### Browsing by Author "Bird, Wyndham Wadham"

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- ItemOpen AccessBeam models for the hangingwall of deep, tabular excavations in stratified rock(1989) De Villiers, N A; Martin, J B; Bird, Wyndham WadhamIn the South African gold mining industry, mining is being conducted at depths of over 3 000 m below the surface. Severe fracturing and deformation of the rock occurs making it unlikely that stress analysis which treats the rock as a homogeneous elastic material will yield useful results about the behaviour around the excavation. The excavation, or stope, considered in this study is tabular. The stope occurs in stratified rock with bedding planes at approximately 1 m intervals. The height of the stope is about 1 m to 1.5 m and the length increases to over 100 m as mining progresses. Shear fractures initiate ahead of the advancing stope, which together with the bedding planes separate the rock into distinct blocks of relatively intact material. The stratified nature of the material in the hangingwall (or roof) of the excavation, and the lack of cohesion in the bedding planes, suggests that separation occurs along the bedding planes, with each layer supporting its own weight. The lowest of these layers is referred to as the "hangingwall beam". Stope closure occurs at a distance of around 30 to 40 m behind the stope face. This study focuses on the mechanics of the hangingwall beam with particular emphasis on the conditions for stable closure. In order to do this the stope is first analysed using a finite element model which treats the rock as a homogeneous elastic medium. By treating the hangingwall beam as a separate layer, 1 m thick, its behaviour is compared to that observed in practice. We find that the hangingwall beam does separate from the overlying rock, but that the axial stresses in the beam are tensile, thus contradicting the observed behaviour. In practice, compressive stresses exist in the hangingwall and footwall. It has been suggested that slip along the shear fractures generates the compressive stresses. In constructing a mathematical model of the hangingwall beam we consider the beam to be made up of blocks 1 m deep and 1 m long. The blocks are treated as a homogeneous elastic material. The behaviour of such a beam is different from that of a fully homogeneous beam, because of the possibility of the formation of hinges. By considering a range of simplified models of a beam composed of blocks, various questions regarding its stability can be addressed. These models consider beams of fixed span in which the weight is increased from zero to the full value. The largest unsupported halfspan which can be stably equilibrated is of the order of 31 m. The maximum stable deflection is 0. 4 m, and therefore additional support is required to allow closure to occur statically. The nature of a single supporting spring that will let down the beam in a limiting, stable manner is identified. Once closure has taken place, the hangingwall beam is stable. In order to obtain a realistic picture of the steady state configuration of the hangingwall beam, an analysis is performed which simulates the advancing stope face. The results show that the distance between the face and the point of closure is around 34 m which is in accord with the behaviour observed in practice. The results have shown that the model which treats the hangingwall as a beam composed of blocks provides useful information about the mechanics of the hangingwall.
- ItemOpen AccessFormulations for incremental elastic-plastic analysis and the consolidation of porous media(1987) Bird, Wyndham Wadham; Martin, JBThe formulation and solution of the problem of an elastic-plastic body subject to successive increments of loading is a fundamental problem in plasticity. A variety of powerful iterative techniques are available for the solution of the problem, mostly based on Newton-Raphson methods using an explicit scheme for the integration of the constitutive relations. The procedures in current use can be criticised in that they are essentially heuristic, and they are not fully linked to the governing mechanical principles of the incremental plasticity problem. Recent work aimed at the improvement of the accuracy and stability of the numerical algorithms in plasticity explores the fundamental relationship between the nature of the forward integration algorithm and the mechanical principles of the problem. In this thesis we attempt to advance this understanding. Through the use of an internal variable formulation of the problem, we are able to explore links between a consistent mathematical programming formulation of the incremental problem in plasticity and the conventional Newton-Raphson iterative solution procedures.
- ItemOpen AccessA model for the time dependent behaviour of rock joints(1989) Camp, Nicholas Julian; Martin, J B; Bird, Wyndham WadhamThis thesis is a theoretical investigation into the time-dependent behaviour of rock joints. Much of the research work that has been conducted to date in the area of finite element analysis has been involved with the development of special elements to deal with these discontinuities. A comprehensive literature survey is undertaken highlighting some of the significant contributions to the modelling of joints. It is then shown how internal variables can be used to model discontinuities in the rock mass. A finite element formulation is described resulting in a system of equations which can easily be adapted to cope with various constitutive behaviours on the discontinuities. In particular, a viscoplastic relationship; which uses a homogeneous, hyperbolic yield function is adopted. The viscoplastic relationship can be used for both time-dependent (creep) or quasi-static (elasto-plastic) problems. Time-dependent behaviour requires a time integration scheme and therefore a generalised explicit/implicit scheme is chosen. The resulting numerical algorithms are all implemented in the finite element program, NOSTRUM. Various examples are presented to illustrate certain features of both the formulation and the numerical algorithm. Jointed rock beams and a jointed infinite rock mass are modelled assuming plane strain conditions. Reasons are proposed to explain the predicted behaviour. The results of the analysis shows that the internal variable formulation successfully models time-dependent joint movements in a continuous media. The method gives good, qualitative results which agree with observations in deep level mines. It is recommended that quantitative mine observations be used to calibrate the model so that usable predictions of joint movement can be made. This would enable any new developments to be implemented in the model. Further work on implicit methods might allow greater modelling flexibility by reducing computer run times.