Super_High-rise_Building

SCIENCE CHINA Technological Sciences © Science China Press and Springer-Verlag Berlin Heidelberg 2011 tech.scichina.com www.springerlink.com *Corresponding author (email: luxz@tsinghua.edu.cn) • RESEARCH PAPER • October 2011 Vol.54 No.10: 2549–2560 doi: 10.1007/s11431-011-4548-0 Collapse simulation of a super high-rise building subjected to extremely strong earthquakes LU Xiao, LU XinZheng*, ZHANG WanKai & YE LiePing Department of Civil Engineering, Tsinghua University, Beijing 100084, China Received April 4, 2011; accepted July 8, 2011 In recent years, super high-rise buildings (>500 m) are developing very quickly and become an important frontier of civil en- gineering. The collapse resistance of super high-rise buildings subjected to extremely strong earthquake is a critical problem that must be intensively studied. This paper builds up a nonlinear finite element model of the tallest building in China, Shang- hai Tower (632 m), and proposes the modeling method and failure criteria for different structural elements. The dynamic char- acters of this building are then analyzed, and the possible failure modes and collapse processes due to earthquakes are pre- dicted, as well as the corresponding collapse mechanism. This work will be helpful in collapse prevention and the seismic de- sign of super high-rise buildings. super high-rise building, collapse simulation, extremely strong earthquake, finite element method Citation: Lu X, Lu X Z, Zhang W K, et al. Collapse simulation of a super high-rise building subjected to extremely strong earthquakes. Sci China Tech Sci, 2011, doi: 10.1007/s11431-011-4548-0 1 Introduction Since the completion of the world’s first super high-rise building, Taipei 101 (which has a total height exceeding 500 m) in 2004, a new wave of competition with respect to the design and construction of super high-rise buildings has started. For example, the Burj Khalifa, 828 m high, located in Dubai and completed in 2010, is currently the tallest building in the world. With the rapid economic develop- ment of China, the development of super high-rise buildings is also very rapid. Currently, there are more than 3 super high-rise buildings higher than 600 m under construction in mainland China, making it the world champion in quantity. Statistical data from the Council on Tall Buildings and Ur- ban Habitat (CTBUH) in 2010 (http://buildingdb.ctbuh.org/) indicated that there were approximately 120 super high-rise buildings higher than 300 m either completed or under con- struction in the world at the beginning of 2010. These buildings are mainly located in China, the Arab Emirates and the USA (there are 47 in China, including 3 in Taipei; 28 in the Arab Emirates and 18 in the USA). Super high-rise buildings promote the development of new structural sys- tems and novel mega-structural components. However, it is difficult to study these new systems and components using traditional experimental research methods. Therefore, the seismic safety of super high-rise buildings and, in particular, their collapse resistances to extreme ground motions, has become an important and urgent research topic. The shaking table test is a traditional method used to study or evaluate the global seismic performance of new structural systems. In 2002, Lu and Zhu [1] conducted a 1: 50-scale shaking table test of a reinforced concrete (RC) tube-in-tube high-rise building 166 m in height and evalu- ated its seismic safety in the Design Earthquake and the Maximum Considered Earthquake in Intensity 7 regions. In 2006, a 1: 50-scale shaking table test of the Shanghai World doi: 10.1007/s11431-011-4548-0 2 Lu X, et al. Sci China Tech Sci October (2011) Vol.54 No.10 Financial Center was conducted by Zou and Lu [2], and they analyzed the dynamic properties and seismic responses when the building was subjected to the Frequently Occur- ring Earthquake, the Design Earthquake, and the Maximum Considered Earthquake in Intensity 7 regions and the Maximum Considered Earthquake in Intensity 8 regions. In 2006, Li and Lam [3] also conducted a 1: 20-scale shaking table test of a high-rise building (120 m) in Hong Kong. In 2010, Mao and Lu [4] performed a 1: 50-scale shaking table test of Shanghai Tower and analyzed the seismic perform- ances when the building was subjected to the Frequently Occurring Earthquake, the Design Earthquake, and the Maximum Considered Earthquake in Intensity 7 regions and the Maximum Considered Earthquake in Intensity 7.5 re- gions. However, none of the structures in these shaking ta- ble tests collapsed, i.e., it was difficult to understand the collapse process and corresponding mechanism from these shaking table tests. In 2007, a collapse test of a 1: 4-scale 3-story, 1-span RC frame was performed by Huang and Gu [5]. In 2008, a collapse test of a 4-story steel moment