Rapid Seismic Damage Prediction of Buildings Rooted on Structural Strength

To promptly assess regional earthquake damage, several seismic alarm systems have been created around the world. This study in the journal Buildings compares the suggested method to refined finite element model analysis and simplified model analysis and recommends a method for the rapid prediction of seismic damage to urban buildings utilizing low-LOD information.

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Study: A Brief Method for Rapid Seismic Damage Prediction of Buildings Based on Structural Strength. Image Credit: schlyx/Shutterstock.com

Earthquake warning systems use fragility curves to assess structural damage quickly after an earthquake occurs. Such fragility curves are created using a small database and a set of preset categories that take into account the change of a few attributes.

This study compares the suggested method to refined finite element model analysis and simplified model analysis and recommends a method for the rapid prediction of seismic damage to urban buildings utilizing low-LOD information.

Methodology

Empirical fragility analysis has been utilized for residential buildings in studies aimed at forecasting seismic damage to urban structures using physics-based methodologies. The capacity spectrum method (CSM) is a computationally efficient method that uses pushover curves to analyze building attributes.

Torsion effects impact the seismic responses of buildings built to have abnormalities, and typical assessment methodologies may not perform well on such structures. Seismic damage indices (DIs) are another extensively used deterministic technique.

DIs can affect a structural component, a structural member, a section of the structure, or the complete structure. It is frequently used to make preliminary damage assessments.

For a few construction categories, simplified stick models of a similar type have been constructed separately, and their correctness is dependent on parameter calibration. Because there is a scarcity of data on urban structures, some of the parameters of the simplified models are established by statistical analysis, which introduces uncertainty into the models.

To analyze uncertainty in structural properties, sensitivity analysis methods such as the Monte Carlo method and the first-order second-moment method are frequently utilized. When the total number of regional buildings is significant, parameter uncertainty has a minor impact on the analysis outcomes.

However, in the case of individual building analyses, the uncertainty cannot be overlooked.

Soft computing techniques have been used in a variety of research to develop quick methods of seismic vulnerability assessment. Based on field observation by professionals, these methods use probabilistic methodologies, meta-heuristics, and artificial intelligence (AI) methods to create correlations between specified preliminary parameters and damage states.

Soft computing techniques applied to quick seismic risk assessment could eliminate biased field judgment by poorly qualified engineers and tackle the difficulties of the inherent uncertainty in the real world.

Data-driven vulnerability correlations of buildings from one area may not work well on buildings from another area due to differences in design and materials used in building construction.

HAZUS recommends overstrength factors for buildings, and the values of overstrength factors for Chinese buildings were determined using statistical analysis in the structural study of Chinese structures.

The seismic resistance index of structures is determined using structural overstrength in a suggested approach for regional seismic structural damage prediction. The result of the design strength level and the overstrength factor is the seismic resistance index.

The design-strength-based strategy is depicted in Figure 1 as a flowchart. The spectral acceleration S_a can be used to express the earthquake load for a particular seismic ground motion (T₁).

With a few parameters and a statistical procedure, the natural period T₁ can be calculated (e.g., number of stories, structure type, basic building plan sizes, and building height). The seismic design code employed in the building’s design can be decided by the building’s construction time and seismic zone.

Figure 1. Flowchart of the design-strength-based seismic damage prediction method. Image Credit: Zhang, et al., 2022

The earthquake intensities are classified as common earthquakes, moderate earthquakes, rare earthquakes, and extremely rare earthquakes in the Chinese Code for Seismic Design of Buildings and the Seismic Ground Motion Parameter Zonation Map of China.

The earthquake intensities related to recurrence periods and performance objectives are provided in Table 1.

Table 1. Design earthquake intensities and performance objectives in Chinese codes. Source: Zhang, et al., 2022

Earthquake Intensity	Recurrence Period (Years)	Probability of Exceedance	Performance Objective
Frequent earthquake	50	63% in 50 years	Operational
Moderate earthquake	475	10% in 50 years	Damage repairable
Rare earthquake	2475	2–3% in 50 years	Collapse prevention
Extremely rare earthquake	10,000	0.01% per year	Probable collapse

 

The seismic resistance indices of four earthquake intensity levels, as indicated in Table 2, are the criterion for structural damage state utilizing the design-based method.

