Study on the Energy Distribution and Dissipation of High-Rise Structures Under Long-Period Ground Motions

Abstract

Seven groups of long-period ground motions (LPGMs) and three groups of ordinary ground motions (OGMs) were selected and bidirectionally input into a high-rise structure; the energy distribution and dissipation characteristics of the structure were studied comparatively. The results show that at the same seismic level, the input energy of the structure under LPGMs is significantly greater than that under OGMs. Under OGMs, the structure mainly dissipates energy through damping the energy, while under LPGMs, hysteretic energy becomes the main way of energy dissipation. During an 8-degree frequent earthquake, coupling beams are the main energy dissipation members, the floors below 2/3 of the structural height mainly dissipate hysteresis energy by coupling beams, with the hysteretic energy ratio ranging from 61% to 99.9%, and the floors above 2/3 of the structural height mainly dissipate hysteretic energy by frame beams. During 8-degree design and rare earthquakes, the hysteretic energy ratio of coupling beams significantly decreases, and frame beams are the main energy-dissipating members; the hysteresis energy on the first to second floors is mainly dissipated by shear walls, while on floors above the third floor, the hysteresis energy is mainly borne by frame beams, the hysteretic energy ratio from the fifth to the twelfth accounts for 56% to 89%, and above the twelfth floor accounts for more than 85% to 90% on that floor.

1. Introduction

When a major earthquake of magnitude six or above occurs, due to the different propagation paths of ground motions, long-period ground motions (LPGMs) are prone to be generated in sedimentary basins far from the epicenter [1]. High-rise buildings, being typical long-period structures, are susceptible to resonance-like effects with LPGMs, leading to severe damage. The 1985 M8.1 Michoacan earthquake [2], the 2004 M7.3 Kii peninsula earthquake [3], the 2008 M8.0 Wenchuan earthquake [4], and the 2011 M9.0 East Japan earthquake [5] all resulted in seismic damage to high-rise structures caused by LPGMs. For example, during the Wenchuan earthquake, high-rise structures in Xi’an, located 700 km from the epicenter, experienced intense shaking with widespread cracking in masonry infill walls and pipeline embedded in the walls and damage to the materials on both sides of the top of seismic joints. Therefore, scholars have conducted extensive study on the seismic behavior of high-rise structures under LPGMs. The analyses show that LPGMs can amplify the seismic response of high-rise structures, and the indicators such as the overturning moment, base shear force, inter-story drift angle, floor displacement, and floor acceleration are significantly larger than those under ordinary ground motions (OGMs) [6,7,8,9,10,11]. However, the existing studies primarily focus on the comparative analysis of internal force, deformation of high-rise structures, and rarely involve energy indicators.

The impact of earthquakes on high-rise structures is essentially a process of energy input and dissipation in the structures due to ground motions. Structures dissipate seismic input energy primarily through their own damping (damping energy dissipation) and elastic–plastic deformation (hysteretic energy dissipation). Compared to single-bearing capacity or displacement indicators, energy indicators used to analyze the structural dynamic response can better evaluate the seismic performance and reveal the damage mechanism of structures [12]. Currently, scholars have conducted extensive research on the energy response of high-rise structures. References [13,14,15] analyzed the influence of ground motion characteristics and structural dynamic characteristics on the energy distribution and dissipation of high-rise structures; references [16,17,18] discussed the distribution ratio and mode of hysteretic energy among various members and along the structural height and proposed a reasonable structural energy dissipation mechanism. However, the aforementioned studies mostly focused on OGMs and rarely considered the impact of LPGMs.

The analysis results show that both horizontal ground motions recorded at the same station may be LPGMs. The “Technical specification for concrete structures of tall building” points out that bidirectional or tridirectional ground motion inputs should be used for the elastic–plastic time-history analysis of high-rise structures. In fact, regardless of whether the high-rise structure is regular or not, the seismic behavior of the structure differs significantly under bidirectional ground motions compared to unidirectional excitation [9]. However, unidirectional input of LPGMs was used in most previous research, and the energy response of high-rise structures under bidirectional LPGMs has hardly been mentioned, which urgently needs further research. In view of this, seven groups of LPGMs and three groups of OGMs were selected and bidirectionally input into a high-rise structure for elastic–plastic time-history analysis, and the energy distribution and dissipation characteristics of the structure under different types of ground motions were studied comparatively, revealing the distribution rules of energy among various members and along the floor height, making up for the current energy research on high-rise structures that neglects LPGMs and bidirectional input. It is expected to provide scientific support for the seismic design of high-rise structures under LPGMs.

