Description:
From Materials to Structures: Advancement Through Innovation - Proceedings of the 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM 2012
Description:
Digital images are increasingly being used as input data for computational analyses. This study presents an efficient numerical technique to perform image-based elastoplastic analysis of materials and structures. The quadtree decomposition algorithm is employed for image-based mesh generation, which is fully automatic and highly efficient. The quadtree cells are modeled by scaled boundary polytope elements, which eliminate the issue of hanging nodes faced by standard finite elements. A novel, simple, and efficient scaled boundary elastoplastic formulation with stablisation is developed. In this formulation, the return-mapping calculation is only required to be performed at a single point in a polytope element, which facilitates the computational efficiency of the elastoplastic analysis and simplicity of implementation. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed technique for performing the elastoplastic analysis of high-resolution images.
Description:
The quadtree is a hierarchical-type data structure where each parent is recursively divided into four children. This structure makes it particularly efficient for adaptive mesh refinement in regions with localised gradients. Compared with unstructured triangles, mesh generation is more efficient using quadtree decompositions. The finite number of patterns in the quadtree decomposition makes it efficient for data storage and retrieval. Motivated by these advantages, a crack propagation modelling approach using a quadtree-based scaled boundary finite element method (SBFEM) is developed. Starting from the formulation of an arbitrary n-sided polygon element, each quadrant in the quadtree mesh is treated as a polygon within the framework of the SBFEM. Special techniques to treat the hanging nodes are not necessary. Moreover, the SBFEM enables accurate calculation of the stress intensity factors directly from its solutions without local mesh refinement or asymptotic enrichment functions. When a crack propagates, it is only necessary to split each quadrant cut by the crack into two. These quadrants are polygons that can be directly modelled by the SBFEM. Changes to the mesh are minimal. The efficiency of this approach is demonstrated using numerical benchmarks.
Description:
The quadtree is a hierarchical-type data structure where each parent is recursively divided into four children. This structure makes it particularly efficient for adaptive mesh refinement in regions with localised gradients. Compared with unstructured triangles, mesh generation is more efficient using quadtree decompositions. The finite number of patterns in the quadtree decomposition makes it efficient for data storage and retrieval. Motivated by these advantages, a crack propagation modelling approach using a quadtree-based scaled boundary finite element method (SBFEM) is developed. Starting from the formulation of an arbitrary n-sided polygon element, each quadrant in the quadtree mesh is treated as a polygon within the framework of the SBFEM. Special techniques to treat the hanging nodes are not necessary. Moreover, the SBFEM enables accurate calculation of the stress intensity factors directly from its solutions without local mesh refinement or asymptotic enrichment functions. When a crack propagates, it is only necessary to split each quadrant cut by the crack into two. These quadrants are polygons that can be directly modelled by the SBFEM. Changes to the mesh are minimal. The efficiency of this approach is demonstrated using numerical benchmarks.
Description:
Numerical methods are a mature field of research and have become an increasingly important tool in mining and geotechnical engineering design practices. Although the advantages of numerical methods in aiding the analysis and solving practical engineering problems have been widely accepted and recognised, there is still a gap for further improvements. One such area is the challenge to consider the complexities of geology and the lack of stratigraphic information in the numerical model. Failure to include geological complexities may lead to overestimating the analysis parameters, such as the safety factor. These difficulties mainly manifest in the form of complex mesh generation due to the need to integrate spatial variable material parameters, capturing complex geological features, requirement of additional meshing algorithms, high human involvement, and long processing time. The scaled boundary finite element method (SBFEM) is a semi-analytical method that has potential to address these types of problems. This thesis focuses on developing the SBFEM to address these challenges so that complex geotechnical and mining engineering can be better modelled. Optimisation problems in geotechnical and mining engineering are also considered by developing a combined SBFEM-genetic algorithm framework for the design and rehabilitation of slopes. To begin with, an image-based mesh generation procedure is developed to automatically integrate the spatially variable material parameters into a computational mesh. The procedure allows the input of large data sets of geological and geometrical information in image format, and the mapping procedure enables the concatenation of any number of material parameters into a single computational mesh. The scaled boundary finite element formulation is used to discretise the governing equations of elasto-plasticity considering a Mohr-Coulomb failure criterion, which is common in soils. A shear strength reduction technique is implemented to analyse the stability of slopes in the form of an output Factor of Safety. The developed method is shown to allow routine changes in the operation of the slopes to consider geometric changes, such as backfilling, excavation and updates to geological sublets, by simply editing the digital image inputs. To extend the SBFEM to more complex geotechnical and mining engineering applications, a formulation that considers the coupled effect of pore pressure and nonlinear deformation of the soil is developed. The image-based mesh generation procedure is incorporated to integrate the geological complexities, which include heterogeneity of strate and phreatic surfaces. The developed technique is applied to study complex case studies of a tailings dam embankment construction and a coal slope rehabilitation project with a construction period. The research also considers geometric optimisation problems within the context of geotechnical and mining engineering applications. Geometric optimisation of slopes such as those in open cut mines is important to reduce the overhead operational cost involved in construction, excavation and rehabilitation backfilling, while ensuring stability at an acceptable level. This is achieved by developing a unified platform combining genetic algorithm (GA) with scaled boundary finite element formulations and image-based meshing procedures. Since the image-based mesh generation procedure is an automatic process, it enables automation of the optimisation, which is an iterative proceeding. The capabilities of this technique are demonstrated by optimising the geometric parameters of complex slopes for given safety factors and rehabilitation geometries for given safety factors during a given construction period. The image-based SBFEM analysis platform is further developed to consider geological uncertainty, such as stratigraphic interfaces and phreatic surface fluctuations, so that their effect on slope stability can be studied. The Brownian bridge statistic technique is integrated into the pre-processing module to produce these instances reflecting the ranii dom fluctuations between two intervals and generate possible geological and hydrological cross-sections. This allows unknown geological stratigraphic interface fluctuation due to a lack of sublet information to be considered. The scaled boundary finite element formulations developed in the earlier parts of this thesis are used to discretise each generated profile and analysis probabilistically. Since the mesh generation method is fully automatic, this probabilistic analysis procedure enables to analyse of a large number of possible variations and their effect on geotechnical structures with limited human intervention. Few parametric studies were conducted on slopes to study the impact of stratigraphic and phreatic surface fluctuation on the probability of failure. Finally, the hydraulic fracture commonly seen in geotechnical and mining engineering applications is considered. The phase field has the potential to model complex fracture mechanisms including crack nucleation, branching and coalescence. However, it requires a very fine mesh in order to accurately regularise the energy resulting from the creation of new crack faces. This leads to longer processing time and high computational requirements. Moreover, fracture propagation modelling with phase field models requires equilibrium iterations and hence repetitive calculation of element matrices. This research develops a scaled boundary finite element formulation with phase field model to address hydraulic fracture problems in fully-saturated poro-elastic media. Adaptive meshing refinement based on quadtree meshes is applied. This restricts the fine mesh requirement to only the regions where damage is present and avoids the need for a very fine mesh throughout the structure. Further, leveraging from the unique number of patterns in a hierarchical mesh, an appropriate scaling technique is applied to transform the relevant matrices and vectors to the physical cell in the mesh. This avoids the need for repetitive calculations during the equilibrium iterations. These features increase the efficiency of fracture modelling while reducing the computational requirement. The benchmark problems and complex fracture network problems are provided to highlight the advantage of the method.