Seismic design and analysis of a high-rise self-centering wall building: Case study

Abstract

Post-tensioning self-centering walls are a well-developed and resilient technology. However, despite extensive research, the application of this technology has previously been limited to low-rise buildings. A ten-story self-centering wall building has now been designed and constructed using the state-of-art design methodologies and construction detailing, as described in this paper. The building is designed in accordance with direct displacement-based design methodology, with modification of seismic demand due to relevant issues including higher-mode effects, second order effects, torsional effects, and flexural deformation of wall panels. Wall sections are designed with external energy-dissipating devices of steel dampers, and seismic performance of such designed self-centering walls is evaluated through numerical simulation. It is the first engineering project that uses self-centering walls in a high-rise building. The seismic design procedure of such a high-rise building, using self-centering wall structures, is comprehensively reviewed in this work, and additional proposals are put forward. Description of construction detailing, including slotted beams, flexible wall-to-floor connections, embedded beams, and damper installation, is provided. The demonstration project promotes the concept of seismic resilient structures and contributes to the most appealing city planning strategy of resilient cities at present. The paper could be a reference for industry engineers to promote the self-centering wall systems worldwide.

Graphical abstract

Keywords

self-centering wall / post-tensioned precast concrete wall / seismic resilient structure / high-rise building / seismic design / engineering practice

1 Introduction

Prefabricated seismic resilient structures represent a leading trend in development of new-generation buildings. Various types of seismic resilient structural systems have been proposed and their low-damage characteristics were studied extensively. A combination of prefabrication techniques, extraordinary seismic performances, and rapid and low-cost post-earthquake recovery, enables such structural systems to be at the forefront of civil engineering development, leading to new engineering accomplishments.

The self-centering post-tensioning rocking wall structure is a well-developed resilient system. The initial conceptualization of rocking and self-centering structures can be traced back to the middle of the 20th century [1]. It was found, during Chilean Earthquakes, that stability of rocking structures during earthquakes was better than conventionally designed structures [1] and later this design concept was introduced more widely in the field of structural engineering.

The self-centering wall is composed of a reinforced concrete shear wall panel and vertically integrated unbonded post-tensioned prestressing steel strands. The constraint between the wall panel and the foundation is released, and the restoring forces that come into play during an earthquake are provided by self-weight of wall panels and the post-tensioning force. Seismic behaviors of such structural systems have been found to be excellent, with only minor damage at the wall toe even at large lateral drifts. There has been extensive research on self-centering walls since it was first tested by Pampanin et al. [2] in the 1990s, in the PRESSS program. For a common self-centering wall system, velocity-correlated or displacement-correlated energy dissipation devices were usually installed, such as viscous dampers or mild steel dampers, to enhance energy-dissipating ability of the system. As for acceleration-correlated dampers, seismic response reduction using inertial mass dampers has also been shown to be efficient in recent studies [3].

As for the seismic design for self-centering wall structures, geometrical nonlinearity due to rotational movement of the wall bottom makes the conventional force-based design (FBD) method unfeasible for predicting seismic resistance during earthquakes. In the newer design, the structural lateral deformation is dominated by such rotational movement and can be predetermined using simplified assumptions, and thus the direct displacement-based seismic design (DDBD) method [4] is generally adopted. Research has found that DDBD could substantially reduce construction cost without sacrificing seismic performance of the structure. Design standards or guidelines have also been proposed in New Zealand [2] and the USA [5,6].

The publication of the design standards resulted in engineering application of self-centering wall systems. In New Zealand, more than ten buildings using self-centering wall systems have been built in high seismicity area, including the first multi-story precast prestressed concrete structure, Alan MacDiarmid Building in Victoria University, Wellington, and the Southern Cross Hospital [7–9] that survived during the 2010/2011 Christchurch Earthquakes.

To verify system-level seismic behavior of self-centering wall systems, as well as to develop efficient and reliable connections between components, a full-scale shaking table test of a two-story low-damage self-centering wall structure was conducted in The State Key Laboratory of Disaster Reduction in Civil Engineering in Tongji University [10–13] as part of a collaborative research project between the International Joint Research Laboratory of Earthquake Engineering (ILEE) and the New Zealand Centre for Earthquake Resilience (QuakeCoRE), as shown in Fig.1. The test was extremely successful with the low-damage design target achieved very well. A demonstration engineering practice project of high-rise seismic resilient structures was conducted following the ILEE-QuakeCoRE shaking table test in China. The project included three ten-story buildings, and two of them utilized self-centering wall systems, as shown in Fig.2. The seismic design methodology of self-centering wall system and several connection technologies for the test building were incorporated in these two demonstration buildings.

Due to the lack of relevant engineering practice regarding seismic resilient structures in high-rise buildings, the objective of this paper is to systematically review and summarize the design procedure of high-rise self-centering wall buildings and present their essential construction detailing. The paper could be a reference for industry engineers for promotion of self-centering wall systems worldwide.

