Collapse Simulation of RC HighRise Building Induced by Extreme Earthquakes Xiao Lu^{1}, Xinzheng Lu^{1} [*] , Hong Guan^{2} and Lieping Ye^{1} ^{1}Department of Civil Engineering, Tsinghua University, Beijing 100084, China; ^{2}Griffith School of Engineering, Griffith University Gold Coast Campus, Queensland 4222, Australia Earthquake Engineering & Structural Dynamics, 2013, 42(5): 705723. ABSTRACT Collapse resistance of highrise buildings has become a research focus due to frequent occurrence of strong earthquakes and terrorist attacks in recent years. Research development has demonstrated that numerical simulation is becoming one of the most powerful tools for collapse analysis in addition to the conventional laboratory model tests and postearthquake investigations. In this paper, a finite element (FE) method based numerical model encompassing fiberbeam element model, multilayer shell model and elemental deactivation technique is proposed to predict collapse process of highrise buildings subjected to extreme earthquake. The potential collapse processes are simulated for a simple 10story reinforced concrete (RC) frame and two existing RC highrise buildings of 18story and 20story framecore tube systems. The influences of different failure criteria used are discussed in some detail. The analysis results indicate that the proposed numerical model is capable of simulating collapse process of existing highrise buildings by identifying potentially weak components of the structure that may induce collapse. The study outcome will be beneficial to aid further development of optimal design philosophy. KEY WORDS: collapse simulation; highrise buildings; elemental deactivation; fiberbeam element model; multilayer shell model; If you need the PDF version of this paper, please email to luxinzheng@sina.com

1. INTRODUCTION Collapse is a critical ultimate state for structures during extreme earthquakes. In the past century, collapse prevention has always been a key topic in earthquake engineering research. This research area has become increasingly significant in recent years due to frequent occurrence of natural (earthquakes) and manmade (terrorist attacks) disasters all over the world. The China¡¯s Wenchuan Earthquake in 2008, Haiti Earthquake in 2010, Chile Earthquake in 2010 and China¡¯s Yushu Earthquake in 2010 are just a few examples of such catastrophes. In order to effectively prevent earthquake induced structural collapse, the collapse process and the failure modes of structures should be properly predicted. Largescale shaking table tests have been used in an attempt to understand the fundamental mechanism and behaviour of earthquake induced structural collapse [13]. However such tests are very expensive and even the largest shaking table in the world cannot simulate the collapse of fullscale highrise buildings. As an alternative, numerical simulation has been widely accepted as an important technique to study earthquake induced structural collapse, by which both collapse modes can be identified and the entire processes can be replicated to certain extent particularly for the initial collapse phases. In this respect, many researchers have conducted collapse simulation [49]. However most of these work only focused on collapse simulation of simple structures, such as simple reinforced concrete frames or bridges. Little work has been reported on the collapse simulation of existing highrise buildings consisting of thousands of beams, columns, shear walls and floor slabs. This research gap has largely limited the applicability of the current collapse simulation technology to real construction projects. From numerical point of view, structural collapse is a complicated process in which a continuum system is deteriorated into a discrete one. This further complicates the collapse simulation by numerical techniques. In numerical analysis, elastoplastic deformation and energy dissipation before collapse must be accurately simulated. During the collapse process, rigid body movement, structural element fracture, and contact and collision of structural fragments must also be correctly modeled. All this brings a very high theoretical and computational requirement to numerical analysis models. Despite of the development of many numerical models, such as Discrete Element Models (DEM) [1011] and Applied Element Method (AEM) [1213] in simulating structural collapse and some important progresses have been made, these methods still have a long way before they can be used to simulate complicated real highrise buildings. In view of this, the present study aims to develop a simulation model that is based on welldeveloped finite element (FE) framework to provide a feasible collapse simulation methodology for practical application. In the proposed FE model, the structural elements in RC buildings are modeled with fiberbeam elements and multilayer shell elements, with which the microscale stressstrain law of materials can be directly related to the macroscale elemental forcedisplacement relations. The fracture of structural elements is modeled by deactivating failed elements and refining element mesh. The contact and collision of structural fragments during collapse are simulated with appropriate contact algorithm. Timehistory analyses are carried out to simulate the entire collapse process. Three numerical examples including two real highrise RC framecore tube buildings of 18 and 20 stories are analyzed to demonstrate the applicability and efficiency of the proposed collapse process. 