2. Structural Analysis Model

SRC frame–RC core tube structures exhibit excellent strength and deformation compatibility, along with superior seismic performance, and are thus widely applied in high-rise structures. Based on the current Chinese structural design codes, a 36-story SRC frame–RC core tube high-rise structure was designed using YJK software (Version 4.0). The structure has a story height of 4.0 m and a total height of 144 m; the standard floor plan is shown in Figure 1. The seismic fortification intensity of the site where the structure is located is 8-degree (0.2 g), which is equivalent to VIII degree in the international intensity scale, the design earthquake group is Class three, and the site category is Class II. The dead load is 5.0 kN/m² for floors and 6.0 kN/m² for the roof, the live load is 2.0 kN/m², the basic wind pressure is 0.5 kN/m², and the ground roughness is Class C. For SRC columns and RC core tube walls, the concrete strength grades are C60 (1st to 12th floors), C50 (13th to 24th floors), and C40 (25th to 36th floors). The concrete strength grade of beams and slabs is C30. The structural steel skeleton is made of Q345 steel, and the reinforcing steel is made of HRB400 steel. The thickness of slabs is 120 mm, and the height of coupling beams is 800 mm with a shear-span ratio of 3.75. The cross-sectional dimensions and reinforcement of RC beams, SRC columns, and shear walls are shown in

Table 1. Section dimensions and reinforcement of RC beams.

Floor Number	Member	Dimension (mm × mm)	Left End	Mid-Span	Right End
1–12	X-axis Marginal Frame Beam	400 × 900	6C25	2C25 + 2C22	4C25 + 2C22
	Y-axis Marginal Frame Beam	400 × 900	4C25 + 4C22	4C25	4C25 + 4C20
	X-axis Internal Frame Beam	400 × 900	9C25	6C25	10C25
	Y-axis Internal Frame Beam	400 × 900	12C25	7C25	12C25 + 2C20
	Secondary Beam	300 × 600	8C25	3C25 + 2C22	2C25
13–24	X-axis Marginal Frame Beam	400 × 900	6C25	2C25 + 2C22	4C25 + 2C20
	Y-axis Marginal Frame Beam	400 × 900	4C25 + 4C22	4C25	4C25 + 4C20
	X-axis Internal Frame Beam	400 × 900	9C25	5C25 + 2C22	11C25
	Y-axis Internal Frame Beam	400 × 900	11C25	6C25 + 2C22	12C25 + 3C22
	Secondary Beam	300 × 600	4C25 + 4C22	5C25	4C25
25–36	X-axis Marginal Frame Beam	400 × 900	5C25	4C22	4C25 + 1C20
	Y-axis Marginal Frame Beam	400 × 900	4C25 + 4C20	2C25 + 2C22	4C25 + 2C22
	X-axis Internal Frame Beam	400 × 900	4C25 + 4C25	6C25	11C25
	Y-axis Internal Frame Beam	400 × 900	9C25	6C25 + 2C22	12C25 + 2C22
	Secondary Beam	300 × 600	8C25	5C25	2C25

,

Table 2. Section dimensions and reinforcement of SRC Columns.

Section Dimension	Floor Number	Longitudinal Reinforcement	Steel Skeleton
	1–12	24C25	2H900 × 600 × 35
	13–24	4C25 + 16C22	2H700 × 400 × 25
	25–36	4C22 + 12C20	2H500 × 300 × 20

and

Table 3. Thickness and section reinforcement of shear walls.

Floor Number	Wall Thickness (mm)	Horizontal Reinforcement	Vertical Reinforcement	Number of Reinforcement Layers
1–5	800	C14@150	C14@150	4
6–12	800	C14@200	C14@200	4
13–24	700	C14@150	C14@150	3
25–36	600	C14@200	C14@200	3

, respectively.

Nonlinear analysis software Perform-3D (Version 7) is used for structural modeling and dynamic elastic–plastic analysis. During the structural modeling process, concrete in areas with dense stirrup reinforcement, such as the reinforced zone of beam and column ends and edge confinement zones of shear walls, is considered as confined concrete and the Mander constitutive model is used; concrete in areas with less stirrup reinforcement is considered as unconfined concrete, and the stress–strain relationship curve of concrete under uniaxial compression given in the “Code for design of concrete structures” is adopted. Bilinear elastic–plastic constitutive relationships without a descending section of steel skeleton and reinforcement is modeled, and RC beams, SRC columns, connecting beams, and shear walls are simulated using a fiber element model. The plastic deformation of RC beams and SRC columns under seismic action is mainly concentrated at the ends, and the plastic zone model of “fiber section segment + elastic section + fiber section segment” is adopted; since coupling beams are prone to shear plastic behavior, the plastic zone model of “fiber section segment + elastic section + shear hinge + elastic section + fiber section segment” is adopted, and the calculation of shear hinge follows the ASCE41 code.

To validate the reliability of the finite element model for the high-rise structure, the comparative analyses of structural mass and seismic response were carried out using Perform-3D and YJK software. The ground motion NBI000 from the 1994 Northridge earthquake was input into the structure for time-history analysis when the PGA was adjusted to 400 gal. The calculated results were summarized in

Table 4. Comparison of seismic behavior of high-rise structures.

Software	Mass (t)	Maximum Inter-story Drift Ratio	Weak Floors	Maximum Top Floor Displacement (mm)	Base Shear Force (kN)
Perform-3D (Version 7)	69,922	0.0067	27	546	66,780
YJK (Version 4.0)	70,052	0.0071	28	617	74,307
Error	0.19%	5.63%	-	11.51%	10.13%

. Results indicate a negligible discrepancy of only 0.19% in structural mass. Differences in the maximum inter-story drift ratio, top floor displacement, and base shear are 5.63%, 11.51%, and 10.13%, respectively. Furthermore, the identified locations of the weak stories are generally consistent. These findings collectively demonstrate a high degree of similarity in the nonlinear structural performance. It can thus be concluded that the structural model developed in Perform-3D is reliable.

