1 Introduction

With rapid development of modern cities, populations and assets are increasingly growing in urban areas. When a strong earthquake occurs, cities will experience critical levels of casualties and economic losses (Kircher et al. 1997; Eguchi et al. 1998). Given that building structures are one of the urban elements with major risk exposure to earthquake hazards (Sa et al. 2013), performing seismic-damage simulations for buildings on a regional scale is both important and highly desirable. These simulations can help develop countermeasures for city-level seismic-damage reduction and improve seismic resilience of cities.

Presently, frequently used seismic-damage simulation methods for buildings fall into four categories, namely, fragility analysis, capacity spectrum method (CSM), nonlinear time-history analysis (THA) based on multiple-degree-of-freedom (MDOF) models, and nonlinear THA based on refined finite element (FE) models.

(1) Fragility analysis

A fragility analysis can be performed using fragility curves or fragility matrixes for different types of buildings (ATC 1985). This method is extensively used because it is easy to implement and has high computational efficiency (Singhal and Kiremidjian 1996; McCormack and Rad 1997; Kircher et al. 1997). The fragility data are usually developed based on statistical data of damages from previous earthquake events and expert judgments. Therefore, the method is especially applicable for non-engineered buildings (e.g., non-engineered adobe buildings) with sufficient damage statistical data and are difficult to be precisely simulated by using a mechanical model. However, fragility analyses cannot capture the frequency- and time-domain characteristics of earthquake hazards and cannot cater for the variation of seismic performance of individual buildings.

(2) CSM

Regional seismic-damage simulations using the CSM are performed by undertaking a pushover analysis for each building. The capacity curve of each building can be obtained from the pushover curve by simplifying the building into a single-degree-of-freedom (SDOF) model. Meanwhile, the demand spectrum is used as earthquake hazard input, and the seismic response of each building can be calculated by obtaining the intersection of the capacity curve and the demand spectrum curve of the building (FEMA 2012; MAE Center 2006). The CSM is extensively used because it (1) can appropriately capture the nonlinear seismic capacity of different building types, (2) can also take into consideration the intensity and frequency-domain characteristics of earthquake hazards, and (3) has high computational efficiency and the required building/earthquake data are easy to access.

(3) Nonlinear THA using MDOF models

Xiong et al. (2016; 2017) proposed the MDOF shear models and MDOF flexural shear models to simulate multi-story and high-rise buildings, respectively. The seismic responses of various stories of different buildings at varied moments of a ground motion excitation can be computed using a nonlinear THA, and the seismic response results of buildings on a regional scale can be visualized via an urban seismic scenario simulation (Xiong et al. 2015). Unlike the CSM, the nonlinear THA based on the MDOF models is applicable to high-rise buildings whose high-order vibration modes have significant effect on the seismic responses. In addition, it can better represent the damage concentration on different stories and the time-domain features of ground motions.

(4) Nonlinear THA using refined FE models

Refined FE models are extensively used to simulate the seismic performance of high-rise buildings (Lu et al. 2013; Shome et al. 2015). The component-level modeling of a refined FE model enables a more comprehensive simulation of the dynamic properties and damages of structures. However, a nonlinear THA by using the refined FE model requires extensive and detailed building design data. Meanwhile, the computational workload is excessive. Therefore, this method is usually applied to investigate the seismic performance of special buildings in urban areas.

The above discussions demonstrate the features of various building seismic-damage simulation methods. In the existing studies, one of the simulation methods was normally adopted for each individual case. However, the practical situation of a modern city is very complex, and a single simulation method is unable to meet the various requirements in practical cases. Such a complexity is reflected by the diversity of the simulation demands which are described below:

(1) Diversity of structural types

Buildings in an urban area can be divided into three categories, namely, non-engineered, regular engineered, and special structures (e.g., super-tall buildings and long-span structures). The seismic performance of non-engineered buildings usually demonstrates large dispersion. Therefore, instead of the CSM and THA methods, the fragility analysis method is a good alternative for non-engineered buildings. Regular engineered buildings account for the majority of urban buildings. Seismic performance of regular engineered buildings are predictable because they are designed in compliance with the building codes, and the CSM and THA methods can be adopted to simulate these types of buildings. However, the seismic performances of special buildings (such as super-tall buildings and long-span structures) can be significantly different from each other due to the distinctive design of each building. Therefore, the refined FE model can be used to simulate such a building type.

