Search Documents

By Dean E. Harris

The realignment of U.S. Highway 95 in Sandpoint, Idaho, is being designed on a site underlain by glaciolacustrine soil that includes very thick deposits of soft, sensitive clay to estimated depths of greater than 200 m. The highway realignment will include construction of numerous embankments, mechanically stabilized earth (MSE) retaining walls, and pile-supported bridges. The area of the proposed new highway corridor also includes existing historic and commercial buildings, a railroad, sensitive environmental areas, and economically vital tourism/recreational assets. The evaluation of pile axial capacity included the use of a variety of methods, including total stress, effective stress, and empirical methods using the results of piezocone soundings and conventional borehole and laboratory tests. These methods were used along with the findings from an instrumented static loading test to design the piled foundations for the bridges. A critical factor throughout the design of the pile foundations was controlling settlements to levels that could be tolerated by the bridges. Also, because of the proximity of the pile foundations to the existing structures and the proposed new embankments, the project has required careful consideration of the potential interaction between these elements. The analysis of piles also considered the potential for settlement of embankments, drag loads on the piles, and downdrag.

Jan 1, 2003

By R. W. O. Kersten

The shrinkage method of stoping with pillar support has been used at Agnes Gold Mine since mining commenced. Until recently, rock instability did not have any detrimental effect on safety or production. Presently sill pillars are failing not only on the current production levels, but also in shallower old worked-out areas. The incidence of failure raises the question as to whether the pillar dimensions are adequate at the current working depths and what their size should be at greater depths. The effect of pillar dimensions on the economics of the mining operation is of paramount importance because of the amount of ore that can be left unmined.

Jan 1, 1982

By F. A. Gates, Bengt Samuelson, James E. Edmunds, S. McCune, Neil Hario, Norman L. Weiss, J. M. Bertram, A. M. Cavaliere, F. M. Jr. Stephens, D. D. Chiang

