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Experimental and numerical study on progressive collapse process of RC frames with full-height infill walls
Engineering Failure Analysis 59 (2016) 57–68
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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/efa
Experimental and numerical study on progressive collapse process of RC frames with full-height infill walls Shuang Li a,b,⁎, Sidi Shan a,b, Changhai Zhai a,b, Lili Xie b,c a b c
Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education (Harbin Institute of Technology), Harbin 150090, China School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
a r t i c l e
i n f o
Article history: Received 24 July 2015 Received in revised form 24 September 2015 Accepted 6 November 2015 Available online 7 November 2015 Keywords: Progressive collapse Experiment Infill wall Reinforced concrete frame Finite element analysis
a b s t r a c t The work presented in this study aimed to investigate the influence of infill walls on the progressive collapse performance of reinforced concrete (RC) frames. An experimental program of a one-third scaled, four-bay by two-story RC frame with full-height infill walls at the second story was conducted. Experimental results indicate that the maximum resistance force and failure mode of the RC frame with full-height infill walls are relevant to the major crack developments in the infill walls. The infill walls behave as equivalent compressive struts during progressive collapse process and can improve the resistance force and initial stiffness but reduce beam ductility and change failure mode of the RC frames. Verification of the test results and material parametric analyses of the test specimen by using finite element (FE) model were conducted to illustrate the factors that influence the behavior of the infilled frame. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction The progressive collapse of structure occurs when the sudden loss of local members leads to a collapse disproportionate to the original damage. Usually, these original damages are triggered by events which may lead to severe consequences, such as accidental explosion, serious fire or terrorist attacks. World-wide known examples of progressive collapses include the collapses of Ronan Point building in 1968, Murrah Federal Building in 1995 and World Trade Center in 2001, etc. Due to these terrible events, many experimental and numerical studies on progressive collapse of frame structures have been performed [1–13]. Nevertheless, very few of them have taken the interaction between the infill walls and the frame members into consideration, even though it is well known that infill walls may have conflicting effects on the structural response. Sasani et al. [14,15] have conducted a field test to investigate the progressive collapse performance of an actual three dimensional, multiple spans, infilled reinforced concrete (RC) frame by removing two adjacent columns located at the first story. It showed that infill walls help carry additional loads by providing the beams with constraints and supports. However, the test frame was strong enough to survive the column removal, therefore the final progressive collapse resistance capacity and damage mode were not evaluated. Furthermore, overall performance of a complete actual frame, rather than a simple sub-structure (e.g., two dimensional planar infilled frame that consists of only basic members including beams, columns and infill walls), is affected by many irrelevant factors which may not be easy to eliminate from the influences of infill walls. By conducting tests with sub-structures, the infill walls, even for the weak ones, were proved to change the seismic behavior of RC frame significantly [16], and contribute to the lateral stiffness and resistance of buildings remarkably [17]. Nevertheless, the
⁎ Corresponding author at: Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education (Harbin Institute of Technology), Harbin 150090, China. E-mail address: [email protected] (S. Li).
http://dx.doi.org/10.1016/j.engfailanal.2015.11.020 1350-6307/© 2015 Elsevier Ltd. All rights reserved.
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progressive collapse behavior of infill walls under a downward load may not be identical with the seismic behavior under a lateral load. To examine the effects of infill walls in progressive collapse performance, Stinger and Orton [18] tested a one-third scaled RC frame with partial-height infill walls by removing the center column. Because the percentage of opening in the infill walls was too high (that is, the infill walls were only approximately one-third high of the column), the effects of infill walls were not significant in their test. Except the experimental studies, a small number of numerical studies [19,20] have also been performed to explore the effects of infill walls on progressive collapse of RC frame; however, the failure mechanism was not investigated in these numerical studies. In a summary, at the present time the pros and cons of infill walls on structural progressive collapse are not clearly understood, and the laboratory experiments in the literature provide very limited data for studying the progressive collapse mechanism and for verifying the results of numerical simulation methods for infilled RC frame structures. Due to the lack of the test with sub-structures regarding the contribution of full-height infill walls in progressive collapse performance, a research program was carried out with the objective to provide the test data in this research aspect and investigate the behavior and influence of the infill walls in the progressive collapse process of the RC frames. Three dimensional finite element (FE) models of the test RC frames were developed at micro level by ABAQUS [21], and validated the experimental results. A series of parameter analyses were conducted and the factors that influenced the failure mechanisms were investigated.
2. Experimental material and methods 2.1. Specimen design A four-bay by six-bay and 5.1 m center-to-center column spacing RC building was designed in accordance with the Chinese building code [22,23] as a prototype frame. The prototype building had eight stories, in which the first story was 4.2 m high, and other stories with infill walls were 3.3 m high. The test model frame represents a one-third scaled sub-structure with four bays (i.e., along the short side) and two bottom stories from middle part of the building. The design detail of the test frame is given in Fig. 1 (the full-height infill walls were located at the second story in each bay, and left half part in Fig. 1 illustrates details of tie rebars constructed in infill walls). The longitudinal reinforcements of the test frame beams and columns comprised deformed rebars with a diameter of 8 mm. The stirrups of the test frame beams and columns comprised smooth surface steel wires with a diameter of 4 mm. The longitudinal reinforcements and stirrups of the test frame foundation comprised deformed rebars with diameters of 18 mm and 8 mm, respectively. The tie rebars used to tie infill walls to the surrounding columns in the second story comprised smooth surface steel wires with a diameter of 2 mm. All the stirrups consisted of 135-degree lap splices, and the tie rebars in infill walls consisted of 90-degree end hooks. The foundation, first story and second story of the test frame were cast separately and had a clear concrete cover of 15 mm. The infill walls
Fig. 1. Design details of test frame specimen. Bays A and B illustrate tie rebars between columns and infill walls, and bays C and D illustrate the infill walls. (Unit: mm).
