the ground motion of the Jiuzhaigou Baihe
station is shown in Fig. 11.4. The predicted results show that the buildings in the
disaster area may be damaged to some extent, but the proportion of collapse is
very small, which is consistent with the actual post-earthquake site investigations
(Dai et al. 2018). The results provide a useful reference for earthquake emergency
response and scientific decision-making of earthquake disaster relief.
11.2.3.3 Mw 7.0 Anchorage Earthquake
The seismic damage assessment of the 2018 Mw 7.0 Anchorage earthquake is another
typical application case (Lu 2018). On November 30, 2018 (local time), an Mw 7.0
earthquake occurred in Alaska, the United States. The epicenter was at 61.35 N,
150.06 W, with a depth of 40 km (StEER and EERI 2018). Six ground motions of
the Alaska earthquake event were recorded. The ground motions recorded at the
8047 station (61.189 N, 149.802 W, shown in Fig. 11.5) is a typical ground motion.
The peak ground accelerations (PGAs) of horizontal and vertical components of
the 8047 ground motion were 807.162 cm/s2and 367.243 cm/s2, respectively. The
ground motions are shown in Fig. 11.6.
Using the ground motions obtained from the strong motion networks and the
city-scale nonlinear THA, the “RED-ACT” system was used to predict the damage
ratio and human sensation distribution of the buildings near different stations in
lessthan1h(includingthetimefordatachecking and report editing/publishing),
as shown in Figs. 11.7 and 11.8. The post-earthquake investigation showed that
this Mw 7.0 earthquake produced less-than-expected damage to buildings, including
businesses, homes, and schools in downtown Anchorage, with most damage limited
to nonstructural elements and contents (StEER and EERI 2018), which is consistent
with the prediction given by the proposed method.
804 11 Post-earthquake Emergency Response and Recovery …
Table 11.1 Applications of the RED-ACT system
ID Earthquake name ID Earthquake name
12016–12-08 M6.2 Xinjiang Hutubi earthquake 18 2018–11-26 M6.2 Taiwan Strait earthquake
22016–12-18 M4.3 Shanxi Qingxu earthquake 19 2018–12-08 M4.5 Xinjiang Changji earthquake
32017–03-27 M5.1 Yunnan Yangbi earthquake 20 2018–12-16 M5.7 Sichuan Yibin earthquake
42017–08-08 M7.0 Sichuan Jiuzhaigou earthquake 21 2018–12-20 M5.2 Xinjiang Kizilsu earthquake
52017–09-30 M5.4 Sichuan Qingchuan earthquake 22 2019–01-03 M5.3 Sichuan Yibin earthquake
62018–02-06 M6.5 Taiwan Hualien earthquake 23 2019–01-07 M4.8 Xinjiang Jiashi earthquake
72018–02-12 M4.3 Hebei Yongqing earthquake 24 2016–04-16 M7.3 Japan Kumamoto earthquake
82018–05-28 M5.7 Jilin Songyuan earthquake 25 2016–08-24 M6.2 Italy earthquake
92018–08-13 M5.0 Yunnan Tonghai earthquake 26 2016–11-13 M8.0 New Zealand earthquake
10 2018–08-14 M5.0 Yunnan Tonghai earthquake 27 2017–09-20 M7.1 Mexico earthquake
11 2018–09-04 M5.5 Xinjiang Jiashi earthquake 28 2017–11-23 M7.8 Iraq earthquake
12 2018–09-08 M5.9 Yunnan Mojiang earthquake 29 2018–06-18 M6.1 Japan Osaka earthquake
13 2018–09-12 M5.3 Shanxi Ningqiang earthquake 30 2018–09-06 M6.9 Japan Hokkaido earthquake
14 2018–10-16 M5.4 Xinjiang Jinghe earthquake 31 2018–10-26 M5.4 Japan Hokkaido earthquake
15 2018–10-31 M5.1 Sichuan Xichang earthquake 32 2018–12-01 M7.0 Alaska earthquake
16 2018–11-04 M5.1 Xinjiang Atushi earthquake 33 2019–01-03 M6.2 Japan Kumamoto earthquake
17 2018–11-25 M5.1 Xinjiang Bole earthquake
11.2 Real-Time Earthquake Damage Assessment Through … 805
(a) Typical town in Aba region (b) Typical county in Aba region
0%
25%
50%
75%
100%
Damage probability distribution
None Slight Moderate Extensive Collapse
0%
25%
50%
75%
100%
Damage probability distribution
None Slight Moderate Extensive Collapse
Fig. 11.4 Seismic results of a typical town and county in the Aba region subjected the ground
motion from the Jiuzhaigou Baihe station
Fig. 11.5 Location of the 8047 ground motion station (CESMD 2019a)
11.2.4 Concluding Remarks
Based on the city-scale nonlinear THA and the regional seismic loss prediction, a
real-time city-scale time-history analysis method is proposed in this work. The main
conclusions are as follows:
806 11 Post-earthquake Emergency Response and Recovery …
(a) EW (b) NS
(c) UD
Fig. 11.6 Ground motion recorded by the 8047 station
(1) The uncertainty problem of ground motion input is solved properly with the
proposed method based on the real-time ground motion obtained from the
seismic stations;
(2) The amplitude, spectrum, and duration characteristics of ground motions as well
as the stiffness, strength, and deformation characteristics of different buildings
are fully considered in this method based on the nonlinear time-history analysis
method and MDOF models;
(3) Using the real-time city-scale nonlinear THA and the corresponding report
system, the assessment of the earthquake damage can be obtained shortly after
an earthquake event, which provides a timely and useful reference for scientific
decision-making for earthquake disaster relief.
11.3 Regional Seismic Damage Prediction of Buildings
Under a Mainshock–Aftershock Sequence
11.3.1 Overview
11.3.1.1 Research Background
Strong aftershocks frequently occur following a severe earthquake, such as the 1976
Tangshan earthquake, the 2008 Wenchuan earthquake, the 2015 Gorkha earthquake,
11.3 Regional Seismic Damage Prediction of Buildings … 807
(a) Global view
(b) Local view
Fig. 11.7 Damage ratio distribution of the buildings near different stations of the 2018 Mw 7.0
Anchorage earthquake
808 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.8 Distribution of human sensation under the ground motions of the 2018 Mw 7.0 Anchorage
earthquake
and the 2016 Central Italy earthquake (Varum et al. 2017; Wan et al. 2017; Zheng
et al. 2010; Valensise et al. 2017). Structures damaged by the mainshock cannot
be repaired in a short time, and the aftershocks can cause further damage to the
buildings that are already weakened by the mainshocks, resulting in a much more
severe consequence (e.g., the 2011 Christchurch Earthquake (Potter et al. 2015),
the 2015 Gorkha earthquake (Chen et al. 2017), and the 2016 Central Italy earth-
quake (Rinaldin and Amadio 2018)). Therefore, damage of buildings subjected to a
mainshock–aftershock (MS–AS) sequence must be considered.
To date, many researchers have investigated the aftershock effects on different
types of buildings (e.g., reinforced concrete (RC) frames (Hatzivassiliou and
Hatzigeorgiou 2015; Hosseinpour and Abdelnaby 2017), wood frames (Goda and
Salami 2014), steel frames (Ruiz-García and Negrete-Manriquez 2011), RC shear
wall–frame structures (Jamnani et al. 2018), etc.). In addition to the damage predic-
tion for individual buildings, the aftershock-induced damage prediction of the build-
ings on a regional scale is also important for post-earthquake decision-making.
However, no satisfactory solution is currently available for the regional damage
prediction of buildings under an MS–AS sequence.
11.3.1.2 Challenges for Regional Seismic Damage Prediction
of Buildings Under an MS–AS Sequence
To realize the regional seismic damage prediction of buildings under an MS–AS
sequence, the following three key challenges must be addressed:
11.3 Regional Seismic Damage Prediction of Buildings … 809
(1) A regional seismic damage prediction method that can consider the effect of an
aftershock.
The existing regional seismic damage prediction methods primarily include:
(a) the damage probability matrix (DPM) method (ATC-13 1985), (b) the
capacity spectrum method (CSM) (FEMA 2012), and (c) the time-history anal-
ysis (THA)-based method (Hori et al. 2018; Lu and Guan 2017).Basedonthe
statistical damage of different types of structures in previous earthquake events,
the DPM method has been widely used for regional seismic damage predic-
tion (Onur et al. 2006). However, the DMP method cannot satisfy the demand
for damage prediction subjected to the MS–AS sequences owing to the limited
historical data of building damage under the MS–AS sequence. The CSM was
developed based on the pushover analyses of single-degree-of-freedom building
models. Although damage accumulation can be considered in the pushover anal-
ysis (Polese et al. 2013), the influence of higher-order vibration modes and some
characteristics of the ground motions (e.g., different durations or velocity pulses)
cannot be considered easily using the CSM (Lu et al. 2014).
In Chap. 7of this monograph, the city-scale nonlinear THA has been proposed,
which can satisfactorily consider the characteristics of different ground motions
and buildings. Particularly, this method can adopt the MS–AS sequence as the
ground motion input to the building models for the THA, enabling the predic-
tion of the regional seismic damage of buildings under the MS–AS sequence.
However, to-date no existing work can be found in the literature regarding the
application of the city-scale nonlinear THA for the regional damage predictions
of buildings under the MS–AS sequence.
(2) Validating the accuracy of the adopted method subjected to the MS–AS sequence
It is critical to ensure the accuracy and reliability of the seismic damage predic-
tion method of buildings. The city-scale nonlinear THA has been validated by
comparing the simulation results with the actual seismic response, experimental
results, and a large number of numerical results. Theoretically, this method can
be applied to the MS–AS analysis of buildings, but further validation of the
accuracy of this method is still required.
The Center for Engineering Strong Motion Data (CESMD) (Haddadi et al. 2012)
provides a large number of valuable actual seismic response data of buildings
under multiple earthquakes, in addition to the building inventories required for
the parameter determination of the MDOF models of the city-scale nonlinear
THA. Meanwhile, many existing studies (Ruiz-García et al. 2018; Ruiz-García
and Negrete-Manriquez 2011; Hatzivassiliou and Hatzigeorgiou 2015)have
provided numerical response data of individual buildings under the MS–AS
sequence, which can be used for the validation of the city-scale nonlinear THA.
(3) The MS–AS sequence generation method.
The MS–AS sequence is required as the input of the MDOF models for the
nonlinear THA of buildings. Thus, a rational MS–AS sequence generation method is
the foundation for the regional seismic damage prediction of the buildings. Currently,
the MS–AS sequence generation method primarily includes:
810 11 Post-earthquake Emergency Response and Recovery …
(a) As-recorded MS–AS sequences (Hatzivassiliou and Hatzigeorgiou
2015; Ruiz-García and Negrete-Manriquez 2011; Zhai et al. 2016,2014).
However, owing to the large differences between the MS–AS mechanisms
of different earthquakes and the limited as-recorded MS–AS sequence, this
method is not suitable for the seismic damage prediction of buildings under
different MS–AS scenarios.
(b) Artificially generated MS–AS sequence. The simplest method to artificially
generate an MS–AS sequence is to repeat the mainshock ground motion
with scaled peak ground acceleration (PGA) as the aftershock ground motion
(Amadio et al. 2003; Fragiacomo et al. 2004; Hatzigeorgiou and Beskos 2009).
The PGA of the generated aftershock ground motion is determined through
the historic MS–AS sequence data regression. However, owing to the signif-
icant magnitude difference of the mainshock and aftershock, the entire time
history of an aftershock can hardly be simulated with the scaled mainshock
ground motions. Thus, a more rational solution is to generate the aftershock
ground motions considering more key parameters (e.g., earthquake magnitude,
response spectrum, PGA, rupture distance, site condition, etc.) in addition to the
PGA. Previous studies have proposed various models considering the acceler-
ation spectrum (Li and Ellingwood 2007), magnitude, PGA (Goda and Taylor
2012), epicenter distance, and site conditions (Goda 2012). However, further,
improvement is still required to encompass additional key parameters in the
model.
11.3.1.3 Overview of This Study
In this work, a framework for predicting the regional seismic damage of buildings
under the MS–AS sequence is proposed aiming at the abovementioned three chal-
lenges (Lu et al. 2020). Specifically, the city-scale nonlinear THA is adopted to imple-
ment the building seismic damage subjected to the MS–AS sequences. The simula-
tion results are validated through the comparison of as-recorded seismic responses
of buildings and simulated building responses in published literature. An MS–AS
sequence generated method is proposed herein, which covers additional key param-
eters (e.g., amplification, spectrum, duration, magnitude, and site condition). Thus,
various MS–AS sequences can be generated using the proposed method. Subse-
quently, the scenarios of buildings on a regional scale subjected to different MS–AS
sequences can be predicted. Finally, the Longtoushan Town that was damaged during
the Ludian Earthquake was used as a case study to predict the building damage
subjected to different MS–AS sequences, for illustrating detailed procedures and
advantages of the proposed framework.
11.3 Regional Seismic Damage Prediction of Buildings … 811
11.3.2 Prediction Methodology
11.3.2.1 The Proposed Framework
The proposed framework for predicting the regional seismic damage of buildings
under the MS–AS sequence is illustrated in Fig. 11.9. The process consists of five
steps:
(1) After an earthquake, the ground motion record of the mainshock near the
epicenter can be obtained quickly through the densely distributed strong-motion
stations, and information such as the magnitude, station location, and fault
parameters can be collected simultaneously.
(2) Allowing for the uncertainty of the time, location, and magnitude of the
aftershocks, a series of aftershock scenarios assuming different magnitudes,
locations, and fault parameters are generated.
(3) Based on the generated aftershock scenarios, the amplitude, response spec-
trum, and duration of the aftershocks are estimated using the proposed MS–AS
sequence generation method.