DESIGN BASIS Size of Project The size of the project generally is expressed in tons of ore milled per day, but company policies differ widely in this respect with a few adhering to this set figure but many expecting the design capacity to be liberal. To some companies that follow the latter practice a 25,000-tpd milling plant that cannot reach 30,000 or 35,000 tpd with¬out major additions is a disappointment. The engineers responsible for planning the operation must know what is intended. Other projects are sized according to the tonnage of product rather than of mine ore; examples are iron ore mills that express size in terms of tons per year of pellets or high-grade concentrates, heavy minerals plants in tons per year of rutile or ilmenite, cement plants in barrels per year, potash in tons per year of muriate, phosphate in tons per year of washer rock and flotation concentrate, and others. However, tons per day milling rate is also the common denominator in most of those instances because the major equipment has to be selected on that criterion. Equally important are operating schedules, particularly the number of operating days per week and shifts per day for ore delivery, crushing, grinding, and processing. Hours per shift also are an impor¬tant factor in design, particularly in the case of ore delivery, and the lost time expected for maintenance, cleanup, inspection, preventive maintenance shutdowns, and many others, has to be taken into ac¬count. Frequently, the ore deposit will vary in hardness and grade to such a degree that the capacity of the mill will vary widely from year to year and cannot be expressed as a fixed figure, but rather as an average over a calculable period, such as ten years, or as a specific daily capacity over the first two years, next four years, etc., or some similar projection. A good example of this kind of situation is Asarco's Mission operation 15 miles southwest of Tucson, Ariz., described by Weiss and Vincent,1 where the major rock types differed widely in hardness, so that a change in the proportion of these types in the mill feed could have imposed difficult design problems if a constant tonnage rate had been expected. Expected Life The life of a mining operation depends upon the size of the deposit and the rate of mining. The latter is a policy decision based on an economic analysis2 which, in turn, is based on many factors. From the point of view of mill planning, the estimated life of the operation determines many criteria and affects many decisions on strength of structures and degree of protection of men and materials, the quality of the materials-handling and process machinery, the type of delivery systems for ore to the mill and concentrates to the smelter or market, environmental considerations, and many others. Costly installations that may be excellent investments for a 20-year project may be waste¬ful for a 5-year operation. An example is the comparison of different methods of crushing or grinding. Take single- vs. multiple-stage grind¬ing-the former may be found more economical for a 5-year operation, and the other, more costly method more economical for a 15- to 20-year life. Mining and Ore Transportation The mining method and the means of transportation of the ore to the first crushing stage have far-reaching effects upon mill design, particularly the crushing sections, and upon site selection (see Chapter 2, Situation of Mill). Consequently, mill design cannot advance until the mine planning has reached at least tentative decisions concerning these important matters, or reach the final stages until much is known about the ore that may be expected month by month and year by year for a reasonable period. Methods of ore transportation used in over 90 underground and open-pit mines are listed briefly in Section 32 (Table 1), and more detail is found later in this section and in Section 10, Storage and Transport. These methods include surface railroad, trucks, conveyors, surface skips, underground skips, and tramming from hoist or tunnel. In surface mining, transportation of the uncrushed ore by rail or truck to the primary crushing plant-conveniently located for lowest overall cost-is most common. Rail transportation provides low perton-mile costs. Truck transportation, though in some cases less eco¬nomical, is more flexible and more adaptable to mountainous terrain; furthermore, recent improvements have reduced the operating costs to keep trucks competitive on low-grade ores. The design of the primary crushing plant will be essentially the same whether delivery is by truck or rail, but the location of the plant is subject to more rigid restrictions in the latter case because of grade limitations, and these in turn may adversely affect the selec¬tion of the mill site as well. The influence of truck haulage in reducing the stripping ratio in open-pit mines is an added reason for predicting a minor role for rail transportation in the future. The use of conveyors to transport ore from the pit to the milling plant involves (in most cases) crushing the ore to a reasonable size (10 to 20 in. maximum with today's crushers) before conveying. The Twin Buttes system3 which went into operation in late 1969, utilizes primary crushers (two) and conveyors to receive rock waste, ore, and low-grade stockpile material from trucks, then transport them to the appropriate destination. Flexibility is dependent upon the porta¬bility of the primary crushers. In the face of this development, inclined skip hoists are no longer important to the mill designers. Underground mines generally pose fewer problems of design; these will be discussed in Chapter 2. Character of Deposit The degree of homogeneity of the ore in various parts of the mine is an important factor. The characteristics that concern the millman (approximately in order of importance) are: hardness, assay, metallurgical response, size distribution,4 and moisture content. Under metallurgical response may be included degree of oxidation, mineral¬ogy, clay content, and reagent consumption, as well as process re¬sponse in general. Short-term variations-hour-to-hour, day-to-day, or even week-to-week-make operation of the plant more difficult, require greater flexibility of process design and, perhaps, also require more instrumentation and manpower. Uniformity of the ore in the characteristics noted previously and