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were composed of concrete bricks with dimension of 130 mm × 63.5 mm × 63.5 mm. The average thicknesses of the bed joints and the cross joints were 8.9 mm and 5.8 mm, respectively. Table 1 gives the mean material properties of rebars based on tensile strength tests. Standard concrete prism with dimension of 150 mm × 150 mm × 300 mm were used for concrete compressive tests. The measured compressive strength was 35.8 MPa, 41.3 MPa and 31.8 MPa for the foundation, first and second story concretes, respectively. The brick and mortar compressive strength was 22.6 MPa and 18.3 MPa, respectively. The measured compressive strength was 12.8 MPa and shear strength was 1.08 MPa for the masonry unit (combination of brick and mortar). 2.2. Test setup In the test program, a progressive collapse situation was simulated by applying quasi-static loading on the center column, as shown in Fig. 2. A hydraulic jack, placed at the top of the center column, apply a vertical load large enough to enforce the downward displacement at the joint. The load applied by hydraulic jack was transmitted to the hand jack through the center column. Then the test was performed under displacement control, and the loading process was initiated by lowering the hand jack stepby-step. Two collar devices, attached to the center column, were installed on the lateral steel braces to prevent the undesired outof-plane deformation and failure of the frame. There were 5 mm gap between the column surface and the collars before the loading to prevent unwanted friction force at the initial stage. Correspondingly, four collar devices, installed on the lateral steel braces, were attached to the adjacent and external columns. As shown in Fig. 3, the load cells installed above and below the center column were monitored to measure the applied vertical load. The difference between the forces at the load cells represents the external vertical load, which is equal to the resistance force against progressive collapse, i.e., the resistance force comes from the center column. Additional instrumentation consisted of relative displacement meters and linear variable differential transformers (LVDTs) to measure the vertical displacement of the center column, and lateral displacements of the adjacent and external columns. 3. Experimental results 3.1. Reference frame Before the test of the frame with infill walls, for comparison purpose, a test of a bare frame (taken as a reference frame) of the same design as shown in Fig. 1 but without infill walls was conducted. One of the curves in Fig. 4 shows the result of resistance force versus vertical displacement of the center column for the bare frame. Under loading, besides the initial state with nearly elastic behavior, the frame experienced two phases of resistance mechanism actions: compressive arch action before the vertical displacement reached 204.5 mm and then the catenary action. It was observed that at the compressive arch action phase, cracks formed in beams in bays B and C were concentrated in regions near the beam ends, which were mainly caused by the bending moment of beams. At the catenary action phase, cracks continually widened near the beam ends and some new cracks emerged and approached the middle region of beams. At the vertical displacement of 317.1 mm, the first rebar fractured in the top left end of beam BB2. The horizontal displacements of joints at the adjacent and external columns versus the vertical displacement of the center column are shown in Fig. 5. The adjacent and external joints firstly moved outward (i.e., horizontally away from the center column) and achieved their maximum values at the vertical displacement of 106.6 mm, then joints continued to move inward until the end of test. The final failure mode at the vertical displacement of 417.7 mm (the end of the test) is shown in Fig. 6. A similar progressive collapse test on a bare planar RC frame was also conducted in the study by Yi et al. [1], and the observations on the failure process in the present test are consistent with the previous study. 3.2. Frame with infill walls 3.2.1. Resistance force and displacement The test frame (frame with infill walls) had identical design to that of the reference frame but with full-height infill walls. Fig. 4 also shows the resistance force versus the vertical displacement of the center column for the frame with infill walls. With increasing vertical displacement, the resistance force gradually increased to its peak value (152.1 kN) at the vertical displacement of 13.5 mm. Then, the cracks formed in the infill walls and failures of beams caused two sudden reductions in the resistance force at the vertical displacements of 20.3 mm and 90.6 mm, respectively. After that point, due to rebar fractures and progressive development of cracks in the infill walls, the resistance force gradually decreased till the vertical displacement of
Table 1 Material properties of rebars. Rebar diameter (mm)
Yield strength (MPa)
Ultimate strength (MPa)
Fracture strain (MPa)
18 8 4 2
338 415 235 339
487 588 322 395
0.19 0.18 0.31 0.28
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Fig. 2. Loading and measure systems of the test specimen.
367.5 mm, then increased again owing to the catenary action. The test ended at the vertical displacement of 458.9 mm. Fig. 7 shows the horizontal displacements of joints at the adjacent and external columns versus the vertical displacement of the center column. Similar to the response of the bare frame, as the vertical displacement increased, the adjacent and external joints firstly moved outward and achieved their maximum values at the vertical displacement of 81.4 mm. Thereafter, the joints continued to move inward until the end of test. The asymmetrical horizontal displacements of joints in left and right parts of the frame were due to the different failure pattern of infill walls in bay B and bay C which will be discussed later. 3.2.2. Crack development and rebar fracture Fig. 8 shows developments of major cracks in infill walls and beams. A diagonal crack formed in the infill wall in bay B at the vertical displacement of only 3.1 mm, and an inclined crack formed in the infill wall in bay C at the vertical displacement of 8.3 mm. The development of another parallel inclined crack in the infill wall in bay C caused the first sudden reduction in the resistance force (see Figs. 8(d) and 4). It should be noted that, at a very small vertical displacement of 20.3 mm, the major cracks in the infill walls had finished formation. The second sudden reduction in the resistance force at the vertical displacement of 90.6 mm was caused by diagonal compression failures near the end of beams in bay B, as shown in Fig. 9. Then, rebars in the failure part of beams in bay B were in tension but with an angle to the rest parts, indicating that dowel actions occurred to resist the shear deformation. At the vertical displacement of 143.4 mm, one rebar fractured in the top of right region of beam BB2 (the region where diagonal compression failure occurred) due to shear deformation. At the vertical displacements of 200.4 mm and 216.5 mm, the rebars in the top of right end of beam BC1 fractured, successively. At the vertical displacements of 225.7 mm and 239.8 mm, the rebars in the bottom of middle region of beam BC1 fractured, successively. At the vertical displacements of
Fig. 3. Test instrumentations of the specimen (Unit: mm).
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Fig. 4. Resistance force versus vertical displacement of the center column for the test specimen.
293.3 mm and 328.6 mm, the rebars in the bottom of left end of beam BC2 fractured, successively. At the vertical displacement of 347.9 mm, the rebars in the top of middle region of beam BC2 fractured. The top three rows of tie rebars connecting column CB2 to the infill wall and bottom three rows of tie rebars connecting the center column to the infill wall deboned or fractured from the infill wall before the vertical displacement reached 90.6 mm. The separations of tie rebars resulted in detachment and rigid-body movement of the infill wall in bay B afterwards. At the vertical displacement of 367.5 mm, the upper triangular part of the infill wall in bay B fell out of plane. The final failure mode of the frame with infill walls at the end of the test is shown in Fig. 10, the damage of which was very different to that inflicted on the bare frame. The failure of the frame occurred where infill walls detached from the surrounding components. Compared to the bare frame, the failure positions in beams changed and more cracks formed along the beams in both the failure bays and adjacent bays.
3.2.3. Failure mechanisms The mechanical behavior of infill walls in the bays bridging the center column (i.e., bays B and C) can be explained by using the equivalent compressive strut model, which was usually used to model the infill walls in the seismic response analyses of infilled frames [24]. Although the parameters and layout of the struts in the equivalent compressive strut model used in seismic analysis and progressive collapse analysis may not be identical, test observations shown that this model is still suitable to describe the behavior of infill wall in the progressive collapse situation. As illustrated in Fig. 11(a), most portion of load on the center column transferred from struts 1 to adjacent bays before the peak resistance. Struts 1 started to fail when their compression capacity were exceeded by the increased transferred load, corresponding to the vertical displacement of 13.5 mm. Thereafter, as illustrated in Fig. 11(b), load from the top of center column redistributed and gradually transferred through struts 2 and 3 to adjacent bays.
Fig. 5. Horizontal displacements of joints versus vertical displacement of the center column for the bare frame. (a) Adjacent columns (b) External columns.
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Fig. 6. Failure mode of the bare frame at the end of the test.