2 Seismic design of high-rise self-centering wall buildings

The seismic design procedure for high-rise buildings with self-centering wall structures can be systematically summarized in a flowchart as shown in Fig.3. The major design process requires determination of seismic demand for structural components, the section design of self-centering wall panels, and the construction detailing. Since the scope of this paper is mainly focused on the feasibility of self-centering wall structures in high-rise buildings, relevant topics such as higher-mode effects, second order effects, torsional effects, and flexural deformation of wall panels are highlighted. Iteration of seismic design is required, with multiple seismic performance indices checked according to the flowchart. Finally, construction detailing including configuration of slotted beams, flexible wall-to-floor connections, embedded beams and damper installation is described in this paper, to provide guidance to engineering practice.

2.1 Performance levels

The DDBD method is generally adopted for seismic design of self-centering wall structures, and thus the code-regulated inter-story drift limits are selected as the seismic design targets. Seismic design of structures in China generally follows a three-level design procedure [14], requiring an appropriately designed structure aimed at: first, resulting in no damage during minor earthquakes, second, being repairable after moderate earthquakes, and, third, having enough ductility for collapse prevention during major earthquakes. Return periods of the three levels of earthquakes are 50, 475, and 2475 years, respectively. However, self-centering wall structures are considered to possess a low-damage seismic performance, and thus can be utilized to protect the system from extremely high earthquakes. A fourth level of seismic fortification has also been proposed with a return period of 10000 years in Standard for Seismic Isolation Design of Building (GB/T 51408-2021) [15]. Maximum seismic influential factor representing seismic intensity is used in the Chinese seismic code, Code for Seismic Design of Buildings (GB 50011-2010) [14], and is defined as the ratio between the peak value of seismic acceleration response spectrum and the gravitational acceleration g. The maximum seismic influential factors for each seismic intensity level are summarized in Tab.1. The corresponding seismic fortification targets for structures under various levels of earthquakes are summarized in Tab.2.

The target inter-story drift of 2% is adopted for seismic design of self-centering wall structures, for the collapse-prevention limit state under mega earthquakes, as suggested by Zhou et al. [16,17]. In addition, the inter-story drift limit for the structure under minor earthquakes is selected as 0.1%, which is identical to the limit for conventional concrete walls in accordance with GB 50011-2010 [14].

2.2 Self-centering index and equivalent damping ratio

DDBD requires iteration and equivalent damping ratio serves as the control parameter. In consideration of the external or internal damping devices added to wall panels, damping ratio of the structural system is not equal to the 5% as regulated in the Chinese code [14], but should be preliminarily predicted through empirical formulas, and later checked with the designed results.

The measurement of self-centering ability, as well as the major influential factor of equivalent viscous damping for self-centering wall structural systems, is the self-centering index λ, which is a feature extracted from the typical flag-shaped hysteresis curves of such structures. Defined in Eq. (1), λ is the ratio of moment contribution for lateral resistance provided by prestressing strands M_pt and vertical loads M_n to that of steel dampers M_D. To achieve a self-centering seismic performance, the contribution of energy-dissipating devices M_D, especially of those utilizing elastoplastic mechanical behaviors such as mild steel, should be limited from the total moment resistance composed of M_pt, M_n, and M_D. A maximum limit value of M_D/(M_pt + M_n + M_D) ≤ 40% is recommended by both PRESSS Design Handbook [2] and ACI ITG-5.1-07 [5], indicating a reasonable range of λ ≥ 1.5. Smith and Kurama [18] also suggested a range of 1.1–2.0 for self-centering index λ, whose lower bound is close to the range λ ≥ 1.15 specially regulated for self-centering wall structures with damping devices of mild steel in the New Zealand code NZS 3101:2006 [19]. Consequently, the range of 1.5 ≤ λ ≤ 2.0 is used in this paper for a conservative seismic design.

(1)\lambda =\frac{M_{\mathrm{p}\mathrm{t}}+M_{\mathrm{n}}}{M_{\mathrm{D}}}.

With the self-centering index determined, the equivalent damping ratio can be approximately predicted. In the case of self-centering walls with mini-sized buckling restrained braces (mini-BRBs), the equivalent damping ratio ξ_eq can be calculated using the interpolation empirical Eq. (2) [20], which takes into consideration both the contribution of the systematic elastic damping (5%), and the reduced contribution (67%) of the hysteretic damping of reinforced concrete walls (28%) using post-tensioning techniques.

(2){\xi }_{\text{eq}}=\frac{\lambda }{\lambda +1}5\mathrm{\%}+\frac{1}{\lambda +1}28\mathrm{\%}\cdot 0.67.

2.3 Single-degree-of-freedom equivalence considering higher-mode effects

Relative deformation of self-centering wall structures tends to be concentrated at the bottom joints between wall panels and the foundation. That is, the opening and closure of the horizontal joints, and the lateral deformation of superstructures are generally regarded as rigid-body rotation about the wall base. A linear pattern of the lateral deformation curve is usually selected for self-centering wall structures for simplification, and thus the target displacement of each story can be calculated from its relative height above the foundation multiplied by the target inter-story drift of 2%.

