Seismic Demand Prediction in Laminated Bamboo Frame Structures: A Comparative Study of Intensity Measures for Performance-Based Design

Abstract

Engineered laminated bamboo frame structures have seen notable advancements in China, driven by their potential in sustainable construction. However, accurately predicting their seismic performance remains a pivotal challenge. Structural and non-structural damage caused by earthquakes can severely compromise building operability, lead to substantial economic losses, and disrupt safe evacuation processes, collectively exacerbating disaster impacts. To address this, three laminated bamboo frame models (3-, 4-, and 5-story) were developed, integrating energy-dissipating T-shaped steel plate beam–column connections. Two engineering demand parameters—peak inter-story drift ratio (PIDR) and peak floor acceleration (PFA)—were selected to quantify seismic responses under near-field and far-field ground motions. The study systematically evaluates suitable intensity measures for these parameters, emphasizing efficiency and sufficiency criteria. Regarding efficiency, the applicable intensity measures for PFA differ from those for PIDR. The measures for PFA tend to focus more on acceleration amplitude-related measures such as peak ground accelerations (PGA), sustained maximum acceleration (SMA), effective design acceleration (EDA), and A₉₅ (the acceleration at 95% Arias intensity), while the measures for PIDR are primarily based on spectral acceleration-related measures such as S_a(T₁) (spectral acceleration at fundamental period), etc. Concerning sufficiency, significant differences exist in the applicable measures for PFA and PIDR, and they are greatly influenced by ground motion characteristics.

1. Introduction

In 2020, China’s construction industry contributed 50.9% of the nation’s total carbon emissions across its entire value chain, as documented in the 2022 Building Energy and Emissions Report [1]. The development of engineered bamboo structures is a primary means for the construction industry to reduce carbon emissions. In recent years, there has been a notable increase in the development of engineered laminated bamboo frame structures in China (Xiao, 2024 [2]; Huang et al., 2023, [3]). Despite their potential, comprehensive seismic testing of these structures under severe earthquake conditions remains limited, leaving their seismic performance under strong shaking uncertain. During severe earthquakes, damage to building components may result in structural failure or collapse, causing significant economic losses. Previous studies on earthquake damage have shown that the economic impact of non-structural component failures far exceeds that of structural damage (Senel et al., 2024 [4]; Devin and Fanning, 2019 [5]; Ozmen et al., 2013 [6]). Consequently, precise evaluation of earthquake-induced loads on laminated bamboo frames—including structural elements and non-structural systems—is essential for ensuring seismic resilience under extreme ground motions.

Damage to structural components is typically assessed using inter-story drift, which is a commonly used structural performance indicator in standards (GB50005, 2017 [7]). In evaluating the seismic demands of non-structural components, the peak inter-story drift ratio (PIDR), and peak floor acceleration (PFA) can be selected as metrics for measurement (Taghavi and Miranda, 2003 [8]; Devin and Fanning, 2019 [5]; Zhang and He, 2019 [9]). Deformation-sensitive non-structural components, such as partition walls, are quantified using the peak inter-story drift ratio (PIDR) as a primary damage indicator. PFA serves as a critical indicator for predicting damage in acceleration-sensitive non-structural elements (e.g., rigid partitions or equipment), as established by Reinoso and Miranda [10] and FEMA P-58-2 [11]. Consequently, PIDR and PFA were integrated into this study to comprehensively assess structural and non-structural damage within laminated bamboo frames under seismic loading.

Effective intensity measures (IMs), serving as critical bridges between seismic hazard inputs and structural outputs, play a pivotal role in minimizing prediction uncertainties for laminated bamboo frames subjected to severe earthquakes. Research indicates that the applicability of IMs varies markedly across structural typologies and their target demand parameters (e.g., inter-story drift or floor acceleration) [12,13,14]. Furthermore, the performance of these metrics is highly sensitive to seismic event features, including near-field pulse effects and far-field record characteristics [15]. Driven by advancements in performance-based earthquake engineering, IM selection frameworks now encompass diverse structural systems, including super-tall buildings (Zhang et al., 2019 [9]; Lu et al., 2013 [16]), typical reinforced concrete frame structures (Muho, 2024 [17]), reinforced concrete frame structures with seismic isolation bearings (Güneş, 2024 [18]), liquid storage tanks (Sengar et al., 2025 [19]), transmission towers (Liu et al., 2024 [20]), urban shield tunnels (Shen, 2025 [21]), and high-speed railway bridges (Wen et al., 2024 [22]). However, there is limited research on ground motion intensity measures specifically for laminated bamboo frame structures, particularly regarding the assessment of the seismic response of different types.

This article evaluates seismic demands on both structural and non-structural components in laminated bamboo frame structures using PIDR and PFA as engineering performance demand parameters. Three laminated bamboo frame structures with varying numbers of floors are considered to reflect the impact of structural height. Furthermore, to accurately assess the structural responses under seismic conditions, this research investigates optimal intensity measures by prioritizing efficiency and sufficiency criteria to quantify seismic demands across structural and non-structural subsystems in engineered bamboo frames. Ground motions with distinct characteristics—specifically pulse-like near-field events and far-field records—were systematically incorporated to evaluate their impact on parameter selection.

