1. Introduction

When subjected to an earthquake, some buildings may avoid collapse but still be demolished owing to their high repair costs ^[1-2]. For example, over 60% of buildings were demolished in the central business district of Christchurch, New Zealand, after an M6.2 earthquake on Feb 22, 2011 ^[3], which cannot satisfy the resilience demand. Predicting the potential seismic loss of a building is critical for its resilience.

The next-generation performance-based design code released by the Federal Emergency Management Agency ^[4-5], i.e., ¡°Seismic performance assessment of buildings¡± (FEMA P-58), provides a systematic methodology for seismic loss predictions. FEMA P-58 contains the prediction methods and sufficient loss data of structural and nonstructural components, and has been widely used in seismic loss predictions ^[6-8]. In FEMA P-58, the performance group (PG) that is a group of components classified by their seismic performances, is regarded as the basic unit for the predictions of seismic damage and loss. The components in a PG share a fragility curve and a consequence function. Specifically, the fragility curves can provide the probabilities of different seismic damage states (DSs) according to the engineering demand parameters (EDPs), such as inter-story drift ratios (IDRs) and peak floor accelerations (PFAs), while the consequence functions contain unit loss data corresponding to different DSs and are used for predicting the seismic losses of PGs. The seismic loss of a building can be calculated by integrating the data of all PGs.

However, some limitations exist for the PGs of FEMA P-58 on the acquisition and visualization of loss data. For data acquisition, defining the unit loss data of PGs for different regions require significant statistic work, which limits the application of FEMA P-58 in different regions. Specifically, the original consequence functions of FEMA P-58 were determined based on the data of building costs in Northern California in 2011 ^[4]. If such functions are used in other regions, these consequence functions must be adjusted according to the local building costs. Otherwise, they will lead to large deviations. For example, the investigation of the L¡¯Aquila earthquake in Italy indicates that the predicted seismic loss using FEMA P-58 has an error range of 30¨C48% compared with the actual loss ^[9]. Regarding visualization, the spatial distribution of the predicted seismic damage and loss cannot be displayed directly, because the prediction results using FEMA P-58 are only related to the PGs and are not connected to specific components. However, components with the same DS may have different repair strategies owing to their different spatial locations. Therefore, the clear visualization of the spatial distributions of seismic damage and loss is critical for deciding repair strategies.

The building information model (BIM) technology can be used to overcome the two limitations above of FEMA P-58. A BIM has component-level information. Consequently, if the loss prediction of FEMA P-58 is based on the BIM, the components can replace the PGs as the basic prediction unit. Such component-based prediction will significantly improve the acquisition and visualization of loss data. On the one hand, the repair cost of components can be calculated by combining the detailed information in a BIM with the database of the unit repair costs in specific regions, such as the database in the MasterFormat code ^[10-11] or Beijing repair code ^[12]. Consequently, the losses of components can be directly calculated, and the time-costing statistic work of consequence functions in a different region can be avoided. On the other hand, the spatial distribution of seismic damage and loss calculated by FEMA P-58 can be displayed on the component level using BIM technology, because a BIM includes a refined three-dimensional (3D) model of a building ^[13-14]. This provides an ideal solution for visualizing the prediction results.

This study proposes a prediction method of seismic losses combining the BIM and FEMA P-58. First, a component-level damage prediction algorithm is designed to establish the mapping from the BIM components to the PGs, and predict the component damage using the BIM-based time-history analysis (THA) and the fragility curves of the PGs. Subsequently, an ontology-based model considering the deduction rules in the local unit-repair-cost database is created for obtaining exact measurement data of component in a BIM. Meanwhile, a component-level loss prediction algorithm is developed using the measurement data and the unit repair costs corresponding to DSs, by which the predicted seismic losses can agree with the actual situation of the specific region. Finally, a component-level visualization algorithm is designed to display the seismic damage and loss in a virtual reality (VR) environment. A six-story office building in Beijing is used as a pilot test to demonstrate the advantages of the proposed method. The outcome of this study produces a component-level and visual loss prediction result that agrees with the actual situation of the specific region, which can be used to evaluate the post-earthquake economic resilience of different buildings.