According to the current Chinese code JGJ 3-2010 [21], a ten-story residential building belongs to the category of high-rise buildings. The linear pattern of a lateral deformation curve may underestimate the inter-story drift of upper stories that is induced by elastic deformation of wall panels as well as higher-mode effects for high-rise buildings. Since the lateral deformation assumption is essential in DDBD, the deformation curve of high-rise self-centering wall buildings needs to be clarified.

The combined vibration mode is composed of a rotational mode, denoted as Mode 0, which is generally selected as the linear pattern of rigid-body rotation about the wall base, and the intrinsic vibration modes of wall panels (Modes 1, 2, 3, …), i.e., the modes calculated through modal analysis for the structure with conventionally designed fixed-base wall panels. The rotational mode and the first three intrinsic vibration modes of a self-centering wall building are illustrated in Fig.4.

The period of the rotational mode is calculated based on the equivalent stiffness at the target drift of the structure, which can be taken as the corresponding secant gradient from the moment-base rotation curve of self-centering walls. The participation factor {\gamma }_j of the jth vibration mode should be calculated according to Eq. (3), where x_ji is the modal displacement of mass point i in the jth vibration mode, n is the number of mass points, and m_i is the lumped mass of mass point i.

(3){\gamma }_j=\frac{{\displaystyle \sum _{i=1}^n{m}_i{x}_{ji}}}{{\displaystyle \sum _{i=1}^n{m}_i{x}_{ji}^{\text{2}}}}.

The equivalent displacement Δ(T_j, ξ_j) of the jth vibration mode is calculated according to Eq. (4). Δ(T_j, 5%) is the displacement corresponding to the period T_j on the displacement spectrum of a SDOF system with a damping ratio of 5%, and ξ_j is the damping ratio or equivalent damping ratio of the jth vibration mode. The displacement X_i of mass point i in the combined vibration mode can thus be calculated with Eq. (5).

(4)\mathrm{\Delta }\left(T_j,{\xi }_j\right)=\mathrm{\Delta }\left(T_j,5\mathrm{\%}\right){\left(\frac{0.07}{0.02+{\xi }_j}\right)}^{0.5},

(5)X_j=\sqrt{\sum _{j=0}^{n^{\prime }}{\left({\gamma }_j\mathrm{\Delta }\left(T_j,{\xi }_j\right)x_{ji}\right)}^2}.

The occurrence of the maximum inter-story deformation of the combined vibration mode can be determined, and the corresponding maximum modal inter-story drift should be amplified with a coefficient D to reach the target inter-story drift of 2%. The target displacement of each story can be obtained by multiplying the combined vibration mode by the coefficient D.

The equivalent SDOF system for the structure is determined using Eqs. (6)–(8) [4]. Δ_d, m_e, and H_e are the target displacement, equivalent mass, and equivalent height of the SDOF system, respectively. Δ_i and H_i are the target displacement and the height of the ith floor to the wall base.

(6){\mathrm{\Delta }}_{\text{d}}=\sum _{i=1}^n(m_i{\mathrm{\Delta }}_i^{\text{2}})/\sum _{i=1}^n(m_i{\mathrm{\Delta }}_i),

(7)m_{\text{e}}=\sum _{i=1}^n(m_i{\mathrm{\Delta }}_i)/{\mathrm{\Delta }}_{\text{d}},

(8)H_{\text{e}}=\sum _{i=1}^n(m_i{\mathrm{\Delta }}_i{H}_i)/\sum _{i=1}^n(m_i{\mathrm{\Delta }}_i).

2.4 Seismic demand of the lateral-resistant system

The acceleration spectrum of an SDOF system with an elastic damping ratio of 5% can be calculated for the level of mega earthquakes, according to the current Chinese code [14], as shown in Fig.5. The reduced displacement spectrum is shown in the same figure, through Eq. (4) based on the equivalent damping ratio. Both figures are plotted on a log-log scale. The period corresponding to the target displacement is then selected as the equivalent period.

The equivalent stiffness K_eq, base shear force V_d and base moment M_d of the equivalent SDOF system at the target displacement are calculated as per Eqs. (9)–(11) [4]. T_eq is the equivalent period calculated in the previous step.

(9)K_{\text{eq}}=m_{\text{e}}\cdot 4{\text{π}}^2/T_{\text{eq}}^{\text{2}},

(10)V_{\mathrm{d}}=K_{\mathrm{e}\mathrm{q}}{\mathrm{\Delta }}_{\mathrm{d}},

(11)M_{\mathrm{d}}=V_{\mathrm{d}}{H}_{\mathrm{e}}.

Specially, for high-rise buildings, if the condition of θ_s > 0.1 is satisfied, see Eq. (12), the second order effect produced by the overturning moment of gravity loads cannot be neglected, and thus the design base shear force should be modified according to Eq. (13).

(12){\theta }_{\mathrm{s}}=\frac{m_{\mathrm{e}}g{\mathrm{\Delta }}_{\mathrm{d}}}{V_{\mathrm{d}}{H}_{\mathrm{e}}},

(13)V_{\mathrm{d}}^{\prime }=\frac{V_{\mathrm{d}}}{1-{\theta }_{\mathrm{s}}}.

