Rapid simulation method for assessing seismic damage to building curtain walls on a regional scale using designed wind load capacity

Abstract

This study introduces a rapid simulation method for assessing seismic damage to building curtain walls at a regional scale. Although the results are approximate, this approach enables quick evaluations, making it an important instrument for emergency responses during disaster situations. This method’s independence from numerical models is a noteworthy advantage. Unlike conventional approaches, it eliminates the need for structural analysis models when evaluating the seismic capacities of curtain walls regionally. Creating reliable structural analysis models is both time-consuming and labor-intensive, primarily due to the detailed design information they require. In contrast, the presented method leverages the wind load capacities for which curtain walls are designed. It is based on the core premise that most curtain walls, primarily designed for wind resistance, possess wind load capacities that could serve as substitutes for their seismic capacities, even if they are not explicitly designed for such seismic loads. To assess the method’s effectiveness, it was applied to seismic damage assessments across regions experiencing varying wind intensities: weak, moderate, and strong. The results suggest the likelihood of curtain walls sustaining seismic damage in regions with weak wind could be five times higher than in regions with strong wind. This underscores the importance of seismic design considerations for curtain walls. Moreover, the findings closely match the actual seismic damage assessment data from a region with a moderate to strong wind intensity.

Keywords

Seismic damage assessment curtain walls regional scale

1. Introduction

Earthquakes cause significant physical and economic damage to buildings and infra structures [1,2,3], often resulting in human casualties [4,5]. These damages cause monetary losses [6,7], and the magnitude of these costs can vary across regions [8,9]. To reduce such monetary losses following an earthquake, it is critical to assess catastrophe-related damages and develop disaster assistance programs suited to each region [10,11,12,13]. This goal can be accomplished through comprehensive regional seismic risk assessments [14,15,16,17,18,19]. Typically, these assessments are carried out by assessing seismic damage to individual structures [20,21] within a specified region [15], considering both structural and nonstructural components [6]. However, damage investigation through visual inspection or analytical modeling has limitations due to its labor-intensive and time-consuming nature [22,23,24]. For rapid post-earthquake recovery, a faster and more efficient earthquake damage inspection method is needed.

Figure 1.

Typical curtain wall images: (a) an example installed in a building; (b) a configuration diagram of the curtain wall system.

Buildings have both structural and nonstructural components [25]. Structural components include key structural elements such as columns, beams, shear walls [26], braces, slabs, and foundations [25], whereas nonstructural components include architectural, mechanical, piping, or electrical elements that are permanently coupled to structural components [27].

Although nonstructural components are not frequently addressed in seismic design [28], they must be included during seismic damage assessment [29,30] owing to their large contribution to monetary losses [31]. Typically, nonstructural components comprise approximately 70–85% of the total construction costs of commercial buildings [32,33]. Given their large proportion in building costs, seismic damage to nonstructural components can lead to substantial economic losses from repairs and replacements [34,35,36,37]. Potentially, damages to nonstructural components may cause human casualties [25,38] as well as affect building functionality significantly [28,39]. Facades, partitions, and ceilings are example of architectural elements that are not structural components [25,28]. Facades can be classified further into claddings and infills [40]. Infills refer to interior building frames, while claddings are related to exteriors [41]. The weight of cladding varies, with heavier options like concrete panels and lighter options like curtain walls [37]. In this context, curtain walls, a subset of lightweight cladding, need to be the primary focus.

Curtain walls serve as the exterior façade of a building and fulfill all the key functions expected of exterior walls [42]. Figure 1-(b) depicts the overall layout of curtain walls, whereas Fig. 1-(a) provides instances of curtain walls installed on structures. Typically, they are made of opaque panels or lightweight glass, supported by aluminum frames and supporting structures. Stone and metal are the materials used to create these opaque panels. Glass is the material of choice because of its light weight, transparency, and energy efficiency [38,43]. Curtain walls can comprise 10–15% [44,45,46] of the total construction cost. Their failure can lead to economic losses [47], pose safety risks [38], and disrupt essential building functions such as insulation and waterproofing. Except for their weight, curtain walls are non-bearing and do not share the building’s vertical load [43]. Curtain walls must be able to transfer lateral loads to the building’s structural component, even though they are nonstructural components [48]. Therefore, they should be designed to ensure appropriate structural performance. Anchoring details, glass, metal, or stone panels, transoms, and mullions are the major component of curtain wall structural design [42]. Wind and seismic loads are example of representative lateral loads [49,50]; often, only the wind load is considered. This is because, the wind demand of curtain walls is typically greater than their seismic demand [43]. However, there are cases where the seismic demand is greater than the wind demand, depending on the type, configuration, and size of the curtain walls. Therefore, curtain walls should be examined to satisfy both seismic and wind demands. Specifically, they should demonstrate structural performance that can transmit the inertia force caused by an earthquake to the structural components of the building and the ability to accommodate the story drift in the building caused by the earthquake [43]. Despite this requirement, few research cases related to the seismic performance of curtain walls have been reported in the literature [43]. In particular, even fewer research cases consider both wind and seismic loads [42]. Based on these circumstances, it is estimated that wind capacity of most curtain walls exceeds the wind demand. However, it cannot be guaranteed whether the same holds true for seismic capacity and seismic demand. An investigation into the damage caused by the magnitude 6.3 Christchurch earthquake in 2011 revealed that a significant number of curtain walls were damaged [37].

