New methodology for calculating damage variables evolution in Plastic Damage Model for RC structures

Abstract

Abstract:The behavior of reinforced concrete (RC) structures under severe demands, as strong ground motions, is highly complex; this is mainly due to joint operation of concrete and steel, with several coupled failure modes. Furthermore, given the increasing awareness and concern for the important seismic worldwide risk, new developments have arisen in earthquake engineering. Nonetheless, simplified numerical models are widely used (given their moderate computational cost), and many developments rely mainly on them. The authors have started a long-term research whose final objective is to provide, by using advanced numerical models, solid basis for these developments. Those models are based on continuum mechanics, and consider Plastic Damage Model to simulate concrete behavior. Within this context, this paper presents a new methodology to calculate damage variables evolution; the proposed approach is based in the Lubliner/Lee/Fenves formulation and provides closed-form expressions of the compressive and tensile damage variables in terms of the corresponding strains. This methodology does not require calibration with experimental results and incorporates a strategy to avoid mesh-sensitivity. A particular algorithm, suitable for implementation in Abaqus, is described. Mesh-insensitivity is validated in a simple tension example. Accuracy and reliability are verified by simulating a cyclic experiment on a plain concrete specimen. Two laboratory experiments consisting in pushing until failure two 2-D RC frames are simulated with the proposed approach to investigate its ability to reproduce actual monotonic behavior of RC structures; the obtained results are also compared with the aforementioned simplified models that are commonly employed in earthquake engineering.

RC structures cyclic behavior simulation with a model integrating plasticity, damage, and bond‐slip

“…This section summarizes the algorithm proposed by Alfarah et al 30 for obtaining the damage variables and its implementation in CDPMs. This section summarizes the algorithm proposed by Alfarah et al 30 for obtaining the damage variables and its implementation in CDPMs.…”

“…30,50 The methodology to obtain the damage evolution proposed by Alfarah et al 30 is based on assuming that compressive and tensile damage variables are the portions of normalized energy dissipated by damage: Equations 3 and 4 show that s c and s t range between 0 and 1.…”

“…The abovementioned concrete uniaxial law provides the behavior of the CDPM under uniaxial loading in any direction. 30,50 Regarding the confinement effect, it is not represented by different concrete constitutive laws, but by the direct consideration of the transverse compression exerted by the stirrups; noticeably, such transverse reinforcement bars are explicitly modeled. 13,31 The selection of these parameters is described in Alfarah et al and Alfarah.…”

“…Concrete behavior is simulated by implementing the methodology described in section 3 30 in Abaqus code 32 by using the particular algorithm described in Alfarah et al 30 Figure 10A displays plots of ratio ε pl c =ε ch c versus ε ch c , where ε pl c refers to plastic compressive strain. Concrete behavior is simulated by implementing the methodology described in section 3 30 in Abaqus code 32 by using the particular algorithm described in Alfarah et al 30 Figure 10A displays plots of ratio ε pl c =ε ch c versus ε ch c , where ε pl c refers to plastic compressive strain.…”

“…Figure 10B displays analogous plots for the tensile behavior (ε pl t =ε ck t vs ε ck t ). 30 Figure 10A points FIGURE 9 Finite element discretization of the bridge column FIGURE 10 Variation of ratios between plastic and crushing/cracking strains for the bridge column experiment out that the average of ε pl c =ε ch c is approximately equal to 0.88; this magnitude is termed b and is a required parameter in the implementation of the algorithm. 30 Figure 10A points FIGURE 9 Finite element discretization of the bridge column FIGURE 10 Variation of ratios between plastic and crushing/cracking strains for the bridge column experiment out that the average of ε pl c =ε ch c is approximately equal to 0.88; this magnitude is termed b and is a required parameter in the implementation of the algorithm.…”