# Real-Time City-Scale Time-History Analysis and Its Application in Resilience-Oriented Earthquake Emergency Responses

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## Abstract

**:**

## 1. Introduction

## 2. Real-Time City-Scale Nonlinear Time-History Analysis

#### 2.1. Framework

- (1)
- Obtaining the real-time ground motion records from the seismic stations;
- (2)
- Establishing the building inventory database for the target region;
- (3)
- Conducting the city-scale nonlinear time-history analysis to predict the seismic damage of the target region; and
- (4)
- Performing the regional seismic loss prediction to assess the seismic economic loss and repair time of the target region.

#### 2.2. Real-Time Recorded Ground Motions

#### 2.3. Building Inventory Database

#### 2.4. City-Scale Nonlinear Time-History Analysis

#### 2.4.1. Parameter Determination Method for Buildings in China

_{0}, and the mass, m, of each story. Equations (1) and (2) show the global stiffness [K] and mass matrices [M] of a structure with a uniform stiffness and mass along the height [15].

_{1}, and the mass per unit area, m

_{1}(Equation (3)) [16]; m

_{1}can be estimated according to the occupancy of each story.

_{1}, can be expressed using Equation (4).

_{1}] is the first mode vector. Given the stiffness matrix [K] and mass matrix [M], [Φ

_{1}] can be computed using a generalized eigenvalue analysis. As shown in Equation (4), m and T

_{1}are required to obtain k

_{0}. The vibration periods of different types of structures can be estimated using empirical equations. For example, the fundamental period of a reinforced concrete (RC) frame can be calculated using the empirical equation (Equation (5)) specified in the Chinese Code [17].

_{design, i}, of each story, where i is the story number [18,19]. Subsequently, according to related statistics of extensive experimental and analytical results, the yield point, peak point, and softening point on the backbone curve can be further obtained. For example, the yield point, peak point, and softening point of an RC frame can be determined by Equations (6)–(8) as follows:

_{yield, i}, V

_{peak, i}, and V

_{ultimate i}are the yield strength, peak strength, and ultimate strength, respectively. Ω

_{1}is the yield overstrength ratio of RC frames, which is determined according to the partial factor of steel reinforcement [20]. Ω

_{2}is the peak overstrength ratio, which is determined by the statistics of 155 pushover results of RC frames designed following the Chinese seismic design code. The deformation parameters of RC frames, including the yield, peak, and ultimate deformations, can be determined using the same procedure.

#### 2.4.2. Parameter Determination for Backbone Curve Based on the HAZUS Data

_{0}, and the mass, m, are determined using Equations (1)–(4). Subsequently, the inter-story backbone curve parameters of story i in Figure 3 are determined as follows:

_{y}, SA

_{y}) and (SD

_{u,}SA

_{u}) are the yield capacity point and ultimate capacity point, respectively, of the capacity curve suggested by HAZUS [7], which are functions of the design intensity and year built; ${\alpha}_{1}$ is the mode factor suggested by HAZUS [7]; and ${\Gamma}_{i}$ is the ratio between the inter-story shear strength of the ith story, (${V}_{y,i}$) and that of the ground story (${V}_{y,1}$), which is calculated as follows:

#### 2.5. Regional Seismic Loss Prediction and Resilience Assessment

#### 2.5.1. Regional Seismic Loss Prediction Using Conventional Method

_{h}and decoration damage loss L

_{d}are calculated using Equations (15) and (16), respectively:

^{2}); D

_{h}and D

_{d}are the loss ratios of the house and decoration damage, given a damage state; P is the building replacement cost; ${\gamma}_{1}$ is the correction factor considering different economic conditions of different regions; ${\gamma}_{2}$ is the building function correction factor; $\xi $ is the proportion of buildings with mid-to-high-quality decoration; and $\eta $ is the ratio of the building decoration cost to the building construction cost. The values of ${\gamma}_{1},\text{\hspace{0.17em}}{\gamma}_{2},\text{\hspace{0.17em}}\xi ,\text{\hspace{0.17em}}\eta $ can be found in Table A.1–A.4 in GB/T 18208.4 [24].

#### 2.5.2. Regional Resilience Assessment Using FEMA P-58

- (a)
- Field survey data and building design drawings

- (b)
- Building information models

- (c)
- GIS database

#### 2.6. High-Performance Computing for Post-Earthquake Emergency Response

## 3. Applications in Earthquake Emergency Response

#### 3.1. Overview of the Applications

#### 3.2. 2017 M7.0 Jiuzhaigou Earthquake

#### 3.3. 2018 M_{w} 7.0 Anchorage Earthquake

_{w}7.0 Anchorage earthquake is another typical application case [33]. On 30 November 2018 (local time), a M

_{w}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 [34]. Six ground motions of the Anchorage earthquake event were recorded. The ground motions recorded at the 8047 station (61.189 N, 149.802 W, shown in Figure 11) are typical ground motions [35]. The peak ground accelerations (PGAs) of horizontal and vertical components of the 8047-ground motion were 807.162 cm/s

^{2}and 367.243 cm/s

^{2}, respectively. The ground motions are shown in Figure 11.