The natural vibration periods and vibration mode characteristics corresponding to the first six vibration modes of the structure are shown in

Table 5. Natural vibration period and vibration mode characteristics of high-rise structures.

Natural Vibration Period (s)	T1	T2	T3	T4	T5	T6
	3.352	2.951	2.495	0.907	0.844	0.819
Vibration Mode Characteristics	Y-direction First-order Translation	X-direction First-order Translation	Z-direction First-order Torsion	Y-direction Second-order Translation	X-direction Second-order Translation	Z-direction Second-order Torsion

. The fundamental period, T₁ = 3.352 s > 5T_g = 2.25 s, indicates that the structure belongs to a typical long-period structure; the ratio of the first torsional period to the first translational period, T_t/T₁ = 2.495/3.352 = 0.74 < 0.85, suggests that the structural layout is reasonable and does not lead to excessive torsional effects.

3. Selection and Characteristics of Long-Period Ground Motions

Currently, the selection of ground motions typically follows criteria including matching site categories and aligning the elastic acceleration response spectrum of ground motions with the code-specified design response spectrum (hereinafter referred to as the “design response spectrum”) within certain frequency ranges. However, the conventional design response spectrum fails to adequately account for the distinctive features of LPGMs, as manifested by the relatively small characteristic period of the design response spectrum, the relatively small response spectrum values in the long-period range, and the failure to reflect the “double-peak” characteristics of the LPGMs’ response spectrum [19,20]. Therefore, it is inappropriate to select LPGMs with the design response spectrum as the matching target. According to the analysis results of LPGMs’ response spectrum, the response spectrum (hereinafter referred to as “fitted response spectrum”) that can reflect the characteristics of LPGMs is fitted [20,21]. Reference [21] used the genetic algorithm to fit the long-period ground motion response spectra one by one, providing the suggested values of the corresponding spectral parameters and verifying the rationality of the suggested spectral parameter values. The fitted response spectrum is adopted to select LPGMs in this paper.

Given that the structural example in this paper is located in the site of Class II, and the soil properties of the Class II site are relatively similar to those of the Class C site, as classified by the U.S. NEHRP code, 32 groups of LPGMs on the Class II site or the Class C site from the Wenchuan earthquake, Tokachi earthquake, and East Japan earthquake were selected by using the selection principles recommended in reference [22,23]. Then, each ground motion was scaled to the peak acceleration (PGA) of 70 gal, and its elastic acceleration response spectrum was calculated. The fitted response spectrum was derived according to the LPGMs’ response spectrum and spectral parameters proposed in reference [20]. Finally, seven groups of LPGMs were selected based on the criteria that the average acceleration response spectrum value both in the period range of [0.1, T_g] and at the period T₁ remain within a 20% deviation from the fitted response spectrum. To analyze comparatively the difference in the energy response of high-rise structures, three groups of OGMs were selected. Although the number of ground motions is limited, the selected ground motions are highly representative, and the characteristic differences between two types of ground motions can be clearly contrasted.

The ground motions were input bidirectionally. For each group, the horizontal ground motion whose acceleration response spectrum value is closest to the fitted or design response spectrum at T₁ was input along the structural Y-axis; the other horizontal ground motion was input along the structural X-axis. In accordance with the “Code for seismic design of buildings”, the PGA of ground motions was scaled with a ratio of the Y-axis to X-axis of 1:0.85. Detailed information of the selected ground motions is provided in

Table 6. Detailed information of selected ground motions.

Type of Ground Motion	No.	Earthquake Name	Recording Station	Ground Motion	PGA (cm/s2)	PGV (cm/s)	Input Direction
Long-Period Ground Motion	1	Wen chuan	14HTG	14HTG-NS	16.47	7.56	Y
				14HTG-EW	16.13	7.34	X
	2		62QSY	62QSY-NS	17.18	5.45	Y
				62QSY-EW	18.08	7.37	X
	3		62CJA	62CJA-NS	13.19	5.83	Y
				62CJA-EW	12.24	7.67	X
	4	Tokachi	HKD130	HKD130-NS	56.16	13.74	Y
				HKD130-EW	51.41	16.39	X
	5	East Japan	AKT013	AKT013-EW	28.59	8.17	Y
				AKT013-NS	44.20	7.23	X
	6		CHBH16	CHBH16-EW	11.83	9.38	Y
				CHBH16-NS	10.52	4.54	X
	7		HKD083	HKD083-NS	14.34	5.51	Y
				HKD083-EW	13.31	8.14	X
Ordinary Ground Motion	8	Kobe	MZH	MZH090	52.38	4.83	Y
				MZH000	69.65	4.44	X
	9	Kocaeli	Eregli	ERG180	89.69	15.15	Y
				ERG090	106.06	10.96	X
	10	Northridge	Newport Bch-Irvine	NBI000	41.24	4.14	Y
				NBI090	60.72	5.25	X

.

