4. Incremental dynamic damage analysis

In the seismic assessment of buildings a wide range stochastic ground motions from PEER strong motion database and seven seismic hazard level (HL) be considered in order to take into account the uncertainties. The main objective of IDA method is to define a curve through a relation between the seismic intensity level and the corresponding maximum response of the structural system. The intensity level and the structural response are described through an intensity measure (IM) and an engineering demand parameters (EDP) which refers also as damage index (DI). Incremental analysis are implemented through the following steps in this research: (i) Construct the local typical digital finite element model for performing nonlinear dynamic analyses; (ii) select a group of stochastic ground motion fitted with local response spectrum; (iii) select a proper intensity measure and an engineering demand parameter; (iv) employ an appropriate algorithm for selecting the record scaling factor in order to obtain the IM-EDP curve by performing the least required nonlinear dynamic analyses and (v) employ a summarization technique for exploiting the multiple waves results. In this work, the Sað Þ T1; 5% for damping equal to 5% is selected as IM indicator, since it is the most commonly used intensity measure in practice today for the analysis of buildings. At the same time, two kind of damage index: the maximum inter-storey drift θmax and maximum floor acceleration are chosen as EDPs, which are based on the maximum deformation of different damage state.

Actually scale factors is a key setting through IM in incremental analysis. The maximum inter-storey drift is recommended by FEMA-350 as the most suitable performance criterion for frame structures and is used in the research [6]. Depending on the problem and the performance that is needed to be calculated different intensity measures and performance factors can also be used. In this work two types of scaling be used: scaling all ground motion records in the same value of spectral acceleration or using a common scaling factor for all ground motion records. The Sað Þ T1; 5% is calculated from the hazard curve of the area of interest, such as Yinchuan of western China in this work shown in Eq. (3).

$$\overline{P}(DI \ge DI\_i) = \frac{\mathcal{Y}}{k^\* a\_{\text{max}}} + \mathcal{c} \tag{3}$$

structural and non-structural damage of every floor of RC buildings must be detected based the two EDPs parameters. The maximum ISD% locates in second floor and the MFA in the top floor at the same time. That means the most structural damage lie in second floor and the severe non-structural damage in top storey,

Drift ratio and floor acceleration limits for RC buildings in Yinchuan.

The regression fitting curve for calculating the earthquake impact factor αmax based China seismic code.

 72/50 Slight damage 2.513 0.148 1.81 1.3 38/50 Light damage 0.951 0.307 0.379 2.1 25/50 Moderate damage I 0.574 0.415 0.227 3.7 4 16/50 Moderate damage II 0.348 0.525 0.139 4.7 10/50 Heavy damage I 0.21 0.627 0.107 6.2 5/50 Heavy damage II 0.103 0.739 0.063 7.2 2/50 Major damage 0.0404 0.824 0.040 9.0

Limit states θisd(%) afloorð Þg (I)-None θ ≤0:1 a≤ 0:05 (II)-Slight 0:1 , θ ≤0:2 0:05 , a ≤0:10 (III)-Light 0:2 , θ ≤0:28 0:10 , a ≤0:16 (IV)-Light II 0:28 , θ ≤0:4 0:16 , a ≤0:20 (V)-Moderate I 0:40 , θ ≤0:55 0:20 , a ≤0:30 (VI)-Moderate II 0:55 , θ ≤0:90 0:30 , a ≤0:50 (VII)-Heavy 0:90 , θ ≤1:70 0:50 , a ≤0:75 (VIII)-Major-Ma θ . 1:70 a . 0:75

<sup>i</sup> % Scaling factors

Hazard level Limit states Pi αmax PDI

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China

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

No. Typical sample buildings in Research

Figure 9.

Table 1.

Table 2.

225

Damage impact indicator in IDA.

Where <sup>γ</sup> <sup>¼</sup> <sup>1</sup>:3253, k <sup>¼</sup> <sup>2</sup>:<sup>9771</sup> � <sup>10</sup>�<sup>2</sup> , c ¼ �0:005in the function and the result was also shown in Figure 9.

P50% is the exceedance probabilities in 50 years, and Pi is annual exceedance probabilities. IDA nonlinear procedure has been chosen for detect structural seismic vulnerability including structural damage and non-structural damage. So we set suggested 7 damage limit states (LS) in calculation on the base of post research. And emphasis of LS is been located in moderate damage and heavy damage corresponding to the damage ratio between 20–45% based structural damage condition. At the same time nonstructural damage also can be classify with 7 HL or LS using peak ground acceleration. Damage scale indicators in IDA have been shown in Table 1.

#### 4.1 Damage analysis of multi-storey RC buildings

The IM scaling factor increase from 1 to 7.2 in IDA analysis. The whole damage LS of maximum inter-storey drift ratio (ISD%) and maximum floor acceleration (MFA) of every storey are shown in Table 2. That means all kind of seismic intensity waves have impacted on RC buildings in life-cycle period. So the

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

#### Figure 9. The regression fitting curve for calculating the earthquake impact factor αmax based China seismic code.


#### Table 1.

4. Incremental dynamic damage analysis

Natural Hazards - Risk, Exposure, Response, and Resilience

ent damage state.