(2) Diversity of available data

Presently, different types of data are available for urban-building seismic-damage simulation and visualization. Earthquake hazard data include seismic intensity, response spectrum, and ground motion time-history. With regard to building data, building inventory data from geographic information system (GIS) can provide descriptive information on urban buildings. Further, design drawings or building information modeling (BIM) data can provide component-level details of special buildings. Regarding visualization, polygonal data of GIS can be used to illustrate the damage distribution in urban buildings. Moreover, a three-dimensional (3D) urban model can be adopted to visualize the 3D seismic scenario of urban buildings. To improve the accuracy of the simulation and the visualization effect, further research is required to make a full utilization of these multi-source urban data.

(3) Diversity of simulation scenarios

Simulation scenarios to be considered include pre- and post-earthquake. On the one hand, a pre-earthquake simulation is performed by assuming a possible earthquake scenario and assessing the seismic performance of each building. Given that the pre-earthquake simulation scenario is implemented before the earthquake, no time restriction is necessary. Consequently, detailed models and methods can be adopted to simulate the seismic performance of regional buildings. On the other hand, a post-earthquake simulation is usually conducted for rapid assessment of regional buildings after the occurrence of an earthquake, requiring a short time completion of the seismic-damage simulation. Thus, simpler and more efficient models are often employed for such a simulation scenario.

The above discussion implies that the conventional seismic-damage simulations of regional buildings, which adopt a single method for each case study, cannot account for the diversity of structural types, data sources, and simulation scenarios. To overcome this limitation, simulation with multiple levels of detail (multi-LOD) (Borrmann et al. 2015; Biljecki et al. 2016) is utilized in this work. Specifically, multi-LOD building models can be constructed for a specific building area by using multi-source data. For a given simulation scenario, an appropriate LOD simulation can be performed according to the available multi-source data, the accuracy requirements, and the time restriction. Particularly, this study has the following three major parts:

(1) The framework of the multi-LOD simulation method is proposed, and the logical relationships among multi-source data, structural simulation methods, and visualization methods are established in different LODs.

(2) A unified city data structure is proposed to enable the management and storage of various LOD data.

(3) A case study is performed in the Beijing central business district (CBD), and the features of different LOD simulations are discussed in detail.

2 Multi-source data and multi-LOD seismic-damage simulation

The seismic-damage simulation of regional buildings requires extensive input data. In practical applications, multi-source data with various formats can be adopted to comprehensively capture the seismic performance of regional buildings. Specifically, three categories of data are indispensable for regional building seismic-damage simulations. Earthquake and structural data are required, to simulate the seismic responses of buildings. In addition, visualization data are necessary to display the seismic responses of buildings. To demonstrate the characteristics of different types of multi-source data, details of the earthquake, structural, and visualization data are compiled and summarized as follows:

(1) Earthquake data. Three most commonly used earthquake data types are summarized in Table 1. The first type is the seismic intensity data of urban areas, which is the simplest type and has only one index value (e.g., Sa, PGA, or PGV, etc.) to indicate the intensity distribution of a target area. For instance, Shakemap is an extensively used seismic intensity data type, which can provide regional intensity distribution data immediately after an earthquake (Wald et al. 2005). The second type is the regional response spectrum data which can better reflect the intensity and frequency characteristics of earthquake hazards. The response spectrum data of an entire region can be obtained from the earthquake scenario settings and attenuation relationships following the PSHA framework (Mcguire 2010). The third type is the ground motion data which can fully reflect the intensity, frequency-domain, and time-domain characteristics of earthquakes. These data can be obtained via wave propagation simulation (Hori and Ichimura 2008; Graves and Pitarka 2010), observation of strong motion networks (Okada et al. 2004), and artificial ground motion generation based on the response spectrum (Gasparini and Vanmarcke 1976).

