1. Introduction

Recent the natural disasters such as earthquakes and hurricanes worldwide, especially those in the Pacific rim region such as Wenchuan Earthquake (2008), Nepal Earthquake (2015) and Indonesia Earthquake & Tsunami (2005, 2018), have demonstrated that the insufficient structural performance of buildings may lead to high disaster vulnerability on human society. Post-disaster recovery and reconstruction also test a country's disaster response capacity and economic strength. The direct loss of Wenchuan Earthquake in Western China (Ms8.0) was 845.1 billion Yuan in 2008, and only 1.66 billion Yuan was paid out by insurance, which can only rely on the huge amount of free economic assistance from the central government. But people in other Asian disaster regions are not always so lucky, Earthquake and tsunami heavily hit local society and economy in some Asian countries such as

Nepal or Indonesia which has no catastrophe insurance, and often leading to longtime local economic decline.

Most of Asian-Pacific regions located around the Pacific Rim seismic activity zone. High seismic intensity leads more high vulnerability to natural disasters due to particular geographic location. Since current building technology cannot avoid the negative effects of natural disasters such as earthquake, typhoons tsunami and atmospheric corrosion on the engineering economic loss, environment loss and human fatalities in whole society. It is necessary to evaluate the severity of the effects of various natural disasters. Such assessment study is not only aimed at the impact of a single disaster, but also should be based on the impact of long-term factors such as the life-cycle performance of engineering products.

Building structures are important places for human to work and live. Its durability, safety and comfort need to be guaranteed during life-cycle service. Building structure is located in the earth's natural environment, so during the service of the inevitable from the nature of wind, sunshine, rain, smog and other external factors. Some of the influences of these external environmental factors on civil engineering structures are beneficial. For example, mild air is beneficial to the strength growth of concrete in the long run, but most of the environmental influences from nature are harmful to the performance of buildings. Some external factors on the impact of buildings are potential and long-term adverse effects, such as due to global greenhouse gas emissions caused by the carbonization of concrete, acid gas corrosion of reinforcement, waves corrosion of Marine engineering structures. Which influence the modern civil engineering life-cycle sustainability. Other natural hazardous factors such as earthquake, typhoon, flood and tsunami are more dangerous and sudden affection. Human have defines such natural hazard as natural disasters. Now with the rapid development of economy in Eastern Asian coastal land, more population flow into metropolis, where infrastructures and buildings face huge pressure to long-term safe service in resisting natural hazards. For example the East Japan Earthquake (Ms9.0) on March 11, 2011 and the tsunami caused the damage of Fukushima nuclear power. The extremely serious accident of nuclear leakage, which caused extremely serious nuclear pollution to the Marine water environment of the western Pacific Ocean, caused long-term immeasurable loss.

civil engineering all of the world. Uncertainties are included and propagated

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China

At present for better approach above targets, many researchers further push the research performance-based engineering forward a great step over the entire lifecycle of the buildings. That is definitely exciting prospect but there also have several

Seismic life-cycle research requires proper integration of following three factors: (i) probability approaches for treating the uncertainties related to the seismic hazard and to the structural dynamic behavior including structural and non-structural components in the buildings, (ii) recovery time and seismic loss estimation methodologies for evaluating the structural performance based random probability and socioeconomic criteria, (iii) algorithms for efficient evaluation of the resultant multidimensional integrals completely quantifying seismic fragility and loss are

In 2013 December super typhoon Haiyan landed in Philippines, and resulted in 6300 life losses, millions people without shelter and \$2 billion in damage. So the most important mechanism is to rescue the refugees and compensate seismic loss from insurance companies. But how to determine buildings insurance premium ratio based seismic or typhoon loss estimation is a key problem in many Asia

through each step of the PBEE process [1].

DOI: http://dx.doi.org/10.5772/intechopen.84159

PBEE framework methodology by PEER.

obstacles must be fronted at same time.

Stochastic parameters of PBEE framework methodology.

shown in Figure 2.

Figure 2.

217

Figure 1.

According to U.S. risk analyst AIR Worldwide, direct earthquake insurance losses from Tohoku Earthquake caused by industrial and civil buildings, infrastructure amount to nearly \$35 billion, which is almost equal to the total disaster losses of the global insurance compensation in 2010.

Now three procedures have be titled to minimize their devastating effects by enhancing resilience in communities, that is, by reducing (1) system failure probability, (2) consequences of system failures, and (3) fee and time to recovery. So in the past several decades Load-and-resistance-factor design (LRFD) was used as the framework under which many new and existing structures are analyzed for seismic adequacy. This approach seeks to assure performance primarily in terms of failure probability of individual structural component, such as strong-column-and-weakbeam requirement. But unfortunately past seismic disasters revealed that LRFD design could not meet the above need for minimizing system failures probabilities and decreasing life and economic losses.

