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By Nobuharu Isago, Atsushi Kusaka, Kosuke Kawata

"Strong earthquakes occur frequently in Japan, and some rock tunnels have sustained severe damages on their permanent lining. Many road tunnels, which were constructed by conventional steel arch support and timber lagging method, exist in Japan and they need risk mitigation measures against earthquakes as per our empirical knowledge. Many reinforcing measures for deformed tunnels that may be effective against earthquakes are developed; however, behaviors during earthquakes are not fully understood.In this study, static loading tests and numerical analysis, which simulate a loading condition during earthquakes, were carried out to clarify the effect of the countermeasures. The Load-bearing capacity is estimated for the tunnel structures facilitated by the installment of an inverted arch; however, a joint between inverted arch and sidewall become structural weakness. Rock bolts and carbon fiber sheets have a potential able to mitigate the risks of collapse of the lining by the forces from an earthquake.INTRODUCTIONA number of rock tunnels with no apparent unfavorable ground conditions suffered severe damage, including the collapse of their permanent lining, in large seismic events such as the Chuetsu Earthquake in 2004 (e.g., Mashimo 2005). Since these tunnels were considered to exhibit the required structural strength to survive earthquakes, studies are being carried out to clarify the mechanical behavior of tunnels during earthquakes and their damage mechanism (e.g., Kusaka et al. 2009); however, the aseismic design methodology for mountain tunnels has not yet been established.In many cases of earthquake-damaged tunnels, some defects already existed, such as improper construction and deterioration of lining concrete. Although countermeasures are usually implemented against such problems, their earthquake-resistant effect was not fully understood.In this study, static loading tests and numerical analyses to reproduce these tests were carried out assuming that a rock tunnel was affected by the earthquake to clarify the mechanism of the lining damage and the effect of the countermeasures."

Jan 1, 2016

By Jaime Lomelin

The brines from the sub-surface of the Laguna del Rey dry lake are pumped to Química del Rey, S. A. plant, where they are cooled in adiabatic crystallizers precipitating sodium sulphate decahydrate. This salt is dehydrated in multiple effect evaporators and dried in rotary kilns producing high purity anhydrous sodium sulphate. The spent brines from the sodium sulphate operation are concentrated in solar ponds, precipitating astrakanite and leaving a brine with a higher concentration of magnesium ions. This brine is treated with calcium chloride solution to eliminate the remainder of sulphates, leaving a solution of magnesium chloride ready for the manufacture of refractory grade magnesium oxide or periclase. The magnesium chloride is reacted with dolime to produce magnesium hidroxide which is washed, filtered, and calcined to produce soft burned magnesium oxide, which is briquetted and dead burned to produce the periclase.

Jan 1, 1984

By A. A. Mathews

INTRODUCTION When Palmer King asked me to prepare a paper for this conference, it seemed quite appropriate, since I am Chairman of Subcommittee No. 4 of the U. S. National Committee on Tunneling Technology and we are presently making a detailed study of contracting practices. Before the end of this year, we expect to publish our report containing guidelines aimed at improving our contracting practices and minimizing the problems which develop therefrom. The American construction and mining industries today are glowing examples of the ingenuity of man pitting his wits against the unknown. Without the promise of rewards commensurate with the perils faced and the effort expended, it is doubtful that these industries could have reached their present state of advancement. Nevertheless, these industries are still primitive compared to many others such as aerospace and electronics. That our present contracting practices leave something to be desired is evidenced by the fact that many of our underground projects wind up with tremendous increases in estimated cost, financial disaster, and costly dispute and litigation. The situation is aggravated by the current economic uncertainty, energy crisis, and shortage of materials. At the same time, if our industries are to develop their maximum technologic potential, we must employ contracting practices which will encourage that development. Most of the contractual problems related to underground construction are associated with risk and its management. Unless all of the ramifications of this subject are understood, it will be difficult

