Physics-informed multiscale modelling of tunnelling-governed percolation and conductivity evolution in carbon black modified cementitious composites

Abstract

Self-sensing cementitious composites (SSCCs) containing conductive nanofillers enable structural health monitoring through measurable electrical responses. However, conventional numerical models generally assume homogeneous interphase conductivity, neglecting the distance-dependent quantum tunnelling that governs conductive network formation near the percolation threshold. This study presents a physics-informed multiscale framework for predicting the effective electrical conductivity (EEC) and percolation threshold (PT) of carbon black nanoparticle (CBN) modified cementitious composites. Stochastic representative volume elements were coupled with finite element simulations, while the tunnelling region surrounding each particle was discretized into concentric layers with exponentially decaying conductivity derived from Simmons’ tunnelling theory. The framework reproduced the experimentally observed percolation threshold near 2 wt.% CBN and captured the conductivity increase from approximately 10⁻⁶ to 10⁻¹ S/m. Compared with the homogeneous interphase model, the discretized tunnelling formulation substantially improved prediction accuracy, with the ten-layer model reducing the logarithmic root mean square error (RMSE) from 0.520 to 0.132. The proposed framework provides a physically realistic and computationally efficient approach for modelling tunnelling-mediated transport and optimizing self-sensing cementitious composites.