The shapes and morphological features of grains in sand assemblies have
far-reaching implications in many engineering applications, such as
geotechnical engineering, computer animations, petroleum engineering, and
concentrated solar power. Yet, our understanding of the influence of grain
geometries on macroscopic response is often only qualitative, due to the
limited availability of high-quality 3D grain geometry data. In this paper, we
introduce a denoising diffusion algorithm that uses a set of point clouds
collected from the surface of individual sand grains to generate grains in the
latent space. By employing a point cloud autoencoder, the three-dimensional
point cloud structures of sand grains are first encoded into a
lower-dimensional latent space. A generative denoising diffusion probabilistic
model is trained to produce synthetic sand that maximizes the log-likelihood of
the generated samples belonging to the original data distribution measured by a
Kullback-Leibler divergence. Numerical experiments suggest that the proposed
method is capable of generating realistic grains with morphology, shapes and
sizes consistent with the training data inferred from an F50 sand database . We
then use a rigid contact dynamic simulator to pour the synthetic sand in a
confined volume to form granular assemblies in a static equilibrium state with
targeted distribution properties. To ensure third-party validation, 50,000
synthetic sand grains and the 1,542 real synchrotron microcomputed tomography
(SMT) scans of the F50 sand, as well as the granular assemblies composed of
synthetic sand grains are made available in an open-source repository.

通过一种新的算法生成合成砂，对比实际收集的砂样数据，基于点云自编码器，通过降噪扩散算法能够生成形态、大小与训练数据一致的现实砂颗粒；确保第三方验证的前提下，附带 50,000 个合成石英砂颗粒、1,542 个同步辐射微计算机断层扫描 (F50 砂)，以及由合成石英砂颗粒组成的颗粒装置在开源仓库中公开。