A time-dependent modeling framework for autogenous self-healing concrete that couples moisture diffusion with damage evolution was developed. Water transport follows Fick's second law with a damage-dependent diffusivity obtained by power-law interpolation between intact concrete and crack space. Healing reduces damage in proportion to the product of local moisture and a smoothed cement availability field computed via a novel Helmholtz filtering approach that models the spatial extent over which cement clinker can travel and form crystals. Two finite element variants were implemented in FEniCSx: a Crack Diffusion Model (CDM) with standard diffusion and a Crack Membrane Model (CMM) that introduces a novel threshold-based gating mechanism to control cross-crack water transport until a critical moisture threshold is reached. Key control parameters are the initial crack orientation and size, the diffusion coefficients of intact and cracked concrete, the healing rate constant, and the cement availability smoothing parameter. Simulations show that healing time varies non-monotonically with crack orientation, peaking near $45^\circ$ and $135^\circ$ and minimizing near $90^\circ$. The dependence on crack width reverses with material parameters. The CMM reproduces staged moisture penetration with delayed gate activation but lengthens total healing time, whereas the CDM is efficient for parametric sweeps. Machine learning regression models were trained on finite element simulation data to predict healing times $H(σ,γ,β)$ with high accuracy ($R^2 > 0.999$), dramatically reducing computational time. SHAP analysis demonstrated that crack orientation influenced healing time the most, followed by crack width and cement availability smoothing. The modeling framework provides a versatile tool for guiding future laboratory studies and implementations of self-healing concrete.

翻译：本文开发了一种时变建模框架，用于模拟自愈合混凝土中水分扩散与损伤演化的耦合过程。水分传输遵循菲克第二定律，其扩散系数与损伤相关，通过完整混凝土与裂缝空间之间的幂律插值获得。愈合过程根据局部水分与平滑水泥可用性场的乘积成比例地减少损伤；该水泥可用性场通过一种新颖的赫尔姆霍兹滤波方法计算，该方法模拟了水泥熟料能够迁移并形成晶体的空间范围。我们在FEniCSx中实现了两种有限元变体：一种是采用标准扩散的裂缝扩散模型（CDM），另一种是裂缝膜模型（CMM），后者引入了一种新颖的基于阈值的门控机制，以控制跨裂缝水分传输，直至达到临界水分阈值。关键控制参数包括初始裂缝取向与尺寸、完整与开裂混凝土的扩散系数、愈合速率常数以及水泥可用性平滑参数。模拟结果表明，愈合时间随裂缝取向呈非单调变化，在接近$45^\circ$和$135^\circ$时达到峰值，在接近$90^\circ$时最小。其对裂缝宽度的依赖关系则随材料参数反转。CMM模型再现了门控延迟激活下的分阶段水分渗透过程，但延长了总愈合时间，而CDM模型在参数扫描方面更为高效。基于有限元模拟数据训练的机器学习回归模型能够高精度（$R^2 > 0.999$）预测愈合时间$H(σ,γ,β)$，显著减少了计算时间。SHAP分析表明，裂缝取向对愈合时间的影响最大，其次是裂缝宽度和水泥可用性平滑参数。该建模框架为指导未来自愈合混凝土的实验室研究和工程应用提供了一个通用工具。