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By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By Rajiv Kalra

This paper reviews the following aspects of the world?s largest manufactured Grinding Mill?s in terms of diameter and power, along with the world?s biggest shop assembly and trial run of the mills delivered to Sino Iron Magnetite Project in Australia. 1. An overview of the basic flow sheet of the Sino Iron (Magnetite) Project located in Australia 2. An overview of in-house designed CITIC Heavy Industries 12.2 m (40ft) F x 11 m(36ft) LG ? 28MW AG mills including FEA and major components 3. In-house manufacturing at CITIC-HIC work in Luoyang China of all major components for 6 off Ø12.2 m(40ft) AG mills and 6 off Ø7.9 m(26ft) x 13.6 m(44.6ft) LG-2 x 7.8 MW Ball Mills 4. Major aspects of design and preparation of the biggest shop trial run of Ø7.9 m(26ft) x 13.6 m(44.6ft) LG Ball Mill witnessed by international EPCM?s and clients in July 2009. 5. Major aspects of one piece assembly of 1300 tonne rotating element of the Ø12.2 m(40ft) x 11 m(36ft) LG AG Mill and Ø7.9 m F (26) x 13.6 m(44.6ft) LG Ball Mill at the port of the export China and transport to Australian Port and then to site. 6. An insight to unique installation methods used for Ø12.2 m(40ft) and Ø7.9 m(26ft) rotating element lifting on the mill foundation in one piece assemblies. 7. CITIC Heavy Industries present capability for in house design and manufacture of Grinding Mills up to Ø13.7 m (45 ft) with 35 MW Gearless drives and Ø12.2 m(40ft) with 2 x 10 MW Geared Mill drives

Jan 1, 2012

By Rajiv Kalra, Ji Jiangang

"This paper reviews the following aspects of the world’s largest manufactured Grinding Mill’s in terms of diameter and power, along with the world’s biggest shop assembly and trial run of the mills delivered to Sino Iron Magnetite Project in Australia.1. An overview of the basic flow sheet of the Sino Iron (Magnetite) Project located in Australia2. An overview of in-house designed CITIC Heavy Industries 12.2 m (40ft) F x 11 m(36ft) LG – 28MW AG mills including FEA and major components3. In-house manufacturing at CITIC-HIC work in Luoyang China of all major components for 6 off Ø12.2 m(40ft) AG mills and 6 off Ø7.9 m(26ft) x 13.6 m(44.6ft) LG – 2 x 7.8 MW Ball Mills4. Major aspects of design and preparation of the biggest shop trial run of Ø7.9 m(26ft) x 13.6 m(44.6ft) LG Ball Mill witnessed by international EPCM’s and clients in July 2009.5. Major aspects of one piece assembly of 1300 tonne rotating element of the Ø12.2 m(40ft) x 11 m(36ft) LG AG Mill and Ø7.9 m F (26) x 13.6 m(44.6ft) LG Ball Mill at the port of the export China and transport to Australian Port and then to site.6. An insight to unique installation methods used for Ø12.2 m(40ft) and Ø7.9 m(26ft) rotating element lifting on the mill foundation in one piece assemblies.7. CITIC Heavy Industries present capability for in house design and manufacture of Grinding Mills up to Ø13.7 m (45 ft) with 35 MW Gearless drives and Ø12.2 m(40ft) with 2 x 10 MW Geared Mill drives"

Jan 1, 2012

By D. Mohapatra

The possibility of using 2,2,4-trimethyl-1,3-pentanediol dissolved in tetrachloromethane as extractant for boron recovery is discussed. The parameters optimized for this purpose are contact time, boron concentration in the aqueous phase, extractant concentration, equilibrium pH and phase ratio. NaOH is used as stripping agent for boron recovery from the loaded organic phase. Boron extraction is found to be a slow process (equilibrium time 20 minutes) compared to boron stripping, which is reasonably fast (equilibrium time 5 min). Maximum boron extraction is possible at a broad pH range from 1.0 to 6.0. Using 1.0M extractant concentration, a 1:1 phase ratio (organic: aqueous) and two stages, ~99% boron extraction is achieved. More than 97% boron stripping is possible using 0.5M NaOH at a 1:1 (organic: aqueous) phase ratio in two stages. Overall, a 95.6% boron recovery was achieved. Loss of solvent into the aqueous phase and co-extraction of Ca, Na and K into the organic phase at higher equilibrium pH are two major concerns in his process.