Jan 1, 1985

By Elisabetta Tedeschi, Razieh Nejati Fard

Deep-sea mining is in the future perspective of mining industry and it is currently in the technological development phase. The focus of this study is on the electrical power system that provides sufficient energy for the mining equipment at the seafloor, excavating Seafloor Massive Sulfide (SMS) deposits. SMS deposits usually exist at water depths between 1500 m and 4000 m. Despite the similarities of SMS deposits excavation to the open-pit terrestrial mines, more energy is required to drill and crush the ores in the hyperbaric conditions [1], which can be done whether by static trench cutters [1] or by mobile mining crawlers [2]. In addition, the ores vertical transportation by subsea pumps requires several MW electrical power that can be supplied by all-electric subsea motors or hydraulically from water injection motors located on the surface. The power requirements can be fulfilled by an offshore or subsea power network. As the SMS mines are usually in remote locations, the straightforward solution will be an isolated offshore grid mounted on a vessel or platform similar to the most of offshore Oil & Gas projects. These power systems resemble the onshore microgrids for industrial purposes operating in island mode. However, in contrast with the onshore power networks, there are space and weight limitations in offshore infrastructures, which impose the design compactness to be a priority. In addition, having a very high reliability is necessary in the design approach of the offshore projects due to the extraordinary high expenses corresponding to repair and maintenance. The other design criterion is to improve the power system efficiency in order to reduce the size of the power equipment cooling apparatus, operational costs and CO2 emissions produced by diesel/LNG onboard generators. There are a few studies considering power system distribution for seafloor mining industry. Among them, [3] has investigated the AC and DC alternatives for SMS mining in 2400 m water depth by considering Solwara 1 project scenario introduced by Nautilus Minerals Inc. [2]. In this study, a power system design tool will be presented taking into account various water depth, power consumption levels, different distribution configurations (AC and DC) and the aforementioned design criteria.

Jan 1, 2018

By Irwan Halim, Seung Han Kim

This paper will describe design of precast segmental tunnel lining for the Pawtucket CSO Tunnel Project in Providence, Rhode Island. The tunnel is 11,700 LF long with 30-foot finished diameter to be constructed in complex sedimentary rocks. Special features of the segments include a large keystone and no connector used on radial joints. The typical segments will be steel fiber reinforced, and hybrid segments with additional steel rebars and shear bicones will be used around the adit openings without use of any structural framing. The important design considerations will be discussed, including special 3D segment to adit connection analyses performed.

Dec 1, 2022

By David Mast, Irwan Halim, Seung Han Kim

Nowadays more infrastructure tunnel projects are procured using design-build method. In this environment, the Owner’s engineer would typically provide performance requirements for the design-builder, and the Contractor’s designer would work with the contractor to design the tunnel lining based on the Contractor’s means and methods and manufacturing process. This paper will describe the typical requirements provided by the Owner based on its design objectives, and the means and methods by the Contractor that would significantly impact the design. Project examples and recommendations for Owner’s requirements will be provided that can optimize the design and still achieve the Owner’s performance objectives.

Jun 13, 2021

"Pilot plants for pressure hydrometallurgy represent special design and project execution challenges. Over the past twenty years, Zeton has designed and fabricated a variety of world-class pressure hydrometallurgical pilot-plant facilities for the nickel industry, and this paper discusses design considerations and strategies related to such projects. Project execution methods are also discussed, and guidance is given for the selection of materials of construction and for the selection of appropriate pressure and temperature design points for pressure hydrometallurgical pilot equipment. The paper concludes with a discussion of the need for process similarity with future commercial operations and the realities of pilot-scale equipment.INTRODUCTION The process technology developer or owner and the designer/fabricator of a new pilot-plant facility are faced with some difficult technical choices even after the decision to build a dedicated plant has been taken. A pilot-plant project is usually on the critical path of a large commercial project involving investments many multiples greater than the capital cost of the pilot plant. Schedule savings in the design, manufacture, and commissioning of the pilot plant or in a rapid completion of the experimental program can be disproportionately beneficial to the overall development project. However, inappropriate shortcuts resulting in major oversights can be disproportionately problematic. A number of considerations and suggestions for both the project execution approach and the process engineering design of pressure hydrometallurgical pilot-plant facilities are presented as a guide for potential owners and operators of new pilot-plant equipment and facilities. These suggestions are particularly applicable to the nickel industry, where the majority of our firm’s prior hydrometallurgical experience was obtained. This paper is an update to an earlier publication (Martin, 2004), offering an opportunity for a new generation of metallurgists and engineers to learn the specialist requirements of pilot- and demonstration-scale plant design, which are key functions in the development and commercialization of new processes."

