An Investigation into the Effect of Near-Fault Ground Motion Duration Parameters on the Nonlinear Seismic Response of Intake Towers

Abstract

Intake towers, essential for hydraulic hub projects, are integral to maintaining safety and efficiency, especially under seismic conditions that are prevalent near fault zones. These structures are vital for the integrity of hydraulic hubs, effective hydropower generation, and downstream safety. The duration of seismic events notably influences the towers’ structural response. In light of China’s initiative to build numerous high dams and large reservoirs, understanding the interplay between seismic duration and the intake tower response is crucial. This study, utilizing a duration-dependent composite parameter method based on seismic intensity, investigates the impact of near-fault ground motion duration effects on the response characteristics of intake towers. It analyzes the correlation between three types of six duration parameters and six duration-related composite parameters with the nonlinear seismic response of the physical model of the intake tower structure, as well as the rapid seismic response of the simplified model. This study investigates the impact of near-fault ground motion duration on intake towers, which is crucial for hydraulic hub projects, particularly in seismic-prone areas like those targeted by China’s dam construction initiative. Utilizing a duration-dependent composite parameter method, the study establishes a strong correlation between seismic duration parameters and the nonlinear response of intake towers, emphasizing the significance of uniform duration-related composite intensity parameters for characterizing near-fault seismic motion features. The findings reveal a pronounced correlation between the elasto-plastic response of intake towers and consistent duration-related composite strength parameters, offering crucial insights for optimizing structural design and enhancing seismic response assessment, particularly in the realm of large-scale dam projects.

1. Introduction

Intake tower structures, which are crucial for water diversion and discharge in dams, are pivotal for the regular operation of these facilities and a key aspect of dam functionality. In recent years, near-fault ground motions with distinct seismic properties have increasingly occurred, attracting substantial attention from the scientific community. Investigations conducted by numerous seismologists have revealed that structures that are exposed to near-fault ground motions often endure more severe damage than those situated closer to the fault. Furthermore, the duration of the ground motion, recognized as one of the three primary characteristics of seismic activity, has consistently demonstrated associations with both the seismic response of structures and their earthquake-resistant characteristics. The effect of seismic duration on the structural seismic response is an aspect that demands thorough consideration [1].

Researchers have been actively involved in ongoing research concerning the influence of earthquake duration on the seismic response. Ma Xiaoyan [2] utilized ANSYS software (2021R1) to input seismic motion records from the Wenchuan earthquake and analyzed the seismic response of a ten-story frame structure in relation to strong seismic duration parameters. The conclusion drawn was that longer durations lead to more pronounced structural responses. Sun Xiaoyun [3] and colleagues employed Open Sees software (2.5.0) for finite element modeling of a six-story reinforced concrete structure. They selected thirty strong earthquake motion records as inputs and scrutinized the effect of duration on the structural seismic response, observing that shear deformation and reinforcement slip deformation are correlated with the duration parameters of seismic motion, with structural response escalating as the duration increases. Gai Xia et al. [4] utilized ABAQUS software (2018) and selected forty natural earthquake waves that had undergone substantial duration processing as input seismic motions to investigate the relationship between long and short durations and the seismic response of transmission towers. Han Jianping [5], on the other hand, selected 140 earthquake waves with varying durations, using significant duration D_s70 as the seismic duration parameter. Through modeling different reinforced concrete structures of five, eight, and ten stories in Open Sees, a vulnerability analysis was conducted on structures of various heights, leading to the conclusion that as seismic intensity rises, the influence of seismic duration on structural vulnerability becomes more pronounced, and a longer duration of seismic motions elevates the vulnerability index of structures. Chen et al. [6] utilized several velocity-based duration measures (DMs), tailored to the low-frequency content in near-fault records, and their study proposed novel nonstructural compound intensity measures (IMs) that include DMs. The researchers found that acceleration-based uniform durations correlate strongly with acceleration-related IMs, while velocity-based durations align more with velocity- and displacement-related IMs. Furthermore, Chen et al. [7] emphasized the critical impact of specific characteristics of near-fault ground motions, such as forward directivity and fling-step effects, on the seismic response of structures like intake towers. This underscores the complexity and variability of seismic responses, which need to be considered in structural analysis and design.