Jan 1, 2008

By Moylan T, Stewart D

A case study examining the procedures and financial benefits of introducing dump leaching to augment the Mt Gibson Gold Project CIP operations is discussed. Metallurgical testwork, followed by pilot dump leach operations, confirmed that gold recoveries of greater than 60 per cent could be achieved by dump leaching Mt Gibson laterite ore. Capital and operating costs were determined. Pit optimisation using the Whittle FOUR-D optimisation program calculated an optimum cutover grade between CIP and dump leaching for one orebody. The resultant recalculation of reserves based on CIP and dump leach operating costs showed that reserves for that orebody could be increased from 329 000 tonnes at 1.9 g/t An, to 1 488 000 tonnes at 1.2 gh An. NPV for the CIP only option of $1.4 m, was increased to $4.0 m for the combined CIP/dump leach option. This technique can be applied to existing gold projects and to new Developments.

Jan 1, 1992

By Donald N. H. Chi

The unsteady, one-dimensional, compressible-flow equations have been solved numerically for a deflagration propagating through a gallery of finite length closed at the ignition end and open at the opposite end. These equations were solved for two situations wherein (1) the propagating flame was extinguished after 0.1 sec or before the return of aerodynamic disturbances reflected from the open end, and (2) the flame was allowed to propagate a full 0.8 sec until it was extinguished. It was found that the process of sudden flame extinguishment creates rarefaction waves that, upon entering the burned zone, produce resonance within the burned cavity. For the relatively small value of the product of the expansion ratio (8.5) and the effective burning velocities of 7.4 m sec-1 for the first experiment and 4.9 m sec-1 for the second experiment, it was found that the acoustic approximation provides an adequate estimate of the pressures developed ahead of the flame during the system&apos;s early history.

Jan 1, 1974

By James M. Prudden, E. P. Jucevic

The Divide mining district occupies the center of a Tertiary caldera hosting the famous Divide silver lode and the crosscutting Gold Mountain mines. The northwest-southeast trending silver lode hosted ore with typically a 100:1 silver:gold ratio, high molybdenum content and argillic alteration dated at 16.5 m.y. within the Fraction Tuff. The east-west trending Oddie Rhyolite flow dome at Gold Mountain experienced possibly several periods of resurgence with repetitive silicification, brecciation and attendant precious metal deposition forming stockwork type mineralization. Silver-gold ratios average 10:1 for the mineralization phase of this 16.4 m.y. intrusive event. Similar chalcedonic mineralization registering a 3:1 silver:gold ratio cements conformable breccias within the Oddie Rhyolite basal flows unconformably overlying the Siebert Tuff on the northern flanks of Gold Mountain. Gray and red chalcedonic breccia matrix in the King Tonopah member of the Fraction Tuff contains a 50:1 silver :gold ratio.

Jan 1, 1990

By G. Sachs, G. Espey

Simple methods can be used for the determination of the residual stresses in thin walled tubing if the stresses consist of high tensile stresses at the one surface and high compressive stresses at the other surface. Such a stress distribution is approximated in sunk tubing and in deep-drawn shells. It is possible to cut sections from such articles in such a manner that a major part of the residual stress is relieved by a bending of the Part that is separated from the adjacent metal. The circumferential stress is evaluated from the change in diameter D, occurring on splitting a length of tubing (Fig. Ib) or from deflection resulting from the cutting out of a circumferential tongue (Fig. Ia) .6 The bending moment M released by such a flexure is. M - EI (I-I) = EI R1-R0 I - u2(R0-R1) I -V2 R0XR1 where E = modulus of elasticity, v = Poisson&apos;s ratio, I = moment of inertia of the section, R0 =. mean radius before splitting, R1 = mean radius after splitting. The release of this bending moment corresponds to the release of stresses, which, in a thin section, vary linearly from one surface to the other, and have the following value in a particular fiber a certain distance (x) from the surface: S = c d I - V2 x c x d 2 2 RI - R0____E (d ) R1 - R0 X R0 X R1 ~ i - u2 (2 x) Ro X R1 where C is the section modulus and d is the thickness of the section, the ratio M:C being d: 2 for a rectallgular section.* The maximum stress values at the surfaces are. Smax = +E X d X R1-R0 I — u2- 2 R0 X R1 For most purposes the simpler equations: EXd AD1 = ± I - u2 x dm2 and will be satisfactory, where D,, is the aver. age of the mean diameters of the tubing

