Uncertainty in rockmass and in situ stress parameters poses a critical design challenge in geotechnical engineering. This uncertainty stems from natural variability (aleatory) due to the complex history of formation and continual reworking of geological materials as well as knowledge-based uncertainty (epistemic) due to a lack of site specific information and the introduction of errors during the testing and design phases. While such uncertainty can be dealt with subjectively through the use of conservative design parameters, this leads to a lack of understanding of the variable ground response and the selection of an over-conservative design that can have a negative impact on both the project cost and schedule. Reliability methods offer an alternative approach that focuses on quantifying the uncertainty in ground conditions and utilizing it directly in the design process. By doing so, a probability of failure can be calculated with respect to a prescribed limit state, providing a measure of design performance. When multiple design options are considered, reliability methods can be paired with a quantitative risk analysis to determine the optimum design on the basis of safety and minimum cost rather than subjective conservatism. Despite the inherent benefits of such an approach, the adoption of reliability methods has been slow in geotechnical engineering due to a number of technical and conceptual challenges. The research conducted pertaining to this thesis aims to address these issues and remove the perceived “cloak of mystery” that surrounds the use of reliability methods. The scientific and engineering research in this thesis was divided into four sections: (1) the assessment of uncertainty in geotechnical input parameters, (2) a review of reliability methods in the context of geotechnical problems, (3) the development of a reliability-based, quantitative risk approach for underground support design and (4) the application of such a method to existing case studies. The completion of these areas is critical to the design of underground structures and may bring about a shift in design philosophy in the geotechnical industry. / Thesis (Ph.D, Geological Sciences & Geological Engineering) -- Queen's University, 2013-09-18 10:35:26.265

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Consider the D-optimal designs for the dth-degree polynomial regression model with a bounded and positive weight function on a compact interval. As the degree of the model goes to infinity, we show that the D-optimal design converges weakly to the arcsin distribution. If the weight function is equal to 1, we derive the formulae of the values of the D-criterion for five classes of designs including (i) uniform density design; (ii) arcsin density design; (iii) J_{1/2,1/2} density design; (iv) arcsin support design and (v) uniform support design. The comparison of D-efficiencies among these designs are investigated; besides, the asymptotic expansions and limits of their D-efficiencies are also given. It shows that the D-efficiency of the arcsin support design is the highest among the first four designs.

Diffraction Enhanced X-ray Imaging (DEI) uses synchrotron X-ray beams prepared and analyzed by perfect single crystals to achieve imaging contrast from a number of phenomena taking place in an object under investigation. The crystals used in DEI for imaging requires high precision positioning due to a narrow rocking curve. Typically, the angular precision required should be on the order of tens of nanoradians.<p>One of the problems associated with DEI is the inability to control, set, and fix the angle of the analyzer crystal in relation to the beam exiting the monochromator in the system. This angle is used to interpret the images acquired with an object present and the usual approach is to determine where the image was taken after the fact. If the angle is not correct, then the image is wasted and has to be retaken. If time or dose is not an issue, then retaking the image is not a serious problem. However, since the technique is to be developed for live animal or eventually human imaging, the lost images are no longer acceptable from either X-ray exposure or time perspectives.<p>Therefore, a mechanical positioning system for the DEI system should be developed that allows a precise setting and measurement of the analyzer crystal angles. In this thesis, the fundamental principles of the DEI method, the DEI system at the National Synchrotron Light Source (NSLS) and the sensitivity of the DEI system to vibration and temperature has been briefly studied to gain a better understanding of the problem. The DEI design at the NSLS was analyzed using finite element analysis software (ANSYS) to determine the defects in the current design which were making the system dimensionally unstable. Using the results of this analysis, the new analyzer support was designed aiming to eliminate the problems with the current design. The new design is much stiffer with the natural frequency spectrum raised about eight times. <p> This new design will improve the performance of the system at the National Synchrotron Light Source (NSLS) of Brookhaven National Laboratory, New York, USA and should assist in the development of a new DEI system for the Bio-Medical Imaging and Therapy (BMIT) beamline at the Canadian Light Source (CLS), Saskatoon, CANADA.

