Olympic Dam underground mine is located in South Australia approximately 520km north-north-west of Adelaide. The copper-gold-uranium deposit is extracted by open stope mining. The empirical Mathews stability method has been applied to open stope stability forecasting at Olympic Dam for the more than 20 years. This method adjusts the rock tunneling quality index (Q’) to allow for a rock stress factor, the orientation of any discontinuity and the orientation of the geometric surface formed by the excavation. The applicability of the Mathews stability method at Olympic Dam was analysed by assessing the volume of over break outside the stope design profile. It was found that 41% of all stope surface predictions were correct, and that 59% (by difference) of all predictions were therefore incorrect. This was found to be primarily due to the method as applied at Olympic Dam, rather than the inherent errors of the Mathews stability method. However there are a number of weaknesses in the Mathews stability method including the inability to identify structural weaknesses in the rock mass, to allow for different stress concentrations around irregular shaped stopes and to account for stope relaxation. A high resolution non-linear, Hoek Brown, numerical model is capable of providing displacement, velocity and strain rates for points within a rock mass. Velocity is the modelled rate of displacement of the points within the rock mass relative to the stope profile. An existing numerical model of this sort at Olympic Dam was used to investigate the relationship of the velocity of points moving toward a stope, and the probability of them becoming over break. It was found that with increasing rates of velocity the probability of a point becoming over break increased. The identified limitations of the application of the Mathews stability method are not enough to justify removing the method from the stope design process at Olympic Dam. With the implementation of recommended improvements such as, increasing the frequency of window mapping collection, live stress measurements and detailed post-mining assessment of stopes, an increase in the methods reliability can be expected. These improvements should be incorporated in conjunction with the continued trial of velocity as a stope performance indicator at Olympic Dam.

This study developed a GC-MS method for the simultaneous detection of piperazines and congeners in street samples of amphetamine type stimulants. This research investigated the clandestine routes of synthesis and chemical profiles of phenylpiperazines, represented by 1- (4-fluorophenyl)piperazine (4-FPP) and 1-(3-trifluoromethylphenyl)piperazine (3-TFMPP). These drugs are part of the increasingly prevalent illicit new psychoactive substances. The presence of (2, 3, 4) FPP and (2, 3, 4) TFMPP positional isomers has been identified by other researchers as a limitation due to their similar chemical profiles. The method was optimized and confirmed as compliant with the International Conference on Harmonisation and the Center for Drug Evaluation and Research guidelines on validation. 4- FPP and 3-TFMPP were synthesised using potential routes for clandestine laboratories. Simple extraction and analysis of 11 street samples was conducted using the method developed. Furthermore, the stability of 22 drugs during analysis was investigated. Limits of detection were in the range 5 – 1.95ng/mL free base on column. The synthesised samples were identified as 4-FPP and 3-TFMPP. Several impurities were observed in the synthesised samples, which were identified and categorised as residual reactants, isomers of 4-FPP and of 3-TFMPP and by-products of synthesis. The percentage yields of the synthesised samples obtained were up to 82.4% 4-FPP and 78.7% 3-TFMPP. The street samples were found to contain MDMA, 3-TFMPP, BZP, caffeine, ephedrine and other impurities. The analytical method simultaneously separates 19 of the most common drugs found in piperazine samples and achieves for the first time the GC-MS separation of (i) 2-FPP, 3-FPP and 4-FPP and (ii) 2-TFMPP, 3-TFMPP and 4-TFMPP at the same time from a sample matrix containing all the 19 compounds. This method provides operational laboratories with a more effective method for the chemical characterisation of street samples of piperazines and also provides novel stability data.