The average acceleration amplification factor β spectra of the selected ground motions are shown in Figure 2. Compared to OGMs, the predominant periods of LPGMs obviously move backward, and the acceleration response spectrum values in the medium-to-long-period segment obviously increase with slow attenuation. Based on the HHT method, the energy characteristics of ground motions were further analyzed. The analysis reveals that the energy of LPGMs is concentrated in the narrow low-frequency range of 0.09 Hz to 3.1 Hz, while the energy of OGMs is dispersed in the broad mid-to-high-frequency range of 0.6 Hz to 6.7 Hz. Through the structural modal analysis, it is found that the frequencies of the first three modes that contribute significantly to the dynamic response of the structure are 0.30 Hz, 0.34 Hz, and 0.40 Hz, all of which are within the frequency distribution range of the main energy of LPGMs. Therefore, the selected LPGMs contain more frequency components that are prone to resonate with high-rise structures and can reflect the impact of LPGMs on the energy response of high-rise structures.

4. Input Energy and Energy Distribution of High-Rise Structures Under Long-Period Ground Motions

The energy calculation equation of a structure under seismic action is as follows:

E_I = E_K + E_D + E_E + E_H

(1)

where E_I, E_K, E_D, E_E, and E_H represent the input energy, kinetic energy, damping energy, elastic strain energy generated by elastic deformation, and hysteretic energy generated by elastic–plastic deformation of the structure, respectively.

From Equation (1), the total energy input into the structure is partly stored in the form of kinetic energy E_K and elastic strain energy E_E, while the other portion is dissipated through damping energy E_D and hysteretic energy E_H.

The PGA of each ground motion input along the structural Y-axis was adjusted to 70 gal, 200 gal, and 400 gal, which correspond to the levels of the 8-degree frequent earthquake, design earthquake, and rare earthquake in the “Code for seismic design of buildings”, respectively, and the PGA of each ground motion input along the structural X-axis was correspondingly adjusted to 59.5 gal, 170 gal, and 340 gal, respectively. Elastic–plastic time-history analysis was performed to comparatively study the input energy and its distribution of high-rise structures under bidirectional LPGMs and OGMs.

4.1. Input Energy of High-Rise Structures

Table 7. Input energy E_I of high-rise structure (×10⁴ kN·m).

Type of Ground Motion	Ground Motion Record	8-Degree Frequent Earthquake		8-Degree Design Earthquake		8-Degree Rare Earthquake
		EI	Average Value	EI	Average Value	EI	Average Value
Long-Period Ground Motion	14HTG	7.37	5.30	55.97	44.86	153.03	139.04
	62QSY	4.97		37.46		104.16
	62CJA	4.27		49.66		138.08
	HKD130	4.96		30.23		79.67
	AKT013	3.59		24.51		81.40
	CHBH16	3.30		37.97		185.66
	HKD083	8.65		78.24		231.27
Ordinary Ground Motion	MZH	0.47	0.39	1.69	1.70	5.32	5.26
	ERG	0.27		1.27		4.35
	NBI	0.44		2.13		6.10

presents the calculation results of the input energy of high-rise structures under two types of ground motions. It can be found that

(1)

At the same seismic level, the input energy of the high-rise structure under the same type of ground motions has a certain difference, but the degree of dispersion is small. According to the mathematical statistics of input energy, the coefficients of the variation in input energy under LPGMs and OGMs are 0.35 to 0.39 and 0.14 to 0.22, respectively, which are within the acceptable range of the structural seismic research, indicating that the input energy of the high-rise structure is relatively stable, and the average value can be analyzed.

(2)

At the same seismic level, the input energy of high-rise structures under LPGMs is significantly greater than that under OGMs. During an 8-degree frequent earthquake, 8-degree design earthquake, and 8-degree rare earthquake, the average input energy of high-rise structures under LPGMs is 13.59 times, 26.38 times, and 26.43 times that under OGMs, respectively.

(3)

At different seismic levels, the input energy of high-rise structures increases significantly as the PGA increases. When the PGA increases from 70 gal to 200 gal and 400 gal, the average input energy under LPGMs is 8.46 times and 26.23 times that of 70 gal, respectively, and the average input energy under OGMs is 4.36 times and 13.49 times that of 70 gal, respectively.

4.2. Input Energy Distribution in High-Rise Structures

Hysteretic energy E_H refers to the energy dissipated through the elastic–plastic deformation of a structure and is directly correlated with the cumulative structural damage. When the input energy is constant, the more hysteretic energy there is, and the more serious the damage degree of the structure may be. Damping energy E_D is the energy consumed by the damping of the structure. If the damping can dissipate a significant portion of the input energy, the structure may not be damaged or only suffer minor damage. Therefore, the proportion of hysteretic energy and damping energy in the total input energy, i.e., hysteretic energy dissipation ratio E_H/E_I and damping energy dissipation ratio E_D/E_I, can better reflect the energy distribution and damage status of the structure. E_H/E_I and E_D/E_I of the high-rise structure under two types of ground motions at different seismic levels are shown in

Table 8. E_H/E_I and E_D/E_I of high-rise structures.