In 2006, Hancock and Bommer [8] summarized prior studies on the diverse effects of seismic duration on structures, acknowledging that the choice of different structural responses affects the results of duration effects, and differing definitions of duration parameters also impact the duration effect on structures. Ruiz [9] examined the effect of a long seismic duration on the residual displacement demand of single-degree-of-freedom (SDOF) systems, scrutinizing the correlation between the significant duration D_s90 of twenty groups of seismic motions and the nonlinear response of structures. The conclusion reached was that an increase in strong seismic duration results in an elevated residual displacement demand on the upper portions of flexible frames. Chandramohan et al. [10] researched the relationship between collapse and significant duration parameters in five-story steel frame structures and reinforced concrete bridge piers, determining that the influence of duration on seismic design, structural damage, and seismic response should be taken into account. Mina and Hamed [11] studied the duration effect on five SDOF systems while considering strength and stiffness degradation, analyzing forty-seven earthquake motions using significant duration as the duration parameter. Their findings indicated that under long-duration seismic motions, the hysteresis energy demand is more prominent in SDOF systems exhibiting evident stiffness and strength degradation. Raghunandan and Liel [12] conducted nonlinear dynamic analyses on seventeen ductile and nonductile reinforced concrete frame structures using Open Sees, investigating the relationship between the significant duration D_s90 of seventy-six groups of seismic motions and the dynamic response of structures. They concluded that, for seismic motions of equal strength, longer duration records have a more pronounced effect on structural damage than shorter duration records, highlighting the necessity of considering the effect of seismic duration in the design of nonlinear structural failures.

Extensive research underscores the considerable influence of seismic motion duration on structural seismic response. Neglecting this factor may lead to an underestimation of the structural response and damage. Furthermore, when designing for nonlinear failure, it is crucial to account for the effect of seismic duration on structural damage. While much scholarly attention has been devoted to the interplay between the period frequency, amplitude, and structural seismic response in seismic motion, relatively limited research has investigated the relationship between “duration” parameters and structural response, particularly in the context of near-fault ground motion. This knowledge gap is especially pronounced concerning the effect of duration parameters that are associated with near-fault seismic motion on the response of intake towers. Thus, studying the impact of near-fault seismic motion duration on intake tower responses is crucial.

This paper investigates the correlation between elastoplastic and simplified seismic responses of intake towers subjected to near-fault seismic motion. The study utilizes a rapid dynamic response analysis program and examines various duration parameters and composite duration parameters. Valuable conclusions are drawn regarding the relationship between structural response and duration parameters in the context of near-fault seismic motion.

To explore the correlation between different duration parameters of near-fault seismic motion and the seismic responses of two distinct intake tower structural models (the finite element model and the simplified model), this study calculated six intensity duration parameters and six composite intensity parameters using 30 carefully selected near-fault seismic motions for computation, in addition to 65 original near-fault seismic motions. By leveraging the dynamic response results obtained for intake towers under near-fault seismic motion, this study analyzed the relationship between composite parameters and the seismic response of intake tower structures. It unveiled the cumulative effect of the duration effect on the nonlinear lateral deformation curvature of intake towers, shedding light on the association between the duration effects of near-fault seismic motion and damage measure indices such as the lateral deformation curvature of the intake towers.

2. Selection of Near-Fault Seismic Motion and Calculation of Duration Parameters

Prior to investigating the analysis of the relationship between seismic motion duration and structural seismic response, it is crucial to carefully choose suitable measurement parameters for assessing the duration of acceleration in seismic records. This selection necessitates the establishment of clear definitions for duration parameters. Presently, there are multiple definitions for duration parameters. In a 2004 publication by Bommer et al. [13], over thirty duration definitions were introduced. Nevertheless, within the domain of duration effect studies, the more commonly employed definitions include bracketed duration, uniform duration, and significant duration. These duration parameters can be further classified based on different threshold values within the same category. Furthermore, the ground motions used in this study were selected following a probabilistic method [14]. The selection was tailored to the specific seismic characteristics of the region, including the soil type and required hazard levels, to ensure a comprehensive and representative analysis of seismic responses [15].

(1)

Bracketed Duration

Bracketed duration, as originally defined by Bolt in 1973, represents the most straightforward form of duration definition, as shown in Figure 1. Notably, Chandramohan et al. [10] highlighted that an acceleration threshold of 0.05 g is highly likely to induce structural damage. Consequently, in investigations concerning duration effects, the acceleration thresholds that are commonly adopted for bracketed duration are 0.05 g and 0.1 g. In the context of this study, which examines the interplay between the seismic response and the duration effect on intake towers subjected to near-fault seismic motion, D_b−0.05g and D_b−0.1g were utilized as the designated duration parameters.