Table 1 Different levels of earthquake, structural, and visualization data

(2) Structural data. Three types of structural data are commonly used to evaluate the seismic performance of different building types, as presented in Table 1. The first refers to the types of the structural systems, which is the most fundamental building data and can be used directly when performing fragility analysis (ATC 1985). The second is the building attribute data (e.g., structural type, story, year of construction, and floor area, etc.), used as input data for the CSM (FEMA 2012) and nonlinear THA of the MDOF models (Xiong et al. 2016, 2017; Lu et al. 2018). The third is the component-level detailed design data (e.g., design drawings), which are often adopted to establish refined FE models that can perform more accurate simulation of the seismic performance of complex buildings.

(3) Visualization data. Firstly, GIS data can be used to demonstrate the spatial distribution of the damage states of regional buildings, which is the most extensively used visualization data for regional seismic-damage simulation. Furthermore, 3D urban model, which is characterized by rich architectural details, can provide a realistic visualization of building and non-building objects (Xiong et al. 2015). Finally, component-level visualization data, which can display the component-level damage results in more detail, are often used for special buildings (Table 1).

To demonstrate the logical relationship between the multi-source data and the multi-LOD simulation methods, the multi-LOD simulation framework is presented in Fig. 1.

Fig. 1 Framework of multi-LOD simulations

The proposed multi-LOD simulation framework mainly consists of two components, namely, (1) multi-source data (which serves as the input data for seismic-damage simulation and is composed of earthquake, structural, and visualization data) and (2) multi-LOD simulation methods (which include four LOD 0每3 visualization and structural simulation methods). The logical relationship between these two components is illustrated in Fig. 1. For example, seismic intensity and structural type data are required for the LOD 0 fragility analysis, and GIS data are necessary for the LOD 0 visualization. In addition, the interdependency of various LOD structural simulation and visualization methods is illustrated in the framework, in which the seismic results of high-LOD structural simulation can be displayed using low-LOD visualization methods. For example, the results of the LOD 0每3 seismic simulations can be displayed with the LOD 0 visualization. However, only the structural simulation results of the refined FE model (LOD 3) can be used as input data for the LOD 3 component-level visualization.

The features of various LOD seismic-damage simulation methods are listed in Table 2. Note that lower LOD methods have lesser computation and data requirements, but they are less accurate than higher LOD methods. On the other hand, higher LOD methods require a larger amount of computational workload and input data; however, the simulation results are more accurate and can better replicate the seismic performance of complex structures.

Table 2 Features of various LOD simulation methods

Based on the proposed multi-LOD simulation framework, for a specific urban area, an appropriate LOD simulation method can be flexibly selected on the basis of the actual requirements. Presently, studies are mainly focused on one of the singular LOD simulation methods. However, to fully use multi-source data, a unified platform should be established for multi-LOD simulations. The implementation details of the multi-LOD simulation platform are discussed in the following sections.

3 Implementation of the multi-LOD seismic-damage simulation

3.1 Implementation process of the multi-LOD simulation

As shown in Fig. 2, the implementation process of a multi-LOD simulation involves three steps, namely, (1) multi-source data processing, (2) building seismic-damage analysis, and (3) visualization. In the first step, various formats of multi-source data may hinder their usage in the following simulation processes. Thus, multi-source data with different formats will be converted and stored in a unified city data structure. In the second step, based on the actual analysis requirements, the appropriate earthquake and structural data can be collected from the unified city data, and the computational models of the building are obtained through automatic structural modeling. After performing the corresponding LOD analysis, the seismic-damage results are acquired in this process. Then, the obtained seismic-damage results are stored back to the unified city data. In the last step, according to the visualization demand, the visualization data, as well as the seismic-damage results, are collected to perform the corresponding LOD visualization.

Fig. 2 Implementation processe of the multi-LOD simulation

3.2 Unified city data structure for multi-LOD simulation

Based on the above discussion, the three steps of the multi-LOD simulation are connected by the unified city data. Details of the unified city data are discussed below.

(1) Class diagram of the unified earthquake data

The class diagram of the unified earthquake data is shown in Fig. 3. An abstract base class EarthquakeData is adopted to accommodate different types of earthquake data. For example, the seismic intensity, response spectrum, and ground motion time-history data are inherited as Intensity, Spectrum, and Timehistory classes, respectively.

Fig. 3 Class diagram of the unified earthquake data

(2) Class diagram of the unified building data

The class diagram in Fig. 4 illustrates the unified building data, which can accommodate all the related data of buildings, including structural, visualization, and seismic result data.