Jan 1, 1942

By G. Sachs, G. Espey

Simple methods can be used for the determination of the residual stresses in thin walled tubing if the stresses consist of high tensile stresses at the one surface and high compressive stresses at the other surface. Such a stress distribution is approximated in sunk tubing and in deep-drawn shells. It is possible to cut sections from such articles in such a manner that a major part of the residual stress is relieved by a bending of the Part that is separated from the adjacent metal. The circumferential stress is evaluated from the change in diameter D, occurring on splitting a length of tubing (Fig. Ib) or from deflection resulting from the cutting out of a circumferential tongue (Fig. Ia) .6 The bending moment M released by such a flexure is. M - EI (I-I) = EI R1-R0 I - u2(R0-R1) I -V2 R0XR1 where E = modulus of elasticity, v = Poisson&apos;s ratio, I = moment of inertia of the section, R0 =. mean radius before splitting, R1 = mean radius after splitting. The release of this bending moment corresponds to the release of stresses, which, in a thin section, vary linearly from one surface to the other, and have the following value in a particular fiber a certain distance (x) from the surface: S = c d I - V2 x c x d 2 2 RI - R0____E (d ) R1 - R0 X R0 X R1 ~ i - u2 (2 x) Ro X R1 where C is the section modulus and d is the thickness of the section, the ratio M:C being d: 2 for a rectallgular section.* The maximum stress values at the surfaces are. Smax = +E X d X R1-R0 I — u2- 2 R0 X R1 For most purposes the simpler equations: EXd AD1 = ± I - u2 x dm2 and will be satisfactory, where D,, is the aver. age of the mean diameters of the tubing

Jan 1, 1942

By Sivilay Sayavong, David Puller, Julian Gatward, David Hard, Martin Stanley

"AbstractThe Thames Water Tideway Tunnels programme involves the upgrade of London’s combined sewer and storm water system. The first section is the Lee Tunnel between the Beckton Sewage Treatment Works (STW) and the Abbey Mills Pumping Station. This will intercept the overflows currently discharging to the River Lee and has the capacity to store and transfer 350,000m3 of storm water and sewage. The project required 4 shafts and a 6.9km 7.2m diameter tunnel. The shafts are some of the largest ever constructed in the UK, with diaphragm walls up to 98m deep and 1800mm thick. As a result of the innovative methods of diaphragm wall design and construction adopted the 4 very large and deep shafts were able to be excavated and completed safely, with minimal water ingress and with extremely high quality.MVB, a joint venture of Morgan Sindall, Vinci Construction Grands Projets and Bachy Soletanche are delivering the £635m contract with Thames Water’s Project Management Team in a collaborative manner under an NEC contract. Mott MacDonald, Morgan Sindall UnPS & Bachy Soletanche are acting as designers.Some of the important advances in diaphragm walling made included:??Diaphragm wall design to both EC2 & EC7 taking into considering the assessment of chalk stiffness, high hoop stresses, large multiple openings and non-axisymmetric loadings.??Formation of shafts as a faceted circle from a series of overlapping panels, with primary panels up to 7.2m wide demanding concrete volumes up to 1300m3 be poured in one go. Overlapping secondary single bite panels cut into the grade C50/60 concrete.??Excavation of the full geological stratigraphy of London making bentonite management complex.??Panel verticality of 1:300 required over the full depth. The results achieved this and in many cases exceeded expectations with some panels coming in at up to 1 in 800 with the majority at 1 in 400 to 1 in 500. The project is also the first in the Soletanche Bachy Group to take data from the ultrasonic drilling monitor used to check the verticalty in electronic format in order to create 3D CAD as-built drawings.??Each diaphragm wall panel was reinforced over its full depth. Up to 18 separate pieces of reinforcing cage had to be installed in primary panels. Cages underwent a full range of temporary works designs to check that lifting, splicing and placing could all be undertaken safely. Fibreglass was used in the tunnel portals in the shafts to ease breakthroughs."

