Adaptive Mesh Generation and Numerical Verification for Complex Rock Structures Based on Optimization and Iteration Algorithms

Abstract

The modelling of rock structure is of great significance in characterizing rock characteristics and studying the failure laws of rock samples. In order to construct a high‐fidelity model of the rock structure efficiently, this paper proposes an adaptive mesh dissection algorithm based on the Voronoi structure. Image processing techniques, including greyscale, threshold segmentation and edge detection, are applied to simplify the original rock image into a feature edge image. Then, a probability density diagram of the feature image is generated, which provides a probabilistic basis for the subsequent spreading of mesh seed points. Moreover, the concept of polygonal representation rate and the mesh quality evaluation system of four‐dimensional metrics are established to suggest values for the seed point parameters of the initial mesh. The initial mesh is continuously optimized and iterated by barycentric iteration and gradient descent optimization methods to form mesh structural models with high representational performance efficiently. The model tests on particle, fracture and multi‐phase rock images show that the optimized mesh model is highly similar to the original image in terms of similarity and edge fit, and the algorithm significantly reduces the short‐edge rate and improves the shape regularity of the mesh structure. Finally, numerical tests of uniaxial compression are carried out based on the optimized mesh model. The results show that the model has computational potential in numerical calculations. This method builds a procedural structure from digital images to numerical models, which can provide a reliable model basis for simulating the physico‐mechanical behaviour of heterogeneous rocks.