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By James S. Browning

Mica mining in the United States is confined largely to pegmatites and schists in a few well-defined areas. The largest region extends from central Virginia southward through western North and South Carolina, northern Georgia, and east-central Alabama. 1, 2, 3 Whereas in western North Carolina these pegmatite dikes are weathered to only a shallow depth, they are deeply weathered in the Carolina Piedmont and in Georgia and Alabama. Particularly in Georgia and Alabama, mica is found in the decomposed slates and schists adjacent to the pegmatites, and in deeply weathered granites. Most flake mica is obtained as the major marketable product by crushing and milling pegmatites.4 To a lesser extent, mica is produced as a byproduct of feldspars and spodumene.6 Past research by the Bureau of Mines has developed two methods for mica flotation. One method utilizes acid-cationic flotation for recovery of mica." This method requires thorough desliming of the ore with consequent fine mica losses. The other method utilizes an alkaline-anionic-cationic process for recovering fine size mica from pegmatite ores after desliming sufficiently to remove clay materials but not so drastically as to remove the fine mica. 8, 9, 10, 11, 12, 13 The latter process has also been successfully applied to a micaceous schist ore from California.14 This report summarizes the results of these research studies. Both of the flotation processes developed by the Bureau of Mines have been adopted by the mica industry and are being commercially utilized separately and in combination for flotation of mica from weathered pegmatite ores.

Jan 1, 1969

By Dale E. Hirschfeld

The clays in Eastern Washington occur in a variety of forms and are extracted for uses in Face Brick, paper coatings, and aggregates. Not in large volumes in comparison to other areas, not even from impressive large mines. However, mans utilization of these clays has progressed from historical clay tablets to the present technically oriented manufactured products of today. White Face Brick, perhaps the whitest produced anywhere is the unique product produced by INTERPACE CORPORATION's Mica Plant from these unusual clays. It is this basic characteristic feature of the clay's in the Mica area that differentiate them from the other clay's in this belt. ORIGIN The significant properties of clay's used in Face Brick are plasticity, fired color, fired strength, dry and fired shrinkage, the PCE or Pyrometeric Cone Equivalent, and extrudability. Testing clay's for these properties is standard laboratory procedure. No two clays are alike, and seldom can one clay be substituted for another. Mica White Clays respond favorable to all these properties, but more especially, the Mica Clays fire to a brilliant white color, from almost the natural state. The geologic history of Eastern Washington is largely conjectural because of the absence of rocks representing segments of geologic time. The oldest rocks in this area are the argillaceous and arenaceous sedimentary rocks which have been slightly metamorphosed. These rocks have been correlated with the Belt Series of the Pre-Cambrian age, although some may be older. These rocks were subsequently intruded by granadiorites and related rocks that are considered to

Jan 1, 1971

By R. C. Freas

The physical and chemical properties of mica are unique relative to most other industrial minerals. As such, mica is suitable for a variety of functional applications in new and emerging markets. This paper examines some of these applications and particularly the contribution mica makes in end product performance.

Jan 1, 1997

By J. R. Goode

ABSTRACT Aurora Energy Ltd. is considering a 10,000 t/d process plant to produce 97 million lb (43,998,460 kg) of U3O8 over a 17-year project from uranium deposits in coastal Labrador. This paper summarizes the test work, mostly done by SGS Mineral Services in Lakefield, Ontario, and the economic studies supporting flowsheet selection. The proposed flowsheet includes semi-autogenous grinding (SAG) and ball milling, acid leaching using air/SO2 as an oxidant, and resin-in-pulp (RIP) extraction of uranium from the leached slurry. Other unit operations examined include ore sorting, heap leaching, liquid- solid separation, solvent extraction, and nanofiltration for eluate upgrading. We also review the extensive environmental test work and studies that were completed.