(2)

Uniform Duration

Uniform duration is defined by considering the general characteristics of a seismic motion record. It is the sum of the intervals during which the acceleration of the seismic motion exceeds a specified acceleration threshold, as shown in Figure 2. This can be represented by D_u, where $\Delta t_i$ is illustrated as follows:

In this study, the chosen duration parameters are D_u−0.05g and D_u−0.1g. Both of these duration types are defined by a fixed value of acceleration, using amplitude to define the duration parameters of seismic motion.

(3)

Significant Duration

Significant duration is a duration parameter defined from an energy perspective. Introduced by Trifunac and Brady [16], it is based on the integral of the square of ground acceleration, as shown in Equation (1):

$$0.05\le \frac{\frac{\pi }{2g}{\displaystyle \underset{0}{\overset{t}{\int }}{a}^{2}dt}}{{\displaystyle \underset{0}{\overset{T_{\max }}{\int }}{a}^{2}dt}}\le 0.95$$

(1)

The provided formula indicates that the specified time interval includes 70% or 90% of the total energy that is associated with the seismic motion. The range of 5–95% (or 5–75%), as mentioned in Equation (3), represents a commonly employed range for cumulative energy. Trifunac and Brady [16] introduced the definition of significant duration as the time interval between the maximum and minimum times that satisfy Equation (3). The seismic motion’s energy release is quantified using the Arias intensity equation [17], as depicted in Equation (2):

$$I_A=\frac{\pi }{2g}{\displaystyle \underset{0}{\overset{T_{\max }}{\int }}{a}^{2}dt}$$

(2)

In Equation (2), $T_{\max }$ represents the total recording time of the seismic motion. In this study, while examining the correlation between the seismic response of intake towers and significant duration, D_s70 and D_s90 were chosen as the duration parameters.

Taking the 1999 Taiwan Chi-Chi earthquake’s recorded TCU068EW ground motion as an example, Figure 3 illustrates the three aforementioned types of seismic duration parameters.

The study cited in [6] has already performed seismic response calculations for nonlinear finite element intake towers. Leveraging these pre-existing seismic computations, a selection of 30 near-fault seismic motions was made to investigate duration effects, with their seismic characteristic parameters detailed in [18]. In accordance with the definitions of the three types of duration parameters, calculations were conducted for six duration parameters pertaining to these 30 near-fault seismic motions. Both bracketed and uniform durations employed thresholds of 0.05 g and 0.1 g, while significant durations utilized thresholds of (5~75%) and (5~95%).

Additionally, apart from computing duration parameters for these 30 near-fault seismic motions, this chapter also incorporated a selection of 65 near-fault pulse-type seismic motions, sourced from the NGA-West2 database of the Pacific Earthquake Engineering Research Center in the United States, as referenced in [19]. To ensure the impartiality of the results, these seismic motions were drawn from various earthquakes occurring at different locations, times, and magnitudes, including events such as the 1979 Coyote Lake (Mw = 5.7), 1997 San Fernando (Mw = 6.6), 1999 Kocaeli (Mw = 7.5), 1999 Chi-Chi (Mw = 6.2), 2009 Chuetsu-oki (Mw = 6.8), and 2011 Christchurch (Mw = 6.1) earthquakes.

Following the definitions of the three types of duration parameters, calculations including three types (equal to six parameters) of duration were executed for these 65 near-fault seismic motions. The bracketed and uniform durations maintained thresholds of 0.05 g and 0.1 g, while the significant durations adhered to thresholds of 5~75% and 5~95%.