Performance-based earthquake engineering (PBEE) methodology finally was be developed in 2000 by Pacific Earthquake Engineering Research (PEER) shown in Figure 1. This approach involves combined numerical integration of all the conditional probabilities to propagate the uncertainties from one level of analysis to the next, resulting in probabilistic prediction of performance. The PBEE frame work consist of four steps, respectively is Hazard analysis, Structural analysis, Damage analysis and Loss analysis, The PBEE now has become future research basis spirit in Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China DOI: http://dx.doi.org/10.5772/intechopen.84159

Figure 1. PBEE framework methodology by PEER.

Nepal or Indonesia which has no catastrophe insurance, and often leading to long-

Most of Asian-Pacific regions located around the Pacific Rim seismic activity zone. High seismic intensity leads more high vulnerability to natural disasters due to particular geographic location. Since current building technology cannot avoid the negative effects of natural disasters such as earthquake, typhoons tsunami and atmospheric corrosion on the engineering economic loss, environment loss and human fatalities in whole society. It is necessary to evaluate the severity of the effects of various natural disasters. Such assessment study is not only aimed at the impact of a single disaster, but also should be based on the impact of long-term

Building structures are important places for human to work and live. Its durability, safety and comfort need to be guaranteed during life-cycle service. Building structure is located in the earth's natural environment, so during the service of the inevitable from the nature of wind, sunshine, rain, smog and other external factors. Some of the influences of these external environmental factors on civil engineering structures are beneficial. For example, mild air is beneficial to the strength growth of concrete in the long run, but most of the environmental influences from nature are harmful to the performance of buildings. Some external factors on the impact of buildings are potential and long-term adverse effects, such as due to global greenhouse gas emissions caused by the carbonization of concrete, acid gas corrosion of reinforcement, waves corrosion of Marine engineering structures. Which influence the modern civil engineering life-cycle sustainability. Other natural hazardous factors such as earthquake, typhoon, flood and tsunami are more dangerous and sudden affection. Human have defines such natural hazard as natural disasters. Now with the rapid development of economy in Eastern Asian coastal land, more population flow into metropolis, where infrastructures and buildings face huge pressure to long-term safe service in resisting natural hazards. For example the East Japan Earthquake (Ms9.0) on March 11, 2011 and the tsunami caused the damage of Fukushima nuclear power. The extremely serious accident of nuclear leakage, which caused extremely serious nuclear pollution to the Marine water environment

factors such as the life-cycle performance of engineering products.

of the western Pacific Ocean, caused long-term immeasurable loss.

the global insurance compensation in 2010.

and decreasing life and economic losses.

216

According to U.S. risk analyst AIR Worldwide, direct earthquake insurance losses from Tohoku Earthquake caused by industrial and civil buildings, infrastructure amount to nearly \$35 billion, which is almost equal to the total disaster losses of

Now three procedures have be titled to minimize their devastating effects by enhancing resilience in communities, that is, by reducing (1) system failure probability, (2) consequences of system failures, and (3) fee and time to recovery. So in the past several decades Load-and-resistance-factor design (LRFD) was used as the framework under which many new and existing structures are analyzed for seismic adequacy. This approach seeks to assure performance primarily in terms of failure probability of individual structural component, such as strong-column-and-weakbeam requirement. But unfortunately past seismic disasters revealed that LRFD design could not meet the above need for minimizing system failures probabilities

Performance-based earthquake engineering (PBEE) methodology finally was be developed in 2000 by Pacific Earthquake Engineering Research (PEER) shown in Figure 1. This approach involves combined numerical integration of all the conditional probabilities to propagate the uncertainties from one level of analysis to the next, resulting in probabilistic prediction of performance. The PBEE frame work consist of four steps, respectively is Hazard analysis, Structural analysis, Damage analysis and Loss analysis, The PBEE now has become future research basis spirit in

time local economic decline.

Natural Hazards - Risk, Exposure, Response, and Resilience

civil engineering all of the world. Uncertainties are included and propagated through each step of the PBEE process [1].

At present for better approach above targets, many researchers further push the research performance-based engineering forward a great step over the entire lifecycle of the buildings. That is definitely exciting prospect but there also have several obstacles must be fronted at same time.

Seismic life-cycle research requires proper integration of following three factors: (i) probability approaches for treating the uncertainties related to the seismic hazard and to the structural dynamic behavior including structural and non-structural components in the buildings, (ii) recovery time and seismic loss estimation methodologies for evaluating the structural performance based random probability and socioeconomic criteria, (iii) algorithms for efficient evaluation of the resultant multidimensional integrals completely quantifying seismic fragility and loss are shown in Figure 2.