Jan 1, 2012

By G. A. Rosario, G. Peach

Twin 8.5 m diameter, 10 km long headrace tunnels under overburdens of up to 1870 m were excavated for the neelum jhelum hydroelectric project in north-eastern pakistan using two main beam gripper tunnel boring machines (tbms). Rock bursts were encountered and presented a significant danger to personnel and equipment. Micro seismic monitoring was installed to analyze rock burst characteristics and to create a database for future reference. Correlation of rock burst characteristics improved the ability to predict the likelihood, location, severity, and number of rock burst events. This paper presents the analysis of the micro seismic data

Dec 1, 2022

By Nomuqhele N. Nkosi, Yasuo Yabe, Musa D. Manzi, Raymond J. Durrheim, Siyanda B. Mngadi

This study examined rock failure in brittle rocks hosting the deep gold-bearing ore bodies on scales between millimeters and kilometres. This research study is part of the International Continental scientific Drilling Program (ICDP) project, “Drilling into Seismogenic Zones of M2.0-M5.5 earthquakes in deep South African gold mines” (DSeis). The broader ICDP-DSeis project aims include the examination of the extent of damage, the stress state around the fringes of the earthquake, and the potential existence of living organisms associated with deep-level earthquakes. Nevertheless, this study focused on two seismogenic zones – the Cooke 4 mine and Moab Khotsong mine. At Cooke 4 mine, the study examined the evolution of mining-induced fractures (M1-4) occurring ahead of the stope face during the extraction of the remnant shaft pillar. These fractures were monitored and delineated by a dense array of acoustic emission sensors that allowed hypocentres to be located with decimeter accuracy. Using this acoustic emission data, the DSeis team drilled and recovered the fractures, rock breccia and gouge using a sophisticated triple-tube drilling rig.

Apr 26, 2022

By Ronaldo Câmara Cozza

Iron aluminide alloy; Ball-cratering wear testing; Rolling abrasion; Wear volume; Coefficient of friction

Jul 31, 2018

By Cristiano José Scheuer

Experiments were carried out aiming to study the influence of micro-abrasive wear test variables and plasma treatment parameters, on the tribological characteristics of low-temperature plasma carburized AISI 420 steel. The first part of this study was conducted in order to evaluate the influence of abrasive particle size, normal load and counter body rotation speed on carburized sample wear behavior; and the second part was conducted in order to evaluate the treatment temperature and time effect on carburized samples wear behavior. Plasma carburizing treatments were performed at 8 and 12 h, for temperatures ranging from 350 to 500°C; and at constant temperatures of 400°C for times between 12 to 48h, and for 450°C for times of 4 to 16h. Micro-abrasive wear test were performed by mean of a calowear ball-cratering equipment using a polished ball of AISI 52100 steel rotating at 80, 120 and 160 rpm, for sliding distances from 2.6 to 104.2 m. Alumina abrasive particles with sizes of 0.05, 0.3 and 1.0 ?m were employed. The normal loads applied on this study were 0.1, 0.3 and 0.5 N. Carburized sample was characterized by mean of OM, XRD and hardness measurements. Worn crater characteristics were evaluated by confocal laser microscopy. Results showed that the transient wear regime prevails along the outer layer length (composed by Fe3C and ?’C), and the steady-state wear stabilizes in the diffusion layer region (composed by ?’C). It was verified that the wear rate and wear coefficient decreases with treatment temperature in the range of 350–450°C and increase for 500°C. It was also verified that the wear rate and wear coefficient decreases with treatment time in the range of 12–36 h (for 400°C cycle) and 4–12 h (for 450°C cycle), and increase for larger treatment times due the chromium carbide precipitation. It was also found that the wear coefficient increases with the increase of abrasive particle size, and decrease with the increase in counter body rotation speed and normal load. Lastly, the analysis of the worn craters indicates the occurrence of grooving and micro-rolling abrasion wear mechanisms.

Aug 17, 2017

By Cristiano José Scheuer

The effect of low-temperature plasma carburizing treatment on the micro-abrasive wear resistance of AISI 420 steel was investigated by mean of a CSM Calowear ball-cratering equipment. Carburized samples were treated at temperatures of 350, 400, 450 and 500°C for a fixed time of 12 h, using a gas mixture containing 99.5% (80% H2+20% Ar)+0.5% CH4. Micro-scale abrasive wear tests were conducted with a 25.4 mm AISI 420 steel sphere, using an abrasive suspension of alumina (Al2O3) with particle size of 1 ?m (abrasive concentration of 0.11 g/cm³). The contact normal force, abrasive flow and ball rotation speed were fixed at: 0.5 N, 0,2 drop/s, and 120 rpm. The wear craters were analyzed using a confocal laser microscope, Olympus OLS 3000. The wear analyses were performed for test times of: 30, 60, 90, 120, 180, 360, 540, 720 and 900 s (equivalent sliding distance: 0.84, 1.68, 2.52, 3.36, 5.04, 10.09, 15.14, 20.19 and 25.23 m, respectively). The results indicate that the wear coefficient in the outer layer and in the diffusion layer are different, being lower in the latter. It was also verified that the wear coefficient on the outer layer region decreases with increasing treatment temperature in the range of 350 to 450 °C, and increase again for 500ºC. The diffusion layer wear coefficient is similar for all the carburized samples. Finally, for all studied conditions, the analysis of the wear craters surface indicates the occurrence of grooving and micro-rolling abrasion wear modes.

