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.

In modern society, the electricity is the foundation of all intelligent facilities. To realize the intelligent development of cementitious materials, electrical conductivity is one of the important directions for the future research of engineering structures and building materials. Of which, ultra-high performance concrete (UHPC) has been widely used in large-span building structures, tunnel and bridge structures, and repair and reinforcement projects, etc. If the conductive properties of UHPC are realized, and its self-sensing characteristics are given to achieve the demand of intelligent monitoring, it is of great theoretical significance and practical value to ensure the service safety of the building structure. It has reached a consensus at present that UHPC is modified by adding conductive materials to reduce the resistivity. However, conductive materials are expensive and difficult to achieve large-scale engineering applications. The use of waste carbon fibers (WCFs) can not only meet the performance requirements, but also reduce the preparation cost, improve the utilization rate of resources, and avoid environmental pollution. But at this stage, there is a lack of research on the influence of WCFs on the electrical conductivity of UHPC, and the relationship between electrical conductivity and load-deflection needs to be explored. Therefore, this paper took the electrical conductivity and bending performance of UHPC as the research point, and analyzed the bending sensitivity and load-deflection relationship of C-UHPC under different WCFs content. And the variation law between stress, strain and resistance was explored.

The UHPC with conductive properties was prepared by WCFs and steel fiber (SF), and the final mix ratio was determined by combining theoretical analysis and pre-experimental research. The water-binder ratio of C-UHPC was 0.16, and the content of WCFs was 0%, 0.5%, 1.0%, 1.5%, and 2% (in volume), respectively. Due to some differences between WCFs and virgin carbon fibers (VCFs), a comparative study of the two fibers was carried out by SEM, Raman spectroscopy, and contact angle. The compressive strength tests of C-UHPC cured for 1, 3, 7 d, and 28 d were carried out. The conductivity of C-UHPC was tested by four-electrode method (28 d). The bending sensitivity of C-UHPC mainly studied the relationship between stress, strain, and resistance under bending load. During the test, the load was automatically recorded by the stress sensor of the test machine, the deflection was measured by the bottom displacement meter of the specimen, and the resistance was measured by the external resistance box. After loading, the change values of load, deflection, and resistance were collected synchronously. Finally, SEM was used to observe the microscopic morphology of fibers and fiber-matrix interface in C-UHPC.

Compared with VCFs, the surface of WCFs was smoother, but the wettability and graphitization degree were relatively poor. Compared with the reference group (WCFs content of 0%), the compressive strength of C-UHPC decreased after the addition of WCFs, which was attributed to the smaller bond force between the interface of WCFs and matrix. In addition, WCFs and SF were easily entangled with each other, and the positive synergism between fibers was weak. The resistivity of C-UHPC decreased with the increase of WCFs content, but when the content of WCFs was greater than or equal to 1%, C-UHPC reached the conductive threshold, that is, the effective lap probability between fibers satisfied the conductive path of electronic transmission. The main conductive pathways of WCFs in C-UHPC included overlapping, connecting cracks, and micropores. When C-UHPC was subjected to bending load, the specimen underwent uncracked, critical cracks, macroscopic cracks, and finally failure. Of which, the macro cracks were mainly axial cracks, which expanded from bottom to top.

A three-stage constitutive equation applicable to the C-UHPC bending load-deflection model was established with high prediction accuracy. When C-UHPC was subjected to bending load, the resistance changed, and this phenomenon indicated that C-UHPC had a bending sensitive property. Taking the peak load as the change node, the resistance curve of the pre-peak load decreased slightly, and the resistance curve of the post-peak load increased rapidly. This was because when C-UHPC was subjected to external loading, the internal microcracks and micropores were closed, resulting in a temporary increased and more complete conductive path, and the resistance decreased. After exceeding the peak load, the matrix gradually cracked, and the axial cracks expanded, interrupting most of the conductive paths, resulting in an increase in resistance. The stress sensitivity could be divided into two stages: first, the stress sensitivity decreased significantly first and then tends to be gentle with the increase of stress; second, the stress began to decrease after reaching the peak value, and the sensitivity increases. The Poisson's ratio was introduced to improve the formula for strain sensitivity, and the strain sensitivity perpendicular to the loading direction was obtained. The strain sensitivity decreased first and then increases with the increase of strain.

The addition of WCFs could reduce the compressive strength of C-UHPC, but improved its conductivity. Under bending stress, the load-deflection curve of C-UHPC could be divided into elastic stage, bending hardening stage, and failure stage. After mixing with WCFs, C-UHPC took the peak load as the change node, and the resistance curve of the pre-peak load basically did not fluctuate, and the resistance curve of the post-peak load increased rapidly. When WCFs content was 1%, C-UHPC reached the conductive threshold, and continuing to increase fiber content had no significant effect on the resistivity. The sensitivity of C-UHPC decreased first and then increases with the increase of stress and strain.