In 2013 December super typhoon Haiyan landed in Philippines, and resulted in 6300 life losses, millions people without shelter and \$2 billion in damage. So the most important mechanism is to rescue the refugees and compensate seismic loss from insurance companies. But how to determine buildings insurance premium ratio based seismic or typhoon loss estimation is a key problem in many Asia

Figure 2.

Stochastic parameters of PBEE framework methodology.

countries. Refugees' buildings loss could not effective estimation because of absence reliable based research of life-cycle loss estimation. That is core reason why many Asia countries have not published normal disasters insurance policy at moment.

stochastic ground motion models including occurrence time point of every earthquake are adopted for the seismic hazard description in terms of detailed and versatile characteristic of seismic risk as well as balance in computation efficiency. Assembly-based vulnerability method is also used in evaluating seismic response of structural components based random probability in damage analysis. Therefore, life-cycle seismic cost is qualified by its expected value over the probability models and stochastic simulation is suggested for its evaluation. In the end, an revised probability life-cycle sensitivity analysis for identification of important risk factors for the life-cycle loss concept is also reviewed based former research results and stochastic sampling concepts. The analysis aims to identify the importance of the various risk-factors towards the overall performance of the structural system.

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China

Predictable ground motions in the special site firstly are considered in research as outer excitation to test structural system's performance. Yinchuan city which locate in high seismic hazard region in Western China was selected as sampling site in the research. A terrible earthquake (Ms8.0) was happened in Yinchuan district in 1739 and thousands of people died and earthquake disaster loss is very huge in record of local history. There are many NE-trending fault zones in the area. The local area is 180 km from north to south and 60 km from east to west. It is roughly

Building Seismic Code (GB50011-2010) [2], the area is 8 degree seismic intensity design area, and the basic seismic acceleration value is 0.2 g. The area is a fault basin formed by the Cenozoic. The exposed strata are dominated by Quaternary sediments. The soil foundation is dominated by soft sand soil and is classified as II sites group, the site basic design period is 0.4 s. The thickness of the soil layer is generally between several hundred meters and 1 km, and the shear wave velocity of the soil

Life-cycle model of a seismic hazard specifies (1) the random arrival times, T1, T2,⋯, of individual events at a site during a reference period τ, and (2) the random properties of the ground motion hazards under considerations at T1, T2,⋯. The random properties involves: stochastic quantification of the earthquake intensity measure based precious activity matrix at the site and creating stochastic

Monte Carlo sampling algorithms can be used for generating samples of lifetime seismic hazard at a given site during a reference period τ. Therefore, a life-cycle hazard sample consists of the arrival times of individual events and the properties

Near-fault ground strong pulse is also considered into research based earthquakes survey recent years in many places of the world. So the final stochastic ground motion consist of low-frequency (long period) and high –frequency com-

The activity matrix of seismic hazard at a given site delivers the annual rate of occurrence for events of the hazard corresponding to earthquake magnitude, M, and rupture distance, r. We can plot activity matrices against the properties which completely define the probability law of the hazard at the site. The plot of mean annual rate of occurrence of earthquake for all ð Þ M;r at the site is called the site

. According to the Chinese

2. Seismic hazard analysis

DOI: http://dx.doi.org/10.5772/intechopen.84159

layer Vs<sup>30</sup> ¼ 150 � 300m=s.

defining their probability law.

seismic activity matrix [3].

219

2.1 Activity matrix and event arrival

30 degrees northeast and has a total area of 7790 Km<sup>2</sup>

ground motions consistent with the intensity hazard.

ponents and be combined to form the acceleration time history.

Earlier methodologies for seismic loss estimation mainly expressed seismic losses in terms of the global reliability characteristic of the structural system. Recent advances in PBEE quantify more appropriately repair cost, casualties, and downtime in relation to the structural or even on a detailed, component level (such as partitions, beams and columns) response [1], using seismic fragility curves to develop such a relationship. Nonlinear time-history as an more powerful analytical tool now accepted by many researchers in calculating seismic damage under a given earthquake excitation.