Given the high financial risk and potential functional paralysis associated with earthquake-damaged curtain walls, as well as knowing that they are currently not adequately designed for seismic resistance, it is necessary to conduct a regional study on seismic damage assessment of curtain walls [28,51]. A rapid regional seismic damage evaluation tool, such as a seismic fragility curve [52,53,54], is crucial for formulating an effective region-specific response plan in disaster situations. A seismic fragility curve is a cumulative distribution function that defines the conditional probability that a structure will be destroyed or reaches a certain damage state or higher, based on the seismic intensity of the ground motion applied to it [43,55,56,57,58]. However, there are few comprehensive studies addressing the regional seismic damage assessment of curtain walls [43], and the existing research faces several challenges.

–

First, to conduct a comprehensive seismic damage assessment in a given region, a large collection of structural analysis models [59,60,61] is essential for determining the seismic capacities of individual curtain wall structures [51]. Creating a reliable numerical/analytical model of nonstructural components requires detailed design information, making it a complex task [23,62,63,64,65]. Due to limited supporting data and information [24], achieving a sufficiently reliable level is difficult [23]. The diverse design intricacies of nonstructural components make gathering such detailed data on a regional scale and integrating into structural analysis models extremely time-consuming and labor-intensive [24], making it unfeasible.

–

Second, some prior studies have developed seismic fragility curves for curtain walls based on structural analysis or mock-up tests [66,67,68]. However, these curves are only applicable to specific curtain wall designs, making them unsuitable for use in regional seismic risk assessment.

–

Third, it is necessary to consider the simultaneous action of wind load and seismic load when developing seismic fragility curves. Unfortunately, very few research cases that have addressed this aspect [42].

Table 1

Pseudo-code of the proposed method.

L01	Select a target region, $R_{t a r g e t}$
L02
L03	Collect normal distributions for $N_{w c}$ ( $μ_{w c}$ , $σ_{w c}^{2})$ , $N_{h c}$ ( $μ_{h c}$ , $σ_{h c}^{2})$ , $N_{d c}$ ( $μ_{d c}$ , $σ_{d c}^{2}$ ) at the target region, $R_{t a r g e t}$
L04	Collect log-normal distributions ln $N_{s}$ ( $μ_{s}$ , $σ_{s}^{2})$ , ln $N_{v n}$ ( $μ_{v n}$ , $σ_{v n}^{2}$ ) at the target region, $R_{t a r g e t}$
L05	Collect uniform distributions $U_{d}$ (d) based on various building codes
L06	Collect uniform distributions $U_{r}$ (r) based on the building code used in the target region, $R_{t a r g e t}$
L07
L08	Dataset_dict $= {}$
L09	for _ in range ( $N_{s a m p l e})$
L10		Generate a simulated curtain wall sample from multiple				w_c	$\sim$	clip( $N_{w c}$ ( $μ_{w c}$ , $σ_{w c}^{2})$ , $w_{c, m i n}$ , $w_{c, m a x}$ )
L11		possible combination of region-specific curtain wall design				h_c	$\sim$	clip( $N_{h c}$ ( $μ_{h c}$ , $σ_{h c}^{2})$ , $h_{c, m i n}$ , $h_{c, m a x}$ )
L12		parameters				d_c	$\sim$	clip( $N_{d c}$ ( $μ_{d c}$ , $σ_{d c}^{2})$ , $d_{c, m i n}$ , $d_{c, m a x}$ )
L13						s	$\sim$	clip(ln $N_{s}$ ( $μ_{s}$ , $σ_{s}^{2})$ , $s_{m i n}$ , $s_{m a x}$ )
L14						V_n	$\sim$	clip(ln $N_{v n}$ ( $μ_{v n}$ , $σ_{v n}^{2})$ , $V_{n, m i n}$ , $V_{n, m a x}$ )
L15						( $a_{p}$ , $R_{p})$	$\sim$	$U_{d}$ (d)
L16						r_s	$\sim$	$U_{r}$ (r)
L17						f_c	$\sim$	U( $s_{m i n}$ , $s)$
L18						V_o	=	V_dict [ $R_{t a r g e t}$ ]
L19
L20		Estimate seismic capacity, $C_{s e i s m i c} \approx D_{w i n d} = f_{W, d e m a n d} (V_{o}$ , $V_{n}$ , $r_{s}$ , $s$ , $f_{c}$ , $w_{c}$ , $h_{c})$
L21
L22		Set PGA $=$ 0.01
L23		Set Done $=$ False
L24		while (done is False):
L25			Calculate code-based seismic demand, $D_{s e i s m i c} = f_{S, d e m a n d}$ (PGA, $a_{p}$ , $R_{p}, s$ , $f_{c}$ , $w_{c}$ , $h_{c}$ , $d_{c})$
L26			if ( $D_{s e i s m i c} > C_{s e i s m i c}$ ):
L27				try:
L28					Dataset_dict [PGA] $+ =$ 1
L29				except:
L30					Dataset_dict [PGA] $=$ 1
L31				Done $=$ True
L32			else:
L33				PGA $+ =$ 0.01
L34
L35	Plot a frequency distribution graph of damage occurrence for all simulated curtain walls
L36	Plot a relative frequency distribution graph by dividing the frequency values by the total sample size
L37	Plot a cumulative relative frequency graph by cumulating the relative frequency values
L38
L39	Conduct regional seismic damage assessment using the cumulative relative frequency graph

Figure 2.

Overall procedure of the proposed method.