Aug 8, 2018

By Piotr D. Moncarz

As major urban areas begin to run out of "good-terrain" for their expansion, they begin to claim high water-table areas within or adjacent to water fronts or swamps. Similarly, major infrastructure projects encroach on or cross high organic content areas. The associated major structures often require deep foundations located in soils investigated through core samples removed at a discrete number of locations. The investigation is nearly always preoccupied with soil mechanical properties, sometimes with soil non-organic chemistry for concrete and metal corrosion, seldom, if ever, for organic-chemistry and bio-conditions as related to concrete longevity. Not surprisingly so, bio-corrosion of concrete is one of the least understood phenomena by practicing civil engineers. This paper shows how low-iron, organic-rich sediments may trigger sulfate degradation of concrete, even when standard pre-construction chemical analyses indicate only a moderate sulfate level. The discussion is illustrated with a case of a pile foundation in the United States driven into marine channel sediments and sediment-derived fill material. The concrete piles lost their structural integrity due to secondary ettringite formation and depletion of iron in the cement paste. Disintegration of concrete occurred only where it contacted superficial marine sediments and sediment-derived fill material. Concrete in direct contact with seawater or native sand and silt materials appeared to be sound. Sediments in contact with the degraded concrete were highly anoxic and had a history of sewage contamination, contained low concentrations of total iron (<2%), Fe(III) (<0.3%) and moderate levels of sulfate (1500ppm), and exhibited high bacterial activity. This environment resulted in the microbial dissolution of Fe(lll)-rich ferrite in hardened cement paste. Iron depletion in the cement paste had made the concrete vulnerable to degradation by sulfate, even at moderate levels of sulfate concentrations in the sediments.

Jan 1, 2002

By T. N. Singh, Vasudev Singh

To explore and exploit the natural resources like oil, gas, economic mineral water drilling is still considered to be the reliable and economical method. When a drill bit penetrates the rock mass either by percussion or by rotary and may be some times a combination generates stress and thrust on the rock mass as well as on the drill bit. The strength and hardness of the rock govern the life of the drill bit and its runnage. Physico- Mechanical properties of rocks have great influence on drillability. It is observed that higher the strength of rock, reduce the life of the drill bit while drilling, ultimately decreases the drillability. An attempt has been made in the present paper to establish relation among various physicomechanical properties i.e. uniaxial compression strength, tensile strength, shear strength, Schmidt hardness and abrasivity with drillability of different rock types. The specific energy of each rock type has been calculated using micro-bit drilling. The rocks from different lithological succession were collected. The rock specimens were prepared according to the norms of International society of Rock Mechanics (ISRM).

Jan 1, 2008

By S. P. Marsh, D. Banerjee

"Casting processes involve phenomena that occur on widely disparate length-scales. Simulation of macroscopic effects, such as heat transfer and convection, are generally addressed by solving the appropriate equations in discretized form on a finite-element mesh. Microscopic phenomena are described by micromodels that may be empirical or analytical in form. Coupling of phenomena in these two regimes is a critical issue in predicting microstructure and defect formation resulting from macroscopic process conditions. A formalism has been developed for expressing micromodels in a consistent manner using stereological parameters to quantify the geometric characteristics of the developing microstructure. This approach provides a robust and physically consistent method for coupling local micromodels with the macroscopic fields. The macroscopic state variables at each node serve as global constraints on the micromodels that are applied to a local unit volume. An outline of an equiaxed solidification model based on this approach is presented, along with preliminary simulation results. Coupling of convection and enthalpy effects between the micro and macro regimes is also discussed. IntroductionThe primary goal of casting simulations is to improve the reliability of cast parts while minimizing cost and development time. Effective simulations can speed up the mold design process and reduce the likelihood of defective parts by refining a particular casting process on a computer, reducing the dependence on cost- and time-intensive prototype castings. The challenge in developing effective simulations stems from the need to address physical processes that occur over a wide range of length-scales, from microscopic (atomic) and mesoscopic (microstructural) scales to macroscopic distances comparable to the size of the casting itself. Overviews of the various thermophysical phenomena and computational factors that are important in solidification modeling are provided in the literature by Rappaz [1] and Tseng et al. [2].Macroscopically, the solidification process is largely governed by the rate of heat flow from the alloy through the mold wall. Another important effect that occurs on the scale of the casting size is convective flow of the melt, which is driven by density-variations in the melt. Macroscopic calculations employ finite-element or finite-difference methods to solve the sets of equations that govern these effects, and the spatial resolution is determined by the grid spacings used for the calculations. Typical spatial resolutions are on the order of 10-2 to 10-3"" meters. This represents a compromise between the resolution required to simulate the continuum transport processes accurately, and the computational time required to model the entire solidification and cooling process."