Nonlinear incremental time-history analysis is most popular methodology, which can facilitate such a description according local hazard levels through Intensity Measures (IMs) that represents the dominant features of the seismic excitation, and subsequent scaling of ground wave records to different IM values, as prescribed by a probabilistic seismic hazard analysis. Stochastic ground waves are chosen by fitting for response spectrum based China seismic code (GB50011-2010, 2] through online searching and selecting tool of PEER ground motion database, which represent samples of possible future ground waves for each hazard level of different regions in China. Additionally recent concerns related to ground motion scaling also in consideration into the stochastic ground wave model. The parameters of these ground wave, for example, duration of strong motion, can be related to earthquake (type of fault, moment magnitude and rupture distance) and site characteristics (shear wave velocity, local site conditions) by appropriate predictive relationship. Description of the uncertainty for the earthquake characteristics (moment and rupture distance) and for the predictive relationships, through appropriate probability models, to show a complete and detailed probabilistic description of potential future ground motion time waves. Therefore, the emphasis of primarily research is located in development of stochastic ground motion models.

In consideration of complexity and different regional characteristic about lifecycle seismic loss analysis, a whole set of innovated life-cycle analysis procedures based stochastic probability have been raised in this article based past PBEE research results.

The methodology indeed expand research time to life-cycle of buildings based PBEE, so basically it also consist of four steps same as PBEE framework. Figure 3 shows the optimized methodology in research based PBEE.

This article is focus on a simulation-based, comprehensive research framework that aims to put the life-cycle loss estimation analysis into reality. Firstly life-cycle

Figure 3. Optimized framework of life-cycle loss estimation in research.

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China DOI: http://dx.doi.org/10.5772/intechopen.84159

stochastic ground motion models including occurrence time point of every earthquake are adopted for the seismic hazard description in terms of detailed and versatile characteristic of seismic risk as well as balance in computation efficiency. Assembly-based vulnerability method is also used in evaluating seismic response of structural components based random probability in damage analysis. Therefore, life-cycle seismic cost is qualified by its expected value over the probability models and stochastic simulation is suggested for its evaluation. In the end, an revised probability life-cycle sensitivity analysis for identification of important risk factors for the life-cycle loss concept is also reviewed based former research results and stochastic sampling concepts. The analysis aims to identify the importance of the various risk-factors towards the overall performance of the structural system.

## 2. Seismic hazard analysis

countries. Refugees' buildings loss could not effective estimation because of absence reliable based research of life-cycle loss estimation. That is core reason why many Asia countries have not published normal disasters insurance policy at moment. Earlier methodologies for seismic loss estimation mainly expressed seismic losses

in terms of the global reliability characteristic of the structural system. Recent advances in PBEE quantify more appropriately repair cost, casualties, and downtime in relation to the structural or even on a detailed, component level (such as partitions, beams and columns) response [1], using seismic fragility curves to develop such a relationship. Nonlinear time-history as an more powerful analytical tool now accepted by many researchers in calculating seismic damage under a given

Natural Hazards - Risk, Exposure, Response, and Resilience

Nonlinear incremental time-history analysis is most popular methodology, which can facilitate such a description according local hazard levels through Intensity Measures (IMs) that represents the dominant features of the seismic excitation, and subsequent scaling of ground wave records to different IM values, as prescribed by a probabilistic seismic hazard analysis. Stochastic ground waves are chosen by fitting for response spectrum based China seismic code (GB50011-2010, 2] through online searching and selecting tool of PEER ground motion database, which represent samples of possible future ground waves for each hazard level of different regions in China. Additionally recent concerns related to ground motion scaling also in consideration into the stochastic ground wave model. The parameters of these ground wave, for example, duration of strong motion, can be related to earthquake (type of fault, moment magnitude and rupture distance) and site characteristics (shear wave velocity, local site conditions) by appropriate predictive relationship. Description of the uncertainty for the earthquake characteristics (moment and rupture distance) and for the predictive relationships, through appropriate probability models, to show a complete and detailed probabilistic description of potential future ground motion time waves. Therefore, the emphasis of primarily research is

In consideration of complexity and different regional characteristic about lifecycle seismic loss analysis, a whole set of innovated life-cycle analysis procedures based stochastic probability have been raised in this article based past PBEE

The methodology indeed expand research time to life-cycle of buildings based PBEE, so basically it also consist of four steps same as PBEE framework. Figure 3

This article is focus on a simulation-based, comprehensive research framework that aims to put the life-cycle loss estimation analysis into reality. Firstly life-cycle

located in development of stochastic ground motion models.

shows the optimized methodology in research based PBEE.

Optimized framework of life-cycle loss estimation in research.

earthquake excitation.

research results.

Figure 3.