2.5 Load demand to wall panels

The vertical loads exerted on the wall panels are composed of self-weight and the vertical loads transmitted through the floor systems. The inertial force sustained by each wall panel should be determined based on the representative structural mass within its corresponding floor area. The allocation of design base shear forces and base moments follow the same pattern as inertial forces, and thus can be calculated for each wall panel.

2.6 Modification considering torsional effects

The plane torsion induced by occasional eccentricity during earthquakes is recommended to be taken into account, especially for high-rise buildings. For buildings whose mass and stiffness are approximately uniformly and symmetrically distributed, a simplified method can be adopted for calculating the torsional effects. The occasional eccentricity, e_i, calculated as 5% of the plane length, is assumed for the centroid of each story, and the additional base torque M_T is calculated as in Eq. (14).

(14)M_{\mathrm{T}}=V_{\mathrm{d}}^{\prime }{e}_{\mathrm{i}}.

The additional base torque of the building can be conservatively assumed to be resisted by the outermost structural members on the perimeter and allocated based on the polar moments of inertia. By dividing half of the plane length by the number of wall panels, the additional base shear force can be calculated, contributing to modification of the design base shear force and base moment.

2.7 Modification considering elastic lateral deformation

Although the higher-mode effects are incorporated into the lateral deformation pattern, such comprehensive effects of elastic deformation cannot guarantee the seismic behaviors at any moment under seismic action. Therefore, additional elastic deformation may be considered to protect the structure, reasonably conservatively, from excessive lateral drifts, especially for tall buildings. The additional elastic lateral deformation of self-centering wall panels is calculated in a simplified way using the assumption of a cantilever beam, with the design base shear force acting at the equivalent height of the wall panel. Gross-section flexural rigidity EI is used and the maximum elastic inter-story drift θ_el,max can be calculated using Eq. (15).

(15){\theta }_{\mathrm{e}\mathrm{l},max}=\frac{V_{\mathrm{d}}^{\prime }{H}_{\mathrm{e}}^2}{2EI}.

3 Application of direct displacement-based seismic design method to a ten-story building

3.1 Building description

A demonstration high-rise building, a ten-story precast concrete shear wall building has been constructed in Haiyan of Zhejiang Province, China, and serves as a residential building inside a prefabrication factory. Seismic precautionary intensity is Intensity 6 with a design basic acceleration of 0.05g in accordance with the current Chinese code GB 50011-2010 [14]. The site soil is classified into Group 1 of Site Class III and so the characteristic period is 0.45 s. The construction site was evaluated as an unfavorable section for seismic deign, and the seismic influence coefficient for the horizontal direction was raised from 0.04 to 0.065 at the level of minor earthquakes in accordance with the evaluation report of seismic safety for engineering sites [14].

The building has a plan of 35.1 m × 13.5 m and a total height of 40.5 m, with each story 3.0 m high, as shown in Fig.6 and Fig.7. The building also has a 4.0 m high locally extruded functional room on the top and a 6.5 m high basement. The total height of the self-centering wall panels is 30 m and sleeve grouted connections are used for the horizontal joints between the upper and lower wall panels. Two different structural schemes are adopted for two directions of the building; conventional precast shear wall structure is used along the longitudinal direction, while a self-centering wall structure is used along the transverse direction. As shown in Fig.6, two self-centering wall panels are used on Grids 1, 4, 7, and 10 respectively. Wall panels on each axis are connected with slotted beams that can be regarded as pin connection at beam ends. The details of the slotted beams are discussed in Subsection 4.2. The self-centering walls are also separated from the adjacent flanges of conventional reinforced concrete walls with isolated vertical joints, which are reserved vertical gaps filled with flexible materials. A flexible wall-to-floor connection is utilized along the transverse direction in order to accommodate the displacement incompatibility between the wall and the floor due to the relative constraints of rotation and vertical movement. The design details of the self-centering wall system along the transverse direction are discussed hereafter.

3.2 Design assumptions

The following assumptions were adopted for calculation of seismic design.

1) Seismic action was considered in the orthogonal directions. Seismic action along the transverse direction was solely carried by the self-centering wall systems.

2) The floor system was connected to wall panels in the transverse direction using flexible connections so the wall seismic action along the transverse direction was distributed according to the allocated floor area of each wall.

3) The slotted beam ends were assumed to be pin connections with no bending moment resistance.

3.3 Seismic demand

As the initial assumption, the moment contribution of damping devices M_D was selected as 60% of M_pt + M_n, i.e., self-centering index λ = 1.67, and the corresponding equivalent damping ratio was calculated as 8.9%. Target displacement of each story of the structure was calculated with and without the consideration of higher-mode effects, and the compared results can be found in Tab.3 and Tab.4.

As compared in Tab.4, only minor differences of the target displacement can be found between the cases with and without higher-mode effects. This may be attributed to the higher-mode effects for a ten-story building not being significant. The 1st intrinsic vibration mode has a period much smaller than the rotational mode, so the combined vibration mode is still dominated by the rotational mode. For taller buildings, the intrinsic periods elongate, and the correlation between intrinsic vibration modes and the rotational mode might be stronger.

