**3.4 Natural period of buildings and ground predominance period at the time of earthquake**

The range in which the natural period of the building transitions can be calculated as the resonance range by specifying the interlayer deformation angle for the assumption of the interlayer deformation at all times and the assumption of the interlayer deformation angle at the time of an earthquake. **Table 3** shows this study.

It is the specification of the specified interlayer deformation angle. In addition, if the calculation of the ground predominant period Shake at the time of an earthquake is available, the predominant period is always obtained from the specified seismic wave by the same method, but if the acquisition of the boring columnar map fails, the ground is always obtained. The multiplication value α is defined from the value of the predominant cycle and is defined as the ground predominant cycle at the time of an earthquake (**Table 4**). Each cycle is considered in a band shape, and the future emergency risk judgment is predicted from the occupancy rate of each area (**Figure 5**):

$$T\_B = \sqrt{\frac{\Theta\_A}{\Theta\_B}} \times T\_A \tag{3}$$

ΘA : Interlayer deformation angle A ΘB : Interlayer deformation angle B TA : Period at inter-story deformation angle A TB : Period at inter-story deformation angle B


**Table 3.**

*Setting the interlayer deformation angle between design and earthquake.*


**Table 4.**

*Setting of ground type and multiplication value α.*

**Figure 5.** *H/V spectral ratio (1) and band determination (2).*

#### **3.5 Analysis by PML**

In the analysis by PML, the probabilistic seismic velocity and s related to the ground [5]. The propagation speed, amplification factor, etc., are obtained from JSHIS, and the building is bilinear.

Apply to the model and calculate its damage rate. Since the PML value at the time of an earthquake obtained here is an index of a general building, considering the

**Figure 6.** *Bilinear model at the time of PML calculation.*

*Perspective Chapter: Building Damage Estimation and Renovation Proposal System Using... DOI: http://dx.doi.org/10.5772/intechopen.112457*


**Table 5.**

*Judgment as PML value.*

validity of the measurement target, the abbreviation formula of the building natural period that is generally used and the building natural period obtained by constant tremor are used. By multiplying the ratio of, the PML value of the seismic motion considering the building to be measured was calculated (**Figure 6**). Additionally, the defined criteria based on the obtained PML values are presented in **Table 5**.