2. Structural Model and Selection of Ground Motions

2.1. Laminated Bamboo Frame Structure

As shown in Figure 1, three laminated bamboo frame structures with 3, 4, and 5 stories were selected for structural response analysis. These structures are designed to withstand seismic precautionary intensity level 8 and are located on a Type II site within the first seismic design group. The seismic precautionary intensity level 8 corresponds to a peak ground acceleration of 0.4 g for a rare earthquake event. A site class of II indicates that the soil has medium stiffness. The seismic design group represents the impact of factors such as the epicentral distance on seismic forces, with the first seismic design group indicating a near epicenter distance. All three structures have identical floor plans. The buildings have heights of 9.9 m, 13.2 m, and 16.5 m, with each floor measuring 3.3 m. The roof supports a dead load of 1.0 kPa and a live load of 2.0 kPa, while the floors below carry a permanent load of 1.5 kPa and a live load of 2.0 kPa. The basic wind pressure is 0.35 kPa. The beam section for these frames is 100 mm by 250 mm, while the column sections vary: 400 mm × 400 mm for the 5-story and 4-story structures, and 300 mm × 300 mm for the 3-story structure. The floor system uses engineered bamboo composite hollow slabs, as suggested by Huang et al. (2024 [3]). As shown in Figure 2, the beam–column joints are equipped with T-shaped steel plates and bolted connections, which are known for their effective energy dissipation (Leng et al., 2020 [23]). In accordance with established specifications for timber, engineered bamboo, and seismic design, the load-bearing capacities of the beams and columns, as well as the beam-column joints, have been verified (T/CECS 1101, 2022 [24]; GB50068, 2019 [25]; GB 55002, 2021 [26]; GB/T 51226, 2017 [27]; Eurocode 5, 2003 [28]; GB50005, 2017 [7]; GB/T 50708, 2012 [29]; GB50017, 2017 [30]). The 5-story laminated bamboo frame’s design methodology, including joint specifications and load-bearing calculations, follows the framework outlined by Zhang et al. [31]. While the 3- and 4-story structures adopt identical joint parameters (refer to [31] for details), their overall design processes are omitted here for brevity.

To enhance computational efficiency, two-dimensional finite element models of the three laminated bamboo frames were constructed within the OpenSees platform, version 2.0, [32], with primary emphasis on the red-highlighted frame (Figure 1). In the modeling of timber/bamboo structures, nonlinearity (e.g., hysteresis, pinching, degradation) is confined to the connections (joints/fasteners), while members (beams/columns) are modeled as linear elastic elements (Rinaldin et al., 2013 [33]; Aloisio et al., 2020 [34]; Cao et al., 2022 [35]; Zhang et al., 2024 [31]). In this study, columns and beams were represented by elastic beam–column members, assigned a Young’s modulus of 13.180 GPa according to experimental validations by Leng et al. [23]. The Pinching4 material model (Table 1) was applied to zero-length joint elements, calibrated against experimental data from Figure 3. A Rayleigh damping ratio of 3% was implemented while considering geometric nonlinearities through P-delta effects. Lightweight wall panels were incorporated in the model; however, their connections to the frame were idealized as non-structural elements to exclude stiffness contributions. The first five vibration periods (T₁, T₂,..., T₅) for each structure are provided in Table 2.

2.2. Selection of Far-Field and Near-Field Ground Motion Records

Two distinct ground motion datasets (30 records each) were selected, categorized as pulse-like near-field and far-field events, to account for aleatory variability. Pulse-like ground motions in the near-field dataset were identified using Baker’s wavelet-based filtering methodology [36]. Table 3 summarizes the seismic event parameters, including moment magnitude (M) and source-to-site distance (R), with a 10 km threshold between near-field and far-field records defined per FEMA P695 guidelines [37]. The ground motion records were curated from the PEER database [38], while detailed selection criteria and metadata are accessible in prior studies [9,39].

3. Seismic Response and Selection of Intensity Measures

3.1. Seismic Response

For the three laminated bamboo frame structures, Figure 4 and Figure 5 show the distribution of PIDR along the floors of the structure under far-field and near-field ground motions, respectively. The peak ground accelerations (PGA) of these ground motion records were amplitude-modulated to 400 Gal, corresponding to the intensity of major earthquakes in the region where the structures are located. Analysis revealed a dominant first-mode vibration pattern in laminated bamboo frames, consistent across both near-field and far-field seismic inputs (Zhang et al., 2024 [31]). A marked increase in structural displacement was observed under near-field ground motions relative to far-field events, as illustrated in Figure 4 and Figure 5.

3.2. Selection of Intensity Measures and Its Evaluation Criteria

The results of probabilistic seismic vulnerability assessments are significantly affected by the choice of seismic intensity measures. Different measures can alter the correlation between seismic hazard intensity and structural damage. For laminated bamboo frame structures, primarily influenced by first-mode vibrations, intensity measures related to seismic motion amplitude and spectral acceleration at the first-mode period are preferred. Twenty-five measures were selected, as detailed in Table 4. These include peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), SMA, SMV, EDA, and the velocity-to-acceleration ratio (V/A). SMA and SMV are abbreviations for sustained maximum acceleration and sustained maximum velocity, respectively, and correspond to the third peaks in the seismic acceleration and velocity histories. High-frequency components above 8–9 Hz are deemed negligible and filtered out, with the peak value identified as EDA. The Arias intensity measure uses total hysteretic energy dissipation per unit mass, while Sarma and Yang (1987 [40]) propose the acceleration at 95% Arias intensity as the A₉₅ measure.

Table 4 includes seismic intensity measures such as spectral acceleration S_a(T₁), spectral velocity S_v(T₁), and spectral displacement S_d(T₁) at the first vibrational period. Additionally, it lists combination-type measures based on S_a(T₁) that account for higher-order modes, including $S_{a12}^{\ast }$, $S_{a123}^{\ast }$, IM₁₂, IM₁₂₃, S_N2, S₁₂, S₁₂₃, and ${\overline{S}}_a$. Some measures consider softening periods, like S*, IM-CR, IM-SR, I_NP, S_N1, or both effects, as with S_a,gm(T_i). Parameters for these combinations are aligned with structural dynamics: S* uses T_f = 2T₁ and α = 0.5; IM-CR and IM-SR use R_IM = 2 and α = 0.5; I_NP has α = 0.4 and T_N = 2T₁; IM₁₂ uses periods T₁ and T₂ with β = 0.5; IM₁₂₃ employs T₁, T₂, and T₃ with β = 1/3 and γ = 1/3; S_N1 uses C = 1.5 and α = 0.5, while S_N2 has β = 0.75. Referring to $S_{a12}^{\ast }$ and $S_{a123}^{\ast }$, the measure S₁₂ uses α = 0.8 and β = 0.2, while S₁₂₃ employs α = 0.8, β = 0.15, and γ = 0.05; ${\overline{S}}_a$, using the first two vibration periods (n = 2), is equivalent to IM₁₂; S_a,gm(T_i) involves five combination terms: (T_i)₅ = {T_2m, min[(T_2m + T_1m)/2, 1.5T_2m], T_1m, 1.5T_1m, 2T_1m}, with T_1m and T_2m representing T₁ and T₂, respectively.