Jan 1, 2017

By H. E. Bartlett

In the operation of some flotation plants treating platinum ores it was found that there were imbalances between the inputs and outputs. The inputs and outputs were sampled as slurries and it was determined that the imbalances arose from biases in the sampling, despite the samplers having been designed according to well-established rules. The launders feeding the sample cutters, and the sample cutters themselves were redesigned using finite element analysis to model the flows. A new set of design rules were formulated. The application of a Components of Variance Analysis, to determine the variance of primary and secondary sampling and of analysis in the lab for a concentrate is presented to illustrate the need for frequent sampling of process streams.

Jan 1, 2002

By P. T. Bissert, J. P. Ducarme, J. L. Carr, A. K. Smith

"The continuous mining machine is a key piece of equipment used in underground coal mining operations. Over the past several decades these machines have been involved in a number of mine worker fatalities. Proximity detection systems have been developed to avert hazards associated with operating continuous mining machines. Incorporating intelligent design into proximity detection systems allows workers greater freedom to position themselves to see visual cues or avoid other hazards such as haulage equipment or unsupported roof or ribs. However, intelligent systems must be as safe as conventional proximity detection systems. An evaluation of the 39 fatal accidents for which the Mine Safety and Health Administration has published fatality investigation reports was conducted to determine whether the accident may have been prevented by conventional or intelligent proximity. Multiple zone configurations for the intelligent systems were studied to determine how system performance might be affected by the zone configuration. Researchers found that 32 of the 39 fatalities (82%) may have been prevented by both conventional and intelligent proximity systems. These results indicate that, by properly configuring the zones of an intelligent proximity detection system, equivalent protection to a conventional system is possible. INTRODUCTION Underground coal miners are exposed to a variety of hazards on a daily basis. Among coal and rock dust exposure, high noise levels, roof and rib falls, and the potential for fires and explosions, operating and working with heavy machinery poses a significant risk to miner safety. One of the most hazardous jobs is operating or working nearby a continuous mining machine (CMM). According to Mine Safety and Health Administration (MSHA) statistics, 39 miners have been fatally struck or pinned by a CMM since 1984. In an effort to prevent future striking and pinning fatalities from occurring, proximity detection systems have been developed and are now required on all operating CMMs in underground coal mines with the exception of full-face CMMs [1]. Commercially available proximity detection (cPD) systems are based on the principle of magnetic flux density (B-field). Typically, four magnetic field generators are positioned on a CMM, and personal alarm devices (PADs) are worn by the miners that detect magnetic flux density difference. As a miner wearing a PAD gets closer to the machine, the flux density increases. Zones can be constructed around the machine so that an alarm will trigger on the PAD based on the flux density."

Jan 1, 2016

By T Ladinig

Raise caving is a novel cave mining method, which has been proposed for mass mining at increasing mining depths in LKAB operations. The method makes use of the raise mining technology and an active stress management approach. For the implementation the method is split into two phases, namely a de-stressing phase and a production phase. In the de-stressing phase, a slot-pillar system is established. The purpose of slots is to provide stress shadows and the purpose of the large pillars is to control stress and seismicity. The production phase follows after the de-stressing phase. Required infrastructure in the production phase is developed delayed in stress shadows and bulk extraction takes place in de-stressed zones. Eventually the pillars crush and they are extracted in the production phase. A comprehensive research and development program has been launched to develop the raise caving method towards implementation. As part of this program a full-scale test site of raise caving will be conducted as well as raise caving operations are planned for depth extensions in LKAB mines. This paper discusses the design of raise caving operations in practice at the LKAB mines. In particular, the purpose of the paper is to focus on requirements for the development and design of a raise caving operation. The development of raise caving is discussed from a systems engineering perspective as well as from a management perspective. The functional requirements in the destressing and production phase are outlined and discussed in the paper. The discussion is on basis of the main elements of the raise caving system, such as slots, stopes, pillars and infrastructure. Critical rock engineering design requirements in the de-stressing and production phase are highlighted and dependencies between individual main elements are identified. The analyses show that pillars are especially important for the success of the mining method. Overall, the analyses show that raise caving is a complex system and that its development demands a multidisciplinary approach.