Jan 1, 1994

By Vaughan R. Voller

"The wide range of length and time scales found in solidification processes are outlined and discussed. Methods for Direct Microstructure Simulation (DMS) are introduced. Key features in sharp interface and phase field models are presented. Concepts in micro-macro solidification modeling are covered. Basic details of microstructure and segregation models are provided. A description of a recent segregation micro-macro model is presented in detail.IntroductionA solidification process involves the containment of a liquid region, which, due to cooling, transforms over time to form a fully solid product. The development of the solid microstructure and the segregation of solute components during this transformation are controlled by phenomena that occur across a wide range of length and time scales. A ""successful"" model of a given solidification process needs to account for these phenomena. Standard models of solidification employ a discrete grid of node points and associated volume elements in the special domain, with a discrete time step to track the transient changes of nodal values, describing the composition and microstructure. Through the use of such models significant progress has been made towards a complete understanding of solidification process and phenomena (see the conference proceedings in Refs [1-9]). As solidification models become more sophisticated, however, they all run into the problem of resolving the full range of disparate space and time scales.Two approaches can deal with this problem1. Direct Microstructure Simulation (DMS) where the grid size and time step are chosen to scale with the smallest length and time scales of the given problem.2. Micro-macro modeling where the grid size and time step scale with the macroscopic process scale and phenomena at smaller scales are accounted for via sub-grid modeling and volume averaging.Currently full DMS of solidification is beyond the reach of available computer power and the application and development of micro-macro models is an important and critical research area."

Jan 1, 2001

By S. S. Yuan, Q. Z. Zhu, J. F. Shao

"This paper aims at enriching a homogenization-based anisotropic damage model for hard rocks under complex loading. A new damage criterion is proposed to capture material strain softening. Within the framework of irreversible thermodynamics, we are particularly concerned with two strongly coupled dissipative mechanisms: frictional sliding and damage by microcracking, which usually take place at cracks within cohesive geomaterials under compression. Focusing on the representative elementary volume containing multiple crack families, the free enthalpy of the matrix-cracks system is obtained. Importantly, a back-stress term is involved in the local stress applied to microcracks. This back stress plays the hardening/softening role in the friction criterion which is formulated at local scale. Strain hardening owns to the accumulation of frictional shearing and dilatancy while strain softening is caused by crack growth. The multiscale damage model is used to simulate laboratory tests on the Westerly granite under true triaxial compressions. INTRODUCTIONWhen subjected to compressive loads, hard rocks present nonlinear mechanical behaviors and induced material anisotropies. In that process, two main dissipative mechanisms have been largely identified: damage by crack growth and frictional sliding along closed crack faces, which are usually strongly coupled to each other on crack scale. Theoretical investigations have shown that the damagefriction coupling analyses allow explaining a large number of experimental phenomena involved in brittle or quasi-brittle materials. Concerning constitutive modeling, the standard Eshelby’s solution-based homogenization procedure for heterogeneous materials was recently applied successfully to describing the mechanical and poromechanical behaviors of cracked frictional solids."

Jan 1, 2015

The current understanding of the mechanics of rock fracturing during smooth blasting is largely empirical and qualitative due to an inability to model the dynamic process at the fundamental level. In order to overcome this difficulty, a numerical simulation of smooth blasting is performed using the Dynamic Lattice Network Model. This model is capable of simulating material inhomogeneities and the dynamic evolution of fragmentation at the micromechanical level. In this study, smooth blasting techniques are numerically analyzed to characterize the development of the damage rock zone during explosive fracturing.