Jan 1, 2014

By M. Board, R. Pakalnis, S. Seldon, R. Brummer

The Kidd operation mines roughly 10 000 tpd of copper and zinc ore from underground and employs about 700 personnel. In the late summer and fall of 1997, major movements in the proximity of the east wall of the Kidd open pit had been observed. The Kidd pit had been mined from 1965 to 1977 to depths of 260 m (850 ft), followed by subsequent mining by underground methods to current depths in excess of 1830 m (6800 ft). The No. 1 Mine (2600 Level to pit bottom) is approximately 90% extracted, with most of the remaining reserve between 2000 and 2500 levels. Although initial concerns centred on the stability of the pit walls, the potential ramifications of the movements to the underground were recognized and measures were implemented to ensure the safety of personnel as well as to minimize the potential damage to existing operations. In late October, damage to underground operations was observed as deep as the 2000 Level. In the final assessment, the global mobilized mass was a “wedge”-shaped hangingwall block extending from surface to about 610 m (2000 ft) below surface. The “wedge” boundaries are defined by a fault and shear zone which have continuous lengths in excess of 1070 m (3500 ft); its base by shearing through the host rock mass; and its eastern face by deep tension cracks (Fig. 1). Mined and filled excavations at the western face of the “wedge” allowed mobilization of a mass in excess of 30 M tonnes. Movements in excess of 75 cm (30 in.) per day were recorded on the surface stations that preceded the complete shutdown of operations on October 29, 1997. The evaluations in the days following the shut-down were centred on mitigation of immediate and future possible negative impacts on infrastructure and mining of the remaining No. 1 Mine reserves while ensuring the safety of the operators. This effort required the rapid assessment of the potential damage of the block movement on underground infrastructure, stope access, drainage and ventilation, as well as airblast potential due to the falling of a large block into the pit near the ventilation intake at the base of the pit. These assessments were presented in a previous paper (Seldon et al., 1999). In total, the lateral movement of the block on the ground surface was over 4.3 m (14 ft). This paper describes the detailed studies performed to understand the failure mechanism and to assess the impacts on future mining in No. 1 Mine.

Jan 1, 2000

By Hans Hamrin

Three drill-blast cycles of 3.1 m advance achieved in one working shift of 7.5 hours at the Holsfjorden Tunnel project in Norway. The tunnel, 5235 m long, with a cross section of 8.6 m2, was completed several months ahead of schedule. This remarkable performance was achieved by a crew of 16 men, using machines specially designed for small tunnel excavation. The integration of drilling and charging into one unit, mucking and transport in another, reduced non-productive time considerably. The average cycle time of 140 min made it possible to complete three rounds in one 7.5 hours shift.

Jan 1, 1987

By Ingunn Opland, Silje M. Tinderholt

Drill and blast project in Norway’s capital. The contract consists of 7 rock caverns (350–950 m2), 9.2 km tunnels, and four shafts. With 110 blue-collar and 31 white-collar, the project produces an average of 16–21,000 m3 hard rock per week, with a total of 19 tunnel faces. Weekly, nine grouting rounds for water control, 800 m3 shotcrete, and 1,200 bolts are required, and 60 trucks leave the site pr. day. Challenges include blasting in densely populated areas, planning and coordination to maintain high production, obtaining a CEEQUAL certification of very good, and transporting rock on Oslo’s main highway.

Jun 13, 2023

By Segundo Velásquez, Enrique Mego, Robert Montes

La pila de lixiviación de minera Coimolache, después de 11 años de operación, actualmente cuenta solo con espacio para cargar mineral en el lift 18 a 150 m. de la geomembrana de base. Esta altura restringe la recepción de leyes pregnant en la poza PLS a 31 días por la velocidad de percolación, que se ha determinado en 5 m/día, considerando una humedad retenida de 10%; sumado a ello la calidad del mineral acarreado de los tajos Ciénaga y Mirador presenta contenidos de fino de hasta 60% m-1/8 en promedio, que perjudican la percolación de la solución cianurada a través de la pila de mineral.

Sep 30, 2022

By Gary B. Hemphill

The 345 km long Taiwan High Speed Rail Project will connect the island’s two most populated cities, Taipei and Kaohsiung. Kaohsiung is the world’s third busiest port. The 23 km of alignment on Contract C230 requires the construction of 5,879 m of shallow mined tunnels ranging from 137 m to 1,285 m in length. All nine of these tunnels are mined using NATM methodology. Two of the tunnels, T01 and T08 are in the Toukoshan Formation. This paper will discuss the mining methods, ground support design, and the instrumentation installed to monitor and verify its effectiveness in the two aforementioned tunnels.