Mar 29, 2023

THE Yallourn chimney has aroused interest, as it is, for the time being, the tallest structural erection in Australia. Its height was not decided on, however, with the object of breaking records, but is purely incidental to the purpose which it serves. Theboiler plant at the briquetting works (first instalment) consists of five Babcock and Wilcox land-type water-tube boilers, each of 4510 sq ft. heating su:r£ace and 225 sq. ft. grate area in the form of step grates. Four boilers will normally produce 73,000 lb. of steam per hour at a gauge pressure of 265 lb. and a temperature of 6500 F., the fifth boiler being a reserve. Each boiler will consume about 100 tons of Yallourn coal per 24 hours. Provision is made for future installation of economizers, should it be found desirable. Designing for this condition, and allowing for a waste gas temperature of 3500 F. and an air temperature exceeding 1000 it was found necessary to have a draft of about 1.3 in. (water gauge) at the base of the chimney, and to deal with about 2000 cub. ft. of gases per second. Estimates were made of the cost of providing the necessary draught by means of fans and by means of a tall chill).ney. The annual charges of the two methods differed only slightly, and the tall chimney wasselected as being the more general practice in briquetting factories.Estimates were prepared for brick and concrete chiIlllleys. Yallourn bricks at that time were hand-made, and, while very suitable for domestic work, were not capable of withstanding high compressive stresses. The chimney design to suit these bricks thus required to be on very ample lines, resulting in high cost. Machine-made bricks from Melbourne would cost about £5 10s. per thousand on the site, with extra for radials, so that high cost again resulted. On the score...

Jan 1, 1924

By Jamal Hematian

Understanding the behaviour of rocks in a high horizontal stress field, such as that in Australia, is critical when analysing the stability of underground structures. This paper addresses the significance of the post-failure behaviour of rocks on the stability of underground structures which are under the influence of a high horizontal stress field. The research work was conducted through a combination of numerical modelling, laboratory testing and field investigation. A number of 2-D FE model of roadways were constructed based on the data obtained from laboratory testing and field investigations. The models were then analysed using three different solution techniques; simple linear-elastic, non-linear elastic-plastic and elastic-plastic with consideration of post-failure behaviour (softening model). Results indicated that the post-failure behaviour of rocks significantly influence the stress and displacement patterns around the roadway. The stress and displacement patterns as well as the extent of the yield zone around the roadway predicted by the softening model were in good agreement with that from the field study. Based on the results of the study, an appropriate support system has been suggested to govern the stability of roadways.

Jan 1, 1994

By Nikolas K. Sokol

Underground construction often requires working within a very congested urban environment, including excavating shafts adjacent to highly sensitive and multistoried structures, sometimes even within such structures. Shafts adjacent to heavily loaded column footings are often required due to space constraints. Invariably, footing surcharges must be considered during the design of shaft rock reinforcement. Rockwedge stability evaluation reveals that column surcharges can greatly impact the ability to meet the desired factor of safety. Design methodologies and examples to deal with these special circumstances are presented.