(4) The ground motions are selected from the NGA-West2 ground motion database
(Ancheta et al. 2014) and are used for the aftershock. The selected ground
motions have similar magnitude, amplification, spectrum, duration, and site
condition as the target aftershock.
(5) The ground motions of the MS–AS sequences are generated using the recorded
mainshock ground motions and the predicted aftershock ground motions. The
Fig. 11.9 Framework for predicting the regional seismic damage of buildings under the MS–AS
sequence
812 11 Post-earthquake Emergency Response and Recovery …
city-scale nonlinear THA is implemented using the ground motions of the MS–
AS sequences and the building inventory of the target region. The regional
seismic damage of the buildings subjected to the MS–AS sequences can be
predicted.
11.3.2.2 Validation of the City-Scale Nonlinear THA Subjected
to MS–AS Sequence
In this section, the accuracy and reliability of the city-scale nonlinear THA subjected
to an MS–AS sequence is validated with the as-recorded seismic responses of
buildings and the simulation results obtained from the published literature.
(1) Comparison with the As-Recorded Seismic Responses of Buildings
The as-recorded seismic responses of buildings under the MS–AS sequence in the
CESMD database (Haddadi et al. 2012) were collected to validate the city-scale
nonlinear THA. The parameters of the MDOF model of each building were deter-
mined using the parameter determination method based on the building inventories
(see Chap. 7). The responses of the buildings under the MS–AS sequence were
calculated by inputting the as-recorded ground motions to the MDOF models. The
details of the buildings and the MS–AS sequences are listed in Table 11.2. The struc-
tural types are classified based on the HAZUS (FEMA 2012) building classes. The
results are compared with the actual responses obtained from the CESMD database,
as shown in Fig. 11.10. A typical comparison of roof displacement histories for
Building #3 in Table 11.2 is shown in Fig. 11.11. It is evident that the simulation
results agree well with the actual observations.
(2) Comparison with the Simulation Results in the Published Literature
To further validate the reliability of the MDOF models in predicting the seismic
responses of buildings under the MS–AS sequence, the results of the MDOF models
are compared with the simulation results of buildings provided in the published liter-
ature. Eight sets of comparison results are given, as shown in Fig. 11.12, in which
the x-axis and y-axis are the inter-story drift ratios (IDRs) calculated by the MDOF
models and those provided in the published literature, respectively. The informa-
tion about the buildings and the MS–AS sequences is listed in Table 11.3. Further
details can be referred to as the corresponding literature. Typical comparisons for
the buildings with IDs 1, 2, and 7 are shown in Fig. 11.13. The maximum floor
displacements of a three-story RC frame with IDs 9 and 10 in Table 11.3, under the
MS–AS sequence and the mainshock, are further compared, as shown in Fig. 11.14.
It is evident that the simulation results of the MDOF models agree well with the
results provided in the published literature.
These comparisons demonstrate that the city-scale nonlinear THA based on the
MDOF models can accurately predict the building responses subjected to the MS–AS
sequences.
11.3 Regional Seismic Damage Prediction of Buildings … 813
Table 11.2 Information of buildings and MS–AS
ID Building name Mainshock
(Mw)
Aftershock
(Mw)
Num. of
stories
Structural
type
Year
built
1Bishop 2-story Office
Bldg
M4.8 Big Pine
Earthquake of
16 Feb 2016
M4.3 Big Pine
Earthquake of
16 Feb 2016
2S1L 1976
2Oakland 11-story
Residential Bldg
M4.0 Berkeley
Earthquake of
20 Oct 2011
M3.8 Berkeley
Earthquake of
20 Oct 2011
11 C2H 1972
3Walnut Creek 10-story
Commercial Bldg
M5.9
Livermore
Earthquake of
24 Jan 1980
M5.8
Livermore
Earthquake of
26 Jan 1980
10 C2H 1970
4Walnut Creek 10-story
Commercial Bldg
M4.0 Berkeley
Earthquake of
20 Oct 2011
M3.8 Berkeley
Earthquake of
20 Oct 2011
10 C2H 1970
5Fortuna
1-Story-Supermarket
Building
M7.1 Petrolia
Earthquake of
25 Apr 1992
M6.5 Petrolia
Aftershock 1
of 26 Apr 1992
1RM1L 1979
6Oakland 24-story
Residential Bldg
M4.0 Berkeley
Earthquake of
20 Oct 2011
M3.8 Berkeley
Earthquake of
20 Oct 2011
24 C2H 1964
7 Berkeley 2-story
Hospital
M4.0 Berkeley
Earthquake of
20 Oct 2011
M3.8 Berkeley
Earthquake of
20 Oct 2011
2S2L 1984
8Piedmont 3-story
School Office Bldg
M4.0 Berkeley
Earthquake of
20 Oct 2011
M3.8 Berkeley
Earthquake of
20 Oct 2011
3C2L 1973
9Oakland 3-story
Commercial Bldg
M4.0 Berkeley
Earthquake of
20 Oct 2011
M3.8 Berkeley
Earthquake of
20 Oct 2011
3S5L 1972
10 San Francisco-6-story
Govt Office Bldg
M4.0 Berkeley
Earthquake of
20 Oct 2011
M3.8 Berkeley
Earthquake of
20 Oct 2011
6S5M 1987
11.3.3 The MS–AS Sequence Generation Method
To determine the suitable ground motions for the MS–AS sequence analysis, an
MS–AS sequence generation method is proposed herein.
(1) Determination of the Amplitude and Response Spectrum of Aftershock
Using the MS–AS paired records at the same station obtained from the NGA-West2
database, Kim and Shin (2017) proposed an empirical model to estimate the intensity
measures of the aftershock. This model is adopted herein to determine the amplitude
and spectral accelerations of the aftershock, which is shown in Eqs. (11.1)–(11.4):
814 11 Post-earthquake Emergency Response and Recovery …
0%
20%
40%
60%
80%
100%
120%
140%
0246810
Mainshock Aftershock
Max. roof disp. (MDOF/As-recorded)
Build i ng ID
Fig. 11.10 Comparison between the as-recorded seismic responses and the results calculated by
the MDOF models
Fig. 11.11 Comparison of roof displacement histories for Building #3
InYAS
YMS =fmag +fdist +fsite (11.1)
fmag =c0+c1(MAS/MMS )MAS/MMS ≥0.75
c2+c3(MAS/MMS )MAS/MMS <0.75 (11.2)
fdistc4+c5InRAS
rup
RMS
rup 1−MAS
MMS (11.3)
fsite =(c6In(Vs30))1−MAS
MMS (11.4)
11.3 Regional Seismic Damage Prediction of Buildings … 815
Fig. 11.12 Comparison of
IDRs provided in the
literature and calculated by
the MDOF model
0
0.003
0.006
0.009
0.012
0.015
0 0.003 0.006 0.009 0.012 0.015
IDRs provided in the literature
IDRs calculated by the MDOF model
ID1 ID2 ID3
ID4 ID5 ID6
ID7 ID8
Table 11.3 Information of buildings and the MS–AS sequence selected from the literature
ID Num. of stories Structural type Information of MS–AS References
120 Steel frame 2010/2011Canterbury
earthquakes
Ruiz-García et al. (2018)
2 3 Steel frame 1980 Mammoth Lakes
earthquakes
3 9 Steel frame 1980 Mammoth Lakes
earthquakes
4 3 Steel frame 2011 Tohoku earthquakes
5 9 Steel frame 2011 Tohoku earthquakes
6 4 Steel frame 1980 Mammoth Lakes
earthquakes
Ruiz-García and
Negrete-Manriquez (2011)
7 8 Steel frame 1980 Mammoth Lakes
earthquakes
812 Steel frame 1980 Mammoth Lakes
earthquakes
9 3 RC frame Imperial Valley
earthquakes (MS-AS)
Hatzivassiliou and
Hatzigeorgiou (2015)
10 3RC frame Imperial Valley earthquake
(Mainshock)
where Yrepresents a ground motion intensity measure (e.g., PGA, peak ground
velocity (PGV), and 5% damped pseudo-spectral accelerations (PSAs)). It is note-
worthy that these ground motion intensity measures are the averages of two hori-
zontal ground motion records referred to as RotD50—the 50th percentile of the two
816 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.13 Typical comparisons of IDRs provided in the literature and calculated by the MDOF
model
Fig. 11.14 Comparison of responses for the RC frame under the MS–AS sequence and mainshock
measures overall non-redundant rotation angles (Kim and Shin 2017). The super-
scripts, AS and MS, denote aftershock and mainshock, respectively; fmag,fdist, and
fsite represent the functions for the magnitude ratio, distance ratio, and site condition,
as expressed in Eqs. (11.2)–(11.4); M,Rrup, and VS30 are the moment magnitude, the
closest distance from the fault rupture, and the time-averaged shear-wave velocities
for the top 30-m soil deposits, respectively; c0to c6are the regression coefficients.
The details of the model can be referred to as Kim and Shin (2017). Two sets of PSAs
computed by this model are compared with the as-recorded MS–AS sequences (Goda
and Taylor 2012) to validate the accuracy, as shown in Fig. 11.15. The simulation
results agree well with the as-recorded PSAs.
11.3 Regional Seismic Damage Prediction of Buildings … 817
Fig. 11.15 Comparison between the as-recorded PSAs and simulation results
(2) Comparison with the simulation results in the published literature
Duration is a key parameter to describe the features of a ground motion. A large
number of definitions of ground motion duration exist in the literature (Bommer
and Martínez-Pereira 1999), and the widely used significant duration (Du and Wang
2017) is adopted herein.
The empirical equations to predict the significant duration proposed by Bommer
et al. (2009) based on the magnitude, depth to the top of rupture, and shear-wave
velocity is used to determine the significant duration of an aftershock. Based on the
NGA-West ground motion database (Chiou et al. 2008), the regression model for
predicting the significant duration is given in Eq. (11.5):
In Ds=c0+m1Mw+(r1+r2Mw)InR2
rup +h2
1+v1In(Vs30)(11.5)
where DSis the significant duration, and the typically used DS5-95 (the time interval
between 5–95% of the Arias intensity) was adopted in this work; Mw,Rrup, and VS30
are the moment magnitude, the closest distance from the fault rupture, and the time-
averaged shear-wave velocities for the top 30-m soil deposits, respectively; Ztor is
the depth to the top of the rupture; c0,m1,r1,r2,h1,v1, and z1are the regression
coefficients. The details of the regression model can be referred to Bommer et al.
(2009).
(3) Selection of Ground Motion to Generate the MS–AS Sequence
After the amplitude, response spectrum, and duration of the aftershock are deter-
mined, the ground motions with these parameters close to the target aftershock can
be selected as the aftershock ground motions. The selection of ground motion can
be implemented in the NGA-West2 ground motion database (Ancheta et al. 2014)
using its online ground motion selection tool (PEER 2019). The MS–AS sequence
can be generated using the proposed method that provides the input ground motion
818 11 Post-earthquake Emergency Response and Recovery …
Table 11.4 Information of
the mainshock and aftershock
of the 2011 Berkeley
earthquake
Magnitude MwLocation Focal depth
(km)
Mainshock 4.0 37.86 N,
122.25 W
8.0
Aftershock 3.8 37.87 N,
122.25 W
9.6
for the regional seismic damage prediction of buildings under the MS–AS sequence.
Multiple sets of ground motion records can be selected as the aftershock for each
analysis, through which the uncertainty caused by the input ground motion can be
represented. The computational efficiency of the MDOF models adopted in this work
can easily handle the computational cost owing to the multiple ground motion inputs.
(4) A Real MS–AS Scenario to Validate the MS–AS Sequence Generation
Method
On October 20, 2011, an Mw4.0 earthquake struck Berkeley, CA. Approximately five
hours later, an Mw3.8 earthquake struck Berkeley again, which is considered as the
aftershock of the first earthquake (Wooddell and Abrahamson 2014). This real MS–
AS scenario (namely the 2011 Berkeley M4.0-M3.8 earthquake (CESMD 2019b,
c), as listed in Table 11.2) is selected to validate the proposed MS–AS sequence
generation method.
(a) First, the basic information of the mainshock and aftershock can be obtained
easily, as listed in Table 11.4. The ground motions and structural seismic
responses of these two earthquakes were recorded on an 11-story building
(namely, the ORB station). The ground motion records are shown in Fig. 11.16.
(b) With the basic information of the aftershock, the estimated significant duration
DS5-95 of the aftershock at this station is 3.08 s using Eq. (11.5). The DS5-95 of
the actual aftershock ground motion record is 2.66 s. The error of DS5-95 given
by Eq. (11.5) is 15.8%.
Fig. 11.16 Ground motions recorded at ORB station
11.3 Regional Seismic Damage Prediction of Buildings … 819
(c) By inputting the basic information of the MS–AS sequence to Eqs. (11.1)–
(11.4), the response spectrum of the aftershock at the ORB station can be
estimated and is close to the response spectrum of the actual ground motion
record, as is evident in Fig. 11.17.
(d) After these key parameters of the aftershock are determined, the ground motions
of the aftershock can be selected from the NGA-West2 database. Fifteen ground
motion sets are selected, as shown in Fig. 11.18.
Fig. 11.17 Comparison between the predicted and actual response spectrum of the ground motion
recorded at the ORB station
Fig. 11.18 Target response spectrum and the response spectrum of the selected ground motions
820 11 Post-earthquake Emergency Response and Recovery …
(e) The ground motion of the mainshock and aftershock are linked together to
generate the MS–AS sequences, and a sufficiently long time interval (greater
than 20 s) with an acceleration equaling 0 is added between the mainshock and
aftershock to ensure that the structure remains static before being subjected to
the aftershock. By inputting the generated and actual MS–AS sequence to the
MDOF model of this building, the structural seismic responses can be obtained.