Jan 1, 1974

By Kwadwo O. Adutwum, George M. Potter, Todd J. Harvey

Ashanti Goldfields Company (AGC) is the largest gold mining company in Western Africa. Their jewel operation is a highly inte­grated set of mines and plants situated in Obuasi, in the Ashanti region of Ghana. This operation is responsible for mining 5.5 mil­lion tonnes of ore at 4.6 git annually from a series of open pits and underground mines. The sulphide ore is highly refractory with untreated gold recoveries in the range of 30-40%. The milling facilities are quite varied and include an oxide treatment plant (OTP), a heap leach, a sulphide roaster circuit (PTP), a tailings treahnent plant (TIP) and the most recent, a sulphide treatment plant (STP). The sulphide treatment plant, the world's largest stirred tank biooxidation circuit, was commissioned in early 1994. This plant treats approximately 800 tonnes of refractory gold con­centrate per day with overall recoveries of75-85o/o(ll, Biooxidation was selected for its ease of operation and less exotic maintenance requirements as well as its ability to achieve comparable gold recoveries. Unfortunately, despite stirred tank biooxidation being one of the lower cost methods of treating refractory ores, it is still too costly for low grade refractory materials. GeoBiotics, Inc. has developed a proprietary technology that allows the economic treatment of lower grade refractory gold ores through heap biooxidation. AGC has a significant resource of low grade refractory sulphide ore. This ore is too low grade to warrant BIOX™ sulphide treatment and its oxide plant recov­ery is low at 35-45%. GeoBiotics and AGC have completed pre­liminary testing and economic analysis of heap biooxidation for this material. Additionally, the feasibility of producing a gravity concentrate from the tailings of the sulphide treatment plant has been explored. This concentrate would be coated onto the low grade sulphide and biooxidized concurrently. Gold recoveries for the biooxidized low grade sulphide have increased to 75% and the gravity recovery from the STP tailings has achieved 80% uti­lizing a Falcon concentrator. The preliminary economics of the proposed full scale plant are very favourable with a pre-tax IRR of 233% and a payback period of 6 months. This paper details the biooxidation testing, flow sheet devel­opment and preliminary economics of employing heap biooxi­dation for low grade refractory ore treatment at Ashanti Goldfields' Obuasi operation.

Jan 1, 1998

By M. P. Evans, Rainer Kahrger

During the last decade or so great advances were made in the solvent extraction, electro winning technologies. They, combined with heap leaching, made it viable to exploit large, relatively low grade oxide copper deposits. The El Abra mine is a good example for such a deposit. Situated in Northern Chile at an elevation of about 4000m (14000 feet), 70 krn north of Calama, the El Abra deposit has been known for many years. In the early 1990's Codelco decided to sell a major holding in the deposit to international mining companies. After lengthy negotiations Cyprus Minerals finalized in June 1994 the purchase of 51% of the deposit with Codelco retaining the balance. lance. Already in 1993 Cyprus and the engineer on the project, began discussions with international materials handling companies with regards to the materials handling system required for the project. These early discussions were considered critical for this fast track project. Immediately after the notice to proceed with the project, several companies were invited to submit competitive conceptual proposals for that portion of the material handling system which was to transport crushed and treated ore from the plant to the leach pad and build the leaching heaps at a rate of up to 150 000 tons per day. A supplier was selected. Additional studies were made for the conveyor system from the mine to the fine crushing plant. Due to the extremely rugged terrain and high altitude at the mine, a decision was made to locate the plant and the leaching operations 15 km east of the mine at an elevation of 3400m. In July 1994 the supplier started the conceptual engineering with a design team at the engineer's San Francisco office. The undertaking was unique in the sense that the supplier's engineering team was integrated into the project for the duration of the conceptual engineering. The open and continuous communication greatly contributed to the success of the design work.

Jan 1, 1996

By Allister McLeod

Coal is expected to play a major role in energy supply in the next 20 years. Oil is a convenient and still reasonably abundant fuel. However, its major sources of supply are regions where there is nervousness about political stability. Uranium is a more efficient fuel - but there is a continuing community apprehension regarding its use. What coal may lack in efficiency, it makes up in long term availability and competitive overall cost. Moreover, diversity of source ensures stable long-term supply. In this way, a major role for coal in the world energy scene is assured. Cyclical considerations aside, demand for coal will increase significantly and it will meet a substantial share of new energy demand, replacing oil and gas in major industrial and electric utility markets. By around the year 2000, coal's share of world energy could reach 30% and rival oil as the largest single source of energy.