To address the limitations and research gaps mentioned earlier, this study presents a rapid simulation method for assessing seismic damage to building curtain walls on a regional scale. Instead of focusing on the complex design details of individual curtain wall structures, this study proposes an efficient approach for region-scale assessment. Although this method does not account for the complex dynamic effects of curtain walls and is limited to considering only out-of-plane behaviors, the results obtained can be approximate. However, it has the advantage of enabling rapid assessments, making it a useful tool for emergency responses in disaster situations. The central hypothesis of this study is that the wind load capacity, which is the primary design consideration for most curtain walls, can serve as a reliable indicator of their seismic capacity. Therefore, this approach bypasses the need for time-consuming structural analysis models, resulting in a fast and efficient assessment tool. To evaluate the effectiveness of the proposed method, regional seismic damage assessments were conducted on curtain walls in areas with weak, moderate, and strong wind intensities. Subsequently, the obtained results were compared with actual seismic damage investigation data from a region with a wind intensity ranging from moderate to strong.

2. Methodology

2.1. Overall procedure

This section presents the pseudo-code in Table 1 and the overall procedure of the proposed method in Fig. 2. The overall procedure is as follows:

–
Process 1: Select a target region (Fig. 2, Table 1: L01).
–
Process 2: Secure probability distributions for region-specific curtain wall design parameters (Table 1: L03–L06).
–
Process 3: Generate a simulated curtain wall sample by considering multiple possible combinations of region-specific curtain wall design parameters based on the secured probability distributions (Table 1: L10–L18).
–
Process 4: Estimate the seismic capacity for the generated simulated curtain wall sample (Table 1: L20).
–
Process 5: Calculate the code-based seismic demand of the simulated curtain wall sample (Table 1: L25) for the peak ground acceleration (PGA) specified (Table 1: L22 or L33).
–
Process 6: Examine whether the calculated seismic demand exceeds the estimated seismic capacity (Table 1: L26). If the result of Process 6 is “not exceeded,” increase the PGA and repeat Processes 5 and 6 until the seismic demand exceeds capacity (Table 1: L22–L33). At this instance, PGA is gradually increased from 0.01 in steps of 0.01 (Table 1: L33). If the result of process 6 is “exceeded,” it indicates that seismic damage has occurred in the simulated curtain wall sample. The corresponding PGA is recorded, and the repetition of processes 5 and 6 is terminated (Table 1: L27–L31). As shown in Fig. 2, during processes 3–6, the PGA that causes seismic damage is investigated for one sample among the simulated curtain wall samples, which can be expressed by various combinations of region-specific curtain wall design parameters. Because the proposed method aims to assess the regional seismic damage for curtain walls, processes 3–6 are repeated until a sufficient number of samples are obtained (Table 1: L09). The required number of sufficient samples may vary depending on the specific situation. Once a sufficient number of iterations of processes 3–6 are complete, the number of simulated curtain wall samples subjected to seismic damage for each PGA is constructed as paired datasets (Table 1: L08). These PGA values correspond to the point at which seismic damage was first observed in the corresponding simulated curtain walls.
–
Process 7: Plot the frequency distribution graph of damage occurrence for all simulated curtain walls based on PGA (Table 1: L35). The graph shows the seismic-damage-occurrence frequency distribution according to PGA for all simulated curtain wall samples.
–
Process 8: Plot the relative frequency distribution graph of damage occurrence for all simulated curtain walls based on PGA (Table 1: L36). The frequency distribution graph, obtained in process 7, is divided by the total number of simulated curtain wall samples to obtain the relative frequency distribution graph.
–
Process 9: Plot the cumulative relative frequency graph of damage occurrence for all simulated curtain walls based on PGA (Table 1: L37). To create this graph, accumulate the relative frequency distribution graph obtained in process 8 for each category, up to that category. The cumulative relative frequency graph of damage occurrence represents the simulation results for a number of simulated curtain wall samples belonging to the selected region in process 1. This graph can be used to perform regional seismic damage assessment for curtain walls in a specific region (Table 1: L39).