A robust evaluation framework is critical for selecting appropriate intensity measures. Key criteria proposed in prior studies include efficiency, sufficiency, proficiency, scaling robustness, hazard computability, and practicality (Bojórquez and Iervolino, 2011 [46]; Jalayer et al., 2012 [52]; Padgett et al., 2008 [53]; Tothong and Luco, 2007 [54]; Giovenale et al., 2004 [55]; Mackie and Stojadinović, 2001 [56]). Among these, efficiency and sufficiency have emerged as primary considerations in IM selection. The relationship between engineering demand parameters (DMs) and IMs is typically modeled through a power function (Equation (1)), where coefficients a and b are determined via regression analysis and ε|IM represent residual errors. The residuals refer to the differences between the actual observed values and the predicted values from the regression model. This nonlinear relationship can be linearized as shown in Equation (2). Efficiency quantifies the predictive capability of an IM through the logarithmic standard deviation β_DM|IM between observed and predicted demands (Equation (3)), where lower β_DM|IM values correspond to superior IM performance. In Equation (3), DM_i and IM_i represent the seismic response and seismic intensity measure corresponding to the i-th record, respectively, and m denotes the number of seismic motions. Sufficiency requires structural responses at a given intensity level to be statistically independent of ground motion characteristics (e.g., magnitude M and epicenter distance R). This criterion is evaluated through p-values derived from regressing residual term ln(ε|IM) against seismic parameters M or ln(R), with p-value < 0.05 indicating insufficiency.

(1)$DM=a\cdot I{M}^b\cdot (\left.\epsilon \right|IM)$

(2)$ln(DM)=\ln a+b\ln (IM)+\ln (\left.\epsilon \right|IM)$

(3)${\beta }_{\left.DM\right|\mathrm{IM}}=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^m{(ln(D{M}_i)-ln(aI{M}_i^b))}^2}}{m-2}}}$

4. Intensity Measures Suitable for PFA

4.1. Efficiency of IMs in Estimating PFA

Figure 6, Figure 7 and Figure 8 illustrate the distribution of peak floor accelerations (PFAs) at different levels for the 3-, 4-, and 5-story laminated bamboo frame structures, respectively. These results were obtained under near-field and far-field seismic excitations without amplitude scaling. For the three-story laminated bamboo frame, the maximum floor accelerations are concentrated on the third floor under both near-field and far-field seismic motions. In the case of the four-story structure, the maximum accelerations occur primarily on the fourth floor, followed by the second and third floors. For the five-story laminated bamboo frame structure, under far-field ground motions, the maximum floor accelerations are primarily distributed on the 3rd and 5th floors, while under near-field seismic excitation, they are mainly distributed on the 5th floor. For a more detailed analysis, the maximum floor acceleration on the third floor (referred to as PFA₃) for each structure was selected as the research focus. Figure 9, Figure 10 and Figure 11 present the linear regression analysis results between PFA₃ and the intensity measures PGA and S_a(T₁) for the 3-, 4-, and 5-story laminated bamboo frame structures, respectively. The research results indicate that, whether under far-field or near-field pulse-type ground motions, compared to S_a(T₁), the correlation between PGA and PFA₃ is more significant, demonstrating higher efficiency (manifested as smaller β_DM|IM values).

Considering the similar dynamic characteristics of the three structures, the trend in seismic response and intensity measures observed across structures with varying story counts is closely aligned. Thus, the 5-story laminated bamboo frame structure is used as an example. Figure 12 shows the distribution of the standard deviation β_DM|IM between the intensity measures and PFAs along the height direction of the 5-story structure. A closer examination reveals a strong correlation between the β_DM|IM values of different seismic intensity measures and the height of the structural floors. Generally, as floor height increases, the β_DM|IM values decrease. Notably, at higher floors, the differences in β_DM|IM values between various measures become more pronounced, especially under near-field earthquake conditions. To highlight the intensity measures with lower β_DM|IM values, these are marked in each figure. From the perspective of β_DM|IM, measures that are strongly correlated with PFA are consistent for both near-field and far-field conditions. The intensity measures shown in Figure 12 can be divided into three distinct sections with clear boundaries.

As shown in Figure 12, in the left part of each figure, the β_DM|IM values are observed to be minimal. And the corresponding seismic intensity measures demonstrate the highest efficiency. Under far-field ground motions, the left part of Figure 12a includes intensity measures such as IM₁₂₃, SMA, PGA, A₉₅ and EDA. PGA, A₉₅, and EDA are all measures extracted from acceleration time histories, roughly or approximately equivalent to peak ground acceleration. Under the influence of near-field ground motions, IM₁₂₃ significantly outperforms other indicators and occupies the entire left part on its own. Through comparative analysis, it can be observed that the efficiency of various intensity measures is greatly influenced by the location of the floor level. Due to the influence of the floor height, IM₁₂ results in the smallest β_DM|IM among all intensity measures on the fifth floor of the structure.

Under far-field ground motions, the middle part of Figure 12a includes seismic intensity indicators such as IM₁₂ (${\overline{S}}_a$), $S_{a123}^{\ast }$, and $S_{a12}^{\ast }$. For near-field ground motions, the middle part includes SMA, PGA, A₉₅, and EDA, and measures considering higher-order modes such as IM₁₂ (${\overline{S}}_a$), $S_{a123}^{\ast }$, and $S_{a12}^{\ast }$. Even though A₉₅, EDA and IM₁₂ are classified into the middle part compared to far-field ground motions, they still exhibit similar β_DM|IM values as those observed under far-field conditions. This indicates that these indicators maintain a high level of stability in their correlation with PFA under different seismic motion characteristics.

