Ordinary cokriging of additive log-ratios for estimating grades in iron ore deposits

Risk assessment and economic evaluation of mining projects are mainly affected by the determination of grades and tonnages. In the case of iron ore, multiple variables must be determined for ore characterization which estimation must satisfy the original mass balances and stoichiometry among granulometric fractions and chemical species. Models of these deposits are generally built from estimates obtained using ordinary kriging or cokriging, most time using solely the global grades and determining the ones present at different granulometric partitions by regression. Alternative approaches include determining the totality of the chemical species and distributing the closing error or leaving one variable aside and determining it by difference afterwards, adding up the error of previous determinations. Furthermore, the estimates obtained are outside the interval of the original variables or even exhibiting negative values. These inconsistencies are generally overridden by post-processing the estimates to satisfy the closed sum condition and positiveness. In this paper, cokriging of additive log-ratios (alr) is implemented to determine global grades of iron, silica, alumina, phosphorous, manganese and loss by ignition and masses of three different granulometric partitions, providing better results than the ones obtained through cokriging of the original variables, with all the estimates within the original data values interval and satisfying the considered mass balances. Key words: iron ore, additive log-ratios, cokriging, compositional data, geostatistic

Meissner effect, Spin Meissner effect and charge expulsion in superconductors

The Meissner effect and the Spin Meissner effect are the spontaneous generation of charge and spin current respectively near the surface of a metal making a transition to the superconducting state. The Meissner effect is well known but, I argue, not explained by the conventional theory, the Spin Meissner effect has yet to be detected. I propose that both effects take place in all superconductors, the first one in the presence of an applied magnetostatic field, the second one even in the absence of applied external fields. Both effects can be understood under the assumption that electrons expand their orbits and thereby lower their quantum kinetic energy in the transition to superconductivity. Associated with this process, the metal expels negative charge from the interior to the surface and an electric field is generated in the interior. The resulting charge current can be understood as arising from the magnetic Lorentz force on radially outgoing electrons, and the resulting spin current can be understood as arising from a spin Hall effect originating in the Rashba-like coupling of the electron magnetic moment to the internal electric field. The associated electrodynamics is qualitatively different from London electrodynamics, yet can be described by a small modification of the conventional London equations. The stability of the superconducting state and its macroscopic phase coherence hinge on the fact that the orbital angular momentum of the carriers of the spin current is found to be exactly $\hbar/2$, indicating a topological origin. The simplicity and universality of our theory argue for its validity, and the occurrence of superconductivity in many classes of materials can be understood within our theory.Comment: Submitted to SLAFES XX Proceeding

Ordinary Cokriging of Additive Log-Ratios for Estimating Grades in Iron Ore Deposits

Risk assessment and economic evaluation of mining projects are mainly affected by the determination of grades and tonnages. In the case of iron ore, multiple variables must be determined for ore characterization which estimation must satisfy the original mass balances and stoichiometry among granulometric fractions and chemical species. Models of these deposits are generally built from estimates obtained using ordinary kriging or cokriging, most time using solely the global grades and determining the ones present at different granulometric partitions by regression. Alternative approaches include determining the totality of the chemical species and distributing the closing error or leaving one variable aside and determining it by difference afterwards, adding up the error of previous determinations. Furthermore, the estimates obtained are outside the interval of the original variables or even exhibiting negative values. These inconsistencies are generally overridden by post-processing the estimates to satisfy the closed sum condition and positiveness. In this paper, cokriging of additive log-ratios (alr) is implemented to determine global grades of iron, silica, alumina, phosphorous, manganese and loss by ignition and masses of three different granulometric partitions, providing better results than the ones obtained through cokriging of the original variables, with all the estimates within the original data values interval and satisfying the considered mass balance

Metodologias de quantificação de heterogeineidades do solo para uso na engenharia geotécnica

Os solos e suas propriedades são raramente considerados homogêneos e, essa heterogeneidade pode ser decorrente de sua formação, estado de tensões in situ e a própria variabilidade espacial intrínseca do solo, entre outros fatores. Assim, o presente artigo tem como objetivo, apresentar as metodologias freqüentemente empregadas no meio geotécnico para auxílio na quantificação das heterogeneidades do solo, indicando seus aspectos positivos e suas limitações. Dentro deste enfoque, será apresentado um estudo de caso da quantificação da heterogeneidade das propriedades do solo numa área urbana, fazendo uso da técnica geoestatística de simulação seqüencial gaussiana (ssG). Este estudo de caso mostrou bons resultados quando comparados à realidade de ensaios de campo, podendo ser considerada uma metodologia eficiente ao objetivo proposto e que apresenta características positivas em comparação a outras metodologias de uso corrent