Table 2. The design-strength-based method’s structural damage criteria. Source: Zhang, et al., 2022

Damage States	Range of Seismic Resistance Index
No damage	[0, Ωy×Sa(T1) (frequent earthquake)]
Slight/minor damage	Ωy×[Sa(T1) (frequent earthquake), Sa(T1) (moderate earthquake)]
Moderate damage	Ωy×[Sa(T1)(moderate earthquake), Sa(T1) (rare earthquake)]
Extensive damage	Ωy×[Sa(T1) (rare earthquake), Sa(T1) (extremely rare earthquake)]
Complete damage	Ωy×[Sa(T1) (extremely rare earthquake), +∞ ]

 

For the structural damage states in the current study, the earthquake design intensities and performance objectives in the Chinese codes were used. The concept of this method can also be used in structures built for other seismic design codes.’

Results

The seismic response of the two methods is compared to that of the proposed method, using simplified models and refined FE models. To validate the correctness of the simplified models, the seismic response of the simplified models is compared to the results of the refined FE models.

The findings of the simplified models and refined FE models are then compared to the seismic performance of the design-strength-based technique.

The MCS-model-based strategy is depicted in Figure 2 as a flowchart. The initial inter-story stiffness and mass of each story are generally considered to be spread uniformly along with the building’s height.

Figure 2. Flowchart of the MCS model analysis. Image Credit: Zhang, et al., 2022

The inter-story force-displacement connections are usually represented using the degenerated three-linearity hysteretic model. The yielding point, peak point, and ultimate point determine the degraded three-linearity hysteretic model.

The overstrength factor is determined by the geometry of the building’s structural parts. To account for the uncertainties, Monte Carlo simulations are used. Table 3 shows a comparison of the models of different MCS-model-based approaches.

Table 3. Comparison of the parameter determination procedures of several MCS models. Source: Zhang, et al., 2022

Reference	Proposed by Xu et al. [42]	Proposed by Wu et al. [43]	Proposed by Marasco et al. [44]
Elastic parameters	The natural period estimated by empirical equations; stiffness estimated by generalized eigenvalue analysis; design strength estimated by design procedures	The natural period estimated by empirical equations; stiffness estimated by generalized eigenvalue analysis; design strength estimated by design procedures	Yield strength and displacement estimated by pushover analysis
Inelastic parameters	Strength estimated by overstrength factors; displacement estimated by strength and stiffness or statistical results	Strength and displacement estimated by statistical results	Strength estimated by collapse analysis; displacement estimated by the reduction factor

 

Table 4 compares the properties of the proposed design-strength-based technique, MCS model with THA, and improved FE model with THA.

Table 4. Comparison of the proposed method, MCS model with THA, and refined FE model with THA. Source: Zhang, et al., 2022

	Design-Strength-Based Method	MCS Model with THA	Refined FE Model with THA
Computational efficiency	High	Moderate	Low
LOD of results	Overall level	Floor level	Component level
Required data	Basic data	Basic data	Detailed data
Application range	All types of structures	Regular structures	All types of structures
General applicability	A universal method for all structure categories	A unique model for each structure category	A unique model for each individual structure

 

The design-strength-based method can be used on any structure, including irregular ones, and it requires less data than the other two methods.

When analyzing a building’s seismic reaction using MCS models, identifying an appropriate simplified model and its parameter determination technique for the building category is the first step. Subsequently, conducting the seismic response analysis using the derived MCS model.

The proposed design-strength-based method, on the other hand, applies to buildings of all structure types.

Validation was explored for five reinforced concrete frames with 3-story, 5-story, 8-story, 12-story, and 18-story designs. The buildings’ architectural elevations were comparable. The first story and standard floor heights for each building were 4.2 m and 3.3 m, respectively.

The structural characteristics of the columns and beams of the buildings are shown in Tables 5 and 6.