Fig. 4 Class diagram of the unified building data

The data of each building are stored in the Building class, which can store some basic information, such as building identification, building location, and ground motion data of the building concerned.

Each Building class is composed of multiple LODGroup classes, and each LODGroup class is used to store the data required for one LOD simulation. The LODGroup class includes building attribute data (structural type, year of construction, number of story, and building height, etc.) for the structural simulation and damage state data, reflecting the global damage state of a building. The LODGroup class also consists of several Floor classes, which contain floor identification, floor damage state data, and several GeoElement classes.

The GeoElement class is used to save the geometric data of each story. For example, a GeoElement object can be used to store the GIS polygon data of each story in the LOD 0每1 simulation, whereas the lines or polygons of a 3D building model can be stored in a GeoElement object in the LOD 2 simulation. For the LOD 3 simulation, the geometric data of beams, columns, and shear walls of refined FE models can be stored in GeoElement objects. The GeoElement class is an abstract base class that can be inherited to different types of elements (e.g., 2NodeEle class for a line element and 3NodeEle class for a triangular element).

Two abstract base classes called EleScalar and the EleTensor are contained in the GeoElement class, which are used to store the seismic-damage results of each geometric element. For example, the EleScalar class can be inherited to the DamageIndex and EquivalentPlasticStrain classes of each component, whereas the EleTensor class can be inherited to the CrackingStrain and PlasticStrain classes.

The abstract base class Section is also included in the GeoElement class. The Section class can be inherited to the BeamSect, ColumnSect, WallSect, and SlabSect classes to store the corresponding information of each section type. Note that sections are only applicable to the refined FE model of the LOD 3 simulation, and the GeoElement classes of the LOD 0每2 simulations contain no Section class.

The Node class is also included in the GeoElement class. The coordinate data, boundary conditions, and point mass data are contained in the Node class. In addition, node-related results are generated after the LOD 2每3 structural simulations, and such results can be stored in the derived classes of NodeScalar, such as the Acceleration, Displacement, and Velocity classes.

Based on the proposed seismic-damage simulation framework and the implementation process of a multi-LOD simulation, a case study of Beijing CBD is conducted to demonstrate the features of the different LOD simulations.

4 Case studies

4.1 Buildings of Beijing CBD

In this section, Beijing CBD is investigated to demonstrate the proposed multi-LOD simulation framework. Beijing CBD is highly suited for performing the case study because of the different types of buildings in this area, including not only super-tall and regular high-rise buildings (Fig. 5a) but also a residential area with dense multi-story buildings (Fig. 5b).

Fig. 5 Buildings in Beijing CBD

The distributions of the structural type and building stories of the area according to statistics are shown in Fig. 6. Evidently, most of the buildings in this area are reinforced masonry (RM) structures with 4每6 stories because of dense residential buildings in the Hujialou district.

Fig. 6 Building distributions of Beijing CBD

To facilitate the multi-LOD simulation, the structural and visualization data of Beijing CBD are obtained in advance. The acquisition of earthquake data is discussed in the subsequent section.

4.2 Earthquake data of Beijing CBD

The adopted earthquake data are mainly based on the ground motion simulation performed by Fu (2012). In Fu＊s study, the 3D basin structure of Beijing area is modeled using a 3D velocity structure model. The ground motion sets of all Beijing CBD buildings are obtained using the finite difference method for the M8.0 Sanhe每Pinggu earthquake scenario. Typical response spectra, acceleration/velocity time histories of the buildings in Beijing CBD are illustrated in Fig. 7. As presented in Fig. 7b, the ground motions of the Sanhe每Pinggu earthquake contain a significant velocity pulse, which is very destructive to the buildings in Beijing CBD.

Fig. 7 Typical ground motions of M8.0 Sanhe每Pinggu scenario in Beijing CBD

To examine the effect of different ground motions on the results of the multi-LOD simulation, two additional ground motions (namely, El-Centro without velocity pulse and CHICHI_CHY101-N with velocity pulse) (PEER 2013) were selected. Further, the peak ground acceleration (PGA) was adjusted to 1.580 m/s², which is the typical PGA of the Sanhe每Pinggu ground motions given in Fig. 7b.