Note that the diagram with symmetrical struts 2 and 3 in bay B and bay C was used in Fig. 11 to present the illustration, but the layout may not be symmetrical which as occurred in the test of this study (see Fig. 9). The asymmetrical deformation of the test frame was caused by the different failure patterns of infill walls in bay B and bay C. During the failure process of the struts 1, different crack development and failure patterns for infill walls were found due to uncertainties of the material property and the construction quality: (a) One major crack appeared on the diagonal region and the infill wall was divided into two main parts (i.e., bay B), indicating that struts 2 and 3 were activated and their positions approached to the beam end, resulted in a diagonal compressive failure that occurred in beams; (b) Two or more major cracks appeared on the diagonal region and the infill wall was divided into three smaller main parts (i.e., bay C), indicating weaker struts 2 and 3 were activated in comparison with those in case (a) and their positions approached to the mid-span of beams, resulted in plastic hinges that formed in beams, as previously illustrated in Fig. 9.
3.2.4. Comparative evaluation Comparison of the test results is shown in Table 2. Due to the existence of infill walls, the initial secant stiffness of the frame with infill walls was 20.41 times that of the bare frame. Both of the specimens contained two deformation phases before the final failures in the progressive collapse processes. In the first phase, the adjacent and external columns moved outwards, indicating the development of compressive arch action in beams or equivalent compressive strut action in infill walls; in the second phase, the adjacent and external columns moved inwards, indicating the development of catenary action provided by rebars in
Fig. 7. Horizontal displacements of joints versus vertical displacement of the center column for the frame with infill walls. (a) Adjacent columns (b) External columns.
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Fig. 8. Major crack developments of the frame with infill walls in the initial deformation state. (a) At the vertical displacement of 3.1 mm (b) At the vertical displacement of 8.3 mm (c) At the vertical displacement of 13.5 mm (maximum resistance force) (d) At the vertical displacement of 20.3 mm (major cracks in the infill walls formed).
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Fig. 9. Cracks, diagonal compression failure and bending failure of the frame with infill walls at the vertical displacement of 90.6 mm.
the beams. The maximum resistance force of the frame with infill walls was 4.58 times that of the bare frame in the first phase. The vertical displacements of the center column corresponding to the maximum outward horizontal displacement of joint of the two specimens were 106.6 mm and 81.4 mm, respectively. The frame with infill walls experienced larger outward horizontal displacements of joints than those of the bare frame. The reason for the first significant reduction in the resistance force of bare frame was the fracture of rebar, however, that of the frame with infill walls was the major cracks formed in the infill walls. The vertical displacements corresponding to the first rebar fracture in the two specimens were 317.1 mm and 143.4 mm, respectively. Hence, it is found that although the resistance force of frame with infill walls was still larger than that of the bare frame across the entire deformation process, significant reduction in the resistance force induced by brittle failure and more damages in beams were also observed. Therefore, ductility performance of the beam was reduced by the presence of infill walls. For practical suggestions of increasing the progressive collapse resistance force of the frame with infill walls, besides the need to focus on enlarging the bending capacity in the beam ends similar as for the bare frame, shear capacity in the beam ends and bending capacity in the mid-span region of beams are also needed to enlarge. However, if the resistance force is already large enough, a simple design method to improve the ductility performance, is that arrangement of the horizontal rebars over beam and joints at the mid-height position of beam cross-section.
Fig. 10. Failure mode of the frame with infill walls at the end of the test.
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Fig. 11. Equivalent compressive struts and alternative load paths in bays B and C for the frame with infill walls. (a) Before peak resistance (b) After peak resistance.
4. Numerical analysis 4.1. Modeling details and verification To verify the test results and facilitate further parameter sensitivity analysis, three dimensional FE models of the test frames in accordance with the experiment specimen were constructed by ABAQUS [21]. Adjacent and external columns were assumed fixed on the ground and the center column was constrained to only allow the vertical displacement. Longitudinal rebars, stirrups and tie rebars were modeled using Truss element. The rebars were embedded into the concrete frame. Bilinear stress–strain relationships were assumed for the longitudinal rebar, stirrup and tie rebar materials. To simulate the fracture of them, the stress was dropped to 5 MPa after fracture strain. The remnant stress was set to 5 MPa, rather than 0 MPa, to avoid the convergence fault. Concrete and masonry bricks were modeled using 3D-Stress element. Concrete damaged plasticity model was adopted for concrete and brick materials, in which the skeleton curves were assumed following by Kent–Scott–Park model [25]. According to the test, the remnant strength for concrete was 20% of the maximum strength, the strain corresponding to the maximum strength was 0.002, and the ultimate strain was 0.006 for the concrete both in the first and second stories; the remnant strength for bricks was 10% of the maximum strength, the strain corresponding to the maximum qffiffiffiffiffi strength was 0.0029, and the ultimate 0 strain was 0.006. The tensile strength of concrete was assumed equal to 0:6228 f c , where fc′ is the compressive strength [26]; and the stress–strain relationship curve include two branches: the stiffening branch till the tensile strength, and the softening branch till the ultimate strain. The tensile strength of bricks ft′ was assumed to be 10% of the corresponding compressive strength [27], and the tensile constitutive law of the bricks was assumed to be similar to that of the concrete. The remnant stress f0 was set to 10%ft′ to avoid the convergence fault. The strain at the tensile strength εcr can be calculated as Ett, and the ultimate strain can be calculated as 6εcr [28]. In the modeling, the mortar joint thickness was halved and attached to the adjacent bricks. The half mortar joint contact with each other through cohesive element. The failures between bricks are at the mortar joints (mortar or the interfaces between brick and mortar), which occurred when the tensile or shear strength exceeds their capacities. Based on
Table 2 Comparison of the test results.
Bare frame Frame with infill walls
Initial secant stiffness (kN/mm)
Maximum resistance force when column moved outward (kN)
Vertical displacement when joints achieved outward maximum displacement (mm)
Vertical displacement when the first fracture of rebar (mm)
1.57 (1.00) 32.05 (20.41)
33.2 (1.00) 152.1 (4.58)
106.6 (1.00) 81.4 (0.76)
317.1 (1.00) 143.4 (0.45)
Note: (∙) denotes normalized ratio to values for the bare frame.
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the Chinese masonry building code [29], the tensile strength can be approximately regarded as equal to the shear strength. The strength of masonry unit (1.08 MPa) was used in the analyses to define the failures between bricks. Explicit dynamic analysis was used in this study to solve quasi-static problems and get a better numerical convergence. The 500 mm loading displacement was applied slowly to impair the dynamic effect. According to research [30], the loading time span is better to be increased to 100T, where T is the fundamental natural period of vibration in the deformation direction of the specimen, for the application of explicit dynamic analysis in quasi-static analysis. Based on the modal analysis, T was 0.0086 s for the test frame with infill walls. During the analysis, the total loading time span was 2 s, the functions in ABAQUS [21] such as smooth loading step and automatic computation of the time increment were used. In all of the analyses, the kinematic energy was monitored to ensure that its magnitude remained negligible. The damping ratio was set to 0.05 for the entire model. The numerical simulation results and the experimental results have been compared in Figs. 4, 5 and 7. It can be observed that the numerical models give acceptable predictions of the experimental responses. Fig. 12 shows the numerical simulation results of deformation state at the end of the test for both the two test specimens, in which similar features are observed when compared with the experimental results shown in Figs. 6 and 10.
