Moisture transport in cementitious materials via x-ray radiography and PINN

The durability and performance of cementitious materials are greatly affected by moisture transport into the microstructure. Understanding unsaturated moisture transport in cementitious materials is essential for designing durable and sustainable infrastructure. Traditional experimental and modeling approaches have either oversimplified the transport process or relied on models that may not completely capture the underlying mechanism. This study aims to develop and demonstrate a data-driven Physics-Informed Neural Network (PINN) framework to discover the moisture-dependent diffusivity relationship in cement paste using in-situ X-ray radiography data. Three types of cement paste specimens targeting different water absorption rates— High Sorptivity (HS), Medium Sorptivity (MS), and Low Sorptivity (LS)—were prepared by varying the water–cement ratio (w/c) and curing duration (0.7 w/c and 1 day curing for HS, 0.7 w/c and 7 day curing for MS, and 0.45 w/c and 1 day curing for LS). Internal water transport was monitored using X-ray radiographs captured in situ at discrete time intervals during capillary absorption in slender prismatic specimens 10mm x 10mm in cross-section. Separate capillary absorption tests were performed on cuboidal specimens ~20mm in height, and ~25mm x 25mm in cross-section, only recording the mass of absorbed water. Internal water content was quantified based on the change in X-ray attenuation relative to the dry specimen radiograph using Beer-Lambert’s Law. The results of absorption tests were used for the calibration of X-ray-based quantification and experimental validation of PINN results. From the two-dimensional water content distribution snapshots, one-dimensional water content profiles along the capillary absorption (vertical) direction were extracted. These sparse one-dimensional water content profiles were then used to train a PINN model, where one network (Sat Net) predicts water content as a function of space and time, and another (Coeff Net) learns the diffusivity as a function of water content. Richards equation was embedded in the loss function to enforce the physical consistency of learned solutions. The trained PINN accurately reconstructed full-field water content distribution and corresponding diffusivity field over the entire experiment duration for each specimen. Ensemble training confirmed low sensitivity to network initialization and yielded consistent predictions across all specimen types. It is found that the popularly used exponential-type: D_o exp(B_r * theta), or power-law-type, D_o * theta^n, diffusivity models cannot capture the PINN-discovered diffusivity–saturation. A new model was proposed that defines diffusivity (D) as the exponential of a fourth-order polynomial of water content, D_o exp(a*theta^4+b*theta^3 +c*theta^2 +d*theta), where D_o, a, b, c and d are fitting parameters. Unlike the exponential and power-law models, this proposed model provides an excellent fit across the full saturation range. Numerical simulations using the proposed model closely matched the experimentally determined initial sorptivity for the MS specimen with a 2.78% error. Higher errors of 23.5% were observed in the HS specimen, possibly due to non-homogeneity in specimens cast with high w/c ratio, short curing time, and the geometry effect. LS samples showed anomalous absorption behavior and deviations from √t scaling, revealing limitations of the classical Richards equation. This study demonstrates that PINN offers a powerful and flexible framework for discovering hidden relationships from sparse, noisy experimental data in porous materials. PINNs can reproduce the observed behavior from limited data and reveal previously unknown relationships and functional forms that help better understand the material and mechanisms. Our results indicate that the diffusivity-water content relationship in hardened cement paste samples is more complex and non-linear—D_o exp(a*theta^4+b*theta^3 +c*theta^2 +d*theta)—than that described by classical exponential and power-law type models.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Dahal, Sunav Raj

Contributors dc:contributor

• Garg, Nishant

• Concrete Durability
• Sorptivity
• Diffusivity
• Moisture Transport
• X-ray
• Physics-informed Neural Networks
• Pinn
• Scientific Machine Learning
• Inverse Problem

Statement dc:rights

• Copyright 2025 Sunav Raj Dahal

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129783

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129783