Size Effect on Cross-Scale Uncertainty Propagation in Concrete Elements: Insights from the Lattice Discrete Particle Model and Explainable Data-Driven Modeling

Abstract

Heterogeneous cementitious composites exhibit pronounced multiscale characteristics, which lead to uncertainty and size effects in the macroscopic mechanical behavior. This study aims to reveal the size effect in the propagation of uncertainty from mesoscale features to macroscale responses of concrete through a combination of mesoscale simulations and data-driven modeling. At the mesoscale, two sources of uncertainty are considered: mesoscale mechanical uncertainty, characterized by seven mesoscale mechanical parameters, and mesoscale spatial uncertainty, represented by the spatial distribution of the constituent phases. At the macroscale, both the stress–strain response and fracture patterns are investigated. The Lattice Discrete Particle Model (LDPM) is first employed to perform mesoscale simulations and establish the relationship between the mesoscale features and macroscale responses. Subsequently, Monte Carlo simulation (MCS) is used to propagate uncertainty across scales. Based on the data generated from MCS, an explainable stochastic data-driven model is developed using heterogeneous sparse Gaussian process regression (HSGPR) to link mesoscale uncertainty to macroscale responses and to interpret how specimen size influences the uncertainty propagation mechanisms and governs the underlying mesoscale uncertainty drivers. The results provide mechanistic insights that can guide the selection of representative element sizes for stochastic multiscale analysis of concrete structures and inform mesoscale material design for controlling macroscale structural performance.