4.2. Parametric analyses The material properties of the mortar joints, bricks, and tie rebars are factors that can influence the infill wall behavior. The strength of mortar joints between masonry bricks, may be varied in an infill wall, caused by the discrepancy of the ratio between cement, sand, aggregate and water among batches of mortar, interface properties between brick and mortar, and even of the bricklayers operating skills. Furthermore, the strength of bed joints and cross joints may be not identical due to their construction quality. To study the effects of strength of mortar joints on the progressive collapse performance of the frame with infill walls, the FE models with the strength of bed joints and cross joints respectively ranged from 0.5 to 1.5 times of the strength in the test were compared with the experimental results in Fig. 13. It can be observed that increasing the strength of the bed joints not only increases the maximum resistance force of the frames but also leads to slower resistance force degradation afterwards, indicating a better structural ductility. However, the strength of the cross joints has nearly no influence on the overall behavior. Some of other parameters, such as the compressive strength of bricks (0.5 to 1.5 times), tensile strength of tie rebars (0.5 to 1.5 times), are not explicitly discussed here because their influences on the progressive collapse performance has been found to be insignificant in the analyses. In the numerical simulation, all bed joints used a same strength and all cross joints used another
Fig. 12. FE result at the vertical displacement corresponding to the end of the test. (a) Bare frame (b) Frame with infill walls.
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Fig. 13. Influence of mortar joints strength on the resistance force of the frame with infill walls. (a) Bed joints (b) Cross joints.
same strength. However, each joint may have different strengths in a practical case and it can't be well predicted, leads to uncertainties in the major cracks formation and difficulties in the accurate numerical prediction of the structural response. 5. Conclusions A quasi-static test of a RC frame under progressive collapse scenario, with an emphasis on the full-height infill wall effects, was carried out to supplement experimental data on this topic and document the complete structural performance during the progressive collapse process. On the basis of the test observations and parametric numerical analyses, the findings of this research are as follows: 1. Compared with the bare frame, the RC frame with infill walls has larger progressive collapse resistance force and initial stiffness but lower beam ductility. At a same vertical displacement of the removed column, more cracks were observed along the beams in both the failure bays and adjacent bays for the frame with infill walls than for the bare frame. The major cracks in the infill walls formed in an early stage of the collapse, i.e., at a very small vertical displacement of the removed column, which corresponds to the reach of the maximum resistance force. 2. The frame with infill walls experience two deformation phases in progressive collapse. In the first phase, the resistance force is provided by beam bending or shear capacities, compressive arch action in beams or compressive strut action in infill walls; in the second phase, the resistance force is provided by catenary action in beams. The equivalent compressive strut model, which is usually used in the seismic response analyses of infilled frames, can also be used to illustrate the failure mechanism of infill walls and beams in progressive collapse. The positions of the struts depend on the major crack pattern in the infill walls, due to uncertainties in the crack formation process, may result in either bending or shear failures in beams. 3. The experimental results were validated by numerical simulation using fine finite element models. The material parameters relevant to infill walls were analyzed by modifying them from 0.5 to 1.5 times of their test values to investigate their influences on the progressive collapse resistance. The results indicate that the strength of bed mortar joints governing the maximum resistance force and resistance force degradation of the frame with infill walls; other parameters, such as the strength of cross mortar joints, compressive strength of bricks, and tensile strength of tie rebars have insignificant influences. Acknowledgments This research project is supported by the National Natural Science Foundation of China (Grant No. 51008101, 51578202, 51278150), and the China Postdoctoral Science Foundation (No. 2012T50361). The financial supports of these research funds are greatly appreciated by the authors. The second author thanks for the finicial support from China Scholarship Council (CSC, File No. 201306120170). The authors acknowledge the constructive comments and feedback of Prof. Halil Sezen at the Ohio State University at Columbus. This work was supported in part by an allocation of computing time from the Ohio Supercomputer Center. References [1] W.J. Yi, Q.F. He, Y. Xiao, S.K. Kunnath, Experimental study on progressive collapse-resistant behavior of reinforced concrete frame structures, ACI Struct. J. 105 (4) (2008) 433–439. [2] S. Kokot, A. Anthoine, P. Negro, G. Solomos, Static and dynamic analysis of a reinforced concrete flat slab frame building for progressive collapse, Eng. Struct. 40 (2012) 205–217.
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[3] J.L. Chen, X. Huang, R.L. Ma, M.J. He, Experimental study on the progressive collapse resistance of a two-story steel moment frame, J. Perform. Constr. Facil. 26 (2012) 567–575. [4] J. Li, H. Hao, Numerical study of structural progressive collapse using substructure technique, Eng. Struct. 52 (2013) 101–113. [5] B.I. Song, H. Sezen, Experimental and analytical progressive collapse assessment of a steel frame building, Eng. Struct. 56 (2013) 664–672. [6] H. Sezen, B.I. Song, K.A. Giriunas, Progressive collapse testing and analysis of a steel frame building, J. Constr. Steel Res. 94 (2014) 76–83. [7] Z.W. Huang, B. Li, P. Sengupta, Reliability assessment of damaged RC moment-resisting frame against progressive collapse under static loading conditions, J. Eng. Mech. 139 (1) (2013) 1–17. [8] J. Yu, K. Tan, Structural behavior of RC beam–column subassemblages under a middle column removal scenario, J. Struct. Eng. 139 (2) (2013) 233–250. [9] S. Sagiroglu, M. Sasani, Progressive collapse-resisting mechanisms of reinforced concrete structures and effects of initial damage locations, J. Struct. Eng. 140 (3) (2014)http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000854. [10] J.L. Le, B. Xue, Probabilistic analysis of reinforced concrete frame structures against progressive collapse, Eng. Struct. 76 (2014) 313–323. [11] K. Qian, B. Li, Research advances in design of structures to resist progressive collapse, J. Perform. Constr. Facil. (2014)http://dx.doi.org/10.1061/(ASCE)CF.19435509.0000698. [12] K. Qian, B. Li, J. Ma, Load-carrying mechanism to resist progressive collapse of RC buildings, J. Struct. Eng. 141 (2) (2015)http://dx.doi.org/10.1061/(ASCE)ST. 1943- 541X.0001046. [13] A. Fascetti, K.S. Kunnath, N. Nisticò, Robustness evaluation of RC frame buildings to progressive collapse, Eng. Struct. 86 (2015) 242–249. [14] M. Sasani, Response of a reinforced concrete infilled-frame structure to removal of two adjacent columns, Eng. Struct. 