Finite Boundary Conditions Due to the Bar Presence in the Model of Chloride Penetration.

Fabiano Tavares,Carmen Andrade

doi:10.3390/ma15041426

Abstract

The chloride penetration is usually modelled through the application of a solution of Fick’s second law of diffusion, based on the assumption of semi-infinite boundary conditions. However, the presence of the bars, on whose surface the chlorides accumulate, makes this assumption incorrect. As the time progresses, the chlorides in the steel/concrete interface increase in concentration more than the chlorides overpassing the bar position without obstacles. This circumstance, although previously studied, has not been introduced in common practice, in spite of it supposes early reaching of the chloride threshold. The study in this paper shows a deterministic analysis of the chloride diffusion process by the finite element method (FEM) which numerically solves Fick’s second law, taking into account the accumulation of the chlorides on the bar surface. Several examples are calculated and factors between the finite/semi-infinite solutions are given. These factors depend on the cover depth and the diffusion coefficient, and with less importance, on the diameter of the bar, which make it unfeasible to propose a general trend.

Highlights

In marine or chloride bearing environments, the chloride ions diffuse through the concrete pores, and when they arrive to the reinforcement surface in a concentration named “critical chloride content”, corrosion develops [1]
3.1.FDiguRreepr2essehnotwatsiotnhse chloride concentration after 25 years at the rebar level of 1 cm for aatDefot=rhea1F0rD−ei9ginc=umfro1e2r0/c2s−i.n9sWghcomibtwah2r/sawstc.hirteiWhticctihhtahlelocacroliadcnrseciseticinccoatanrllacecteriornoontnrrcaoeftunfiontcrhncatltioaioorfntindesreoos2fl,u5cCthyixole=onar0r(i.sdE4qe%asut,attChthiexoen=rtei(m0b2.a)e4)r%tiolse,8dvt2hee2pel0aotdsifmsa1iyvecs-mtogwbhairlewiifththtehbeacrlapsosiscitailoenrrisorcofunnsicdtieorneds,otlhuetiotinm(eEwquoautlidonbe(2o))f is 1088202d0adyasy(asr(oauronudn3dy2e2arys)e.aTrshuasn,dthaehoavlef)rewsthimileatiifotnhoefbtahrepseorsvitiicoenliifse cinonthsiedcearseedo, fthseemtiim- e inwfinoiuteldbboeunodf a1r0y80codnadyisti(oanrosuwnodu3ldyebaeros)f.aTlmhuoss,tt2h0eyoevaerrse.stimation of the service life in the case of semi-infinite boundary conditions would be of almost 20 years
CoInncpluresvioionuss works, it has been mentioned that present models based in Fick’s second law oIfndpirfefuvsioiouns,wwoirthksa, istohlaustiboenencomnseindteiorinnegdstehmati-pinrefisneintet mboudneldsabraysceodnidniFtiiocnks’s, dseoconnodt alalwwaoyfs dfoiflfluoswiotnh,ewrietahl aprsoocluestiso, nancdonistsidbeoriunngdsaermy ic-oinnfidnitiitoenbsofuonr dsaorlvyincogntdhietiodnifsf,erdeontniaolt eaqlwuaatyiosnfoinllonwont-hsteeraedayl sptraotececsosn, daintidonitssdboounnotdtaarkyecionntodiatcioconusnftotrhseoplvriensgentcheeodfiaffneroebnsttiaa-l celqeuaastitohne irnebnaorni-ss.teTahduys,stthateebcaornrdeiptiroenssendtos naobtatrarkieerinfotor tahcecocuhnlotrtihdeeppreenseentrcaetioofna,nanobdstthacelne the ions accumulate at the bar’s surface, aiming to increase the chloride concentration, with respect to when the calculation is based in the classical error function equation resulting when solved considering semi-infinite boundaries (Equation (2))

Summary

Introduction

In marine or chloride bearing environments, the chloride ions diffuse through the concrete pores, and when they arrive to the reinforcement surface in a concentration named “critical chloride content”, corrosion develops [1]. The rust produced has an expansive nature occupying a higher volume than the original materials and in most of the cases originating the cracking of the concrete cover [2] This process has generated numerous studies, either on the phenomenon of the transport of ions through the concrete pores and its modelling [2,3,4,5,6,7,8,9,10,11], as in the decrease of the diffusion coefficient with time (aging factors) [12,13] or the critical chloride concentration that induces steel depassivation [14,15,16,17]. Relation of finite/semi-infinite results are named “semi-infinite/finite conversion ratio” and they are analysed with respect to their possible generalisation in order to facilitate the direct calculation from the present analytical Equation (2)

Experimental

Results

D Representations

Conclusions