In addition, in order to perform the LOD 0每1 simulation, seismic intensity and response spectrum data are obtained based on the ground motion time-history data presented above.

4.3 LOD 0 simulation

Given that the LOD 0 simulation is more applicable to multi-story buildings, the LOD 0 simulation is performed for the Hujialou residential district. The buildings of the Hujialou district consist of reinforced concrete (RC) frame, RM, unreinforced masonry (URM), and shear wall structures. The structural type and building story distribution in the Hujialou residential district are illustrated in Fig. 8.

Fig. 8 Buildings of the Hujialou residential district

Seismic intensity data are required as earthquake input for the LOD 0 simulation. According to the research of Ding et al. (2017), the PGA of a region with the Chinese seismic intensity scale of VII ranges from 118 to 219 cm/s². Note that the PGA of the Hujialou residential district under the M8.0 Sanhe每Pinggu scenario falls in this range (Fig. 7). Thus, the seismic intensity of VII is used for the following fragility analysis. Given such an intensity, the seismic-damage results can be obtained according to the damage probability matrices for different types of Chinese buildings recommended by Yin (1996), as shown in Fig. 9. Fig. 9a presents the probability distribution of different damage states for the RC frame, RM, and URM structures. The damage state of maximum probability of each building is displayed using the LOD 0 visualization based on 2D-GIS data, as shown in Fig. 9b.

Note that the earthquake data used for the LOD 0 fragility analysis is the seismic intensity level, and the seismic results of the Sanhe每Pinggu, Chichi, and El-Centro earthquakes are the same because their seismic intensities are identical.

Fig. 9 Seismic-damage results of the LOD 0 simulation

The advantages and disadvantages of the LOD 0 simulation can be summarized as follows:

(1) The structural seismic damage can be easily obtained using damage probability matrices, and the analysis can be completed within 1 second for 514 multi-story buildings in the Hujialou residential district. Furthermore, the simulation only requires the structural type and seismic intensity data, which are easy to obtain in urban-scale simulations.

(2) The differences in the frequency and duration of ground motions cannot be considered in the LOD 0 simulation. Hence, the predicted seismic-damage results of the Sanhe每Pinggu, Chichi, and El-Centro earthquakes are the same.

(3) The variation in the seismic performance of different individual buildings cannot be considered in the LOD 0 simulation. Thus, different buildings of the same structural type have the same seismic-damage result.

(4) Due to the lack of fragility data from previous earthquake events, the LOD 0 simulation is not performed for shear wall high-rise structures in this region, and these buildings are labeled with ※N/A§ (Fig. 9b).

4.4 LOD 1 simulation

The capacity curves of the buildings can be obtained according to the building attribute data and performance database for different types of buildings (FEMA 2012; Lu et al. 2014). Then, according to the response spectra of the Sanhe每Pinggu, El-Centro, and Chichi earthquakes (Fig. 10), the seismic-damage results of the buildings in the Hujialou residential district can be obtained through the LOD 1 CSM. The computation of all 514 multi-story buildings consumes 10.2 CPU seconds on a desktop computer (with Intel i5-4590 CPU @3.30 GHz and 8GB RAM). The results are displayed in Fig. 11 using the LOD 0 visualization with 2D-GIS data.

Fig. 10 Response spectra of three ground motion records

Fig. 11 Seismic-damage results of the LOD 1 simulation

The advantages and disadvantages of the LOD 1 simulation can be summarized as follows:

(1) Building attribute data are required as the building data; thus, the simulation is relatively easy to implement at the city level.

(2) The CSM of the LOD 1 simulation takes into account the amplitude and frequency-domain characteristics of the ground motion. Hence, the results of the Sanhe每Pinggu and Chichi earthquakes vary. However, the results of the Sanhe每Pinggu and El-Centro earthquakes are the same. The reason is that although the ground motion time-history records of these two earthquakes are different, the response spectra within the range of 0每2 s are similar. The LOD 1 simulation based on the CSM cannot fully consider the time-domain properties of ground motions.