In Table 1, $R_{t a r g e t}$ denotes the target region. $N_{w c}$ ( $μ_{w c}$ , $σ_{w c}^{2})$ is the normal distribution for curtain wall width at the target region. $μ_{w c}$ and $σ_{w c}$ are the mean and standard deviation of the curtain wall width, respectively. $N_{h c}$ ( $μ_{h c}$ , $σ_{h c}^{2}$ ) is the normal distribution for curtain wall height at the target region. $μ_{h c}$ and $σ_{h c}$ are the mean and standard deviation of the curtain wall height, respectively. $N_{d c}$ ( $μ_{d c}$ , $σ_{d c}^{2}$ ) is the normal distribution for mass per curtain wall unit area at the target region. $μ_{d c}$ and $σ_{d c}$ are the mean and standard deviation of the mass per curtain wall unit area, respectively. ln $N_{s}$ ( $μ_{s}$ , $σ_{s}^{2}$ ) is the log-normal distribution for total number of building stories at the target region. $μ_{s}$ and $σ_{s}$ are the mean and standard deviation of the natural logarithm of the total number of building stories, respectively. ln $N_{v n}$ ( $μ_{v n}$ , $σ_{v n}^{2}$ ) is the log-normal distribution for normal wind speed at the target region. $μ_{v n}$ and $σ_{v n}$ are the mean and standard deviation of the natural logarithm of the normal wind speed, respectively. $U_{d}$ (d) is the uniform distribution for tuples of dynamic factors based on various building codes. d is a vector of tuples composed of the ordered pairs of the dynamic factors presented in each building code as elements. $U_{r}$ (r) is the uniform distribution for surface roughness based on the building code used in the target region. r is a vector with surface roughness specified in the building code used in the target region as elements. In addition, in Table 1, $N_{s a m p l e}$ denotes the total number of simulated curtain wall samples for the target region. $w_{c}$ is the width of a simulated curtain wall sample generated according to the clip ( $N_{w c}$ ( $μ_{w c}$ , $σ_{w c}^{2}$ ), $w_{c, min}$ , $w_{c, max}$ ), where $w_{c, min}$ and $w_{c, max}$ are the minimum and maximum values of the curtain wall width determined based on region-specific data, respectively. $h_{c}$ is the height of a simulated curtain wall sample generated according to the clip ( $N_{h c}$ ( $μ_{h c}$ , $σ_{h c}^{2})$ , $h_{c, min}$ , $h_{c, max}$ ), where $h_{c, min}$ and $h_{c, max}$ are the minimum and maximum values of the curtain wall height determined based on region-specific data, respectively. $d_{c}$ is the mass per curtain wall unit area of a simulated curtain wall sample generated according to the clip ( $N_{d c}$ ( $μ_{d c}$ , $σ_{d c}^{2})$ , $d_{c, min}$ , $d_{c, max}$ ), where $d_{c, min}$ and $d_{c, max}$ are the minimum and maximum values of the mass per curtain wall unit area determined based on region-specific data, respectively. $s$ is the total number of building stories of a simulated curtain wall sample generated according to the clip (ln $N_{s}$ ( $μ_{s}$ , $σ_{s}^{2})$ , $s_{m i n}$ , $s_{m a x}$ ), where $s_{m i n}$ and $s_{m a x}$ are the minimum and maximum values of the total number of building stories based on region-specific data. $V_{n}$ is the normal wind speed of a simulated curtain wall sample generated according to the clip (ln $N_{v n}$ ( $μ_{v n}$ , $σ_{v n}^{2}$ ), $V_{n, min}$ , $V_{n, max}$ ), and $V_{n, min}$ and $V_{n, max}$ are the minimum and maximum values of the normal wind speed determined based on region-specific data. $a_{p}$ is the component acceleration amplification factor of the simulated curtain wall generated according to $U_{d}$ (d). $R_{p}$ is the component response modification factor of the simulated curtain wall generated according to $U_{d}$ (d). $r_{s}$ is the surface roughness of the building location of the simulated curtain wall generated according to $U_{r}$ (r). $U (s_{min, s})$ is a uniform distribution that uses integers between $s_{m i n}$ and s as random variables. $f_{c}$ denotes floor at which the curtain wall is installed for a simulated curtain wall sample generated according to $U (s_{m i n}, s)$ . V_dict is a dictionary-type database wherein basic wind speed for design is summarized by region, and $V_{o}$ is the basic wind speed essential for designing in the target region determined according to V_dict. $C_{s e i s m i c}$ is the seismic capacity of a simulated curtain wall sample. $D_{w i n d}$ is the wind demand of a simulated curtain wall sample, $f_{W, d e m a n d}$ is a function that determines $D_{w i n d}$ of a simulated curtain wall sample. PGA is the peak ground acceleration. $D_{s e i s m i c}$ is the seismic demand of a simulated curtain wall sample. $f_{S, d e m a n d}$ is a function that determines $D_{s e i s m i c}$ of a simulated curtain wall sample.
2.2. Detailed instructions for each process

2.2.1. Collection of probability distribution for region specific curtain wall design parameters

Initially, the proposed method is used to select a target region (Table 1: L01) and secure probability distributions for region-specific curtain wall design parameters (Table 1: L03–L06). In total, seven regional probability distributions are required. First, normal distributions are needed for the width, height, and areal density of the curtain wall unit in the target region. These are established by considering the specifications of the curtain wall unit typically constructed in the target region (Table 1: L03). Since choosing which distribution to use could itself be a research topic, this study assumes the normal distribution, which is commonly known to accurately describe many natural phenomena. Next, log-normal distributions are required for the number of stories and normal wind speed acting on buildings at normal times in the target region (Table 1: L04). The corresponding probability distributions are established as log-normal distributions because they exhibit a convex shape biased to the left. Finally, uniform distributions are needed for the dynamic factors used to calculate the seismic demand and surface roughness used to calculate the wind demand (Table 1: L05–L06). The former is established by respecting all the values proposed by various building codes, whereas the latter is established based on the building code (version of the recent past) used in the target region.

2.2.2. Generating a simulated curtain wall sample for multiple possible combination of region-specific curtain wall design parameters

The collected regional probability distributions were established in Section 2.2.1 to generate a simulated curtain wall sample by probabilistically selecting and combining region-specific curtain wall design parameters (Table 1: L10–L18). The region-specific design parameters that constitute a simulated curtain wall sample are the width, height, and area density of the curtain wall as well as the total number of stories in the building where the curtain wall is installed, the floor where the curtain wall is installed, component acceleration amplification factor, component response modification factor, surface roughness of the building location, and normal wind speed (Table 1: L10–L18).

2.2.3. Estimating seismic capacity by substituting code-based wind demand for seismic capacity

The seismic capacity of the simulated curtain wall sample is estimated in the proposed method (Table 1: L20). This approach does not require a complex structural analysis model or mock-up test to assess the seismic capacity of curtain walls. Instead, it relies on a different approach where the seismic capacity of curtain walls is replaced by wind capacity. It recognizes that although most curtain walls today are primarily designed to be wind resistant, seismic design considerations may not have been explicitly applied to them. Using code-based wind demand as a proxy for wind capacity makes the assessment more conservative and safer by reflecting the minimum expected wind capacity. Therefore, this method treats code-based wind demand as equivalent to wind capacity.