Jan 1, 1982

By K. Komnitsas

Activities in the mixed sulphides industry, such as mining and beneficiation, cause adverse impacts to the environment due to excavation, treatment and disposal of low-grade ores and tailings containing residual sulphide minerals. The greatest impact is caused by the oxidation of sulphide phases contained in the tailings and waste rock and the subsequent production of leachates characterized by low pH and high concentration of heavy and toxic elements and sulphates, called acid mine drainage, that contaminates soils, surface- and groundwater. Therefore, rehabilitation of these sites is required in order to render these pollution sources inactive and minimize environmental impacts. The calculation of risk, based on acid mine drainage probability and magnitude of consequences at the disposal sites offers engineers, environmental scientists and authorities a valuable tool for the selection and application of the best remediation technology. Several parameters, such as the chemical and mineralogical properties of the wastes, the most probable pathways the contaminants follow, the potential receptors and the exposure scenarios have to be taken into account. Therefore, risk is the most critical parameter in decision-making regarding management of mining wastes and rehabilitation of disposal sites.

Jan 1, 2002

By Richard H. Olson

The following discussion will deal with the domestic talc industry only, inasmuch as the writer has had no experience in this field outside of the U. S. This is strictly a geological-mining approach; no attempt is made to assess in depth the effects which milling technology and marketing capability might have in determining the potential of any given talc deposit.

Jan 1, 1970

By Pierre Mousset-Jones, Felipe Calizaya, Malcolm J. McPherson

The algorithm presented in this study determines the combination of fans that provide all working districts of a mine with predefined airflows at the minimum operating cost. It is based on an existing ventilation simulator, VNETPC, and a set of linear equations associating fan pressures and the added resistance of regulators. Two assumptions are undertaken: (1) fan locations are predetermined and (2) the number of working districts is equal to or greater than the number of fans. By means of this algorithm, the optimal solution to an n fan ventilation system may be found after n + 1 simulation runs.

Jan 1, 1987

By D. A. Barr

The Galore Creek copper deposits lie in the Stikine River district of northwest British Columbia, a largely undeveloped region which possesses rugged mountain terrain with deeply incised valleys which support dense undergrowth. Timberline is normally at about 1300 m (4265 ft) and the higher levels contain glacial systems and large ice fields with peaks rising to 3500 m (I 1,483 ft). A location map of the Galore Creek area is given in Fig. 1. In the late 1920s, field parties under the direction of F.A. Kerr (1948) of the Geological Survey of Canada completed geological surveys of the district. Primary access for this work was provided by riverboats on the Stikine and Iskut Rivers. Kerr's party had to contend with extremely difficult travel conditions that required considerable backpacking, augmented by pack dogs in certain cases. Absence of ground control led Kerr to establish his own topographic maps. Among the geological data established was the recognition [ ] that small bodies of orthoclase porphyry in the district are often well mineralized with base metal sulfides. Copper mineralization in the upper Galore Creek valley, a tributary of Scud River which flows into the Stikine River some 80 km (50 miles) south of the small settlement of Telegraph Creek, was originally discovered during aerial reconnaissance by M. Morrison and W. Buckholz while prospecting for Hudson Bay Exploration and Development Co. Ltd. in 1955. Malachite- and azurite-stained out- crops in several parts of the Galore Creek watershed are clearly visible from distances of 500 m ( 1640 ft) or more. Claims were staked in 1956 and the copper showings were partly mapped, trenched, and investigated by shallow diamond drilling. Because of the remoteness of the area and higher priorities for expenditures elsewhere, no further work was undertaken and most of the claims were allowed to expire.

Jan 1, 1991

Many of the deeper ore reserves in current gold operations as well as new gold deposits consist of refractory ore types. As process development for these mineralizations remains time-consuming and costly, minimization of exploratory testwork and the early identification of feasible process routes is critical. Since most of the processing parameters are related to the mineralogy of the ore (Marsden & House, 1992), thorough mineralogical analyses during exploration and development phases have become a technical and economical requirement. The determination of mineralogy-related processing parameters and especially the gold mineralogy is even more important for these ore types because refractory gold ores consist of many transitions from partially leachable to totally refractory. In addition to sulfide and gangue encapsulation, various other refractory conditions may exist. Together with accessory mineralogical detriments (e.g., alteration/ slimes, reagent consumers, scale formation, mineral preg robbing) they may complicate process selection and hamper optimal plant operation.