Jan 1, 2003

By Gordon T. Clark

The preliminary design of four mined stations and 7.2 km (4.5 miles) of tunnels for Seattle’s light rail transit system is described. Constraints that influenced the design and options that were studied are discussed. The hilly post-glacial soft-ground geology of the Puget Sound Region pushed the alignment deep. Mined underground stations at depths up to 75 m (250 ft) and shafts with excavated diameters of 20-m (65-ft) are required. A 460 m (1,500 ft) sub-aqueous crossing of Portage Bay and undercrossing of an active 12-lane multi-level freeway were two of the more significant design constraints.

Jan 1, 2001

By K. L. Branham, D. W. Steeples

Surface collapse over abandoned sub- surface coal mines continues to be a problem in many parts of the world. High-resolution P-wave reflection seismology was successfully used to locate water-filled cavities in a 1-m (3-ft) thick coal seam at depths of 9 m (29 ft) in southeastern Kansas. A dominant frequency of 275 Hz was attained enabling us to delineate the top of the coal seam. To our knowledge, this study is one of the first to locate water-filled coal mine cavities at depths of less than 30 m (100 ft) wing high-resolution P-wave seismic reflection techniques.

Jan 1, 1987

By S. Michael Feroz, Michael J. Britch, Frank S. Buehler

The City of Portland is constructing the Columbia Slough Consolidation Conduit as a part of its commitment to reduce combined sewer overflows into the Willamette River and the Columbia Slough. Known as “The Big Pipe,” the conduit has a 3.7 m. (12 ft.) internal diameter and is 5,640 m. (18,500 ft.) long. Construction Segment 1 of the project includes 250 m. (814 ft.) of reinforced concrete pipe (RCP) installed by boring and jacking. Five separate crossings were constructed beneath Union Pacific Railroad tracks and Columbia Boulevard, an adjacent arterial roadway. This paper describes the design and construction of these bored and jacked crossings.

Jan 1, 1999

By Yuji Tsuneno, Yoshikazu Mikami, Yasuo Takeuchi

A new device was successfully developed in order to overcome the difficulty of drilling longer holes for anchors in soft soil bedrocks or swelling bedrocks, which is one of the major impediments to rapid excavation by NATM (New Austrian Tunnelling Method). With higher rotation (1200 - 1800 r.p.m.) and lower percussion energy (4 - 6 kg.m), the new drill has following advantages: (1) Applicability covers soils and medium hard rocks with the same drifter. (2) Longer hole (more than 9m) is achievable only with air flushing even in cohesive soils or rocks. (3) Better borehole stability is obtainable even in earth or in fissured rocks.

Jan 1, 1981

By L. Maday, V. J. Perrone, M. B. Gilbert

INTRODUCTION The Brightwater conveyance system project in King County, Washington consists of constructing about 21 km (13 mile) of effluent and combined influent and effluent tunnels. The influent tunnels will collect sanitary sewerage from the service area and convey it to the new wastewater treatment plant (WTP) site at Route 9 in Woodinville, Snohomish County, Washington. The effluent tunnels will convey treated effluent from the WTP to an outfall at Puget Sound. The tunnels will be constructed primarily under residential areas, busy suburban roads and state highways. This 21 Km (13-mile) soft ground tunneling project faced many design challenges because of the geologic and hydrostatic conditions, long tunnel reaches, and large overburden depths. Boring depths typically varied from 45.7 M (150 ft) to 114 M(375 ft) with a maximum depth of 185.6 M (566 ft) deep. Conventional empirical methods for non-mountain terrain based on a 1:1 ratio of drilled footage per foot of tunnel bore (National Research Council, 1984) for evenly spaced borings provided a good start for the Phase 1 explorations. However a continuation of this approach with closer spacing was deemed inadequate by the geotechnical team for efficiently allocating geotechnical exploration resources for the final design. This paper presents a rational approach that was used to evaluate the value of a particular geotechnical exploration boring, pump test or other in-situ test. The method of analysis, which was initially developed for rock tunnels (Einstein et al., 1978), was modified for the Brightwater project. The method considers the potential construction cost risks resulting from variable geologic conditions, the cost and reliability of the geotechnical exploration and the earned value (cost risk reduction) of performing the geotechnical exploration. PROJECT DESCRIPTION In total the land portion of the conveyance system will include approximately21 Km (13 miles) of tunnels ranging in size from 3.0 to 5.2 M (10 to 17 ft) minimum inside diameter with overburden depths of 30.0 to 168 M (100 to 550 ft) and

Jan 1, 2005