Table 5. The properties of the columns. Source: Zhang, et al., 2022

RC Frame	Stories	fcu* (MPa)	Dimensions (mm)		Longitudinal Reinforcement		Transverse Reinforcement
			Side	Center	Side	Center	Side		Center
					Ratio (%)	Ratio (%)	Φ*(mm)	s*(mm)	Φ (mm)	s (mm)
3-story	1–3	30	500 × 500	500 × 500	0.91	0.91	8	100	8	100
5-story	1–5	30	500 × 500	500 × 500	0.91	0.91	8	100	8	100
8-story	1–8	30	550 × 550	550 × 550	1.09	1.09	8	100	8	100
12-story	1–4	35	700 × 700	700 × 700	1.20	1.20	8	100	8	100
	5–8	35	600 × 600	600 × 600	1.27	1.27	8	100	8	100
	9–12	35	500 × 500	500 × 500	1.02	1.02	8	100	8	100
18-story	1–4	40	700 × 700	700 × 700	1.20	1.20	8	100	8	100
	5–10	40	600 × 600	600 × 600	1.27	1.27	8	100	8	100
	11–18	40	500 × 500	500 × 500	1.02	1.02	8	100	8	100

 

* f_cu = compressive strength; Φ = diameter of reinforcement bar; s = transverse reinforcement spacing.

Table 6. The properties of the beams. Source: Zhang, et al., 2022

RC Frame	Stories	fcu* (MPa)	Dimensions (mm)	Longitudinal Reinforcement Ratio (%)				Transverse Reinforcement
				Side		Center		Side				Center
				Mid-Span	Bearings	Mid-Span	Bearings	Mid-Span		Bearings		Mid-Span		Bearings
								Φ* (mm)	s* (mm)	Φ  (mm)	s (mm)	Φ  (mm)	s (mm)	Φ  (mm)	s (mm)
3-story	1–3	30	250 × 500	0.91	1.04	0.91	1.04	8	100	8	200	8	100	8	200
5-story	1–4	30	250 × 500	0.91	1.18	0.71	1.18	8	100	8	200	8	100	8	200
	5	30	250 × 500	0.91	0.81	0.71	0.81	8	100	8	200	8	100	8	200
8-story	1–5	30	250 × 600	0.72	0.98	0.72	0.98	8	100	8	200	8	100	8	200
	6–8	30	250 × 600	0.72	0.76	0.72	0.76	8	100	8	200	8	100	8	200
12-story	1–4	35	300 × 600	0.70	0.97	0.70	0.97	8	100	8	200	8	100	8	200
	5–11	35	250 × 500	1.09	1.52	1.09	1.52	8	100	8	200	8	100	8	200
	12	35	250 × 500	1.09	0.86	1.09	0.86	8	100	8	200	8	100	8	200
18-story	1–4	40	300 × 650	0.52	1.17	0.89	1.17	8	100	8	200	8	100	8	200
	5–7	40	250 × 600	0.72	1.64	1.13	1.64	8	100	8	200	8	100	8	200
	8–10	40	250 × 600	0.72	1.64	0.91	1.64	8	100	8	200	8	100	8	200
	11–17	40	250 × 600	0.72	1.13	0.72	1.13	8	100	8	200	8	100	8	200
	18	40	250 × 600	0.72	0.63	0.72	0.63	8	100	8	200	8	100	8	200

 

* f_cu = compressive strength; Φ = diameter of reinforcement bar; s = transverse reinforcement spacing.

As an example, Figure 3 depicts the plan and elevation layout of a three-story structure. The structures were planned to be installed on-site with a shear-wave velocity of (250, 500) m/s and a design peak ground acceleration of 0.15 g, with a 10% chance of exceeding the design in 50 years.

Figure 3. Layouts of the structure (3-story frame as an example): (a) plan layout (unit: mm); (b) elevation layout (unit of elevation: m; unit of bay: mm). Image Credit: Zhang, et al., 2022

The response spectra of six ground motion records from the PEER NGA WEST2 database were shown in Figure 4a, b. The chosen ground motions were well-suited to the target response spectrum.

Figure 4. Spectral characteristics of the selected ground motions: (a) each response spectrum and target response spectrum; (b) mean response spectrum and target response spectrum. Image Credit: Zhang, et al., 2022

Table 7 summarizes the basic facts on ground motions.