The other intensity measures in Figure 12 (indicated by gray lines) are all classified into the right-hand side part. These intensity measures include S_a(T₁), S_v(T₁), and S_d(T₁), as well as S*, IM-CR, IM-SR, and I_NP based on S_a(T₁) considering the effects of softening period. These intensity measures have been proven to have a good correlation with inter-story drift ratios, which also indicates that intensity measures with high efficiency for inter-story drift ratios may not necessarily be suitable for peak floor acceleration.

Combining the results of the above analyses, it can be concluded that floor position and the spectral characteristics of ground acceleration significantly influence the correlation between the IMs and PFA, with variations observed across different floors. Additionally, while the correlation between each measure and PFA changes in near-field and far-field scenarios, the measures that are highly correlated with PFA remain consistent in both contexts. These measures mainly include acceleration amplitude-based indices such as SMA, PGA, A₉₅ and EDA, as well as S_a(T₁)-based indices that consider higher mode effects, such as IM₁₂₃, IM₁₂ (${\overline{S}}_a$), $S_{a123}^{\ast }$, and $S_{a12}^{\ast }$.

4.2. Sufficiency of IMs in Estimating PFA

Taking the PFA at the third floor (PFA₃) of the laminated bamboo structure as an example, Figure 13, Figure 14 and Figure 15 present the p-values of ln(ε|PGA) in the regression analysis of ln(ε|PGA) on M and ln(R) for three different structures. Here, the residual error ln(ε|PGA) is derived from the regression analysis between PFA₃ and PGA, as detailed in the analysis of Figure 9, Figure 10 and Figure 11, respectively. By comparing the effects of far-field earthquakes and near-field pulse-type earthquakes, it can be observed that there is no significant correlation (i.e., p-value greater than 0.05) between the residual ln(ε|PGA) and ln(R) or M. This result effectively demonstrates the sufficiency of PGA.

Taking the five-story structure as an example, Figure 16 shows the distribution of p-values for the regression analysis of the residual ln(ε|IM_i) of each selected seismic intensity measures against ln(R) along the height direction of the laminated bamboo frame structure. Under the action of far-field earthquakes, all IMs did not show a significant dependence on the epicentral distance ln(R) on each floor (all p-values exceeded 0.05). This indicates that these intensity measures show the sufficiency of epicentral distance R along the whole height of the laminated bamboo frame structure under the action of far-field earthquake. Under the effect of near-field earthquakes, SMA, IM₁₂₃ and IM₁₂ (${\overline{S}}_a$) demonstrated insufficiency with respect to epicentral distance R in the mid-to-low floors of the laminated bamboo frame structure. IM₁₂ (${\overline{S}}_a$) and $S_{a12}^{\ast }$ demonstrated insufficiency with respect to epicentral distance R in the high floors of the laminated bamboo frame structure.

Figure 17 displays the distribution of p-values obtained from regression analysis of the residuals ln(ε|IM_i) with respect to the earthquake magnitude M for the selected intensity measures in the five-story structure. As shown in Figure 17a, under the influence of far-field earthquakes, only the residual of SMA in the first and second floors of the laminated bamboo frame structure exhibit a slight dependency on the earthquake magnitude M. This phenomenon indicates that under far-field seismic conditions, this measure is not sufficient. However, when considering the effect of near-field ground motion, as shown in Figure 17b, the residuals of PGV and S* significantly depend on the earthquake magnitude M over the entire height range of the structure. The intensity measures circled in red in Figure 17b are not sufficient for both the bottom and top floors with respect to the earthquake magnitude M. These measures include I_NP, IM-CR, S_a,gm(T_i), S_v(T₁), S₁₂, S₁₂₃ and S_N1, etc. In conclusion, under the influence of near-field earthquakes, many seismic intensity measures are not sufficient with respect to earthquake magnitude M. These intensity measures are mostly based on spectral acceleration considering the effect of softening period or considering higher-mode effects. Compared to far-field earthquakes, this insufficiency may stem from the limited range of earthquake magnitudes in the selected near-field ground motions. However, in Section 4.1, intensity measures such as SMA, PGA, EDA, A₉₅, IM₁₂(${\overline{S}}_a$) and IM₁₂₃, which have high efficiency, still demonstrate good sufficiency with respect to the earthquake magnitude M along the entire height of the laminated bamboo frame structure under the influence of near-field ground motion. PGD and V/A also exhibit good sufficiency with respect to earthquake magnitude M under the influence of near-field ground motion.

5. Intensity Measures Suitable for PIDR

5.1. Efficiency of IMs in Estimating PIDR

Figure 18, Figure 19 and Figure 20 illustrate the distribution of PIDR along the height of the 3-, 4-, and 5-story laminated bamboo frame structures, respectively. For laminated bamboo frame structures, the PIDR typically increases progressively with the height of the structure, irrespective of far-field or near-field conditions. Only a few seismic records display irregular characteristics. This highlights the significant influence of the first mode of vibration, as previously mentioned. Focusing on the PIDR of the third story of the laminated bamboo frame structure (hereafter referred to as PIDR₃), Figure 21, Figure 22 and Figure 23 present a detailed linear regression analysis of PIDR₃ in relation to the seismic intensity indices PGA and S_a(T₁) for 3-, 4-, and 5-story structures, respectively. In comparing the effects of far-field earthquake and near-field pulse-type earthquake, it is evident that, compared to PGA, the correlation between S_a(T₁) and the PIDR₃ is more significant, demonstrating higher efficiency (reflected by smaller values of β_DM|IM). This phenomenon is closely linked to the vibration characteristics of laminated bamboo frame structures, primarily governed by the first mode of vibration (Zhang et al., 2024 [31]). Compared to PGA, S_a(T₁) better reflects the fundamental dynamic properties of the structure.

