From plastic hinge to shell models: Recommendations for RC wall models

The severe damage and collapse of many reinforced concrete (RC) wall buildings in the recent earthquakes of Chile (2010) and New Zealand (2011) have shown that RC walls did not perform as well as expected based on the design calculations required by the modern codes of both countries. In this context, it seems appropriate to intensify research efforts in more accurate simulations of damage indicators, in particular local engineering demand parameters such as material strains, which are central to the application of performance-based earthquake engineering. Potential modelling improvements will necessarily build on a thorough assessment of the limitations of current state-of-the-practice simulation approaches. This work aims to compare the response variability given by a spectrum of numerical tools commonly used by researchers and specialized practitioners, namely: plastic hinge analyses, distributed plasticity models, and detailed finite element simulations. It is shown that a multi-level assessment—wherein both the global and local levels are jointly investigated from the response analysis outcomes—is fundamental to define the dependability of the results. The latter is controlled by the attainment of material strain limits and the occurrence of numerical problems. Finally, the influence of shear deformations is analysed according to the same methodological framework

Axially equilibrated displacement-based beam element for simulating the cyclic inelastic behaviour of RC members

Distributed plasticity beam elements are commonly used to evaluate limit state demands for performance based analysis of reinforced concrete (RC) structures. Strain limits are often preferred to drift limits since they directly relate to damage and are therefore less dependent on member geometry and boundary conditions. However, predicting accurately strain demands still represents a major simulation challenge. Tension shift effects, which induce a linear curvature profile in the plastic hinge region of RC columns and walls, are one of the main causes for the mismatch between experimental and numerical estimates of local level quantities obtained through force-based formulations. Classical displacement-based approaches are instead suitable to simulate such linear curvature profile. Unfortunately, they verify equilibrium only on an average sense due to the wrong assumption on the axial displacement field, leading to poor deformation and force predictions. This paper presents a displacement-based element in which axial equilibrium is strictly verified along the element length. The assumed transversal displacement field ensures a linear curvature profile, connecting accurately global displacement and local strain demands. The proposed finite element is validated against two sets of quasi-static cyclic tests on RC bridge piers and walls. The results show that curvature and strain profiles for increasing ductility demands are significantly improved when axially equilibrated rather than classical displacement-based or force-based elements are used to model the structural members

Modelling approaches for inelastic behaviour of RC walls: Multi-level assessment and dependability of results

The severe damage and collapse of many reinforced concrete (RC) wall buildings in the recent earthquakes of Chile (2010) and New Zealand (2011) have shown that RC walls did not perform as well as required by the modern codes of both countries. It seems therefore appropriate to intensify research efforts towards more accurate simulations of damage indicators, in particular local engineering demand parameters such as material strains, which are central to the application of performance-based earthquake engineering. Potential modelling improvements will necessarily build on a thorough assessment of the limitations of current state-of-the-practice simulation approaches for RC wall buildings. This work compares different response parameters obtained from monotonic analyses of RC walls using numerical tools that are commonly employed by researchers and specialized practitioners, namely: plastic hinge analyses, distributed plasticity models, and shell element models. It is shown that a multi-level assessment—wherein both the global and local levels of the response are jointly addressed during pre- and post-peak response—is fundamental to define the dependability of the results. The displacement demand up to which the wall response can be predicted is defined as the first occurrence between the attainment of material strain limits and numerical issues such as localization. The present work also presents evidence to discourage the application of performance-based assessment of RC walls relying on non-regularized strain EDPs

Elemento de Viga Baseado em Formulação de Rigidez Enriquecido com Funções de Forma Adaptativas para Garantir Equilíbrio Axial

In the framework of Performance Based Earthquake Engineering (PBEE), assessing the inelastic behaviour of structures both at the global (force-displacement) and local (stress-strain) level is of priority importance. This goal is typically achieved by advanced nonlinear analysis that rely on the use of increasing computational power. Due to a good compromise between accuracy and processing time, distributed plasticity beam elements represent the most employed finite element in nonlinear structural analysis. In particular, displacement-based elements are the simplest in terms of implementation and the most efficient from the state determination viewpoint. However, a fundamental drawback of classical displacement-based formulations is related to the assigned axial displacement field. This limitation implies that equilibrium is only verified on an average sense and, in case of material nonlinearity, it yields different values of the axial force in distinct integration sections. This results in a misevaluation of the moment capacity of the structural member and therefore in a poor local and global performance of the finite element. In this paper a new displacement-based element strictly verifying the axial equilibrium condition is introduced. The latter was implemented by the authors in an ad hoc finite element software and its performance is presented by means of two application examples. Comparisons between classical displacement-based and force-based formulations are made, both at the global and local level

