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ArayaLetelier, G., Parra, P. F., LopezGarcia, D., GarciaValdes, A., Candia, G., & Lagos, R. (2019). Collapse risk assessment of a Chilean dual wallframe reinforced concrete office building. Eng. Struct., 183, 770–779.
Abstract: Several codeconforming reinforced concrete buildings were severely damaged during the 2010 moment magnitude (Mw) 8.8 Chile earthquake, raising concerns about their real collapse margin. Although critical updates were introduced into the Chilean design codes after 2010, guidelines for collapse risk assessment of Chilean buildings remain insufficient. This study evaluates the collapse potential of a typical dual system (shear walls and moment frames) office building in Santiago. Collapse fragility functions were obtained through incremental dynamic analyses using a stateoftheart finite element model of the building. Sitespecific seismic hazard curves were developed, which explicitly incorporated epistemic uncertainty, and combined with the collapse fragility functions to estimate the mean annual frequency of collapse (lambda(c)) values and probabilities of collapse in 50years (Pc(50)). Computed values of lambda(c) and Pc(50) were on the order of 10(5)10(4), and 0.10.7%, respectively, consistent with similar studies developed for buildings in the US. The results also showed that the deaggregation of lambda(c) was controlled by small to medium earthquake intensities and that different models of the collapse fragility functions and hazard curves had a nonnegligible effect on lambda(c) and Pc(50), and thus, propagation of uncertainty in risk assessment problems must be adequately taken into account.

Cando, M. A., Hube, M. A., Parra, P. F., & Arteta, C. A. (2020). Effect of stiffness on the seismic performance of code conforming reinforced concrete shear wall buildings. Eng. Struct., 219, 14 pp.
Abstract: This study assesses the effect of the stiffness on the seismic performance of residential shear wall buildings designed according to current Chilean regulations, including DS60 and DS61. Specifically, the paper focuses on the effect of stiffness on the building overstrength, displacement ductility, fragility for Life Safety (LS) and collapse limit states, as well as the probability of achieving these two limits states in 50 years. The seismic performance is assessed for a group of four 20 story residential shear wall buildings archetypes located in Santiago. Walls were modeled using the multiple vertical line element model (MVLEM) with inelastic hysteretic materials for the vertical elements, and a linear elastic shear behavior. Pushover analyses were considered to estimate the buildings overstrength and displacement ductility, while incremental dynamic analyses were per formed to estimate fragility curves. A probabilistic seismic hazard analysis, which considered the seismicity of Chile central zone, was performed to estimate the probability of achieving the two limits states in 50 years. The results show that an increase in the stiffness reduces the chance of exceeding the LS and collapse limit states for the same intensity level. Additionally, the probabilistic seismic hazard analysis shows that, when the stiffness increases, the probability of reaching the LS limit state in 50 years also decreases. Counterintuitively, the probability of collapse in 50 years increases as the stiffness increases, due to the considered seismic hazard and the design requirements. Since society is moving towards resilient structural designs that minimize damage, disruption and economic losses, it is concluded that the performance of reinforced concrete shear wall buildings is improved by increasing the stiffness.
Keywords: Reinforced concrete; Shear wall; Building; Collapse; Life safety; Stiffness; Fragility; Risk

Parra, P. F., & Moehle, J. P. (2017). Stability of Slender Wall Boundaries Subjected to Earthquake Loading. ACI Struct. J., 114(6), 1627–1636.
Abstract: Global instability of slender reinforced concrete walls occurs when the concrete section buckles outofplane over a portion of the wall length and height. Theoretical and numerical analyses were conducted on axially loaded prismatic members to evaluate the onset of global instability under tension/compression load cycles. A buckling theory suitable for hand calculations is introduced and evaluated using data available in the literature from tests conducted on columns. Computer simulations using forcebased nonlinear elements with fibers are used to numerically simulate the tests and to study the influence of nonuniform strain profiles along the height of the member. The study shows that the onset of buckling can be identified using either the proposed buckling theory or finite element models. Furthermore, buckling is affected by gradients of axial load or strain along the length of the member. Design recommendations are made to inhibit global wall buckling during earthquakes.
Keywords: buckling; earthquake; reinforced concrete; slenderness; wall boundary element

