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Images, eqnz.chch.2010

Column reinforcement exposed under spalled concrete after the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, eqnz.chch.2010

Column reinforcement exposed under spalled concrete after the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, eqnz.chch.2010

Column reinforcement exposed under spalled concrete after the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, eqnz.chch.2010

Column reinforcement exposed under spalled concrete after the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, eqnz.chch.2010

Column reinforcement exposed under spalled concrete after the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, eqnz.chch.2010

Column reinforcement exposed under spalled concrete after the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, eqnz.chch.2010

Column reinforcement exposed under spalled concrete after the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, eqnz.chch.2010

Column reinforcement exposed under spalled concrete after the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Research papers, University of Canterbury Library

Geosynthetic reinforced soil (GRS) walls involve the use of geosynthetic reinforcement (polymer material) within the retained backfill, forming a reinforced soil block where transmission of overturning and sliding forces on the wall to the backfill occurs. Key advantages of GRS systems include the reduced need for large foundations, cost reduction (up to 50%), lower environmental costs, faster construction and significantly improved seismic performance as observed in previous earthquakes. Design methods in New Zealand have not been well established and as a result, GRS structures do not have a uniform level of seismic and static resistance; hence involve different risks of failure. Further research is required to better understand the seismic behaviour of GRS structures to advance design practices. The experimental study of this research involved a series of twelve 1-g shake table tests on reduced-scale (1:5) GRS wall models using the University of Canterbury shake-table. The seismic excitation of the models was unidirectional sinusoidal input motion with a predominant frequency of 5Hz and 10s duration. Seismic excitation of the model commenced at an acceleration amplitude level of 0.1g and was incrementally increased by 0.1g in subsequent excitation levels up to failure (excessive displacement of the wall panel). The wall models were 900mm high with a full-height rigid facing panel and five layers of Microgird reinforcement (reinforcement spacing of 150mm). The wall panel toe was founded on a rigid foundation and was free to slide. The backfill deposit was constructed from dry Albany sand to a backfill relative density, Dr = 85% or 50% through model vibration. The influence of GRS wall parameters such as reinforcement length and layout, backfill density and application of a 3kPa surcharge on the backfill surface was investigated in the testing sequence. Through extensive instrumentation of the wall models, the wall facing displacements, backfill accelerations, earth pressures and reinforcement loads were recorded at the varying levels of model excitation. Additionally, backfill deformation was also measured through high-speed imaging and Geotechnical Particle Image Velocimetry (GeoPIV) analysis. The GeoPIV analysis enabled the identification of the evolution of shear strains and volumetric strains within the backfill at low strain levels before failure of the wall thus allowing interpretations to be made regarding the strain development and shear band progression within the retained backfill. Rotation about the wall toe was the predominant failure mechanism in all excitation level with sliding only significant in the last two excitation levels, resulting in a bi-linear displacement acceleration curve. An increase in acceleration amplification with increasing excitation was observed with amplification factors of up to 1.5 recorded. Maximum seismic and static horizontal earth pressures were recorded at failure and were recorded at the wall toe. The highest reinforcement load was recorded at the lowest (deepest in the backfill) reinforcement layer with a decrease in peak load observed at failure, possibly due to pullout failure of the reinforcement layer. Conversely, peak reinforcement load was recorded at failure for the top reinforcement layer. The staggered reinforcement models exhibited greater wall stability than the uniform reinforcement models of L/H=0.75. However, similar critical accelerations were determined for the two wall models due to the coarseness of excitation level increments of 0.1g. The extended top reinforcements were found to restrict the rotational component of displacement and prevented the development of a preliminary shear band at the middle reinforcement layer, contributing positively to wall stability. Lower acceleration amplification factors were determined for the longer uniform reinforcement length models due to reduced model deformation. A greater distribution of reinforcement load towards the top two extended reinforcement layers was also observed in the staggered wall models. An increase in model backfill density was observed to result in greater wall stability than an increase in uniform reinforcement length. Greater acceleration amplification was observed in looser backfill models due to their lower model stiffness. Due to greater confinement of the reinforcement layers, greater reinforcement loads were developed in higher density wall models with less wall movement required to engage the reinforcement layers and mobilise their resistance. The application of surcharge on the backfill was observed to initially increase the wall stability due to greater normal stresses within the backfill but at greater excitation levels, the surcharge contribution to wall destabilising inertial forces outweighs its contribution to wall stability. As a result, no clear influence of surcharge on the critical acceleration of the wall models was observed. Lower acceleration amplification factors were observed for the surcharged models as the surcharge acts as a damper during excitation. The application of the surcharge also increases the magnitude of reinforcement load developed due to greater confinement and increased wall destabilising forces. The rotation of the wall panel resulted in the progressive development of shears surface with depth that extended from the backfill surface to the ends of the reinforcement (edge of the reinforced soil block). The resultant failure plane would have extended from the backfill surface to the lowest reinforcement layer before developing at the toe of the wall, forming a two-wedge failure mechanism. This is confirmed by development of failure planes at the lowest reinforcement layer (deepest with the backfill) and at the wall toe observed at the critical acceleration level. Key observations of the effect of different wall parameters from the GeoPIV results are found to be in good agreement with conclusions developed from the other forms of instrumentation. Further research is required to achieve the goal of developing seismic guidelines for GRS walls in geotechnical structures in New Zealand. This includes developing and testing wall models with a different facing type (segmental or wrap-around facing), load cell instrumentation of all reinforcement layers, dynamic loading on the wall panel and the use of local soils as the backfill material. Lastly, the limitations of the experimental procedure and wall models should be understood.