Taking the 5-story structure as an example, Figure 24 illustrates in detail the distribution of the standard deviation β_DM|IM, which represents the variability between different seismic intensity measures and PIDR, across the height of the 5-story laminated bamboo frame structure. From the two figures, it can be observed that some measures exhibit significant variations in the values of β_DM|IM along the vertical direction of the floors. The figures are marked to identify measures with lower β_DM|IM values. Based on the magnitude of β_DM|IM, the measures in the figures can generally be divided into three parts.

As shown in Figure 24, the seismic intensity measures displayed on the left side of the diagram have the smallest values of β_DM|IM, which also indicates that these seismic intensity measures are the most efficient. Under the effect of far-field ground motion, the IMs on the left side, including the first mode spectral acceleration S_a(T₁) and the spectral displacement S_d(T₁), exhibit the highest effectiveness. This may be related to the dynamic characteristics of laminated bamboo frame structures, which are primarily governed by the first mode period. In addition, S_a(T₁) and S_d(T₁) are approximately linearly proportional, thus showing a correlation that is similar to the structural response (Zhang et al., 2018 [39]). At the same time, the spectral velocity measure S_v(T₁) also exhibits high effectiveness. Some intensity measures that considered higher-order vibration modes based on S_a(T₁), such as S₁₂, S₁₂₃ S_N1 and S_N2, as well as intensity measures considering softening periods like IM-CR, IM-SR and I_NP, also achieved relatively high effectiveness. Under the effect of near-field ground motions, the left part of Figure 24b includes S_a(T₁), S_d(T₁) and S_v(T₁). In addition, intensity measures such as S₁₂, S₁₂₃, and I_NP,along with higher-order vibration mode metrics like $S_{a12}^{\ast }$, $S_{a123}^{\ast }$, and S_N2 based on Sa(T₁), as well as IM-CR, IM-SR, and S_N1, which account for softening periods, all exhibit low β_DM|IM values.

For far-field earthquakes, the intensity measures in the middle part of Figure 24a include S*, $S_{a123}^{\ast }$, $S_{a12}^{\ast }$, IM₁₂ (${\overline{S}}_a$) and S_a,gm(T_i). In near-field ground motions, the intensity measures in the middle part of Figure 24b include S*, IM₁₂ (${\overline{S}}_a$) and S_a,gm(T_i). The remaining measures in Figure 24 are all categorized in the right-hand section. Under both far-field and near-field seismic actions, the right-hand portion includes seismic intensity measures analyzed earlier in this document, which exhibit higher efficiency for PFA, such as PGA, SMA, EDA, and A₉₅. These measures all demonstrate lower effectiveness correlating with peak inter-story drift angles.

After in-depth comparison, it can be concluded that there is a significant difference between the seismic intensity measures for PIDR and those used to measure PFA. Under the influence of far-field ground motions and near-field pulse-type ground motions, indicators such as S_a(T₁), S₁₂ and S₁₂₃ all exhibit higher efficiency for PIDR. Additionally, intensity measures such as S_d(T₁), S_v(T₁), S_N2, IM-CR and I_NP also demonstrate a good correlation with PIDR under the effects of far-field ground motion or near-field pulse-type ground motion. It can be observed that these indicators are almost related to spectral acceleration. However, the IMs that show better correlation with PFA are all acceleration-related, such as PGA, SMA, EDA, and A₉₅, as well as S_a(T₁)-based indices that consider higher mode effects, such as IM₁₂₃, IM₁₂(${\overline{S}}_a$), $S_{a123}^{\ast }$ and $S_{a12}^{\ast }$.

5.2. Sufficiency of IMs in Estimating PIDR

Taking the PIDR on the third floor (PIDR₃) of the laminated bamboo frame structure as an example, Figure 25, Figure 26 and Figure 27, respectively, show the p-value results of the regression analysis for the three structures, respectively, where M and ln(R) serve as independent variables, and ln(ε|PGA) as the dependent variable. The residual error ln(ε|PGA) mentioned here originates from the regression analysis between PIDR₃ and PGA, as specifically shown in Figure 22 and Figure 23. Under the influence of near-field ground motions, a significant dependence can be observed between the residuals ln(ε|PGA) and ln(R) (i.e., p-value less than 0.05), indicating the insufficiency of PGA with respect to the epicentral distance R. As for the magnitude M, PGA has sufficiency under both types of ground motions (Figure 25b, Figure 26b and Figure 27b).

Taking the 5-story structure as an example, Figure 28 presents the distribution of p-values obtained from the regression analysis of the residuals ln(ε|IMi) with respect to the ln(R) along the height of the laminated bamboo frame structure. It can be observed that the sufficiency of some seismic intensity measures is correlated with the height of the floors. Under the influence of far-field earthquakes, S_v(T₁) demonstrates insufficiency with respect to the epicentral distance R across almost the entire 5-story structure, which are identified as highly efficient in Section 5.1. Under the influence of near-field ground motions, intensity measures such as V/A, IM₁₂ (${\overline{S}}_a$), PGA, PGD, A₉₅, ${\overline{S}}_a$ and EDA demonstrate insufficiency with respect to the epicentral distance R across all floor heights. Conversely, SMV and IM₁₂ (${\overline{S}}_a$) exhibit insufficiency at the lower floors of the five-story laminated bamboo frame structure.

Figure 29 displays the p-values from the regression analysis of the residuals ln(ε|IMi) against the magnitude M along the structural height for the selected seismic intensity measures in the 5-story structure. As shown in Figure 29a, under the influence of far-field ground motions, PGV and PGD significantly depend on the magnitude M across the entire structural height, indicating that both of them are insufficient under far-field earthquakes. According to Figure 29b, under the influence of near-field ground motions, I_NP and S* are not sufficient along the entire floor height. PGV is inadequate on almost all floors. Moreover, in Section 5.1 above, IM-CR, which is proved to be highly efficient considering the effect of softening period, shows a little inadequacy in the first layer under the influence of near-field ground motions.