As mentioned earlier, the seismic capacity of a simulated curtain wall sample is assessed using code-based wind demand (Table 1: L20). Specifically, the seismic capacity is assessed using $f_{W, d e m a n d} (V_{o}$ , $V_{n}$ , $r_{s}$ , $s$ , $f_{c}$ , $w_{c}$ , $h_{c})$ based on the building code. In this case, the building code that was in effect in the past in the target region should be considered rather than the latest version. This is because the proposed method focuses on assessing the seismic capacity of existing curtain walls that have already been installed and put into use. Therefore, it is more appropriate to consider the seismic capacity using the building code of the recent past rather than the latest building code. Because $f_{W, d e m a n d} (V_{o}$ , $V_{n}$ , $r_{s}$ , $s$ , $f_{c}$ , $w_{c}$ , $h_{c})$ is based on the building code of the recent past used in the target region, the details of the functional expression may vary depending on the target region. Equation (1) represents the functional expression for $f_{W, d e m a n d} (V_{o}$ , $V_{n}$ , $r_{s}$ , $s$ , $f_{c}$ , $w_{c}$ , $h_{c})$ based on KBC2009 [69], which is a building code used in Korea in the recent past. It is expressed as:

\begin{aligned} f_{W, demand} (V_{o}, V_{n}, r_{s}, s, f_{c}, w_{c}, h_{c}) \\ = \frac{1}{2} \times ρ \times (V_{o}^{2} - V_{n}^{2}) \\ = \times {K_{z r} (r_{s}, f_{c}, h_{c}, s) \times K_{z t} \times I_{w}}^{2} \\ \times {{G C}_{p e} (s, h_{c}, w_{c}) - {G C}_{p i}} \times w_{c} \times h_{c} \end{aligned}

(1)

where

ρ

is the air density,

K_{z r}

is the velocity pressure exposure coefficient,

K_{z t}

is the topographic factor,

I_{w}

is the importance factor, GC_pe is the peak external pressure coefficient, and GC_pi is the peak internal pressure coefficient. The definition of each argument is described in Section 2.1.

Note that ( $V_{o}^{2} - V_{n}^{2}$ ) is used instead of $V_{o}^{2}$ . This reduces the seismic capacity estimate of a simulated curtain wall sample due to the normal wind load demand induced by the normal wind speed $V_{n}$ at normal times. Based on this, the proposed method can estimate seismic damage by considering the simultaneous action of seismic and wind loads during normal times.

In this study, certain parameters, such as $K_{z t}$ and $I_{w}$ , are assumed to have a value of 1.0. Because $f_{W, demand} (V_{o}$ , $V_{n}$ , $r_{s}$ , $s$ , $f_{c}$ , $w_{c}$ , $h_{c})$ must be established based on the building code of the recent past used in the target region, the functional expression may appear in various forms. Therefore, Eq. (1) is an example for estimating seismic capacity and is not an absolute expression.

2.2.4. Calculating code-based seismic demand corresponding to gradually increasing PGA

The seismic demand for a simulated curtain wall sample is based on ASCE-7-16 [27]; however, it is calculated using slightly deformed $f_{S, demand}$ (PGA, a $_{p}, R_{p}, s, f_{c}, w_{c}, h_{c}, d_{c})$ as shown in Eq. (2).

\begin{aligned} f_{S, demand} (P G A, a_{p}, R_{p}, s, f_{c}, w_{c}, h_{c}, d_{c}) \\ = \frac{a_{p}}{R_{p} / I_{p}} (1 + 2 \frac{z}{h}) \times 0.4 S_{D S} \times W_{p} \\ \approx \frac{a_{p}}{R_{P} / I_{p}} (1 + 2 \frac{f_{c}}{s}) \times P G A \times (w_{c} \times h_{c} \times d_{c} \times g) \end{aligned}

(2)

where

S_{D S}

is the spectral acceleration,

W_{p}

is the component operating weight,

I_{p}

is the component importance factor,

z

is the height in structure of point of attachment of component with respect to the base,

h

is the average roof height of the structure with respect to the base, and

g

is the gravitational acceleration. The definition of each parameter is described in Section 2.1.

As stated, Eq. (2) includes the following assumptions and transformations compared to ASCE-7-16. First, 0.4 $S_{D S} \approx$ PGA is assumed. In general, PGA is at the level of 0.4 $S_{D S}$ [70]. In addition, $z / h$ is replaced by fc/s in Eq. (2) because they represent the same aspect. Among additional transformations of the equation, $W_{p} = w_{c} h_{c} d_{c} g$ is self-evident. Note that the seismic demand in Eq. (2) cannot be lower than that in Eq. (3) nor exceed that in Eq. (4), as restricted by ASCE-7-16 [27].

\begin{aligned} 0.3 S_{D S} I_{p} W_{p} s & \approx \frac{3}{4} \times P G A \times (w_{c} \times h_{c} \times d_{c} \times g) \times I_{g} \end{aligned}

(3)

\begin{aligned} 1.6 S_{D S} I_{p} W_{p} & \approx 4 \times P G A \times (w_{c} \times h_{c} \times d_{c} \times g) \times I_{p} \end{aligned}

(4)

where

a_{p}

and

R_{p}

in Eq. (2) were probabilistically selected whenever a simulated curtain wall sample was generated (Table 1: L15) to indirectly reflect the uncertainty about the dynamic response of the curtain wall. This implies that the dynamic factors of each curtain wall can be different, as the difference between

a_{p}

and

R_{p}

is stated in several standards today. Table 2 lists the selectable ordered pairs of

a_{p}

and

R_{p}

considered in the proposed method.