Jan 1, 1993

By Denis Murphy, James Gusek, Carl Mann, Thomas Wilderman

An active underground lead mine produces water having a pH of 8.0 with 0.4 to 0.6 mg/L of Pb and 0.36 mg/L. of Zn. This water is pumped at the rate of 1.200 gpm into a five-cell, bioreactor system covering about 5 acres. The gravity flow system is composed of a settling basin followed by two anaerobic bioreactors arranged in parallel which discharge into a rock filter polishing cell that is followed by a final aeration polishing pond. The primary lead removal mechanism is sulfate reduction/sulfide precipitation. The discharge has met stringent in-stream water quality requirements since its commissioning in 19%. However, there have been startup and operational difficulties. The system was designed to last about 12 years, but estimates suggest a much longer life based on anticipated carbon consumption in the anaerobic cells.

Jan 1, 2000

By Wade W. Bristol

The Jerritt Canyon Joint Venture project is located about 80 km (50 miles) north of Elko, NV. It produces approximately 9.3 t/a (300,000 oz/year) of gold. The joint venture is 70% owned by Independence Mining and 30% by Meridian Gold. Independence Mining is the operator. The Jerritt Canyon Joint Venture started operations in 1980 by mining a series of open-pit mines. The discovery of deeper ores during early 1990s made it neccessary for the operation to mine a large portion of its annual production by underground mining methods. Underground production started in 1993 at the West Generator Mine. This was followed by the Murray Mine in late 1994. Two additional underground projects are being developed. Underground mining at Jerritt Canyon is scheduled to produce about 3.9 t (128,000 oz) in 1997.

Jan 1, 1997

By R. Corriveaau

This paper is about a horizontally curved conveyor, which carries 6,050 stph of limestone over land from a new quarry to the owner's plant. The conveyor is 5,012 ft long with a horizontal curve radius of5,OOOft Site conditions made a curved conveyor design the most optimal and economic solution. Using our unique custom conveyor calculation program, TKRI was able to accurately model and design the conveyor to properly track the belt and prevent any spillage through the horizontal curve radius. A data monitoring system was installed that allows monitoring of the conveyor both locally and remotely. The remote monitoring allows TKRI to contact the owner for preventive maintenance. Preventive maintenance can reduce the conveyor downtime during normal operating hours.

Jan 1, 2004

By A. D. Davis, G. A. Zabolotney

A ground-water flow model was developed to simulate the postmining recharge rate from precipitation at the Belle Ayr surface coal mine, which is located in the Powder River Basin near Gillette, WY Wyoming state regulations require that reclaimed lands should provide a rate of recharge that approximates the premining rate. Steady-state calibration and transient simulations showed that the postmining recharge rate through spoil is at least 50 mm (2 in.) per year, exceeding the original infiltration rate of 4 mm (0.16 in.) per year to shallow overburden aquifers. Major reasons for the increase include the flat topography of the reclaimed areas and the decreased spoil density. It is expected that the backfill will disaggregate and settle over time, eventually resulting in a nearly constant recharge rate that is less than 50 mm (2 in.) per year but still somewhat greater than the premining rate.

Jan 1, 1997

By D. E. Munson

To assure the safety of a radioactive-waste repository, the performance of the repository must be predicted far into the future. The Waste Isolation Pilot Plant (WIPP) Program is responsible for developing the technology for such performance predictions in bedded salt. An important technology-development activity concerns the, fielding of very large-scale in situ tests to determine the time-dependent deformation of underground openings in salt as a basis for validation of the predictive technology. This technology is necessary to predict repository seal performance and final closure times of rooms and may be of value to the salt and potash mining community, as well.

