Abstract A small opencast coal mine has been developed over previous underground workings in the Malvern Hills, inland Canterbury, New Zealand. The coal measure strata dip at ~45° to the southeast, and consist of finely laminated mudrocks with multiple coal seams of varying thickness. Production is in the range 10,000 to 15,000 tonnes per annum from two principal seams with an aggregate thickness of ~4.5m. The open pit has been designed with footwall batters parallel to bedding, vertical bench separation of 15m, and the highwall formed to a nominal 4V:1H. Preliminary examination of the open pit mine site in 2003 indicated that footwall failures involved de-lamination due to drying out on exposure, and buckling and/or shearing along bedding surfaces. During mine development it became apparent that the batters formed easily where thin (less than 0.3m thick) coal seams were present in the sequence. In the 2004 campaign the pit floor was lowered, with a new batter and bench formed to expose the 3m thick Main Seam coal. The day after completion of this batter, a large buckle failure occurred involving the entire length of the pit (85m along strike), and a 2m thick intact slab with a total volume of ~3700m³ translated down dip 6.2m on the base of a thin coal seam to form a pronounced buckle at the toe. Even though footwall batters are cut to the angle of dip, which is entirely realistic geotechnically, the de-coupling and buckling that occurred compromised the safety and economics of the whole operation. Buckling failure in moderately dipping soft rock sequences has been identified in footwall slopes of coal mining operations. Models used in the literature to simulate similar footwall failures include: the Euler solution using column and beam buckling theory to calculate the kinematic feasibility of a slab-buckle, conceptual modelling using a base friction table, and numerical modelling using distinct element analysis. Back analysis of the Malvern Hills failure was necessary to investigate the controls on the footwall stability, and for future mine design. Engineering geological description of the pit and slab materials was done, and an engineering geological model created. Samples of the slab material and failure surface were collected by coring and trenching, with testing of these materials to establish the required parameters for use in the Euler solution. Back analysis using three different forms of the Euler solution provided unrealistic results that overestimated the overall length of a stable slope by more than 10 times. An engineering geology reassessment was undertaken, and a number of inadequacies in the Euler solution methodology were identified particularly in relation to pore pressure and elasticity considerations. Given that the Malvern Hills toe-buckle slab failure displays both elastic and plastic deformation components in the soft mudrocks, and the slab itself cannot be considered as homogenous, reservations must exist about conventional predictive analytical techniques for pit slope failures of this type. No further large scale slab-buckle failures have developed at the mine site, in part because of the slow rate of coal extraction, but precautionary drainage of the footwall slopes has been undertaken to improve overall batter stability. The location of the slab-buckle failure on a critically positioned pre-sheared thin coal seam with full hydrostatic head is considered the most probable cause, rather than inherent instability of the generic bench and batter arrangement adopted. The adoption of a precedent based engineering geology approach to future mine design is considered the most appropriate solution in the circumstances.

In this thesis we describe the development of Reynolds- averaged Navier Stokes code for the flow past two- dimensional configuration. Particularly, emphasis has been laid on the study of low Reynolds number airfoil aerodynamics. The thesis consists of five chapters covering the back ground history, problem formulation, method of solution and discussion of the results and conclusion. Chapter I deals with a detailed background history of low Reynolds number aerodynamics, problem associated with it, state of the art, its importance in practical applications in aircraft industries. Chapter II describes the mathematical model of the flow physics and various levels of approximations. Also it gives an account of complexity of the equations at low Reynolds number regarding flow separation, transition and reattachment. Chapter III describes method of solution, numerical algorithm developed, description of various upwind schemes, grid system, finite volume discrieti-zation of the governing equations described in Chapter II. Chapter IV describes the application of the newly developed Navier Stokes code for the test cases from GAMM Workshop proceedings. Also it describes validation of the code for Euler solutions, Blasius solution for the flow past flat plate and compressible Navier Stokes solution for the flow past NACA 0012 Airfoil at low Reynolds number. Chapter V describes the application of the Navier Stokes code for the more test cases of current practical interest . In this chapter laminar separation bubble characteristics are investigated in detail regarding formation, growth and shedding in an unsteady environment. Finally the conclusion is drawn regarding the robustness of the newly developed code in predicting the airfoil aerodynamic characteristics at low Reynolds number both in steady and unsteady environment. Lastly, suggestion for future work has been highlighted.