Type of Ground Motion	Ground Motion Record	8-Degree Frequent Earthquake		8-Degree Design Earthquake		8-Degree Rare Earthquake
		EH/EI	ED/EI	EH/EI	ED/EI	EH/EI	ED/EI
Long-Period Ground Motion	14HTG	0.264	0.692	0.478	0.512	0.464	0.529
	62QSY	0.217	0.742	0.437	0.549	0.458	0.536
	62CJA	0.215	0.719	0.489	0.502	0.455	0.539
	HKD130	0.260	0.656	0.418	0.560	0.443	0.537
	AKT013	0.094	0.849	0.354	0.631	0.468	0.525
	CHBH16	0.175	0.763	0.503	0.482	0.542	0.449
	HKD083	0.300	0.676	0.461	0.525	0.467	0.524
Ordinary Ground Motion	MZH	0	0.596	0.025	0.779	0.123	0.798
	ERG	0	0.584	0.148	0.697	0.332	0.597
	NBI	0	0.506	0.117	0.718	0.206	0.683

.

It can be seen that

(1)

Under LPGMs, the coefficients of variation of E_H/E_I for the structure during an 8-degree frequent earthquake, 8-degree design earthquake, and 8-degree rare earthquake are 0.289, 0.105, and 0.064, respectively, and the coefficients of variation of E_D/E_I are 0.083, 0.085, and 0.057, respectively. All of them are less than 0.3, and the majority are less than 0.1, indicating that the results have a small degree of dispersion and good robustness.

(2)

During an 8-degree frequent earthquake, the E_H/E_I of high-rise structures under OGMs is 0, and the structure remains elastic without plastic damage, while the structure enters the elastic–plastic state under LPGMs, generating a certain amount of E_H, with the E_H/E_I ranging from 0.094 to 0.3 and an average of 0.218. The E_H/E_I is not large, indicating the structural damage is not serious, mainly relying on E_D.

(3)

During an 8-degree design earthquake, the high-rise structure has a certain degree of plastic damage under the two types of ground motions. The E_H and E_D of the structure under OGMs account for more than 80% of the input energy, but the E_H/E_I is not large, with a maximum of no more than 0.15 and an average of only 0.097, which is far less than the E_D/E_I. At this time, the damage development of high-rise structures is not sufficient. Under LPGMs, the E_H and E_D of high-rise structures jointly dissipate more than 94% of the input energy, and the E_H/E_I significantly increases, with an average of 0.449, which is 4.63 times that of OGMs. Hysteretic energy gradually becomes the main way of energy dissipation.

(4)

During 8-degree rare earthquake, the plastic development of high-rise structures under two types of ground motions further deepens. The average E_H/E_I of the structure under LPGMs is 0.471, which is slightly higher than that during 8-degree design earthquake and approximately 2.14 times that of OGMs, demonstrating that the plastic damage development of the structure under LPGMs is more extensive. In comparison, it is found that the E_D/E_I under OGMs is significantly greater than the E_H/E_I, and damping the energy remains the main way of energy dissipation, while the structure mainly relies on E_H and E_D under LPGMs.

(5)

Under LPGMs, from an 8-degree frequent earthquake to design earthquake, the E_H/E_I of high-rise structures increases rapidly, with an increase range of 1.61 to 5.99 times, indicating that the plastic deformation of the structure increases rapidly, and the structure resists input energy through severe damage to various members. From an 8-degree design earthquake to rare earthquake, the E_H/E_I increases only 1.05 times; the plastic development amplitude of the structure decreases. Meanwhile, the increase in the damping ratio caused by structural damage reduces the increase in the E_H/E_I.

5. Distribution of Hysteretic Energy Dissipation in High-Rise Structures Under Long-Period Ground Motions

The damage degree of a high-rise structure not only depends on the magnitude of hysteretic energy E_H but is also closely related to the distribution of E_H among structural members and floors. When the same amount of E_H is distributed in different members and floors in different proportions, the seismic performance and damage degree of high-rise structures may be significantly different. Building upon the energy calculation results in Section 4, the distribution laws of E_H among structural members and floors under two types of ground motions were further studied.

5.1. Distribution of Hysteretic Energy Dissipation Among Structural Members of High-Rise Structures

The hysteretic energy E_H of high-rise structures is mainly dissipated by frame beams, coupling beams, shear walls, and SRC columns. The distribution of the total hysteretic energy among various members is represented by the ratio, which is the hysteretic energy of various members to the total hysteretic energy of the structure.

Figure 3 lists the distribution ratio of E_H among various members of high-rise structures under LPGMs during an 8-degree frequent earthquake. The high-rise structure is still in the elastic stage under OGMs and does not generate E_H, so it is not analyzed here. It can be observed that, under LPGMs, SRC columns and shear walls remain elastic, while frame beams and coupling beams have entered the elastic–plastic stage and dissipated the hysteretic energy. Among them, coupling beams account for approximately 55% to 90% of the total hysteretic energy, serving as the primary energy-dissipating members, and frame beams dissipate the remaining E_H. Further analysis shows that the coupling beams yield and dissipate energy first during an earthquake. Although the quantity is not large, the coupling beams dissipate an average of about 78% of the total hysteretic energy, protecting the other members from damage and acting as the first line of defense for structural seismic resistance. Therefore, specific measures should be incorporated in the structural design to improve the energy dissipation capacity of coupling beams.