2. NUMERICAL MODEL For RC structural elements, there exist a number of simplified numerical models such as the concentrated plastic hinge model for beams and columns [14], the threeverticallineelement model [15] and the multipleverticallineelement model [16] for shear walls. In an attempt to properly simulate complex nonlinear behavior of structures and structural elements before and after collapse, in particular the complicated interaction between axial loads and bending moments in columns and coupled inplane/outplane bending and coupled inplane bendingshear behavior in RC shear walls, the present study employs the fiberbeam element model for beams and columns, and multilayer shell model for shear walls. For clarity of discussion, these models are briefly introduced as follows. 
2.1. Fiberbeam element model Fiberbeam element model has been widely accepted to model RC frames whose failure is predominately controlled by flexural behavior [1718]. In the fiberbeam element model, the structural frames (beams and columns) are modeled with beam elements, and their sections are divided into individual fibers (Figure 1). Each fiber has its own uniaxial constitutive law, and different fibers in the same section follow the assumption that ¡°plane section remains plane¡±. The fiberbeam element model is capable of simulating the axialflexural coupling of RC frames and is adaptive to different sectional shapes. The confinement effect of the stirrups in the columns can also be considered by using confined uniaxial constitutive relationship for core concrete and unconfined one for other concrete fibers. It is necessary to note that brittle shear failure is considered in the proposed fiberbeam mode. In other words, when the internal shear force exceeds the prescribed shear strength of the fiberbeam element, the strength and the stiffness of the element abruptly drop to zero. The stressstrain model proposed by L¨¦geron et al. [19] is used in this study to model the backbone curve of concrete (Figure 2), which also considers the confinement of stirrups to concrete. Parabolic curves proposed by Mander et al. [20] are adopted to model the unloading and reloading paths of concrete where degradation of strength and stiffness due to cyclic loading (Figure 2) can be taken into account. An exponential model proposed by Jiang et al.[21] is used to model the softening branch of cracked concrete, with which the ¡°tensionstiffening effect¡± of reinforced concrete can be considered (Figure 2). The stressstrain model proposed by Esmaeily and Xiao [22] is adopted to model the backbone curve of steel (Figure 3). The model proposed by L¨¦geron et al. [19] is adopted to model the unloading and reloading paths, in which the Bauschinger effect of steel can be considered (Figure 3).
Figure 1 Member section
Figure 2 Stressstrain curve of concrete
Figure 3 Stressstrain curve of steel Based on the above material models, the fiberbeam element model is embedded into the general purpose FE software MSC.MARC with the user subroutine UBEAM [23]. Each RC frame element (beam or column) is subdivided into 6 to 8 fiberbeam elements to ensure sufficient accuracy. Two compressiveflexural column tests, referred to as S1 [24] and YW0 [25] respectively, are simulated to validate the proposed fiberbeam element model. Detailed dimensions of S1 and YW0 are shown in Figures 4 and 5, respectively. It can be seen that S1 has a larger reinforcement ratio (2.65%) and a smaller axial load ratio (0.03) whereas YW0 has a smaller reinforcement ratio (1.29%) and a larger axial load ratio (0.44). Figures 4 and 5 also indicate that the numerical simulations perform fairly well to capture the model yielding, hardening and unloading characteristics. Even for the final stage of the hysteretic response when the deterioration becomes evident, the discrepancies between the simulation and test results are still within the acceptable range in engineering practice.
