硅酸盐学报

基于结晶压力理论的温度场与硫酸盐侵蚀共同作用下混凝土损伤数值模拟

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张少辉 ¹^,² , 王艳 ¹^,³ , 刘西光 ²^,³ , 牛荻涛 ²^,³

硅酸盐学报 | 混凝土耐久性机理表征与预测方法专题—研究论文 2026,54(2): 731-741

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硅酸盐学报 |混凝土耐久性机理表征与预测方法专题—研究论文 2026 , 54 (2) : 731 -741

基于结晶压力理论的温度场与硫酸盐侵蚀共同作用下混凝土损伤数值模拟

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张少辉¹^,², 王艳¹^,³, 刘西光²^,³, 牛荻涛²^,³

作者信息

^1．西安建筑科技大学材料科学与工程学院，西安 710055

^2．西安建筑科技大学土木工程学院，西安 710055

^3．绿色建筑全国重点实验室，西安 710055

通讯作者:

王艳（1982—），女，博士，教授。

作者简介:

张少辉（1994—），男，博士，副教授。

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

Shaohui ZHANG¹^,², Yan WANG¹^,³, Xiguang LIU²^,³, Ditao NIU²^,³

Affiliations

^1.School of Materials Science and Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China

^2.School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China

^3.State Key Laboratory of Green Building, Xi'an University of Architecture and Technology, Xi'an 710055, China

Corresponding Author:

WANG Yan (1982-), female, Ph.D., Professor. E-mail: wangyanwjx@126.com

ZHANG Shaohui (1994-), male, Associate Professor. E-mail: zhangshaohui999@126.com

出版时间: 2026-02-20 doi: 10.14062/j.issn.0454-5648.20250348

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摘要

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结晶压力理论在模拟硫酸盐侵蚀混凝土损伤时的精度局限，源于其对10～100 nm孔隙内钙矾石的形成未充分考虑，而该尺度孔隙中钙矾石产生的结晶压力恰是硫酸盐侵蚀破坏的主要成因。本研究针对高地热环境隧道衬砌混凝土温度场与硫酸盐侵蚀单向共同作用，融合结晶压力理论，建立了一种新型“离子传输-化学反应-膨胀-损伤”数值模型，并通过设计的加速劣化实验验证了模型的预测精度。取得的主要结论有：1）发现温度场作用下混凝土中SO₄^2-扩散具有明显的分层特征，即SO₄^2-扩散系数随深度的增加而逐渐降低，内部SO₄^2-扩散系数比表层扩散系数降低了35.9%；2）精确量化了侵蚀过程中混凝土孔隙内侵蚀产物的含量；3）成功计算了纳米级孔隙（10～100 nm）内钙矾石结晶压力。该建模框架为结晶压力理论在混凝土硫酸盐侵蚀数值模拟中的应用提供了路径。

关键词

硫酸盐侵蚀 / 温度场作用 / 损伤数值模拟 / 纳米级孔隙

Abstract

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Introduction

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.

Methods

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.

Results and discussion

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.

Conclusions

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.

Key words

sulfate attack / temperature field effect / damage numerical simulation / nano-scale pores

引用本文

张少辉, 王艳, 刘西光, 牛荻涛. 基于结晶压力理论的温度场与硫酸盐侵蚀共同作用下混凝土损伤数值模拟. 硅酸盐学报, 2026 , 54 (2) : 731 -741 . DOI: 10.14062/j.issn.0454-5648.20250348

Shaohui ZHANG, Yan WANG, Xiguang LIU, Ditao NIU. Numerical Simulation of Concrete Damage under Combined Action of Temperature Field and Sulfate Attack Based on Crystallization Pressure Theory[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (2) : 731 -741 . DOI: 10.14062/j.issn.0454-5648.20250348

基金

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国家优秀青年科学基金项目(52222806)
国家自然科学基金项目(52508306)
陕西省杰出青年科学基金(2022JC-20)
陕西省科技厅自然科学基金青年项目(2025JC-YBQN-732)
陕西省教育厅专项科研计划项目(24JK0512)
深圳市科技创新委员会(20220811152251005)

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2026年第54卷第2期

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文章信息

doi: 10.14062/j.issn.0454-5648.20250348

接收时间：2025-04-30
首发时间：2026-10-27
出版时间：2026-02-20

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出版历史

收稿日期：2025-04-30
修回日期：2025-05-15

基金

国家优秀青年科学基金项目(52222806)

国家自然科学基金项目(52508306)

陕西省杰出青年科学基金(2022JC-20)

陕西省科技厅自然科学基金青年项目(2025JC-YBQN-732)

陕西省教育厅专项科研计划项目(24JK0512)

深圳市科技创新委员会(20220811152251005)

作者信息

^1．西安建筑科技大学材料科学与工程学院，西安 710055

^2．西安建筑科技大学土木工程学院，西安 710055

^3．绿色建筑全国重点实验室，西安 710055

通讯作者:

王艳（1982—），女，博士，教授。

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https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20250348

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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