In the seismic assessment of buildings a wide range stochastic ground motions from PEER strong motion database and seven seismic hazard level (HL) be considered in order to take into account the uncertainties. The main objective of IDA method is to define a curve through a relation between the seismic intensity level and the corresponding maximum response of the structural system. The intensity level and the structural response are described through an intensity measure (IM) and an engineering demand parameters (EDP) which refers also as damage index (DI). Incremental analysis are implemented through the following steps in this research: (i) Construct the local typical digital finite element model for performing nonlinear dynamic analyses; (ii) select a group of stochastic ground motion fitted with local response spectrum; (iii) select a proper intensity measure and an engineering demand parameter; (iv) employ an appropriate algorithm for selecting the record scaling factor in order to obtain the IM-EDP curve by performing the least required nonlinear dynamic analyses and (v) employ a summarization technique for exploiting the multiple waves results. In this work, the Sað Þ T1; 5% for damping equal to 5% is selected as IM indicator, since it is the most commonly used intensity measure in practice today for the analysis of buildings. At the same time, two kind of damage index: the maximum inter-storey drift θmax and maximum floor acceleration are chosen as EDPs, which are based on the maximum deformation of differ-

Actually scale factors is a key setting through IM in incremental analysis. The maximum inter-storey drift is recommended by FEMA-350 as the most suitable performance criterion for frame structures and is used in the research [6]. Depending on the problem and the performance that is needed to be calculated different intensity measures and performance factors can also be used. In this work two types of scaling be used: scaling all ground motion records in the same value of spectral acceleration or using a common scaling factor for all ground motion records. The Sað Þ T1; 5% is calculated from the hazard curve of the area of interest,

> γ k∗ αmax

þ c (3)

, c ¼ �0:005in the function and the result

such as Yinchuan of western China in this work shown in Eq. (3).

Where <sup>γ</sup> <sup>¼</sup> <sup>1</sup>:3253, k <sup>¼</sup> <sup>2</sup>:<sup>9771</sup> � <sup>10</sup>�<sup>2</sup>

4.1 Damage analysis of multi-storey RC buildings

was also shown in Figure 9.

Table 1.

224

P DI ð Þ¼ . DIi

emphasis of LS is been located in moderate damage and heavy damage

P50% is the exceedance probabilities in 50 years, and Pi is annual exceedance probabilities. IDA nonlinear procedure has been chosen for detect structural seismic vulnerability including structural damage and non-structural damage. So we set suggested 7 damage limit states (LS) in calculation on the base of post research. And

corresponding to the damage ratio between 20–45% based structural damage condition. At the same time nonstructural damage also can be classify with 7 HL or LS using peak ground acceleration. Damage scale indicators in IDA have been shown in

The IM scaling factor increase from 1 to 7.2 in IDA analysis. The whole damage LS of maximum inter-storey drift ratio (ISD%) and maximum floor acceleration (MFA) of every storey are shown in Table 2. That means all kind of seismic intensity waves have impacted on RC buildings in life-cycle period. So the

Damage impact indicator in IDA.


#### Table 2.

Drift ratio and floor acceleration limits for RC buildings in Yinchuan.

structural and non-structural damage of every floor of RC buildings must be detected based the two EDPs parameters. The maximum ISD% locates in second floor and the MFA in the top floor at the same time. That means the most structural damage lie in second floor and the severe non-structural damage in top storey,

stochastic damage scattered points can be viewed in Figure 12 with different color

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China

The damage zone of limit state can be represented from left to right respectively: none damage, slight damage, light damage, moderate damage, heavy damage and major damage or collapse. Statistics mean values and median values also be drawn

Limit state Inter-storey drift ratio% PGA (g)

 (I) None θ ≤0:11 α ≤0:07 (II) Slight 0:11 , θ ≤ 0:21 0:07 , α ≤ 0:10 (III) Light 0:21 , θ ≤0:31 0:10 , α ≤ 0:14 (IV) Moderate I 0:31 , θ ≤0:45 0:14 , α ≤0:18 (V) Moderate II 0:45 , θ ≤0:66 0:18 , α ≤0:23 (VI) Heavy I 0:66 , θ ≤1:12 0:23 , α ≤0:30 (VII) Heavy II 1:12 , θ ≤2:55 0:30 , α ≤ 0:45 (VIII) Major θ . 2:55 α . 0:45

stripe, which represent limit state has shown in Table 3.

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

Damage scattered distribution based limit states (i: ISD, ii: PGA).

Limit state drift ratio, floor acceleration of factory buildings.

The annual seismic column vulnerability in 50 years.

No. Single-storey industrial buildings

Figure 12.

Table 3.

Figure 13.

227

Figure 10. The damage analysis based two EDPs parameters in IDA for Friuli Italy-02 (i: ISD%; ii: MFA).

which are shown in Figure 10. The tendency of the seismic vulnerability changed more obvious than ever.

The relation between the drift ratio limits with the limit state. Employed in this study is partly based on the work of Ghobarah [7] for ductile RC moment resisting frames, and at the same time vast stochastic sampling based Monte Carlo method based local construction code in Western China also impact the limit state setting in this research. The relation of the limit state with the values of the floor acceleration is partly based on the work of Elens and Meskouris [8].

The damage scatter distribution of multi-storey RC buildings is shown in Figure 11. The middle black curve means median values of whole damage data and blue curves means 15% deviation limit.

#### 4.2 Damage analysis of industrial buildings

Damage, in the context of life-cycle cost assessment, refers not only to structural damage but also to non-structural damage. The latter including the case of architectural damage, mechanical, electrical and plumbing damage and also the damage of furniture, equipment and other contents in factory buildings. The maximum inter-storey drift has been considered as the structural damage response parameter. On the other hand, the peak ground acceleration (PGA) is associated with the loss of contents, like furniture and equipment which located in ground.

Five thousand times stochastic calculation has been made using Monte Carlo sampling method consideration of random materials and structural variables and

Figure 11. The damage scatter distribution of RC buildings.
