PSI - Issue 13

Tuan Duc Le et al. / Procedia Structural Integrity 13 (2018) 1702–1707 T.D. Le, P. Lehner, P. Konečný / Structural Integrity Procedia 00 (2018) 000 – 000

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In addition, parameters governing the durability of RC structures are variable. Thus, probabilistic approach based modelling has been a trend to take into account of these variation both in 1D and 2D (Ghosh et al., 2017; Stewart and Rosowsky, 1998; Teplý and Vořechovská, 2012; Tikalsky et al., 2005) . These mentioned works covered not only chloride induced corrosion initiation but also ultimate flexural resistance. Typically, models of chloride ingress into RC structures consider concrete as homogeneous material. An example of such a kind of model elaborated in 2D was built by (Lehner et al., 2014). This model examined the transport of chloride ions through a RC bridge deck with a transverse crack and estimated chloride concentration with several protective strategies for steel reinforcement. This work was then further developed with a study on indicative evaluation of the effect of random scatter of input parameters in case of durability of RC bridge deck (Konečný and Lehner, 2016) . However, concrete heterogeneity is also a vital aspect in RC modelling to capture a more realistic description of effects of concrete aggregate and matrix. This can be done by applying discrete models capable of embracing the heterogeneity of the material directly by their nature. Such a case of model was first introduced in the past as classical lattice model (Herrmann et al., 1989), using elasto-brittle 1D elements with independence of the inner heterogeneous structure of the material (only lattice structure). In this case, elements were divided into three phases: aggregate, matrix and interface and hence this model is suitable only for small test specimens which required high resolution and computation demanding. Lattice model was then further developed with taking into account of three-dimensional rotations of particles and inter-particle contacts (G. Cusatis et al., 2003; G. Cusatis and Cedolin, 2007; Gianluca Cusatis et al., 2011). The model was also improved with cooperating the random fluctuation of mechanical properties of material (Eliáš et al., 2015; Grassl and Bažant, 2009) . In these works, fluctuation either resulted from random properties of concrete components or the induced irregularities during concrete casting and mixing. In practice, measurement of chloride penetration is conducted typically as 1D profile, see e.g. (AASHTO-T259, 2012; Hooton et al., 2001). However, evaluation of properties of such a heterogeneous material like RC requires a scheme capable of providing on-site fast and reliable analysis of concrete. One of the emerging technologies is Laser-induced Breakdown Spectroscopy System (LIBS). It is considered as an alternative method providing spatial resolved chloride distributions and quantified ingress profiles regarding to the cement (Gottlieb et al., 2017). On-site application of LIBS in civil engineering was noted with the development of a mobile LIBS by the Federal Institute for Materials Research and Testing – BAM, Germany last decade (Millar et al., 2015). Considering availability of a chloride profile reflecting concrete heterogeneity, it is desirable to have also a model capable of modelling of such properties with spatial variation. It is important, therefore, to build a profile of spatial variation of RC material. Example of such mesoscopic model is represented in case of chloride ingress by (Jiang et al., 2018). The model considered the aggregates as spaces with zero penetrability and diffusion was considered to occur only in cement matrix. It is worth mentioning that the application of random field with respect to penetration of chloride has not been performed upon author’s knowledge yet. This task is challenged by the complication of measurement of random entities due to their fluctuations. To deal with modelling of the fluctuations of certain variable parameters, stationary random field was exploited (Grassl et al., 2012; Syroka- Korol et al., 2015; Miroslav Vořechovský and Sadílek, 2008) . In addition, type of probability distribution, correlation function and inter-dependent relation among these random variables are needed to be identified to extend the model into probabilistic one. To simplify modelling process, correlation length, a parameter representing the rate of fluctuation of random variables was introduced and considered as a characteristic length of the random field (Ba ž ant et al. , 2007; M. Vořechovský, 2007) . This article is targeted at a preliminary 2D chloride penetration probabilistic model of RC beam on which heterogeneous property of concrete is considered. Random variation of resisting ability of concrete to chloride penetration with taking into account spatial change of material property – concrete diffusion, is evaluated. Random field of the beam was generated using the Expansion Optimal Linear Estimation method (EOLE) approach (Li and Der Kiureghian, 1993) according to the implementation conducted by (Eliáš et al., 2015) of which basic points are centres of mass of elements. The model was studied and evaluated under the scheme of finite element method (FEM).