re- sisting frame was conducted using the three-dimensional shake table facility of E-Defense to evaluate the structural and functional performance of the building under de- sign-level ground motions [6, 7]. The safety margin against collapse subjected to extremely strong ground motions was also evaluated. The research outcomes indicated that the failure mode of the building when subjected to 100% Taka- tori ground motion records was a weak story failure mode in the first story, which was induced by deterioration in the strength of columns due to local buckling at the top and bottom of the columns. In 2009, van de Lindt et al. [8] per- formed a collapse test of a full-scale, 6-story, light-frame wooden building on the shaking table of E-Defense. It demonstrated that the wooden structure had an excellent seismic performance with only slight damage caused even subjected to an earthquake of 2500-year return period. Wu and Kuo [9] also conducted a collapse test of a non-ductile concrete frame using a shaking table in 2009. Although great progress has been achieved in researching earth- quake-induced collapse resistance using shaking table tests, only scaled multi-story buildings or full-scale low rise buildings can be tested on shaking tables due to the limited capacity of the shaking table facility and experimental safety considerations. It is very difficult to study the seismic collapse resistances of super high-rise buildings using con- ventional shaking table tests. In addition, the shaking table test is very expensive. Alternatively, numerical simulation is gradually playing an important role in the study of seismic performance and collapse resistance. In 2001, based on the finite element (FE) code of LS-DYNA, Lu et al. [10] developed an FE model to simulate the collapse process of the World Trade Center in New York, which had been impacted by aircraft, and ex- plained the main reasons for the progressive collapse. In 2004, Pan and Brownjohn [11] presented a numerical study on the dynamic responses of the tallest building in Singa- pore and compared the FE results with 21 field measure- ments of the structural response to far-field ground motions. The predicted roof displacement of the structure agreed well with the field observations. In 2006, Pekau and Cui [12] developed a distinct element method (DEM) program to simulate the earthquake-induced collapse of a 20-story, 3-span precast-panel shear wall structure. The results indi- cated that if the design of this precast-panel shear wall satis- fies seismic requirements, it will automatically meet the ductility demands of progressive collapse prevention. In 2007, Mattern and Blankenhorn [13] compared the progres- sive collapse processes of a 3-span frame as predicted using finite-element and rigid-body methods. The study showed that the rigid-body method gave similar results to the fi- nite-element method at a lower computational cost. In 2009, Fan and Li [14] constructed an FE model of Taipei 101 and analyzed its seismic performance. Their research indicated that the super high-rise building, which has a mega-frame system, has sufficient safety margins and it satisfies the de- sign requirements for the Maximum Considered Earth- quake. Many numerical simulations on the seismic behavior of high-rise buildings have been reported in the literature, but most of these studies are conventional elasto-plastic analyses. The entire process of simulating structural seismic response, including yielding, hardening and collapse, has rarely been reported, especially for super high-rise buildings. Several im- portant problems need to be solved in the collapse simulation of super high-rise buildings, including the modeling of com- plex structures, solving of extreme nonlinearity and large- scale computation. Therefore, this has become an important frontier of earthquake engineering. With the support of the Key Research Plan “Dynamic Disaster Evolution of Important Engineering Structures” of the National Natural Science Foundation of China (NSFC), this paper builds up a nonlinear finite element model of the tallest building in China, Shanghai Tower (632 m). The dynamic characters of this building are analyzed, and the possible failure modes and collapse processes due to earth- quakes are predicted, as well as the corresponding collapse mechanism. This work will be helpful in collapse preven- tion and the seismic design of super high-rise buildings. 