Figure 4 Comparison between numerical simulation and test results of S1
Figure 5 Comparison between numerical simulation and test results of YW0
In order to further validate the reliability of the proposed model in predicting the actual strength deterioration, the progressive collapse test of a threestory fourbay planar frame carried out by Yi et al. [26] is simulated herein. The test setup and detailed dimensions are displayed in Figure 6. To represent the failure or removal of the middle column in the ground floor, the lower jacks unload gradually when the upper jack was balanced with load. Figure 7a shows a comparison between the experimental and simulated unloading curves for the middle column and Figure 7b presents the displacement comparison at selected points (located at the top of the columns on the first floor). Details of the simulation process can be found in Li et al. [27]. It is evident that the simulation results agree well with the experimental observations.
Figure 6 Collapse test of the planar frame by Yi et al.[26]
(a) (b) Figure 7 Comparison between simulation and test result of a fourbay threestory planar frame: (a) Unloading curve of middle column; (b) Displacement at the top of firststory columns Furthermore, another compressiveflexural column test with large deterioration, conducted by Tang et al. [28], is also simulated to validate the capacity of the proposed fiberbeam model in predicting the strength deterioration in particular. Detailed dimensions and reinforcement arrangement are presented in Figure 8. The longitudinal reinforcement ratio of the specimen is 1.29% and the corresponding axial load ratio is 0.348. The hysteretic loaddisplacement comparison shown in Figure 8 indicates that the proposed fiberbeam model is able to replicate the strength deterioration within the considered acceptable range.
Figure 8 Comparison between numerical simulation and test results by Tang [28]

2.2. Multilayer shell model The shearwall members (walls and coupling beams) in the proposed FE model are simulated with multilayer shell elements as illustrated in Figure 9. This type of element is based on the principles of composite material mechanics and is capable of simulating coupled inplane/outofplane bending as well as inplane direct shear and coupled bendingshear behavior of RC shear walls [29]. The multilayer shell element is made up of a number of layers with different thicknesses and different material properties [30]. The rebars are smeared into one or more layers and these rebar layers can be either isotropic or orthotropic depending on the reinforcement ratio in the longitudinal and transverse directions, as shown in Figure 10. For the boundary zones of the shear wall, the essentially concentrated reinforcing bars are simulated using truss elements which are incorporated into the shell model. The elastoplasticfracture constitutive models [21, 31] provided by MSC.MARC and the steel model shown in Figure 3 are applied to the concrete and rebar materials, respectively. Since the multilayer shell element directly relates the nonlinear behavior of the shear wall to the constitutive laws of concrete and steel, it has many advantages over other models in representing the complicated nonlinear behavior.
Figure 9 Multilayer shell element
Figure 10 Location of the rebar layers
Figure 11 Specimen dimensions and reinforcement details A shear wall test specimen [32] is simulated to validate the multilayer shell element. The specimen is 1900mm in height, 1000mm in width and 100mm in thickness (Figure 11). The experimental and numerical loaddisplacement responses shown in Figure 12 demonstrate a good correlation in the yielding and hardening phases. Numerical predictions of the cracking strain contours at peak load state and the vertical compressive strain contours at ultimate state are respectively demonstrated in Figures 13a and 13b.
Figure 12 Comparison of loaddisplacement relation curves
(a) (b) Figure 13 Deformation and strain contour predicted by the numerical model: (a) Cracking strain at peak load state; (b) Vertical compressive strain at ultimate state Two RC tube specimens (referred to as TC1 and TC2) tested by Du et al. [33] are also simulated to further validate the proposed multilayer shell model for shear walls. The size of both tubes is 1380mm¡°1380mm¡°3690mm. The axial load ratios of TC1 and TC2 calculated based on concrete compressive strength are 0.15 and 0.36 respectively. Inverted triangular lateral loads are applied to the middle and the top of the tubes. The FE model of shear walls and coupling beams are shown in Figure 14 and the arrangement of steel reinforcement in the specimens are detailed in Figure 15. All material data in the numerical model are determined based on the actual tests of Du et al. [33]. The concrete and distributed rebars in the longitudinal and transverse directions are simulated by the multilayer shell model. The diagonal reinforcements in the coupling beams are simulated by traditional truss elements. For TC1 and TC2, the base shear force versus the top displacement curves are plotted in Figures 16 and 17 respectively. Again good agreements with the experimental results are achieved for both RC tube specimens. It is worth mentioning that the above validations confirm the ability of the FE model to accurately predict the yielding and hardening behavior of the test specimens. These laboratory tests however do not report on the strength deterioration and failure at ultimate stage therefore unable to provide a validation of the ability of the multilayer shell model in replicating the deterioration pattern.