Jan 1, 1995

By B. K. Saikia

A preliminary attempt has been made to study the particle size distribution (PSD) of minerals in one of the industrially important pulverized Indian coal sample using computer-controlled scanning electron microscopy (CCSEM). The results show that clay minerals, quartz, pyrite, and pyrrhotite form the bulk of the mineral matter. Minor minerals, such as calcite, dolomite, ankerite, barite, oxidized pyrrhotite, and gypsum are also observed in the coal sample. The PSD of the included minerals is generally observed to be finer than that of the excluded ones in the coal. Thus, the coal rich in included minerals has more small mineral particles, which may affect its reactivity. The proportion of included to excluded is found to be higher in major cases. Si is found to be mostly occurred as quartz and clay minerals, while Al mostly occurs as silicate minerals. Fe is primarily present as iron sulfides, iron oxide, and Fe-Al-silicate. S is partitioned into iron sulfides and gypsum. Most Ca occurs as carbonates and gypsum, with a minor fraction associated with clay minerals. Mg is found to be mainly present as dolomite and clay minerals, with a very minor fraction present as ankerite. The majority of alkali elements are associated with aluminosilicates. P is mostly associated with kaolinite and/or present as more complex compounds containing Al, Si, and other elements as apatite are found to be absent in the coal studied. Ti is mainly present as rutile and kaolinite. The geo-chemical association of the trace elements has also been discussed. Keywords: minerals, Assam coals, Indian coals, CCSEM study

Sep 1, 2012

By D. Dreher Whetstone, Paul M. Blakita, Christopher M. Reith, Ravi P. Malviya

"Micro-piles are small diameter (5 to 10 inches), cast-in-place piles which can develop high load capacities by bonding with soil or rock. Micro-piles are particularly well-suited for moderate to heavily loaded structures requiring deep foundations in difficult subsurface conditions, such as karst, bouldery mine spoil, or unsuitable fills with concrete debris or other obstructions. Attempts to install conventional deep foundations including driven piles, drilled piers, or auger-cast piles are likely to be fraught with construction difficulties and disputes, delays, cost overruns, and may be unfeasible in some cases. Micro-pile installation equipment is very effective in installing foundations through such overburden or rock materials.This paper presents case histories of Micro-pile installations on two projects with difficult soil/rock materials. The project sites are located in Charles Town, West Virginia and Masontown, Pennsylvania.Charles Town, West Virginia ProjectThe Charles Town project entailed construction of a four-story pre-cast concrete garage. Triad Engineering, Inc. performed a geotechnical investigation for this project (Triad, 2001). The subsurface, geologic, and project specific information described in th is paper are largely based on the aforementioned geotechnical report.Ground ConditionsThe project site is located in Jefferson County, West Virginia, and is mapped to be underlain by the Elbrook Formation. This formation is described as argillaceous, dolomitic limestone with beds of dolomite and aphanitic and algal limestone (Dean, et al. , 1990). The carbonate rocks at the site were characterized as ""moderately solution-prone, highly calcareous and weathers differentially to produce a pinnacled or ""sawtooth"" top of rock profile. (Triad, 2001 )"" Overburden soils consist of low to high plasticity, fine grained residual soils formed by weathering of the parent carbonate rock. The residual soils include variable proportion of sand and rock fragments."

Jan 1, 2005

By Luttrell. G.

The profitability of coal mining operations is highly dependent on the performance of the coal blending and processing facilities. Many companies have recognized this fact and have instituted optimization programs that require large amounts of coal characterization data, extensive operational information and complex costing models. Unfortunately, this brute force approach to optimization is often overwhelming in terms of time and cost and is generally too inaccurate to be of value in day-to-day field operations. A simpler and more practical approach involves the use of ?micro-price? optimization throughout the coal supply chain. This fundamental concept assigns unit values to each type product (particle or groups of particles) passing through the production units. True optimization occurs whenever all particles with positive worth are recovered and passed to market, while all particles with negative worth are rejected. This paper describes the fundamental workings of the micro-price concept as applied to coal blending and processing operations. Several examples are also included to demonstrate the economic gains that can be realized via the application of this concept.

