Image‐based simulation of complex fracture networks by numerical manifold method

Abstract

Complex geometric features of fracture networks contained in rock masses can be captured by digital images quickly and accurately. However, the continuous and discontinuous deformation simulation of rock masses directly based on digital images is still challenging. Based on the Numerical Manifold Method (NMM), a simple and efficient image-based simulation method is developed for rock masses containing complex fracture networks. A new crack model, named as "voxel crack model," is generated based on pixel values of the digital image and a user-defined resolution. With the voxel crack model, physical cover and manifold elements in NMM are then efficiently generated for complex fracture networks. After this, the continuous and discontinuous displacement fields of rock masses are simulated straightforwardly. In the present work, conventionally burdensome tasks, like boundary detections to transform digital images into computer aided design (CAD) models, generating conforming meshes, and explicitly tracking of fracture surfaces, are avoided. Several benchmarks validate the developed method. The calculated continuous and discontinuous deformation field of the San Leo rock slope containing a complex fracture network demonstrates the capability of the proposed method for practical engineering application. K E Y W O R D Scomplex fracture networks, continuous and discontinuous simulation, image-based simulation, numerical manifold method, rock mass engineering, voxel crack model 3100

A phase‐field formulation based on an extended F‐criterion for rock fracture

“…The three possible cracking angles are then used to compute $$F( \theta )$$, and the angle which gives the maximum $$F( \theta )$$ is chosen as the local potential crack direction. The calculated θ can be inherited by the voxel crack model 46,47 used in numerical manifold method (NMM) for the further contact simulation of the crack detached rock blocks, to complete the whole process from fracture initiation, propagation to the collapse of rock masses. More details will be introduced and investigated in our future work.…”

3D simulation of complex fractures with a simple mesh

“…The 2D cutting algorithm 59 of discrete physical patches based on the voxel crack model is readily extended into 3D. A major difference is that, in 2D, pixels are connected if their edges touch, that is, 4‐connected, while in 3D, voxels are connected if their faces touch, that is, 6‐connected.…”

“…The accuracy differences between these two kinds of physical patches are talked about in our previous work. Interested readers may refer to Reference 59.…”

“…In this section, the voxel crack model described in 2D 59 is further implemented in 3D. Its differences and connections with the other two crack models, including the smeared crack model, and discrete crack model are talked about.…”

“…In this article, As an extension of the 2D image‐based simulation, 59 the continuous‐discontinuous displacement field of 3D complex fracture networks is calculated with a structured mesh. As to the geometric model, in this article, analysis domains with simple geometric features, such as benchmarks one and two, are simulated with CAD models as the input to save memory.…”