Figure 14 Concrete element mesh
Figure 15 Spatial distribution of rebars
Figure 16 Comparison of shear forcedisplacement curves of TC1 (axial load ratio=0.15)
Figure 17Comparison of shear forcedisplacement curves of TC2 (axial load ratio=0.36) Consequently, another steel reinforced concrete (SRC) low shear wall test carried out by Wei et al.[34], is simulated to replicate the strength deterioration at large deformation. The specimen is 1050 mm in height, 1100mm in width and 120 mm in thickness. Reinforced concrete blocks were used at the top and the base to anchor the specimen. The distributed horizontal and vertical reinforcement were placed in two layers. The dimension, reinforcement and material properties of the specimen are briefly displayed in Figure 18. The horizontal cyclic load, initially controlled by the applied force and subsequently by displacement upon yielding, is applied at the top of the wall with a 1700kN axial compression load. The hysteretic loaddisplacement comparison between the simulation and test results is shown in Figure 19. It indicates that the multilayer shell model performs well to simulate the load capacity and captures large deterioration of the specimen to some extent. The difference between the prediction and test results are considered acceptable. Based on the above validations, it can be concluded that the multilayer shell model is capable of replicating shear wall behavior in collapse simulation.
Figure 18 Specimen dimensions and reinforcement details
Figure 19 Comparison of loaddisplacement relation curves

2.3. Proposed elementalfailure criterion During the process of structural collapse, the whole structure changes from a continuum system into discrete parts through structural fracturing and element crushing. This process can be simulated by elemental deactivation technique, where the failed elements are deactivated when a specified elementalfailure criterion is reached. Since both elemental models (fiberbeam element model and multilayer shell model) are based on material stressstrain relations, corresponding materialrelated failure criterion must be adopted to monitor the failure of structural elements. For the fiberbeam element model, each element has at least 36 concrete fibers and 4 steel rebar fibers and each fiber has 3 Gauss integration points. Similarly, for the multilayer shell model, each element has at least 10 layers (the number of layers depends on the specific situation of the actual reinforcement) and each layer has 4 Gaussian integration points. If the strain at any integration point in a fiber or layer (either concrete or steel) exceeds the material failure criterion, the stress and the stiffness of this fiber/layer are deactivated, which means that the fiber/layer no longer contributes to the stiffness computation of the whole structure. If all fibers/layers of an element are deactivated, the element is considered fully deactivated from the model. Simultaneously, the nodes that are connected to the deactivated element are checked. A node is considered ¡°isolated¡± when all its belonging elements are deactivated, which implies that this node carries zero stiffness in relation to the degree of freedoms (DOFs). The ¡°isolated¡± nodes are more likely to cause convergence problems. Therefore all DOFs of the ¡°isolated¡± nodes are removed from the global stiffness matrix [35]. Confined concrete (e.g. columns with sufficient stirrups) exhibits much better ductility than unconfined concrete (e.g. concrete in cover layer). Hence different criteria for concrete crushing are necessary for confined and unconfined concrete. Tensile rupture of rebar is also an important failure criterion for rebar fibers or layers. The fracture strain of rebar varies for different types of steel. Therefore it is treated as a variable factor and its influence is discussed herein. The rebar buckles following concrete crushing due to lack of concrete confinement. Due to complicated interaction between the confinement reinforcement (stirrups) and longitudinal rebars, the buckling strain of steel also varies significantly as demonstrated in different tests [36, 37] and is treated as a variable factor as well. Summarized below are typical material deactivating criteria proposed for this study: (1) For unconfined concrete crushing: compressive strain exceeds 0.33% [38]; (2) For confined concrete crushing: the softening branch in Figure 2 approaching zero; (3) For rebar fracture: tensile strain exceeds 10% or 15% [38]; (4) For rebar buckling: compressive strain exceeds 0.5% or 1.0%. The influence of the above material failure criteria will be further discussed through presentation of numerical examples. 