Table 7. Summary of ground motion records. Source: Zhang, et al., 2022

No.	Earthquake Event	Time	Component	Magnitude	Earthquake Station
1	El Centro	1940	180	7.0	El Centro-lmp Vall lrr Dist
2	El Centro	1940	270	7.0	El Centro-lmp Vall lrr Dist
3	Northridge	1994	90	6.6	TaTzana Cedar Hill Nur.A
4	Northridge	1994	360	6.6	TaTzana Cedar Hill Nur.A
5	Chi-Chi Taiwan	1999	E	7.3	KAU082
6	Chi-Chi Taiwan	1999	N	7.3	KAU082

 

The earthquake ground motions were scaled according to the earthquake intensities of common, rare, and extremely rare earthquakes.

Table 8 shows the resulting PGAs and recurrence periods of recurring earthquake intensity, rare earthquake intensity, and extremely rare earthquake intensity levels when the PGA of moderate earthquake intensity is 0.15 g.

Table 8. Earthquake recurrence periods and corresponding PGAs when the PGA of moderate earthquake intensity is 0.15 g. Source: Zhang, et al., 2022

Earthquake Intensity	Recurrence Period (Year)	PGA (g)
Frequent earthquake	50	0.056
Rare earthquake	2475	0.316
Extremely rare earthquake	10,000	0.45

 

Figure 5 depicts the inter-story drift ratios of the MCS and refined FE models at three different earthquake intensities.

Figure 5. Validation of the MCS-model-based method (maximum IDR): (a) 3-story structure; (b) 5-story structure; (c) 8-story structure; (d) 12-story structure; (e) 18-story structure. Image Credit: Zhang, et al., 2022

GA represents the refined FE model with PGA = 0.056 g, GB represents the MCM model with PGA = 0.056 g, GC represents the refined model with PGA = 0.316 g, GD represents the MCM model with PGA = 0.316 g, GE represents the refined FE model with PGA = 0.45 g and GF represents the MCM model with PGA = 0.45 g.

When the structure’s inter-story ratio is low, the results of the MCM model analysis are more similar to the results of the refined FE model analysis.

The difference between MCS models and refined FE models is that the seismic response of multistory RC frames using the MCS-model-based method is determined by its inter-story force-displacement relationship, which is heavily influenced by the accuracy of the three-linearity hysteretic model parameters.

The MCS models’ seismic damage state assessment criteria are a combination of force-based and deformation-based criteria. Table 9 lists the seismic damage state assessment criteria for the refined FE models developed in the IDARC-2D program.

Table 9. Damage criteria for models built in the IDARC-2D program. Source: Zhang, et al., 2022

Damage State	Overall Damage Index
No damage	[0, 0.05)
Slight/minor damage	[0.05, 0.3)
Moderate damage	[0.3, 0.6)
Extensive damage	[0.6, 1)
Complete damage	≥1.0

 

In the software, the five damage states are classified based on the overall structural damage index. Figure 6 depicts the structural damage state results obtained by applying the design-strength-based method.

Figure 6. Structural damage states using the proposed design-strength-based method: (a) 3-story structure; (b) 5-story structure; (c) 8-story structure; (d) 12-story structure; (e) 18-story structure. Image Credit: Zhang, et al., 2022

Figure 7 depicts the results of three different seismic damage state prediction methods. In the legend, the letters FE, MCM, and DS represent the refined FE model with THA, the MCM model with THA, and the proposed design-strength-based method, respectively.

Figure 7. Seismic damage state prediction results using the refined FE model with THA, the MCS model with THA, and the design-strength-based method: (a) 3-story structure; (b) 5-story structure; (c) 8-story structure; (d) 12-story structure; (e) 18-story structure. Image Credit: Zhang, et al., 2022

Figure 8 compares the error between the design-strength-based method and the MCS model with THA, using the refined FE model results as true values. The dispersion coefficient in the range [0, 1] represents the accuracy.

