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Seismic isolation devices are usually designed to protect structures from the strong horizontal component of earthquake ground shaking. However, the effect of near-fault (NF) vertical ground motions on seismic responses of buildings has become an important consideration due to the observed building damage caused by vertical excitation. As the structure needs to maintain its load bearing capacity, using the horizontal isolation strategy in vertical seismic isolation will lead to the problem of larger static displacement. In particular, the bearings may generate large deformation responses of isolators for NF vertical ground motions. A seismic isolation system including quasi-zero stiffness (QZS) and vertical damper (VD) is used to control NF vertical earthquakes. The characteristics of vertical seismic isolated structures incorporating QZS and VD are presented. The formula for the maximum bearing capacity of QZS isolation considering the stiffness of vertical spring components is obtained by theoretical derivation. From the static analysis, it is found that the static capacity of the QZS isolation system with vertical seismic isolation components increases when the configurative parameter reduces. Seismic response analyses of the seismic isolated structure model with QZS and VD subjected to NF vertical earthquakes are conducted. The results show that seismic responses of the structure can be controlled by setting the appropriate static equilibrium position, vertical isolation period, and vertical damping ratio. Adding a damping ratio is effective in controlling the vertical large deformation of the isolator.

Seismic isolation is one of most effective control ways to protect structural systems, nonstructural systems, and content from damage due to horizontal earthquake ground motions [

Vertical seismic isolation of a base-isolated structure has gained the interest of researchers. Various kinds of vertical seismic isolation devices have been developed to mitigate earthquakes, such as the low shape factor (LSF) elastomeric bearings [

Near-fault (NF) ground motions are characterized by long-period velocity and displacement pulses [

In this paper, the characteristics of static load bearing capacity dynamic response of isolated structures with QZS under NF vertical ground motions are studied. The formula of maximum bearing capacity of quasi-zero stiffness isolation incorporating vertical seismic isolation components is theoretically derived. Subsequently, the effects of the static equilibrium position, vertical period, and damping ratio on the seismic responses for the isolated system with QZS are analyzed. Finally, comparison analyses of the QZS system and the seismic isolated system without QZS are presented to check the isolation effectiveness for the model against NF vertical ground motions.

Figure

Model of seismic isolated structure with QZS.

Model of oblique spring: (a) 3D, (b) cross section.

When it has a downward motion due to a vertical force

If the oblique spring yields axial deflection, the relationship of

Initially, the mass is held in equilibrium by the compression force of the system, which is counterbalanced by the weight of the mass. Therefore, it is necessary to meet the load bearing capacity demand for seismic isolated structures with QZS. The static property should be considered in engineering design. Define

It is rational to obtain the maximum force of vertical capacity of a seismic isolated structure with QZS by differentiating (

Setting

By substituting (

By substituting (

The nondimensional maximum force of vertical capacity of a seismic isolated structure with QZS is plotted in Figure

The nondimensional maximum force of vertical capacity of seismic isolated structures.

With a mass loaded, when the system reaches the horizontal position (

In practice, engineers need to choose a convenient angle of the oblique spring to the horizon in degrees to design the seismic isolated structure with QZS. Normally, some special degrees such as 10°, 30°, 45°, and 60° need be used to design the isolation bearing. When

Parameters for different angles.

Degree | | | |
---|---|---|---|

10 | 0.98 | 24.5 | 0.17 |

30 | 0.87 | 3.36 | 0.50 |

45 | 0.71 | 1.22 | 0.71 |

60 | 0.50 | 0.50 | 0.87 |

Figure

Seismic isolated structure model with QZS under vertical ground motion.

A time-stepping integration procedure has been applied to solve the equation of motion (

Due to the uncertainty of earthquake events, selection of ground motion records has a significant impact on the variability of the structural response. Seismic codes for seismic design of buildings have prescribed general guidelines but they do not provide specifics for selecting the type of earthquake records for nonlinear dynamic analysis. Full agreement has not yet been reached regarding the establishment of commonly accepted selection criteria for earthquake records [

Selection criteria for earthquake records are given as follows:

These motions cover a moment magnitude range from 6.0 to 7.6.