Table 2

Dynamic factors from various building codes [43].

Building code	A_p	R_p
ASCE-SEI 7–10/IBC2012	1.0	2.5
UBC1997	2.5	3.0
EC8 (BS EN 1998–1.2004)	1.5	2.0
NZS 1170.5:2004	2.0	1.82
CSA-S832 2006	1.0	2.5
DGJ08-56-2012	2.0	1.11
BS ISO 13033–2013	1.5	1.0

2.2.5. Investigating the minimum PGA that induces seismic damage to the simulated curtain wall sample

After determining the seismic capacity and seismic demand for a simulated curtain wall sample, it is determined if the calculated seismic demand exceeds the estimated seismic capacity (Table 1: L26). If the result of process 6 is “not exceeded,” the seismic demand is re-calculated by increasing PGA, and then processes 5 and 6 illustrated in Fig. 2 are repeated until it is exceeded (Table 1: L22–L33). In this situation, PGA is gradually increased from 0.01 (Table 1: L33) by 0.01. If the result of process 6 is “exceeded,” seismic damage has occurred in the simulated curtain wall sample. The corresponding PGA is recorded, and the repetition of processes 5 and 6 illustrated in Fig. 2 is terminated (Table 1: L27–L31).

The proposed method is limited in its ability to account for various seismic damage states; it can only determine whether seismic damage has occurred or not in a simulated curtain wall sample. Here, seismic damage to the curtain wall accurs when the elastic behavior range is exceeded or when the curtain wall is destroyed owing to the required strength of any element such as mullions, transoms, glass panels, and anchoring exceeding their nominal strength.

2.2.6. Plotting frequency distribution graph of damage occurrence for all simulated curtain walls according to PGA

Processes 3–6 illustrated in Fig. 2 depict the process of examining PGA that causes seismic damage to a sample among simulated curtain wall samples that can be expressed by various combinations of region-specific curtain wall design parameters. Because the purpose of the proposed method is regional seismic damage assessment for curtain walls, processes 3–6 are repeated until a sufficient number of samples are obtained (Table 1: L09). In this instance, the number of sufficient samples may vary depending on the situation. When sufficient iterations of processes 3–6 are complete, the number of simulated curtain wall samples subjected to seismic damage for each PGA is constructed as paired datasets (Table 1: L08). Note that these PGA values correspond to the point at which seismic damage was initially observed in the respective simulated curtain walls.

When a sufficient dataset is constructed through processes 3–6, it is used to plot the frequency distribution graph of damage occurrence for all simulated curtain walls according to PGA (Table 1: L35). In this instance, the $x$ - and $y$ -axes values are PGA (g) and frequency (count), respectively. The graph shows the frequency distribution of seismic damage according to PGA for all simulated curtain wall samples.

2.2.7. Plotting relative probability distribution graph for damage occurrence for all simulated curtain walls according to PGA

When creating the frequency distribution graph in process 7, as shown in Fig. 2, the relative frequency distribution graph of damage occurrence for all simulated curtain walls according to PGA is plotted as shown in process 8 in Fig. 2 (Table 1: L36). This is achieved by dividing the $y$ -axis values of the frequency distribution graph by the total number of simulated curtain wall samples. Consequently, the $x$ - and $y$ -axes values are PGA ( $g)$ and relative frequency (ratio), respectively.

However, the relative frequency distribution graph does not indicate the proportion of curtain walls subjected to seismic damage among all curtain walls within the target region when a ground motion with a specific PGA is applied to the region. It indicates the proportion of curtain walls where seismic damage first occurs owing to the PGA among all curtain walls within the target region under the influence of the same ground motion. Therefore, the relative frequency distribution graph should be transformed into a cumulative relative frequency graph in process 9, as depicted in Fig. 2. This process is detailed in Section 2.2.2.

2.2.8. Plotting cumulative relative frequency graph of damage occurrence for all simulated curtain walls according to PGA

When the relative frequency distribution graph is obtained in process 8 illustrated in Fig. 2, the cumulative relative frequency graph of damage occurrence for all simulated curtain walls according to PGA is plotted as shown in process 9 in Fig. 2 (Table 1: L37).

The cumulative relative frequency graph of damage occurrence for the proposed method represents the proportion of curtain walls within the target region when subjected to a ground motion with specific PGA. Consequently, if the PGA of the ground motion applied to the target region is determined following an earthquake, regional seismic-damage assessment for curtain walls in the target region can be performed using the cumulative relative frequency graph of damage occurrence generated by the proposed method.

3. Evaluation

3.1. Target regions for application

To assess the applicability of the proposed method, regional seismic-damage assessments of curtain walls were conducted in various Korean cities, Seoul, Daejeon, Daegu, Busan, and Jeju, with differing wind intensities. Daegu was considered a weak wind region; Seoul and Daejeon were moderate wind regions; and Busan and Jeju were strong wind regions. The cumulative relative frequency graph of damage occurrences was derived by region. Subsequently, these results were compared with actual seismic damage investigation data collected following the 2011 Christchurch earthquake, which occurred in a region characterized by moderate-to-strong wind intensity.

Figure 3.

Normal distribution for curtain wall dimensions.