Figure 8. Error of the design-strength-based method and the MCS model with THA, taking the results of the refined FE model with THA as true values. Image Credit: Zhang, et al., 2022

Application

A university campus was used to test the proposed method. The university campus structures were designed in accordance with the seismic design code, and their seismic design PGA is 0.15 g, with a 10% probability of exceeding 50 years. The shear-wave velocity at this location is in the (250, 500) m/s range. Figure 9 depicts a plan view of the campus.

Figure 9. Plan view of the campus. Image Credit: Zhang, et al., 2022

Table 10 displays basic information about the campus’s buildings, such as structural type, number of stories, and construction time. Due to the revision of the Chinese seismic codes, buildings built before 1989 were calculated in the same way as buildings built after 1989.

Table 10. Basic information of the buildings on the investigated campus. Source: Zhang, et al., 2022

Building Name	Structural Type	Number of Stories	Construction Time	Building Name	Structural Type	Number of Stories	Construction Time
Dorm 1	RM	6	1985	School building 3	RC	4	2002
Dorm 2	RM	6	1985	School building 4	RC	1	2002
Dorm 3	RC	6	1998	School building 5	RC	5	2010
Dorm 4	RC	6	1999	Lab 2	RC	5	2002
Dorm 5	RC	7	2001	Lab 3	RC	4	2010
Dorm 6	RC	7	2002	Lab 4	RM	4	1985
Restaurant 1	RC	2	2003	Electric building	RM	1	1985
Restaurant 2	RC	2	2003	Health center	RC	2	2002
Restaurant 3	RC	2	1998	Lab 5	RC	1	1985
Restaurant 4	RC	1	1999	Hospital	RC	5	2002
Main building	RC	10	2002	Garage	RM	5	1986
Academic building	RC	4	1986	Lab 6	RC	3	2002
Library	RC	5	2005	Activity center	RC	1	2009
School building 1	RC	6	2007	Lab 7	RC	5	2002
School building 2	RM	5	1986

 

The proposed design-strength-based method was used to predict the seismic structural damage states of buildings in the case study region. Buildings in the case study area were assumed to have been designed and constructed in strict accordance with design codes.

The average damage conditions of the buildings are shown in Figure 10 for earthquake intensities that are common, rare, and extremely rare.

Figure 10. Structural damage states under different earthquake intensities: (a) frequent earthquake; (b) rare earthquake; (c) extremely rare earthquake. Image Credit: Zhang, et al., 2022

The findings show that under regular earthquake intensity, all buildings in the case study region are unaffected, most buildings suffer minor damage under rare earthquake intensity, and most buildings suffer moderate damage under extremely rare earthquake intensity.

The seismic structural damage states show that all of the structures in the case study region meet the design performance targets, implying that the suggested design-strength-based method might provide a good forecast of the building damage state.

Conclusion

This study proposes a quick structural design-strength-based method for predicting seismic damage to urban buildings. To validate the proposed design-strength-based method, five typical RC-frame buildings were subjected to refined FE element model analysis and MCS model analysis.

To show the feasibility and benefits of the suggested technology, the structural seismic damage prediction was applied on a university campus.

By comparing the results of the improved FE model analysis and the MCS model analysis, the proposed method was shown to be both acceptable, accurate, and efficient.

Unlike the MCS-model-based method, the suggested method can theoretically be applied to any type of structure, including irregular structures. Using only a few preliminary parameters of the buildings, the proposed method might offer rapid seismic damage assessment findings for urban buildings, according to the case study.

The objective of this study was to offer a quick method for predicting post-earthquake seismic damage to urban structures. This method is suited for rapid preliminary damage assessment in seismic alarm systems, and it can be used as a guide for government decision-making in emergencies.

The prediction of seismic reaction, including building displacement and acceleration, should be more carefully studied in the future based on structural parameters. As a result, the suggested seismic damage prediction method’s results will be used to assess earthquake losses and casualties as well as predict quick building collapse.

Journal Reference:

Zhang, S., Liu, Y., Li, S. (2022) A Brief Method for Rapid Seismic Damage Prediction of Buildings Based on Structural Strength. Buildings, 12(6), p. 783. Available Online: https://www.mdpi.com/2075-5309/12/6/783/htm

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