Numerical Simulation of Concrete Damage under Combined Action of Temperature Field and Sulfate Attack Based on Crystallization Pressure Theory

Although numerical modeling becomes a crucial tool in studying sulfate attack, focusing on key processes such as ion transport, chemical reactions, expansion force, and mechanical response, accurately quantifying the expansion force induced by the erosion product ettringite remains a challenge. This problem becomes particularly complex as considering the influence of temperature gradients present in real-world environments. Temperature gradients can accelerate the transport of sulfate ions and significantly alter the kinetics of the chemical reactions governing the formation of erosion products. Furthermore, the existing models for simulating these multi-field coupling effects and the corresponding experimental data for validation are relatively scarce.

This study was to develop a fully coupled numerical model for concrete under sulfate attack, integrating ion transport, chemical reactions, crystallization pressure, and damage, based on the crystallization pressure theory. The primary objective was to quantitatively elucidate the damage evolution of concrete under the coupled action of a non-uniform temperature field and sulfate attack.

This study employed an integrated approach combining numerical simulation and laboratory accelerated tests.

First, in the ion transport phase, the temperature-dependent Arrhenius equation was incorporated into the classic Fick's second law. This integration provided a mathematical characterization of sulfate ion diffusion under non-uniform temperature fields, thereby accurately describing the accelerating effect of temperature gradients on ion migration rates.

Second, in the chemical reaction investigation, a computational model for estimating ettringite formation under the influence of temperature fields was established based on chemical reaction kinetics. This method quantified the enhancing effect of temperature variations on the crystallization kinetics of erosion products via accounting for the relationship between reaction activation energy and temperature, enabling the prediction of ettringite quantities at different depths and stages of the attack.

Subsequently, for the crystallization pressure calculation, the conventional volume expansion theory was abandoned in favor of the crystallization pressure theory as the physical basis of the model. In this step, the amount of ettringite calculated by the chemical reaction module was converted into the crystallization pressure generated by its growth within confined pores.

Finally, in the damage computation study, continuum damage mechanics was introduced to define the damage variable and its evolution law for concrete. Through numerical solution, the spatiotemporal distribution of concrete damage induced by the accumulation of crystallization pressure was quantitatively computed. This ultimately established a quantitative relationship between the duration and depth of sulfate attack and the extent of concrete damage.

The diffusion coefficient of SO₄^2– exhibits an enhanced dependence on time, while showing a more pronounced reduction with depth, demonstrating a positive correlation with exposure duration and a negative correlation with penetration depth.

During the initial stage of exposure (≤ 30 d), no ettringite formation is detected. The ettringite content gradually increases as the exposure period progresses. However, a distinct transition point in ettringite formation occurs within the approximate range of 40 to 100 d, beyond which the rate of ettringite generation decelerates.

SO₄^2– continues to accumulate in the concrete pore solution and reacts with hydrated aluminate phases to form ettringite with prolonging exposure time, leading to an increase in the proportion of ettringite. At this stage, the amount of ettringite formed is controlled by SO₄^2– diffusing into the concrete. After the diffused SO₄^2– is fully consumed, residual aluminate phases remain in the hydration products. The ettringite subsequently formed within small pores (i.e., 10–100 nm) generates crystallization pressure, although the magnitude of this pressure remains relatively low (below the tensile strength of the concrete) at this stage, resulting in a minimal structural damage.

Under the coupled effects, the damage in concrete evolves through three distinct stages with exposure time, i.e., 1) An initiation stage without measurable damage,2) An accelerated damage stage characterized by a rapid increase in damage extent, and 3) A stabilized damage stage where the progression of damage plateaus.

Based on the crystallization pressure theory, this study established a fully coupled transport-chemical-expansion-damage model for concrete that could account for the synergistic effects of temperature fields and sulfate attack. The main conclusions were summarized as follows:

The diffusion coefficient of SO₄^2– in concrete under a temperature field exhibited a significant layered distribution characteristic, with the coefficient at the surface being approximately 1.5 times higher than that at greater depths.

The calculation results of erosion product formation based on chemical reaction kinetics indicated that the generation process could be dually controlled by the concentration of diffusing SO₄^2– and the content of initial hydration products. A distinct "turning point" existed, marking a transition from sulfate-ion limitation to aluminate-phase limitation.

The crystallization pressure theory was applied to quantify the internal stress generated by ettringite formation within nano-scale pores (i.e., 10–100 nm), providing a new paradigm for the application of this theory in studies of sulfate attack on concrete.

The sulfate-induced damage predicted by the numerical model exhibited a depth-time dependence and developed through three characteristic stages, i.e., an initiation stage, an accelerated damage stage, and a stabilized damage stage. The damage progression rate at the surface layer (i.e., 2–10 mm) was significantly higher than that at deeper layers (i.e., 14–20 mm), demonstrating a spatiotemporal differential evolution pattern.