2 Overview of Shanghai Tower Shanghai Tower, located in Lujiazui, Shanghai, is a mul- ti-functional office building (as shown in Figure 1). The total height of the main tower is 632 m, and the structural height is 580 m. This building contains 124 stories. A hy- brid lateral-force-resisting system (as shown in Figure 2) referred to as “mega-column/core-tube/outrigger” was Lu X, et al. Sci China Tech Sci October (2011) Vol.54 No.10 3 Figure 1 The location of the 3 super high-rise buildings in Shanghai (From: http://www.eastday.com). Figure 2 Sketch of lateral-force-resisting system of Shanghai Tower. adopted for the main tower. The details of this system are described briefly as follows. (i) The main part of the core-tube is a 30 m by 30 m square RC tube. The thickness of the flange wall of the tube at the bottom is 1.2 m, and the thickness decreases with the height of the tube and reduces to 0.5 m at the top. Similarly, the thickness of the web wall decreases from 0.9 m at the bottom to 0.5 m at the top. According to the architectural functional requirements, the four corners of the core-tube are gradually removed above Zone 5. Finally, the core-tube becomes X-shaped at the top [4, 15]. (ii) The mega-column system consists of 12 shaped-steel reinforced concrete columns with a maximum cross-sec- tional dimension of 5300 mm×3700 mm [15]. 8 mega- columns extend from the bottom to the top of the building, and the section size gradually reduces to 2400 mm×1900 mm at the top. The remaining 4 columns are located at each corner and only extend from the ground floor to Zone 5. (iii) The outrigger system, located at the mechanical sto- ries, consists of circle trusses and outriggers with a total height of 9.9 m. All of the components of the outriggers are composed of H-shaped steel beams. 3 Finite element model Based on the general-purpose finite-element program MSC.MARC, which has an excellent nonlinear computa- tional capacity, the nonlinear FE model of Shanghai Tower is built up using the material constitutive laws, element models and elemental failure criteria proposed by Tsinghua University. Thus, the special requirements of the collapse simulation of super high-rise buildings subjected to strong earthquakes, such as the modeling of complex structures, solving of extreme nonlinearity and large-scale computation, are satisfied. Four element types are used in this model: the spatial beam elements used for the external frames and outriggers, the multi-layer shell elements used for the shear walls and the mega-columns, the truss elements used for the rebar and the shaped-steels, and membrane elements for the floor slabs. The details are described in the following subsec- tions. 3.1 Material constitutive laws In this work, the material-based constitutive law was adopted for all components to accurately simulate the nonlinear behavior and failure under the complex stress state (i.e., the coupled axial force, bending moment and shear force) during the collapse process [16]. The main construction materials used in Shanghai Tower are con- crete and steel. The von Mises yielding criterion and the isotropic hardening rule were adopted for the concrete, and the normalized equivalent uniaxial compressive stress- strain relationship [17] is shown in Figure 3. The strengthening branch was based on the model proposed by Hongnestad. The softening branch used was a straight line with 0.3fc residual strength, where fc is the peak strength. The smeared crack model was adopted for concrete under tension [17]. Similarly, the von Mises yielding crite- rion-based plastic constitutive model was adopted for the steel. The model proposed by Wang et al. [18] with four stages (elastic, yield, hardening and post-capping) was adopted for the backbone curve of the stress-strain rela- tionship as shown in Figure 4. 4 Lu X, et al. Sci China Tech Sci October (2011) Vol.54 No.10 Figure 3 The normalized stress-equivalent plastic strain relationship for concrete in compression. Figure 4 The stress-strain relationship of steel. 3.2 Core-tube The multi-layer shell element (as shown in Figure 5) pro- posed by Lu et al. [19–21] with outstanding nonlinear per- formance was adopted to model the core-tube, which con- siders the bending and shear coupling both in-plane and out-plane. Men et al. [19], Lin et al. [20], Miao et al. [21] have verified the accuracy and efficiency of the multi-layer shell element model for application to shear walls. The FE models of typical core-tubes are shown in Figure 6. 3.3 Outrigger, external frame and other components The external frame, outrigger and steel tower at the top are constructed with H-shaped steel beams and simulated using a fiber-beam element model. To ensure computational ac- curacy, each segment of the cross-section (i.e., the flange and web) is divided into 9 fibers. In total, therefore, there are 27 fibers in each section. The fiber-beam element model has been widely used in the elasto-plastic analysis of earth- quake engineering, and its accuracy has been verified for many times [22–25]. 