3. Nonlinear Seismic Response Calculation for Intake Tower Structures

3.1. Seismic Structural Response Calculation for Intake Towers

The intake tower structure analyzed in this study is representative of large-scale hydraulic projects that are typically encountered in China, specifically within the seismic-prone region of Sichuan Province. The finite element model employed for the intake tower structure in this study is based on a large dam which is situated in Sichuan Province. The water tower’s intake is positioned at the same elevation as the dam crest, with a connection to a traffic tunnel via a bridge that is located at the rear of the tower and an attachment to the platform on the right side of the spillway. Figure 4 illustrates a cross-sectional view of the intake tower structure. The tower’s base measures 26.0 m in width, and the length of the spillway tunnel of the intake tower structure in the water flow direction is 15.0 m, while the top of the intake tower is situated at an elevation of 88.00 m, resulting in a total height of 8 m. C30-strength concrete constitutes the primary structural material for the tower, with steel reinforcement being distributed throughout the intake tower body. The modeling process employed the large-scale finite element software ABAQUS, with the finite element model depicted in Figure 5. The primary components of the model consisted of hexahedral solid elements, which are divided into a total of 145,641 elements and 167,550 nodes. This model accounts for concrete’s nonlinear, inelastic behavior, including damage due to compressive and tensile stresses, cracking, and crushing. It employs a combination of isotropic damage and plasticity theories to simulate the complex behavior of concrete under seismic loads accurately. For the steel reinforcement, the model incorporated the Steel Plasticity model, which accurately represents the cyclic behavior of steel bars, including aspects such as yield strength, the Bauschinger effect, and strain-hardening. The core analysis involved 30 sets of distinct near-fault seismic motions, under which various seismic responses of the intake tower structure, including acceleration, displacement, and lateral deformation curvature, were quantified. The detailed results are accessible in [20].

As previously indicated, this study opted for three types of duration parameters: bracketed duration, uniform duration, and significant duration. These parameters were applied to multiple near-fault seismic motions originating from events such as the Chi-Chi Northern Ridge earthquake. The elasto-plastic seismic response results of the intake tower structure are detailed in [6].

To accurately characterize the linear correlation between the seismic response, duration parameters, and composite seismic intensity parameters, this paper employs the Pearson correlation coefficient. The Pearson correlation coefficient quantifies the degree of linear association between two sets of random variables. It is defined as the covariance of the two variables divided by the product of their standard deviations. In cases where the sample size is n, it can be further defined as presented in Equation (3):

$$r=\frac{{\displaystyle \sum _{i=1}^n(X_i-\overline{X})(Y_i-\overline{Y})}}{\sqrt{{\displaystyle \sum _{i=1}^n{(X_i-\overline{X})}^2}}\sqrt{{\displaystyle \sum _{i=1}^n{(Y_i-\overline{Y})}^2}}}$$

(3)

Generally, the Pearson correlation coefficient ranges between −1 and 1. The degree of correlation between two data sets is associated with the value of this coefficient $r$: A positive correlation is indicated when the coefficient is greater than zero, a negative correlation when it is less than zero, and no correlation when it equals zero. The degree of correlation between two sets of data is associated with the magnitude of the absolute value of the Pearson correlation coefficient, $\left|r\right|$. When $\left|r\right|$ is between 0.9 and 1.0, it indicates an extremely high correlation between the data sets. If $\left|r\right|$ falls within the range of 0.70 to 0.89, the data sets are considered to have a high degree of correlation. A value of $\left|r\right|$ between 0.40 and 0.69 suggests a moderate correlation. When $\left|r\right|$ is between 0.2 and 0.39, it implies a low degree of correlation. Finally, an $\left|r\right|$ value between 0 and 0.19 indicates a very low correlation between the data sets.

3.2. Correlation Analysis between Nonlinear Seismic Response of Intake Tower Structures and Duration Parameters

With a focus on the elasto-plastic seismic responses of intake towers, derived from practical engineering computations that are conducted using ABAQUS software, as presented in [6], this study conducted an analysis of the linear correlation between six distinct duration parameters (D_b−0.05g, D_b−0.1g, etc.) and the nonlinear seismic response of intake tower structures in the context of 30 near-fault seismic motions. This analysis aimed to assess the duration effects that are induced by near-fault earthquakes on intake towers. Figure 6, Figure 7 and Figure 8 visually depict the correlation coefficients between the six duration parameters and various seismic responses of intake towers, including parameters such as the maximum acceleration at the tower’s summit, displacement, and the maximum lateral deformation curvature at the base, all under the influence of the 30 near-fault seismic motions. Specific data concerning the correlation coefficients can be found in

Table 1. Correlation coefficients between seismic response and duration parameters of intake towers.

	Db−0.05g	Db−0.1g	Du−0.05g	Du−0.1g	Ds70	Ds90
	r
Maximum acceleration at the top	0.296	0.219	0.399	0.258	0.061	0.086
Maximum relative displacement at the top	0.174	0.04	0.03	−0.034	−0.385	−0.285
Maximum lateral deformation curvature	0.378	0.414	0.376	0.557	−0.037	−0.122

.