The error between the average maximum roof displacements calculated using
the 15 MS–AS sequence sets and the maximum roof displacement calculated
using the actual MS–AS sequence is 11.54%. The validation results proof the
reliability of the proposed MS–AS sequence generation method.
11.3.4 Case Study: Seismic Damage Prediction of Buildings
at the Longtoushan Town Damaged in the Ludian
Earthquake
The buildings in the Longtoushan Town damaged in the 2014 Ludian Earthquake are
selected to perform a case study to illustrate the detailed procedures and advantages
of the proposed regional seismic damage prediction of buildings under the MS–AS
sequence.
(1) First, four aftershock scenarios are generated as a demonstration. The basic
information of the mainshock and the generated aftershocks are listed in Table
11.5. The mainshock ground motions recorded from the Longtoushan Town are
given in Fig. 11.19.
(2) With the basic information of the aftershock, the significant duration DS5-95 for
each aftershock is estimated using Eq. (11.5), as listed in Table 11.5.
(3) By inputting the basic information of the MS–AS to Eqs. (11.1)–(11.4), the
response spectrum for each generated aftershock can be estimated, as shown in
Fig. 11.20.
(4) After the determination of those key parameters of the aftershocks, the ground
motions of the aftershocks can be selected from the NGA-West2 database.
Twenty ground motions sets are selected for each aftershock scenario.
Table 11.5 Information of mainshock and aftershocks
Magnitude (Mw) Rupture distance
(km)
Focal depth (km) Significant duration
DS5-95 (s)
Mainshock 6.1 14.9 12.0 –
Aftershock 1 6.1 14.9 12.0 5.55
Aftershock 2 5.5 14.9 12.0 4.57
Aftershock 3 5.0 14.9 12.0 3.73
Aftershock 4 5.5 13.0 12.0 4.28
11.3 Regional Seismic Damage Prediction of Buildings … 821
(a) EW direction (b) NS direction
-10
-5
0
5
10
0 5 10 15 20
Acceleration (m/s
2
)
Time (s)
-10
-5
0
5
10
0 5 10 15 20
Acceleration (m/s
2
)
Time (s)
Fig. 11.19 Ground motions recorded at Longtoushan Town station
Fig. 11.20 Response spectrums of different aftershocks
(5) The ground motions of the mainshock and aftershock are linked together to
generate the MS–AS sequences, and a sufficiently long time interval (greater
than 20 s) with an acceleration equaling 0 is added to ensure that the struc-
ture remains static before being subjected to the aftershock. By inputting the
generated MS–AS sequences to each building, the regional seismic damage
of buildings subjected to the MS–AS sequences can be predicted. The results
under the mainshock and different MS–AS scenarios are compared as shown in
Fig. 11.21. For each MS–AS scenario, the average damage ratio of 20 ground
motion sets is given in Fig. 11.21a. It is noteworthy that only two damage states,
namely the “extensive damage” and “complete damage,” were encountered in
this case study. The standard deviations of the “complete damage” ratio under
different scenarios can also be given, as shown in Fig. 11.21b. As shown in
Fig. 11.21, when the magnitude of the aftershock decreases, its impact on the
building decreases simultaneously.
822 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.21 Seismic damage results of buildings for different earthquake scenarios
The structural responses of individual buildings under different MS–AS scenarios
can also be obtained using the proposed framework. For example, the maximum
inter-story drift ratio and damage states of two buildings (namely, Building_1 and
Building_2) in Longtoushan Town under different MS–AS scenarios are listed in
Table 11.6, which clearly demonstrate the consequence of different aftershocks to
the two buildings.
The predicted regional seismic damage of the buildings under different MS–AS
scenarios can provide a useful reference for earthquake emergency response and
decision-making in earthquake disaster relief. For example, according to Table 11.5
and Fig. 11.21, the following conclusions can be drawn: When an aftershock with
a magnitude of less than 5.0 occurs, no more additional damage will occur in the
buildings in the earthquake-stricken area, and the existing disaster relief plan can be
undertaken continually. In contrast, an aftershock with a magnitude of greater than
5.5 will cause more seismic damages to the buildings, and the rescue forces and
supplies should be increased correspondingly according to the additional damages
caused by the aftershock.
It is noteworthy that only 70 s are required to calculate an MS–AS scenario (with
Intel Xeon E5 2630 @2.40 GHz and 64 GB RAM), indicating a high computational
efficiency. Consequently, the regional seismic damage prediction of buildings under
Table 11.6 Maximum inter-story drift ratio and damage state of typical buildings
Structural
type
Num.
of
stories
Mainshock MS–AS1 MS–AS2 MS–AS3 MS–AS4
Building_1 RM2L 30.0206 0.0474 0.0231 0.0206 0.0232
Extensive Complete Extensive Extensive Extensive
Building_2 RM2L 20.0203 0.0452 0.0226 0.0203 0.0227
Extensive Complete Extensive Extensive Extensive
11.3 Regional Seismic Damage Prediction of Buildings … 823
the MS–AS sequence proposed in this work can satisfy the requirement of post-
earthquake emergency response. After an earthquake, a variety of MS–AS scenarios
can be quickly constructed and the corresponding seismic damage of buildings can
be obtained. This in turn offers assistance to earthquake emergency response efforts
and decision-makings of earthquake disaster relief.
11.3.5 Concluding Remarks
A framework for regional seismic damage prediction of buildings under the MS–AS
sequence was proposed herein. The city-scale nonlinear THA was adopted to simulate
the regional seismic damage of buildings under the MS–AS sequence. The accuracy
and reliability of the city-scale nonlinear THA was validated with as-recorded seismic
responses of buildings and simulation results in the published literature. An MS–AS
sequence generation method was proposed to provide the input ground motion by
determining the key parameters (i.e., amplitude, response spectrum, duration) of the
aftershock from the statistic data and selecting ground motions matching the key
parameters with the target aftershock. Based on this work, the following conclusions
can be drawn:
(1) The regional seismic damage of buildings under the MS–AS sequence could be
predicted reasonably and accurately using the city-scale nonlinear THA.
(2) The MS–AS sequence could be generated reasonably using the proposed MS–
AS sequence generation method.
(3) The regional seismic damage of buildings under different MS–AS scenarios
could be obtained efficiently using the proposed framework to provide a useful
reference for the earthquake emergency response and scientific decision-making
of earthquake disaster relief.
11.4 Improving the Accuracy of Near-Real-Time Seismic
Loss Estimation Using Post-earthquake Remote
Sensing Images
11.4.1 Overview
Rapid and accurate estimation of the building seismic loss is of great value to the
development of rational disaster relief and reconstruction plan. Existing methods to
estimate building seismic loss after an earthquake mainly include those: (1) through
site investigation (Masi et al. 2016); (2) using seismic loss estimation models (Erdik
et al. 2011; Jaiswal and Wald 2011); and (3) using remote sensing image data (Dong
and Shan 2013). Method (1) is relatively most accurate yet time-consuming. Site
investigation often takes weeks or even months and very labor-intensive. Hence this
824 11 Post-earthquake Emergency Response and Recovery …
method cannot adapt to the needs of timely post-earthquake loss assessment. Methods
(2) and (3), on the other hand, are much more time-efficient, hence have been widely
used in rapid earthquake loss assessment (Yeh et al. 2006; Vu and Ban 2010).
The loss estimation models (i.e., Method (2)) can be used for estimating building
seismic loss of a large area, in particular. Given correct seismic inputs and building
fragility models, the loss estimation models can take account of the influence of
different damage states (e.g., slight, moderate, extensive and collapse) on the building
seismic loss. However, the rationality of the loss estimation models depends largely
on the quality of the input parameters (i.e., building information and ground motion).
For example, for the THA-based regional seismic loss estimation method, if there
happens to be no seismic station near the disaster area, the appropriate selection of
ground motion input should be carefully considered.
By using satellite or unmanned aerial vehicle (UAV), remote sensing images of
the disaster area can be obtained soon after an earthquake. The collapsed and non-
collapsed buildings can then be identified by analyzing the images (Gusella et al.
2005; Ehrlich et al. 2009), so as to rapidly identify the building collapse scene
of the disaster area. Nevertheless, it is difficult to identify the damage inside the
buildings from the available images, resulting in an underestimation of the seismic
loss (Rathje and Adams 2008). Although quite a few studies attempted to recognize
more refined damage states using aerial images, so far, the accuracy of identification
remains relatively low. For example, studies show that the accuracy of identifying
“extensively damaged” buildings is merely 20~30% (Yamazaki et al. 2005; Rathje
and Adams 2008). Therefore, to date identifying the collapse status of a building is
technically more mature and reliable than identifying refined damage states.
Overall, using the THA-based regional seismic loss estimation method, the
seismic loss of buildings with different damage states can be obtained easily, but
the reliability of the estimated loss is largely affected by the quality of the input
parameters. When lacking proper ground motion input, the accuracy of the estima-
tion can be significantly reduced. On the other hand, remote sensing image analysis
is able to reliably identify the collapsed buildings in a timely manner, but the esti-
mation accuracy for non-collapsed buildings is relatively low. Therefore, it is logical
to combine the advantages of the THA-based method and the remote sensing image
analysis techniques so as to improve the accuracy and reliability of the loss estima-
tion. To achieve this objective, a possible solution is proposed herein: When lacking
rational ground motions as input, a large quantity of (e.g., thousands of) ground
motions with different intensities and time histories are selected as an input, and a
series of THA are performed, generating a suite of simulation results. Simultane-
ously, the building collapse scene of the disaster area can be identified via remote
sensing image analyses. Among the suite of simulation results, those that bear strong
similarities to the remote sensing collapse scene are identified as the optimal solu-
tions, which will subsequently be used to estimate the seismic loss. One of the key
issues is how to select the optimal simulation results. To address this issue, a frame-
work of such a near-real-time seismic loss estimation is described, and two methods
for selecting the optimal simulation results are proposed in this work. Validation is
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 825
performed using a simulated 1730 Western Beijing earthquake and the actual 2014
Ludian earthquake in China, by which the advantages of the proposed method are
demonstrated.
11.4.2 Framework of Near-Real-Time Seismic Loss
Estimation
The proposed framework of seismic loss estimation of regional buildings, incor-
porating both the THA-based method and post-earthquake remote sensing image
analysis techniques, consists of five components (Fig. 11.22). (1) Identify collapsed
and non-collapsed buildings by analyzing the post-earthquake remote sensing images
so as to obtain the building collapse scene of the disaster area. (2) Generate a large
number of seismic analysis load cases. For example, use a large number of ground
motions with different intensities and time histories as input. (3) Perform city-scale
nonlinear THA for each load case, resulting in a suite of simulation results. These
results not only include the information of the collapse status of the building but also
cover different damage states (i.e., none, slight, moderate, or extensive damage). (4)
From the suite of simulation results, identify those that are mostly similar to the
identified collapse scene as the optimal. (5) Estimate the seismic loss of the building
using the optimal simulation results.
Much of the existing studies can be referred to for Components (1), (3), and (5). For
the integrity of the presentation, they are briefly introduced herein without detailed
discussions. Note that Component (4) is one of the main focuses of this study, in which
two similarity measures of building collapse distributions are proposed. Component
(2) is also briefly described. It should also be noted that the framework proposed in
Fig. 11.22 The framework proposed in this work. * Source of the building collapse distribution
image: Gusella et al. (2005)
826 11 Post-earthquake Emergency Response and Recovery …
this work (Fig. 11.22) is generic and adaptable, that is, each of the five components
can be implemented through alternative means, not limiting to the implementation
described in this work.
11.4.2.1 Identification of Collapsed Buildings
There exist many approaches to identify collapsed and non-collapsed buildings from
the post-earthquake remote sensing images. For example, through crowdsourcing,
images can be distributed to a group of people and collapsed buildings can be rapidly
identified by human intelligence (Xie et al. 2016). Using image classification tech-
niques (Li et al. 2014), collapsed/non-collapsed buildings can also be automatically
identified.
It should be noted that existing studies on collapsed building identification from
remote sensing images demonstrate the likelihood of having some omission errors
(i.e., false-negative rate). For example, Booth et al. (2011) reported a 42% omis-
sion error in the identification of the collapsed buildings during the 2010 Haitian
earthquake; Yamazaki et al. (2005) reported a 37.5% omission error for the 2003
Bam Earthquake, Iran. Notwithstanding, some published literature also shows that
the omission error can be reduced by using ancillary data (e.g., vector map of build-
ings), multi-perspective, and oblique images (Dong and Shan 2013). For example,
Samadzadegan and Rastiveisi (2008) combined the QuickBird images and building
vector maps for collapsed building identification subsequent to the 2003 Bam earth-
quake, leading to a reduced omission error of 25%; Turker and Cetinkaya (2005) used
digital elevation models for the 1999 Izmit earthquake, Turkey, and the omission error
was reduced to 16%. Therefore, identifying collapsed buildings from remote sensing
images is both feasible and achievable.
Nevertheless, identifying non-collapsed damage states is a more challenging task.
For instance, Foulser-Piggott et al. (2016) attempted to identify the red-tagged or
yellow tagged non-collapsed buildings from the 2011 Christchurch earthquake, and
the omission error was found to be 56~86%. Note that currently, there is no feasible
solution to effectively reduce such an error.
Given the accuracy of the current remote sensing image identification techniques,
this work thus suggests identifying collapse (rather than other refined damage states)
from the remote sensing images. Extensive research and practical applications of
remote sensing technologies have been well summarized and documented in several
review articles (Rathje and Adams 2008; Dong and Shan 2013). As such, related
topics are not discussed herein in detail. With respect to the case study of the 2014
Ludian earthquake presented in this work, the UAV aerial images from the China
Earthquake Administration and news media, together with the building vector map
were used. Visual interpretation was performed to identify the collapse situation of
56 buildings in the disaster area by human intelligence. Hence, the identified collapse
is consistent with the actual collapse situation.