(3) The CSM of the LOD 1 simulation simplifies each building to a SDOF model, which is not appropriate for high-rise buildings. Therefore, the LOD 1 simulation is not performed herein for the shear wall high-rise structures in this region, which were also labeled with ※N/A§ in Fig. 11. In addition, when a building is severely damaged, its vibration mode shape may change. Hence, the SDOF model of the CSM is not applicable. Further discussion will be presented in the subsequent section.

4.5 LOD 2 simulation

According to the attribute data of regional buildings, the method of Xiong et al. (2016; 2017) is adopted to generate the MDOF model of each building. Subsequently, the LOD 2 seismic-damage simulation is performed using a nonlinear THA. The THA of all buildings in the Hujialou residential district consumes 80.2 CPU seconds on a desktop computer (with Intel i5-4590 CPU @3.30 GHz and 8 GB RAM). The results are presented in Fig. 12.

Fig .12 Seismic-damage results of the LOD 2 simulation

As shown in Fig. 12, the results of different earthquakes are varied, thus indicating that the LOD 2 level simulation can also consider the characteristics of various ground motions. Both the Sanhe每Pinggu and Chichi earthquakes have velocity pulses. Hence, the seismic damages of several buildings subjected to these two earthquakes are more severe than that of the El-Centro earthquake.

To compare the features of the LOD 1 (CSM) and LOD 2 (THA) simulations in more detail, a typical RC frame, RM, and URM structures are analyzed using the LOD 1 and LOD 2 methods. As shown in Figs. 13a and 13b, the inter-story drift ratio (IDR) results indicate that the damages of the RC frame and RM structures are relatively small, and the mode shapes have not changed significantly. Therefore, the calculated results of the CSM and THA methods agree well to each other. However, the URM structure is severely damaged, and the damage concentration occurs in the first story, as shown in Fig. 13c. In this case, the mode shape of the LOD 2 simulation (THA) changes significantly, and the prediction results of the LOD 1 (CSM) and LOD 2 (THA) simulations vary remarkably.

Fig. 13 Comparison of the LOD 1 and LOD 2 simulations for an individual building subjected to the Sanhe每Pinggu earthquake

Thus, the LOD 2 simulation has the following advantages and disadvantages:

(1) The structural data required for the LOD 2 simulation are basically the same as those for the LOD 1 simulation. Hence, the simulation is easy to implement at the city level.

(2) The LOD 2 simulation can better reflect the seismic performance of different individual buildings, and the frequency-/time-domain characteristics of various ground motions.

(3) The LOD 2 simulation adopts the MDOF model. Hence, the variation of the mode shape caused by damage concentration can be satisfactorily considered.

(4) The computational workload of the LOD 2 simulation is relatively large compared with that of the LOD 0每1 simulation, and the ground motion time-history records of an entire region are difficult to obtain. Therefore, several difficulties may be encountered when applying this method to large cities under emergency circumstances.

The seismic-damage results of the LOD 2 simulation can be presented using the LOD 0每2 visualization methods. Fig. 12 shows the result of the LOD 0 visualization by using 2D-GIS data. The LOD 0 visualization is very simple. Thus, the damage distribution of buildings in a region can be clearly presented. Fig. 14a shows the LOD 1 visualization. This visualization method can be used to present 3D seismic-damage scenes showing the story-level results (such as the displacement or damage state of each story). Fig. 14b presents the LOD 2 visualization, which can more realistically display the façade of each building and the 3D scene of the entire urban area.

Fig. 14 LOD 1每2 visualization methods

4.6 LOD 3 simulation

The nonlinear dynamic characteristics of high-rise buildings and super-tall buildings are complex. Hence, using the LOD 0 and LOD 1 methods to simulate the nonlinear seismic response of high-rise buildings is difficult. In Section 4.5, the MDOF flexural shear model (Xiong et al. 2016) is adopted in the LOD 2 simulation to compute the seismic responses of regular high-rise buildings, which can not only obtain the flexural shear behavior of high-rise buildings but also consider the influence of high-order vibration modes to the structure. Apart from the regular high-rise buildings, Beijing CBD also houses a large number of super-tall buildings with more complex nonlinear dynamic characteristics. Owing to the existence of outriggers or strengthening stories, the assumption of the MDOF flexural shear model (Xiong et al. 2016) that a continuous stiffness distribution along the building height is no longer applicable. Therefore, a refined FE model is adopted herein in the LOD 3 simulation to represent the complex buildings. In the refined FE model, fiber beam elements are used to simulate the nonlinear performance of the beam and column components, and multi-layered shell elements are adopted to simulate the shear wall components. The fiber beam and multi-layered shell elements (Lu et al. 2013) have been proven to effectively evaluate the seismic performance of high-rise buildings and super-tall buildings, and have been extensively used in seismic-damage and collapse simulations of such building types.