6. Conclusions

This study analyzes the seismic demands of three laminated bamboo frame structures, each with 3, 4, and 5 stories, under near-field and far-field seismic motions. It uses PFA and PIDR as engineering performance demand parameters. Additionally, the study identifies appropriate seismic intensity measures for evaluating the seismic demands of laminated bamboo frame structures, considering both efficiency and sufficiency. The principal conclusions are as follows:

The structural response of three bamboo frame structures under both near-field and far-field ground motions is primarily dominated by the first mode of vibration. The type of ground motion significantly influences the selection of seismic intensity measures for PFA and PIDR. Specific seismic intensity measures may become more prominent depending on the type of ground motion, and the building height also affects the performance of these seismic intensity measures. From an efficiency perspective, acceleration-related measures are more suitable for evaluating PFA, while spectral acceleration-related measures are better suited for assessing PIDR. Regarding sufficiency, the trends are not particularly distinct.

In the case of PFA, efficiency evaluations highlighted substantial variations in the effectiveness of different intensity measures across different structural heights. Under the action of far-field ground motion and near-field pulse-type ground motion, IM₁₂₃, SMA, PGA, A₉₅ and EDA all maintain stable efficiency for PFA. From the sufficiency standpoint, for the epicentral distance R, all intensity measures maintain sufficiency throughout the height of the structure under far-field earthquake conditions, while under near-field seismic excitations, SMA, IM₁₂₃, and IM₁₂(${\overline{S}}_a$), measures exhibit insufficiency in the mid-to-low floors of the structure. Additionally, IM₁₂(${\overline{S}}_a$) demonstrates insufficiency with respect to epicentral distance R in the upper floors of the structure.

The seismic intensity measures applicable to PIDR differ from those for PFA. In terms of efficiency, several measures, including S_a(T₁), S₁₂ and S₁₂₃, demonstrate effectiveness for PIDR under both far-field and near-field pulse-type ground motions. Regarding sufficiency, the adequacy of many seismic intensity measures is closely related to the height of the structure. For epicentral distance R, under far-field ground motions, only S_v(T₁) shows insufficiency, while many measures exhibit insufficiency for R under near-field ground motions. For magnitude M, under far-field seismic motion, PGV and PGD display a dependency on M, while under near-field seismic motion, PGV, IM-CR, I_NP, and S* all show insufficiency for M.

In the course of this study, the number of selected ground motions was limited, and they were not well-matched with the standard spectra, nor were the effects of different site conditions considered. Additionally, the impact of ground motion scaling was not taken into account, nor was the influence of specific structural damage states on the selection of seismic intensity measures considered.

Author Contributions

Conceptualization, Y.Z.; Methodology, Y.G. and J.Z. (Jinglong Zhang); Software, J.Z. (Jingpu Zhang) and Y.G.; Validation, K.Z.; Formal analysis, J.Z. (Jingpu Zhang) and K.Z.; Investigation, Y.G. and J.Z. (Jinglong Zhang); Data curation, J.Z. (Jingpu Zhang) and J.Z. (Jinglong Zhang); Writing—original draft, Y.Z. and K.Z.; Writing—review and editing, Y.Z.; Visualization, Y.G.; Supervision, Y.Z. and K.Z.; Project administration, K.Z.; Funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data and material for producing the presented results will be made available upon request.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1 Structural configurations of three engineered bamboo frames for seismic performance assessment: (a) plan view; (b) elevation view of the 3-story frame; (c) elevation view of the 4-story frame; (d) elevation view of the 5-story frame.

Figure 2 Beam–column joints with T-shaped steel plate bolted connections (Leng et al., 2020 [23]).

Figure 3 Numerical simulation process for laminated bamboo frame structure in OpenSees (Leng et al., 2020 [23]; Zhang et al., 2024 [31]).

Figure 4 PIDR distribution of these three bamboo frame structures under far-field earthquakes: (a) 3-story building; (b) 4-story building; (c) 5-story building.

Figure 5 PIDR distribution of these three bamboo frame structures under near-field earthquakes: (a) 3-story building; (b) 4-story building; (c) 5-story building.

Figure 6 Distribution of PFAs along the structural height of the 3-story structure: (a) far-field ground motion; (b) near-field ground motion.

Figure 7 Distribution of PFAs along the structural height of the 4-story structure: (a) far-field ground motion; (b) near-field ground motion.

Figure 8 Distribution of PFAs along the structural height of the 5-story structure: (a) far-field ground motion; (b) near-field ground motion.

Figure 9 Regression analyses of PFA₃ on PGA and S_a(T₁) of the 3-story structure: (a) PGA; (b) S_a(T₁).

Figure 10 Regression analyses of PFA₃ on PGA and S_a(T₁) of the 4-story structure: (a) PGA; (b) S_a(T₁).

Figure 11 Regression analyses of PFA₃ on PGA and S_a(T₁) of the 5-story structure: (a) PGA; (b) S_a(T₁).

Figure 12 β_DM|IM between IMs and PFA along the 5-story laminated bamboo frame structure: (a) far-field ground motion; (b) near-field ground motion.

Figure 13 Regression analysis of the residuals ln(ε|PGA) on ln(R) and M for the PFA₃ of the 3-story structure: (a) ln(R); (b) M.

Figure 14 Regression analysis of the residuals ln(ε|PGA) on ln(R) and M for the PFA₃ of the 4-story structure: (a) ln(R); (b) M.

Figure 15 Regression analysis of the residuals ln(ε|PGA) on ln(R) and M for the PFA₃ of the 5-story structure: (a) ln(R); (b) M.

Figure 16 p-values corresponding to the regression of the residuals ln(ε|IM_i) on ln(R) with respect to PFA: (a) far-field ground motion; (b) near-field ground motion.

Figure 17 p-values corresponding to the regression of the residuals ln(ε|IM_i) on M with respect to PFA: (a) far-field ground motion; (b) near-field ground motion.

Figure 18 Distribution of peak inter-story drift ratio along the structural height of the 3-story structure: (a) far-field ground motion; (b) near-field ground motion.