Figure 6 reveals that the maximum acceleration response at the top of the intake tower exhibits a positive correlation with all six duration parameters, with the acceleration response intensifying as the duration parameters increase. However, it is noteworthy that the correlations between the maximum acceleration response and both bracketed duration and significant duration are not as robust as that observed with uniform duration. Specifically, the correlation coefficients between the acceleration response and bracketed durations D_b−0.05g and D_b−0.1g are 0.296 and 0.219, respectively, indicating a relatively low degree of correlation. The acceleration response demonstrates a notably weaker correlation, with significant durations D_s70 and D_s90, as evident from the correlation coefficients of 0.061 and 0.086, respectively.

In contrast, concerning uniform duration, the correlation coefficient between the acceleration response and D_u−0.05g is 0.399, signifying a moderate degree of correlation. Meanwhile, the correlation coefficient with D_u−0.1g is 0.258, suggesting a relatively lower degree of correlation. When assessing the ranking of correlation coefficients among the three types of duration parameters, it becomes apparent that the correlation is more pronounced with uniform duration, whereas it is weaker with significant duration. This underscores that the acceleration response exhibits a stronger and positive correlation with the uniform duration parameter D_u−0.05g.

Figure 6. Correlation coefficients between accelerations of the top node of the intake tower and duration measures of ground motions.

Figure 6. Correlation coefficients between accelerations of the top node of the intake tower and duration measures of ground motions.

Figure 7 demonstrates that the maximum displacement response at the top of the intake tower exhibits a positive correlation with the bracketed duration parameters, implying that the displacement response increases with an elevation in bracketed duration. Conversely, it displays a negative correlation with both uniform duration and significant duration, indicating that the displacement response decreases as these durations increase. In terms of absolute correlation coefficients, it is noteworthy that the correlation of the maximum displacement at the tower’s summit is more pronounced with significant duration compared to bracketed and uniform durations. Specifically, the correlation coefficients with significant durations D_s70 and D_s90g are −0.385 and −0.285, respectively, signifying a relatively low degree of correlation. On the other hand, the correlation coefficients with bracketed durations D_b−0.05g and D_b−0.1g are 0.173 and 0.04, respectively, indicating low and very weak correlations. For uniform durations D_b−0.05g and D_b−0.1g, the coefficients are −0.03 and −0.034, respectively, implying a very low degree of correlation.

Upon scrutinizing the correlation coefficients across the three types of duration parameters, it can be concluded that the maximum displacement occurring as a seismic response of the intake tower exhibits a low or very weak correlation with all three types of duration parameters. This suggests that the correlation between the displacement response and the duration parameters is not significant.

Figure 7. Correlation coefficients between relative displacements of the top node of the intake tower and duration measures of ground motion.

Figure 7. Correlation coefficients between relative displacements of the top node of the intake tower and duration measures of ground motion.

Figure 8 reveals that the seismic response that is associated with the lateral deformation curvature at the base of the intake tower displays a positive correlation with both bracketed and uniform durations. This implies that the lateral deformation curvature increases as these duration parameters increase. In contrast, it exhibits a negative correlation with significant duration, indicating that the lateral deformation curvature decreases as significant duration increases. When examining the absolute values of the correlation coefficients, it becomes evident that the correlation coefficient between the uniform duration D_u−0.05g and the lateral deformation curvature response is 0.376, denoting a low degree of correlation. Moreover, the correlation coefficient with D_u−0.1g stands at 0.557, suggesting a moderate degree of correlation. Regarding the correlation of the lateral deformation curvature response with bracketed duration, D_u−0.05g exhibits a correlation coefficient of 0.378, indicating a low correlation, while D_u−0.1g shows a correlation coefficient of 0.141, implying a very low degree of correlation. Finally, the correlation coefficients with significant durations D_s70 and D_s90 are −0.037 and −0.122, respectively, demonstrating very weak correlations.

Consequently, based on the correlation coefficients that are associated with these six duration parameters, it can be inferred that the seismic response of the lateral deformation curvature at the base of the intake tower exhibits a stronger and positive correlation with the uniform duration parameter D_u−0.1g.

Figure 8. Correlation coefficients between lateral curvatures of the intake tower and duration measures of ground motions.

Figure 8. Correlation coefficients between lateral curvatures of the intake tower and duration measures of ground motions.