3.2. Application results

The proposed method is implemented using probability distributions established for region-specific curtain wall design parameters for each target region selected in Section 3.1. First, the normal distribution for the width of the curtain wall unit $N_{w c}$ ( $μ_{w c}$ , $σ_{w c}^{2})$ and the normal distribution for the height $N_{h c}$ ( $μ_{h c}$ , $σ_{h c}^{2})$ are established, as shown in Fig. 3. In this instance, $μ_{w c}$ is assumed 1,500.00 mm, $σ_{w c}$ is 333.33 mm, $μ_{h c}$ is 4,000.00 mm, and $σ_{h c}$ is 333.33 mm. To extract $w_{c}$ and $h_{c}$ from these normal distributions, $w_{c, min}$ is assumed to be 500.00 mm, $w_{c, max}$ is 2,500.00 mm, $h_{c, min}$ is 3,000.00 mm, and $h_{c, max}$ is 5,000.00 mm. The definition of each symbol is summarized in Section 2.1.

Figure 4.

Normal distribution for mass per curtain wall unit area.

Additionally, the normal distribution for the area density of the curtain wall $N_{d c}$ ( $μ_{d c}$ , $σ_{d c}^{2})$ was established as shown in Fig. 4. $μ_{d c}$ was assumed to be 65.00 kg/m² and $σ_{d c}$ as 5.00 kg/m². To extract $d_{c}$ from these normal distributions, $d_{c, min}$ was assumed 50.00 kg/m² and $d_{c, max}$ as 80.00 kg/m². These assumptions were based on the typical specifications of the curtain walls constructed in Korea. Because all the target regions are cities in Korea, the same probability distribution was applied to each of them for the applicability assessment.

One of the previous studies defined the areal density of lightweight cladding, which is the classification category of curtain walls, as 80 kg/m² or less [37]. In addition, a research case was identified in which the weight of a representative curtain wall unit specimen with a height of approximately 4 m was 280 kgf [71].

The log-normal distribution for the number of stories in the building in target region, ln $N_{s}$ ( $μ_{s}$ , $σ_{s}^{2}$ ) was established as shown in Fig. 5. This was established based on the building statistics of the Ministry of Land, Infrastructure, and Transport in Korea, which were surveyed in 2021. Figure 5 shows $μ_{s}$ and $σ_{s}$ for each region. Note that $μ_{s}$ and $σ_{s}$ are the mean and standard deviation of the natural logarithm of the total number of building stories, respectively.

Figure 5.

Log-normal distributions for total number of building stories at each region.

Figure 6.

Log-normal distribution for normal wind speed at each region.

For each target region, the log-normal distribution for normal wind speed, ln $N_{v n}$ ( $μ_{v n}$ , $σ_{v n}^{2}$ ), was established as shown in Fig. 6. This is based on statistical data from the open weather data portal of the Korea Meteorological Administration, which was collected during a survey conducted from 2020 to 2021. Figure 6 shows $μ_{v n}$ and $σ_{v n}$ for each target region. Note that they are the mean and standard deviation of the natural logarithm of the normal wind speed in each region, respectively. In addition, the normal wind speed corresponds to the average wind speed measured over a 10 min period, which is likely to occur under typical conditions.

For each region, the basic wind speed considered for the design purpose is listed in Table 3. It is based on KBC2009 [69], which is the building code (version of the recent past) used in the target region. It indicates the average wind speed over a 10-minute period, the highest value likely to occur within a hundred years.

Table 3

Basic wind speed for the design at each region.

Region	Basic wind speed (m/s)
Daegu	25
Daejeon	30
Seoul	30
Jeju	40
Busan	40

A simulated curtain wall sample was created considering the multiple possible combinations of region-specific curtain wall design parameters for each target region using the secured probability distributions. The details of the process are described in Section 2.2.2.

For each target region, a simulated curtain wall sample was generated, and its seismic capacity was estimated. As explained above, the seismic capacity of curtain walls was replaced with code-based wind demand for the proposed method. Given that all target regions are cities in Korea, the code-based wind demand was calculated based on KBC2009 [69], which is the building code (version of the recent past) used in Korea. Essentially, the seismic capacity was replaced by wind demand of the curtain wall in Eq. (1). The details of the process are available in Section 2.2.3.

Figure 7.

Relative frequency distribution graph of damage occurrence at (1) Daegu, (2) Daejeon, (3) Seoul, (4) Jeju, and (5) Busan.

Figure 8.

Cumulative relative frequency graph of damage occurrence at (1) Daegu, (2) Daejeon, (3) Seoul, (4) Jeju, and (5) Busan.

For each target region, the seismic capacity of a simulated curtain wall sample was assessed, and its code-based seismic demand was calculated according to PGA. The seismic demand was calculated using Eq. (2) while gradually increasing PGA from 0.01 in increments of 0.01. Subsequently, a comparison between the calculated seismic demand and the estimated seismic capacity was conducted. If the seismic demand exceeded the estimated seismic capacity, seismic damage has occurred in the simulated curtain wall sample, and the corresponding PGA value was recorded. This process is detailed in Sections 2.2.4 and 2.2.5.

The process described above is used to examine PGA that causes seismic damage to a sample among the simulated curtain wall samples. It can be expressed by various combinations of region-specific curtain wall design parameters tailored for each target region. To perform regional seismic damage assessment for curtain walls using the proposed method, the process must be repeated until a sufficient number of samples are obtained. In this instance, the number of sufficient samples may vary depending on the situation. Determining an appropriate range for this value could itself constitute a separate research topic. However, the main focus of this study is to introduce a new method and to confirm its utility on a large scale. Therefore, further exploration of this issue is deferred to future research. For the present study, a sufficiently large number was selected arbitrarily, despite the higher computational costs, to ensure robust results. The process was repeated for 100,000 samples in each target region to obtain effective results.

