Finite Element and Machine Learning Modeling of Autogenous Self-Healing Concrete

TL;DR

Autogenous self-healing concrete is modeled with two coupled FE frameworks, CDM and CMM, implemented in $\text{FEniCSx}$ to simulate moisture diffusion interacting with damage evolution and cement availability. CDM uses a damage-dependent diffusivity interpolated by a power-law between $D_{\text{intact}}$ and $D_{\text{cracked}}$, while CMM adds a moisture-gated transport mechanism via a logistic gate $G(U)$ that suppresses cross-crack diffusion until $U$ reaches $U_{\text{critical}}$, with a Helmholtz-smoothed cement availability field $\chi_{\text{eff}}$. A large-scale data-driven surrogate is built by training five classifiers on $10^6$ simulation samples to predict binary healing outcomes $H(\\sigma,\\gamma,t)$, achieving up to $0.998$ accuracy with a neural network. Together, these models provide a versatile framework for exploring parametric healing behavior, guiding laboratory studies, and informing infrastructure design, while highlighting the need for experimental calibration and extensions to three dimensions.

Abstract

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 local moisture and a smoothed cement availability field computed via a Helmholtz filter. Two finite element variants were implemented in FEniCSx over time horizons up to $5\times10^6$ seconds: a Crack Diffusion Model (CDM) with standard diffusion and a Crack Membrane Model (CMM) that gates cross-crack 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 on a unit square domain show that healing time varies non-monotonically with crack orientation, peaking near $45^\circ$ and $135^\circ$ and minimizing near $90^\circ$, consistent with diffusion distance to crack endpoints dominating the process. The dependence on crack width reverses with material parameters: healing time increases when $D_{\text{cracked}}<D_{\text{intact}}$ and decreases when $D_{\text{cracked}}>D_{\text{intact}}$. 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 classifiers trained on one million simulation samples predict binary healing outcomes $H(σ,γ,t)$ (healed or not) with high accuracy (up to 0.998 for neural networks). Although experimental calibration is still required, the framework provides a versatile tool for guiding laboratory studies and implementations of self-healing concrete.

Figures (13)

• Figure 1: Autogenous Self-Healing Concrete Simulation Workflow using CDM with Parameters, Phenomena, and Scalar Fields
• Figure 2: Crack Membrane Model Logic Workflow
• Figure 3: Comparison of the Computing Complexities between Finite Element Analysis and Machine Learning
• Figure 4: Initial Condition for the Damage Field: (a) Definition of inclining angle $\beta$, (b) Example Scalar Damage Field During Pre-Cracking ($\beta=0$, $\sigma^2 = 0.0005$)
• Figure 5: Healing Progress for $\beta = 45^\circ$ at four different representative times. (a) Beginning of the simulation, (b) $\sim$1/3 of the simulation time, (c) $\sim$2/3 of the simulation time, (d) Final time.