The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

A contribution to understanding the effects of curing temperature on the mechanical properties of mine cemented tailings backfill

A cycle is the quantitative characterization of the flows of a specific material into, within, and from a given system. An anthropogenic elemental cycle can be static (for a point in time) or dynamic (over a time interval). The about 350 publications collected for this review contain a total of 1074 individual cycle determinations, 989 static and 85 dynamic, for 59 elements; more than 90% of the publications have appeared since 2000. The cycles are of varying quality and completeness, with about 80% at country- or territory-level, addressing 45 elements, and 5% at global-level, addressing 30 elements. Despite their limitations, cycles have often been successful in revealing otherwise unknown information. Most of the elements for which no cycles exist are radioactively unstable or are used rarely and in small amounts. For a variety of reasons, the anthropogenic cycles of only perhaps a dozen elements are well characterized. For all the others, with cycles limited or nonexistent, our knowledge of types of uses, lifetimes in those uses, international trade, losses to the environment, and rates of recycling is quite limited, thereby making attempts to evaluate resource sustainability particularly problematic.

Anthropogenic cycles of the elements: a critical review.

Although hard rock is not usually associated with large creep deformation, significant time-dependent behaviour is observed in the tabular excavations of the South African gold mines. Time-dependent closure data was collected in stopes of the Ventersdorp Contact Reef and Vaal Reef. This data typically consists of a primary closure phase after blasting, followed by a steady-state closure phase. This closure behaviour is the result of the rheology of the fracture zone around these excavations and the time-dependent extension of this zone following a mining increment. An elasto-viscoplastic approach was developed to simulate the time-dependent nature of the fracture zone. This model proved successful in simulating the experimental closure profiles. It appears that the closure data may provide useful diagnostic information of the stress conditions in the fracture zone ahead of the face. This may possibly be used to identify hazardous conditions such as areas prone to face bursting. The effect of preconditioning on the time-dependent closure behaviour is also illustrated.

Time-dependent Behaviour of Deep Level Tabular Excavations in Hard Rock

A general analytical model of materials flow analysis (MFA) incorporating physical waste input-output is proposed that is fully consistent with the mass balance principle. Exploiting the triangular nature of the matrix of input coefficients, which is obtained by rearranging the ordering of sectors according to degrees of fabrication, the material composition matrix is derived, which gives the material composition of products. A formal mathematical definition of materials (or the objects, the flow of which is to be accounted for by MFA) is also introduced, which excludes the occurrence of double accounting in economy-wide MFAs involving diverse inputs. By using the model, monetary input-output (IO) tables can easily be converted into a physical material flow account (or physical input-output tables [PIOT]) of an arbitrary number of materials, and the material composition of a product can be decomposed into its input origin. The first point represents substantial saving in the otherwise prohibitive cost that is associated with independent compilation of PIOT. The proposed methodology is applied to Japanese IO data for the flow of 11 base metals and their scrap (available as e-supplement on the JIE Web site).

The Waste Input-Output Approach to Materials Flow Analysis

An Expert System for Selecting Mining Method

No matter whether much more resources extracted from the deposit due to advances in technology, it is clear that the amount of metal resources is finite as long as they are non-renewable. To suppress resources consumption through recycling and substitution is effective way to retard the depletion of resources.This study is concerned with substitutions of non-ferrous metals. Consumption model of copper, lead, and zinc is constructed considering the substitutions.The end uses of the metals are classified into 18 categories. Demands for each categories are decided exogenously. Those demands are satisfied with the ordinary metals and seven kinds of substitutive materials. In this model, linear programming is used to decide the consumption of materials for each period. The objective function is the total extraction cost of these resources.Sensitivity analysis for several parameters has been performed in connection with extraction cost and R / P of respective metals in the last period. As the result, in most cases substitution mitigates the depletion of metals as well as the increase of extraction cost. Especially, the substitution by aluminum and iron promotes the final R / Ps of copper increase. However, this is only true for copper and zinc, not lead. As initial reserve of lead is scarce compared to other base metals, lead will gradually be exhausted.

Optimum Modeling for Non-ferrous Metals Substitutions.

The paper describes the first attempt of introducing paste backfill in Japan at the Toyoha mine. In 1997, the Metal Mining Agency of Japan (MMAJ), which was reorganized in February of 2004 and currently works as the Japan Oil, Gas and Metals National Corporation (JOGMEC), launched a five year long research program to innovate mining technologies and systems required to save and efficiently use energy in mines. As a part of the program, studies on paste backfill technology and its implementation in Japan were involved.The Toyoha mine was selected as the site for testing paste backfill, since the mine is being operated under an extremely high rock temperature environment. In order to improve the underground climate, the mine decided to introduce paste backfilling and effectively reduce heat flows from mined-out stopes.The first flow test was performed on surface in 1998 and the second flow test was carried out underground in 2001 after having installed the paste fill plant and underground pipelines. The underground test was, however, abruptly discontinued by a mechanical failure, which happened to the PPSM thickener whose bolts holding the drive head at the top of the thickener were broken.After the unpredicted interruption of the paste backfilling test, we have carried out a series of ventilation analyses to evaluate the energy saving effects with paste backfilling under a high rock temperature condition. And we have clarified that remarkable energy saving can be expected by reducing heat flows from mined-out stopes and energy consumption required for underground refrigeration. In addition, it is found that significant cost saving can be also anticipated by curtailing volume of the tailings impoundment and its construction cost.

https://www.jstage.jst.go.jp/article/shigentosozai/121/7/121_7_330/_pdf

Underground Tests for Paste Backfilling at the Toyoha Mine and Energy-Cost Saving Effects of Paste Fill

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An Expert System for Selecting Mining Method

Optimum Modeling for Non-ferrous Metals Substitutions.

Underground Tests for Paste Backfilling at the Toyoha Mine and Energy-Cost Saving Effects of Paste Fill