Figure 4 lists the comparison of the distribution ratio and average value of E_H among various members of high-rise structures under two types of ground motions during 8-degree design earthquake. Under OGMs, SRC columns and shear walls remain elastic, and the structure mainly relies on frame beams and coupling beams to dissipate hysteretic energy. Coupling beams are the main energy dissipation members, accounting for an average of 64% of the total hysteretic energy, while frame beams contribute a smaller proportion, averaging 36%. Under LPGMs, the proportion of E_H by frame beams significantly increases, ranging from 72% to 86%, with an average of 80%, becoming the primary energy-dissipating members; the proportion of E_H by coupling beams notably decreases, accounting for only 9% to 27%. As the seismic action increases, the bending moment borne by shear walls increases, and shear walls enter the elastic–plastic stage, beginning to dissipate a certain amount of E_H, but the proportion is small, averaging about 3.5% and not exceeding 9%; SRC columns remain elastic. The analysis suggests that the plastic deformation of the structure under LPGMs is relatively large, and the inter-story drift angle exceeds the elastic–plastic inter-story drift angle limit of 1/100. As the first line of seismic defense, coupling beams first yield and dissipate hysteretic energy. However, due to the small number, the energy consumption capacity of coupling beams is limited. At this time, frame beams, through the full development of their own plastic performance, take on a larger proportion of hysteretic energy, forming the second line of seismic defense in the structure, while the plastic development of shear walls is not yet deep, and the proportion of E_H is very small.

Figure 5 lists the comparison of the distribution ratio and average value of E_H among various members of the high-rise structure under two types of ground motions during an 8-degree rare earthquake. Under OGMs, SRC columns and shear walls basically remain elastic, and the E_H of the structure is mainly dissipated by frame beams and coupling beams. Among them, the E_H of coupling beams and frame beams account for approximately 34% to 63% and 37% to 65% of the total hysteretic energy, respectively, with relatively balanced proportions of total hysteretic energy. Under LPGMs, SRC columns almost remain elastic, while frame beams bear the vast majority of the E_H, accounting for 76% to 88% of the total hysteretic energy, and are the main energy-dissipating members; the proportion of E_H of coupling beams in the total hysteretic energy greatly decreases, which is only 3%~14%; and the proportion of E_H of shear walls in the total hysteretic energy increases, ranging from 5% to 20%, with an average energy dissipation proportion slightly larger than that of the coupling beams, gradually becoming an important energy dissipation member in the structure. The reason is that, as the PGA increases, the seismic action and bending moment borne by shear walls under LPGMs significantly increase, and the wall limbs gradually yield and fully develop, dissipating significantly more hysteretic energy, and the proportion of E_H in the total hysteretic energy accordingly increases.

The average E_H ratio of various members of high-rise structures under two types of ground motions from an 8-degree frequent earthquake to rare earthquake is as shown in Figure 6. Under OGMs, the hysteretic energy is mainly dissipated by coupling beams and frame beams; with the increase in the PGA, the average energy dissipation ratio of coupling beams gradually decreases from 64% to 36%, and the average energy dissipation ratio of frame beams gradually increases from 36% to 62%, while the shear walls and SRC columns basically remain elastic. Under LPGMs, the hysteretic energy is mainly dissipated by coupling beams, frame beams, and shear walls. The coupling beams yield and dissipate energy first, as the PGA increases, the average energy dissipation ratio of the coupling beams decreases rapidly from 78% to 6.5%; the average energy dissipation ratio of frame beams increases rapidly, which bears about 80% of the E_H and is the main energy dissipation member, with relatively serious damage; and the proportion of E_H of shear walls increases gradually, taking about 10%, while SRC columns remain basically elastic. This is because when the PGA is small, the seismic action borne by the structure is small, the plastic development of the structure is not sufficient, and the hysteretic energy is mainly dissipated through the coupling beams; with the increase in the PGA, the seismic action borne by the structure also increases, resulting in the continuous development of plastic damage and a significant increase in the total hysteretic energy of the structure. Since the number of coupling beams is small and the E_H of coupling beams is limited, more hysteretic energy is transferred to the frame beams, causing the proportion of E_H by frame beams to increase rapidly. Due to the continuous increase in seismic action and the bending moment, the E_H of shear walls increases gradually, and the energy dissipation ratio increases accordingly. In general, multiple anti-seismic lines of coupling beams, frame beams, and shear walls under two types of ground motions are formed, realizing the failure mechanism of “strong columns and weak beams” and “strong walls and weak coupling beams”. This failure mechanism orderly dissipates seismic energy, maximizing the integrity and anti-collapse capacity of the structure. In structural design, it is necessary to further optimize the energy dissipation capacity of coupling beams (for example, using replaceable energy-dissipating devices for coupling beams) and also ensure that frame beams have a sufficient and stable energy-dissipating capacity to undertake the energy-dissipating task once coupling beams exit the load-bearing system.

Under LPGMs, during an 8-degree frequent earthquake, design earthquake, and rare earthquake, the coefficients of variation in the proportion of E_H by coupling beams are 0.196, 0.348, and 0.439, respectively, while those of frame beams are 0.671, 0.065, and 0.045, respectively. Generally, the coefficients of variation are mostly less than 0.5, which is within the acceptable range of structural energy response research, indicating that the hysteretic energy distribution of the structure is relatively stable and has low dispersion. However, the proportion of E_H by frame beams during an 8-degree frequent earthquake reaches 0.671 with relatively high dispersion. In engineering practice, this uncertainty can be reasonably handled by increasing the number of ground motions. During an 8-degree rare earthquake, shear walls dissipate a certain hysteretic energy, and the coefficient of variation in the proportion of E_H is 0.481, showing good robustness.