30 (9) (2008) 2478–2491. [15] M. Sasani, S. Sagiroglu, Progressive collapse resistance of Hotel San Diego, J. Struct. Eng. 134 (3) (2008) 478–488. [16] B.A. Mehrabi, B.P. Shing, P.M. Schuller, L.J. Noland, Experimental evaluation of masonry-infilled RC frames, J. Struct. Eng. 122 (3) (1996) 228–237. [17] R.S. Ju, H.J. Lee, C.C. Chen, C.C. Tao, Experimental study on separating reinforced concrete infill walls from steel moment frames, J. Constr. Steel Res. 71 (2012) 119–128. [18] S.M. Stinger, S.L. Orton, Esxperimental evaluation of disproportionate collapse resistance in reinforced concrete frames, ACI Struct. J. 110 (3) (2013) 521–530. [19] M.H. Tsai, T.C. Huang, Progressive collapse analysis of an RC building with exterior partially infilled walls, Struct. Des. Tall Spec. Build. 22 (4) (2013) 327–348. [20] S. Farazman, B.A. Izzuddin, D. Cormie, Influence of unreinforced masonry infill panels on the robustness of multistory buildings, J. Perform. Constr. Facil. 27 (6) (2013) 673–682. [21] Abaqus 6.13, Theory Guide, Dassault Systèmes Simulia Corp, 2013. [22] GB50010-2010, Code for Design of Concrete Structures, Ministry of Housing and Urban Rural Development, China, 2010. [23] GB50011-2010, Code for Seismic Design of Building, Ministry of Housing and Urban Rural Development, China, 2010. [24] W.W. El-Dakhakhni, M. Elgaaly, A.A. Hamid, Three-strut model for concrete masonry-infilled steel frames, J. Struct. Eng. 129 (2) (2003) 177–185. [25] E. Spacone, Flexibility-Based Finite Element Models for the Nonlinear Static and Dynamic Analysis of Concrete Frame Structures(PhD Dissertation) University of California, Berkeley, 1994. [26] M.H.M. Yassin, Nonlinear Analysis of Prestressed Concrete Structures Under Monotonic and Cyclic Loads(PhD Dissertation) University of California, Berkeley, 1994. [27] A. Mohyeddin, M.H. Goldsworthy, F.E. Gad, FE modeling of RC frames with masonry infill panels under in-plane and out-of-plane loading, Eng. Struct. 51 (2013) 73–87. [28] F.J. Crisafulli, Seismic Behaviour of Reinforced Concrete Structures with Masonry Infills(PhD Dissertation) University of Canterbury, 1997. [29] GB50003-2011, Code for Design of Masonry Structures, Ministry of Housing and Urban Rural Development, China, 2011. [30] M. Dhanasekar, W. Haider, Explicit finite element analysis of lightly reinforced masonry shear walls, Comput. Struct. 86 (1–2) (2008) 15–26.
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/efa
Experimental and numerical study on progressive collapse process of RC frames with full-height infill walls Shuang Li a,b,⁎, Sidi Shan a,b, Changhai Zhai a,b, Lili Xie b,c a b c
Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education (Harbin Institute of Technology), Harbin 150090, China School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
a r t i c l e
i n f o
Article history: Received 24 July 2015 Received in revised form 24 September 2015 Accepted 6 November 2015 Available online 7 November 2015 Keywords: Progressive collapse Experiment Infill wall Reinforced concrete frame Finite element analysis
a b s t r a c t The work presented in this study aimed to investigate the influence of infill walls on the progressive collapse performance of reinforced concrete (RC) frames. An experimental program of a one-third scaled, four-bay by two-story RC frame with full-height infill walls at the second story was conducted. Experimental results indicate that the maximum resistance force and failure mode of the RC frame with full-height infill walls are relevant to the major crack developments in the infill walls. The infill walls behave as equivalent compressive struts during progressive collapse process and can improve the resistance force and initial stiffness but reduce beam ductility and change failure mode of the RC frames. Verification of the test results and material parametric analyses of the test specimen by using finite element (FE) model were conducted to illustrate the factors that influence the behavior of the infilled frame. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction The progressive collapse of structure occurs when the sudden loss of local members leads to a collapse disproportionate to the original damage. Usually, these original damages are triggered by events which may lead to severe consequences, such as accidental explosion, serious fire or terrorist attacks. World-wide known examples of progressive collapses include the collapses of Ronan Point building in 1968, Murrah Federal Building in 1995 and World Trade Center in 2001, etc. Due to these terrible events, many experimental and numerical studies on progressive collapse of frame structures have been performed [1–13]. Nevertheless, very few of them have taken the interaction between the infill walls and the frame members into consideration, even though it is well known that infill walls may have conflicting effects on the structural response. Sasani et al. [14,15] have conducted a field test to investigate the progressive collapse performance of an actual three dimensional, multiple spans, infilled reinforced concrete (RC) frame by removing two adjacent columns located at the first story. It showed that infill walls help carry additional loads by providing the beams with constraints and supports. However, the test frame was strong enough to survive the column removal, therefore the final progressive collapse resistance capacity and damage mode were not evaluated. Furthermore, overall performance of a complete actual frame, rather than a simple sub-structure (e.g., two dimensional planar infilled frame that consists of only basic members including beams, columns and infill walls), is affected by many irrelevant factors which may not be easy to eliminate from the influences of infill walls. By conducting tests with sub-structures, the infill walls, even for the weak ones, were proved to change the seismic behavior of RC frame significantly [16], and contribute to the lateral stiffness and resistance of buildings remarkably [17]. Nevertheless, the
⁎ Corresponding author at: Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education (Harbin Institute of Technology), Harbin 150090, China. E-mail address: [email protected] (S. Li).
http://dx.doi.org/10.1016/j.engfailanal.2015.11.020 1350-6307/© 2015 Elsevier Ltd. All rights reserved.
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progressive collapse behavior of infill walls under a downward load may not be identical with the seismic behavior under a lateral load. To examine the effects of infill walls in progressive collapse performance, Stinger and Orton [18] tested a one-third scaled RC frame with partial-height infill walls by removing the center column. Because the percentage of opening in the infill walls was too high (that is, the infill walls were only approximately one-third high of the column), the effects of infill walls were not significant in their test. Except the experimental studies, a small number of numerical studies [19,20] have also been performed to explore the effects of infill walls on progressive collapse of RC frame; however, the failure mechanism was not investigated in these numerical studies. In a summary, at the present time the pros and cons of infill walls on structural progressive collapse are not clearly understood, and the laboratory experiments in the literature provide very limited data for studying the progressive collapse mechanism and for verifying the results of numerical simulation methods for infilled RC frame structures. Due to the lack of the test with sub-structures regarding the contribution of full-height infill walls in progressive collapse performance, a research program was carried out with the objective to provide the test data in this research aspect and investigate the behavior and influence of the infill walls in the progressive collapse process of the RC frames. Three dimensional finite element (FE) models of the test RC frames were developed at micro level by ABAQUS [21], and validated the experimental results. A series of parameter analyses were conducted and the factors that influenced the failure mechanisms were investigated.