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 827
It should be noted, however, that regional seismic loss estimation is a challenging
issue. This work proposes an alternative approach, which is most suitable for cases
with sufficient accuracy in collapse identification. With the potential advancement of
the remote sensing techniques, the omission errors are expected to be further reduced.
For cases when the omission errors are significant by large, the predicted seismic
loss will be underestimated, which would require further studies to be undertaken.
11.4.2.2 Generation of Different Load Cases
The rationality of the THA results is influenced by (a) the building data, (b) the
building models and parameters, and (c) the ground motion inputs. Firstly, with the
advances in technologies such as big data and smart city, abundant urban building data
become available (Qi et al. 2017). Secondly, with respect to the building models and
parameters, the city-scale nonlinear THA introduced in Chap. 7of this monograph
with satisfactory modeling accuracy is adopted in this study. Thirdly, Sect. 7.4 of
this monograph and Lu et al. (2017a,b) studied the uncertainty of the parameters
of the structural models (e.g., the yield point, peak point, and soft point at the inter-
story backbone curves) and its influence on the regional seismic damage simulation.
Their results demonstrate that assuming the parameters of the structural models of
different buildings being independent, the uncertainty of those parameters has a
small influence on the overall analysis results of a region. As a result, only ground
motion uncertainty is considered when generating different load cases in this study.
Therefore, the uncertainty of ground motion becomes the dominant factor influencing
the accuracy of the THA results. Published studies also confirm that the randomness
in structural seismic responses is mainly attributable to the uncertainty of the ground
motion in particular when the seismic intensity is large (Kwon and Elnashai 2006).
In order to obtain a suitable ground motion input, the following strategy is adopted
in this work: a number of different ground motions are used as input so as to generate
a series of THA load cases; then determine which ground motion input yields the
building collapse results that are most similar to the identified collapse. For a region
lacking sufficient ground motion input, a total of pdifferent ground motion prediction
equations (GMPE) are adopted, and a total of qground motion records are selected
for each GMPE, hence generating n=pq load cases.
11.4.2.3 Regional Seismic Damage Simulation
In terms of regional seismic damage simulation, the city-scale nonlinear time-history
analysis proposed in Chap. 7is adopted in this work.
828 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.23 The flow chart of similarity measure of collapse distribution
11.4.2.4 Similarity Measure of Collapse Distribution
Among all the simulation results, in order to identify which one is most similar to
the identified collapse distribution, each simulation result should be evaluated with
a score. A higher score indicates a higher similarity with the identified collapse
distribution, and those results with the highest scores are identified as the optimal
simulation results (Fig. 11.23).
The similarity (or distance) measure quantifies the similarity between two objects,
which plays an important role in pattern recognition, clustering, classification, and
recommendation problems (Guo et al. 2013; Mahmoud et al. 2011). In particular,
binary similarity and distance measure is one of the most commonly used similarity
measures. Since the building being collapsed or non-collapsed is a binary event,
the binary similarity and distance measure are thus considered in this work. Choi
et al. (2010) summarized 76 binary similarity measures, including the widely used
Jaccard similarity measure and Euclidean distance, etc. In this work, one of those
measures is described in Sect. 11.4.3 and denoted as the “simple counting method.”
However, further discussions in that section show that binary similarity measures
may not deliver reasonable outcomes for some cases. Hence the “weighted counting
method” is proposed in this work taking into account the correction factors. Details
are described in Sect. 11.4.3.
11.4.2.5 Seismic Loss Estimation
In this section, the building level loss estimation method (Eqs. (8.1) and (8.2)) is
adopted. The damaged state of the building is first determined. Afterward, the loss
can be calculated based on the damage state and the replacement cost of the building.
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 829
11.4.3 Evaluation of the Similarity Measures of Collapse
Distribution
Two methods to evaluate the similarity measures of collapse distribution are proposed
herein, as shown in Fig. 11.23. Note that the two methods are independent of each
other.
11.4.3.1 Method A, Simple Counting Method
Naturally, a simple yet effective method is to compare the simulated collapse results
with the identified ones for each building. This idea is equivalent to the binary simi-
larity measure (Choi et al. 2010), denoted as a “simple counting method” hereafter.
Specifically, let the random variable ybe the collapse status of a building, where y
obeys a Bernoulli distribution, i.e., y~B(1, p). y=1 refers to a collapsed building
and y=0 for a non-collapsed building. For any simulation result iand any building
j,letyij be the simulated collapse status of this building, and yjbe the identified
collapse status of the same building. Then the score is defined as
Saij =1,yij =yj
0,yij = yj
(11.6)
Let mbe the total number of buildings, then the total score of the simulation result
iis defined as
SAi =1
m
m
j=1
Saij (11.7)
It can be seen from Eqs. (11.6) and (11.7) that the score of the simulation result,
SAi, only takes account of the building collapse status. Other important building infor-
mation, such as building location and structural type, is not considered. Hence the
simple counting method may not be rational under some circumstances. Assuming a
region consisting of 12 buildings, Fig. 11.24 shows the identified situation of building
collapse (Fig. 11.24a) and three simulation results (Fig. 11.24b–d), in which solid red
legends denote the collapsed buildings. The identified collapse situation shows that
all collapsed buildings are masonry structures, indicating that the masonry structures
have a higher collapse probability than reinforced concrete (RC) frame structures
in this earthquake. It can be seen that Simulation result 1 (Fig. 11.24b), having the
lowest score (SA1 =7/12), is least similar to the identified collapse situation. This
result is considered reasonable. Simulation result 2 (Fig. 11.24c) indicates that an RC
frame structure is collapsed, which is unlikely to happen according to the identified
collapse situation, although the simulation score is as high as 10/12. Having the same
score (i.e., SA3 =SA2), Simulation result 3 (Fig. 11.24d) is obviously most similar to
830 11 Post-earthquake Emergency Response and Recovery …
(a) Ident ified situation
of building collapse
(b) Simulation result 1
S
A1
=7/12
S
B1
=0.596
(c) Simulation result 2
S
A2
=10/12
S
B2
=0.857
(d) Simulation result 3
S
A3
=10/12
S
B3
=0.882
RC frame structure
Masonry structure
Solid red denotes
collapsed buildings
Fig. 11.24 Example showing the outcomes of the simple counting method and the weighted
counting method
the identified collapse situation. This example demonstrates that the simple counting
method is unable to identify the differences between the Simulation results 2 and 3.
11.4.3.2 Method B, Weighted Counting Method
The above discussions show that Eq. (11.7) should be modified by multiplying the
correction factors, which are related to the collapse probability of different buildings.
Note that different buildings exhibit different collapse probabilities, depending on
the features and locations of the building. In view of this, the weighted counting
method is proposed herein. The scoring rule is defined as follows.
Sbi j =Sai j (11.8)
wbj =pj,yj=1
1−pj,yj=0(11.9)
where wbj and pjare the weighted factors and the collapse probability of building j,
respectively. The total score of the simulation result iis defined as
SBi =
m
j=1
Sbi j wbj
m
j=1
wbj
(11.10)
At this point, the problem becomes how to calculate the collapse probability for
each building. Let vector xbe the determining factors for building collapse proba-
bility, and xcomprises building location coordinates, structural type, construction
type, number of stories, etc. Assuming
pj=P(y=1|x=xj;θ)=h(θTxj)=1
1+e−θTxj
(11.11)
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 831
1−pj=P(y=0|x=xj;θ)=1−h(θTxj)(11.12)
where θis the vector of factors to be calculated; the range of the logistic function
h(z) is (0, 1). Equations (11.11) and (11.12) can be merged into a single equation:
P(y|x;θ)=h(θTx)y[1−h(θTx)]1−y(11.13)
Since the identified situation of building collapse is known, this information can
be used to estimate θfollowing the maximum likelihood principle, that is, the value of
θshould maximize the value of pjof the collapsed buildings and minimize the value
of pjof the non-collapsed buildings. Therefore, solving θis equivalent to solving an
optimization problem described by Eq. (11.14)
ˆ
θ=arg max
θ
L(θ)=arg max
θ
m
j=1
P(y=yj|x=xj;θ)
=arg max
θ
m
j=1
h(θTxj)yj[1−h(θTxj)]1−yj(11.14)
In practice, in order to avoid overfitting problem, Eq. (11.14) is often regular-
ized by adding the regularization terms into Eq. (11.15), where λis a non-negative
regularization parameter.
ˆ
θ=arg max
θ
e−λθTθ
m
j=1
h(θTxj)yj[1−h(θTxj)]1−yj(11.15)
The above process is described by Eqs. (11.11)to(11.15) belongs to a logistic
classification (Bishop 2006), which represents a machine learning algorithm. The
vector xjand identified collapse status yjof any building jmake a training sample.
The number of training samples is equal to the number of buildings, m. Generally,
only a portion of the training samples (e.g., 60%) is used as the training set to calculate
the parameter vector θ; another portion of the training samples (e.g., 20%) are used
for cross-validation to determine the value of θ; and the remaining training samples
for testing the accuracy of the learning algorithm (Bishop 2006).
After solving θ, the collapse probability of each building can be calculated using
Eq. (11.11). Note that h(θTxj)and the training samples are only related to the
identified situation of building collapse, but not the simulation results.
As shown in Fig. 11.24,SB3 of Simulation result 3 is higher than SB2 of Simula-
tion result 2 using the weighted counting method. Therefore, the weighted counting
method is more advantageous than the simple counting method.
Given proper training samples (not only collapse states but refined damage states),
the machine learning method alone could be used as a loss estimation basis. However,
832 11 Post-earthquake Emergency Response and Recovery …
as described in Sects. 11.4.1 and 11.4.2.1 above, the accuracy of identifying non-
collapsed damage states from remote sensing images is relatively low. Hence it
is difficult to provide qualified training data. A possible solution would be to use
field investigation data and statistics of building seismic damage during historical
earthquake events. This might be regarded as a viable option. However, similar to
the damage probability matrix method, for those regions lacking historical seismic
damage statistics, further study is necessary to investigate whether the classifier
trained via statistics of other regions can produce reasonable results.
11.4.4 Case Study: Virtual Earthquakes Occurring
on Tsinghua University Campus
11.4.4.1 Earthquake Scenario
To further illustrate the performance of the above similarity evaluation methods, the
campus of Tsinghua University (consisting of 619 buildings) in China is selected to
conduct a case study. Detailed descriptions about the region can be found elsewhere
in Zeng et al. (2016). A nearby strong earthquake event of 300 years ago was the
1730 Western Beijing earthquake. Given this event, a scenario-based seismic damage
simulation (FEMA, 2012b) was performed and denoted as the “target scenario”.
According to the literature, the magnitude of the 1730 Western Beijing earthquake
was M6.5, the epicenter was approximately located at 40.0°N, 116.2°E (Huan et al.
1996), which is approximately 4.3 km from the center of Tsinghua Campus. As shown
in Fig. 11.25, this earthquake was caused by F3Qinghe Fault (Huan et al. 1996). Due
to the lack of ground motion records of this ancient earthquake, one of the widely
used GMPEs developed by the Next Generation Attenuation (NGA) research group,
the CB14 model (Campbell and Bozorgnia 2014), was used in this work to calculate
the target acceleration spectrum of the Tsinghua University campus. Note that the
CB14 model is merely used to generate a simulated “target scenario” to compare
the accuracy of different similarity measures. An actual earthquake scenario is used
in the validation section of this work to further demonstrate the outcomes of the
proposed method. Using the NGA-West2 online tool (Ancheta et al. 2014) provided
by the Pacific Earthquake Engineering Research Center (PEER), a ground motion
record that matches the target spectrum was selected as input (Fig. 11.26). As the
campus area (4 km2) is not very large, the same ground motion record was used
for every building for simplicity but was scaled to different values of PGA using
the CB14 model. Since the epicenter was in the northwest of the campus, the PGAs
of the buildings at the northwest campus were higher than those on the southeast
campus.
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 833
Fig. 11.25 The isoseismal map of the 1730 M6.5 Western Beijing earthquake. Modified from Hua
et al. (2005)
11.4.4.2 Identification of Collapsed Buildings
Given the above-ground motion input, different building seismic damage states of the
“target scenario” is simulated. Then the building collapse distribution (Fig. 11.27)of
the “target scenario” can be easily obtained from the simulated damage states. The
two axes x’ and y’ indicate building coordination. The positive directions of x’ and
y’ axes point to the east and north, respectively.
11.4.4.3 Generation of Different Load Cases
As described above, due to the lack of ground motion records and suitable GMPEs of
the 1730 Western Beijing earthquake, four GMPE models were adopted, that is, the
BSSA14 (Boore et al. 2014), ASK14 (Abrahamson et al. 2014) and CY14 (Chiou and
Youngs 2014) model proposed by NGA group, and the elliptical attenuation model
834 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.26 The target spectrum at the central campus and the spectrum of the selected ground
motion
Fig. 11.27 The building collapse distribution of the “target scenario” (i.e., the 1730 M6.5 Western
Beijing earthquake). A-A is a profile shown in Fig. 11.28b
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 835
proposed by the national standard of China (GB18306-2015). The distribution of the
mean PGA values calculated from the four GMPEs is shown in Fig. 11.28. It can be
seen from the figure that within the target region, the PGA values are approximately
linear to the building coordinates. However, the PGA values and the attenuation
slope calculated by different GMPEs vary significantly, implying that only using the
above four GMPEs may not generate a good simulation result that bears a strong
similarity to the collapse distribution of the “target scenario.” Therefore, five linear
attenuation functions as given in Eq. (11.16) were defined, where PGAmax represents
the maximum PGA in the target area. The domain of PGAmax is {0.1 g, 0.2 g, …
1.0 g}. Hence a total of 50 different GMPEs were defined using Eq. (11.16) (including
five formulas, in which PGAmax takes 10 different values).