The correlation analysis conducted between the elasto-plastic seismic response of the intake tower, as obtained through finite element software modeling, and the various duration parameters reveals notable trends. Among the three types of seismic responses considered, both the maximum acceleration response at the top and the lateral deformation curvature at the base exhibit a higher correlation with the duration parameters compared to the top displacement response. Remarkably, among the three duration parameters, the maximum acceleration response at the top and the lateral deformation curvature response at the base of the intake tower, when subjected to near-fault seismic motions, display a more significant correlation with uniform duration. This observation aligns with the findings presented in [18], where an investigation involving an SDOF system analyzed the correlation between the structural seismic response and uniform duration parameters for 65 near-fault seismic motions, demonstrating the most substantial correlation. Conversely, the maximum displacement response at the top manifests a higher correlation with significant duration.

3.3. Correlation Analysis between Nonlinear Seismic Response of Intake Tower Structures and Composite Intensity Parameters

3.3.1. Composite Earthquake Intensity Parameters

In the process of seismic research, different earthquake intensity parameters have been proposed for various research purposes, such as peak ground acceleration (PGA) and peak ground velocity (PGV). Riddell and Garcia [19] proposed a composite earthquake intensity parameter related to the duration of seismic motion in 2001, which can be represented by Equation (4):

$$I=Q^A\cdot t_d^{\mathrm{B}}$$

(4)

where $Q$ represents a single seismic motion parameter.

Based on Equation (4), the composite intensity parameters related to seismic acceleration and velocity are represented as follows:

$$I_{\mathrm{a}}=PGA\cdot t_{\mathrm{d}}^{1/3}$$

(5)

$$I_{\mathrm{F}}=PGV\cdot t_d^{0.25}$$

(6)

Based on the aforementioned Equations (4)–(6), this paper combines single seismic intensity parameters with three types of duration parameters to formulate six composite earthquake intensity parameters, $PGA\cdot D_{\mathrm{b}-0.1\mathrm{g}}$, $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, $PGA\cdot D_{\mathrm{s}90}$, $PGV\cdot D_{\mathrm{b}-0.1\mathrm{g}}$, $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, and $PGV\cdot D_{\mathrm{s}90}$, thereby obtaining 30 near-fault seismic motions.

3.3.2. Correlation Analysis between the Nonlinear Seismic Response of Intake Tower Structures and Composite Intensity Parameters

As previously mentioned, the seismic response results for the intake tower structure, calculated using finite element software, are already obtained and documented in [16]. In conjunction with seismic intensity parameters, namely, PGA and PGV, six composite intensity parameters related to the duration parameters of the 30 near-fault seismic motions are derived: $PGA\cdot D_{\mathrm{b}-0.1\mathrm{g}}$, $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, $PGA\cdot D_{\mathrm{s}90}$, $PGV\cdot D_{\mathrm{b}-0.1\mathrm{g}}$, $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, and $PGV\cdot D_{\mathrm{s}90}$, as shown in

Table 2. Correlation coefficients between seismic response and composite intensity parameters of intake towers.

	Db−0.05g	Db−0.1g	Du−0.05g	Du−0.1g	Ds70	Ds90
	r
Maximum acceleration at the top	0.6	0.782	0.449	0.022	0.234	0.207
Maximum relative displacement at the top	−0.063	0.002	0.026	0.496	0.629	0.608
Maximum lateral deformation curvature	0.378	0.414	0.376	0.557	−0.037	−0.122

. Using Pearson correlation coefficient analysis, the correlation coefficients between the seismic response of the intake tower structure under near-fault seismic motions and the composite intensity parameters can be obtained, as shown in Figure 9, Figure 10 and Figure 11.

From Figure 9, it is evident that the maximum acceleration response at the top of the intake tower is positively correlated with the three composite intensity parameters related to PGA, $PGA\cdot D_{\mathrm{b}-0.1\mathrm{g}}$, $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, and $PGA\cdot D_{\mathrm{s}90}$, increasing as these parameters increase. From the absolute values of the correlation coefficients, it can be seen that the maximum acceleration response at the top of the intake tower has the highest correlation with the uniform-duration-related composite intensity parameter $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, with a correlation coefficient of 0.782. Since the absolute value of the coefficient is greater than 0.7, it indicates a high degree of correlation with $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$. The correlation coefficients with the other two duration-related composite intensity parameters, $PGA\cdot D_{\mathrm{b}-0.1\mathrm{g}}$ and $PGA\cdot D_{s90}$, are 0.599 and 0.449, respectively, which are both greater than 0.4, indicating moderate correlation. Among the three duration-related composite intensity parameters related to PGA, the correlation with $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$ is most significant, followed by $PGV\cdot D_{\mathrm{b}-0.1\mathrm{g}}$ and, finally, $PGV\cdot D_{\mathrm{s}90}$.