To demonstrate the LOD 3 simulation method, the 74-story China World Trade Center (CWTC) tower is simulated using the LOD 2每3 methods. The time-history responses of the top story and IDR results are shown in Fig. 15. As presented in the figure, the time-history responses of the two methods are in good agreement (Fig. 15a), but the IDR results are slightly different (Fig. 15b). The reason is that the CWTC tower has outriggers and perimetric trusses on several stories, which can effectively reduce the IDR on these stories. Moreover, the LOD 3 simulation by using the refined FE model can comprehensively cover such design details. The LOD 3 simulation of the super-tall building consumes 26,452 CPU seconds, whereas the LOD 2 simulation consumes only 64 CPU seconds (with Intel i5-4590 CPU @3.30 GHz and 8 GB RAM). In addition, detailed design information is required to establish a LOD 3 model. Therefore, the LOD 3 simulation can be applied to a small number of special buildings.

Fig. 15 Results of the CWTC tower by using the LOD 2 and LOD 3 simulations

In summary, the LOD 3 simulation has the following advantages and disadvantages:

(1) The refined FE model of the LOD 3 simulation can appropriately reproduce the complex seismic performance of special buildings.

(2) The detailed design information is required for the LOD 3 simulation and its modeling, and the computational workload is excessive. Therefore, the LOD 3 simulation can be applied to a small number of special buildings with complicated seismic performance.

The LOD 3 visualization by using the component-level building data is performed to display the seismic-damage results of Beijing CBD high-rise building district, as shown in Fig. 16. Note that only three buildings possess the component-level building data. These three super-tall buildings are displayed using the LOD 3 visualization, and all the other buildings are presented using the LOD 2 visualization. Unlike the LOD 2 visualization shown in Fig. 14b, the LOD 3 visualization method is able to present the seismic responses (Fig. 16a) and damage states (Fig. 16b) of each building at the component level.

Fig. 16 LOD 2每3 hybrid visualization

5 Conclusions

A multi-LOD urban-building seismic-damage simulation framework, as well as its implementation method, are proposed in this study. The multi-LOD simulation framework can make a full utilization of the multi-source data, simulate various types of structures, and meet the requirements of different simulation scenarios. Through a case study of the Beijing CBD, the features of different LOD simulation methods can be summarized as follows:

(1) The LOD 0 simulation can yield a probabilistic result for various structural types, and this method is the easiest one to implement. However, the influences of different earthquakes are not considered.

(2) The LOD 1 simulation can reasonably obtain the nonlinear properties of multi-story buildings and consider the frequency-domain characteristic of earthquakes. Nevertheless, the CSM of the LOD 1 simulation uses a fixed vibration mode shape that cannot simulate the soft story failure of multi-story buildings. Furthermore, the CSM is based on a SDOF simulation, which is not applicable for high-rise buildings.

(3) The LOD 2 simulation based on the THA of a MDOF model can comprehensively reflect the seismic performance of regular buildings and the frequency-/time-domain characteristics of ground motions. However, the MDOF model cannot simulate the component-level details of complex structures, such as super-tall buildings.

(4) The LOD 3 simulation based on the THA of a refined FE model is the most accurate method. Nevertheless, the required computational time is more than 400 times that needed by the LOD 2 method for the case of the CWTC tower.

By considering the features of all the LOD simulation methods, the proposed multi-LOD simulation framework enables a flexible selection of the appropriate LOD simulation method under various circumstances, which may facilitate future applications of urban-building seismic-damage simulations for complex cities.

Acknowledgements The authors are grateful for the financial support received from the Natural Science Foundation of Guangdong Province (Grant No. 2017A030310076), the Natural Science Foundation of SZU (Grant No. 2017064) and the National Natural Science Foundation of China (Grant No. 51708361, U1709212).

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