Jan 1, 1992

By R. M. Bricka, T. J. Olin

Heavy metals contamination is an environmental problem at Army installations engaged in firearms training and munitions production. At these facilities, weathering and corrosion of expended munitions and leaching from wastewater lagoons, landfills and burn pits have resulted in heavy metals contamination of the soil. The principal metals encountered in firing-range soils are lead, copper and zinc. Cadmium and other metals, such as antimony, that are often incorporated in the munitions are sometimes seen in lesser concentrations. Mercury is associated with various propellants and, while present in much smaller concentrations, is of concern because of its acute toxicity. Chromium is primarily associated with plating operations. The transport of metals into groundwater has been confirmed at some locations, which has required treatment of the soil and groundwater at these sites. Certain treatment processes for contaminated soil produce metals-laden extracts, which also require treatment before reuse or disposal. Ion exchange is generally quite effective for removing metals from aqueous streams. However, resins are expensive and must be regenerated, and activated carbon is generally less effective for most metals and also requires regeneration. Therefore, alternative effective and economic sorbents are needed. Twelve sorbents were screened in initial batch testing. These included activated carbon, bark, chitosan, crown ether, corn cob, xanthate, clay (kaolinite and montmorillonite), peat moss, seaweed and reagent-grade zeolite (aluminosilicate, Sigma Product No. Z3125). Of these, zeolite demonstrated the highest capacity for Pb, Cr and Cd. For this reason, zeolite was selected for further testing in batch, kinetic and column studies. Materials and methods Zeolite. The zeolite used in the second-phase batch and column studies was obtained from a natural deposit of clinoptilolite-rich rock located in South Dakota (Rocky Ford SDH) (Desborough, 1996). Large blocks of the material were crushed and sieved into the following three particle size ranges: 0.5 to 1.0, 1.0 to 4.0 and 2.0 to 4.7 mm. This material demonstrates high structural stability in acidic solutions (pH 2.5) (Desborough 1996) and has a measured surface area of 30 m2/g. The measured total cation-exchange capacity (TCEC) was approximately 10 meq/100 g. This is well below what has been indicated for commercially available zeolite, which has been reported to be about 180 to 220 meq/ 100 g. The TCEC test was repeated (Method 9081, SW 846) using sodium acetate. The test resulted in a TCEC of 54.5 meq/100 g. The difference between values obtained for this material and published values for zeolites may be attributable to the greater heterogeneity in the material used in this study, compared to commercially available materials, or to the effect of the relatively large particle sizes utilized. Batch studies. Seven batch studies were conducted using synthetic metal solutions and soil extracts (Table 1). Extract composition: The P-extract was prepared by sequential surfactant extraction of organics from a burnpit soil followed by acid extraction of metals. The pH of this solution is approximately 1.1. A number of metals and organic compounds were present in the soil. Analysis of the extract was restricted to Pb, Zn and Cu concentrations for this study. The FBH extract was produced from a firing-range soil that was oxidized with a 0.01 M CaO solution and then extracted with 0.1 M acetic acid. This was filtered through 0.5-µm Whatman No. 5 filter paper and stored at room temperature. The pH of the FBH extract was approximately 4.5. pH Control: Calcium carbonate (CaCO3) may be present in the zeolite horizon or bed. Calcium ion (Ca") is released from the exchange sites when in contact with solutions containing ions for which it is more selective, such as lead. This results in a rise in solution pH over time. Acid washing removes most of the carbonates, eliminating the need for a buffer. Batch studies were conducted using both acid-washed zeolite (AW) and unwashed zeolite (UW) for performance comparison. The UW zeolite was rinsed with distilled deionized (DDI) water to remove fine soil particles. Both materials were dried at 105°C (220°F) overnight, so that the dry mass could be determined. Column studies. Ten column studies were conducted. Because it was expected to have the best hydraulic properties, the largest particle

