Analysis of solute transport in discrete fracture–matrix system using bipartite graph–based backbones

Although graph–based backbone methodologies have demonstrated promising potential for identifying dominant flow paths and enhancing computational efficiency in discrete fracture network (DFN) models, its effectiveness and applicability to discrete fracture–matrix (DFM) systems have not been investigated. This study extends the bipartite graph–based backbone framework to DFM systems and systematically evaluating its applicability to solute transport under different hydraulic property distributions. Stochastic numerical simulations with 30 realizations are conducted using the bipartite graph–based backbone approach and the results are compared with direct simulation results using DFM method. The comparison results reveal that the bipartite graph–based backbone approach can successfully reduce computational cost while maintaining predictive accuracy, with the complete Sub–DFM ( n –paths) achieving a mean relative error of only 7.43 % in breakthrough curve predictions compared with the Full–DFM (original–network models), and accurately preserve early breakthrough characteristics. The results also demonstrate that hydraulic property distributions strongly influence transport processes. For log–normally hydraulic distributions, the Sub–DFM ( n –paths) reproduces breakthrough curves (BTCs) with high accuracy (R 2 > 0.93), although saturation times t s are generally overestimated due to reduced connectivity. In contrast, for truncated power law (TPL) fracture size distributions substantially accelerate breakthrough and prolong saturation compared with the log–normal hydraulic distributions. These findings demonstrate that graph–based backbone reduction is a computationally efficient strategy to capture dominant advective transport processes and early contaminant arrivals. However, for natural rock masses with strong geometric heterogeneity, Full–DFM models remain important for accurately predicting long–term retention and tailing behavior.