The rupture distance (closest distance from site to fault rupture plane) ranges from 0 to 10 km.

Their shear-wave velocities at the uppermost 30 m (

20 different earthquake records (Table

Near-fault pulse-like record data.

Number | Event | Station | Moment | | Mechanism | |
---|---|---|---|---|---|---|

| Loma Prieta, USA, 1989 | Saratoga-Aloha Ave., CMP | 6.9 | 8.50 | Reverse | 380.89 |

| Kocaeli, Turkey, 1999 | Izmit, IZT | 7.4 | 7.21 | Strike slip | 811.00 |

| Chi-Chi, Taiwan, 1999 | TCU089 | 7.6 | 8.88 | Reverse | 671.52 |

| Chi-Chi, Taiwan, 1999 | CHY080 | 7.6 | 2.69 | Reverse | 496.21 |

| Chi-Chi, Taiwan, 1999 | TCU049 | 7.6 | 3.76 | Reverse | 487.27 |

| Chi-Chi, Taiwan, 1999 | TCU051 | 7.6 | 7.64 | Reverse | 350.06 |

| Chi-Chi, Taiwan, 1999 | TCU052 | 7.6 | 0.66 | Reverse | 579.1 |

| Chi-Chi, Taiwan, 1999 | TCU068 | 7.6 | 0.32 | Reverse | 487.34 |

| Chi-Chi, Taiwan, 1999 | TCU075 | 7.6 | 0.89 | Reverse | 573.02 |

| Chi-Chi, Taiwan, 1999 | TCU076 | 7.6 | 2.74 | Reverse | 614.98 |

| Imperial Valley, 1979 | El Centro #4 | 6.53 | 7.05 | Strike slip | 208.91 |

| Imperial Valley, 1979 | El Centro #5 | 6.53 | 3.95 | Strike slip | 205.63 |

| Imperial Valley, 1979 | El Centro #7 | 6.53 | 0.56 | Strike slip | 201.51 |

| Imperial Valley, 1979 | El Centro #10 | 6.53 | 8.6 | Strike slip | 202.85 |

| Imperial Valley, 1979 | El Centro Differential Array | 6.53 | 5.09 | Strike slip | 202.26 |

| Loma Prieta, USA, 1989 | Los Gatos-Lexington Dam | 6.9 | 5.02 | Reverse | 1070.32 |

| Tabas, Iran, 1978 | Tabas | 7.35 | 2.05 | Reverse | 767.77 |

| Northridge, USA, 1994 | LA Dam | 6.7 | 5.92 | Reverse | 628.99 |

| Northridge, USA, 1994 | Pacoima Dam (upper left) | 6.7 | 7.01 | Reverse | 2016.33 |

| Kobe, Japan, 1995 | KJMA | 6.9 | 0.96 | Strike slip | 312 |

Elastic earthquake acceleration response spectra for 5% critical damping.

In the previous researches, the horizontal position was a static equilibrium position. But in actual design, because of the limited deformation ability and the uncertainty static estimation, the position of quasi-zero stiffness and static equilibrium is not always the same. It is essential to study the effect of static equilibrium on the seismic isolation performance of the system. The seismic responses of a base-isolated structure with different static equilibrium positions are investigated. Numerical studies are carried out using a mathematical model of the base-isolated structure to calculate the response of interest such as the peak absolute acceleration and the peak relative displacement of the isolation structure. A simplified 1-DOF model of base isolation is shown in Figure

The dynamic analysis model of a QZS isolator at a static equilibrium position.

The numerical procedure has been programmed by MATLAB software. To evaluate the performance of the system, the acceleration amplification coefficient (AAC) is an index to represent the isolation effect as follows:

Seismic responses of seismic isolated structures with QZS under vertical near-fault earthquakes are conducted to analyze the isolation effects. The comprehensive influences of static equilibrium position, vertical period, and damping ratio are investigated numerically. The length of oblique spring is

Comparison of elastic displacement versus force response curves for a seismic isolated structure with QZS: (a) Loma Prieta-Saratoga-Aloha Ave.; (b) Kocaeli-Izmit; (c) Chi-Chi-TCU089; (d) Chi-Chi-CHY080.