Figure 9. Correlation coefficients between accelerations of the top node of the intake tower and seismic intensity parameters of ground motions.

Figure 9. Correlation coefficients between accelerations of the top node of the intake tower and seismic intensity parameters of ground motions.

The maximum acceleration response at the top of the intake tower is positively correlated with $PGV\cdot D_{\mathrm{b}-0.1\mathrm{g}}$ and $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, the PGV-related composite intensity parameters, and negatively correlated with $PGV\cdot D_{\mathrm{s}90}$. The uniform-duration-related composite intensity parameter $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$ shows the highest correlation, followed by the significant-duration-related parameter $PGV\cdot D_{\mathrm{s}90}$, and the smallest correlation is found with the bracketed-duration-related parameter $PGV\cdot D_{\mathrm{b}-0.1\mathrm{g}}$. This suggests that among the six composite intensity parameters, the highest correlation with the acceleration response is with the uniform-duration-related parameter. The acceleration response shows a low correlation with PGV-related composite intensity parameters, and this correlation is lower than that with the PGA-related parameters. This implies that the acceleration response of the intake tower is more closely related to the PGA-related composite intensity parameters, with $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$ showing the most significant correlation.

From Figure 10, it can be seen that the maximum displacement response at the top of the intake tower has a negative correlation with two of the PGA-related composite intensity parameters, $PGA\cdot D_{\mathrm{b}-0.1\mathrm{g}}$ and $PGA\cdot D_{\mathrm{s}90}$, and a positive correlation with $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$. The correlation coefficient between the maximum displacement response and the bracketed-duration-related composite intensity parameter $PGA\cdot D_{\mathrm{b}-0.1\mathrm{g}}$ is 0.063, indicating a low degree of correlation. The displacement response shows very weak correlations with the uniform-duration-related and significant-duration-related composite intensity parameters, $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$ and $PGA\cdot D_{\mathrm{s}90}$, with coefficients of 0.002 and 0.026, respectively.

Figure 10. Correlation coefficients between relative displacements of the top node of the intake tower and seismic intensity parameter of ground motions.

Figure 10. Correlation coefficients between relative displacements of the top node of the intake tower and seismic intensity parameter of ground motions.

The maximum displacement response at the top of the intake tower shows positive correlations with all three PGV-based duration composite intensity parameters, $PGV\cdot D_{\mathrm{b}-0.1\mathrm{g}}$, $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, and $PGV\cdot D_{\mathrm{s}90}$. The absolute values of the correlation coefficients indicate that the maximum displacement response has moderate correlations with all three PGV-related duration parameters, with absolute values greater than 0.4. The correlation coefficient with the uniform-duration-related composite parameter $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$ is the highest at 0.629, followed by the significant-duration-related parameter $PGV\cdot D_{\mathrm{s}90}$, and the smallest correlation is found with the bracketed-duration-related parameter $PGV\cdot D_{\mathrm{b}-0.1\mathrm{g}}$. This suggests a stronger correlation between the maximum displacement at the top of the intake tower and $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$. The correlation of the maximum displacement response with PGV-related composite intensity parameters is higher than that with PGA-related parameters, indicating that the displacement response of the intake tower is more closely related to the PGV-related composite intensity parameters, with the most significant correlation being with $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$.

From Figure 11, it is evident that the maximum lateral deformation curvature response at the base of the intake tower positively correlates with all three PGA-related composite intensity parameters, $PGA\cdot D_{\mathrm{b}-0.1\mathrm{g}}$, $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, and $PGA\cdot D_{\mathrm{s}90}$. The absolute value of the correlation coefficient between the maximum lateral deformation curvature response and the uniform-duration-related composite intensity parameter $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$ is 0.553, the highest among the composite intensity parameters, indicating a moderate degree of correlation. The coefficients with $PGA\cdot D_{\mathrm{b}-0.1\mathrm{g}}$ and $PGA\cdot D_{\mathrm{s}90}$ are 0.375 and 0.354, respectively, showing a low degree of correlation. This suggests that the maximum lateral deformation curvature at the base of the intake tower has the highest correlation with the uniform-duration-related composite intensity parameter $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$.