2.4. Contact between failed structural segments The contact and collision of failed structural fragments significantly influence the collapse failure mode. In this study, a contact algorithm specified in MSC.MARC software is adopted to simulate the interaction between failed structural segments and remaining active segments [35]. In the FE model, all the elements are defined as deformable contact bodies. During the incremental procedure, each potential contact node is checked to see whether it is in vicinity of a contact segment (elements defined as deformable contact bodies). If a node is within the contact tolerance, it is considered to be in contact with this segment. The default contact tolerance suggested in MSC.MARC is: the smaller of 5% of the smallest element side or 25% of the smallest (beam or shell) element thickness [35]. 
3. COLLAPSE PROCESS SIMULATION In general, collapse under strong earthquakes being considered in the design codes can be prevented in structures designed by the latest seismic design regulations. In practice, on the other hand, earthquakes are of complicated nature. As such, structures may experience extreme earthquakes that are much larger than those considered in the design regulations. Furthermore, for some research purposes such as collapse fragility analysis based on incremental dynamic analysis [39,40], and for building code development using collapse modeling [41], very large earthquake ground motions are required to be used as input to obtain a full collapse fragility curve from 0% to 100% of collapse. In view of the above, this study takes into account extreme ground motions which are 5 to 10 times larger than those specified in the design code [42]. Despite this assumption, the collapse simulation undertaken in this study aims to offer fundamental understanding of the ultimate structural behavior which will be beneficial for both scientific research and engineering application. 
3.1. Tenstory RC frame The collapse process of a simple tenstory RC frame is simulated with the proposed fiber beam element model. The frame is assumed to be subjected to ElCentro EW Ground Motion [43] which is scaled to PGA=2000 gal. The overall configuration of the frame is presented in Figure 20. The columns are spaced at 5m with their feet fixing to the ground. The ground story is 4.5m high whereas all the other stories are 3m in height. The dimensions and longitudinal reinforcement of the beams and columns are given in Table 1. The material parameters of the analytical model are as follows: Young¡¯s Modulus E_{0} of 30GPa and the compressive strength f_{c} of 30MPa for concrete, and Young¡¯s Modulus E_{s} of 200GPa and the yield strength f_{y} of 400MPa for reinforcement. The implicit singlestep Houbolt algorithm [35] is adopted to compute the dynamic response of the frame. The iteration convergence criterion is the residual force being smaller than 1% of the maximum reaction force. The predicted collapse process is shown in Figure 21 where soft stories are clearly identified. The numerical simulation reveals that failures of the frame initiate firstly in columns of the 8^{th} story where the column sections change from 600mm´600mm to 500mm´500mm. Subsequent failures take place at ground story, where the columns carry the largest lateral force. The colored contours in Figure 21 represent the longitudinal reinforcement yielding in the columns and beams. Upon yielding of the longitudinal reinforcement in the columns of the 1^{st} and 8^{th} floors, the loadcarrying capacities of the columns start to decline. The columns are therefore unable to resist the increased seismic loads and the additional bending moments caused by large displacement and PD effect. Consequently, the 1^{st} and 8^{th} stories collapse completely at 4.4s at which very large lateral displacements are observed at the ground level. These results clearly show the potential failure mode and collapse process under the specific ElCentro ground motion which is scaled to PGA=2000 gal.