Figure 19 Distribution of peak inter-story drift ratio along the structural height of the 4-story structure: (a) far-field ground motion; (b) near-field ground motion.

Figure 20 Distribution of peak inter-story drift ratio along the structural height of the 5-story structure: (a) far-field ground motion; (b) near-field ground motion.

Figure 21 Regression analyses of PIDR₃ on PGA and S_a(T₁) of the 3-story structure: (a) PGA; (b) S_a(T₁).

Figure 22 Regression analyses of PIDR₃ on PGA and S_a(T₁) of the 4-story structure: (a) PGA; (b) S_a(T₁).

Figure 23 Regression analyses of PIDR₃ on PGA and S_a(T₁) of the 5-story structure: (a) PGA; (b) S_a(T₁).

Figure 24 β_DM|IM between IMs and PIDR along the structural height of the 5-story structure: (a) far-field ground motion; (b) near-field ground motion.

Figure 25 Regression analyses of the residuals ln(ε|PGA) on ln(R) and M regarding the PIDR of the 3rd story in the 3-story structure: (a) ln(R); (b) M.

Figure 26 Regression analyses of the residuals ln(ε|PGA) on ln(R) and M regarding the PIDR of the 3rd story in the 4-story structure: (a) ln(R); (b) M.

Figure 27 Regression analyses of the residuals ln(ε|PGA) on ln(R) and M regarding the PIDR of the 3rd story in the 5-story structure: (a) ln(R); (b) M.

Figure 28 p-values corresponding to the regression of the residuals ln(ε|IM_i) on ln(R) with respect to PIDR in the case of 5-story frame structure: (a) far-field ground motion; (b) near-field ground motion.

Figure 29 p-values corresponding to the regression of the residuals ln(ε|IMi) on M with respect to PIDR in the case of 5-story frame structure: (a) far-field ground motion; (b) near-field ground motion.

Table 1

The parameters used in of Pinching4 model (Zhang et al., 2024 [31]).

Parameters	Definition	Parameters	Definition
$ePf1, $ePf2, $ePf3, $ePf4	21.0, 38.0, 43.0, 34.0	$ePd1, $ePd2, $ePd3, $ePd4	0.017, 0.050, 0.076, 0.086
$eNf1, $eNf2, $eNf3, $eNf4	−32.0, −45.0, −53.0, −42.0	$eNd1, $eNd2, $eNd3, $eNd4	−0.035, −0.049, −0.067, −0.080
$rDispP, $rDispN	0.3 0.3	$gK1, $gK2, $gK3, $gK4, $gKLim	0.0 0.0 0.0 0.0 −2.0
$fFoceP, $fFoceN	0.2 0.2	$gD1, $gD2, $gD3, $gD4, $gDLim	0.5 0.5 1.0 1.0 0.25
$uForceP, $uForceN	0.001 0.05	$gF1, $gF2, $gF3, $gF4, $gFLim	0.0 0.0 0.0 0.0 0.0
$gE	10.0	$dmgType	energy

Table 2

First five vibration periods for each frame structure.

Frame Structure	Vibration Periods
	T 1	T 2	T 3	T 4	T 5
3-story	1.23	0.28	0.12	0.04	0.04
4-story	1.41	0.29	0.11	0.06	0.04
5-story	1.50	0.29	0.11	0.06	0.05

Table 3

Selected ground motion records [9,39].

No.	Near-Field Records					Far-Field Records
	Year	Earthquake	File Names	M	R (km)	Year	Earthquake	File Names	M	R (km)
1	1971	San Fernando	SFERN/PUL164	6.61	1.81	1971	San Fernando	SFERN/PEL090	6.61	22.77
2	1979	Imperial Valley-06	IMPVALL.H/H-EMO000	6.53	0.07	1979	Imperial Valley-06	IMPVALL.H/H-DLT262	6.53	22.03
3	1979	Imperial Valley-06	IMPVALL.H/H-E04140	6.53	7.05	1979	Imperial Valley-06	IMPVALL.H/H-E11140	6.53	12.56
4	1979	Imperial Valley-06	IMPVALL.H/H-E06140	6.53	1.35	1984	Morgan Hill	MORGAN/G03090	6.19	13.02
5	1979	Imperial Valley-06	IMPVALL.H/H-E07140	6.53	0.56	1987	Superstition Hills-02	SUPER.B/B-ICC000	6.54	18.20
6	1992	Cape Mendocino	CAPEMEND/PET000	7.01	8.18	1987	Superstition Hills-02	SUPER.B/B-IVW360	6.54	23.85
7	1994	Northridge-01	NORTHR/RRS228	6.69	6.50	1989	Loma Prieta	LOMAP/A02043	6.93	43.23
8	1995	Kobe	KOBE/KJM000	6.9	0.96	1989	Loma Prieta	LOMAP/AND250	6.93	20.26
9	1999	Kocaeli	KOCAELI/YPT060	7.51	4.83	1989	Loma Prieta	LOMAP/OHW000	6.93	74.26
10	1999	Chi-Chi	CHICHI/TCU052-E	7.62	0.66	1989	Loma Prieta	LOMAP/SFO000	6.93	58.65
11	1999	Chi-Chi	CHICHI/TCU065-E	7.62	0.57	1992	Landers	LANDERS/CLW-LN	7.28	19.74
12	1999	Chi-Chi	CHICHI/TCU068-E	7.62	0.32	1992	Landers	LANDERS/YER270	7.28	23.62
13	1999	Chi-Chi	CHICHI/TCU101-E	7.62	2.11	1995	Kobe	KOBE/ABN090	6.9	24.85
14	1999	Chi-Chi	CHICHI/TCU102-E	7.62	1.49	1995	Kobe	KOBE/FKS090	6.9	17.85
15	1999	Duzce	DUZCE/DZC180	7.14	6.58	1999	Kocaeli	KOCAELI/ARE000	7.51	13.49
16	1989	Loma Prieta	LOMAP/LEX000	6.93	5.02	1999	Kocaeli	KOCAELI/DZC180	7.51	15.37
17	2003	Bam	BAM/BAM-L	6.6	1.70	1999	Chi-Chi	CHICHI/CHY101-E	7.62	9.94
18	2010	Darfield	DARFIELD/GDLCN55W	7	1.22	1999	Chi-Chi	CHICHI/TCU045-E	7.62	26.00
19	2010	Darfield	DARFIELD/LINCN23E	7	7.11	1999	Duzce	DUZCE/BOL000	7.14	12.04
20	2010	Darfield	DARFIELD/TPLCN27W	7	6.11	1999	Hector Mine	HECTOR/HEC000	7.13	11.66
21	1979	Imperial Valley-06	IMPVALL.H/H-ECC002	6.53	7.31	1989	Loma Prieta	LOMAP/WAH000	6.93	17.47
22	1979	Imperial Valley-06	IMPVALL.H/H-E10050	6.53	8.60	1994	Northridge-01	NORTHR/TAR360	6.69	15.60
23	1979	Imperial Valley-06	IMPVALL.H/H-E05140	6.53	3.95	1999	Chi-Chi	CHICHI/TCU088-E	7.62	18.16
24	1979	Imperial Valley-06	IMPVALL.H/H-EDA270	6.53	5.09	1999	Chi-Chi	CHICHI/TCU095-E	7.62	45.18
25	1979	Imperial Valley-06	IMPVALL.H/H-HVP225	6.53	7.50	2004	Niigata	NIIGATA/NIG023EW	6.63	25.82
26	1992	Landers	LANDERS/LCN260	7.28	2.19	2007	Chuetsu-oki	CHUETSU/65005EW	6.8	22.74
27	1999	Chi-Chi	CHICHI/CHY024-E	7.62	9.62	2007	Chuetsu-oki	CHUETSU/65025EW	6.8	11.09
28	1999	Chi-Chi	CHICHI/TCU049-E	7.62	3.76	2007	Chuetsu-oki	CHUETSU/65056EW	6.8	20.03
29	1999	Chi-Chi	CHICHI/TCU075-E	7.62	0.89	2007	Chuetsu-oki	CHUETSU/65057EW	6.8	20.00
30	1999	Chi-Chi	CHICHI/TCU082-E	7.62	5.16	2007	Chuetsu-oki	CHUETSU/6CB51EW	6.8	11.48

