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<p>Accurate fracture modeling helps clarify the mechanical behavior of rock masses. However, traditional statistical and random simulation methods ignore correlations among fracture parameters and surface roughness and assume uniformly random fracture networks within the domain, while current advanced generative models suffer from training instability and limited ability to capture complex spatial distributions. We propose a denoising diffusion probabilistic model (DDPM)-based framework that learns the multivariate joint distribution of fracture parameters—dip direction, dip angle, trace length, aperture, roughness, and center coordinates (<i>x,y,z</i>)–to generate DFNs with realistic attributes while maintaining stable and efficient training. The method derives and integrates fracture center positions within a sampling window into joint generation for location optimization, aiming to improve the representation of spatial variability in fractures. Fractal-dimension analysis is coupled with non-uniform rational B-spline (NURBS) tensor products to model rough fracture surfaces. Validations on real engineering data under the presented implementation, using descriptive statistics, Kullback–Leibler (KL) divergence and Wasserstein distance, show that the proposed method achieves lowest deviation among baselines for dip direction, dip angle, trace length, aperture, and roughness. The mean aggregated KL and Wasserstein distances across five parameters and three random seeds are reduced by at least 59.41% and 18.84% versus Generative Adversarial Networks/Variational Autoencoders/Normalizing Flows, and by 70.29% and 26.94% relative to Monte Carlo. Section-level analyses confirm the correctness of the derived fracture centers and improved structual feature fidelity. The rough-surface model reasonably reproduces real fracture roughness at the two-dimensional trace level, with the Normalized Relative Error (NRE) of fractal dimension being approximately 30%, representing a reduction of around 70% compared with the smooth-plane model assumption.</p>

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A denoising diffusion probabilistic model-based method for rough discrete fracture network fine modeling considering location optimization and multivariate distribution of parameters

  • 期刊论文

  • 发表日期：

    2026年5月16日

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  • Shuyang Han,
  • Jiajun Wang,
  • Dawei Tong,
  • Xiaoling Wang,
  • Wanyu Zhang,
  • Jinkun Du

摘要

Accurate fracture modeling helps clarify the mechanical behavior of rock masses. However, traditional statistical and random simulation methods ignore correlations among fracture parameters and surface roughness and assume uniformly random fracture networks within the domain, while current advanced generative models suffer from training instability and limited ability to capture complex spatial distributions. We propose a denoising diffusion probabilistic model (DDPM)-based framework that learns the multivariate joint distribution of fracture parameters—dip direction, dip angle, trace length, aperture, roughness, and center coordinates (x,y,z)–to generate DFNs with realistic attributes while maintaining stable and efficient training. The method derives and integrates fracture center positions within a sampling window into joint generation for location optimization, aiming to improve the representation of spatial variability in fractures. Fractal-dimension analysis is coupled with non-uniform rational B-spline (NURBS) tensor products to model rough fracture surfaces. Validations on real engineering data under the presented implementation, using descriptive statistics, Kullback–Leibler (KL) divergence and Wasserstein distance, show that the proposed method achieves lowest deviation among baselines for dip direction, dip angle, trace length, aperture, and roughness. The mean aggregated KL and Wasserstein distances across five parameters and three random seeds are reduced by at least 59.41% and 18.84% versus Generative Adversarial Networks/Variational Autoencoders/Normalizing Flows, and by 70.29% and 26.94% relative to Monte Carlo. Section-level analyses confirm the correctness of the derived fracture centers and improved structual feature fidelity. The rough-surface model reasonably reproduces real fracture roughness at the two-dimensional trace level, with the Normalized Relative Error (NRE) of fractal dimension being approximately 30%, representing a reduction of around 70% compared with the smooth-plane model assumption.