For subsequent calculation, higher-mode effects were considered; the target displacement was 417.4 mm, the equivalent mass was 1875.8 t, and the equivalent height was 21.0 m. The target displacement of 417.4 mm only slightly exceeded the maximum value of the displacement spectrum at 6 s, as can be seen in Fig.5, and consequently the equivalent period was selected as 6 s. Through Eqs. (9)–(13), the design base shear force of the case building was calculated as 1494.7 kN.

Within the structural layout of the case building, conventional reinforced concrete walls along the longitudinal direction served as the main load bearing members for vertical loads, and the flexible joints between self-centering walls and floor slabs were not intentionally designed for transfer of shear forces. Therefore, the self-centering walls were considered to only sustain their self-weights in the vertical direction. The vertical load exerted on each self-centering wall panel was calculated as N_w = 680.4 kN.

The plan layout of the case building is shown in Fig.8. Eight self-centering wall panels were arranged along 4 axes in the transverse direction. According to the aforementioned allocation rules, the design base shear force and base moment were calculated as 124.5 kN and 2615.7 kN·m for self-centering wall panels on Grids 1 and 10, respectively. For wall panels on Grids 4 and 7, the calculated shear and bending moment are 249.1 kN and 5231.5 kN·m, respectively. The sketch of self-centering wall panels for calculation and seismic design is shown in Fig.9.

The length-to-width ratio of the structural plan was 2.6, and the torsional effect was considered accordingly. The additional base torque of the case building was 2623.2 kN·m. Through calculation, 51.9% of the base torque was resisted by the self-centering wall panels along Grids 1 and 10, as 1361.5 kN·m. Divided by half the plane length and the number of wall panels, the additional base shear force was calculated as 19.4 kN for each wall panel, and thus the design base shear force of self-centering wall panels along Grids 1 and 10 was modified to 143.9 kN, with the base moment increased to 3023.3 kN·m.

The maximum elastic inter-story drifts of wall panels on Grid 1/Grid 10 and Grid 4/Grid 7 are 0.071% and 0.12%, respectively. As a consequence, the elastic inter-story drift around 0.1% was deducted from the target drift of 2%, and the section design of wall panels was based on the target angle of 1.9% for rigid-body rotation about the wall base.

4 Section design and construction detailing

4.1 Section design

The design of self-centering wall sections focuses on adequately choosing material properties, determining section dimensions, as well as arranging prestressing strands and damping devices, so that the base moment of the designed wall panel at the target base rotation angle can meet the requirement of the design base moment.

The calculation assumption of “plane section remains plane” is still approximately adopted at horizontal opening joint and sectional equilibrium of force and moment is iteratively balanced. The methodologies of sectional equilibrium have previously been well developed for the design of self-centering wall sections. Detailed design flowchart or design examples can be referenced from Refs. [2,18], and the calculation method of confined concrete can be found in Ref. [22]. Shear failure of wall panels and interfacial shear slip at the bottom joints should be prevented, and was checked according to Ref. [23]. Configuration of cross ties should be designed in accordance with GB 50011-2010 [14], and four pieces of rolled steel are suggested to be mounted on the perimeter of wall toes of each wall panel for protection and better rotation performances.

The section design results of wall panels along Grid 1/Grid 10 and Grid 4/Grid 7 for the demonstration project are summarized in Tab.5–Tab.8. The section details of self-centering wall panels are illustrated in Fig.10.

4.2 Construction detailing

The full-scale shaking table test of a two-story post-tensioned wall building, conducted by the QuakeCoRE and the ILEE, has provided remarkable state-of-the-art engineering experience on construction detailing, for post-tensioned reinforced concrete structures with a low-damage design philosophy [12]. Such configurations include slotted beams, flexible wall-to-floor connections, and installation of energy-dissipating devices. Their seismic performances have been shown to be exceptionally advantageous for self-centering wall structures. The demonstration building was configured with similar construction detailing in accordance with the physical tests.

4.2.1 Slotted beams

The slotted beams utilized in the ILEE shaking table test are shown in Fig.11(a). The longitudinal reinforcement at the bottom of the beam was not extended into the vertical load bearing components (frames or walls), and two slots were reserved at both ends of the beam. With such a configuration, the center of rotation was shifted to the hinge of the slotted beam, and thus the relative rotational deformation was accommodated by opening and closing of the slots, so that the elongation effect of beams under lateral loads was significantly reduced. To increase the energy-dissipating ability of the system, dampers are suggested to be installed at the beam ends, where large relative deformation can be experienced. Possible choices include installation of dampers using the embedment as shown in Fig.11(a), or extension of bottom reinforcement of the beam into the wall panel, through which the mild steel within the end slots can yield and thereby dissipate energy. The shear at beam ends was resisted by the shear hangers that were diagonally installed at beam−column interface.