2. Experimental material and methods 2.1. Specimen design A four-bay by six-bay and 5.1 m center-to-center column spacing RC building was designed in accordance with the Chinese building code [22,23] as a prototype frame. The prototype building had eight stories, in which the first story was 4.2 m high, and other stories with infill walls were 3.3 m high. The test model frame represents a one-third scaled sub-structure with four bays (i.e., along the short side) and two bottom stories from middle part of the building. The design detail of the test frame is given in Fig. 1 (the full-height infill walls were located at the second story in each bay, and left half part in Fig. 1 illustrates details of tie rebars constructed in infill walls). The longitudinal reinforcements of the test frame beams and columns comprised deformed rebars with a diameter of 8 mm. The stirrups of the test frame beams and columns comprised smooth surface steel wires with a diameter of 4 mm. The longitudinal reinforcements and stirrups of the test frame foundation comprised deformed rebars with diameters of 18 mm and 8 mm, respectively. The tie rebars used to tie infill walls to the surrounding columns in the second story comprised smooth surface steel wires with a diameter of 2 mm. All the stirrups consisted of 135-degree lap splices, and the tie rebars in infill walls consisted of 90-degree end hooks. The foundation, first story and second story of the test frame were cast separately and had a clear concrete cover of 15 mm. The infill walls
Fig. 1. Design details of test frame specimen. Bays A and B illustrate tie rebars between columns and infill walls, and bays C and D illustrate the infill walls. (Unit: mm).
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were composed of concrete bricks with dimension of 130 mm × 63.5 mm × 63.5 mm. The average thicknesses of the bed joints and the cross joints were 8.9 mm and 5.8 mm, respectively. Table 1 gives the mean material properties of rebars based on tensile strength tests. Standard concrete prism with dimension of 150 mm × 150 mm × 300 mm were used for concrete compressive tests. The measured compressive strength was 35.8 MPa, 41.3 MPa and 31.8 MPa for the foundation, first and second story concretes, respectively. The brick and mortar compressive strength was 22.6 MPa and 18.3 MPa, respectively. The measured compressive strength was 12.8 MPa and shear strength was 1.08 MPa for the masonry unit (combination of brick and mortar). 2.2. Test setup In the test program, a progressive collapse situation was simulated by applying quasi-static loading on the center column, as shown in Fig. 2. A hydraulic jack, placed at the top of the center column, apply a vertical load large enough to enforce the downward displacement at the joint. The load applied by hydraulic jack was transmitted to the hand jack through the center column. Then the test was performed under displacement control, and the loading process was initiated by lowering the hand jack stepby-step. Two collar devices, attached to the center column, were installed on the lateral steel braces to prevent the undesired outof-plane deformation and failure of the frame. There were 5 mm gap between the column surface and the collars before the loading to prevent unwanted friction force at the initial stage. Correspondingly, four collar devices, installed on the lateral steel braces, were attached to the adjacent and external columns. As shown in Fig. 3, the load cells installed above and below the center column were monitored to measure the applied vertical load. The difference between the forces at the load cells represents the external vertical load, which is equal to the resistance force against progressive collapse, i.e., the resistance force comes from the center column. Additional instrumentation consisted of relative displacement meters and linear variable differential transformers (LVDTs) to measure the vertical displacement of the center column, and lateral displacements of the adjacent and external columns. 3. Experimental results 3.1. Reference frame Before the test of the frame with infill walls, for comparison purpose, a test of a bare frame (taken as a reference frame) of the same design as shown in Fig. 1 but without infill walls was conducted. One of the curves in Fig. 4 shows the result of resistance force versus vertical displacement of the center column for the bare frame. Under loading, besides the initial state with nearly elastic behavior, the frame experienced two phases of resistance mechanism actions: compressive arch action before the vertical displacement reached 204.5 mm and then the catenary action. It was observed that at the compressive arch action phase, cracks formed in beams in bays B and C were concentrated in regions near the beam ends, which were mainly caused by the bending moment of beams. At the catenary action phase, cracks continually widened near the beam ends and some new cracks emerged and approached the middle region of beams. At the vertical displacement of 317.1 mm, the first rebar fractured in the top left end of beam BB2. The horizontal displacements of joints at the adjacent and external columns versus the vertical displacement of the center column are shown in Fig. 5. The adjacent and external joints firstly moved outward (i.e., horizontally away from the center column) and achieved their maximum values at the vertical displacement of 106.6 mm, then joints continued to move inward until the end of test. The final failure mode at the vertical displacement of 417.7 mm (the end of the test) is shown in Fig. 6. A similar progressive collapse test on a bare planar RC frame was also conducted in the study by Yi et al. [1], and the observations on the failure process in the present test are consistent with the previous study. 3.2. Frame with infill walls 3.2.1. Resistance force and displacement The test frame (frame with infill walls) had identical design to that of the reference frame but with full-height infill walls. Fig. 4 also shows the resistance force versus the vertical displacement of the center column for the frame with infill walls. With increasing vertical displacement, the resistance force gradually increased to its peak value (152.1 kN) at the vertical displacement of 13.5 mm. Then, the cracks formed in the infill walls and failures of beams caused two sudden reductions in the resistance force at the vertical displacements of 20.3 mm and 90.6 mm, respectively. After that point, due to rebar fractures and progressive development of cracks in the infill walls, the resistance force gradually decreased till the vertical displacement of
Table 1 Material properties of rebars. Rebar diameter (mm)
Yield strength (MPa)
Ultimate strength (MPa)
Fracture strain (MPa)
18 8 4 2
338 415 235 339
487 588 322 395
0.19 0.18 0.31 0.28
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Fig. 2. Loading and measure systems of the test specimen.
367.5 mm, then increased again owing to the catenary action. The test ended at the vertical displacement of 458.9 mm. Fig. 7 shows the horizontal displacements of joints at the adjacent and external columns versus the vertical displacement of the center column. Similar to the response of the bare frame, as the vertical displacement increased, the adjacent and external joints firstly moved outward and achieved their maximum values at the vertical displacement of 81.4 mm. Thereafter, the joints continued to move inward until the end of test. The asymmetrical horizontal displacements of joints in left and right parts of the frame were due to the different failure pattern of infill walls in bay B and bay C which will be discussed later. 3.2.2. Crack development and rebar fracture Fig. 8 shows developments of major cracks in infill walls and beams. A diagonal crack formed in the infill wall in bay B at the vertical displacement of only 3.1 mm, and an inclined crack formed in the infill wall in bay C at the vertical displacement of 8.3 mm. The development of another parallel inclined crack in the infill wall in bay C caused the first sudden reduction in the resistance force (see Figs. 8(d) and 4). It should be noted that, at a very small vertical displacement of 20.3 mm, the major cracks in the infill walls had finished formation. The second sudden reduction in the resistance force at the vertical displacement of 90.6 mm was caused by diagonal compression failures near the end of beams in bay B, as shown in Fig. 9. Then, rebars in the failure part of beams in bay B were in tension but with an angle to the rest parts, indicating that dowel actions occurred to resist the shear deformation. At the vertical displacement of 143.4 mm, one rebar fractured in the top of right region of beam BB2 (the region where diagonal compression failure occurred) due to shear deformation. At the vertical displacements of 200.4 mm and 216.5 mm, the rebars in the top of right end of beam BC1 fractured, successively. At the vertical displacements of 225.7 mm and 239.8 mm, the rebars in the bottom of middle region of beam BC1 fractured, successively. At the vertical displacements of
Fig. 3. Test instrumentations of the specimen (Unit: mm).