In dieser Arbeit wird zuerst das Theorem von Chung, Graham und Wilson über quasi-zufällige Graphen zur sogenannten schwachen Quasi-Zufälligkeit für k-uniforme Hypergraphen verallgemeinert und somit eine Reihe äquivalenter Eigenschaften bestimmt. Basierend auf diesen Resultaten werden nichtbipartite Graphen gefunden, welche die Quasi-Zufälligkeit für Graphen ``forcieren''''. Zuvor waren nur bipartite Graphen mit dieser Eigenschaft bekannt. Desweiteren ist ein konzeptionell einfacher Algorithmus zum Verifizieren nicht erfüllbarer zufälliger k-SAT Formeln angegeben. Dann richtet sich der Fokus auf Anwendungen verschiedener Regularitätslemmata für Hypergraphen. Zuerst wird die Menge aller bezeichneten 3-uniformen Hypergraphen auf n Knoten, die keine Kopie des Hypergraphen der Fano Ebene enthalten, studiert. Es wird gezeigt, dass fast jedes Element aus dieser Menge ein bipartiter Hypergraph ist. Dies führt zu einem Algorithmus, der in polynomiell erwarteter Zeit einen zufälligen Fano-freien (und somit einen zufälligen bipartiten 3-uniformen) Hypergraphen richtig färbt. Schließlich wird die folgende extremale Funktion studiert. Es sind r Farben gegeben sowie ein k-uniformer Hypergraph F. Auf wie viele verschiedene Arten kann man die Kanten eines k-uniformen Hypergraphen H färben, so dass keine monochromatische Kopie von F entsteht? Welche Hypergraphen H maximieren die Anzahl erlaubter Kantenfärbungen? Hier wird ein strukturelles Resultat für eine natürliche Klasse von Hypergraphen bewiesen. Es wird für viele Hypergraphen F, deren extremaler Hypergraph bekannt ist, gezeigt, dass im Falle von zwei oder drei Farben die extremalen Hypergraphen die oben beschriebene Funktion maximieren, während für vier oder mehr Farben andere Hypergraphen mehr Kantenfärbungen zulassen. / This thesis presents first one possible generalization of the result of Chung, Graham and Wilson to k-uniform hypergraphs, and studies the so-called weak quasi-randomness. As applications we obtain a simple strong refutation algorithm for random sparse k-SAT formulas and we identify first non-bipartite forcing pairs for quasi-random graphs. Our focus then shifts from the study of quasi-random objects to applications of different versions of the hypergraph regularity lemmas; all these versions assert decompositions of hypergraphs into constantly many quasi-random parts, where the meaning of ``quasi-random'''' takes different contexts in different situations. We study the family of hypergraphs not containing the hypergraph of the Fano plane as a subhypergraph, and show that almost all members of this family are bipartite. As a consequence an algorithm for coloring bipartite 3-uniform hypergraphs with average polynomial running time is given. Then the following combinatorial extremal problem is considered. Suppose one is given r colors and a fixed hypergraph F. The question is: In at most how many ways can one color the hyperedges of a hypergraph H on n vertices such that no monochromatic copy of F is created? What are the extremal hypergraphs for this function? Here a structural result for a natural family of hypergraphs F is proven. For some special classes of hypergraphs we show that their extremal hypergraphs (for large n) maximize the number of edge colorings for 2 and 3 colors, while for at least 4 colors other hypergraphs are optimal.

En las últimas cuatro décadas, el método gráfico de estabilidad de Mathews ha constituido el abanico de herramientas indispensables para el dimensionamiento de tajeos; caracterizándose por su eficiencia en costos, ahorro de tiempo y esfuerzo. Asimismo, el aporte de diversos autores por optimizar su rendimiento ha permitido desplegar una serie de criterios que han permitido abordar cada vez más escenarios. No obstante, con la diversificación de la minería en diferentes contextos geológicos y la necesidad trabajar a profundidades más altas se ha mostrado que el método gráfico de estabilidad ha desestimado escenarios con presencia de agua y distintos regímenes de confinamiento. Es por este motivo, que la presente investigación busca incorporar dichos escenarios por medio del algoritmo Gradient Boosting Machine. Para dicho fin, se simuló escenarios con diversos niveles de presión de agua y se consideró el grado de confinamiento alrededor de las excavaciones. El modelo generado se basó en el criterio de la clasificación binaria, siento las clases predichas, “estable” e “inestable”; con lo que se obtuvo un valor AUC de 0.88, lo que demostró una excelente capacidad predictiva del modelo GBM. Asimismo, se demostró las ventajas frente al método tradicional, puesto que se añade una componente de rigurosidad y de generalización. Finalmente, se evidencia el logro de un método de estabilidad que incorpora los esfuerzos activos y que ostenta un adecuado rendimiento predictivo. / In the last four decades, the Mathews' graphical stability method has constituted the range of indispensable tools for the dimensioning of stopes; characterized by its cost efficiency, time and effort savings. Likewise, the contribution of several authors to optimize its performance has made it possible to deploy a series of criteria that have made it possible to address more and more scenarios. However, with the diversification of mining in different geological contexts and the need to work at higher depths, it has been shown that the graphical stability method has neglected scenarios with the presence of water and different confinement regimes. For this reason, the present research sought to incorporate such scenarios by means of the Gradient Boosting Machine algorithm. For this purpose, scenarios with different levels of water pressure were simulated and the degree of confinement around the excavations was considered. The model generated was based on the binary classification criterion, feeling the predicted classes, "stable" and "unstable"; with which an AUC value of 0.88 was obtained, which demonstrated an excellent predictive capacity of the GBM model. Likewise, the advantages over the traditional method were demonstrated since a component of rigor and generalization is added. Finally, the achievement of a stability method that incorporates the active stresses and has an adequate predictive performance is evidenced. / Trabajo de investigación