Browsing by Author "MacHutchon, Keith"

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    Investigated physical/strength properties and elastic constants of fimbul granular ice applied to ice cliff stability analysis
    (2024) Econi, Jonathan Arthur Olivu; Kalumba, Denis; MacHutchon, Keith; Skatulla, Sebastian; Govender, Reuben
    During the 2020-2021 South African National Antarctic Programme Antarctic resupply voyage, a Ground Penetrating Radar (GPR) survey was conducted on the Fimbul ice shelf edge to determine a safe cargo offloading zone from the SA Agulhas II ship. The survey showed subsurface cracks which created concerns of shelf failure, risking the lives of crew and the ship stationed at the bottom of the cliff. To assess the risk of failure, this study was carried out to quantify the stability of the vertical cliff. A slope stability analysis model was required to achieve this, which in turn needed inputs such as cliff geometry and ice material properties. Therefore, laboratory tests to obtain these properties preceded the cliff modelling. Ice cores were retrieved from the shelf, and these were observed to be granular in structure, with different grainsizes and ice lenses. The analysis began with a core characterisation based on the grainsize percentages, ice lens concentrations, and due to ice's relationship to rock, Rock Quality Designation (RQD) of the cores. The grainsize segmentation was fine, medium, and large grained, with medium grained being the most abundant in the cores. The ice lens concentrations showed areas on the ice shelf with high meltwater which were to be avoided. The physical properties needed were density, elastic modulus, and Poisson's ratio. The mass/volume method was used to obtain an average density of 569.9±157.7kg/m3 . The elastic modulus and Poisson's ratio were both tested using ultrasonic methods to give 1.66±0.87GPa and 0.37±0.06 respectively. Each of the values were comparable to values mentioned in literature with the granular ice lying between the stiffnesses of snow ice structures and crystalline ice. The strength value tested was Uniaxial Compressive Strength (UCS), with shear strength and tensile strength determined afterwards. The UCS tests gave a value of 0.9±0.27MPa. The compression was carried out at a strain rate of 10-4.3 s -1 for ductile failure. Shear strength was then determined using the Rock Mass Rating (RMR) method, giving cohesion and friction angle readings of 0.25MPa and 30. The shear strength was then calculated to 0.77MPa. The tensile strength was equal to the ice bond strength, which was equal to the cohesion value of 0.25MPa. Modelling was then embarked for a base scenario, horizontal crack variation, and vertical crack depth variation scenario. The base critical Factor of Safety (FS) was 5.56. Failure occurred in both tension and shear, through the Mohr Coulomb failure criterion. In the horizontal variation, the critical crack zone lay between 9 - 20m away from the shelf edge with the lowest FS of 4.24 at 13m. The failure types observed were toppling failure, planar failure, crumbling of the overhanging part of the ice. Finally, the increasing crack depth at the critical horizontal location led to decrease in FS. The scenarios output FS values showing that the ice shelf cliff is safe. Despite this, the models run were an oversimplification of the entire shelf with a number of factors assumed due to the unavailability of data. To provide a detailed analysis of the entire ice shelf, a thorough survey of the entire shelf would need to be carried out to provide accurate layering data, precise material properties at depth, actual crack locations and dimensions on the shelf edge.
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    Towards a material damage model using the logarithmic strain, with von Mises plasticity considerations
    (2022) Namalomba, Paul; Skatulla, Sebastian; MacHutchon, Keith
    Damage is briefly defined as the presence and growth of micro-defects in a material. This study serves to describe the computational implementation of the material damage theory adopted for ductile materials. Thus, pays attention to the computational analysis of the physical behaviour of materials under finite deformations — in particular, the stress-strain behaviour, load-deformation behaviour and location of weak zones. Throughout this study, non-linear continuum mechanics is utilised as the mathematical basis of the constitutive and general finite element framework. In continuum mechanics, there exists no requirement to discretely characterise each microcrack that grows in a material, thus making it possible to provide analysis of the stress and strain response affected by micro-defects using material particles, which are localised collections of many atomic-scale particles. The continuum is thus a sum of its material particles. To complement this description of mechanics, constitutive and phenomenological equations are adopted from the non-linear thermodynamic phenomena of elasticity, plasticity, and damage; the laws of thermodynamics will therefore apply and are shown as such. The proposed material damage model is developed and implemented in the backend of the in-house computational mechanics toolbox SESKA, which uses finite element-based discretisation and approximation techniques. Field and scalar quantities, such as stress and strain, are computed with the use of the return-mapping method. The stress measures utilised are the 2nd Piola-Kirchhoff stress S and the Mandel stress Σ. The Newton-Raphson update scheme is applied in the plasticity evolution equations via the plastic multiplier (denoted λ), which innately controls the evolution of all other inelastic phenomena. Damage is a function of plastic evolution and thus plays a role in the plasticity multiplier calculation. Moreover, this proposed model makes the assumption of full isotropy, all material properties at a material point are the same in tension and compression and the same regardless of the dimension. Finally, several examples are utilised to showcase the model and all the intricacies are presented — the problem setup, boundary condition assignment and multi-layered analysis are detailed in the content of this study and the examples perform well under qualitative scrutiny. These examples include a cantilevered beam model, a simply supported bending model and a plane strain example to evaluate whether the material model achieves qualifiable correlation to expected behaviour and to assess whether the damage-related parameters affect the stress and strain behaviour as expected. In brief conclusion, this paper shows that the model achieves qualifiable correlation and all the material parameters function as expected.