In total, 51 ground motion records were selected as an input, including the widely
used El-Centro 1940 ground motion, and the 22 far-field and 28 near-field ground
motions proposed by the FEMA P695 report (FEMA 2009). Hence a total of 2550
different THA load cases were generated.
PGA =
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
PGAmax100% +(y−y
max)(100%−80%)
y
max−y
min
PGAmax100% +(y−y
max)(100%−60%)
y
max−y
min
PGAmax100% −(x−x
min)(100%−80%)
x
max−x
min
PGAmax100% −(x−x
min)(100%−60%)
x
max−x
min
PGAmax
(11.16)
It should be noted that a widely-used approach of ground motion selection is to
adopt sufficient and proper GMPEs to calculate target spectra based on the source
parameters of a particular earthquake, then select and scale the ground motion records
accordingly. This approach involves two types of uncertainties, i.e., target spectra
uncertainty (further classified as aleatory variability and epistemic uncertainty), and
record-to-record uncertainty. If a target spectrum is well selected so that it is close
to the actual spectrum, it can be used for the selection of ground motion records
in the proposed method. Note that target spectra only represent the amplitude and
spectrum of ground motions, the record-to-record uncertainty still exists given a
target spectrum. As a result, the proposed method can be used to further reduce
record-to-record uncertainty.
However, due to the complexity of ground motion records, the target spectra
uncertainty could be fairly large. For example, Fig. 11.28 shows that the mean PGA
calculated by different GMPEs varies significantly. Hence the target spectra calcu-
lated using GMPEs may differ from the actual spectrum. As a result, a sufficient
number of GMPEs are needed to fully address the target spectra uncertainty. For
simplicity, a set of GMPEs is defined using Eq. (11.16) in this work. These GMPEs
“cover” the results calculated using some widely used GMPEs shown in Fig. 11.28.
Hence it is expected that among those generated load cases, there is at least one case in
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 837
which the simulation result is “similar” to the actual result. Other reasonable GMPEs
can (and are encouraged to) be used in addition to those defined by Eq. (11.16), on
the condition that the epistemic uncertainty is fully addressed. Note that quantifying
the epistemic uncertainty requires a reasonable selection of multiple GMPEs with
different branch weights (Kale and Akkar 2017). In this work, however, the purpose
is not to quantify the ground motion uncertainty but to obtain a set of ground motion
input that can produce a reasonable loss estimation using extra information (i.e., the
identified collapse scene of the disaster area).
Overall, if the target spectra are well selected, they can then be used by
the proposed method to reduce efforts of ground motion selection. In addition,
the proposed method can further reduce record-to-record uncertainty. Otherwise,
a sufficient number of GMPEs should be adopted to reflect the target spectra
uncertainty.
11.4.4.4 Regional Seismic Damage Simulation
By performing the above THA load cases, a total of 2550 simulation results were
generated. Each result contains building-level damage states. Figure 11.29ashows
the number of buildings in each damage state of each load case. The load cases are
sorted by seismic intensity; hence the damage generally becomes severer from load
case 1–2550.
11.4.4.5 Similarity Measure and Seismic Loss Estimation
Using the proposed two similarity measures, the scores of each simulation result were
calculated, and the optimal simulation results were identified. The economic loss
corresponding to each simulation result was also calculated. The similarity scores
(using weighted counting method) and estimated loss are shown in Fig. 11.29b,
c, respectively. In order to evaluate whether the calculated scores can effectively
measure the similarity between the simulation results and the actual collapse distri-
bution, the score-loss relationship is displayed in Fig. 11.30. The blue dots in the
figure represent the loss Vjfor each simulation result j. The red solid lines denote the
actual loss Vactual, which was calculated based on the damage states of the buildings
under the target scenario. The black dashed lines signify the loss calculated using the
damage probability matrix proposed by Yin (1996), VYin. This damage probability
matrix has been widely used for the seismic loss estimation of past earthquakes in
China. Note that the damage probability matrix method requires the use of the modi-
fied Mercalli intensity (MMI), and the relationship between PGA and MMI has been
shown to have great uncertainty (Wald et al. 1999). In this work, the relationship
suggested by the National Standard of China, “The Chinese seismic intensity scale”
(GB/T 17,742–2008), is adopted, that is, PGA of 0.09~ 0.177 g corresponds to MMI
of VII; PGA of 0.178~0.353 g corresponds to MMI of VIII; and PGA of 0.354~
0.707 g corresponds to MMI of IX.
838 11 Post-earthquake Emergency Response and Recovery …
Figure 11.30 illustrates that:
(1) The seismic loss Vjtends to converge towards the actual loss Vactual when the
simulation scores are increased.
(2) The two methods of similarity measures are very close to each other. In partic-
ular, both methods lead to one optimal simulation result. The simulation score
Fig. 11.29 Simulation results for each load case. aNumber of buildings in each damage states.
bSimilarity scores using the weighted counting method. cEstimated loss
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 839
Fig. 11.29 (continued)
being “1” indicated that the simulated building collapse distribution was exactly
the same as that of the “target scenario” (Fig. 11.27).
(3) The estimated economic loss of the optimal simulation result Vopt was 1315.6
million RMB (Fig. 11.30c). Compared to the actual loss Vactual (1100.4 million
RMB), the error was 19.6%. This implies a reasonably good estimation. The
difference between Vopt and Vactual is due to the different damage states of the
non-collapsed buildings, though the distribution of collapsed buildings are the
same.
(4) The seismic loss of the optimal simulation result was much better estimated
than the loss VYin (286.9 million RMB) using the damage probability matrix
(Fig. 11.30c). The damage probability matrix method greatly underestimates
the seismic loss of the target scenario. This may be due to the fact that Beijing
has not experienced any strong earthquake for nearly three hundred years. The
rationality of a damage probability matrix relies on historical building damage
statistics. Hence, this method may not accurately describe the seismic resistance
of buildings in Beijing. In addition, the building seismic design code is contin-
ually being developed, and the overall building seismic resistance is improving,
which is difficult to be considered using historical seismic damage statistics.
11.4.4.6 Additional Earthquake Scenarios
To evaluate the performance of the proposed method at the other hazard levels, two
additional earthquake scenarios were studied: While other source parameters remain
unchanged, the magnitude of the 1730 Western Beijing earthquake was set to be (1)
M5, and (2) M8. For the two target scenarios, the CB14 model is still used to calculate
PGA of each building. The same set of 2550 load cases and their simulation results
were used in which the optimal results would be selected. The similarity score and
840 11 Post-earthquake Emergency Response and Recovery …
(b)
Simula ted los s, V
j
Actual loss, V
actual
Damage probability
mat rix lo s s, V
Yin
(a)
Simu la te d lo s s, V
j
Actual loss, V
actual
Damage probability
mat rix lo s s, V
Yin
Fig. 11.30 The score-loss relationship of the simulation results (1730 Western Beijing earthquake).
aSimple counting method (Method A). bWeighted counting method (Method B). cComparison
of simulated loss and actual loss
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 841
(c)
1100.4
1315.6
286.9
0
200
400
600
800
1000
1200
1400
Actual opt DPM
Ec o nomic lo s s (106RMB)
V
actual
V
opt
V
Yin
Fig. 11.30 (continued)
estimated loss are shown in Fig. 11.31b, c. The results of the two similarity measures
are close; hence only the results of the weighted counting method are shown. For
the M5 scenario, five optimal simulation results with the highest score of 1.0 were
identified (Fig. 11.31a), the median loss of those simulation results were calculated
as the estimated loss Vopt; while for the M8 scenario, 302 optimal simulation results
with the highest score of 1.0 were identified. Figure 11.31c, d show that in both the
M5 and the M8 scenarios, Vopt is close to Vactual, being a much better prediction than
VYin using the damage probability matrix.
The case studies of the three virtual scenarios (earthquake magnitudes M5, M6.5,
and M8) demonstrated the applicability of the proposed method for different hazard
levels. It should be noted, however, that the proposed method is more suitable for
high levels of seismic intensity. On the one hand, the ground motion uncertainty is
dominant when the seismic intensities are large (Kwon and Elnashai 2006). On the
other hand, if an earthquake is so weak to cause only a few buildings to collapse, the
remote sensing images may not provide sufficient information to achieve the optimal
solutions effectively.
11.4.5 Validation Using 2014 Ludian Earthquake
The case study presented above confirms that the proposed similarity evaluation
methods are able to offer a relatively good loss estimation. Nevertheless, the “target
scenarios” are merely virtual cases based on the ancient 1730 Western Beijing
earthquake.
842 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.31 The results of the two additional earthquake scenarios. aThe loss-score relationship
of M5 scenario. bThe loss-score relationship of M8 scenario. cComparison of simulated loss and
actual loss of M5 scenario. dComparison of simulated loss and actual loss of M8 scenario
In order to further validate the rationality of the proposed methods, the seismic loss
estimation was performed using August 31, 2014, Ludian earthquake data recorded
in the Yunnan Province of China. The magnitude of the earthquake was M6.5, the
focal depth was 12 km, and the epicenter was located at 27.189° N, 103.409° E. The
Ludian earthquake caused severe damage to the Longtoushan town 9 km away from
the epicenter (Xu et al. 2015;Huetal.2016). The next day after the earthquake,
China Earthquake Administration utilized UAVs and obtained aerial images of the
disaster area. Using these images, the building collapse scene at Longtoushan town
was timely identified (Fig. 11.32a). According to the refined damage states of the
buildings obtained through site investigations (Lin et al. 2015), the actual seismic
loss Vactual can be calculated. Nevertheless, the Vactual was only obtained after nearly
a month since the earthquake occurred.
Similar to Sect. 11.4.4 outlining the case study of Tsinghua Campus, five linear
attenuation functions were defined by Eq. (11.16), where the domain of PGAmax is
{0.2 g, 0.4 g, … 1.2 g}. Hence a total of 30 different GMPEs were defined. The
28 near-field ground motions proposed by FEMA (2009) were selected as input.
As a result, a total of 840 different THA load cases were generated, leading to 840
simulation results. Using the two similarity measures proposed above, the scores
of each simulation results were calculated, and the optimal simulation results were
identified. The score-loss relationship is presented in Fig. 11.33.
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 843
Fig. 11.32 The aidentified, and bsimulated building collapse distribution at Longtoushan town in Ludian earthquake
844 11 Post-earthquake Emergency Response and Recovery …
In addition, the National Strong Motion Observation Network System of China has
captured more than 70 ground motion records of the mainshocks (Xu et al. 2015;Hu
et al. 2016), one of which was recorded by the strong motion station located rightly at
Longtoushan town. This ground motion record, together with a regressed attenuation
relationship (Xiong et al. 2017), was also used for comparison. The THA using this
input was performed, the similarity score of the simulation result was calculated,
and the corresponding loss was calculated and denoted as Vrecorded. The score-loss
pair of this load case is presented as a star in Fig. 11.33a, b. Note that the recorded
ground motion only represents the earthquake tremor on a certain point. The inputted
ground motion for different buildings may differ from the recorded one. Hence, the
predicted collapse scene using the recorded ground motion, although being also very
close to the real collapse scene, is not 100% identical.
(1) Both the simple counting method (Method A) and the weighted counting
method (Method B) led to the same optimal simulation results. The score of
the optimal simulation results was less than 1, indicating that the simulated
collapse distribution was not completely identical to the actual collapse distri-
bution. However, comparing the simulated collapse (Fig. 11.32b) with the actual
collapse (Fig. 11.32a), they were fairly similar.
(2) The loss estimation of the optimal simulation results was close to the actual
loss, and far better than that estimated using the damage probability matrix
(Fig. 11.33c). The underlying key reason is that the proposed method takes
advantage of important information, that is, the identified situation of building
collapse.
(3) The estimated loss using the recorded Ludian ground motion, Vrecorded, agrees
well with the actual loss, Vactual.
The seismic loss estimation was performed on a multi-core desktop computer
(CPU: Intel E5-2695 v4@2.10 Hz, 36 cores; RAM: 64 GB). It should be noted
that it took only 4 min to perform the above 840 nonlinear THAs in parallel. The
similarity measures were computed within seconds. The computational efficiency can
be further improved if using GPU parallel computing (Sect. 9.5 of this monograph)
or distributed computing (Sect. 9.6 of this monograph), so that computation can
be completed within several minutes even for a much larger region or much more
THA load cases. With advances in remote sensing technologies, the satellite or aerial
images of disaster areas are expected to be available within 24 h, facilitating rapid
attainment of the identified collapse situation of the buildings. Therefore, the methods
proposed in this work represent a near-real-time seismic loss estimation method. The
loss estimation can be provided within one or two days after an earthquake, with
satisfactory accuracy compared to the site investigated loss, which may take weeks
to obtain.
In this work, the optimal simulation results are identified merely based on
matching collapse scene. This involves an assumption that if the collapse distri-
bution of a simulation result is similar to the identified collapse distribution from the
remote sensing images, then the simulated building damage states and the estimated
loss are also regarded to be similar. In other words, the regional building seismic loss
11.4 Improving the Accuracy of Near-Real-Time Seismic Loss Estimation … 845
0.4 0.5 0.6 0.7 0.8 0.9 1
5
10
15
20
25
30
35
40
45
50
Simplec ountingmethod
Scores
Economic loss( 10
6
RMB)
Simulatedloss,
V
j
Actu a l lo s s ,
V
actual
Damage probability matrix loss,
V
yin
Recorded ground motion loss,
V
recorded
Simulated loss, V
j
Actual loss, V
actual
Damageprobabilitymatrixloss,V
Yin
Reco rde d ground motion los s, V
Recorde d
0.4 0.5 0.6 0.7 0.8 0.9 1
5
10
15
20
25
30
35
40
45
50
Weighted counting method
Scores
Economic loss(10
6
RMB)
27.72
30.51
14.00
30.39
0
5
10
15
20
25
30
35
Actua l op t DPM Rec
Ec on om ic los s (1 0
6
RMB)
V
actual
V
opt
V
Yin
V
recorded
(a) (b)
(c)
Fig. 11.33 The score-loss relationship of the simulation results (2014 Ludian earthquake). aSimple
counting method (Method A). bWeighted counting method (Method B). cComparison of simulated
loss and actual loss
is highly correlated to the building collapse distribution. Due to the complexity of the
nonlinear behaviors of the structures subjected to earthquake excitation, currently,
an analytical proof to this assumption was not given in this study. Nevertheless, the
case studies (three virtual earthquakes on Tsinghua Campus and the Ludian earth-
quake) could be treated as numerical experiments. The results of these case studies
(Figs. 11.31,11.32, and 11.33) confirm that this assumption is relatively reasonable.