The shaking table test results showed excellent seismic performance of the slotted beams. No significant seismic cracking or damage was observed on the beams and the frame columns, and only slight spalling of cover concrete occurred at the top of the beam ends. Vertical slip and torsional rotation were not experienced at beam ends, indicating reliable shear resistance of the shear hangers. The engineering practice of the demonstration building was designed accordingly and is shown in Fig.11(b). No external dampers were installed at beam ends as self-centering walls could sufficiently resist lateral earthquake effects, so the slotted beam was calculated as a simply supported beam. The vertical loads were composed of self-weight and a small vertical load transferred from the floor systems through the flexible connection; no additional moments were considered at their connections to self-centering wall panels. Only moment resistance at the middle section and shear resistance at end sections, as well as detailing requirements of reinforcement anchorage, were checked for the beam [14].

4.2.2 Flexible wall-to-floor connection

The construction detailing of flexible wall-to-floor connections was tested in the ILEE project, and the joint configuration is shown in Fig.12(a). Since the double-tee slabs were used to compose the floor system, the diaphragm rigidity was high and measures were taken to reduce its deformation constraints on the self-centering wall panels. Between the floor and the wall panel, a link slab was used so that the deformation incompatibility between such structural components could be accommodated during earthquakes. The link slab was composed of a piece of wooden plank and a thin layer of superimposed cast-in situ concrete. The configuration was designed so that, during earthquakes, it would be sufficient to transfer in-plane diaphragm loads. Large relative deformation was expected at the link slab due to its low rigidity, and the constraints of floor systems to self-centering wall panels could thus be reduced correspondingly.

The results of the shaking table test show that, with the flexible wall-to-floor connections, the out-of-plane deformation of the link slab matched the uplift of the wall base at its contacting surface to the wall panel. This suggests that the relative deformation was concentrated at the link slab, which is consistent with the test phenomena whereby distributed cracks were found at the link slab, while the double-tee slabs remained undamaged. The flexible wall-to-floor connection minimized the structural damage to a reparable level, and it also helped to reduce the overstrength of wall panels induced by the out-of-plane diaphragm effect of the floor systems. As for the demonstration building, precast prestressed hollow core slabs were used to construct the floor system, and they added to the diaphragm rigidity. Consequently the flexible wall-to-floor connection was applied, as shown in Fig.12(b). The link slab used for the flexible wall-to-floor connection was 600 mm wide, composed of the 20 mm-thick wooden plank and the 120 mm-thick superimposed reinforced concrete layer. The longitudinal reinforcement within the superimposed concrete layer was extended and anchored into the composite floor systems and the self-centering walls, to enhance integrity of the connection.

4.2.3 Embedded beams

The configuration of the inter-story connection of self-centering wall panels served as the main difference between the ILEE project and the demonstration building. Instead of the inter-story connection beams shown in Fig.12(a), embedded beams were designed within each wall panel for the demonstration building, as shown in Fig.12(b). Such a configuration was intended to compose an integrated structural joint to connect inter-story wall panels using extruded tendons and sleeves, as well as to connect wall panels to slotted beams with longitudinal reinforcement and shear hangers. It can be concluded from Fig.11 and Fig.12 that the incorporation of embedded beams into the precast concrete component of wall panels could not only reduce the amounts of precast elements and structural joints, but could also enable a more convenient inter-story connection of wall panels and thus facilitate construction efficiency. Section analysis was performed at the joints between adjacent wall segments at the target inter-story drift, to arrange connection reinforcement and protect the inter-story joints from opening during earthquakes. Self-centering precast concrete walls with multiple rocking joints have previously been researched by Wu and Zhou [24], but this technology was not used in this engineering practice.

4.2.4 Damper installation

Damping devices are suggested to be installed at the locations with expected large relative deformation during earthquakes, e.g., at the bottom joints of wall panels, or at the ends of the slotted beams. Steel fuses were utilized at the bottom joints of wall panels in the ILEE shaking table tests, and its seismic performance matched the design expectation to protect the structure from excessive lateral deformation through hysteretic energy dissipation induced by its elastoplastic deformation. The configuration of the steel damper used in the demonstration building is shown in Fig.13. The top section of the basement load-bearing wall was enlarged, not only to provide a reliable rocking interface for self-centering walls, but also to enable the installation of external steel dampers. Yield forces of the dampers were used for design and verification of connection details between dampers and wall panels or the foundation (basement wall). The dampers were fixed through binding bolts and steel plates at the top and were anchored at the bottom using steel plates and anchor bolts. However, it is worth noting that the connections of both ends were designed as one-way hinges, to release possible out-of-plane constraints due to structural deformation in the orthogonal directions. Dowels, anchor bolts, weld joints, as well as strength of steel plates were checked, and relative slip between such connectors was prevented, since that could diminish the energy dissipation ability of steel dampers.

For detailed damper installation of the demonstration building, two dampers were installed at one side of each wall panel for Grid 1/Grid 10 at base, while two dampers were installed at the bottom on both sides of each wall panel for Grid 4/Grid 7, due to the increased seismic energy dissipation demand.

