Edson Denner Leonel

Dual BEM Formulation Applied to Analysis of Multiple Crack Propagation

The boundary element method (BEM) is used in this paper for modelling multiple crack propagation in two-dimensional domains. The formulation adopted is based on the dual BEM, in which singular and hyper-singular integral equations are used. An iterative scheme is proposed in order to predict the crack growth path and the crack length increment at each load step. This scheme is accurate enough to simulate localisation and coalescence phenomena, which is the main contribution of this paper. The displacement correlation technique is used to evaluate the stress intensity factors and the theory of maximum circumferential stress is adopted to determine the crack propagation angle and the equivalent stress intensity factor. One application is presented in order to illustrate the robustness and applicability of the proposed model.

PROBABILISTIC FAILURE MODELLING OF REINFORCED CONCRETE STRUCTURES SUBJECTED TO CHLORIDE PENETRATION

Structural durability is an important criterion that must be evaluated for every type of structure. Concerning reinforced concrete members, chloride diffusion process is widely used to evaluate durability, especially when these structures are constructed in aggressive atmospheres. The chloride ingress triggers the corrosion of reinforcements; therefore, by modelling this phenomenon, the corrosion process can be better evaluated as well as the structural durability. The corrosion begins when a threshold level of chloride concentration is reached at the steel bars of reinforcements. Despite the robustness of several models proposed in literature, deterministic approaches fail to predict accurately the corrosion time initiation due the inherent randomness observed in this process. In this regard, structural durability can be more realistically represented using probabilistic approaches. This paper addresses the analyses of probabilistic corrosion time initiation in reinforced concrete structures exposed to chloride penetration. The chloride penetration is modelled using the Ficks diffusion law. This law simulates the chloride diffusion process considering time-dependent effects. The probability of failure is calculated using Monte Carlo simulation and the first order reliability method, with a direct coupling approach. Some examples are considered in order to study these phenomena. Moreover, a simplified method is proposed to determine optimal values for concrete cover.

Reliability algorithms applied to reinforced concrete structures durability assessment

This paper addresses the analysis of probabilistic corrosion time initiation in reinforced concrete structures exposed to ions chloride penetration. Structural durability is an important criterion which must be evaluated in every type of structure, especially when these structures are constructed in aggressive atmospheres. Considering reinforced concrete members, chloride diffusion process is widely used to evaluate the durability. Therefore, at modelling this phenomenon, corrosion of reinforcements can be better estimated and prevented. These processes begin when a threshold level of chlorides concentration is reached at the steel bars of reinforcements. Despite the robustness of several models proposed in the literature, deterministic approaches fail to predict accurately the corrosion time initiation due to the inherently randomness observed in this process. In this regard, the durability can be more realistically represented using probabilistic approaches. A probabilistic analysis of ions chloride penetration is presented in this paper. The ions chloride penetration is simulated using the Fick’s second law of diffusion. This law represents the chloride diffusion process, considering time dependent effects. The probability of failure is calculated using Monte Carlo simulation and the First Order Reliability Method (FORM) with a direct coupling approach. Some examples are considered in order to study these phenomena and a simplified method is proposed to determine optimal values for concrete cover.

Abordagem numérica sobre o efeito da corrosão de armaduras na capacidade mecânica de vigas em concreto armado ao longo do tempo considerando modelos não lineares dos materiais

Resumo Every structure is subjected to the effects of time and environment on which they are located. The consideration of these effects and their consequences in design phase is called nowadays as durability analysis of the structural system. The corrosion of the reinforcement steel through the chloride penetration inside the concrete is the main cause of the lifetime deterioration of the reinforced concrete structures. As a direct consequence, the corrosion affects the resistant capacity of the structural elements as the process evolves over time. Therefore, the appropriate prediction of the structural lifetime depends directly of the prevision capacity of those effects over the behavior of the structural systems. In this work, a mechanical model that combines the corrosion effects over the reinforcement and the concrete and steel material nonlinear responses is proposed to predict the resistant loss of reinforced concrete beams over the time. The steel and concrete nonlinear behavior was modeled by model based on unidimensional plasticity theory and damage mechanics, respectively. The Fick’s laws and empirical methods based on the Faraday’s laws were used to represent chloride penetration inside concrete and reinforced degradation, respectively. A simplified process was adopted to simulate the corrosion beginning in different times over the structure. The results showed that the rate of loss resistant capacity of the analyzed beam is higher in the first years after the beginning of corrosion and tend to stabilized in subsequent years. Furthermore, the structural behavior is very sensitive regarding the considered corrosive effects in the analyses.