Table 4

Selected ground motion intensity measures.

No.	IM	Reference
1	Peak ground acceleration, PGA	N.A.
2	Peak ground velocity, PGV	N.A.
3	Peak ground displacement, PGD	N.A.
4	PGV/PGA, V/A	Sucuoǧlu and Nurtuǧ, 1995 [41]
5	Sustained maximum acceleration, SMA	Nuttli, 1979 [42]
6	Sustained maximum velocity, SMV
7	Effective design acceleration, EDA	Benjamin J. R., & Associates, 1988 [43]
8	A 95	Sarma & Yang, 1987 [40]
9	Sa(T1)	N.A.
10	Sv(T1)	N.A.
11	Sd(T1)	N.A.
12	$S^{\ast }={(S_a(T_1))}^{1-\alpha }{(S_a(T_f))}^{\alpha }$	Cordova et al., 2001 [44]
13	$\mathrm{IM}‐\mathrm{CR}=S_a{\left(T_1\right)}^{1‐\alpha }{S}_a{(\sqrt[3]{R_{\mathrm{IM}}}\cdot T_1)}^{\alpha }$	Mehanny, 2009 [45]
14	$\mathrm{IM}‐\mathrm{SR}=S_a{\left(T_1\right)}^{1‐\alpha }{S}_a{(\sqrt{R_{\mathrm{IM}}}\cdot T_1)}^{\alpha }$
15	$I_{Np}=S_a(T_1)N_p^a$ $N_p=\sqrt[N]{S_a(T_1)\cdot \dots \cdot S_a(T_N)}/S_a(T_1)$	Bojórquez and Iervolino, 2011 [46]
16	$S_{a12}^{\ast }=0.80S_a(T_1)+0.20S_a(T_2)$	Shome and Cornell, 1999 [47]
17	$S_{a123}^{\ast }=0.80S_a(T_1)+0.15S_a(T_2)+0.05S_a(T_3)$
18	$I{M}_{12}=S_a{({\tau }_a,5\%)}^{1-\beta }{S}_a{({\tau }_b,5\%)}^{\beta }$	Vamvatsikos and Cornell, 2005 [48]
19	$I{M}_{123}=S_a{({\tau }_a,5\%)}^{1-\beta -\gamma }{S}_a{({\tau }_b,5\%)}^{\beta }{S}_a{({\tau }_c,5\%)}^{\gamma }$
20	$N_p=\sqrt[N]{S_a(T_1)\cdot \dots \cdot S_a(T_N)}/S_a(T_1)$ $S_{N1}=S_a{(T_1)}^{\alpha }\cdot S_a{(C{T}_1)}^{1-\alpha }$	Lin et al., 2011 [49]
21	$S_{N2}=S_a{(T_1)}^{\beta }\cdot S_a{(T_2)}^{1-\beta }$
22	$S_{12}={[S_a(T_1)]}^{\alpha }\cdot {[S_a(T_2)]}^{\beta }$	Zhou et al., 2013 [50]
23	$S_{123}={[S_a(T_1)]}^{\alpha }\cdot {[S_a(T_2)]}^{\beta }\cdot {[S_a(T_3)]}^{\gamma }$
24	${\overline{S}}_{{}_a}=\sqrt[n]{{\displaystyle \prod _{i=1}^n{S}_a(T_1)}}$ $n=\left\{{}_{0.39T_1 + 1.15,1s < T_1 \le 10s}^{1, T_1 \le 1s}\right.$	Lu et al., 2013 [16]
25	$S_{a,gm}(T_i)={\left[{\displaystyle \prod _{i=1}^n{S}_a(T_i)}\right]}^{1/n}$	Kazantzi and Vamvatsikos, 2015 [51]

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