Denoising Diffusion Probabilistic Model-Based Multivariate Parameter Distributions for Rough Discrete Fracture Network Modeling

Fractures significantly influence rock mass geotechnical behavior, necessitating precise characterization of their geometric parameters. Traditional modeling approaches, based on standard statistical descriptions and random simulations, often disregard parameter correlations and assume smooth fractures, compromising accuracy. This study introduces a Denoising Diffusion Probabilistic Model (DDPM) to capture dip direction, dip angle, trace length, aperture, and roughness correlations and generate discrete fracture network (DFN) modeling data. By integrating fractal dimensions and non-uniform rational B-splines (NURBS) tensor products, our approach accommodates fracture roughness, enhancing overall realism. Validation on real-world datasets using Kullback–Leibler(KL) divergence and Wasserstein distance indicates that DDPM significantly outperforms generative adversarial networks (GAN), variational autoencoders (VAE), normalizing flow (NF), and Monte Carlo methods, achieving average KL/Wasserstein distance reductions of 72.44%/57.08% against other generative models and 74.84%/36.83% against Monte Carlo. Furthermore, the modeled rough fractures accurately match the roughness of real fracture traces, confirming the improved fidelity of the DFN simulations.