218

Predictable ground motions in the special site firstly are considered in research as outer excitation to test structural system's performance. Yinchuan city which locate in high seismic hazard region in Western China was selected as sampling site in the research. A terrible earthquake (Ms8.0) was happened in Yinchuan district in 1739 and thousands of people died and earthquake disaster loss is very huge in record of local history. There are many NE-trending fault zones in the area. The local area is 180 km from north to south and 60 km from east to west. It is roughly 30 degrees northeast and has a total area of 7790 Km<sup>2</sup> . According to the Chinese Building Seismic Code (GB50011-2010) [2], the area is 8 degree seismic intensity design area, and the basic seismic acceleration value is 0.2 g. The area is a fault basin formed by the Cenozoic. The exposed strata are dominated by Quaternary sediments. The soil foundation is dominated by soft sand soil and is classified as II sites group, the site basic design period is 0.4 s. The thickness of the soil layer is generally between several hundred meters and 1 km, and the shear wave velocity of the soil layer Vs<sup>30</sup> ¼ 150 � 300m=s.

Life-cycle model of a seismic hazard specifies (1) the random arrival times, T1, T2,⋯, of individual events at a site during a reference period τ, and (2) the random properties of the ground motion hazards under considerations at T1, T2,⋯. The random properties involves: stochastic quantification of the earthquake intensity measure based precious activity matrix at the site and creating stochastic ground motions consistent with the intensity hazard.

Monte Carlo sampling algorithms can be used for generating samples of lifetime seismic hazard at a given site during a reference period τ. Therefore, a life-cycle hazard sample consists of the arrival times of individual events and the properties defining their probability law.

Near-fault ground strong pulse is also considered into research based earthquakes survey recent years in many places of the world. So the final stochastic ground motion consist of low-frequency (long period) and high –frequency components and be combined to form the acceleration time history.

#### 2.1 Activity matrix and event arrival

The activity matrix of seismic hazard at a given site delivers the annual rate of occurrence for events of the hazard corresponding to earthquake magnitude, M, and rupture distance, r. We can plot activity matrices against the properties which completely define the probability law of the hazard at the site. The plot of mean annual rate of occurrence of earthquake for all ð Þ M;r at the site is called the site seismic activity matrix [3].

The average number of events per year irrespective of the values of ð Þ M;r is

$$\nu = \sum\_{i=\overline{M},r} \upsilon\_{i\_{\mathcal{M}},i\_r} \tag{1}$$

The model parameters include two seismological parameters M and r, describing the seismic hazard, the white-noise sequence Z<sup>ω</sup> and predictive relationship for function A f ð Þ ; M;r and e tð Þ ; M;r . Figure 4 shows A f ð Þ ; M;r and e tð Þ ; M;r based functions for different values of M and r. It can be seen that as the moment

magnitude increases the duration of the envelope function for strong component in motions also increases and the spectral amplitude becomes larger at all frequencies with a shift of dominant frequency content towards the lower frequency regime. As the epicenter distance increases, the spectral amplitude decreases uniformly and the

Figure 5 shows the detailed process of seismic wave fitting in view of different earthquake magnitude M and rupture distance r. And near-fault rupture influence

envelope function also decreases, but at a relatively smaller amount.

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China

DOI: http://dx.doi.org/10.5772/intechopen.84159

Figure 4.

Figure 5.

221

Fitting process of stochastic time history wave.

Time and frequency envelope with different M and R.

We assume that the events in time according to a homogeneous Poisson counting process f g Nð Þτ ; τ ≥ 0 of intensity ν so that

$$P(N(\tau) = n) = \frac{(\nu \tau)^n}{n!} \exp\left(-\nu \tau\right), n = 0, 1, 2, \dots \tag{2}$$

We note several properties of homogeneous Poisson counting process f g Nð Þτ ; τ ≥ 0 . First, the inter-arrival time Tk � Tk�1, k ¼ 1,…, Nð Þτ , T<sup>0</sup> ¼ 0, are independent exponential random variables with rate ν since P Tð Þ¼ . τ P Nð Þ ð Þ¼ τ 0 ¼ exp ð Þ �ντ . Second, conditional on Nð Þ¼ τ n, the unordered Poisson events f g <sup>s</sup>1; <sup>s</sup>2; <sup>⋯</sup>; sn occurring in 0ð Þ ; <sup>τ</sup> have the probability density function 1=τ<sup>n</sup>. Therefore, the unordered Poisson events are independent and uniformly distributed on 0ð Þ ; τ conditional on Nð Þ¼ τ n.The calculation method is based on the above properties to program. Samples of inter-arrival times are generated consecutively using their conditional distributions as long as the generated Poison events remain in 0ð Þ ; τ .