Axially Equilibrated Displacement-based Beam Element: Implementation in OpenSees and Application to Dynamic Analysis of Structures

Experimental tests on the inelastic behavior of RC bridge piers have shown that, due to tension shift effects, the curvature profile above the base section of the structural member differs from the one that would develop according to a force-based or a classical displacement-based beam formulation with plane section hypothesis. Due to the inclined cracks in concrete members, it was found that the curvature distribution evolves in a bilinear shape along the member height during the inelastic phase of the response, and that the length of plastification increases with increasing ductility demands. Recently, it was shown that axially equilibrated displacement-based elements can more effectively predict the local-level response of RC members. The process of imposing the equilibrium of the axial forces along the element length allows the beam element to improve the simulation of both curvature and strain profiles. The finite element was originally implemented in the authors’ structural analysis software SAGRES, which was developed for nonlinear static analysis and is not freely available to the engineering community. This paper presents the validation of the implemented axially equilibrated displacement-based element in the open source finite element software OpenSees and provides some application examples of both nonlinear static and dynamic analyses. The results are compared against classical approaches (force-based and displacement-based), pinpointing the advantages of the axially equilibrated displacement-based beam element

Influence of Lap Splices on the Deformation Capacity of RC Walls. II: Shell Element Simulation and Equivalent Uniaxial Model

Spliced longitudinal reinforcement may result in a reduction of both strength and displacement capacity of reinforced concrete (RC) members. This applies in particular when lap splices are located in regions where inelastic deformations concentrate, such as the plastic zone at the base of RC walls. This paper introduces a simple numerical model suitable for engineering practice to simulate the force-displacement response of RC walls with lap splices. Based on experimental data from 16 test units, an equivalent uniaxial steel stress-strain law is proposed that represents the monotonic envelope of the cyclic response of spliced rebars in RC walls up to the onset of strength degradation. It allows for modeling lap splice response with finite element (FE) models while avoiding the use of complex interface bond-slip elements. A new semi-empirical expression for the strain at the onset of strength degradation is derived, which expresses the strain capacity of the lap splice as a function of the confining reinforcement ratio and the ratio of lap splice length to shear span of the wall. The proposed equivalent constitutive law was included in shell element models to predict the force-displacement response of the test unit set of RC walls. Results demonstrated the ability of this approach to adequately capture the peak strength and displacement capacity of the spliced units

Adequabilidade de deformações locais como parâmetro na avaliação sísmica de paredes de betão armado

O dano severo e o colapso de diversos edifícios com paredes estruturais em betão armado (BA) durante os recentes sismos do Chile (2010) e Nova Zelândia (2011) revelaram que muitas paredes de BA não tiveram o desempenho que seria expectável da aplicação das modernas técnicas de dimensionamento requeridas pelos regulamentos de ambos os países. Esta observação pode indiciar uma incapacidade dos actuais modelos em simular adequadamente indicadores de dano. Nesse âmbito, o presente artigo compara a variabilidade da resposta estimada por diversas técnicas de modelação correntemente utilizadas por investigadores e especialistas, em particular: análises de rótula plástica, elementos de viga com plasticidade distribuída, e modelos com elementos de membrana. Tendo em conta que estimativas de deformações locais, tais como extensões e curvaturas, têm sido progressivamente adoptadas como parâmetros de resposta estrutural, este estudo mostra e interpreta a variabilidade dos resultados das técnicas anteriores no contexto de uma avaliação multi-nível, em que a resposta ao nível local é analisada simultaneamente com a mais tradicional resposta ao nível global

Influence of Lap Splices on the Deformation Capacity of RC Walls. I: Database Assembly, Recent Experimental Data, and Findings for Model Development

Recent postearthquake missions have shown that reinforced concrete (RC) wall buildings can experience critical damage owing to lap splices, which led to a recent surge in experimental tests of walls with such constructional details. Most of the 16 wall tests described in the literature thus far were carried out in the last six years. This paper presents a database with these wall tests, including the description of a new test on a wall with lap splices and a corresponding reference wall with continuous reinforcement. They complement the existing tests by investigating a spliced member with a shear span ratio smaller than two, which is the smallest among them. The objective of this database is to collect information not just on the force capacity but mainly on the deformation capacity of lap splices in reinforced concrete walls. It is shown that (1) well-confined lap splices relocate the plastic hinge above the lap splice, (2) lap splices with adequate lengths but insufficiently confined attain the peak force but their deformation capacity is significantly reduced, and (3) short and not well-confined lap splices fail before reaching the strength capacity. The analysis of the test results, which are used in the companion paper for the finite element analysis of walls with lap splices, indicates in particular that the confining reinforcement ratio and the ratio of shear span to lap splice length influence the lap splice strain capacity