2. Literature review

The combination of BIM and FEMA P-58 is the key challenge in this study. However, the relevant research in literature is very limited ^{[6, 15-18]}. Ferner et al. ^[15] summarized the existing assessment methods on seismic performances, and recommended BIM and FEMA P-58 for seismic loss predictions of buildings. Yang et al. ^[16] and Zeng et al. ^[6] predicted the seismic losses of a building and an urban area, respectively, using the FEMA P-58 method. Both studies pointed out the possibility of using BIM to provide the detailed data for the loss predictions using FEMA P-58. Note that the BIM technology is not actually adopted in their work ^{[6, 15, 16]}. Xu et al. ^[17] used BIM and FEMA P-58 to simulate the post-earthquake fires considering the overall seismic damage of sprinkler systems. Perrone and Filiatrault ^[18] also used BIM and FEMA P-58 for the automated seismic designs of non-structural elements. However, the seismic loss of structural components is not considered in these studies ^{[17, 18]}. Therefore, the prediction method of building seismic loss combining BIM and FEMA P-58 requires in-depth studies.

The BIM-based predictions and visualizations on the seismic loss of building components are also important problems in this study. However, the relevant literature is very limited ^{[11, 19]}. Christodoulou et al. ^{[11, 19]} proposed a BIM-based framework for forecasting and visualizing the seismic damage and loss. In this framework, the damage predictions are not integrated with BIM, leading to plenty of the additional work that inputs the damage results to BIM for each component. Besides, the above damage predictions are based on the fragility curves of components without considering the differences of the seismic performances of components (i.e., the PG in FEMA P-58), which causes the accuracy of prediction results lower than that of FEMA P-58. Thus, the damage predictions using FEMA P-58 need to be fully integrated with BIM. In addition, the visualization of loss is not considered in the above framework ^{[11, 19]}, which also needs to be solved in this study.

Considering the similarity between the loss predictions and cost estimations, the existing researches on the BIM-based construction cost estimations ^[20-28] are also reviewed for technical references. To conduct an automatic construction cost estimation with high efficiency and accuracy, the ontology technology is wildly used for analyzing building components automatically according to the relevant specifications on construction cost estimations ^[23-28]. For instance, Ma and Wei ^[28] proposed a framework for automatic construction cost estimation based on BIM and ontology technology, by which the bill-of-quantity (BQ) data which are critical for cost estimations can be automatically generated. Nevertheless, the current ontology-based research has seldom been conducted for assessing the repair costs of buildings ^[23-28]. Due to the differences between the cost specifications of constructions and repairs, a specialized ontology-based model needs to be established to accurately predict the seismic repair costs of buildings.

According to the above literature review, the building seismic loss prediction combining BIM and FEMA P-58 requires in-depth studies. Specifically, the damage predictions using FEMA P-58 need to be fully integrated with BIM; a visualization algorithm for seismic loss and an ontology-based model for repair costs need to be designed, respectively. To address these challenges, the corresponding method is proposed in this study, as elaborated in details in the following sections.

3. Framework

The framework of the proposed seismic loss prediction method based on BIM and FEMA P-58 is shown in Figure 1. It includes three steps: damage prediction, loss prediction, and result visualization.

Step 1: The damage prediction aims at predicting the seismic damage of each component using BIM and FEMA P-58. The FEMA P-58 method can only be used to predict the damage of PGs; therefore, the mapping relationships from the components in the BIM to the PGs in FEMA P-58 are first established in this step. Subsequently, the THA based on the BIM is performed to obtain the EDPs, which avoids the manual modeling workload of structural models. Subsequently, the damage of PGs can be calculated using the fragility curves in FEMA P-58. Finally, the damage of PGs is mapped back to the components in the BIM. Thus, the DS of each component can be obtained.