The effect of the static equilibrium position and vertical period on the nondimensional displacement and AACs of the system is shown in Figure

Comparison of nondimensional displacement and AAC for a seismic isolated structure with QZS (

Figure

Comparison of nondimensional displacement for a seismic isolated structure with QZS (

Figure

Comparison of AAC for a seismic isolated structure with QZS (

According to previous static and seismic response results, QZS system parameters design and seismic performance evaluation are conducted. The design chart of the QZS system is shown in Figure

The design procedures.

Substituting the given parameters into (

In order to compare the performance between the QZS system and the seismic isolated system without QZS, we consider isolating the same mass under the same external excitation conditions. Here, rubber bearings are used for the seismic isolated system without QZS. The vertical stiffness is 1683.2 kN/mm [^{2}, and the corresponding AAC is 2.80. The results presented in Figure

Comparison of ACCs for the QZS system and the seismic isolated system without QZS: (a) Loma Prieta-Saratoga-Aloha Ave.; (b) Kocaeli-Izmit; (c) Chi-Chi-TCU089; (d) Chi-Chi-CHY080.

The static and seismic response analysis results show that the seismic isolation system including QZS and vertical damper is a promising strategy in NF vertical ground motions. However, the limitation of the study is that if the rated load of the system exceeds a value, it is hard to realize a good isolation efficiency. Moreover, optimization selection of the complex parameters and superior ability on deformation and load capacity for materials of this system should be taken into account for the isolation system to obtain better isolation efficiency.

Vertical static and nonlinear time history analyses were performed to investigate the static capacity, acceleration, and displacement responses of the seismic isolated system with QZS. From the results presented in this paper, the following conclusions are drawn:

The maximum force of the vertical capacity of a seismic isolated structure with QZS is highly related to the configurative parameter, the ratio of spring stiffness, vertical stiffness, and the length of the oblique spring. For fixed vertical stiffness, the length of the oblique spring, and the ratio of spring stiffness, the maximum force of vertical capacity of a seismic isolated structure with QZS increases when the configurative parameter reduces.

The effect of static equilibrium position, vertical period, and damping ratio on seismic responses for the seismic isolated system with QZS under near-fault ground motions is significant. These studies demonstrate that the seismic isolated system with QZS can provide reasonable isolation effects to control near-fault earthquakes by designing key model parameters.

Although the investigation suggests that the QZS concept might be a promising strategy to achieve vertical seismic protection of base-isolated buildings, further detailed analysis and bearings product are needed when the rated load of the system exceeds a value.

It is noted that the analysis results presented in this paper do not consider the effects of horizontal, rocking, and rotational ground motions. These effects are likely important and studies are needed to better quantify them and develop additional methods for their consideration in analysis and design.

The analysis model in this paper is assumed to be symmetrical, without considering the eccentricity effect. It is possible to change the critical load capacity and isolation efficiency of the analysis model under vertical and horizontal ground motions simultaneously. Particularly, if the supported structure has an excessive vertical eccentricity for mass and vertical stiffness, there will be a need to control rocking responses. In addition, overturning effects can be considered when a base-isolated structure has a large length-to-width ratio.

The feasibility of the seismic isolation system presented in this paper would need to be further explored including specific details of the vertical spring, damper, and oblique springs. Due to the effects of horizontal, rocking, and rotational ground motions, methods to restrain lateral deformation and rocking angle can be further studied.

Mass of a lumped parameter model for a seismic isolated structure

The length of the oblique spring

Horizontal projection length of the oblique spring

The vertical spring stiffness and damping coefficient

Vertical displacement of a seismic isolated structure

Vertical force applied to the mass of a seismic isolated structure

The oblique spring stiffness

The angle of the oblique spring to the horizon in degrees

The axial deflection of the oblique spring

The ratio of spring stiffness

The configurative parameter of the system

Vertical seismic acceleration.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (no. 51508414), Yunnan Science Technology Department Fund Project (2016RA079), and Yunnan Provincial Department of Education Fund Project (2015Y298).