5.2. Distribution of Hysteretic Energy Dissipation of Members Along the Floors of High-Rise Structures

5.2.1. Hysteretic Energy Dissipation Distribution of Members Along the Floors Under the 8-Degree Frequent Earthquake

Figure 7 shows the distribution of the E_H of coupling beams and frame beams along the floors under LPGMs during an 8-degree frequent earthquake, that is, the ratio of E_H of coupling beams and frame beams on each floor to the total hysteretic energy of coupling beams and frame beams, respectively.

Under LPGMs, the E_H ratio of coupling beams increases rapidly from the bottom to the upper floors, reaching the maximum value at the sixth to eighth floors, approximately 6% to 8% of the total hysteretic energy of coupling beams; thereafter, the E_H ratio of coupling beams rapidly decreases with the rise in the floor, and approaches zero near the thirtieth floor. The E_H of coupling beams under LPGMs is mainly concentrated in the lower floors. The E_H ratio of frame beams increases gradually from the bottom to the upper floors, reaching the maximum value at about floor 12, approximately 3% to 5% of the total hysteretic energy of frame beams; thereafter, the E_H ratio of frame beams decreases slowly with the rise in the floor, reaching about 1.5% to 2% at the top of the structure. Overall, the energy dissipation of frame beams under LPGMs is relatively evenly distributed among floors, other than the bottom.

To more clearly understand the distribution of E_H along the floors of high-rise structures under LPGMs, Figure 8 presents the distribution of the average ratio of E_H of coupling beams, frame beams, and floor structures on each floor to the total hysteretic energy of the structure along the floors. It can be seen that under LPGMs, the E_H of the structure first increases and then decreases with the rise in floors. The E_H ratio is relatively high from the 4th to the 16th floors, all above 4%, reaching the maximum of 5.1% at the 8th floor. The E_H of each floor below 2/3 of the structure mainly depends on coupling beams, and the E_H ratio is 61% to 99.9% of the floor hysteretic energy, while the E_H of each floor above 2/3 of the structure gradually depends on the frame beams.

5.2.2. Hysteretic Energy Dissipation Distribution of Members Along the Floors Under the 8-Degree Design and Rare Earthquake

As mentioned earlier, during the 8-degree design earthquake and rare earthquake, the high-rise structure primarily dissipates hysteretic energy through frame beams, coupling beams, and shear walls under LPGMs, while the structure mainly relies on frame beams and coupling beams under OGMs. Figure 9 and Figure 10 present the distribution of the E_H of frame beams, coupling beams, and shear walls along the floors under two types of ground motions under the 8-degree design and rare earthquake, respectively, that is, the ratio of the E_H on each floor to the total hysteretic energy of each member.

It can be seen that the distribution of E_H of frame beams, coupling beams, and shear walls along the floors is roughly the same under LPGMs during 8-degree design and rare earthquakes:

(1)

As the floor increases, the E_H ratio of the frame beams gradually increases, reaching the maximum value between the 18th and 22nd floors, accounting for approximately 3.5% to 5% of the total hysteretic energy of frame beams. Thereafter, as the floors increase, the E_H ratio of the frame beams begins to decrease slowly, reaching about 1.5% to 2.5% at the top floor. Overall, the E_H of frame beams is mainly concentrated in the middle and upper floors of the structure.

(2)

The E_H ratio of coupling beams increases gradually from the bottom floor upwards, reaching the maximum at the 6th to 12th floors, which is about 3.5% to 6% of the total hysteretic energy of coupling beams. Thereafter, as the floor increases, the E_H ratio of coupling beams gradually decreases, with almost no energy dissipation in floors above the 32nd. Overall, the E_H of coupling beams is mainly concentrated in the lower floors of the structure.

(3)

The E_H of the shear walls is concentrated in the first to second floors. During an 8-degree design earthquake and rare earthquake, the shear walls on the first floor dissipate the most hysteresis energy, accounting for approximately 82% and 62% of the total hysteresis energy of shear walls. As the floor rises, the E_H ratio of shear walls decreases sharply; on the second floor, there is approximately 10% and 16% of the total hysteresis energy of shear walls, respectively. Above the third floor, shear walls remain almost elastic.

The distribution of the E_H of frame beams and coupling beams along the floors under OGMs is basically the same and different from that of LPGMs during 8-degree design and rare earthquakes:

(1)

The E_H ratio of frame beams oscillates with the rise in the floor, reaching the maximum value at about the 28th to 32nd floors, and the floor with the maximum value increases significantly, showing that OGMs are more likely to excite the high-order mode response of high-rise structures. It is not difficult to find that the E_H of the middle and upper frame beams is relatively large.

(2)

The distribution of E_H of coupling beams shows significant differences. Under the ground motion MZH, the E_H ratio of coupling beams oscillates violently, and the distribution of E_H of coupling beams in each floor is very uneven; under the ground motion NBI, the E_H ratio of coupling beams first increases and then decreases with the rise in floors, and the energy dissipation distribution is relatively average. The uncertainty of the energy distribution of coupling beams may cause the uncontrollable energy distribution of other members.