Step 2: The loss prediction is used to predict the seismic loss of each component using the BIM and the unit-repair-cost database. First, an ontology-based model is created to extract the exact measurement data of the components considering the deduction rules in the local unit-repair-cost database from a BIM. Subsequently, the unit repair costs corresponding to different DSs of the components are calculated based on the unit-repair-cost database and the FEMA P-58 method. Finally, the losses of different components and the entire building can be calculated, separately.

Step 3: The visualization is designed to display the spatial distribution of the component damage and loss using BIM technology. First, a unified standard for the visualization of damage and loss is established. Subsequently, a visualization algorithm of damage and loss is developed to meet the multiple requirements of observation. Finally, a VR program is developed to allow users to observe the detailed information and spatial distribution of damage and loss in a virtual walkthrough.

4. Technical implementation

4.1 Seismic damage prediction based on BIM and FEMA P-58

As shown in Figure 2, the seismic damage prediction for the components includes four steps: (1) establish the mapping relationships between the components in the BIM to the PGs in FEMA P-58; (2) convert the BIM into a structural analysis model and perform THA for predicting the EDPs and structural deformations; (3) predict the damage of the PGs based on the EDPs in step (2) and the fragility curves in FEMA P-58; (4) reversely map the damage of the PGs to the components and obtain the DSs of the components. The details of these four steps are illustrated below.

Step 1: Mapping from components to PGs

In FEMA P-58, each PG has a unique ID and a detailed classification criterion. The mapping from a component to the PG is to determine the corresponding PG¡¯s ID for each component according to its classification criterion. The classification of the PGs in FEMA P-58 considers the geometries, materials, constructions, and damage mechanisms. Generally, the geometrical and material properties can be obtained from the BIM; however, the information of construction and damage mechanism must be added manually. Therefore, a solution combining the automatic and manual procedure (see Figure 3) is adopted to establish the mapping relationships from the components to the PGs herein.

Specifically, the mapping process is divided into four levels (as shown in Figure 3): building, story, component category, and PG. In FEMA P-58, the seismic damage is predicted story by story; therefore, the mapping is also conducted story by story to be consistent with FEMA P-58. A BIM (Level 1) is first split by stories (Level 2) according to the elevations of stories; then, different categories of components on each story (Level 3) are identified in BIM; finally, the PGs (Level 4) are identified manually according to the attributions of component categories in BIM and the necessary information on constructions and damage mechanisms.

In this study, Revit ^[29], a widely-used BIM program, is adopted for the modeling. Accordingly, the mapping process of the above four levels can also be implemented on Revit as follows:

Level 1: A BIM including architectural and structural information is created by Revit for the following mapping.

Level 2: The elevations of stories are used to split a BIM into different story models. Specifically, the class ElementCategoryFilter in the Revit API is used to collect the elevation elements. Using the elevation elements and the class ElementLevelFilter, the components on different stories are filtered to generate the story models.

Level 3: Generally, the components are named differently during the modeling, leading to difficulties on the identification of the component categories. Consequently, Family Instance is used to identify different component categories. In Revit, the hierarchy of components includes Category, Family, Family Symbol, and Family Instance. Each component is a Family Instance with the information of its hierarchy. The name of Category is pre-defined by Revit and cannot be changed by users, so that the component categories can be identified by Category in the hierarchy of Family Instance. In the Revit API, ElementCategoryFilter() can implement such an identification function.

Level 4: In a component category, each component will be marked with an ID manually according to the classification criteria of the corresponding PG in FEMA P-58.

To store the IDs of the PGs, a new attribute named P58_ID is added to the attribute table of each component. It is noteworthy that a component may have more than one PG¡¯s ID. In FEMA P-58, the corresponding PGs to calculate the damage of beams, slabs, and columns are their common joints. Therefore, some structural components, such as beams, slabs, and columns, will store multiple P58_IDs according to the numbers of their joints.