Diffraction Enhanced X-ray Imaging (DEI) uses synchrotron X-ray beams prepared and analyzed by perfect single crystals to achieve imaging contrast from a number of phenomena taking place in an object under investigation. The crystals used in DEI for imaging requires high precision positioning due to a narrow rocking curve. Typically, the angular precision required should be on the order of tens of nanoradians.<p>One of the problems associated with DEI is the inability to control, set, and fix the angle of the analyzer crystal in relation to the beam exiting the monochromator in the system. This angle is used to interpret the images acquired with an object present and the usual approach is to determine where the image was taken after the fact. If the angle is not correct, then the image is wasted and has to be retaken. If time or dose is not an issue, then retaking the image is not a serious problem. However, since the technique is to be developed for live animal or eventually human imaging, the lost images are no longer acceptable from either X-ray exposure or time perspectives.<p>Therefore, a mechanical positioning system for the DEI system should be developed that allows a precise setting and measurement of the analyzer crystal angles. In this thesis, the fundamental principles of the DEI method, the DEI system at the National Synchrotron Light Source (NSLS) and the sensitivity of the DEI system to vibration and temperature has been briefly studied to gain a better understanding of the problem. The DEI design at the NSLS was analyzed using finite element analysis software (ANSYS) to determine the defects in the current design which were making the system dimensionally unstable. Using the results of this analysis, the new analyzer support was designed aiming to eliminate the problems with the current design. The new design is much stiffer with the natural frequency spectrum raised about eight times. <p> This new design will improve the performance of the system at the National Synchrotron Light Source (NSLS) of Brookhaven National Laboratory, New York, USA and should assist in the development of a new DEI system for the Bio-Medical Imaging and Therapy (BMIT) beamline at the Canadian Light Source (CLS), Saskatoon, CANADA.

This thesis addresses the problem of designing roof support systems in coal mines. When designing the roof support, it is necessary to account for the uncertainties that are inherently exist within the rock mass and support elements. The performance of a support system is affected by these uncertainties, which are not taken into account in the current design methodologies used in South Africa. This study sets out to develop a method which takes all uncertainties into account and quantitatively provides a risk-based design. Despite the fact that the roof bolting is probably one of the most researched aspects of coal mine ground control, falls of ground still remain the single major cause of fatalities and injuries in South African collieries. Mainly five different support design methodologies have been used; namely, analytical modelling, numerical modelling, physical modelling, design based on geotechnical rating systems and field testing. As part of this study, it is shown that there are many elements of a support system that can impact the support and roof behaviour in a coal mine and the characteristics of these elements as well as the interaction between them is complex and can vary significantly within a short distance. These variations account for uncertainties in coal mine roof support and they are usually not taken into account in the above design methodologies resulting in falls of ground and/or over design of support systems. The roof and support behaviour were monitored at 29 sites at five collieries. It is found that there was no evidence of a dramatic increase in the stable elevations as experienced in some overseas collieries. A roadway widening experiment was carried out to establish the critical roof displacements. The maximum width attained was 12 m at which stage 5 mm displacement was measured. During the monitoring period no roof falls occurred at any of the 29 sites and road widening experiment site, even where 12 mm displacements were measured. The in situ monitoring programme was continued in additional 26 monitoring stations in 13 sites with the aim of establishing the effect of unsupported cut-out distance on roof and support performances. The results showed that the lithological composition of the roof strata plays a major role in the amount of deflection that was recorded. Bedding separation was seen to occur at the contacts between different strata types. It is concluded that the roof behaved like a set of composite beams with different characteristics. It is also found that the amounts of deflection corresponded with the deflection that would be expected from gravity loaded beams. During this monitoring programme variable nature of roof and support systems are also demonstrated. As many mines use different geotechnical rating systems, an evaluation of the currently used classification techniques were conducted to determine their effectiveness in design of roof support strategies. It is found that currently used systems cannot quantitatively determine the required support system in a given geotechnical environment. Impact splitting tests are found to be the appropriate system for South African conditions. It is however concluded that the roof lithology, stress regime and roof characteristics can change within meters in a production section. Therefore, in order to predict these changing conditions many boreholes are required for a section, which would be costly and time consuming. An in-depth study into the roof support elements was conducted for the purpose of obtaining an understanding of the fundamental mechanisms of roof support systems and developing guidelines for their improvement. All of the currently available roof bolt support elements and related machinery were evaluated using in situ short encapsulated pull tests. The results showed that, on average, bond strengths obtained from the roof bolts supplied by different manufacturers can vary as much as 28 per cent. The test results conducted on different resins showed that the strength of resin currently being used in South Africa is adequate. Differences between commonly used bit types were established. It is concluded that the 2-prong bit outperforms the spade bit in sandstone and shale rock types. In addition, the effect of hole annulus was also investigated as part of this study. The results show that an annulus between 2.5 mm to 3.8 mm resulted in the most effective bond strengths. The effect of wet and dry drilling was noted. It is found that bond strengths and overall support stiffnesses are greater with the use of the wet drilling in all resin types. The results from the tests in different rock types highlighted the very distinct differences between bolt system performances. Quality control procedures for compliance with the design, support elements and quality of installation are presented. Recommendations for improving the quality control measures and for developing testing procedures for bolt system components, installation quality and resin performance are provided. Finally, a roof support design methodology that takes into account all natural variations exist within the rock mass and the mining process has been developed and presented. This was achieved by adapting a probabilistic design approach using the well established stochastic modelling technique. This methodology enables rock engineers to design roof support systems with greater confidence and should result in safer and economic extraction of coal reserves. / Thesis (PhD)--University of Pretoria, 2008. / Mining Engineering / unrestricted

