Non-Equilibrium Thermodynamics-Based Electrochemical Model for Multi-Ion Coupled Transport in Concrete

As one of the most widely used engineering materials in modern infrastructure, concrete is prone to premature deterioration under chloride-rich conditions such as marine environments and deicing salt exposure, which severely compromises the service life of structures. The ingress of chloride ions involves complex physicochemical processes, including dissolution and precipitation of minerals, adsorption and transport of ions, chemical reactions among ions, and the self-induced electric field generated arising from ionic interactions. Moreover, concrete is inherently a heterogeneous multiphase material, which comprises the cement paste, aggregates, and interfacial transition zone (ITZ) phases. Traditional experimental methods are often time-consuming and difficult to quantitively characterize the coupling mechanism between the electric and chemical fields. Alternatively, various theoretical models at different length scales for concrete durability were developed based on the assumption of fixed concentration at the concrete surface, while their predictive results contradict the experimental findings, where the ion concentration is dynamically changed at the concrete surface. Herein, this work introduces a non-equilibrium thermodynamics-based electrochemical model for multi-ion coupled transport in exterior solution, interior concrete, and their interface. The model enables to capture the dynamically change in ion concentration at the concrete surface. The model is numerically solved by finite element method and validated with several experimental results, where good agreements are achieved. Afterwards, the model is employed to investigate the impacts of initial diffusion coefficients, aggregate particle size, ITZ thickness, and external electric fields on the chloride ion transport behavior, the evolutions of mineral amounts and electric potential.

Based on non-equilibrium thermodynamics, an electrochemical model at mesoscale level is developed to simulate chloride-induced degradation in concrete. The model starts from the derivation of reaction rates for chemical reactions between the minerals and mobile ions, where the forward and backward reactions are fully considered to reflect the real scenario. The diffusion of multi-ions is governed by the conservation law of mass and the electric polarization is achieved based on Gauss’s theorem. The constitutive relations are derived based on the second law of thermodynamics. Regarding the free energy density, it is formulated with consideration of mixing and polarization effects. For direct calculation of ion concentrations at the concrete surface, the computational domains include the exterior ionic solution, interior concrete, and their interface. By setting the appropriate boundary and initial conditions, the model is then implemented into the finite element software. Afterwards, the effect of solution domain size is investigated on the ion concentration, where a optimum solution domain size is finalized via the balance of computational accuracy and cost. For ensuring the accuracy of the developed model, it is validated with experimental data in open literature, where satisfactory agreements are achieved. After that, the effects of initial diffusion coefficient, aggregate size, ITZ thickness, and external electric fields are carried out on the transport of multi-ions, the dissolution of minerals, and the electric field evolution.

The diffusion of Cl^- ion is required to span different spatial domains, for example from the exterior solution to solution-concrete interface, and then the interior concrete. Due to the difference in diffusion coefficients between the solution and the concrete, the ion concentration exhibits a sharp discontinuity at the solution-concrete interface zone. Moreover, the ion concentration at the concrete surface is dynamically changed with time, which is consistent with the experimental findings. Additionally, it is found that the ingress depth increases obviously with increasing diffusion coefficient, and the concentration distribution profile is significantly varied for different kinds of mobile ions. Under the condition of a constant aggregate volume fraction, the aggregate particle size and the ITZ thickness have a limited effect on Cl^- transport. It is because that the ITZ generally fails to form a connected network within the concrete, preventing the establishment of continuous fast diffusion pathways at the mesoscale. With the increase of the applied electric field, Cl^- continuously accumulates at the concrete interface and migrates more rapidly into the interior concrete. Compared with a 2 V electric field, when the applied electric field is increased to 6 V, the penetration depth of Cl^- increases by about 40%.

A non-equilibrium thermodynamics-based electrochemical model has been developed theoretically to capture chloride transport and reactions within concrete. The model reveals that chloride ingress is driven by diffusion coefficient, weakly affected by aggregate size and ITZ thickness, and significantly accelerated by the external electric fields. A sharp variation of ion concentration is found at the concrete-solution interface, and the ion concentration at the interface is dynamically changed. The model framework is derived based on the constitutive theory of non-equilibrium thermodynamics, offering a rigorous physical foundation. It is conventionally extended to couple stress, temperature, or moisture field, thereby simulating ion transport process and multi-field coupled degradation behaviors under complex environments, such as salt-freeze cycles and stress-corrosion conditions. This work may also provide a theoretical guidance for design and optimization of concrete durability.