#### 2.2 High-frequency component

For the higher frequency component of ground motions in the seismic hazard model means the frequency of wave larger than 0.1–0.2 Hz here. The approach corresponds to a 'source-based'stochastic ground motion model, developed by considering the type of the fault rupture at the source as well as of the propagation of seismic waves through the underground soil site till the structural foundation. It is based on a parametric description of the ground motion's radiation spectrum A f ð Þ ; M;r , dependent on the earthquake magnitude, M, and rupture distance, r, and expressed as a function including the frequency f of seismic wave. This spectrum consists of many factors that account for the spectral effects from the source (source spectrum) as well as propagation through the earth's crust. The duration of the ground motion is addressed through an envelope function e tð Þ ; M;r , which is also depends on M and r. More details on them are shown in article [3]. These frequency and time domain function A f ð Þ ; M;r and e tð Þ ; M;r , completely describe the earthquake motion model and their characteristics are provided by predictive relationships that relate them directly to the seismic hazard such as M and r.

The time history for a specific event magnitude, M, and rupture distance, r, is obtained according to this model by modulating a white-noise sequence Z<sup>ω</sup> ¼ ½ � Zωð Þ iΔt : i ¼ 1; 2;…; NT by e tð Þ ; M;r and subsequently by A f ð Þ ; M;r through the following steps:


Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China DOI: http://dx.doi.org/10.5772/intechopen.84159

The model parameters include two seismological parameters M and r, describing the seismic hazard, the white-noise sequence Z<sup>ω</sup> and predictive relationship for function A f ð Þ ; M;r and e tð Þ ; M;r . Figure 4 shows A f ð Þ ; M;r and e tð Þ ; M;r based functions for different values of M and r. It can be seen that as the moment magnitude increases the duration of the envelope function for strong component in motions also increases and the spectral amplitude becomes larger at all frequencies with a shift of dominant frequency content towards the lower frequency regime. As the epicenter distance increases, the spectral amplitude decreases uniformly and the envelope function also decreases, but at a relatively smaller amount.

Figure 5 shows the detailed process of seismic wave fitting in view of different earthquake magnitude M and rupture distance r. And near-fault rupture influence

Figure 4. Time and frequency envelope with different M and R.

Figure 5. Fitting process of stochastic time history wave.

The average number of events per year irrespective of the values of ð Þ M;r is

viM,ir (1)

<sup>n</sup>! exp ð Þ �ντ , n <sup>¼</sup> <sup>0</sup>, <sup>1</sup>, <sup>2</sup>,… (2)

ν ¼ ∑ <sup>i</sup>¼M,r

We assume that the events in time according to a homogeneous Poisson

We note several properties of homogeneous Poisson counting process f g Nð Þτ ; τ ≥ 0 . First, the inter-arrival time Tk � Tk�1, k ¼ 1,…, Nð Þτ , T<sup>0</sup> ¼ 0, are independent exponential random variables with rate ν since P Tð Þ¼ . τ P Nð Þ ð Þ¼ τ 0 ¼ exp ð Þ �ντ . Second, conditional on Nð Þ¼ τ n, the unordered Poisson events f g <sup>s</sup>1; <sup>s</sup>2; <sup>⋯</sup>; sn occurring in 0ð Þ ; <sup>τ</sup> have the probability density function 1=τ<sup>n</sup>.

Therefore, the unordered Poisson events are independent and uniformly distributed on 0ð Þ ; τ conditional on Nð Þ¼ τ n.The calculation method is based on the above properties to program. Samples of inter-arrival times are generated consecutively using their conditional distributions as long as the generated Poison events remain

For the higher frequency component of ground motions in the seismic hazard model means the frequency of wave larger than 0.1–0.2 Hz here. The approach corresponds to a 'source-based'stochastic ground motion model, developed by considering the type of the fault rupture at the source as well as of the propagation of seismic waves through the underground soil site till the structural foundation. It is based on a parametric description of the ground motion's radiation spectrum A f ð Þ ; M;r , dependent on the earthquake magnitude, M, and rupture distance, r, and expressed as a function including the frequency f of seismic wave. This spectrum consists of many factors that account for the spectral effects from the source (source spectrum) as well as propagation through the earth's crust. The duration of the ground motion is addressed through an envelope function e tð Þ ; M;r , which is also depends on M and r. More details on them are shown in article [3]. These frequency and time domain function A f ð Þ ; M;r and e tð Þ ; M;r , completely describe the earthquake motion model and their characteristics are provided by predictive relationships that relate them directly to the seismic hazard such as M and r.

The time history for a specific event magnitude, M, and rupture distance, r, is

Z<sup>ω</sup> ¼ ½ � Zωð Þ iΔt : i ¼ 1; 2;…; NT by e tð Þ ; M;r and subsequently by A f ð Þ ; M;r through

1. The sequence Z<sup>ω</sup> is multiplied by the time envelope function e tð Þ ; M;r .

2. This modified sequence is then transformed to the frequency domain.

3. It is normalized by the square root of the mean square of the amplitude spectrum.

4.The normalized sequence is multiplied by the radiation spectrum A f ð Þ ; M;r .