Information visualization dashboards are a widely used supportive tool in decision making. These tools can be difficult to create and utilize especially for the novice user. There is an extensive collection of company related data for decision making, resulting in a need of assistive tools. Prototypes were developed to research and identify design guidelines how to support fund managers in their decision making. This was carried out as a qualitative study involving 7 experts in fund management. The results provide insights and guidelines in decision supportive design for dashboards. The results indicate that there is a threshold in the number of displayed elements without limiting the cognitive analysis by the user. Three aspects; size, distribution and time should be included in the generating of suitable graphics. Assistive tools for connecting multiple context domains has been identified as a crucial element of decision support design. These guidelines should be investigated further in larger and more diverse studies in order to prove its full validity. / Information visualiserings dashboards är ett väl etablerat verktyg i beslutsfattning. Sådana verktyg kan vara utmanande att skapa och använda speciellt för en oerfaren användare. Idag samlas det in stora mängder av företagsrelaterad data för beslutsfattning vilket resulterar i ett behov av hjälpande verktyg. I den här studien utvecklades flera prototyper för att undersöka och tag fram designriktlinjer för hur man ska utforma och hjälpa fondförvaltare i sitt beslutsfattande. En kvalitativ studie genomfördes med 7 experter inom fond och kapitalförvaltning i framtagandet av designriktlinjer. Resultaten visar riktlinjer för beslutsstöd i utformningen av dashboards. Resultaten indikerar att det finns en gräns för hur många element man bör presentera för en användare utan att försvåra användarens kognitiva analysförmåga. Tre karaktärsdrag; storlek, distribution och tid påverkar utformningen av passande grafik. Studien har även identifierat behovet av verktyg för sammankopplingen mellan flera olika kontextdomäner i och med den kollaborativa delen av beslutsfattning. Dessa designriktlinjer ligger till grund för fortsatt undersökning i större och mer varierade studier för att styrka dess validitet.

Consider the minimally-supported D-optimal designs for dth degree polynomial regression with bounded and positive weight function on a compact interval. We show that the optimal design converges weakly to the arcsin distribution as d goes to infinity. Comparisons of the optimal design with the arcsin distribution and D-optimal arcsin support design by D-efficiencies are also given. We also show that if the design interval is [−1, 1], then the minimally-supported D-optimal design converges to the D-optimal arcsin support design with the specific weight function 1/¡Ô(£\-x^2), £\>1, as £\¡÷1+.