Probabilistic mechanical modelling of concrete creep based on the boundary element method

The prediction of the future structural behaviour is an essential activity during the design phase. In this study, a novel numerical framework is proposed for investigating the future structural behaviour of two-dimensional structures. The model utilizes the boundary element method for obtaining the mechanical responses. The constitutive material is admitted to manifest viscoelastic response, which enables it to creep. The input parameters such as material, loads parameters and geometry dimensions are considered to possess random characteristics. A probabilistic criterion is proposed using metamodelling by the response surface method. All these features make the proposed numerical model more realistic. As an application, a specific structure is utilized, which is inspired from the real world. The results demonstrate that small geometric deviations do not necessarily impact the global reliability of the structure. At the same time, load estimations have major influence on the global structural reliability. The numerical framework proposed can be utilized for preliminary investigations on the design phase in order to aid the engineers into the decision-making process. Moreover, these observations demonstrate that the boundary element method can be efficiently coupled to other numerical strategies in order to elaborate new robust numerical frameworks able to represent realistically engineering problems.

Failure analysis of reinforced concrete structures subjected to chloride penetration and reinforcements corrosion

Abstract Structural durability is an important design criterion, which must be assessed for every type of structure, especially for reinforced concrete (RC) structures. When RC structures are located in aggressive environments, its durability is strongly reduced by physical/chemical/mechanical processes that trigger reinforcements corrosion. Among such processes, the diffusion of chlorides is recognized as one of major responsible of corrosion phenomenon start. In this context, this study presents a nonlinear formulation based on the finite element method applied to mechanical analysis of RC structures subjected to chloride penetration and reinforcements corrosion. The physical nonlinearity of concrete is described by Mazars damage model whereas for reinforcements elastoplastic criteria are adopted. The steel loss along time due to corrosion is modeled using an empirical approach and the chloride concentration growth along structural cover is represented by Ficks law. The proposed model is applied to analysis of bended structures. The results obtained by the proposed nonlinear approach are compared to responses available in literature in order to illustrate the evolution of structural resistant load after corrosion starts.

Influência da corrosão de armaduras em vigas hiperestáticas em concreto armado: uma análise probabilística dos cenários de falha

This work aims to study the mechanical effects of reinforcements corrosion in hyperstatic reinforced concrete beams. The focus is the probabilistic determination of individual failure scenarios change as well as global failure change along time. The limit state functions assumed describe analytically bending and shear resistance of reinforced concrete rectangular cross sections as a function of steel and concrete resistance and section dimensions. It was incorporated empirical laws that penalize the steel yield stress and the reinforcements area along time in addition to Ficks law, which models the chloride penetration into concrete pores. The reliability theory was applied based on Monte Carlo simulation method, which assesses each individual probability of failure. The probability of global structural failure was determined based in the concept of failure tree. The results of a hyperstatic reinforced concrete beam showed that reinforcements corrosion make change into the failure scenarios modes. Therefore, unimportant failure modes in design phase become important after corrosion start.

Influência da corrosão da armadura na capacidade resistente à flexão de vigas em concreto armado: uma abordagem via teoria da confiabilidade estrutural

Reinforced concrete structures are, certainly, one of the most used types of structure around world. When it is located in non-aggressive environments, it respects, in general, the structural life predicted. Unless the structure be used improperly. However, the durability of these structures is strongly connected to degradation processes whose origin is environmental and/or functional. Among these processes, it is worth to mention those related to corrosion of reinforcements. The reinforcements corrosion is directly related to the durability and safety of concrete structures. Moreover, the chlorides diffusion is recognized as one of major factors that triggers the corrosion. Therefore, at modelling accurately the chloride diffusion, the corrosion of reinforcements can be better evaluated. Consequently, design criteria can be more realistically proposed in order to assure safety and economy into reinforced concrete structures. Due to the inherent randomness present on chloride diffusion and corrosion, these phenomena can only be properly modelled considering probabilistic approaches. In this paper, the durability of a beam designed using the criteria proposed by ABNT NBR 6118:2003 [1] is assessed using probabilistic approaches. The corrosion time initiation is determined using Ficks diffusion law whereas Faradays corrosion laws are adopted to model the steel loss. The probability of structural failure is determined using Monte Carlo simulation. The mentioned beam is analysed considering different failure scenarios in order to study the influence of water/cement ratio and environmental aggressiveness on the probability of failure. Based on these results, some remarks are performed considering NBR recommendations and the real probability of failure.

BEM and Tangent Operator Technique Applied to Analysis of Contact Problems

The boundary element method (BEM) is a robust and accurate numerical technique to deal contact problems, because the contact among solids occurs along its boundaries. In this regard, this work presents a nonlinear BEM formulation applied to contact problems simulation. The formulation is based on the use of singular or hyper-singular integral equations of BEM, for multi-region contact, and the dual version of BEM to simulate the contact between crack surfaces. The mechanical nonlinear behaviour introduced by the contact is represented by the Coulomb’s friction law. The nonlinear formulation uses the tangent operator technique, in which one uses the derivate set of algebraic equations to construct the corrections field for the nonlinear process. This implicit formulation has shown accurate as the classical approach. However it is faster, in terms of computational time consuming, than the classical nonlinear approach. Examples of simple and multi-region contact problems are presented in order to illustrate the applicability of the proposed nonlinear numerical scheme.