Feb 23, 2014

By F. Stanley, A. Noble, G. Luttrell

"The supply chain for coal-fired power stations involve a multi-stage network of mining units, preparation plants, blending facilities and transportation systems. Attempts to optimize the supply chain have historically been difficult due to the lack of communication/coordination between the various groups involved in coal production, transportation and utilization. In light of this issue, a new approach for globally optimizing the coal supply chain called Micro-Price Optimization has been developed to simplify the optimization problem and to provide coal producers with fundamental insight needed to improve the profitability of their operations. This fundamental concept assigns unit values to each particles (or groups of particles) passing through production units. Optimization occurs whenever the maximum tonnage of positive value particles are recovered and passed to market, while the minimum tonnage of negative value particles are recovered. Elements considered by the concept include factors such as target boiler cost/efficiency, waste disposal costs, coal quality parameters, emission penalties, transportation charges, or other quantifiable impact factors. This article reviews the basis for the micro-price concept and provides a detailed industrial case study involving the determination of optimum coal qualities that need to be supplied by mine operators to feed a coal-fired power station. INTRODUCTION The performance of coal preparation plants have long been known to play an important role in determining the overall profitability of mining operations. This significance is due to the fact that the misplacement of just 1 ton/hr of clean coal to reject resulting from poor plant performance can represent nearly $300,000 per year in lost revenues for a mine producing a steam market coal (i.e., 1 ton/hr x $50/ton x 6,000 hr/yr = $300,000/yr). This loss can be even more pronounced, occasionally approaching $1 million per year for each 1 ton/hr of misplaced clean coal, for operations producing high-quality coking coal products sold into the premium metallurgical market (i.e., 1 ton/hr x $150/ton x 6,000 hr/yr = $900,000/yr). Detailed economic studies indicate that improvements in plant yield resulting from increases in organic efficiency have one of the largest overall impacts on mine revenue when compared to other cost centers within the mining operation. One of the first studies to show this important financial impact was reported by Norton-Hambleton Consultants (Norton, 1979). Their study indicated that an unfavorable change in plant efficiency was second only to coal transportation in terms of its impact on profitability, while an unfavorable change in the cost of underground mining was a distance third. This longstanding realization has continued to provide a strong financial incentive for coal producers to optimize the separation efficiency of their coal processing and blending operations."

Jan 1, 2015

By A. Noble

"In coal and mineral processing, several numeric parameters are used to quantify the separation performance of unit operations. For density-based separations, the partition curve is used as the starting point for many stages of diagnostic analyses. The curve is often quantified by its midpoint slope sharpness, and this single value is subsequently used for technical evaluation, benchmarking, and comparison. While this analytical approach does depict misplacement by relative density class, it inherently prioritizes middling separation and does not consider process economics or the micro-price value of individual classes. Alternatively, the organic efficiency parameter does consider process economics; however, it does not reveal information on the root cause of lost revenue or misplacement. In this paper, a new analytical approach is introduced which reconciles the technical misplacement data derived from the partition curve with the economic data derived from micro-pricing. The result is a new analytical procedure which reflects a better use of performance data. INTRODUCTION Partition curves are commonly used in the characterization, evaluation, and simulation of various physical separators. In mineral processing, partition curve analysis is routinely applied to hydrocyclones, screens, and density separators. Graphically, the partition curve depicts the recovery of particles as a function of a physical property on which the separation is based (e.g. particle density, size, magnetic susceptibility, etc.). Given the probabilistic nature of many real separators, the partition curve often exhibits a characteristic “S” shape (Fig. 1), similar to a cumulative normal distribution. Other geometric features of the curve are also depicted in Fig. 1, including the high and low closeout (or bypass) values, the midpoint slope, and the separation cut point (property value with 50% recovery). Partition curve analysis was originally proposed to evaluate coal washability (Tromp, 1937). Given the limited computational resources at the time, the analytical methods relied heavily on graphical construction and interpretation of the curve. Owing to the simplicity of the calculation and interpretation, many of these graphical approaches are still widely used for performance analysis today. The most common calculations are based on the slope of the partition curve at the midpoint. Increased slopes correspond to enhanced separation performance, since a perfect separation exhibits a stepwise transition from 0 to 1 at the desired cut point (i.e. an infinitely large slope). One common formulation of this slope, the Ecart Probable (Ep), is derived by evaluating the slope between the 25% and 75% recovery points:"

Jan 1, 2015