Evaluating the Effects of Non-coaxial Charges for Contour Blasting

Contour blasting is commonly performed by employing linear charges, decoupled from the boreholes. This method is common in surface and underground excavations, either for civil or mining purposes. To achieve the best results in terms of rock breakage and respect of the excavation profile, blasting theory suggests that charges should be inserted coaxial to the holes to grant uniform distribution of the explosive energy and therefore obtaining a uniform Radius of Damage. Nonetheless, due to readiness of operations or lack of availability of specific products on the market, non-coaxial charges are often employed in blasting practice. Non-coaxial charging methods include the employ of high-power detonating cord (40 to 100 g/m), low-power detonating cord connecting small-diameter cartridges (commonly 10 g/m detonating cord priming 1" cartridges) or string loading (a thin layer of bulk emulsion pumped with controlled flow and controlled extraction of the injecting rod). This research focuses on evaluating the effects of the first two charging methods on the quality of final walls in open-pit and underground operations. Different drilling geometries and charging configurations were applied to both quarrying and tunneling blasts. The Half-Cast Factor (HCF), the Over-break (OB) and the Under-Break (UB) were evaluated as control indicators. Rock Quality Designation (RQD) and Rock Mass Rating (RMR) were used to classify the rock mass. The research was aimed to push contour blasts to their limits, observing for which geometry and charge configuration the blast lost its design threshold with respect to the final wall for every given rock mass. Results show the operational limits of non-coaxial charges encountered in the rock masses object of this study. In good-quality rock, smooth blasting with decoupled linear charge of 40 g/m can be extended to a spacing S = 22Øf with little or no detectable drawbacks in terms of final wall quality, in contrast with theoretical formulae for the determination of the radius of damage. On the other hand, when the rock is poor, any quality of the final wall is hardly achieved at all, in spite of any care in the details of execution of smooth blasting. It is concluded that any design criterion and theoretical approach modeling the effects of contour blasting cannot ignore the features of the rock mass

Evaluating the Effects of Non-coaxial Charges for Contour Blasting

Contour blasting is commonly performed by employing linear charges, decoupled from the boreholes. This method is common in surface and underground excavations, either for civil or mining purposes. To achieve the best results in terms of rock breakage and respect of the excavation profile, blasting theory suggests that charges should be inserted coaxial to the holes to grant uniform distribution of the explosive energy and therefore obtaining a uniform Radius of Damage. Nonetheless, due to readiness of operations or lack of availability of specific products on the market, non-coaxial charges are often employed in blasting practice. Non-coaxial charging methods include the employ of high-power detonating cord (40 to 100 g/m), low-power detonating cord connecting small-diameter cartridges (commonly 10 g/m detonating cord priming 1" cartridges) or string loading (a thin layer of bulk emulsion pumped with controlled flow and controlled extraction of the injecting rod). This research focuses on evaluating the effects of the first two charging methods on the quality of final walls in open-pit and underground operations. Different drilling geometries and charging configurations were applied to both quarrying and tunneling blasts. The Half-Cast Factor (HCF), the Over-break (OB) and the Under-Break (UB) were evaluated as control indicators. Rock Quality Designation (RQD) and Rock Mass Rating (RMR) were used to classify the rock mass. The research was aimed to push contour blasts to their limits, observing for which geometry and charge configuration the blast lost its design threshold with respect to the final wall for every given rock mass. Results show the operational limits of non-coaxial charges encountered in the rock masses object of this study. In good-quality rock, smooth blasting with decoupled linear charge of 40 g/m can be extended to a spacing S = 22Øf with little or no detectable drawbacks in terms of final wall quality, in contrast with theoretical formulae for the determination of the radius of damage. On the other hand, when the rock is poor, any quality of the final wall is hardly achieved at all, in spite of any care in the details of execution of smooth blasting. It is concluded that any design criterion and theoretical approach modeling the effects of contour blasting cannot ignore the features of the rock mas