Figure 7 shows the results of plotting the relative frequency distribution graph of damage occurrence for all simulated curtain walls according to PGA. The details of the process are available in Section 2.2.7.

Finally, Fig. 8 shows the results of summarizing the cumulative relative frequency graph of damage occurrence for all simulated curtain walls according to PGA based on the results presented in Fig. 7. The details of the process are available in Section 2.2.8.

4. Discussion

The proposed method was used to obtain the cumulative relative frequency graph of damage occurrence for all simulated curtain walls in each target region. This graph illustrates the proportion of curtain walls expected to experience seismic damage among all curtain walls within the target region when subjected to a ground motion with a specific PGA. As such, it serves as a valuable tool for regional seismic damage assessment of curtain walls. To assess the reliability of the graph indirectly, the actual damage investigation results for the 2011 Christchurch earthquake [40] are also shown in Fig. 9.

Upon examination of the cumulative relative frequency graph of damage occurrence derived from the proposed method (Fig. 9), it becomes apparent that the proportion of curtain walls expected to incur seismic damage is inversely correlated with the basic wind speed. Notably, the proportion is approximately five times greater in Daegu, categorized as a weak wind region, compared to Busan, classified as a strong wind region, particularly evident at PGA $=$ 0.3g. This observation underscores the pronounced vulnerability of Daegu and highlights the imperative for seismic design considerations in curtain walls within weak wind regions.

Furthermore, the proportion varies even for the same basic wind speed through the cumulative relative frequency graph of damage occurrence in Daejeon, Seoul, Busan, and Jeju. This is due to the differing seismic capacities, which are replaced with wind demand, as region-specific data such as the distribution of the number of building stories and normal wind speed differ by region. As shown in Fig. 9, the difference is not significant, and similar cumulative relative frequency graphs of damage occurrence are obtained for the same basic wind speed.

Figure 9.

Cumulative relative frequency graph of damage occurrence in each region using the proposed method, with the seismic damage investigation result of 2011 Christchurch earthquake.

The trend observed in the cumulative relative frequency graph of damage occurrence in Fig. 9 was compared with the 2011 Christchurch earthquake damage investigation result to emphasize that the outcomes of the proposed method were dominated and determined by the basic wind speed. Additionally, the reliability of the proposed method was indirectly examined by focusing solely on the difference in basic wind speed. The magnitude of the 2011 Christchurch earthquake was recorded as 6.2 [19] with the PGA measured in the horizontal direction in the urban area at approximately 0.7 g [72]. According to the damage investigation results, the earthquake damaged approximately 35% of lightweight cladding [40]. Here, the criterion for damage encompasses all instances where investigation results indicate a performance level below the operational level, including cases meeting criteria for immediate occupancy, life safety, or high hazard. As outlined in Section 1, given that curtain walls fall within the category of lightweight cladding, it is reasonable to approximate the investigation results for lightweight cladding as those for curtain walls. To compare the damage investigation result of the earthquake with the cumulative relative frequency graph of damage occurrence in Fig. 9, it is necessary to examine the basic wind speed for the design presented in the building code used in the Christchurch area. The instantaneous wind speed observed was 46 m/s for 3 s, which corresponds to approximately 35 m/s when converted into a 10-min average wind speed (under a gust factor of 1.3). Based on this information, the results are compared as follows: PGA was based on 0.7 g, which was measured in the horizontal direction in the urban area during the 2011 Christchurch earthquake. Consequently, based on the magnitude of the basic wind speed, seismic damage cases were expected to represent approximately 50% in Seoul ( $V_{o} =$ 30 m/s). Seismic damage cases were reported to account for approximately 35% for the lightweight cladding in Christchurch ( $V_{o} =$ 35 m/s) [40]. In Jeju ( $V_{o} =$ 40 m/s), seismic damage cases were expected to represent approximately 30%. The 2011 Christchurch earthquake damage investigation result emphasized the inversely proportional relationship between the basic wind speed and the proportion of seismic damage occurrence in curtain walls by region, as corroborated by the cumulative relative frequency graph of damage occurrence obtained using the proposed method. This indirectly indicates the meaningfulness of the proposed method.

5. Conclusions

In this study, a rapid simulation method for regional seismic damage assessments of curtain walls was presented. Its effectiveness was validated through comparison with actual seismic damage data from the 2011 Christchurch earthquake, which occurred in a region experiencing moderate to strong wind intensity. The main findings are as follows:

–

Rapid and efficient regional seismic damage assessments were achieved without the need for complex structural analysis models, as the seismic capacity was effectively represented by the designed wind capacity of the curtain walls.

–

In regions of Korea with varying wind intensities, it was observed that the seismic fragility of curtain walls in regions with weak winds could be five times greater than in regions with strong winds. This emphasizes the importance of seismic design considerations in regions prone to weak winds.

–

The probability of seismic damage was found to be primarily influenced by the basic wind speed, suggesting an inversely proportional relationship. These findings are consistent with the actual seismic damage investigations from the Christchurch earthquake.

However, the study faced limitations such as insufficient data for comprehensive verification, the inability to assess detailed seismic damage states, and a focus solely on out-of-plane damage. Additionally, to investigate the effective of each component of the model, further ablation analysis should be conducted. Future research will aim to address these limitations.

Footnotes

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government Ministry of Science, ICT & Future Planning (MSIP) (No. 2021R1A2C3008989 and No. 2018R1A5A1025137).

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