Parra, P. F., & Moehle, J. P. (2020). Effects of strain gradients in the onset of global buckling in slender walls due to earthquake loading. Bull. Earthq. Eng., 18(7), 3205–3221.
Abstract: Global buckling of slender walls, reported only in a few laboratory tests before 2010, became a critical issue in design of reinforced concrete buildings after it was observed following the 2010 Mw 8.8 Chile earthquake and the 2011 Mw 6.3 New Zealand earthquake. Researchers have proposed theoretical buckling models based on prismatic columns subjected to uniform tension/compression cycles, where the key parameters are slenderness ratio, number of curtains of reinforcement, and maximum tensile strain before buckling during load reversal. These models have shown sufficient accuracy in comparison with laboratory tests on columns under such loading conditions. However, buckling in walls is more complex because of variation of strains through the wall depth and variation of moment along the wall height. Nonlinear finite elements are used to evaluate the effects of these more complex loadings on buckling of wall boundary elements. Analyses showed that the maximum tensile strain (averaged over the wall outofplane unsupported height) required to buckle the wall during load reversal does not depend on the moment variation along the wall height. Moreover, for typical wall lengths, the wall boundary behaves like an isolated column subjected to axial force cycles, with minimal apparent bracing provided by the wall web. This allows to analyze a broad range of practical cases for buckling susceptibility using simplified approaches based on buckling models of axially loaded columns.
Keywords: Walls; Global buckling; Reinforced concrete; Earthquake

Parra, P. F., Arteta, C. A., & Moehle, J. P. (2019). Modeling criteria of older nonductile concrete framewall buildings. Bull. Earthq. Eng., 17(12), 6591–6620.
Abstract: The purpose of seismic provisions included in modern building codes is to obtain a satisfactory structural performance of buildings during earthquakes. However, in the United States and elsewhere, there are large inventories of buildings designed and constructed several decades ago, under outdated building codes. Some of these buildings are classified as nonductile buildings. Currently, under the ATC78 project, a methodology is being developed to identify seismically hazardous framewall buildings through a simple procedure that does not require full nonlinear analyses by the responsible engineer. This methodology requires the determination of the controlling plastic collapse mechanism, the base shear strength, and the ratio between the story drift ratio and the roof drift ratio, called parameter alpha, at collapse level. The procedure is calibrated with fully inelastic nonlinear analyses of archetype buildings. In this paper we first introduce an efficient scheme for modeling framewall buildings using the software OpenSees. Later, the plastic collapse mechanism, the base shear strength, and values of alpha are estimated from nonlinear static and dynamic analyses considering a large suite of groundmotion records that represent increasing hazard levels. The analytical experiment included several framewall combinations in 4 and 8story buildings, intended to represent a broad range of conditions that can be found in actual buildings, where the simplified methodology to evaluate the risk of collapse can be applicable. Analysis results indicate that even walls of modest length may positively modify the collapse mechanism of nonductile bare frames preventing soft story failures.

Ugalde, D., LopezGarcia, D., & Parra, P. F. (2020). Fragilitybased analysis of the influence of effective stiffness of reinforced concrete members in shear wall buildings. Bull. Earthq. Eng., 18(5), 2061–2082.
Abstract: When modeling RC shear wall buildings for seismic analysis there is little consensus in the literature on the appropriate value of the wall effective shear stiffness (GA(eff)) and the slab effective bending stiffness (EIeff). A probabilistic analysis based on fragility curves is a robust technique to assess the influence of these parameters on the expected seismic performance, but such studies are scarce because they require computationally expensive analysis such as Incremental Dynamic Analysis (IDA). In this paper, fragility curves are developed following the recently introduced SPO2FRAG procedure, a simplified methodology that does not require IDA but the computationally more affordable incremental static (pushover) analysis. The fragility curves provided by SPO2FRAG are used to evaluate the influence of the values of GA(eff) and EIeff on the analytical seismic response of full 3D nonlinear models of two actual (and representative) residential wall buildings of 17 and 26 stories located in Santiago (Chile). The accuracy of SPO2FRAG is also evaluated through comparisons with empirical fragilities.

Ugalde, D., Parra, P. F., & LopezGarcia, D. (2019). Assessment of the seismic capacity of tall wall buildings using nonlinear finite element modeling. Bull. Earthq. Eng., 17(12), 6565–6589.
Abstract: Two existing RC shear wall buildings of 17 and 26 stories were analyzed using fully nonlinear finite element models, i.e., models that include nonlinear material behavior and geometric nonlinearities. The buildings are located in Santiago, Chile and are representative of Chilean residential buildings in the sense that they have a large number of shear walls. The buildings withstood undamaged the 2010 Chile earthquake even though they were subjected to demands much larger than the codespecified demand. The approach to model the RC shear walls was validated through comparisons with results experimentally obtained from cyclic static tests conducted on isolated wall specimens. Several pushover analyses were performed to assess the global response of the buildings under seismic actions and to evaluate the influence of several modeling issues. Response history analyses were performed considering a ground motion recorded in Santiago during the 2010 Chile earthquake. In general, results (in terms of both global and local response quantities) are consistent with results given by pushover analysis and with the empirically observed lack of damage, a consistency that was not found in a previous study that considered linearly elastic models. The tangential interstory drift deformation was found to correlate much better with the lack of observable damage than the total interstory drift deformation typically considered in practice. The analysis also revealed that foundation uplift is possible but does not seem to significantly influence the response. Other modeling issues that were found to deserve further research are the shear stiffness of the walls and the influence of the slabs.