Step 2: THA based on BIM

Converting a BIM into a structural analysis model can reduce the workload in modeling. Several structural analysis programs contain such a conversion function, such as ETABS ^[30], Robot ^[31], and YJK ^[32]. In this study, YJK is selected as the structural analysis program. This is because numerous structural sub-models for the joints and sections in Revit have been developed in YJK ^[33], resulting in high conversion efficiency from a BIM to a structural analysis model.

The process of THA based on the BIM is shown in Figure 4. Using the YJK plug-in in Revit, the structural components that will be converted to the structural analysis model are selected. These selected components will be matched to the sections and joints (e.g., columns and beams) with the predefined sub-models in YJK. Finally, these sub-models are exported in the format of a .ydb file. In YJK, the structural model is first created by importing the .ydb file. Subsequently, the structural loads such as gravity are assigned to the model, and the corresponding ground motion is selected for a nonlinear THA. Finally, the EDPs (e.g., IDRs and PFAs) and structural deformations (e.g., plastic-hinge rotations) produced by the THA are output for the following damage prediction of components.

Step 3: Seismic damage prediction of PGs

FEMA P-58 provides the fragility curves for all PGs, as shown in Figure 5. Through the fragility curves, the probabilities of a PG at different DSs can be determined under a given EDP.

The algorithm of damage prediction of the PGs is designed in this study, as illustrated in Figure 6. Generally, the damage of PGs is predicted story by story. Firstly, a configuration file including the numbers of PGs (denoted as N_PG), and the required EDPs on each story is built. On each story, the N_PG and the corresponding EDPs are obtained from the configuration file. Subsequently, the numbers of components at different DSs are calculated for each PG. For the j^th PG (i.e., PG_j), P(DSk) represents the probability at damage state k, which can be obtained through the fragility curves, and  denotes the number of components at DSk, i.e., the product of P(DSk) and the total number of components in PG_j (denoted as N_j). It is noteworthy that the function Max(DS, j) represents the maximum DS of PG_j. Finally, the values of    at different DSs of all PGs are exported for calculating the damage of the components.

Step 4: Reverse mapping of DSs from PGs to components

Even though the components belong to the same PG on the same story, they may exhibit different DSs. For example, in a PG of masonry walls on a certain story, the probabilities of DS1, DS2, and no damage predicted by FEMA P-58 are 22%, 28%, and 50%, respectively, when the corresponding peak IDR is 0.002. However, FEMA P-58 does not provide the DS of each component. Hence, a reverse mapping algorithm of DSs from PGs to components is designed to determine the DS of each component.

The mapping principles of nonstructural and structural components are different. For nonstructural components, the distribution of DSs on the same story exhibits a large uncertainty ^{[34, 35]}. Therefore, DSs can be randomly assigned to the components belonging to the same PG. For structural components, the distribution of DSs should be consistent with the results of the THA. The rotations of plastic hinges calculated by the THA are adopted as an indicator to map the DSs to the joints of structural components (e.g., beams, slabs, and columns).

The detailed process of the reverse mapping of DSs can be implemented story by story, as shown in Figure 7. First, the DSs of the joints of structural components are imported, and the array DS_J[N_joint] that stores the DSs of all the joints on the story (the total number is N_joint) is obtained. Specifically, the higher DSs correspond to the joints with larger plastic-hinge rotations in DS_J[N_joint]. Subsequently, a new void array DS[N_comp] is created to store the DSs of all the components on the story (the total number is N_comp). Finally, for a component j, the DS[j] will be determined in two different methods according to whether it is a structural component. If it is a structural component, the maximum DS of the connected joints will be assigned to this component. Specifically, DS[j] = Max(DS_J[J₁], DS_J[J₂], ...). Here, J₁ and J₂ are the IDs of the joints connected to this component in the BIM. If the component is a nonstructural component, a random DSk will be assigned to this component according to the statistics of different DSs in the corresponding PG. This process will be repeated until all components on this story have been mapped with the corresponding DSs.