Images, UC QuakeStudies

Two workers inspect fuses placed in an embankment during reinforcement work. The photographer comments, "This is the reinforcing of an embankment in the port of Lyttelton, which partly collapsed in the Christchurch earthquakes. They are using the same equipment as used for blowing up rock faces to mend them".

Research papers, University of Canterbury Library

This thesis is concerned with the effects of lateral confining reinforcement on the ductile behaviour of reinforced concrete columns. The contents of the chapters are summarized as follows. In Chapter one, the general problems in seismic design are discussed and earthquake design methods based on the ductile design approach are described. Japanese, New Zealand and United States design codes are compared. Finally, the scope of this research project is outlined. In Chapter two, after reviewing previous research on confined concrete, the factors which affect the effectiveness of lateral confinement are discussed. Especially the effects of the yield strength of transverse reinforcement, the compressive strength of plain concrete and the strain gradient in the column section due to bending are discussed based on tests which were conducted by the author et al at Kyoto University and Akashi Technological College, Japan. In the axial compression tests on spirally reinforced concrete cylinders (150 mm in diameter by 300 mm in height), the yield strength of transverse reinforcement and the compressive strength of plain concrete were varied from 161 MPa to 1352 MPa and from 17 MPa to 60 MPa, respectively, as experimental parameters. It is found that, when high strength spirals are used as confining reinforcement, the strength and ductility of the confined core concrete are remarkably enhanced but need to be estimated assuming several failure modes which could occur. These are based on the observations that concrete cylinders with high strength spirals suddenly failed at a concrete compressive strain of 2 to 3.5 % due to explosive crushing of the core concrete between the spiral bars or due to bearing failure of the core concrete immediately beneath the spiral bars, while the concrete cylinders with ordinary strength spirals failed in a gentle manner normally observed. In addition, eccentric loading tests were conducted on concrete columns with 200 mm square section confined by square spirals. It is found that the effectiveness of confining reinforcement is reduced by the presence of the strain gradient along the transverse section of column. In Chapter three, the effectiveness of transverse reinforcement with various types of anchorage details which simplify the fabrication of reinforcing cages are investigated. Eight reinforced concrete columns, with either 400 mm or 550 mm square cross sections, were tested subjected to axial compression loading and cyclic lateral loading which simulated a severe earthquake. The transverse reinforcement consisted of arrangements of square perimeter hoops with 135° end hooks, cross ties with 90° and 135° or 180° end hooks, and 'U' and 'J' shaped cross ties and perimeter hoops with tension splices. Conclusions are reached with regard to the effectiveness of the tested anchorage details in the plastic hinge regions of columns designed for earthquake resistance. In Chapter four, the effectiveness of interlocking spirals as transverse reinforcement is studied. Firstly, the general aspects and the related problems of interlocking spirals to provide adequate ductility in the potential plastic hinge region of columns are discussed, referring to the provisions in the New Zealand code,the CALTRANS (California Transportation Authority) code and other related codes. Secondly, based on those discussions, a design method to securely interlock the spirals is proposed. Thirdly, the effectiveness of interlocking spirals is assessed based on column tests conducted as part of this study. Three columns with interlocking spirals and, for comparison, one rectangular column with rectangular hoopsandcross ties, were tested under cyclic horizontal loading which simulated a severe earthquake. The sections of those columns were 400 mm by 600 mm. In Chapter five, analytical models to investigate the buckling behaviour of longitudinal reinforcement restrained by cross ties with 90° and 135° end hooks and by peripheral hoops are proposed. The analyzed results using the proposed models compare well with the experimental observations described in Chapter three. Using those proposed models, a method to check the effectiveness of cross ties with 90° and 135° end hooks is proposed for practical design purposes. In Chapter six, a theory for the prediction of the ultimate longitudinal compressive concrete strain at the stage of first hoop fracture referred to as the "Energy Balance Theory", which has been developed by Mander, Priestley and Park at University of Canterbury, is introduced. After discussing the problems in the "Energy Balance Theory", a modified theory for the prediction of the ultimate longitudinal compressive concrete strain at the stage of first hoop fracture is proposed. The predictions from the modified theory are found to compare well with previous experimental results.