Jan 1, 1999

By Robert L. Cheek, Sid McIlveen

Sodium sulfate is an important industrial chemical. As recently as ten years ago it was produced and consumed in the United States in quantities exceeding 1 Mtpy. Since then, both its production and use have declined; however, approximately half the production still comes from natural sources. [Fig. 1] illustrates the history of production of natural sodium sulfate in the United States. Production of natural sodium sulfate from various types of deposits is the main source of this chemical in Canada and Mexico, and probably in Argentina, Chile, Iran, Spain, and the Russian Republics. MINERALOGY AND PHYSICAL PROPERTIES Sodium sulfate is widespread in occurrence and is a common constituent of many mineral waters, as well as seawater. Atmospheric precipitation contains sulfate; it is one of the major dissolved constituents of rain and snow (Davis and Dewiest, 1966). Many of the saline lakes throughout the world contain varying amounts of sodium sulfate. Because sodium is usually the dominant cation, some workers make an anionic distinction, referring to lakes containing predominantly sulfate as bitter lakes and those containing predominantly carbonate as alkali or soda lakes (Bateman, 1950). Sodium sulfate in its natural form is found in two principal minerals, mirabilite and thenardite. Mirabilite, the hydrous form, is commonly called Glauber's salt. It was discovered by the German chemist, J.R. Glauber (1603-1668), who derived its name from the Latin, sal mirabile, meaning wonderful salt. Thenardite, the anhydrous variety, was named for the French chemist, Louis Jacques Thenard (1777-1857) of the University of Paris (Mitchell, 1979). The largest quantities occur in the form of mirabilite. Sodium sulfate is found in varying degrees of purity, from theoretically pure efflorescent crystals of mirabilite to combinations and admixtures of other salts and impurities. It is a common constituent of some brines; from this source much is extracted commercially. Sodium sulfate also is found in compounds, such as the minerals glauberite, the double salt of anhydrous sodium and calcium sulfate, bloedite, the hydrous double-salt of sodium sulfate and magnesium sulfate, and burkeite, the anhydrous double-salt of sodium carbonate and sodium sulfate. Over 40 minerals contain sodium sulfate in varying proportions; many are of special interest because of their frequent occurrence. Table 1 lists some sodium-sulfate bearing minerals. The reader is referred to other publications (Cole, 1926, Dana, 1932, Grabau, 1920, and Dietrich, 1969) for descriptions of these minerals. Only mirabilite and thenardite will be described herein. Mirabilite Na$04.10H20, contains 55.9% water of crystallization. It is noted for its efflorescence or spontaneous loss of water. On dehydration it changes to the anhydrous form, Na2S0,. Mirabilite is an opaque to colorless, water-soluble mineral that tastes first cool, then slightly bitter. It has a specific gravity of 1.48. It frequently forms as efflorescent, needlelike monoclinic crystals, but generally is found in the massive form. Thenardite, the anhydrous mineral, Na2S04, contains 43.68% Na20 and 56.32% SO3. It ranges from colorless to white and may be tinted shades of gray or brown. It is a water soluble mineral with a slightly salty taste. Its specific gravity (2.67) and hardness (2.5 to 3) exceed those of mirabilite. It commonly occurs in the massive form without visible crystals. Its crystals are frequently tabular pyramids of the orthorhombic system. Sodium sulfate also occurs as a heptahydrate, containing seven molecules of water, but this is unstable and has not been found in the natural environment. The solubility of sodium sulfate has an important effect on the crystallization of the salt in nature, as well as in its production. Its solubility in water generally increases as a nonlinear function of temperature. Below 1.2°C, ice and mirabilite form. As the temperature is increased above O°C, increasing amounts of sodium sulfate become soluble. At 32.4°C, a transition point on the solubility curve is reached, as the decahydrate melts in its own water of crystallization and the anhydrous form crystallizes. With in- creasing temperatures, solubility decreases somewhat. The presence of other dissolved salts changes the transition temperature and solubility characteristics of sodium sulfate.

Jan 1, 1994

By L. B. Rothfeld, R. L. Dolzani

This paper presents preliminary results of a US Bureau of Mines (USBM) study of potential costs of compliance with possible federal regulations for copper heap and dump leaching. The regulations could arise under amendments to the Resource Conservation and Recovery Act (RCRA) and/or the General Mining Law. Estimates are given for the cost of compliance with possible technology standards that would require the use of liners and closure caps regardless of terrain and underlying geology and hydrology. This cost is compared to the cost of compliance with 1992 state requirements for terrains typical of those found at existing copper leach sites in the southwestern United States. Incremental compliance costs are found to widely exceed screening criteria used by the US Environmental Protection Agency (EPA) to denote significant economic impact.

Jan 1, 1995

By R. J. Sweigard, G. T. Lineberry, B. K. Slone, F. A. James III, D. S. Maggard

The depth at which it becomes more economical to use slope access instead of box-cut access for nearsurface coal reserves is termed the "transition depth." The transition depth can be established for a given coal property by considering cost estimates for those parameters that determine respective access methods. Fourteen parameters that influence access cost were identified, and ranges for these parameters were determined. A transitiondepth formula was developed to permit the determination of which is the better method of accessing a reserve, given information such as high wall slope, road width, total bench width, pit dimensions, road grade, belt component costs, pumping costs and the cost of overburden removal and reclamation. In most cases in Appalachia, especially in eastern Kentucky, the observed transition depth ranges from 20 to 30 m (66 to l00 ft). This indicates that actual practice is consistent with the analytical approach used.

Jan 1, 2002