## 4. Conclusions

- (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 and MDOF models;
- (3)
- Using the real-time city-scale time-history analysis and the corresponding report system, the assessment of the earthquake’s destructive power, repair time, and economic loss can be obtained shortly after an earthquake event, which provides a useful reference for scientific decision-making for earthquake disaster relief. This work is highly significant to enhancing the resilience of earthquake-stricken areas.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Multiple-degree-of-freedom (MDOF) shear model; (

**b**) MDOF flexural-shear model; and (

**c**) trilinear backbone curve adopted in the MDOF model.

**Figure 6.**Distribution of human uncomfortableness under the ground motions of the 11/26/2018 M6.2 Taiwan Strait earthquake.

**Figure 9.**Distribution of median (

**a**) building loss ratios and (

**b**) repair/rebuild time for Tsinghua Campus.

**Figure 10.**Seismic results of a (

**a**) typical town and (

**b**) country in the Aba region subjected the ground motion from the Jiuzhaigou Baihe station.

**Figure 11.**(

**a**) Location of the 8047-ground motion station, and the ground motion recorded by the 8047 station: (

**b**) EW direction, (

**c**) NS direction, (

**d**) UD direction.

**Figure 12.**Damage ratio distribution of the buildings near different stations of the 2018 M

_{w}7.0 Anchorage earthquake: (

**a**) Global view, and (

**b**) local view.

**Figure 13.**Distribution of human uncomfortableness under the ground motions of the 2018 M

_{w}7.0 Anchorage earthquake.

Number of stories | 1 | 2–3 | 4–6 | 7–9 | >9 |

Proportions | 20.6% | 10.6% | 36.3% | 4.9% | 27.6% |

Year built | <1990 | 1990–1999 | >1999 | ||

Proportions | 30.3% | 29.8% | 39.9% | ||

Structural type | Steel and reinforced concrete | Masonry | Wood | Other structures | |

Proportions | 47.9% | 40.3% | 11.6% | 0.2% |

ID | Earthquake Name | ID | Earthquake Name |
---|---|---|---|

1 | 12/08/2016 M6.2 Xinjiang Hutubi earthquake | 18 | 11/26/2018 M6.2 Taiwan Strait earthquake |

2 | 12/18/2016 M4.3 Shanxi Qingxu earthquake | 19 | 12/08/2018 M4.5 Xinjiang Changji earthquake |

3 | 03/27/2017 M5.1 Yunnan Yangbi earthquake | 20 | 12/16/2018 M5.7 Sichuan Yibin earthquake |

4 | 08/08/2017 M7.0 Sichuan Jiuzhaigou earthquake | 21 | 12/20/2018 M5.2 Xinjiang Kizilsu earthquake |

5 | 09/30/2017 M5.4 Sichuan Qingchuan earthquake | 22 | 01/03/2019 M5.3 Sichuan Yibin earthquake |

6 | 02/06/2018 M6.5 Taiwan Hualien earthquake | 23 | 01/07/2019 M4.8 Xinjiang Jiashi earthquake |

7 | 02/12/2018 M4.3 Hebei Yongqing earthquake | 24 | 04/16/2016 M7.3 Japan Kumamoto earthquake |

8 | 05/28/2018 M5.7 Jilin Songyuan earthquake | 25 | 08/24/2016 M6.2 Italy earthquake |

9 | 08/13/2018 M5.0 Yunnan Tonghai earthquake | 26 | 11/13/2016 M8.0 New Zealand earthquake |

10 | 08/14/2018 M5.0 Yunnan Tonghai earthquake | 27 | 09/20/2017 M7.1 Mexico earthquake |

11 | 09/04/2018 M5.5 Xinjiang Jiashi earthquake | 28 | 11/23/2017 M7.8 Iraq earthquake |

12 | 09/08/2018 M5.9 Yunnan Mojiang earthquake | 29 | 06/18/2018 M6.1 Japan Osaka earthquake |

13 | 09/12/2018 M5.3 Shanxi Ningqiang earthquake | 30 | 09/06/2018 M6.9 Japan Hokkaido earthquake |

14 | 10/16/2018 M5.4 Xinjiang Jinghe earthquake | 31 | 10/26/2018 M5.4 Japan Hokkaido earthquake |

15 | 10/31/2018 M5.1 Sichuan Xichang earthquake | 32 | 12/01/2018 M7.0 Alaska earthquake |

16 | 11/04/2018 M5.1 Xinjiang Atushi earthquake | 33 | 01/03/2019 M6.2 Japan Kumamoto earthquake |

17 | 11/25/2018 M5.1 Xinjiang Bole earthquake |

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**MDPI and ACS Style**

Lu, X.; Cheng, Q.; Xu, Z.; Xu, Y.; Sun, C. Real-Time City-Scale Time-History Analysis and Its Application in Resilience-Oriented Earthquake Emergency Responses. *Appl. Sci.* **2019**, *9*, 3497.
https://doi.org/10.3390/app9173497

**AMA Style**

Lu X, Cheng Q, Xu Z, Xu Y, Sun C. Real-Time City-Scale Time-History Analysis and Its Application in Resilience-Oriented Earthquake Emergency Responses. *Applied Sciences*. 2019; 9(17):3497.
https://doi.org/10.3390/app9173497

**Chicago/Turabian Style**

Lu, Xinzheng, Qingle Cheng, Zhen Xu, Yongjia Xu, and Chujin Sun. 2019. "Real-Time City-Scale Time-History Analysis and Its Application in Resilience-Oriented Earthquake Emergency Responses" *Applied Sciences* 9, no. 17: 3497.
https://doi.org/10.3390/app9173497