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Fig. 4. Resistance force versus vertical displacement of the center column for the test specimen.
293.3 mm and 328.6 mm, the rebars in the bottom of left end of beam BC2 fractured, successively. At the vertical displacement of 347.9 mm, the rebars in the top of middle region of beam BC2 fractured. The top three rows of tie rebars connecting column CB2 to the infill wall and bottom three rows of tie rebars connecting the center column to the infill wall deboned or fractured from the infill wall before the vertical displacement reached 90.6 mm. The separations of tie rebars resulted in detachment and rigid-body movement of the infill wall in bay B afterwards. At the vertical displacement of 367.5 mm, the upper triangular part of the infill wall in bay B fell out of plane. The final failure mode of the frame with infill walls at the end of the test is shown in Fig. 10, the damage of which was very different to that inflicted on the bare frame. The failure of the frame occurred where infill walls detached from the surrounding components. Compared to the bare frame, the failure positions in beams changed and more cracks formed along the beams in both the failure bays and adjacent bays.
3.2.3. Failure mechanisms The mechanical behavior of infill walls in the bays bridging the center column (i.e., bays B and C) can be explained by using the equivalent compressive strut model, which was usually used to model the infill walls in the seismic response analyses of infilled frames [24]. Although the parameters and layout of the struts in the equivalent compressive strut model used in seismic analysis and progressive collapse analysis may not be identical, test observations shown that this model is still suitable to describe the behavior of infill wall in the progressive collapse situation. As illustrated in Fig. 11(a), most portion of load on the center column transferred from struts 1 to adjacent bays before the peak resistance. Struts 1 started to fail when their compression capacity were exceeded by the increased transferred load, corresponding to the vertical displacement of 13.5 mm. Thereafter, as illustrated in Fig. 11(b), load from the top of center column redistributed and gradually transferred through struts 2 and 3 to adjacent bays.
Fig. 5. Horizontal displacements of joints versus vertical displacement of the center column for the bare frame. (a) Adjacent columns (b) External columns.
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Fig. 6. Failure mode of the bare frame at the end of the test.
Note that the diagram with symmetrical struts 2 and 3 in bay B and bay C was used in Fig. 11 to present the illustration, but the layout may not be symmetrical which as occurred in the test of this study (see Fig. 9). The asymmetrical deformation of the test frame was caused by the different failure patterns of infill walls in bay B and bay C. During the failure process of the struts 1, different crack development and failure patterns for infill walls were found due to uncertainties of the material property and the construction quality: (a) One major crack appeared on the diagonal region and the infill wall was divided into two main parts (i.e., bay B), indicating that struts 2 and 3 were activated and their positions approached to the beam end, resulted in a diagonal compressive failure that occurred in beams; (b) Two or more major cracks appeared on the diagonal region and the infill wall was divided into three smaller main parts (i.e., bay C), indicating weaker struts 2 and 3 were activated in comparison with those in case (a) and their positions approached to the mid-span of beams, resulted in plastic hinges that formed in beams, as previously illustrated in Fig. 9.
3.2.4. Comparative evaluation Comparison of the test results is shown in Table 2. Due to the existence of infill walls, the initial secant stiffness of the frame with infill walls was 20.41 times that of the bare frame. Both of the specimens contained two deformation phases before the final failures in the progressive collapse processes. In the first phase, the adjacent and external columns moved outwards, indicating the development of compressive arch action in beams or equivalent compressive strut action in infill walls; in the second phase, the adjacent and external columns moved inwards, indicating the development of catenary action provided by rebars in
Fig. 7. Horizontal displacements of joints versus vertical displacement of the center column for the frame with infill walls. (a) Adjacent columns (b) External columns.
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Fig. 8. Major crack developments of the frame with infill walls in the initial deformation state. (a) At the vertical displacement of 3.1 mm (b) At the vertical displacement of 8.3 mm (c) At the vertical displacement of 13.5 mm (maximum resistance force) (d) At the vertical displacement of 20.3 mm (major cracks in the infill walls formed).
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Fig. 9. Cracks, diagonal compression failure and bending failure of the frame with infill walls at the vertical displacement of 90.6 mm.
the beams. The maximum resistance force of the frame with infill walls was 4.58 times that of the bare frame in the first phase. The vertical displacements of the center column corresponding to the maximum outward horizontal displacement of joint of the two specimens were 106.6 mm and 81.4 mm, respectively. The frame with infill walls experienced larger outward horizontal displacements of joints than those of the bare frame. The reason for the first significant reduction in the resistance force of bare frame was the fracture of rebar, however, that of the frame with infill walls was the major cracks formed in the infill walls. The vertical displacements corresponding to the first rebar fracture in the two specimens were 317.1 mm and 143.4 mm, respectively. Hence, it is found that although the resistance force of frame with infill walls was still larger than that of the bare frame across the entire deformation process, significant reduction in the resistance force induced by brittle failure and more damages in beams were also observed. Therefore, ductility performance of the beam was reduced by the presence of infill walls. For practical suggestions of increasing the progressive collapse resistance force of the frame with infill walls, besides the need to focus on enlarging the bending capacity in the beam ends similar as for the bare frame, shear capacity in the beam ends and bending capacity in the mid-span region of beams are also needed to enlarge. However, if the resistance force is already large enough, a simple design method to improve the ductility performance, is that arrangement of the horizontal rebars over beam and joints at the mid-height position of beam cross-section.
Fig. 10. Failure mode of the frame with infill walls at the end of the test.
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Fig. 11. Equivalent compressive struts and alternative load paths in bays B and C for the frame with infill walls. (a) Before peak resistance (b) After peak resistance.
4. Numerical analysis 4.1. Modeling details and verification To verify the test results and facilitate further parameter sensitivity analysis, three dimensional FE models of the test frames in accordance with the experiment specimen were constructed by ABAQUS [21]. Adjacent and external columns were assumed fixed on the ground and the center column was constrained to only allow the vertical displacement. Longitudinal rebars, stirrups and tie rebars were modeled using Truss element. The rebars were embedded into the concrete frame. Bilinear stress–strain relationships were assumed for the longitudinal rebar, stirrup and tie rebar materials. To simulate the fracture of them, the stress was dropped to 5 MPa after fracture strain. The remnant stress was set to 5 MPa, rather than 0 MPa, to avoid the convergence fault. Concrete and masonry bricks were modeled using 3D-Stress element. Concrete damaged plasticity model was adopted for concrete and brick materials, in which the skeleton curves were assumed following by Kent–Scott–Park model [25]. According to the test, the remnant strength for concrete was 20% of the maximum strength, the strain corresponding to the maximum strength was 0.002, and the ultimate strain was 0.006 for the concrete both in the first and second stories; the remnant strength for bricks was 10% of the maximum strength, the strain corresponding to the maximum qffiffiffiffiffi strength was 0.0029, and the ultimate 0 strain was 0.006. The tensile strength of concrete was assumed equal to 0:6228 f c , where fc′ is the compressive strength [26]; and the stress–strain relationship curve include two branches: the stiffening branch till the tensile strength, and the softening branch till the ultimate strain. The tensile strength of bricks ft′ was assumed to be 10% of the corresponding compressive strength [27], and the tensile constitutive law of the bricks was assumed to be similar to that of the concrete. The remnant stress f0 was set to 10%ft′ to avoid the convergence fault. The strain at the tensile strength εcr can be calculated as Ett, and the ultimate strain can be calculated as 6εcr [28]. In the modeling, the mortar joint thickness was halved and attached to the adjacent bricks. The half mortar joint contact with each other through cohesive element. The failures between bricks are at the mortar joints (mortar or the interfaces between brick and mortar), which occurred when the tensile or shear strength exceeds their capacities. Based on
Table 2 Comparison of the test results.