The above process can be implemented through the Revit API. The P58_IDs of the components are obtained from the attribute tables through the function Element.get_Parameter(). The predicted DSs of the components are also written in the attribute tables for the following prediction of seismic losses. The writing process of the DS to the component can be implemented through functions ExternalDefinitonCreationOptions(), InstanceBinding(), and Parameter.Set().

4.2 Loss prediction based on BIM and the unit-repair-cost database

(1) Ontology-based acquisitions for the measurement data of components

In the unit-repair-cost database, there are plenty of deduction rules for measuring components. For instance, the volume of a wall should subtract the holes of the windows and doors on this wall. To calculate such deductions automatically, an ontology-based model is created following these deduction rules strictly.

The creation of an ontology-based model includes two important steps: (a) establish ontological relationships of components; (b) define semantic reasoning rules for the deductions between components.

(a) Establish ontological relationships

A free, open-source ontology editor, Prot¨¦g¨¦ ^[36], and a widely-used semantic language, Web Ontology Language (OWL) ^[37], are adopted to establish the ontological relationships. The ontologies and instances of the components related to the seismic structural losses (e.g., beams, columns and walls) and their attached components (e.g., doors and windows) are created using OWL in Prot¨¦g¨¦. The ontologies of different types of components are created based on a root ontology Owl:Thing. The instances correspond to specific components in a BIM. Thereby, they are created by importing the data of component properties (e.g., ID, area and volume) from a BIM.

The ontological relationships of the components are designed as illustrated in Figure 8. There are three types of relationships: IS-A, Instance-Of and Member-Of. The IS-A relationship means A is a subclass of B, e.g. a masonry wall is a subclass of a wall; while the Instance-Of relationship means A is an instance of B. The Member-Of relationship means A is a member of B, e.g. a door is a member of a wall, which can be used to calculate the deductions between components.

(b) Define semantic reasoning rules

A semantic web rule language (SWRL) ^[38], is adopted to define the semantic reasoning rules of different ontologies following the local unit-repair-cost database. Taking a Chinese database ^[12] for example, the database demands that if the hole area of a window or a door on a wall is greater than 0.3 m², the hole must be subtracted from the wall. The semantic reasoning rules in SWRL can be expressed as follows:

Hole(?name) ¡Ä elementID(?name, ?element_ID) ¡Ä holeArea(?name, ?area) ¡Ä swrlb:greaterThan(?area, 0.3) ¡ú deducted(?name, true)

In the first line of the above code, Hole means a type of an ontology, and the symbol of ¡°?¡± is used to extract the data of variables (e.g., name, element_ID and area). In addition, the ¡°¡Ä¡± means ¡°and¡±. Thus, the first line is used to obtain the information of windows and doors. In the second line, the function of swrlb:greaterThan can judge whether the area is greater than 0.3 m². If so, the function of deducted(?name, true) will deduct the corresponding component.

Similarly, the other deduction rules of components (e.g., a beam should subtract its joints with columns) can also be defined using SWRL, and the deducted results can be automatically calculated according to the defined rules.

Based on the deduction results, the exact measurement data of components can be easily extracted in a BIM. For most components, the volumes and projected areas are selected as measurement units for loss predictions. In the Revit API, the volume of each component can be obtained through the function get_Parameter(), while the projected area of a component can be obtained through the function get_BoundingBox(). The obtained measurement data will be used for the following loss predictions.