Experiments with both quantitative and qualitative factors always complicate the selections of experimental settings and the statistical analysis for data. Response surface methodology (RSM) provides the systematic procedures such as the steepest ascent method to develop and improve the response models through the optimal settings of quantitative factors. However the sequential method lacks of exploring the direction of the maximum increase in the response among the qualitative levels. In this dissertation the optimal designs for experiments with both qualitative and quantitative factors are investigated. Focused on the second-order response surface model for quantitative factors, which is widely used in RSM as a good approximation for the true response surface, the approximate and exact D-optimal designs are proposed for the model containing the qualitative effects. On spherical design regions, the D-optimal designs have particular structures for considering the qualitative effects to be fixed or random. In this study, the exact D-optimal designs for a second-order response surface model on a circular design region with qualitative factors are proposed. For this model, the interactions between the quantitative and qualitative factors are assumed to be negligible. Based on this design region, an exact D-optimal design with regular polygon structure is made up according to the remainder terms of the numbers of experimental trials at each qualitative levels divided by 6. The complete proofs of exact D-optimality for models including two quantitative factors and one 2-level qualitative factor are presented as well as those for a model with only quantitative factors. When the qualitative factor has more than 2 levels, a method is proposed for constructing exact designs based on the polygonal structure with high efficiency. Furthermore, a procedure for minimizing the number of support points for the quantitative factors of exact D-optimal designs is also proposed for practical consideration. There are no more than 13 support points for the quantitative factors at an individual qualitative level. When the effects between the quantitative and qualitative factors are taken into consideration, approximate D-optimal designs are investigated for models in which the qualitative effects interact with, respectively, the linear quantitative effects, or the linear effects and 2-factor interactions of the quantitative factors or quadratic effects of the quantitative factors. It is shown that, at each qualitative level, the corresponding D-optimal design consists of three portions as a central composite design but with different weights on the cube portion, star portion and center points. Central composite design (CCD) is widely applied in many fields to construct a second-order response surface model with quantitative factors to help to increase the precision of the estimated model. A chemical study is illustrated to show that the effects of the qualitative factor interacts with 2-factor interactions of the quantitative factors are important but absent in a second-order model including a qualitative factor treated as a coded variable. The verification of the D-optimality for exact designs has become more and more intricate when the qualitative levels or the number of quantitative factors increase, even when the patterns of the exact optimal designs have been speculated. The efficient rounding method proposed by Pukelsheim and Rieder (1992) is a model-free approach and it generates an exact design by apportioning the number of trials on the same support points of a given design. For constructing the exact designs with high efficiencies, a modified efficient rounding method is proposed and is based on the polygonal structure of the approximate D-optimal design on a circular design region. This modification is still based on the same rounding approach by apportioning the number of trials to the concentric circles where the support points of the given design are standing on. Then a regular polygon design will be assigned on the circles by the apportionments. For illustration, the exact designs for a third-order response surface model with qualitative factors are presented as well as those for the second-order model. The results show that nearly D-optimal designs are obtained by the modified procedure and the improvement in D-efficiency is very significant. When the factors with the levels selected randomly from a population, they are treated as with random effects. Especially for the qualitative effects caused by the experimental units that the experimenter is not interested in, one should consider the model with random block effects. In this model, the observations on the same unit are assumed to be correlated and they are uncorrelated between different units. Then the mean response surface is still considered as second-order for quantitative factors but the covariance matrix of the observations is different from the identity matrix. In the fourth part of this dissertation, the locally D-optimal designs on a circular design region are proposed for given the value of the correlations. These optimal designs with the structures based on the regular polygons are similar to the D-optimal designs for the uncorrelated model.

Die stetige Weiterentwicklung von Mess- und Überwachungstechnik ermöglicht Setzungsprozesse und Gebirgsdeformationen mit zunehmender Genauigkeit in numerischen Modellen abzubilden. Mit Hilfe von Laserscans, durchgeführt sowohl vor als auch während der Bauarbeiten, können genauere numerische Modelle erstellt werden. Die baubegleitende Anpassung der Modellgeometrie ermöglicht zudem eine weitere Nachkalibrierung der Simulationen und erhöht damit die Zuverlässigkeit von Prognoseberechnungen. Die Simulationsergebnisse können fortlaufend mit den ursprünglichen Planungen abgeglichen und somit Ausbauplanungen angepasst und optimiert werden. / The ongoing development of monitoring and surveillance technology enables us to reproduce subsidence and rock mass deformation in numerical models with increasing precision. Laserscans prior to and during the construction work increase the spatial accuracy of numerical models. Adjustments of the model geometry during the construction work allow a recalibration of models and increase the reliability of forecast simulations. Simulation results can be successively compared to construction plans and allow adjustments and optimizations of support designs.