11.4.6 Concluding Remarks
In this work, a framework for near-real-time regional building seismic loss estimation
is proposed. By taking advantage of the building collapse scene of the disaster area,
which can be rapidly identified through remote sensing image analysis, the accuracy
of the THA-based loss estimations is improved. The fact that the seismic loss estima-
tion can be done within one or two days after an earthquake confirms a near-real-time
efficiency. Two methods for selecting the optimal simulation results are proposed,
that is, a simple counting method, and a weighted counting method. Through the
validation using the simulated cases of the 1730 Western Beijing earthquake and the
actual 2014 Ludian earthquake in China, the advantages of the proposed methods
are demonstrated. The results indicate that:
846 11 Post-earthquake Emergency Response and Recovery …
(1) The two proposed similarity measure methods of collapse distribution can
reasonably evaluate the similarity between simulated results and the identi-
fied building collapse situation. The simulated seismic loss tends to converge
towards the actual loss when the similarity increases.
(2) Even for the case of lacking rational ground motion input, the loss estimation
of the optimal simulation results can be very close to the actual loss. The key
reason behind this is that the proposed method takes advantage of important
information, that is, the identified situation of building collapse.
(3) The THAs can be completed within several minutes, while the similarity
measure takes mere seconds. Using the satellite or aerial images of disaster
areas that are expected to be available within 24 h, the proposed method can
adapt to the needs of rapid post-earthquake loss assessment.
11.5 Post-earthquake Repair Scheduling of City-Scale
Buildings with Labor Constraints
11.5.1 Overview
To quantify the seismic resilience of a community, Bruneau et al. (2003) proposed
a conceptual framework. The seismic resilience of a community can be calculated
according to Eq. (11.17), as follows:
R=tend
t0
[Q0−Q(t)]dt(11.17)
where R, the seismic resilience of a community, is defined as the functional loss
integral from the onset of a disaster (at time t0) to the moment of full recovery (tend);
Q0is the pre-event functionality of the community, and Q(t) is the post-event residual
functionality of the community that varies with time. The resilience index, R, is easy
to implement and has been applied in the seismic resilience assessment of medical
facilities, residential buildings, and bridges (Bruneau and Reinhorn 2007; Cimellaro
et al. 2010; Burton et al. 2015; Bocchini and Frangopol 2012; Decò et al. 2013).
The seismic resilience presented in Eq. (11.17) consists of two resilience dimen-
sions: (1) the community’s ability to maximize its residual functionality after an earth-
quake (referred to as robustness) and (2) the capability of a community to achieve fast
recovery (known as rapidity) (Miles and Chang 2006). The residual functionality of
a community following an earthquake is normally measured in terms of certain indi-
cators of community utilities (e.g., available housing capacity (Burton et al. 2015)).
To quantify the residual functionality, the damage states of each building together
with the relationship between damage states and the loss of building functionalities,
have to be obtained. However, enormous building inventories and diverse building
11.5 Post-earthquake Repair Scheduling … 847
types in an urban area make it considerably difficult to quantify the residual func-
tionality of a community. The second dimension of resilience (i.e., rapidity) reflects
the temporal evolution of functional recovery, which is greatly influenced by public
policies, available technical or labor resources, and social preparedness. A reasonable
simulation of such a recovery process is also a considerably challenging task.
In the existing literature, it is reported that fragility analysis is extensively used
to calculate the residual functionality of buildings after an earthquake. Bruneau
and Reinhorn (2007) adopted the fragility curves of buildings to determine their
structural and non-structural losses. Lin and Wang (2016) classified buildings into
different groups and determined building losses according to the building portfolio
fragility function of the corresponding building group. In addition to fragility anal-
yses, the city-scale nonlinear THA can fully consider the characteristics of ground
motions and the seismic performance of different buildings. Moreover, the city-scale
nonlinear THA can output multiple types of engineering demand parameters (EDPs)
for each story of a structure; accordingly, this can facilitate the seismic performance
assessment of regional buildings using the method proposed by the FEMA P-58
report (FEMA 2012; Zeng et al. 2016). For example, Burton et al. (2015) obtained
the EDPs of a typical building and subsequently evaluated the damage of different
building components by using the FEMA P-58 method (FEMA 2012), such that the
residual functionality of a building was determined. Nevertheless, the link between
component-level damage to the overall residual functionality of a building remains
unclear. Furthermore, the problem of how to evaluate the residual functionality of
an entire community based on city-scale nonlinear THA and FEMA P-58 method
(FEMA 2012) remains unresolved.
As for the simulation of community functional recovery process after an earth-
quake, most available methods have primarily focused on the functional restoration
of lifeline infrastructures (Isumi et al. 1985; Ballantyne and Taylor 1990; Chang
et al. 1999); and methods for calculating the temporal variation of building residual
functionality, Q(t), is rather limited (Cimellaro et al. 2010). Miles and Chang (2006)
proposed a conceptual model to generate a community recovery curve, taking into
consideration the influences of various environmental and social factors on the
recovery process. Based on the conceptual model of Miles and Chang (2006), Cimel-
laro et al. (2010) proposed linear, exponential, and trigonometric recovery curves.
Consequently, a proper recovery curve can be selected according to social prepared-
ness and resourcefulness. By capitalizing on the EDPs obtained through the THA,
Burton et al. (2015) adopted the FEMA P-58 damage assessment method (FEMA
2012) to determine the necessary repair time of building components and determine
the recovery curve of residential buildings.
A recovery curve can be considerably affected by community resourcefulness.
Bocchini and Frangopol (2012) simulated the restoration process of bridge networks
considering the repair funding allocated to each bridge, in which the repair schedule
was optimized by maximizing the network resilience and minimizing the repair time
and total cost. Luna et al. (2011) proposed a model for post-earthquake recovery of
water distribution systems, by which the labor required for the restoration of pipeline
848 11 Post-earthquake Emergency Response and Recovery …
damage was estimated, and the resource allocation module was employed to priori-
tize the recovery process. In the field of resilience evaluation of individual buildings,
the method of Resilience-based Earthquake Design Initiative (REDi) (Almufti and
Willford 2013) is able to predict the repair time and labor demand for each building
according to the widely accepted methods in construction scheduling. This method
has been extensively used for the seismic resilience assessment of individual build-
ings (Hutt et al. 2015; Tian et al. 2016;Luetal.2016; Dong and Frangopol 2016).
In the REDi method, the repair sequences of individual buildings and the calculation
method of each repair sequence are explicitly presented; accordingly, it can also be
a good candidate for the repair simulation of a group of buildings with resource
constraints.
In view of the foregoing, the framework of the city-scale THA-driven building
seismic resilience evaluation and repair schedules are proposed by the author of
this monograph (Xiong et al. 2020). Moreover, combined with the FEMA P-58
damage assessment method (FEMA 2012), a probabilistic calculation method for
building residual functionality based on component-level damage is introduced.
Subsequently, based on the repair time and labor demand calculation methods of
REDi (Almufti and Willford 2013), a community repair scheduling method that
considers repairing resource constraints together with a community repair simula-
tion method is proposed. Finally, a city-scale building seismic resilience simulation
is performed for Beijing City, and the effectiveness of different repair schemes is
discussed.
11.5.2 Methodology Framework
The proposed framework for the city-scale building seismic resilience simulation
based on the THA mainly consists of five components, as outlined in Fig. 11.34
(1) Hazard analysis.
Fig. 11.34 Framework for city-scale building seismic resilience simulation based on THA
11.5 Post-earthquake Repair Scheduling … 849
According to the predefined earthquake scenario, the ground motion of a region
can be obtained through wave propagation simulation (Hori and Ichimura
2008; Graves and Pitarka 2010) or probabilistic hazard seismic analysis
(Mcguire 2008) together with artificial ground motion generation (Gasparini
and Vanmarcke 1976).
(2) Seismic response analysis.
The city nonlinear THA is performed based on ground motion records obtained
from the hazard analysis. Thereafter, the EDPs of each building story can be
calculated.
(3) Damage assessment.
Following the seismic response analysis, damage assessments are performed for
structural and non-structural components according to the EDPs of each story
of all buildings. For example, the probabilities of different damage states of
structural and non-structural components at different stories of a building can
be calculated using the seismic damage assessment method proposed by FEMA
P-58 (FEMA 2012).
(4) Calculation of residual functionality.
Based on the damage states of each component, the residual functionality of each
component is calculated. Thereafter, by integrating the residual functionalities
of all building components, the residual functionality of a particular building
can be determined (Burton et al. 2015).
(5) Recovery analysis.
The number of workers required to repair each building is estimated based on
the component-level structural and non-structural damage of each story together
with the individual and total floor areas of a building (Almufti and Willford
2013). Subsequently, according to the residual functionality and labor demand
of each building, the repair scheme is determined. Finally, based on the repair
scheme, the recovery simulation of each building in the region is performed to
obtain the recovery curve and resilience index, R, of the region.
The first three components of the framework have been extensively studied in
previous research. However, existing research in relation to Components 4 and 5 of
the framework is limited. Accordingly, in the subsequent sections of this chapter, the
proposed methodologies for these two components are introduced.
11.5.3 Calculation of Residual Functionality
11.5.3.1 Weighted Functionality
The functionality of urban buildings can be divided into two categories: physical and
socio-economic functionalities. The physical functionality denotes the utility and
the amount of services provided by a building. For example, the housing capacity
is the physical functionality of residential buildings (Burton et al. 2015). The socio-
economic functionality describes the relationship of a building with its social and
850 11 Post-earthquake Emergency Response and Recovery …
economic environment. For example,during the post-event recovery process, hospital
buildings are more important than ordinary office buildings; this indicates a higher
socio-economic functionality. In order to consider both the physical and socio-
economic functionalities of buildings on a regional scale, the calculation method
using Eq. (11.18) is adopted to determine the functionality of a building:
Q0=αQPhysical (11.18)
where QPhysical is the index of physical functionality (such as the total floor area of a
residential building); αis the building weight, which represents its socio-economic
functionality.
11.5.3.2 Residual Functionality of Individual Buildings
After an earthquake, the functionalities of a building may be reduced or completely
lost. According to the simulation framework presented in Fig. 11.34, the residual
functionalities of buildings are the prerequisites for the subsequent recovery analysis.
In this study, based on the FEMA P-58 method (2012) and the work of Burton
et al. (2015), a probabilistic method is proposed to quantitatively determine the post-
earthquake residual functionality of buildings in a community. In particular, building
damage is divided into four limit states; the residual functionality of each limit state
is presented as follows:
(1) LS0: No damage.
This state indicates that the structural and non-structural components of a building
remain intact; hence, the functionality of the building is not affected. In this state,
the proportion of building functional loss is 0.0, as shown in Eq. (11.19):
P(Qloss|LS
0)=0.0 (11.19)
where P(Qloss |LS0) represents the proportion of the functional loss of a building
when the limit state LS0is attained. It is noteworthy that the value of P(Qloss |LS0)
can be larger than 0.0 even if none of the structural and non-structural components
of the building is damaged. For example, this may occur when buildings sustain the
functional loss of external power or water supply.
To calculate the probability of a building in the LS0limit state, the concept of
performance group (PG) is adopted (FEMA 2012). The PG is a group of components
with similar seismic fragility and is vulnerable to the same type of EDP. Because the
probability of no-damage state (DS0) in different PGs are independent events, the
probability of a building reaching limit state LS0is the product of the probabilities
of all PGs in the DS0damage state, as given in Eq. (11.20):
11.5 Post-earthquake Repair Scheduling … 851
Fig. 11.35 Functional groups and performance groups of a typical building
P(LS
0|EDP)=
l
i=1
P(PGi_DS0|EDP)(11.20)
where PGi_DS0is the state of the ith PG with no damage (DS0); P(PGi_DS0|EDP)
is the probability of the ith PG in the DS0damage state given the corresponding EDP
obtained through the THA in Component 2 of the proposed framework (Fig. 11.34);
lis the number of PGs.
(2) LS1: Occupiable damage with loss of functionality.
Limit state LS1indicates that the structural PGs of the building are not seriously
damaged, and the building remains safe for occupancy. However, the non-structural
PGs of the building is damaged, and the functional loss should be considered.
In order to consider the functional loss caused by the damage of non-structural
PGs, a system reliability approach is adopted (Burton et al. 2015). As shown in
Fig. 11.35, different PGs of a building can be classified into multiple functional
groups (FGs) according to their utility; different FGs are connected in series. Once
the FG fails, the overall functionality of the building is completely lost or severely
impaired. For example, in Fig. 11.35, if the functionality of the Floor Access FG
is completely lost, the building is no longer useable; thus, the functionality of the
building is completely lost. Nevertheless, if the functionality of Water Supply FG is
lost and no alternative housing is available, the building can still be used with limited
functionality. Therefore, the proportion of the functional loss, P(Qloss |LS1), of a
building in the limit state LS1can be calculated by Eq. (11.21).