(2) Acquisitions of unit repair costs

Many governments and professional associations have published the official construction codes, such as the MasterFormat code ^[10-11], and the Beijing repair code ^[12]. By using the unit-repair-cost database in these codes, the loss prediction result will agree with the actual situations in the local area. However, these cost data only correspond to the state of complete damage. The consequence functions in FEMA P-58 provide the unit repair costs corresponding to different DSs. Therefore, the ratio of costs between different DSs in FEMA P-58 can be used to calculate the unit repair costs corresponding to different DSs in the database.

In this study, the function F(P58_ID, DSn) was established. This function will obtain the unit repair cost of a component with a P58_ID at DSn from the consequence functions in FEMA P-58. Define the unit repair cost of a component in the database as Unit_Cost_Max. If this component is a nonstructural component, the unit repair cost corresponding to DSn, denoted as Unit_Cost_DSn, can be calculated by Equation (1):

where, P58_ID is the ID of the corresponding PG of this component, and DS_Max represents the maximum DS of the PG.

If the component is a structural component, it has more than one P58_IDs. Thus, the average of the repair costs for the joints is used to calculate its repair cost. The unit repair cost of a structural component corresponding to DSn is as shown in Equation (2):

where J means the number of joints connected to this component, and P58_ID_i is an ID of the PG of the joints.

(3) Loss predictions

Assume the DS of component i is DSn, and the corresponding measurement data is V_i, the repair cost of this component, Repair_Cost_i, can be calculated by Equation (3):

where Unit_Cost_DSn_i is the corresponding unit repair cost of the component.

Repair_Cost, which is the repair cost of the entire building, can be calculated by Equation (4):

where N represents the total number of components in this building.

4.3 Visualization of seismic damage and loss

(1) A unified visualization standard

According to FEMA P-58, the numbers of DSs of the components are different. For example, the joints of beams and columns generally contain three DSs, while masonry walls generally contain two DSs. To visualize the DSs of the components in a unified manner, two different visualization modes are designed in this study: the absolute mode and the relative mode.

In the absolute mode, each DS is marked with a certain color, as shown in Table 1. It is noteworthy that white with half transparency is used to represent a non-damaged state, which can highlight the other DSs.

Table 1 Colors of DSs in the absolute mode

The absolute mode can display the DSs of a component directly; however, it is difficult to demonstrate whether the components can be repaired. For example, a beam-column joint at DS2 can be repaired, while a masonry wall at DS2 will be generally dismantled. Therefore, in this study, a relative mode is established to demonstrate the reparability of the components. Specifically, DSs are classified as repairable and irreparable. Hence, only three states need to be presented, using three colors, as shown in Table 2.

Table 2 Colors of reparability states in the relative mode

The losses of different components vary significantly. Therefore, a relative mode is used. The losses are divided into four categories based on the ratio of repair cost and construction cost. Four colors are used to represent the four categories, as shown in Table 3.

Table 3 Colors of seismic losses of components

(2) 3D Visualization and virtual walk through  

Taking the DSs of the components for example, the 3D visualization process and the virtual walk through is shown in Figure 9. First, the components in the BIM are divided into two groups by filtering their DSs. For damaged components, different colors will be assigned to them corresponding to their DSs. For undamaged components, their color is white with half transparency to highlight the damaged components. Subsequently, a 3D model with different colors is loaded into the VR platform, and the parameters of the virtual environment (e.g., lights and the sky) are set. Finally, a virtual walk through is performed to observe the distribution of seismic damage inside the building. It is noteworthy that the 3D visualization process and the walk through of the losses is similar to that of the DSs.

The 3D visualization of damage and losses is implemented through the Revit API. Specifically, the FilteredElementCollector class is used to filter the components according to their DSs or losses. Functions SetColorFaceColor() and SetSurfaceTransparency() are used to set the color and transparency of the components. In addition, function IsolateElementsTemporary() can be used to isolate the components according to their DSs, and therefore display the components at a certain DS independently.