Figure 20 The plane and elevation of the 10story RC frame
Figure 21 Collapse process of the 10story RC frame (Ground motion: ElCentro EW, 1940, PGA=2000gal): (a) t=2s; (b) t =3s; (c) t =4s; (d) t =4.4s 
3.2. Eighteenstory framecore tube building Shown in Figures 22 is the plane view of an existing highrise building which has 18 stories above the ground and a 4story basement with a total height of 74.8m. The coretube is made up of four subtubes connected by coupling beams. The thickness of the shear wall changes from 500mm (at the bottom story) to 350mm (at the top story). The three dimensional FE model is presented in Figure 23a. The columns and beams are simulated by the fiberbeam element model, and the RC shear wall and coupling beams are simulated using the multilayer shell model. Modal Analysis is conducted herein which demonstrates three mode shapes. The first mode is translation in the Ydirection with a fundamental period T_{1}=1.55s; the second mode is planar torsion with a natural period T_{2}=1.30s; and the third mode is translation in the Xdirection with secondary torsion, with a natural period T_{3}=1.15s. The planar torsion in the second mode is caused by the asymmetric cantilevered portions of the building in the upper stories. The secondary torsion in the third mode is caused by the asymmetric layout of walls in the Xdirection, which separates the center of rigidity from the center of mass. ElCentro EW Ground Motion [43] which is scaled to PGA=1500gal is used as an earthquake input to the structure along the Xaxis. Figure 23 clearly displays the potential collapse process of this highrise building under ElCentro ground motion. The ground story is identified to be the weakest part of the building due to its much larger height than the other stories. As can be seen from Figure 23b, the failure of the shear wall starts from the outer flange of the coretube in the ground floor, which is caused by the gravity load of the building and the overturning effect of the seismic load. Note that in the outer flange of the coretube, the compressive load is much larger than the shear force. Therefore, the failure of the shear wall is dominated by concrete crushing induced by the axial load and bending moment. Subsequently, significant force redistribution occurs in the ground floor. This in turn results in a steady increase in the vertical and horizontal forces in the columns thereby leading to buckling of the columns (as shown in Figure 23c). With an increase in time, collision occurs between the basement and the upper stories (Figure 23d) which in turn results in a total collapse of the ground floor and subsequently the whole building.
Figure 22 Standard plane layout of the 18story building (Unit: mm)
(a) (b)
(c) (d) Figure 23 Collapse process of the 18story framecore tube building (Ground motion: ElCentro EW, 1940, PGA=1500gal): (a) t=0.0s; (b) t=3.9s; (c) t=4.9s; (d) t=6.8s

3.3. Twentystory framecore tube building This structure is an existing 79.47m tall, 20story office with a 4story skirt building. The finite element model is shown in Figure 24. The lateral force resisting system of the building consists of reinforced concrete external frame and core tube. The crosssectional dimensions of the columns from bottom to top of the building are 800mm´800mm, 700mm´700mm, 600mm´600mm. The beam sections are 350mm´650mm in the Xdirection and 350mm´600mm in the Ydirection. The thickness of the core tube is 350mm. Modal analysis is carried out using the proposed FE model. Three mode shapes are identified. The first mode is translation in the Ydirection with a natural period T_{1}=2.25s; the second mode is translation in the Xdirection with a secondary torsion due to asymmetric distribution of the shear wall in the Xdirection and the corresponding natural period is T_{2}=2.02s; the third mode is planar torsion, with a natural period T_{3}=1.63s. Illustrated in Figure 24 is the collapse process of this building subjected to ElCentro Ground Motion [43] which is scaled to PGA=4000gal. At t=4.5s, the shear wall at the 10^{th} story has its concrete strength changed from C40 to C30 and the column section changes from 700mm´700mm to 600mm´600mm. This results in a sudden change in stiffness which in turn causes high stress concentration. In consequence, the shear wall at the flange of the coretube in this story is crushed as demonstrated in Figure 24b. With propagation of the failed structural elements including buckled columns (Figure 24c), the stories above the 10^{th} story comes down and impacts on the lower stories (Figure 24d), thereby leading to a progressive collapse of the whole building. The failure mechanism is similar to the eighteenstory framecore tube building (Section 3.2) in which collapse