Research papers, University of Canterbury Library

Reinforced concrete structures designed in pre-1970s are vulnerable under earthquakes due to lack of seismic detailing to provide adequate ductility. Typical deficiencies of pre-1970s reinforced concrete structures are (a) use of plain bars as longitudinal reinforcement, (b) inadequate anchorage of beam longitudinal reinforcement in the column (particularly exterior column), (c) lack of joint transverse reinforcement if any, (d) lapped splices located just above joint, and (e) low concrete strength. Furthermore, the use of infill walls is a controversial issue because it can help to provide additional stiffness to the structure on the positive side and on the negative side it can increase the possibility of soft-storey mechanisms if it is distributed irregularly. Experimental research to investigate the possible seismic behaviour of pre-1970s reinforced concrete structures have been carried out in the past. However, there is still an absence of experimental tests on the 3-D response of existing beam-column joints under bi-directional cyclic loading, such as corner joints. As part of the research work herein presented, a series of experimental tests on beam-column subassemblies with typical detailing of pre-1970s buildings has been carried out to investigate the behaviour of existing reinforced concrete structures. Six two-third scale plane frame exterior beam-column joint subassemblies were constructed and tested under quasi-static cyclic loading in the Structural Laboratory of the University of Canterbury. The reinforcement detailing and beam dimension were varied to investigate their effect on the seismic behaviour. Four specimens were conventional deep beam-column joint, with two of them using deformed longitudinal bars and beam bars bent in to the joint and the two others using plain round longitudinal bars and beam bars with end hooks. The other two specimens were shallow beam-column joint, one with deformed longitudinal bars and beam bars bent in to the joint, the other with plain round longitudinal bars and beam bars with end hooks. All units had one transverse reinforcement in the joint. The results of the experimental tests indicated that conventional exterior beam-column joint with typical detailing of pre-1970s building would experience serious diagonal tension cracking in the joint panel under earthquake. The use of plain round bars with end hooks for beam longitudinal reinforcement results in more severe damage in the joint core when compared to the use of deformed bars for beam longitudinal reinforcement bent in to the joint, due to the combination of bar slips and concrete crushing. One interesting outcome is that the use of shallow beam in the exterior beam-column joint could avoid the joint cracking due to the beam size although the strength provided lower when compared with the use of deep beam with equal moment capacity. Therefore, taking into account the low strength and stiffness, shallow beam can be reintroduced as an alternative solution in design process. In addition, the presence of single transverse reinforcement in the joint core can provide additional confinement after the first crack occurred, thus delaying the strength degradation of the structure. Three two-third scale space frame corner beam-column joint subassemblies were also constructed to investigate the biaxial loading effect. Two specimens were deep-deep beam-corner column joint specimens and the other one was deep-shallow beam-corner column joint specimen. One deep-deep beam-corner column joint specimen was not using any transverse reinforcement in the joint core while the two other specimens were using one transverse reinforcement in the joint core. Plain round longitudinal bars were used for all units with hook anchorage for the beam bars. Results from the tests confirmed the evidences from earthquake damage observations with the exterior 3-D (corner) beam-column joint subjected to biaxial loading would have less strength and suffer higher damage in the joint area under earthquake. Furthermore, the joint shear relation in the two directions is calibrated from the results to provide better analysis. An analytical model was used to simulate the seismic behaviour of the joints with the help of Ruaumoko software. Alternative strength degradation curves corresponding to different reinforcement detailing of beam-column joint unit were proposed based on the test results.