Fuzor ^[39] is used as the VR platform in this study, because it can load a BIM into the VR scene with sufficient information corresponding to the components. Through the "Fuzor Plugin" in Revit, the colored BIM is synchronized to the VR scene for a walk through. During the walk through, not only the distribution of the DSs or losses can be observed by the colored components, but also the value of loss of each component can be checked in the VR scene of Fuzor, which benefits the decision making of repair strategies.

5. Pilot test

5.1 Introduction of a pilot test

An office building in Beijing is selected for a pilot test. It is a reinforced concrete (RC) frame building with a length of 33.6 m and a width of 25.2 m. The building encompasses 921 m² and has six stories with a total height of 25.5 m. The BIM of this building is established in Revit, as shown in Figure 10.

5.2 Seismic damage prediction

Using the YJK plug-in in Revit, the structural model in the BIM is converted into a structural analysis model in YJK directly, as shown in Figure 11. Hence, the workload of modeling can be eliminated.

According to the seismic design code ^[40], the peak ground acceleration (PGA) for the maximum considered earthquake is 400 cm/s² in Beijing. Therefore, the widely used El-Centro ground motion with a PGA of 400 cm/s² is selected as the input in both the X and Y directions of the structure. Nonlinear THA is performed in YJK, and the EDPs required by the following predictions are calculated (see Table 4):

Table 4 The EDPs from the nonlinear THA

The proposed methods of seismic damage and loss prediction, and the visualization are developed as the Revit plug-in (see Figure 12). After reading the EDPs above, the DSs and losses of all the components are predicted using the developed plug-in and written to the attribute tables of the components (see Figure 13).

Figure 14 shows the results of the seismic damage prediction. Only 1% of the beam-column joints exhibit repairable damage, while the remainders are intact. The reinforced masonry walls exhibit severe damages. In detail, 51% and 16% of them exhibit irreparable and repairable damages, respectively. Further, 70% of the stairs are damaged but repairable. Owing to the slight damage in the structural components, the entire building is slightly damaged.

5.3 Acquisitions of measurement data

The measurement units of components between the FEMA P-58 method and the database in Beijing repair code are compared in Table 5. From this table, the measurement units in Beijing repair code are more precise than that in FEMA P-58.

Table 5 The measurement units between FEMA P-58 and Beijing repair code

In addition, the deduction results of components are conducted following the rules in Beijing repair code by using the designed ontology-based model. By importing such deduction results, the exact measurement data can be calculated by Revit API. Taking the main components (i.e., masonry walls and beams) on the ground floor for example, the volumes of these two types of components considering the ontology-based deduction results are shown in Table 6. Comparing with the volumes without deductions, the corresponding deduction ratios of two types of components are 20.14% and 6.55%, respectively, which indicates that the deduction results using the designed ontology-based model can be used to calculate more accurate measurement data for seismic loss predictions.

Table 6 The volumes considering the ontology-based deduction results for main components on the ground floor

5.4 Seismic loss predictions and comparisons

To compare the FEMA P-58 method and the proposed method, three scenarios are considered, as shown in Table 7. The differences between these three scenarios are the prediction methods and the unit-repair-cost database.

Table 7 Prediction scenarios

Through the proposed method, the seismic losses of different components and the entire building in three scenarios can be predicted. Figure 15 shows the distributions of the repair costs in scenario 1 (using the FEMA P-58 method and the U.S. repair cost data), and scenario 2 (using the method proposed in this study and the U.S. repair cost data). This figure shows that the repair costs of different components predicted by these two methods are almost the same. The total repair costs in scenarios 1 and 2 are $3,267,847 and $3,280,737, respectively. From the comparison, when using the same unit-repair-cost database, the prediction of the proposed method is almost the same as the FEMA P-58 method, which indicates the accuracy of the proposed method.