5 Numerical simulation

5.1 Quasi-static pushover analysis

The finite element analysis software OpenSees was utilized for seismic behavior verification of the designed self-centering walls. Detailed modeling techniques can be found in Ref. [25], with elastic beam/column elements applied for main body of the wall panel, and fiber sections adopted at wall base, as shown in Fig.14. Prestressing strands and steel dampers were both simulated using truss elements with Steel02 material for simplification, and the wall concrete was simulated with Concrete02 material.

The pushover analysis results of wall panels along Grid 1/Grid 10 and Grid 4/Grid 7 are plotted in Fig.15(a) and 15(b), respectively. The base moments at the target base rotation angle of 1.9% are 3377 and 6481 kN·m for wall panels along Grid 1/Grid 10 and Grid 4/Grid 7, respectively, satisfying the design requirements for load bearing capacities.

As mentioned above, the equivalent damping ratio had to be checked against the initial assumption of 8.9%. The base moment-base rotation angle diagrams of the wall panels under cyclic loads are shown in Fig.16, and the simplified theoretical flag-shape hysteretic rules are plotted for comparison. The equivalent damping ratios of wall panels along Grid 1/Grid 10 and Grid 4/Grid 7 were calculated as 8.5% and 8.6%, respectively, which are consistent with the initial assumption, indicating that the iterative design process eventually converged. Still, further optimization of seismic design for this kind of nonlinear building structures with passive dampers can be carried out subsequently, referring to relevant studies [26, 27].

5.2 Dynamic time history analysis

Time history analysis was performed for self-centering walls. Lateral deformation of self-centering walls under minor earthquakes was checked so that damage could be avoided, corresponding to a maximum inter-story drift limit of 0.1%. Also maximum inter-story drifts of wall panels under mega earthquakes were checked against the design target of 2%. 10 natural seismic records from NGA-West2 of PEER [28] and 4 manually generated artificial seismic records were selected, since the characteristic period of site should be increased by 0.05 s for time history analysis of higher levels of earthquakes, i.e., mega earthquakes, as regulated by the current Chinese code GB 50011-2010 [14]. Information of seismic records is summarized in Tab.9, and comparison of acceleration spectra is shown in Fig.17.

The elastic time history analysis results for inter-story drifts under minor earthquakes are summarized in Fig.18, and the elastoplastic time history analysis results under mega earthquakes are listed in Fig.19. As shown in Fig.18 and Fig.19, the maximum inter-story drift did not occur at the top of the wall panel, which indicated that wall panels of such an aspect ratio were indeed influenced by higher-mode effects. Wall panels along Grid 1/Grid 10 and Grid 4/Grid 7 had similar amounts of lateral deformation when subjected to earthquakes of the same intensity, indicating deformation compatibility between structural members within the building. Deformation of wall panels along Grid 1/Grid 10 was slightly smaller than that of wall panels along Grid 4/Grid 7 as the occasional eccentricity-induced base torque was not considered during the plane model design, and thus the load bearing capacities of such wall panels were underutilized.

Maximum inter-story drifts of wall panels along Grid 1/Grid 10 and Grid 4/Grid 7 under minor earthquakes were 0.04% and 0.05%, satisfying the drift limit of 0.1%. Maximum inter-story drifts under mega earthquakes were 0.3% and 0.4%, respectively, which are smaller than the target drift of 2%. This is attributed to the fact that the response spectrum regulated by the current Chinese code GB 50011-2010 [14] conservatively describes structural responses of SDOF systems, and thus is inconsistent with the DDBD philosophy.

The lateral deformation of the structure under wind loads was also checked, with the maximum inter-story drift calculated as 0.03%, satisfying the requirement of 0.1% by the current Chinese code JGJ 3-2010 [21]. For resilience evaluation of high-rise buildings, further details can be found in Ref. [29] and are beyond the scope of this paper.

6 Conclusions

The seismic design procedure of high-rise buildings with self-centering wall structures is systematically proposed in this paper. Distinctive features of high-rise buildings including higher-mode effects, second order effects, torsional effects, and flexural deformation of wall panels are considered in the design of the building. The construction detailing including configuration of slotted beams, flexible wall-to-floor connections, embedded beams and damper installation is presented. The demonstration high-rise building in Zhejiang Haiyan is able to achieve a four-level seismic behavior target, i.e., “no damage under minor and moderate earthquakes, reparable after major earthquakes, and no collapse under mega earthquakes”, verified through quasi-static and dynamic numerical analysis. The demonstration project is the first one using self-centering wall systems. The project promotes the concept of seismic resilient structures and contributes to city planning strategy of resilient cities.