To more clearly grasp the distribution of E_H along the floors of high-rise structures, Figure 11 and Figure 12, respectively, show the distribution of the average ratio of E_H of frame beams, coupling beams, shear walls, and floor structures on each floor to the total hysteretic energy of the structure along the floors under two types of ground motions during 8-degree design and rare earthquakes. It can be seen that

(1)

Under LPGMs, the E_H of the structure first decreases, then increases, and then decreases with the rise in the floor. During the 8-degree design earthquake, the 12th to 24th floors of the structure dissipate the most hysteretic energy, accounting for approximately 3.5% to 3.7%, with the 1st floor also having a relatively high hysteretic energy of about 2.7%. During the 8-degree rare earthquake, the 1st floor dissipates the most hysteretic energy, accounting for 5.8%, with the 12th to 24th floors also having relatively high hysteretic energy of about 3.0% to 3.3%.

(2)

Under LPGMs, the E_H of the first floor is mainly borne by the shear walls, which account for 87% to 93% of the total hysteretic energy on that floor. The shear walls remain almost elastic above the third floor, and the hysteretic energy is dissipated by the frame beams and coupling beams, with the frame beams being the primary energy consumption. During the 8-degree design and rare earthquake, the E_H of frame beams on each floor from the 5th to the 12th accounts for 56% to 80% and 70% to 89% of the total hysteretic energy dissipation on that floor, respectively, and above the 12th floor, it accounts for more than 85% and 90%, respectively.

(3)

The distribution of E_H under OGMs is very uneven. Under an 8-degree design earthquake, the E_H below the 18th floor is basically borne by coupling beams, accounting for 91% to 99.9% of the total hysteretic energy on each floor; with the rise in the floor, the E_H of frame beams increases gradually, and the E_H of frame beams above the 24th floor accounts for about 75% to 99% of the total hysteretic energy on each floor. Under an 8-degree rare earthquake, the E_H below the 20th floor is mainly borne by coupling beams, accounting for 59% to 99.6% of the total hysteretic energy on each floor; as the floors rise, the E_H of the floors is gradually dissipated by frame beams.

6. Conclusions

Seven groups of LPGMs and three groups of OGMs were selected according to certain principles, the PGAs of which were adjusted according to the level of 8-degree frequent, design, and rare earthquakes and were bidirectionally input into high-rise structure for elastic–plastic time-history analysis. The energy distribution and dissipation characteristics of the structure were studied comparatively. The following conclusions were drawn:

(1)

At the same seismic level, the input energy of the structure under LPGMs is significantly larger than that under OGMs, and the input energy increases significantly with the increase in PGA. Under OGMs, the average hysteretic energy of the structure is relatively small, mainly due to damping energy dissipation. Under LPGMs, the hysteretic energy gradually becomes an important way of dissipating energy; the structure mainly relies on hysteretic energy and damping energy to dissipate seismic input energy, with the dissipated energy reaching 91% to 99% of the total input energy.

(2)

Under LPGMs, the hysteretic energy of the structure is mainly dissipated by coupling beams, frame beams, and shear walls. During an 8-degree frequent earthquake, the coupling beams are the main energy dissipation members, accounting for approximately 55% to 90% of the total hysteretic energy, and frame beams dissipate the remaining hysteretic energy. During an 8-degree design earthquake, the hysteretic energy ratio of frame beams significantly increases between 72% and 86%, the hysteretic energy ratio of coupling beams significantly decreases between 9% and 27%, and shear walls start to dissipate a small proportion of hysteretic energy. During an 8-degree rare earthquake, frame beams bear the majority of hysteretic energy, the hysteretic energy ratio of coupling beams greatly reduces, and the hysteretic energy ratio of shear walls increases between 5% and 20%.

(3)

Under LPGMs, during an 8-degree frequent earthquake, the hysteretic energy of the structure first increases and then decreases with the rise in the floor. Each floor below 2/3 of the structure mainly relies on coupling beams to dissipate hysteretic energy, with the hysteretic energy ratio ranging from 61% to 99.9%, while each floor above 2/3 of the structure gradually relies on the frame beams to dissipate hysteretic energy. During 8-degree design and rare earthquakes, the hysteretic energy dissipation of the structure first decreases, then increases, and then decreases with the rise in the floor. The hysteresis energy on the first to second floors is mainly dissipated by shear walls, while on floors above the third floor, the hysteresis energy is mainly borne by frame beams.

(4)

During structural design practices under LPGMs, for the energy dissipation concentration zones of high-rise structures, the reinforcement should be strengthened and ductility construction measures should be guaranteed. For high-rise structures potentially subjected to LPGMs, since the seismic demand may far exceed the prediction based on the design response spectrum in the code, it is advisable to adopt a long-period response spectrum or conduct specialized time-history analyses in the structural design.

However, in this paper, the influence of the soil–structure interaction (SSI) was not considered, the number of ground motions selected was relatively small, and few response indicators showed certain dispersion; we will establish an overall model considering SSIs and increase the number of ground motions in subsequent studies to more comprehensively reveal the energy response laws of high-rise structures under LPGMs.