Figure 16 shows the distribution of the repair costs in scenario 3 (using the proposed method and the Chinese repair cost data). As shown, the loss distribution among different components is consistent with that of scenario 2. However, the total repair cost predicted in scenario 3 is much lower than that of scenario 2. The total repair cost of scenario 3 is 463,728 RMB (the U.S. $70,003 according to the exchange rate ^{[41, 42]} between RMB and U.S. dollar in 2011), which is only 2% of the total repair cost ($3,267,847) of scenario 1.

Reinforced masonry walls constitute the largest proportion of losses in all scenarios. In the database of FEMA P-58, the unit repair cost of the reinforced masonry wall in this pilot test is $15,800/225 ft², while the corresponding data in the Chinese database is only $334/225 ft². A significant difference of 47 times exists between these two databases. Therefore, such significant differences result in a significantly different loss prediction.

According to the investigations from several earthquakes that occurred in China, the ratio between the loss and construction cost for an RC structure with slight damage is 5¨C10% ^[43]. The average construction cost in 2011 in Beijing is $227/m^{2 [44]}; therefore, the total construction cost of this building is $1,204,235. Through the calculations, the ratio between the loss and construction cost is 5.8% in scenario 3, which agrees with the empirical result (5¨C10%), while the ratio in scenario 2 is 272.4%, which is much larger than the empirical range. Therefore, the proposed method of earthquake loss predictions agrees much better with the actual investigations in China.

In addition, the proposed methods including the predictions of seismic damage and loss as well as the corresponding visualizations are integrated with BIM (see Figure 12), which can be implemented in an efficient and nearly-automatic way; whereas the FEMA P-58 method cannot directly use the detailed data in a BIM, leading to a lot of manual work for obtaining the required data of predictions. On the other hand, the FEMA P-58 method has no visualization function, which limits its application effects. The advantages of the visualization function in the proposed method are clarified as follows.

5.5 Visualization

The seismic damage of components is shown using the absolute and relative modes (see Figure 17 (a) and (b)), respectively. In addition, the components corresponding to a DS or repair state can be displayed independently (see Figure 17 (c) and (d)). Therefore, the spatial distributions of seismic damage and reparability can be observed clearly using the proposed visualization method.

According to the ratios between the repair cost and construction cost, the earthquake losses of all the components are shown in Figure 18. Additionally, the colored BIM in Figure 18 is loaded in Fuzor. The virtual walk through inside the building is performed (see Figure 19), so that the distribution of losses inside the building can be clearly observed and the detailed information about the seismic damage and loss of the selected component can be obtained. The virtual walk through can help users to fully understand the spatial distribution of seismic damage and losses, so that a reasonable repair strategy can be crafted.

6. Conclusions

A prediction method for seismic loss based on BIM and FEMA P-58 was proposed in this study. The method was validated using a pilot test of a six-story office building in Beijing. The conclusions from this study are as follows:

(1) By integrating FEMA P-58 with BIM, the proposed method mapped the seismic damage results of PGs in FEMA P-58 to specific components in BIM, and could save the manual works (e.g., the structural modeling for THAs and the data collections for determining the PG¡¯s ID in FEMA P-58).

(2) Based on the designed ontology-based model, the exact reduction results following the rules in the local code of repair costs were obtained for calculating accurate measurement data for seismic loss predictions.

(3) In the seismic loss predictions, the proposed method exhibited the same accuracy as the FEMA P-58 method when using the same database. Moreover, the loss predictions through the proposed method were in agreement with the actual investigations in different regions when using the local database.

(4) The proposed method was able to display the spatial distribution of seismic damage and losses of all the components in a virtual walk-through way, which helps users make a specific repair strategy considering the loss distributions.

(5) The outcome of this study produced a component-level and visual loss prediction result that agrees with the actual situation of the specific region, which can be used to evaluate the post-earthquake economic resilience of different buildings.

Acknowledgments

The authors are grateful for the financial support received from the National Key R&D Program of China (No. 2018YFC0809900), National Natural Science Foundation of China (No. U1709212) and the China Scholarship Council (No. 201806465044).

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