5. It is transformed back to the time domain to yield the desired acceleration time

obtained according to this model by modulating a white-noise sequence

counting process f g Nð Þτ ; τ ≥ 0 of intensity ν so that

Natural Hazards - Risk, Exposure, Response, and Resilience

in 0ð Þ ; τ .

the following steps:

history.

220

2.2 High-frequency component

P Nð Þ¼ ð Þ¼ <sup>τ</sup> <sup>n</sup> ð Þ ντ <sup>n</sup>

Figure 6. Optimized wave in consideration of near-fault pulse.

also be considered so as to reflect actual situation in most high seismic intensity areas in China as shown in Figure 6.

> The structure consists with general configuration of bent widths and bay widths of 6 m and 24 m respectively, so the construction area of whole building is 1584 m<sup>2</sup> and which has 66 m long with 12 columns and 24 m width, structure is symmetrical

At the same time RC bent frame columns are variable cross-section columns, rein-

which is on the bracket. Track beams are confined frame element array on the brackets along the interior side of the building between bent frame columns. The roof of building which height is 9.6 m consist in reinforced concrete truss, the truss length is changed from 2.4 m in center to 1.5 m of two sides, moreover there are four kind of circular hollow steel bar be using with diameter from 0.03 m to 0.05 m,

The building's wall between columns generally consist of load-bearing infill masonry walls in China, confined by reinforced concrete bent frame columns and thickness of wall is 0.37 m commonly according China masonry code. Columns must have four 32 and 25 mm diameter longitudinal reinforcements, 8 mm diameter stirrups must be spaced 100 mm apart at the terminal and 200 mm at the center of

The masonry brick strength must at least MU15 and the mortar strength must at least M10 according to China masonry code, so typical masonry shear strength is 0.27–1 Mpa. Bilinear stress-strain relationships with strain hardening were used for reinforced members which yield strength is 335 Mpa [4] .Concrete axial compressive strength is 20–25 Mpa in considering of that many industrial frames in Western China regions. And coefficient with variation of 0.3 has been considered for steel and concrete respectively. Uniaxial nonlinear constant confinement concrete model that constant confining pressure is assumed throughout the entire stress-strain

) on the bracket of two side longitudinal columns of the building.

) is 1.86% (4ϕ32 þ 8ϕ22) which

) is 1.96% ( 4ϕ25 þ 4ϕ22)

, which is typical for

in plan and elevation, and rectangular reinforced concrete track beam

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China

forcement ratio of down columns (0.40 � 0.80 m<sup>2</sup>

The representative RC frames- (i) front view (ii) plan view.

DOI: http://dx.doi.org/10.5772/intechopen.84159

is under the bracket and up-columns (0.40 � 0.40 m<sup>2</sup>

Industrial building model (i: Overview, ii: Section detail reinforcement).

and thickness of bar'section is also verify from 2 to 3 mm.

range is proposed by Mander to apply to element of concrete [5]. The roof live load of industrial frame usually was 1.0 kN/m2

an industrial building including snow load. And dead load is 2.0 kN/m<sup>2</sup> which

(0.30 � 0.90 m<sup>2</sup>

Figure 7.

Figure 8.

the elements.

223

considering worst condition.

## 3. Classic buildings modeling

China is known as the country of the most population and the world's factory, so industrial construction plays an important role in China's economic growth. Two kinds of classic buildings were be considered in the research including public buildings and industrial buildings in the research.

#### 3.1 Multi-storey RC public buildings

A classic six storey reinforced concrete (RC) moment resisting buildings have been constructed in order to obtain the seismic insurance ratio and influence of various sources of uncertainties on the life-cycle cost in select Western China region. Steel of class with yield stress of 335 Mpa and modulus of elasticity equal to 210 Gpa has been considered, while concrete of cubic strength of 25 Mpa and modulus of elasticity equal to 30 Gpa. The structural layout of the building represents six bay in longitudinal direction with 6–8 m span lengths and three bay in transverse direction with 6–2.5–6 m span lengths respectively. The storey height is 3.3 m. The column elements size is 0.5 m 0.5 m 0.5 m 0.7 m. The beam size is 0.25 m 0.6 m. The slab thickness is equal to 12 cm, while in addition to the selfweight of the beams and the slabs, a distributed permanent load of 2 kN=m<sup>2</sup> due to floor-finishing partitions and live load of 1.5 kN=m2. For the analysis a three dimensional fiber model is created in Seismostruct software shown in Figure 7.