Research papers, University of Canterbury Library

The recent earthquakes in Christchurch have made it clear that issues exist with current RC frame design in New Zealand. In particular, beam elongation in RC frame buildings was widespread and resulted in numerous buildings being rendered irreparable. Design solutions to overcome this problem are clearly needed, and the slotted beam is one such solution. This system has a distinct advantage over other damage avoidance design systems in that it can be constructed using current industry techniques and conventional reinforcing steel. As the name suggests, the slotted beam incorporates a vertical slot along part of the beam depth at the beam-column interface. Geometric beam elongation is accommodated via opening and closing of these slots during seismically induced rotations, while the top concrete hinge is heavily reinforced to prevent material inelastic elongation. Past research on slotted beams has shown that the bond demand on the bottom longitudinal reinforcement is increased compared with equivalent monolithic systems. Satisfying this increased bond demand through conventional means may yield impractical and economically less viable column dimensions. The same research also indicated that the joint shear mechanism was different to that observed within monolithic joints and that additional horizontal reinforcement was required as a result. Through a combination of theoretical investigation, forensic analysis, and database study, this research addresses the above issues and develops design guidelines. The use of supplementary vertical joint stirrups was investigated as a means of improving bond performance without the need for non-standard reinforcing steel or other hardware. These design guidelines were then validated experimentally with the testing of two 80% scale beam-column sub-assemblies. The revised provisions for bond within the bottom longitudinal reinforcement were found to be adequate while the top longitudinal reinforcement remained nominally elastic throughout both tests. An alternate mechanism was found to govern joint shear behaviour, removing the need for additional horizontal joint reinforcement. Current NZS3101:2006 joint shear reinforcement provisions were found to be more than adequate given the typically larger column depths required rendering the strut mechanism more effective. The test results were then used to further refine design recommendations for practicing engineers. Finally, conclusions and future research requirements were outlined.

Images, eqnz.chch.2010

The Westpac building suffered damage at its beam / column joints during the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, eqnz.chch.2010

This shop on Riccarton Road was badly damaged in the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010, and had to be demolished.

Images, eqnz.chch.2010

This shop caught fire when power restored caused sparks that ignited leaking gas, in the aftermath of the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, eqnz.chch.2010

Repairs being carried out on this restaurant (converted from a church) at the Hereford Street / Manchester Street intersection;aftermath of the magnitude 7.1 earthquake that struck Christchurch on Saturday 4 September 2010.

Images, UC QuakeStudies

A digitally manipulated photograph of twisted reinforcing rods amongst the rubble from the demolition of QEII. The photographer comments, "These rarely seen worms live in the pressurised earth under the foundations of buildings. They need a damp soil and be under at least 100 pounds of pressure per square inch. After the destructive force of an earthquake they swiftly rise to the surface through gaps in the rubble. Unfortunately they quickly die and then crystallise as hard as iron in the dry low pressure air".