Figure 11. Correlation coefficients between lateral curvatures of the top node of the intake tower and seismic intensity parameters of ground motions.

Figure 11. Correlation coefficients between lateral curvatures of the top node of the intake tower and seismic intensity parameters of ground motions.

The maximum lateral deformation curvature response at the base of the intake tower shows negative correlations with the PGV-based composite intensity parameters $PGV\cdot D_{\mathrm{b}-0.1\mathrm{g}}$ and $PGV\cdot D_{\mathrm{s}90}$ and a positive correlation with $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$. The absolute values of the correlation coefficients with these three parameters are all less than 0.19, indicating a very low degree of correlation. Compared to the three PGA-related composite intensity coefficients, the correlation of the maximum lateral deformation curvature at the base of the intake tower with PGA-related composite intensity parameters is higher than that with PGV-related parameters. This indicates that the lateral deformation curvature response of the intake tower is more closely related to PGA-related composite intensity parameters, with the most significant correlation being with $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$.

The correlation analysis conducted among the three types of seismic responses and the six composite intensity parameters reveals distinctive patterns. Specifically, the acceleration response at the top of the intake tower and the lateral deformation curvature response at the base display a stronger correlation with composite intensity parameters that are related to PGA. Conversely, the displacement response at the top of the intake tower exhibits a higher correlation with composite intensity parameters that are associated with PGV. This observation is consistent with the findings documented in [21], which noted a correlation between the acceleration response of the intake tower and PGA, as well as between the displacement response and PGV.

When examining the absolute values of the correlation coefficients between the three seismic responses and the composite intensity parameters, it becomes evident that all three seismic responses exhibit a significant correlation with composite intensity parameters that are linked to uniform duration. This suggests that, for seismic responses under near-fault seismic motion, the adoption of uniform-duration-related composite parameters for characterizing seismic motion is more suitable. This conclusion aligns with the analysis of duration parameters presented in [18] and underscores the critical effect of uniform duration in near-fault seismic motion on the seismic response of intake tower structures, warranting substantial attention.

4. Conclusions

This paper calculated bracketed duration, uniform duration, and significant duration parameters for 30 near-fault seismic motions and 65 near-fault seismic motions, as well as six composite intensity parameters related to PGA and PGV: $PGA\cdot D_{\mathrm{b}-0.1\mathrm{g}}$, $PGA\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, $PGA\cdot D_{\mathrm{s}90}$, $PGV\cdot D_{\mathrm{b}-0.1\mathrm{g}}$, $PGV\cdot D_{\mathrm{u}-0.1\mathrm{g}}$, and $PGV\cdot D_{\mathrm{s}90}$. The linear correlation between the elasto-plastic seismic response of intake tower structures and the three types of duration parameters and six composite intensity parameters under near-fault seismic motion was analyzed, yielding beneficial conclusions about the duration effects. The conclusions are as follows:

(1)

In the nonlinear seismic response of intake tower structures, the correlation of the maximum acceleration response at the top and the lateral deformation curvature at the base with duration parameters is higher than that of the top displacement response. Among the three duration parameters, the acceleration response and the lateral deformation curvature response of the intake tower under near-fault seismic motion show a higher degree of correlation with uniform duration, while the top displacement response shows a higher correlation with significant duration.

(2)

The correlation analysis between the nonlinear seismic response of intake tower structures and six composite intensity parameters reveals that the acceleration response at the top of the intake tower and the lateral deformation curvature response at the base exhibit a higher correlation with PGA-related composite intensity parameters, whereas the top displacement response shows a higher correlation with PGV-related composite intensity parameters. All three types of seismic responses of the intake tower under seismic effects show significant correlation with the uniform-duration-related composite intensity parameters, suggesting that for seismic responses under near-fault seismic motion, the use of uniform-duration-related composite intensity parameters is more suitable for characterizing near-fault seismic motion features.

(3)

Future research could explore the application of the duration-dependent composite parameter method to different types of structures beyond intake towers, such as high-rise buildings or bridges, to verify its broader applicability. Additionally, another promising direction involves integrating advanced computational techniques like machine learning to more accurately predict seismic responses. This approach may entail training models on extensive earthquake data, thereby revealing deeper insights into the complex dynamics of earthquake–structure interactions.