Bare frame Frame with infill walls
Initial secant stiffness (kN/mm)
Maximum resistance force when column moved outward (kN)
Vertical displacement when joints achieved outward maximum displacement (mm)
Vertical displacement when the first fracture of rebar (mm)
1.57 (1.00) 32.05 (20.41)
33.2 (1.00) 152.1 (4.58)
106.6 (1.00) 81.4 (0.76)
317.1 (1.00) 143.4 (0.45)
Note: (∙) denotes normalized ratio to values for the bare frame.
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the Chinese masonry building code [29], the tensile strength can be approximately regarded as equal to the shear strength. The strength of masonry unit (1.08 MPa) was used in the analyses to define the failures between bricks. Explicit dynamic analysis was used in this study to solve quasi-static problems and get a better numerical convergence. The 500 mm loading displacement was applied slowly to impair the dynamic effect. According to research [30], the loading time span is better to be increased to 100T, where T is the fundamental natural period of vibration in the deformation direction of the specimen, for the application of explicit dynamic analysis in quasi-static analysis. Based on the modal analysis, T was 0.0086 s for the test frame with infill walls. During the analysis, the total loading time span was 2 s, the functions in ABAQUS [21] such as smooth loading step and automatic computation of the time increment were used. In all of the analyses, the kinematic energy was monitored to ensure that its magnitude remained negligible. The damping ratio was set to 0.05 for the entire model. The numerical simulation results and the experimental results have been compared in Figs. 4, 5 and 7. It can be observed that the numerical models give acceptable predictions of the experimental responses. Fig. 12 shows the numerical simulation results of deformation state at the end of the test for both the two test specimens, in which similar features are observed when compared with the experimental results shown in Figs. 6 and 10.
4.2. Parametric analyses The material properties of the mortar joints, bricks, and tie rebars are factors that can influence the infill wall behavior. The strength of mortar joints between masonry bricks, may be varied in an infill wall, caused by the discrepancy of the ratio between cement, sand, aggregate and water among batches of mortar, interface properties between brick and mortar, and even of the bricklayers operating skills. Furthermore, the strength of bed joints and cross joints may be not identical due to their construction quality. To study the effects of strength of mortar joints on the progressive collapse performance of the frame with infill walls, the FE models with the strength of bed joints and cross joints respectively ranged from 0.5 to 1.5 times of the strength in the test were compared with the experimental results in Fig. 13. It can be observed that increasing the strength of the bed joints not only increases the maximum resistance force of the frames but also leads to slower resistance force degradation afterwards, indicating a better structural ductility. However, the strength of the cross joints has nearly no influence on the overall behavior. Some of other parameters, such as the compressive strength of bricks (0.5 to 1.5 times), tensile strength of tie rebars (0.5 to 1.5 times), are not explicitly discussed here because their influences on the progressive collapse performance has been found to be insignificant in the analyses. In the numerical simulation, all bed joints used a same strength and all cross joints used another
Fig. 12. FE result at the vertical displacement corresponding to the end of the test. (a) Bare frame (b) Frame with infill walls.
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Fig. 13. Influence of mortar joints strength on the resistance force of the frame with infill walls. (a) Bed joints (b) Cross joints.
same strength. However, each joint may have different strengths in a practical case and it can't be well predicted, leads to uncertainties in the major cracks formation and difficulties in the accurate numerical prediction of the structural response. 5. Conclusions A quasi-static test of a RC frame under progressive collapse scenario, with an emphasis on the full-height infill wall effects, was carried out to supplement experimental data on this topic and document the complete structural performance during the progressive collapse process. On the basis of the test observations and parametric numerical analyses, the findings of this research are as follows: 1. Compared with the bare frame, the RC frame with infill walls has larger progressive collapse resistance force and initial stiffness but lower beam ductility. At a same vertical displacement of the removed column, more cracks were observed along the beams in both the failure bays and adjacent bays for the frame with infill walls than for the bare frame. The major cracks in the infill walls formed in an early stage of the collapse, i.e., at a very small vertical displacement of the removed column, which corresponds to the reach of the maximum resistance force. 2. The frame with infill walls experience two deformation phases in progressive collapse. In the first phase, the resistance force is provided by beam bending or shear capacities, compressive arch action in beams or compressive strut action in infill walls; in the second phase, the resistance force is provided by catenary action in beams. The equivalent compressive strut model, which is usually used in the seismic response analyses of infilled frames, can also be used to illustrate the failure mechanism of infill walls and beams in progressive collapse. The positions of the struts depend on the major crack pattern in the infill walls, due to uncertainties in the crack formation process, may result in either bending or shear failures in beams. 3. The experimental results were validated by numerical simulation using fine finite element models. The material parameters relevant to infill walls were analyzed by modifying them from 0.5 to 1.5 times of their test values to investigate their influences on the progressive collapse resistance. The results indicate that the strength of bed mortar joints governing the maximum resistance force and resistance force degradation of the frame with infill walls; other parameters, such as the strength of cross mortar joints, compressive strength of bricks, and tensile strength of tie rebars have insignificant influences. Acknowledgments This research project is supported by the National Natural Science Foundation of China (Grant No. 51008101, 51578202, 51278150), and the China Postdoctoral Science Foundation (No. 2012T50361). The financial supports of these research funds are greatly appreciated by the authors. The second author thanks for the finicial support from China Scholarship Council (CSC, File No. 201306120170). The authors acknowledge the constructive comments and feedback of Prof. Halil Sezen at the Ohio State University at Columbus. This work was supported in part by an allocation of computing time from the Ohio Supercomputer Center. References [1] W.J. Yi, Q.F. He, Y. Xiao, S.K. Kunnath, Experimental study on progressive collapse-resistant behavior of reinforced concrete frame structures, ACI Struct. J. 105 (4) (2008) 433–439. [2] S. Kokot, A. Anthoine, P. Negro, G. Solomos, Static and dynamic analysis of a reinforced concrete flat slab frame building for progressive collapse, Eng. Struct. 40 (2012) 205–217.
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