#### 3.2 Single-storey industrial buildings

A regular, single-storey industrial digital finite element model is chosen in Figure 8 to represent the system. The model is designed according China seismic code [2] to the prescriptions for loading, material, member dimensioning and detailing of the seismic design and gravity load.

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China DOI: http://dx.doi.org/10.5772/intechopen.84159

#### Figure 7.

also be considered so as to reflect actual situation in most high seismic intensity

China is known as the country of the most population and the world's factory, so industrial construction plays an important role in China's economic growth. Two kinds of classic buildings were be considered in the research including public

A classic six storey reinforced concrete (RC) moment resisting buildings have been constructed in order to obtain the seismic insurance ratio and influence of various sources of uncertainties on the life-cycle cost in select Western China region. Steel of class with yield stress of 335 Mpa and modulus of elasticity equal to 210 Gpa has been considered, while concrete of cubic strength of 25 Mpa and modulus of elasticity equal to 30 Gpa. The structural layout of the building represents six bay in longitudinal direction with 6–8 m span lengths and three bay in transverse direction with 6–2.5–6 m span lengths respectively. The storey height is 3.3 m. The column elements size is 0.5 m 0.5 m 0.5 m 0.7 m. The beam size is 0.25 m 0.6 m. The slab thickness is equal to 12 cm, while in addition to the selfweight of the beams and the slabs, a distributed permanent load of 2 kN=m<sup>2</sup> due to floor-finishing partitions and live load of 1.5 kN=m2. For the analysis a three dimensional fiber model is created in Seismostruct software shown in Figure 7.

A regular, single-storey industrial digital finite element model is chosen in Figure 8 to represent the system. The model is designed according China seismic code [2] to the prescriptions for loading, material, member dimensioning and

areas in China as shown in Figure 6.

Optimized wave in consideration of near-fault pulse.

Natural Hazards - Risk, Exposure, Response, and Resilience

Figure 6.

3. Classic buildings modeling

3.1 Multi-storey RC public buildings

3.2 Single-storey industrial buildings

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detailing of the seismic design and gravity load.

buildings and industrial buildings in the research.

The representative RC frames- (i) front view (ii) plan view.

Figure 8. Industrial building model (i: Overview, ii: Section detail reinforcement).

The structure consists with general configuration of bent widths and bay widths of 6 m and 24 m respectively, so the construction area of whole building is 1584 m<sup>2</sup> and which has 66 m long with 12 columns and 24 m width, structure is symmetrical in plan and elevation, and rectangular reinforced concrete track beam (0.30 � 0.90 m<sup>2</sup> ) on the bracket of two side longitudinal columns of the building. At the same time RC bent frame columns are variable cross-section columns, reinforcement ratio of down columns (0.40 � 0.80 m<sup>2</sup> ) is 1.86% (4ϕ32 þ 8ϕ22) which is under the bracket and up-columns (0.40 � 0.40 m<sup>2</sup> ) is 1.96% ( 4ϕ25 þ 4ϕ22) which is on the bracket. Track beams are confined frame element array on the brackets along the interior side of the building between bent frame columns. The roof of building which height is 9.6 m consist in reinforced concrete truss, the truss length is changed from 2.4 m in center to 1.5 m of two sides, moreover there are four kind of circular hollow steel bar be using with diameter from 0.03 m to 0.05 m, and thickness of bar'section is also verify from 2 to 3 mm.

The building's wall between columns generally consist of load-bearing infill masonry walls in China, confined by reinforced concrete bent frame columns and thickness of wall is 0.37 m commonly according China masonry code. Columns must have four 32 and 25 mm diameter longitudinal reinforcements, 8 mm diameter stirrups must be spaced 100 mm apart at the terminal and 200 mm at the center of the elements.

The masonry brick strength must at least MU15 and the mortar strength must at least M10 according to China masonry code, so typical masonry shear strength is 0.27–1 Mpa. Bilinear stress-strain relationships with strain hardening were used for reinforced members which yield strength is 335 Mpa [4] .Concrete axial compressive strength is 20–25 Mpa in considering of that many industrial frames in Western China regions. And coefficient with variation of 0.3 has been considered for steel and concrete respectively. Uniaxial nonlinear constant confinement concrete model that constant confining pressure is assumed throughout the entire stress-strain range is proposed by Mander to apply to element of concrete [5].

The roof live load of industrial frame usually was 1.0 kN/m2 , which is typical for an industrial building including snow load. And dead load is 2.0 kN/m<sup>2</sup> which considering worst condition.
