Stochastic micromechanical predictions for the probabilistic behavior of saturated concrete repaired by the electrochemical deposition method

Abstract

A stochastic micromechanical framework is proposed to quantitatively characterize the probabilistic behavior of the mechanical performance of the saturated concrete healed by the electrochemical deposition method. Micromechanical model for the healed saturated concrete is presented based on the material microstructures, and new multilevel homogenization procedures are proposed to quantitatively predict the effective properties of the repaired concrete considering the inter-particle interactions. The evolutions of the deposition products are characterized by non-stationary random process, which is represented by Karhunen–Loeve approximations with limited random variables. The probabilistic behavior for the effective properties of the repaired concrete is reached by incorporating the maximum entropy principle and Monte Carlo simulations. The predictions obtained by the proposed stochastic micromechanical framework are then compared with the available experimental data, existing models, and commonly used probability density functions, which indicate that the presented stochastic micromechanical framework is capable of describing the electrochemical deposition method healing process, considering the inherent randomness of the material microstructures. Finally, the influences of the deposition products on the probabilistic behavior of the repaired concrete are discussed on the basis of the proposed models.

Stochastic micromechanics-based investigations for the damage healing of unsaturated concrete using electrochemical deposition method

“… KF and KS are the bulk modulus of the equivalent inclusion and the equivalent matrix, respectively; μF and μS are the shear modulus of the equivalent inclusion and the equivalent matrix, respectively; ϕF is the volume fraction of the equivalent inclusion in the equivalent matrix. The properties of the equivalent inclusion ( KFand μF) can be arrived with the following expressions (Chen et al., 2020a) where the parameters A, B, C are dependent on the volume fractions and properties of the water and the deposition products (Chen et al., 2020a). With regard to the effect of water viscosity in pores, the similar modifications are adopted using the effective saturation degrees as below (Yan et al., 2013) where μ¯S′ is the effective shear modulus of the equivalent matrix considering the water effects, …”

“…As a promising approach for repairing the damaged concrete in the water conditions, many researches have been conducted on the electrochemical deposition method (EDM) (Chen, 2014; Mohankumar, 2005; Otsuki et al., 1999; Ryu and Otsuki, 2002). Meanwhile, due to the difficulties in detailing the exact predetermined microstructural composites, there is an inherent randomness of the microstructures even under the same manufacturing or healing process (Chen et al., 2015a, 2018a, 2018b, 2020a; Huang et al., 2018, 2019; Jiang et al., 2019; Liu et al., 2020; Rahman and Chakraborty, 2007; Sun and Wang, 2018; Zhu et al., 2015). Recently, many deterministic micromechanics-based frameworks are proposed to disclose the damage-healing mechanism of the EDM (Chen et al., 2015b, 2015c, 2016a, 2017a, 2017b, 2018c, 2018d; Yan et al., 2013; Zhu et al., 2014), which do not consider the inherent randomness among the material’s microstructures before healing and during the healing process (Chen, 2014; Mohankumar, 2005; Otsuki et al., 1999; Ryu and Otsuki, 2002).…”

“…Recently, many deterministic micromechanics-based frameworks are proposed to disclose the damage-healing mechanism of the EDM (Chen et al., 2015b, 2015c, 2016a, 2017a, 2017b, 2018c, 2018d; Yan et al., 2013; Zhu et al., 2014), which do not consider the inherent randomness among the material’s microstructures before healing and during the healing process (Chen, 2014; Mohankumar, 2005; Otsuki et al., 1999; Ryu and Otsuki, 2002). To incorporate these random behaviors, a stochastic micromechanical framework is presented to describe the damage-healing process of the saturated concrete (Chen et al., 2020a).…”

“…However, the assumption that the concrete specimen is fully saturated ignores the unsaturated phenomenon in the real concrete specimen (Chatterji, 2004; Li et al., 2020a, 2020b; Persson, 1997). As an extension of our previous deterministic model for the repaired unsaturated concrete (Yan et al., 2013) and the latest stochastic model for the repaired saturated concrete (Chen et al., 2020a), a stochastic micromechanical framework is proposed for the unsaturated concrete repaired by EDM. The effective saturation degree and the effective porosity are employed to represent the unsaturated pores.…”

Investigation of the unbiased probabilistic behavior of the fiber-reinforced concrete's elastic moduli using stochastic micromechanical approach

“…On one hand, the common probability density functions (PDFs) are employed to represent the FRC's real statistical characters, which will lead to the biased results (Bai and Liu, 2016; Jaynes, 1957; Li et al., 2014; Zhu et al., 2015). On the other hand, the micromechanics-based models were presented to set up the relationship between the microstructure and the macroscopic properties, which do not consider the material's random behavior (Chen et al., 2016, 2019; Dutra et al., 2010; Galand and Kryvoruk, 2011; Ju and Yanase, 2011; Ju and Zhang, 1998; Teng et al., 2004). To address these issues, this study aims to develop a stochastic multiphase micromechanical framework to investigate the unbiased probabilistic behavior of the FRC's moduli with Legendre orthogonal polynomial.…”