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Unexpected failure modes were observed in RC walls in the 2010 Chile and 2011 New Zealand earthquakes. A peculiar failure mode, not previously reported in the structural engineering literature, was the brittle collapse of one of the structural walls of the 28-story Grand Chancellor Hotel in Christchurch, New Zealand. As one of the first steps toward the understanding of this failure mode, three rectangular RC walls were tested under bidirectional quasi-static cyclic loading. The only parameter varied among the three specimens was the structural detailing associated to various level of ductility design of the wall cross section. It was found that whereas the wall with nominal ductility section detailing (μ=1.25) experienced an out-of-plane shear-axial failure, those with higher ductility section detailing (1.25<μ<3 and μ>3) performed reasonably well. However, a relatively abrupt axial crushing failure was observed in the ductile walls at higher drift levels that needs further investigation. The bidirectional loading, rarely adopted in experimental tests or in numerical simulation due to its inherent complexity, was found to be one of the key factors in the development of out-of-plane shear-axial failure. Moreover, it was observed that walls with 0.3Agfc′ axial load, which is the maximum limit of the current New Zealand standard for concrete structures, and designed according to nominal ductile detailing might be prone to out-of-plane shear-axial failure. [ABSTRACT FROM AUTHOR]

On 22 February 2011, one of the main structural walls of one of the tallest buildings in Christchurch, New Zealand (Grand Chancellor Hotel), had an extremely brittle and unusual failure that significantly damaged the building, severely compromising its structural stability. To this date, this peculiar failure mode has not yet been fully investigated and understood. Moreover, currently, it is not possible to identify and assess walls that are prone to this failure mode. Following recent findings based on experimental investigations, this failure mode was identified as out‐of‐plane shear‐axial failure. A Finite Element (FE) model was developed in DIANA to capture this failure mode, and through a numerical parametric study, the key parameters that contribute to the development of this failure mode in rectangular reinforced concrete (RC) walls were identified. Solid elements were used for the concrete material and embedded truss elements for the steel reinforcement. Bar buckling was not included in this investigation due to the limitation of DIANA in implementing the bar buckling and Menegotto‐Pinto models together, among which the latter was found to be more influential on the behaviour of RC walls investigated in this study. Based on the numerical and experimental studies conducted, an analytical method is proposed to: (1) identify rectangular walls prone to out‐of‐plane shear‐axial failure as a first‐level check for both design and assessment purposes; and (2) determine the out‐of‐plane drift capacity of rectangular walls prone to out‐of‐plane shear‐axial failure. Design recommendations are provided for rectangular walls prone to out‐of‐plane shear‐axial failure. [ABSTRACT FROM AUTHOR]

Following observations of out-of-plane instability in slender ductile structural walls in some recent earthquakes, this mode of wall failure has been and is being investigated by several research groups. Analytical, numerical and experimental investigations have been conducted to study this failure mechanism as well as its controlling parameters. Both singly reinforced and doubly reinforced concrete walls have been studied under unidirectional and bidirectional loading. A simplified approach making use of concrete columns representing boundary zones of rectangular walls has also been used to reduce the computational and experimental costs of the research programs. This paper provides a state-of-the-art on the research conducted on this failure mechanism and the corresponding findings, with the main focus on the walls with rectangular cross-sections and under unidirectional loading. The out-of-plane response of walls is classified into five different modes and the likely forms of force-displacement and out-of-plane displacement history plots corresponding to each mode are discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this experimental study, three identical reinforced concrete (RC) walls were tested under three different lateral loading patterns. These loading patterns were cyclic in‐plane, skewed with 45° angle and clover leaf. The main objective was to investigate the effects of these bi‐directional loading patterns on the seismic behavior of slender rectangular RC walls. The results showed significant increase in tensile and compressive strains in concrete and longitudinal bars that led to earlier cover concrete spalling and bar buckling in the specimens subjected to bi‐directional loading. The neutral axis depth and compression zone were found to be substantially larger when subjected to bi‐directional loading and this led to the occurrence of concrete crushing and bar buckling in the web. Moreover, lateral instability failure triggered earlier in the specimens under bi‐directional loading, as a result of reduction of out‐of‐plane stiffness of the wall. However, bi‐directional loading did not significantly increase out‐of‐plane buckling of the wall in terms of out‐of‐plane displacement. In‐plane and out‐of‐plane shear cracks formed in one of the specimens subjected to bi‐directional loading, whereas the same wall under in‐plane loading developed only flexural cracks. It was also found that in‐plane shear deformation was larger when the wall was subjected to bi‐directional loading. The results of this experimental study emphasize the need for further investigation of the effects of bi‐directional loading on RC structural walls. [ABSTRACT FROM AUTHOR]