References

[1] Housner G W. The behavior of inverted pendulum structures during earthquakes. Bulletin of the Seismological Society of America, 1963, 53(2): 403–417

[2] PampaninSMarriottDPalermoA. PRESSS Design Handbook. Auckland: New Zealand Concrete Society, 2010

[3] Takewaki I, Murakami S, Yoshitomi S, Tsuji M. Fundamental mechanism of earthquake response reduction in building structures with inertial dampers. Structural Control and Health Monitoring, 2012, 19(6): 590–608

[4] PriestleyM J NCalviG MKowalskyM J. Displacement-Based Seismic Design of Structures. Pavia: IUSS Press, 2007

[5] ACIITG-5.1-07. Acceptance Criteria for Special Unbonded Post-Tensioned Precast Structural Walls Based on Validation Testing. Farmington Hills, MI: American Concrete Institute, 2007

[6] ACIITG-5.2-09. Requirements for Design of a Special Unbonded Post-Tensioned Precast Shear Wall Satisfying ACI ITG-5.1 and Commentary. Farmington Hills, MI: American Concrete Institute, 2009

[7] Kam W Y, Pampanin S. The seismic performance of RC buildings in the 22 February 2011 Christchurch earthquake. Structural Concrete, 2011, 12(4): 223–233

[8] BuchananA HBullDDhakalRMacRaeGPalermoAPampaninS. Base Isolation and Damage-Resistant Technologies for Improved Seismic Performance of Buildings. Research Report 2011-02. 2011

[9] InternationalFederation for Structural Concrete. Precast-Concrete Buildings in Seismic Areas. FIB Bulletin No. 78. 2016

[10] ZhouYGuALuYSongGHenryRRodgersG. Large-scale shaking table experimental study on a low-damage self-centering wall building. China Civil Engineering Journal, 2020, 53(10): 62 (in Chinese)

[11] Gu A, Zhou Y, Henry R S, Lu Y, Rodgers G W. Simulation of shake-table test for a two-story low-damage concrete wall building. Structural Control and Health Monitoring, 2022, 29(10): e3038

[12] Henry R S, Zhou Y, Lu Y, Rodgers G W, Gu A, Elwood K J, Yang T Y. Shake-table test of a two-storey low-damage concrete wall building. Earthquake Engineering & Structural Dynamics, 2021, 50(12): 3160–3183

[13] Lu Y, Henry R S, Zhou Y, Rodgers G W, Yang Q, Gu A. Data set for a shake-table test of a 2-story low-damage concrete wall building. Journal of Structural Engineering, 2022, 148(7): 04722002

[14] GB50011-2010. Code for Seismic Design of Buildings. Beijing: China Architecture & Building Press, 2016 (in Chinese)

[15] GB/T51408-2021. Standard for Seismic Isolation Design of Building. Beijing: China Planning Press, 2021 (in Chinese)

[16] ZhouYGuA Q. Displacement-based seismic design of self-centering shear walls under four-level seismic fortifications. Journal of Building Structures, 2019, 40(3): 118–126 (in Chinese)

[17] ZhouYWuHGuA. Earthquake engineering: From earthquake resistance, energy dissipation, and isolation to resilience. Engineering Mechanics, 2019, 36(6): 1–12 (in Chinese)

[18] SmithBKuramaY. Seismic Design Guidelines for Special Hybrid Precast Concrete Shear Walls. Research Report NDSE 2012-02. 2012

[19] NZS3101:2006. Concrete Structures Standard—The Design of Concrete Structure. Wellington: Standards New Zealand, 2006

[20] TwigdenK M. Dynamic response of unbonded post-tensioned concrete walls for seismic resilient structures. Dissertation for the Doctoral Degree. Auckland: University of Auckland, 2016

[21] JGJ3-2010. Technical Specification for Concrete Structures of Tall Building. Beijing: China Architecture & Building Press, 2010 (in Chinese)

[22] Mander J B, Priestley M J N, Park R. Theoretical stress–strain model for confined concrete. Journal of Structural Engineering, 1988, 114(8): 1804–1826

[23] Yang B, Lu X. Displacement-based seismic design approach for prestressed precast concrete shear walls and its application. Journal of Earthquake Engineering, 2018, 22(10): 1836–1860

[24] WuHZhouY. Parametric study on seismic performance of self-centering precast concrete walls with multiple rocking joints. In: Proceedings of the 17th World Conference on Earthquake Engineering. Tokyo: Japan Association for Earthquake Engineering, 2020, 2c-0159

[25] Gu A, Zhou Y, Xiao Y, Li Q, Qu G. Experimental study and parameter analysis on the seismic performance of self-centering hybrid reinforced concrete shear walls. Soil Dynamics and Earthquake Engineering, 2019, 116: 409–420

[26] Takewaki I, Akehashi H. Comprehensive review of optimal and smart design of nonlinear building structures with and without passive dampers subjected to earthquake loading. Frontiers in Built Environment, 2021, 7: 631114

[27] Akehashi H, Takewaki I. Bounding of earthquake response via critical double impulse for efficient optimal design of viscous dampers for elastic-plastic moment frames. Japan Architectural Review, 2022, 5(2): 131–149

[28] PEER. PEER Ground Motion Database. Berkeley: University of California, 2020

[29] Akehashi H, Takewaki I. Resilience evaluation of elastic-plastic high-rise buildings under resonant long-duration ground motion. Japan Architectural Review, 2022, 5(4): 373–385

RIGHTS & PERMISSIONS

Higher Education Press