P(Qloss|LS
1)=1−
m
j=1
[1−P(Qloss|FLj)P(FLj|LS
1,EDP)](11.21)
where mis the number of FGs; P(Qloss |FLj) is the proportion of building functional
loss with the jth functional group being completely lost. The value of P(Qloss |FLj)
for different FGs can be determined according to expert judgment. For example, if
the Floor Access FG fails, then the building is inaccessible and the value of P(Qloss
852 11 Post-earthquake Emergency Response and Recovery …
|FLj) can be set to 1.0; P(FLj|LS1,EDP) is the probability of complete functional
loss of the jth FG given the EDP and the building being in the LS1limit state. This
value is related to the damage of each PG within the FG, as presented below.
An FG consists of multiple PGs. The functional loss of a PG reduces the func-
tionality of the FG. The functionality of the FG is completely lost only when all PGs
within the FG fail. For example, in Fig. 11.35, the functionality of Floor Access FG
is completely lost when both Stairs and Elevator PGs fail. Therefore, the probability
of the complete functional loss of the jth FG P(FLj|LS1,EDP), given the EDP and
the building being in the LS1limit state, can be calculated according to Eq. (11.22):
P(FLj|LS
1,EDP)=
n
k=1
P(FLj|LS
1,PLk)P(PLk|LS
1,EDP)(11.22)
where nis the number of PGs; P(FLj|LS1,PLk) is the proportion of functional loss
of the jth FG when the functionality of the kth PG is completely lost and the building
is in the LS1limit state. This value represents the functional contribution of a PG to
the overall functionality of the FG. Therefore, the summation of these values of all
the PGs is 1.0. P(PLk|LS1,EDP) is the probability of the complete functional loss
of the kth PG given the EDP, and the building being in the LS1limit state, which can
be calculated using Eq. (11.23):
P(PLk|LS
1,EDP)=
p
x=1
P(PLk|LS
1,PGk_DSx)P(PGk_DSx|LS
1,EDP)
(11.23)
where pis the number of damage states; P(PLk|LS1,PGk_DSx) is the probability
of the complete functional loss of the kth PG with the assumption that the current
PG reaches the damage state DSx, and the building is in the LS1limit state. This
value can be determined through expert judgment. For example, if DS1of the PG
means cosmetic damage, then P(PLk|LS1,PGk_DS1) can be set to a relatively small
value. On the other hand, if DS2of the PG indicates complete damage, the P(PLk
|LS1,PGk_DS2) can be set to 1.0; P(PGk_DSx|LS1,EDP) is the probability of k
PG when it reaches DSxunder the circumstance of LS1and the given EDP.
Because the limit state LS1of a building is primarily determined according to
the damage of structural components (FEMA 2012), and the building functional
loss discussed in this section is mainly calculated based on the damage of non-
structural components, the occurrence of PGk_DSxand LS1are independent events.
Therefore, P(PGk_DSx|LS1,EDP) can be calculated by Eq. (11.24), and the value of
P(PGk_DSx|EDP) can be computed according to the component fragility database
of FEMA P-58 (FEMA 2012):
P(PGk_DSx|LS
1,EDP)=P(PGk_DSx|EDP)(11.24)
11.5 Post-earthquake Repair Scheduling … 853
The probability of a building reaching limit state LS1, given the EDP, can be
obtained by Eq. (11.25):
P(LS
1|EDP)=
n
k=0
p
x=1
P[LS
1|P(PGk_DSx|EDP)]−P(LS
0|EDP)(11.25)
where P(PGk_DSx|EDP) is the proportion of the kth structural PG when it reaches
damage state DSxat the given EDP; P[LS1|P(PGk_DSx|EDP)] is the probability
of the building being occupiable given the proportion of structural PGkreaching the
damage state DSx. This value can be obtained according to the unsafe placarding
determination method in FEMA P-58 (FEMA 2012).
(3) LS2: Unoccupiable damage.
This limit state indicates that the structural components of the building sustained
moderate or extensive damage to the extent that the building cannot be occupied
and the functionality of the building is completely lost. Therefore, the proportion of
functional loss of the building in LS2can be calculated according to Eq. (11.26):
P(Qloss|LS
2)=1.0 (11.26)
The probability of a building reaching limit state LS2, given a certain EDP, can
be calculated by Eq. (11.27):
P(LS
2|EDP)=1−P(LS
0|EDP)−P(LS
1|EDP)−P(LS
3|EDP)(11.27)
where P(LS3|EDP) is the probability of the building reaching LS3with the given
EDP.
(4) LS3: Irreparable damage.
This limit state means that the building is severely damaged or collapsed. If a building
attains this limit state, then the building has to be demolished and rebuilt. Therefore,
building functionality is also completely lost, and the proportion of functional loss
in LS3can be calculated by Eq. (11.28):
P(Qloss|LS
3)=1.0 (11.28)
The probability, P(LS3|EDP), of a building reaching irreparable limit state LS3,
given the EDP, has been studied extensively (FEMA 2012; Ramirez and Miranda
2012). It can be calculated based on the fragility data of different types of buildings,
according to the EDP of building residual inter-story drift ratios.
According to the foregoing discussions, the probability of a building reaching
limit state LSy, given a certain EDP P(LSy|EDP) together with the functional losses
854 11 Post-earthquake Emergency Response and Recovery …
of different limit states, P(Qloss |LSy), can be obtained. Therefore, the expectation
of the building residual functionality under the condition of EDP can be calculated
by Eq. (11.29):
E(Qres|EDP)=[1−
4
y=1
P(Qloss|LSy)·P(LSy|EDP)]·Q0(11.29)
where Q0is the weighted functionality of a building before an earthquake
(Eq. (11.18)).
11.5.4 Recovery Curve and Labor Demand Curve
The recovery curve of a building is considerably affected by the processes of
post-event inspection, engineering mobilization and review or redesign, financing,
contractor mobilization, permitting, and building repairs (Almufti and Willford 2013;
Burton et al. 2015). As these former factors are location-dependent, and the time
required for each process can be determined according to local situations, this study
is focused on the time required for building repairs.
11.5.4.1 Repair-Scheduling Unit (RSU)
It is extremely difficult to determine the repair priority for each building in the city-
scale simulation because of the enormous building inventory involved. Accordingly,
the concept of the repair-scheduling unit (RSU) is proposed for the repair simula-
tion. Each RSU contains buildings in the same neighborhood with similar seismic
performance. In repair simulation, the repair scheme is determined as long as the
repair priority of each RSU is obtained.
11.5.4.2 Repair Time and Labor Demand Curve of an Individual
Building
According to REDi (Almufti and Willford 2013), the repair sequences of a building
isshowninFig.11.36. Particularly, the structural repair sequence is prior to non-
structural repair sequences. Note that the non-structural repair sequences A–F can be
performed simultaneously. The repair time of each PG within a sequence is calculated
according to FEMA P-58 (FEMA 2012). Based on the repair sequence scheduling
and labor assignment method described in the REDi report (Almufti and Willford
2013), the repair time and labor demand curve, DBlgi(t), of a typical building can be
computed as shown in Fig. 11.37.
11.5 Post-earthquake Repair Scheduling … 855
Fig. 11.36 Repair sequences of a typical building (Almufti and Willford 2013)
Fig. 11.37 Labor demand
curve of a typical building
11.5.4.3 Recovery Curve and Labor Demand Curve
of a Repair-Scheduling Unit
According to the repair-scheduling method in the REDi report (Almufti and Willford
2013), the repair time of a building depends on the available workers. In this section, a
sufficient number of workers is assumed for the RSU, and all buildings in the RSU are
simultaneously repaired with the required maximum number of workers. The repair
time, TBlgi, and the labor demand curve, DBlgi(t), of each building can be obtained
according to the method described in the REDi report (Almufti and Willford 2013).
It is noteworthy that in practical applications, some RSUs may not be allocated with
sufficient numbers of workers; this means that the maximum worker demand cannot
be satisfied. Consequently, the recovery process of the RSU is delayed. Further details
on the repair process with insufficient workers are discussed in Sect. 11.5.5.3.
The recovery curve of a typical RSU is shown in Fig. 11.38.
856 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.38 Schematic of
RSU recovery curve
After the earthquake, the functional loss of each building in the
RSU can be calculated according to the method presented in
Sect. 11.5.3. The total functional loss, QLoss, RSU, can be obtained by aggregating
the functional losses of all the buildings in the RSU, as shown in Fig. 11.38.
Consider that the functionality of a single building is relatively small compared
with that of an RSU; accordingly, the functional variation of a single building during
the repair process can be ignored. Therefore, it is assumed that the functionality of a
building is abruptly restored to its pre-earthquake functionality when the repair time,
TBlgi, of this building is attained. Based on this assumption, the recovery curve of an
RSU exhibits a stepped shape, as shown in Fig. 11.38.
As for the labor demand curve of an RSU, DRSU(t), because all buildings in the
RSU are simultaneously repaired with the abundant labor force, according to the
aforementioned assumption, the labor demand curve of an RSU can be obtained by
aggregating the labor demand curve of all the buildings in the RSU, as shown in
Eq. (11.30):
DRSU(t)=
q
i=1
Dblgi(t)(11.30)
where qis the number of buildings in the RSU.
11.5.5 Repair Scheduling and Simulation
11.5.5.1 Community Recovery Curve
In real practice, the repair resource is limited, and not all RSUs can be assigned with
sufficient workers. Hence, it is important to prioritize each RSU so as to improve
11.5 Post-earthquake Repair Scheduling … 857
Fig. 11.39 Community
recovery curves of two types
of repair schemes
the repair efficiency of available resources. Various RSU repair schemes result in
different types of community recovery curves. Two types of repair schemes are
presented in Fig. 11.39. The objective of Type 1 repair scheme is to achieve full
recovery in the quickest possible manner. For this scheme, more severely damaged
RSUs, which requires a longer time to repair, are allocated with higher priority.
Therefore, the recovery rapidity at the early stage of the repair process is slow
and gradually accelerates as the repair progresses. The objective of the Type 2
repair scheme is to minimize the resilience index proposed by Bruneau et al. (2003)
(Eq. (11.17)). Therefore, slightly damaged buildings, which can easily be restored,
are assigned with a higher priority. This repair scheme satisfies the requirements of
shelter-in-place (Cimellaro et al. 2010; SPUR 2012) and can minimize the necessity
of interim housing. Therefore, the Type 2 repair scheme is adopted herein, and the
resilience index, R(Eq. (11.17)), is used to evaluate the effectiveness of different
repair-scheduling methods.
11.5.5.2 Repair-Scheduling Methods
Repair scheduling of regional buildings with limited labor forces is a non-
deterministic polynomial-time-hard (NP-hard) problem (Garey and Johnson 1979).
Moreover, the number of buildings in a city is enormous, which makes it extremely
difficult to find the global minimum of the recovery index, R. Therefore, a simpli-
fied repair scheduling method based on the characteristics of resilience index, R,is
presented in this section.
As shown in Fig. 11.39 and Eq. (11.17), the resilience index, R, is the integral of
the functional loss of regional buildings in a specific duration. Therefore, Rcan be
reduced by increasing the recovery rapidity at the early stage of the recovery process
(Cimellaro et al. 2010).
Based on the foregoing, two repair priority indices, P1and P2, are proposed, as
given by Eqs. (11.31) and (11.32):
P1=Qloss, RSU_i
TRSU_i
(11.31)
858 11 Post-earthquake Emergency Response and Recovery …
P2=Qloss, RSU_i
TRSU_iDmean, RSU_i
(11.32)
where Qloss, RSU_iis the post-earthquake functional loss of the ith RSU; TRSU_iis the
repair time of the ith RSU given a sufficient labor force; Dmean, RSU_iis the mean
labor demand of the ith RSU during the repair period of TRSU_i.
As evident in Eqs. (11.31) and (11.32), high repair priority indices (P1and P2)
indicate that the RSU can achieve large functional recovery within a given time; this
implies a more rapid recovery. Therefore, an RSU with larger repair priority index
values is assigned with a higher repair priority. That is, if the repair priority indices of
all RSUs in the region are calculated, rapid functional recovery of regional buildings
can be achieved according to the descending order of the repair priority index of each
RSU.
Note that repair priority index P2, compared to P1, considers the labor demand. If
the labor force is unlimited, then the repair priority factor, P1, is an ideal option for
rapid recovery. However, in most cases where the labor force of a region is limited, the
repair scheme that uses repair priority index P2can better utilize the available labor
force. Detailed comparisons of the effectiveness between these two repair priority
indices are discussed in Sect. 11.5.6.3.
11.5.5.3 Repair Simulation Method
Practically, repair resources in an urban area are always limited, and not all RSUs can
acquire sufficient resources for repairs. For an RSU with insufficient labor resources,
the repair time is longer than that given in Sect. 11.5.4.3. Accordingly, the job block
concept is introduced to calculate the repair time of an RSU with limited labor
resources.
The labor demand curve of an RSU according to the method described in
Sect. 11.5.4 is shown in Fig. 11.40. The labor demand curve describes the maximum
labor demand of an RSU at different repair stages and the duration of each repair stage.
Therefore, the repair procedure of an RSU can be regarded as multiple sequential
job blocks, and the workload of each job block is the product of the maximum labor
Fig. 11.40 Labor demand
curve and job blocks of a
typical RSU
11.5 Post-earthquake Repair Scheduling … 859
demand and the corresponding duration. For example, if the number of workers avail-
able is less than the maximum labor demand of the first job block, the time required
to complete the first job block can be computed by dividing the total workload of this
job block by the number of available workers. The repair procedures of the sequential
job blocks follow the same rule, and the repair work of the RSU is completed only
if all job blocks in it are repaired. Based on the presented method, the repair time of
an RSU with limited workers can be obtained.
Based on the job block concept, the city-scale repair simulation of large numbers
of RSUs with limited labor resources can be performed according to the following
steps.
1. Determine the time interval of each simulation time step (e.g., one day and one
week).