The effects of different parameters on the evolution of Out-Of-Plane (OOP) instability in rectangular walls were studied using a validated FEM model. Based on this parametric analysis, a test matrix was designed to experimentally investigate the progression of this mode of failure in rectangular walls. Results of the parametric study were presented within a companion paper, while the experimental observations as well as the numerical versus experimental comparisons are presented in this paper. The wall specimens were tested under in-plane cyclic loading and they exhibited different OOP responses. The development of OOP mechanisms was observed in all tested specimens, albeit with different values of maximum OOP displacement and followed by different types of instability. Progression of OOP deformation was suppressed by other failure modes in all specimens except one which failed due to large OOP displacement and global instability. In this study, the progression of OOP deformation and its relationship with the inelastic strain gradients of the longitudinal reinforcement along the length and height of the specimens are scrutinized and the numerical predictions are compared with the test measurements. The experimental findings regarding the evolution of this mode of failure and the influential parameters are in good agreement with the numerical predictions. However, the onset of OOP deformation typically had a delay in the numerical model when compared to the test results. One of the factors inducing this difference could be the effect of inherent and mostly unmeasurable eccentricities, including material, geometry as well as loading imperfections, which were not included in the model. [ABSTRACT FROM AUTHOR]

The research presented here seeks to address the key parameters influential on out-of-plane (OOP) instability of rectangular walls, which was observed in the 2010 Chile and the 2011 New Zealand earthquakes in some well-confined modern walls. For this purpose, a finite element model, previously verified for its capability to reliably simulate different failure modes of this type of structural walls, was adopted. The parametric matrix included a series of specimens designed to be tested by the authors and other specimens already tested by other researchers. The effect of slenderness (unsupported height-to-thickness) ratio, reinforcement ratio, length and axial load on the OOP response of these specimens is scrutinized using the predicted response of the boundary region longitudinal reinforcement at the elevation corresponding to the maximum OOP displacement in each case. For a given slenderness and longitudinal reinforcement ratio, development of a critical average tensile strain over a certain height can lead to formation of OOP instability in walls. Therefore, the effect of these parameters on the strain history, strain gradient along the wall height, as well as the stress–strain response of the longitudinal bars throughout the cyclic loading are evaluated and the variation of the OOP response attributable to the effect of each parameter is discussed. This parametric study indicated that the initiation of OOP displacement in doubly reinforced walls after unloading from a peak displacement and during reloading in the opposite direction is in line with the significant reduction of compressive stiffness (yielding in compression) in the boundary region longitudinal bars along a specific height (at least 60% of the wall height). Based on the findings of this study, an experimental campaign was designed and four of the parametric models were experimentally tested under in-plane cyclic loading. In addition to the parameters noted above, the effects of shear strength, boundary conditions and eccentricity of material properties across the wall thickness on the OOP response of the benchmark parametric model are also briefly discussed. The experimental observations as well as the numerical versus experimental comparisons are presented in a companion paper. [ABSTRACT FROM AUTHOR]

This study investigates the ability of a finite element model based on curved shell element formulation in predicting nonlinear behavior of planar RC structural walls, identifying the strengths and limitations of this modeling approach. For this purpose, a parametric validation is conducted in addition to verification of the model simulation against experimental results of several wall specimens tested in literature. The effects of variations in total length, thickness, shear-span ratio, axial load ratio, confinement, as well as the horizontal and vertical reinforcement ratios are investigated at both global and local levels. For scrutinizing the global response, lateral load versus total, flexural and shear deformation predictions are used. For local response, sensitivity of the stress and strain distributions throughout the length and height of the wall models to the parameters noted above is evaluated. The capabilities and deficiencies of the modelling approach are discussed in detail in light of the numerical versus experimental as well as parametric verifications. The model is found to be able to predict most of the experimentally observed failure mechanisms of rectangular walls including global out-of-plane instability under in-plane loading, concrete crushing at the base, diagonal tension and diagonal compression as well as sliding shear. The model is not able to represent bar buckling, bar fracture and the potential subsequent secondary failure modes such as instability of the compression boundary zone due to progressive asymmetric concrete crushing at the base. The parametric study indicated sensitivity of the model response to the variation of the parameters known to be influential on the nonlinear response of planar RC walls. [ABSTRACT FROM AUTHOR]