3.4 Mega-columns One of the most interesting components in Shanghai Tower is the mega-column system, which includes 12 mega-col- umns, among them 8 extend to the top, and the remaining 4 end at Zone 5. These mega-columns are constructed with shaped-steel reinforced concrete, and a typical cross- section is shown in Figure 7(a). The area of this section is nearly 20 m2 and has a steel ratio of 6.22% and a rein- forcement ratio of 1.16%. The dimensions of these mega- columns are so large that they go far beyond the general conception of “columns”, and the reinforcement and steel in the columns significantly confine the mechanical behavior of the concrete. Hence, the traditional fiber-beam element model cannot meet the computational accuracy. Meanwhile, the computational workload would be too big if solid elements were adopted for the mega-columns in the analysis of the whole structure. Because few experimental data regarding the mega-columns can be found in the literature, a multi-layer shell element-based simplified model was pro- posed for the mega-columns to find a balance between computational accuracy and cost, and the parameters of the simplified model were determined based on the detailed FE model of mega-columns with solid elements. In the detailed FE model, the concrete, shaped-steel and rebar were modeled using hexahedral solid elements, quadri- lateral shell elements and truss elements, respectively. In contrast, the simplified model was combined with multi-layer shell elements and truss elements. The concrete, rebar dis- tributed along the Y-direction and the web of the shaped steel were modeled using multi-layer shell elements, while the shaped-steel flange and the rebar distributed along the X-direction were modeled using truss elements. The dis- placement compatibility among the shell and truss elements was achieved using shared nodes as shown in Figure 7(c). Numerical simulations of the mega-columns under pure compression, pure bending, bending with compression in one direction and bending with compression in the biaxial direction etc. were conducted to evaluate the simplified model. Details of the load cases are shown in Figure 8. Typical results are compared in Figure 9, and further details regarding the comparison can be found in ref. [26]. The proposed simplified method can predict the nonlinear be- havior of the mega-columns with acceptable tolerance compared to the detailed FE model. In addition, the degree of freedom in the simplified model is much less than that in the detailed model (see the comparison in Table 1). Therefore, the proposed simplified model of the mega-columns can be used in the global structural seismic response analysis. Finally, the complete FE model of Shanghai Tower is shown in Figure 10. 3.5 Failure criteria Collapse is a very complicated process in which the struc- tural components reach their load capacities and the entire structure changes from a continuum system into discrete parts through structural fracturing and element crushing. Lu X, et al. Sci China Tech Sci October (2011) Vol.54 No.10 5 This process can be simulated using elemental deactivation technology, where the failed elements are deactivated when a specified elemental-failure criterion is reached. Shell, beam and truss elements are included in the FE model of Shanghai Tower, and different elemental-failure criteria are adopted for different elements. For the multi-layer shell model, each element has at least 11 layers (the number of layers depends on the specific situation of the actual rein- forcement), and each layer has 4 Gaussian integration points. If the principal compressive strain at any integration point Figure 5 Multi-layer shell element. Figure 6 FE models of typical core-tubes. (a) The core-tube from Zone 1 to Zone 5; (b) the core-tube of the junction of Zone 4 and Zone 5; (c) the core-tube of the junction of Zones 6 and 7. Figure 7 Typical cross-section of mega-column and detailed and simplified FE models. (a) Typical cross section of mega-column (unit: mm); (b) detailed FE model of mega-column; (c) simplified FE model of mega- column. Figure 8 Typical load cases of mega-columns. (a) Axial compression; (b) bending in X direction without compression; (c) bending in Y direction without compression; (d) bending in X direction with varied compression; (e) bending in Y direction with varied compression; (f) bending in X and Y directions with varied compression. 6 Lu X, et al. Sci China Tech Sci October (2011) Vol.54 No.10 Figure 9 Comparison between detailed and simplified FE models for typical load cases. (a) Biaxial bending at the axial load ratio equal to 0.45; (b) corre- lation between the maximum axial force and maximum bending moment under 2:1 biaxial bending (strong axis); (c) correlation between the maximum axial force and maximum bending moment under 1:1 biaxial bending (weak axis). Table 1 Element and node numbers of detailed and simplified FE models Detailed FE model Simplified FE model Element number 86563 706 Node number 54542 400 Figure 10 The whole FE model of Shanghai T