Research papers, University of Canterbury Library

Capacity design and hierarchy of strength philosophies at the base of modern seismic codes allow inelastic response in case of severe earthquakes and thus, in most traditional systems, damage develops at well-defined locations of reinforced concrete (RC) structures, known as plastic hinges. The 2010 and 2011 Christchurch earthquakes have demonstrated that this philosophy worked as expected. Plastic hinges formed in beams, in coupling beams and at the base of columns and walls. Structures were damaged permanently, but did not collapse. The 2010 and 2011 Christchurch earthquakes also highlighted a critical issue: the reparability of damaged buildings. No methodologies or techniques were available to estimate the level of subsequent earthquakes that RC buildings could still sustain before collapse. No repair techniques capable of restoring the initial condition of buildings were known. Finally, the cost-effectiveness of an eventual repair intervention, when compared with a new building, was unknown. These aspects, added to nuances of New Zealand building owners’ insurance coverage, encouraged the demolition of many buildings. Moreover, there was a perceived strong demand from government and industry to develop techniques for assessing damage to steel reinforcement bars embedded in cracked structural concrete elements. The most common questions were: “Have the steel bars been damaged in correspondence to the concrete cracks?”, “How much plastic deformation have the steel bars undergone?”, and “What is the residual strain capacity of the damaged bars?” Minimally invasive techniques capable of quantifying the level and extent of plastic deformation and residual strain capacity are not yet available. Although some studies had been recently conducted, a validated method is yet to be widely accepted. In this thesis, a least-invasive method for the damage-assessment of steel reinforcement is developed. Based on the information obtained from hardness testing and a single tensile test, it is possible to estimate the mechanical properties of earthquake-damaged rebars. The reduction in the low-cycle fatigue life due to strain ageing is also quantified. The proposed damage assessment methodology is based on empirical relationships between hardness and strain and residual strain capacity. If damage is suspected from in situ measurements, visual inspection or computer analysis, a bar may be removed and more accurate hardness measurements can be obtained using the lab-based Vickers hardness methodology. The Vickers hardness profile of damaged bars is then compared with calibration curves (Vickers hardness versus strain and residual strain capacity) previously developed for similar steel reinforcement bars extracted from undamaged locations. Experimental tests demonstrated that the time- and temperature-dependent strain-ageing phenomenon causes changes in the mechanical properties of plastically deformed steels. In particular, yield strength and hardness increases, whereas ductility decreases. The changes in mechanical properties are quantified and their implications on the hardness method are highlighted. Low-cycle fatigue (LCF) failures of steel reinforcing bars have been observed in laboratory testing and post-earthquake damage inspections. Often, failure might not occur during a first seismic event. However, damage is accumulated and the remaining fatigue life is reduced. Failure might therefore occur in a subsequent seismic event. Although numerous studies exist on the LCF behaviour of steel rebars, no studies had been conducted on the strain-ageing effects on the remaining fatigue life. In this thesis, the reduction in fatigue life due to this phenomenon is determined through a number of experimental tests.

Research papers, University of Canterbury Library

A major lesson from the 2011 Christchurch earthquake was the apparent lack of ductility of some lightly reinforced concrete (RC) wall structures. In particular, the structural behaviour of the critical wall in the Gallery Apartments building demonstrated that the inelastic deformation capacity of a structure, as well as potentially brittle failure of the reinforcement, is dependent on the level of bond deterioration between reinforcement and surrounding concrete that occurs under seismic loading. This paper presents the findings of an experimental study on bond behaviour between deformed reinforcing bars and the surrounding concrete. Bond strength and relative bond slip was evaluated using 75 pull-out tests under monotonic and cyclic loading. Variations of the experiments include the loading rate, loading history, concrete strength (25 to 70 MPa), concrete age, cover thickness, bar diameter (16 and 20 mm), embedded length, and the position of the embedded bond region within the specimen (deep within or close to free surface). Select test results are presented with inferred implications for RC structures.

Research papers, University of Canterbury Library

Reconnaissance reports have highlighted the poor performance of non-ductile reinforced concrete buildings during the 2010-11 Canterbury earthquakes. These buildings are widely expected to result in significant losses under future earthquakes due to their seismic vulnerability and prevalence in densely populated urban areas. Wellington, for example, contains more than 70 pre-1970s multi-storey reinforced concrete buildings, ranging in height from 5 to 18 storeys. This study seeks to characterise the seismic performance and evaluate the likely failure modes of a typical pre-1970s reinforced concrete building in Wellington, by conducting advanced numerical simulations to evaluate its 3D nonlinear dynamic response. A representative 9-storey office building constructed in 1951 is chosen for this study and modelled in the finite element analysis programme DIANA, using a previously developed and validated approach to predict the failure modes of doubly reinforced walls with confined boundary regions. The structure consists of long walls and robust framing elements resulting in a stiff lateral load resisting system. Barbell-shaped walls are flanked by stiff columns with sufficient transverse reinforcement to serve as boundary regions. Curved shell elements are used to model the walls and their boundary columns, for which the steel reinforcement is explicitly modelled. Line elements are used to model the frame elements. The steel reinforcement in each member is explicitly modelled. The floor slabs are modelled using elastic shell elements. The model is analysed under short and long duration ground motions selected to match site specific targets in Wellington at the DBE and MCE intensity levels. The observed response of the building including drift profiles at each intesity level, strain localization effects around wall openings, and the influence of bidirectional loading are discussed.