The simple lateral mechanism analysis (SLaMA) is an analytical method to assess the force–displacement capacity curve of Reinforced Concrete (RC) structures composed of frames, cantilever walls or dual wall/frame systems. The current version of the method was proposed in the 2017 New Zealand guidelines for the seismic assessment (NZSEE in New Zealand Society for Earthquake Engineering, the seismic assessment of existing buildings—technical guidelines for engineering assessments, Wellington, 2017). Regarding frame structures, the possible influence of infill walls is currently considered locally with checks on the RC members. However, it is universally known that infills have a major effect on the global capacity curve of the frame. In this paper, a comprehensive SLaMA method for infilled frames is proposed, which allows considering the influence of the infills on the global force–displacement curve without any numerical algorithm. The extended SLaMA method is herein formalised and it is validated in a companion paper (part 2) through an extensive parametric analysis. The extended SLaMA is based on the possibility to separately calculate the base shear contributions of the frame and the infills, in turn based on global equilibrium considerations. Such considerations also allow defining a novel procedure to post-process the results of pushover or time-history analyses where infills are modelled as diagonal struts, or to interpret experimental tests. This allows, within a single numerical analysis, to decouple the frame and infills contributions to the base-shear capacity. The decoupling procedure is herein demonstrated for an ideal two-storey, one-bay masonry-infilled frame with different infills configurations. [ABSTRACT FROM AUTHOR]

Highlights • A by-hand procedure for the non-linear capacity curve of RC wall/frame systems is proposed. • The mechanical interaction among frame(s) and wall(s) is explicitly considered. • 28 case studies: different geometry, wall-to-frame strength ratio and plastic mechanism. • Comparison with pushover analyses shows a maximum 5% error (base shear and displacement). Abstract A paramount step in seismic assessment of existing structures is the determination of the structural capacity. It is widely recognised that non-linear numerical approaches are arguably the most reliable tool to achieve this goal. However, reliable yet simple analytical procedures are needed to identify potential structural weaknesses and their influence on the overall capacity, to cross-check and/or interpret numerical analyses. This paper presents a novel analytical -or "by-hand"- procedure to calculate the non-linear capacity curve of RC dual wall/frame systems within the framework of the Simple Lateral Mechanism Analysis (SLaMA). The mechanical interaction among frame(s) and wall(s) is explicitly considered to calculate their base shear and overturning moment contributions. The procedure is outlined and applied to 28 case studies with different geometry, wall(s) position, wall-to-frame strength ratio and plastic mechanism. The results are compared to refined numerical pushover analyses, showing a maximum 5% error both in terms of ultimate base shear and displacement for the majority of the case studies. [ABSTRACT FROM AUTHOR]

• Nonlinear constitutive laws for simulating glued connections shear failure. • Numerical applications on two-storey masonry assemblages under seismic load. • Sensitivity study of mechanical parameters of the vertical glued connection. • Adoption of smeared crack models for the nonlinear behaviour of masonry. • Investigation of numerical issues caused by the brittle failure of the connection. Terraced houses built in the Netherland after 1980 are often characterized by the use of large units connected at corners by continuous thin layer mortar joints. Unlike the running bond pattern, usually modelled as a rigid connection, the vertical continuous connection may fail in shear and influence the global seismic capacity of the entire building. This work aims at investigating and comparing different numerical modelling approaches for simulating the vertical connections. Two different constitutive models are adopted to simulate the quasi-brittle nonlinear behaviour of the continuous joint, and their advantages and limitations are pointed out in terms of robustness and accuracy. The study considers both the component level in terms of U-shaped pier-wall configuration, and the full-scale structural level in terms of the global capacity for a two-storey masonry house assemblage, characterized by a running bond arrangement. The results of this work show that the shear failure involving the continuous joint usually reduces the strength capacity of the structure. Both the selection of constitutive models for the connection interface and masonry material are demonstrated to affect the results significantly. Decoupled direct traction-displacement relations for the interfaces appear to provide more robust results than coupled plasticity-based Coulomb friction laws. The selection of either a pre-fixed orthotropic smeared crack model for the masonry or a standard isotropic concrete-like rotating smeared crack formulation is demonstrated to strongly influence the activation of the different failure mechanisms and hence the response of the structure. [ABSTRACT FROM AUTHOR]