is initiated by concrete crushing in the outer flange of the coretube in the weak story. It is worthwhile noting that due to the complicated nature of earthquakes and structures themselves, there may exist various failure modes and weak structural components. If the input ground motion of this building is changed to Duzce, Kocaeli, Turkey, 1999[43], the weak portion of the building is then changed to the first floor where there is a sudden change of stiffness induced by the discontinued underground diaphragm wall of the basement. The collapse process is presented in Figure 25. The discrepancy of the two collapse modes is attributable to different frequency components of the two ground motions. The Duzce ground motion is a pulselike earthquake; however, the ElCentro ground motion is a durationlike earthquake. Therefore, the two ground motions excite different structural vibration modes which induce different collapse modes and processes. The collapse process under the Duzce ground motion suggests that further reinforcement should be provided in the first floor to improve the safety of the entire building. To further compare the influence of failure criteria on the collapse simulation of the 20story framecore tube building, three different types of material failure criteria are adopted to determine collapse probability. A total of 22 farfield ground motions proposed by FEMA P695 [41] are input into the model and the fundamental period spectral acceleration (S_{a}(T_{1})) of each ground motion is scaled to 4.0g, where g is the acceleration of gravity. The respective collapse probabilities of the building under the 22 farfield ground motions are summarized in Table 2. Table 2 clearly displays that if the tensile fracture strain of rebar changes from 15% to 10%, the collapse possibilities of the 20story building remain the same; however if the bulking strain of the rebar changes from 1.0% to 0.5%, the collapse possibilities would increase from 63.6% to 81.8%. This implies that the buckling strain of rebar has a greater influence on the collapse probability. For this 20story framecore tube structure, collapse is mainly caused by compressive failure of the shear wall. Upon spalling of the concrete cover of the shear wall, the vertical rebar can easily buckle which has a great impact on the load bearing capacity of the shear wall. Therefore, the influence of buckling strain of rebar is evidently greater than the tensile fracture strain.
(a) (b)
(c) (d) Figure 24 Collapse process of the 20story framecore tube building (Ground motion: ElCentro, 1940, PGA=4000 gal): (a) t=0.0s; (b) t=4.5s; (c) t=5.1s; (d) t=7.5s
(a) (b)
(c) (d) Figure 25 Collapse process of the 20story framecore tube building (Ground motion: Kocaeli, Turkey, PGA=4000 gal): (a) t=0.0s; (b) t=14.5s; (c) t=15.5s; (d) t=16.3s

4. SUMMARY AND CONCLUSIONS A numerical model based on the finite element framework, which consists of fiberbeam element model for beams/columns, multilayer shell model for shear walls, and elemental failure criterion, is proposed. The possible failure modes, collapse processes, and weak portions of a simple 10story RC frame and two existing RC framecore tube highrise buildings are simulated under specified ground motions. This study has provided a better understanding of the collapse mechanism of highrise building structures under extreme earthquakes. The outcome of this study can also be used as references in engineering practice for collapse resistance design of similar building structures. More importantly, the study has offered some insight into the design philosophy in preventing collapse under extreme earthquakes which may contribute to further development of optimum design and structural health monitoring methodologies. This paper presents a stateoftheart approach to progressive collapse modeling. It should be noted that due to modest numbers of largerscale collapse tests available in the literature, it is rather difficult to validate the collapse models of fullscale building systems presented in this study. Further work and validation are thus necessary on collapse simulation of fullscale structures or largescale structural elements. ACKNOWLEDGMENT The authors are grateful for the financial support received from the National Nature Science Foundation of China (No. 90815025, 51178249), the National Key Technologies R&D Program (No. 2009BAJ28B01), Tsinghua University Research Funds (No. 2010THZ021, 2011THZ03) and the Program for New Century Excellent Talents in University (NCET100528). 
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Table 2 Collapse probabilities with different elemental failure criteria
[*] Corresponding author. Tel: +861062795364; fax: +861062795364 Email address: luxz@tsinghua.edu.cn 