Research papers, University of Canterbury Library

The performance of conventionally designed reinforced concrete (RC) structures during the 2011 Christchurch earthquake has demonstrated that there is greater uncertainty in the seismic performance of RC components than previously understood. RC frame and wall structures in the Christchurch central business district were observed to form undesirable cracks patterns in the plastic hinge region while yield penetration either side of cracks, and into development zones, were less than theoretical predictions. The implications of this unexpected behaviour: (i) significantly less available ductility; (ii) less hysteretic energy dissipation; and (iii) the localization of peak reinforcement strains, results in considerable doubt for the residual capacity of RC structures. The significance of these consequences has prompted a review of potential sources of uncertainty in seismic experimentation with the intention to improve the current confidence level for newly designed conventional RC structures. This paper attempts to revisit the principles of RC mechanics, in particular, to consider the influence of loading history, concrete tensile strength, and reinforcement ratio on the performance of ‘real’ RC structures compared to experimental test specimens.

Research papers, University of Canterbury Library

A building boom in the 1980s allowed pre-stressed hollow-core floor construction to be widely adopted in New Zealand, even though the behaviour of these prefabricated elements within buildings was still uncertain. Inspections following the Canterbury and Kaikōura earthquakes has provided evidence of web-splitting, transverse cracking and longitudinal splitting on hollow-core units, confirming the susceptibility of these floors to undesirable failure modes. Hollow-core slabs are mainly designed to resist bending and shear. However, there are many applications in which they are also subjected to torsion. In New Zealand, hollow-core units contain no transverse reinforcement in the soffit concrete below the cells and no web reinforcement. Consequently, their dependable performance in torsion is limited to actions that they can resist before torsional cracking occurs. In previous work by the present authors, a three-dimensional FE modelling approach to study the shear flexural behaviour of precast pre-stressed hollow core units was developed and validated by full-scale experiments. This paper shows how the FE analyses have been extended to investigate the response of HC units subjected to torsional actions. Constitutive models, based on nonlinear fracture mechanics, have been used to numerically predict the torsional capacity of HC units and have been compared with experimental results. The results indicate that the numerical approach is promising and should be developed further as part of future research.

Research papers, University of Canterbury Library

Observations of out-of-plane (OOP) instability in the 2010 Chile earthquake and in the 2011 Christchurch earthquake resulted in concerns about the current design provisions of structural walls. This mode of failure was previously observed in the experimental response of some wall specimens subjected to in-plane loading. Therefore, the postulations proposed for prediction of the limit states corresponding to OOP instability of rectangular walls are generally based on stability analysis under in-plane loading only. These approaches address stability of a cracked wall section when subjected to compression, thereby considering the level of residual strain developed in the reinforcement as the parameter that prevents timely crack closure of the wall section and induces stability failure. The New Zealand code requirements addressing the OOP instability of structural walls are based on the assumptions used in the literature and the analytical methods proposed for mathematical determination of the critical strain values. In this study, a parametric study is conducted using a numerical model capable of simulating OOP instability of rectangular walls to evaluate sensitivity of the OOP response of rectangular walls to variation of different parameters identified to be governing this failure mechanism. The effects of wall slenderness (unsupported height-to-thickness) ratio, longitudinal reinforcement ratio of the boundary regions and length on the OOP response of walls are evaluated. A clear trend was observed regarding the influence of these parameters on the initiation of OOP displacement, based on which simple equations are proposed for prediction of OOP instability in rectangular walls.