Rock fracture morphology influences two-phase fluid flow in rock fractures. However, the role of the surface morphology of rock fractures in two-phase flow remains to be fully quantified. In this study, an analytical model for gas and water relative permeability in rough rock fractures was developed, incorporating surface roughness factor, hydraulic tortuosity, and surface tortuosity to quantify fracture morphology. The performance of the proposed model was evaluated through a comparison with empirical permeability models and experimental data. The proposed model accurately characterized two-phase fluid flow in rough fractures and examined the impact of surface morphology and flow dynamics on the relative permeability of two-phase fluids in rock fractures, demonstrating that increased surface roughness shifts the equal-permeability point toward higher water saturation and lower relative permeability. To investigate the influence of the flow dynamics on relative permeability, the proposed model was extended to express the Reynolds number of two-phase fluids as a function of water saturation and relative permeability, enabling a detailed exploration of the evolution law of relative permeability with Reynolds number.

The large‑scale accumulation of coal gangue poses serious environmental and land‑use challenges, yet its direct use as concrete aggregate has been hindered by low reactivity, high porosity, and weak interfacial bonding. Although prior studies have examined thermal activation of coal gangue, the interplay among calcination temperature, pore‑size evolution, and mesoscale failure mechanisms in a unified multi‑scale framework remains underexplored. This study presents a multi‑scale experimental and numerical investigation of thermally activated coal gangue aggregate concrete, focusing on ITZ evolution and failure mechanisms. Coal gangue was calcined at 500, 600, 700, and 800 °C and substituted for natural coarse aggregate in C30 concrete. Uniaxial compression testing, SEM, XRD, NMR, and PFC3D meso‑scale simulations were employed to elucidate the effects of calcination temperature on 28‑day compressive strength, ITZ microstructure, pore‑size distribution, and crack initiation and propagation. Calcination at 700–800 °C maximized the release of active SiO₂/Al₂O₃, resulting in a denser ITZ, reduced porosity, and a 15.6–22.8% increase in compressive strength over uncalcined concrete. Calibrated meso‑scale models demonstrated that enhanced ITZ bond strength delayed crack onset and altered damage patterns. These findings offer theoretical insight and practical guidance for the sustainable valorization of coal gangue in high‑performance concrete applications.

Accurate calibration of mesoscopic contact model parameters is essential for ensuring the reliability of Particle Flow Code in Three Dimensions (PFC3D) simulations in geotechnical engineering. Trial-and-error approaches are often used to determine the parameters of the contact model, but they are time-consuming, labor-intensive, and offer no guarantee of parameter validity or simulation credibility. Although conventional machine learning techniques have been applied to invert the contact model parameters, they are hampered by the difficulty of selecting the optimal hyperparameters and, in some cases, insufficient data, which limits both the predictive accuracy and robustness. In this study, a total of 361 PFC3D uniaxial compression simulations using a linear parallel bond model with varied mesoscopic parameters were generated to capture a wide range of rock and geotechnical material behaviors. From each stress–strain curve, eight characteristic points were extracted as inputs to a multi-objective Automated Machine Learning (AutoML) model designed to invert three key mesoscopic parameters, i.e., the elastic modulus (E), stiffness ratio (k_s/k_n), and degraded elastic modulus (E_d). The developed AutoML model, comprising two hidden layers of 256 and 32 neurons with ReLU activation function, achieved coefficients of determination (R²) of 0.992, 0.710, and 0.521 for E, k_s/k_n, and E_d, respectively, demonstrating acceptable predictive accuracy and generalizability. The multi-objective AutoML model was also applied to invert the parameters from three independent uniaxial compression tests on rock-like materials to validate its practical performance. The close match between the experimental and numerically simulated stress–strain curves confirmed the model’s reliability for mesoscopic parameter inversion in PFC3D.

An evolutive phase field model (PFM) that incorporates cement hydration process is developed to predict Mode-I fracture behavior in cemented paste backfill (CPB). The model seamlessly integrates hydration-dependent stiffness and toughness evolution into a standard finite element framework, regularizing sharp cracks through a diffusive phase field variable. In all three case studies, the PFM reproduces key experimental observations—narrow crack bands and stable propagation in single-edge notched bending (SENB) test, mode-I dominated crack paths and post-peak softening in semi-circular bending (SCB) test, and wide, diffuse fracture zones in splitting tensile tests. The coupled hydration damage formulation captures the time- and temperature-sensitive strengthening of CPB, successfully matching the delayed crack initiation and gradual load-bearing increases seen across varied curing ages and temperatures. The robustness of a single parameter set across multiple test configurations underscores the model potential for generalized CPB fracture prediction without geometry-specific calibration. By accurately forecasting crack patterns and load–displacement responses, this evolutive PFM offers a powerful tool for optimizing CPB mix design, service-life prediction, and curing protocol development in deep-mine applications.