2. Allocate available labor resources according to the descending order of repair
priority indices of RSUs in the current time step.
3. Calculate the remaining workload of each RSU at the end of the current time
step.
4. Record the restored functionality if an RSU is completely repaired by the end of
the current time step and proceeds to the next time step.
In addition to the constraint in labor resources, other recovery constraints, such
as the constraints of limited recovery funding or construction materials, also signifi-
cantly affect the recovery process. It is worthwhile noting that the influence of other
recovery constraints can also be considered following the methodology proposed in
this work.
11.5.6 Case Study
Beijing City is selected as an example to demonstrate the methods proposed in this
study. Firstly, the nonlinear THA is implemented for residential buildings in the
studied area. Secondly, the residual functionality and labor demand curve of all
buildings are calculated through the method proposed in Sects. 11.5.3 and 11.5.4.
Thirdly, the repair scheduling is performed, and the effectiveness between the two
different repair schemes is compared.
11.5.6.1 Buildings in Beijing City
In this case study, 68 930 residential buildings within the 16 administrative districts
of Beijing City are simulated. The distributions of structural types and the number
of stories of residential buildings in the Beijing urban area are shown in Fig. 11.41.
As evident in the figure, a large proportion of the studied building inventory is
composed of shear wall structures and high-rise residential buildings. This is mainly
because the housing data of Beijing City are obtained from the online apartment
860 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.41 Structural types and number of stories of Beijing City’s residential buildings. RM:
reinforced masonry, RC: reinforced concrete, URM: unreinforced masonry
rental website (Fang 2018). A large proportion of the obtained building inventory
includes the late 2000 high-rise residential buildings because of the accessibility
of more comprehensive data of these newly constructed buildings. Note that the
primary purpose of this case study is not to obtain an accurate evaluation of the
seismic resilience of Beijing City but to demonstrate the effectiveness of the proposed
methods. If more comprehensive data become available in the future, a more accurate
simulation can be performed using the methods presented in this work.
As discussed in Sect. 11.5.3.1, the weighted functionality reflects the physical
and socio-economic functionalities of a building. In this case study, the number of
buildings in the area is enormous; accordingly, it is impractical to determine the
socio-economic parameter, α, of each building manually. Note that rental price is a
good alternative to represent the socio-economic attributes of residential buildings.
A residential building with a higher rental price is usually located in areas with more
economic activities and is closer to the workplace. Rapid recovery of this type of
residential buildings can facilitate economic recovery and relieve traffic pressure.
Therefore, the rental price per square meter per month is used as the socio-economic
functionality index, α, for each RSU. The rental price of each RSU in Beijing City can
be obtained through the online apartment rental website (Fang 2018); the rental price
distribution of each RSU is shown in Fig. 11.42. It is evident in this figure that the
rental price is considerably higher in the core area of Beijing City. For example, the
rental price can be more than 200 RMB/m2per month in the central area, whereas
the rental price in the suburban area of the city can be less than 50 RMB/m2per
month; hence, the difference is significant.
11.5 Post-earthquake Repair Scheduling … 861
Fig. 11.42 Rental price distribution of Beijing City (RMB/m2per month)
11.5.6.2 Earthquake Data of Beijing City
Earthquake data are the prerequisites for the city-scale nonlinear THA of buildings.
In this case study, the response spectra of the entire Beijing City are acquired through
a probabilistic seismic hazard analysis (Mcguire 2008). The response spectral atten-
uation functions (Yu 2002) and site amplification factors (Lu and Zhao 2007) of
the area are adopted. Subsequently, the artificial ground motion generation program,
SIMQKE (Gasparini and Vanmarcke 1976), is used to generate the ground motion
data of the region. The response spectral attenuation functions adopted in this study
are shown in Fig. 11.43a; the typical acceleration and velocity time–history data are
shown in Fig. 11.43b.
Two earthquake scenarios are considered: M8.0 and M7.0, with the epicenter
located at the eastern suburb of Beijing; the fault strike is 50° (Fu 2012). The epicenter
location and distribution of the 0.3-s spectral acceleration response (Sa_0.3 s) of the
M8.0 earthquake scenario are presented in Fig. 11.44.
After acquiring the ground motion data of Beijing, multi-story and high-rise, resi-
dential buildings were simulated with the MDOF shear models (Sect. 7.2) and MDOF
flexural shear models (Sect. 7.3), respectively. Subsequently, the unweighted residual
functionality of each RSU is computed using the method presented in Sect. 11.5.3.
The unweighted residual functionality can reflect the damage of each RSU in the
862 11 Post-earthquake Emergency Response and Recovery …
(a) The adopted response spectral attenuation functions (M8.0)
(b) Typical acceleration/velocity time–history
0
5
10
15
20
25
30
0 50 100 150 200
Sa_0.3s (m/s
2
)
Distance (km)
Short axis
Long axis
-4
-3
-2
-1
0
1
2
3
4
0 5 10 15 20 25 30 35 40 45
Acceleration (m/s
2
)
Time (s)
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0 5 10 15 20 25 30 35 40 45
Velocity (m/s)
Time (s)
Fig. 11.43 Earthquake data of Beijing City
11.5 Post-earthquake Repair Scheduling … 863
Fig. 11.44 Sa_0.3 s distribution and epicenter location of the Beijing M8.0 earthquake scenario
region, as shown in Fig. 11.45. In the M7.0 earthquake scenario (Fig. 11.45a), the
residential buildings in the region experienced slight seismic damage. The buildings
at the eastern part of the city exhibited more severe damage than the buildings on the
west; these agree with the Sa_0.3 s distribution in Fig. 11.44. It is noteworthy that in
the M7.0 earthquake scenario, some buildings scattered in the core area of Beijing
City were encountered severe damage. These buildings are unreinforced masonry
structures with a relatively weak seismic performance. The buildings in the M8.0
earthquake scenario are more severely damaged compared to the buildings in the
M7.0 earthquake scenario. Nevertheless, the damage distribution is similar to the
Sa_0.3 s distribution shown in Fig. 11.44.
11.5.6.3 Repair Simulation
Based on the repair scheduling method presented in Sect. 11.5.5, repair priority
indices P1and P2of all RSUs (Eq. (11.31) and (11.32)) are calculated; the distribution
of the repair priorities is presented in Fig. 11.46. The red dots in Fig. 11.46 represent
RSUs with higher repair priorities. Both the distributions of repair priority using
P1and P2indicate that RSUs in the core area tend to have higher repair priorities
864 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.45 Distribution of unweighted residual functionality of RSUs
11.5 Post-earthquake Repair Scheduling … 865
Fig. 11.46 Distribution of RSU repair priority
866 11 Post-earthquake Emergency Response and Recovery …
Table 11.7 Summary of repair simulation scenarios
Scenario ID Earthquake scenario Repair priority index Labor constraint
IM8-P1-Con M8.0 earthquake scenario P1724 000 workers
IM8-P2-Con M8.0 earthquake scenario P2724 000 workers
IM8-P1-Uncon M8.0 earthquake scenario P1Unlimited workers
IM8-P2-Uncon M8.0 earthquake scenario P2Unlimited workers
IM7-P1-Con M7.0 earthquake scenario P1724 000 workers
IM7-P2-Con M7.0 earthquake scenario P2724 000 workers
IM7-P1-Uncon M7.0 earthquake scenario P1Unlimited workers
IM7-P2-Uncon M7.0 earthquake scenario P2Unlimited workers
because the rental prices of RSUs in the core area of the city are substantially higher
(Fig. 11.42).
The repair simulation method proposed in Sect. 11.5.5.3 is adopted for the M8.0
and M7.0 earthquake scenarios. The number of construction workers for repair simu-
lation is set to 724 000 according to Beijing statistical data (BMBS 2018). For
comparison, repair simulations with no labor constraints are also performed for both
earthquake scenarios. Considering all the foregoing parameters, a total of eight repair
simulation scenarios are simulated, as summarized in Table 11.7. The simulated
community recovery curves are shown in Fig. 11.47.
As evident in Fig. 11.47a, the recovery process of Beijing City with a labor
constraint is considerably slower compared with that when there is no labor
constraint. Moreover, the recovery process in the M7.0 earthquake scenario is signif-
icantly faster because the seismic damage is milder (Fig. 11.45) compared with that
caused by the M8.0 earthquake.
In Fig. 11.47, the community recovery curves that adopt priority indices P1and
P2approximate each other. To further demonstrate the differences between the repair
scheduling scenarios using P1and P2, the community resilience indices of different
simulation scenarios are presented in Fig. 11.48. The results indicate that when the
available labor force is limited, the resilience index using P2is smaller than that
when P1is employed. This is because P2can fully utilize the limited resource, such
that it yields a more rapid recovery regardless of the labor constraint. The results in
Fig. 11.48 also show that when there is no labor constraint, the resilience index using
P1is smaller than that when P2is employed. According to the definition of P1in
Eq. (11.32), this is because an RSU with a larger repair priority index (in this case,
P1) is ensured of a higher recovery rapidity when the repair resource is abundant.
The community labor demand curves of different repair simulation scenarios
are shown in Fig. 11.49. The results indicate that the community labor demand
curves that use priority indices P1and P2are considerably similar. In Fig. 11.49,
because of the labor constraints, the number of days during which the assigned
workers were maintained at a full capacity is 56 and 17 days for the M8.0 and M7.0
11.5 Post-earthquake Repair Scheduling … 867
Fig. 11.47 Community recovery curves of Beijing City with or without labor constraints
earthquake scenarios, respectively. Subsequently, after the repair of some RSUs has
been completed, the labor demand significantly decreased.
To further demonstrate the repair process of regional buildings, the temporal
evolution of worker distribution of the M8.0-P2-Con repair simulation scenario is
presented in Fig. 11.50. The figure shows the number of workers per square kilometer
at different moments and displays the progress of repair in the area. For example, the
repair work is mainly centered in the core area for 10 d because the rental price in this
region is considerably higher; accordingly, the repair priorities of RSUs in this area
are higher. As the repair work proceeds, the repair of some RSUs in the core area of
the city is completed. Thereafter, the repair work gradually moves to the suburban
868 11 Post-earthquake Emergency Response and Recovery …
Fig. 11.48 Comparison of resilience indices, R, among different repair simulation scenarios
0
100000
200000
300000
400000
500000
600000
700000
800000
0 50 100 150 200 250 300
Number of workers
Time ( day )
IM8-P1-Con
IM8-P2-Con
IM7-P 1-Con
IM7-P 2-Con
Fig. 11.49 Labor demand curves of different repair simulation scenarios
area for the next 30–50 d. More repair works are finished, and the labor demand
decreases to less than the number of workers available for the following 70–110 d
(Fig. 11.49a). For the subsequent 130–170 d, most of the lightly damaged RSUs are
repaired, and only a few of the severely damaged RSUs at the eastern part of the city
continue to undergo repair.
11.5 Post-earthquake Repair Scheduling … 869
(a) 10 d (b) 30 d (c) 50 d
(d) 70 d (e) 90 d (f) 110 d
(g) 130 d (h) 150 d (i) 170 d
Fig. 11.50 Temporal evolution of worker distribution for the M8.0-P2-Con repair simulation
scenario (workers per square kilometer)
11.5.7 Concluding Remarks
A city-scale THA-driven building seismic resilience simulation framework is intro-
duced in this work. The framework uses the story-level EDPs obtained from the
THA of each building to achieve a more reasonable seismic resilience evaluation
and repair scheduling. Some of the conclusions are drawn below.
(1) A probabilistic calculation method of the post-earthquake residual functional-
ities of communities is proposed based on the building seismic performance
assessment method of FEMA P-58. Adopting the EDPs of each building
obtained from THA and the fragility database of FEMA P-58, the residual func-
tionality of each building can be reasonably obtained by aggregating damages
of all structural and non-structural components.
(2) Both physical and socio-economic functionalities of each building can be
considered by the building functionality index. In the case study of Beijing City,
the rental price was used to represent the socio-economic functionality index of
870 11 Post-earthquake Emergency Response and Recovery …
residential buildings. Accordingly, this can better guide decision-making and
repair scheduling.
(3) The introduced repair priority indices P1and P2, with or without labor
constraints considered, can facilitate the rapid recovery of regional buildings.
In the case study of Beijing City, repair priority index P2can fully utilize the
available labor force and realize the rapid recovery of community function-
alities when the number of construction workers is limited. If there are no
labor constraints, repair scheduling using repair priority index P1exhibits better
performance.
Based on the city-scale building nonlinear time–history analysis, together with the
component-level seismic damage assessment method of FEMA P-58 and the repair
simulation method of REDi, the proposed framework provides an insight into the
community repair simulation with labor constraints. Accordingly, these can assist in
the seismic resilience evaluation of the built environment so as to ultimately achieve
a resilient community.
11.6 Summary
Having successfully performed city-scale nonlinear time-history analyses (THA) for
earthquake disaster simulation and prediction in preceding chapters, this chapter aims
to employ the same technique for post-earthquake emergency response and recovery
simulation. Several methodological frameworks are proposed to perform a number
of challenging tasks, including real-time earthquake damage assessment taking
into account the key characteristics of recorded ground motions; regional seismic
damage prediction of buildings under the sequence of mainshock-aftershock; accu-
rate, efficient and rapid near-real-time seismic loss estimations using post-earthquake
remote sensing image analysis techniques; and post-earthquake repair simulation and
scheduling of city-scale buildings with labor constraints. All these proposed frame-
works are proven to be feasible and reliable through validations conducted on typical
Chinese towns, a university campus and the capital city of China. The methodologies
developed herein can be used for scientific and rational decision-making for earth-
quake disaster relief and reconstruction planning. This, in turn, provides assistance
to much-needed seismic resilience evaluation of the fast-growing built environment,
especially those seismic-prone regions in the world. This development will also
contribute to improving the resilience of the wider community.
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