Jan 1, 2008

By Sahendra Ram, Arnn Kr Singh, Dheeraj Kumar, Rajendra Singh

"Inherent existence of different rooms (openings) along the extraction line in a depillaring panel provides an easy path for the goaf to encroach the working area. Each of these openings in a mechanized depillaring (MD) operation along the extraction line is supported by the roof bolt-based breaker line support (RBBLS) to restrict the goaf encroachment. Different field studies by Council for Scientific and Industrial Research - Central Institute of Mining and Fuel Research (CSIR-CIMFR) found that the RBBLS works effectively during the depillaring under the shadow of stable surrounding ribs/fenders only. It is observed that, generally, these natural supports experience high value of induced stresses after a large amount of void creation inside the goaf. The induced stress creates spalling/loosening of the sides of the natural supports. Field studies also found that the positions of the RBBLS at the goaf edge need to be adjusted according to the depth of this spalling/ loosening. However, a systematic study in field for the correct positioning of the breaker line as per the spalling/loosening under different site conditions is difficult. Therefore, on the basis of the data and guidance provided by these field investigations, a detailed parametric investigation was conducted in the laboratory on simulated models for an effective design of RBBLS in a MD panel. FLAC3D is used for the simulation of the depillaring, and the available empirical formulations for Indian coalfields are used for subsequent calibration. An analysis of stress redistribution for different stages of the MD in simulated models showed the significance of the nature of overlying strata/induced stress for the RBBLS design. Discussing some results of field studies, this paper presents results of the laboratory investigations for an effective design of the RBBLS.INTRODUCTIONContinuous Miner (CM)-based mechanized depillaring (MD) is an important issue for Indian coalfields, where huge amounts of coal are locked up in standing pillars (Dixit and Mishra, 2010). Considerable variations in site conditions of these developed pillars bring a number of technical challenges into consideration during their final extraction. One of these challenges is goaf encroachment/overriding during caving of the competent roof strata. Goaf encroachment/overriding can effectively be controlled, mainly, by suitable design of natural supports (rib/snook/fender). However, there is a requirement of applied supports against the immediate roof as a considerable portion of this roof is exposed due to the presence of different openings along the line of extraction. These applied supports act as a fulcrum at the goaf edge between the working area and the goaf to facilitate the break out of the hanging roof inside the goaf. This is called breaker line support. An effective breaker line support is important for the efficiency of a depillaring operation. Generally, MD adopts roof bolt-based breaker line support (RBBLS) at the goaf edge (Singh, et al., 2014). For the first time in India, roof bolts were applied at the goaf edge as RBBLS in a CM-based MD (Leeming, 2003). In the beginning, three rows of roof bolts were installed as primary and secondary breaker lines support. On the basis of the observations of instrumented bolts, only two rows of roof bolts were used as secondary RBBLS (Ram, et al., 2014). Now, most of the MD operations in India are using only two rows of bolts as RBBLS (Table 1). However, the strata mechanics studies at different MD operations showed interesting characteristics resulting from this support (Ram, et al., 2015)."

Jan 1, 2016

By Madan M. Singh

Although roof bolting has been a major means of strata support for nearly two decades, little attention has been directed towards the design of bolt Installations. The variables involved are interdependent and their study complex. However, some simple tests may be employed to serve as guides to the efficient design of roof bolt systems. Local conditions are continually varying and are important to pattern design. This paper discusses such considerations and suggests techniques which may be employed to effect improved roof control with bolts.

Jan 1, 1967

By Christopher Mark

Roof bolt system design means the selection of the type, length, capacity, and pattern of bolts for a particular application. Despite research efforts dating back 50 years, no design methodology has found wide acceptance. This paper begins by identifying four mechanisms that roof bolts use to reinforce the ground. It argues that the reinforcement mechanism is determined by the roof geology and stress level, not by the type of bolt. Next, the attributes of roof bolts are discussed in the light of recent research, including anchorage mechanism, installed tension, length, capacity, timing of installation, and installation quality. Several significant areas of controversy are identified. Design methods from around the world are discussed, including those based on empirical research, numerical modeling, and roof monitoring. Finally, some simple guidelines for preliminary design of roof bolt systems are proposed based on statistical analysis of roof support performance at 37 U.S. mines.

Jan 10, 2000

By Fred D. Wright

In this paper the principal theories used to design roof bolting systems are presented and discussed. Then the characteristics of various types of roof bolts are presented and finally the interaction between rock and roof bolt characteristics on choice of roof bolts is discussed. Theories can be considered design tools which may or may not be appropriate for a specific situation. It is good for a design engineer to have a number of such tools available and also important that he understand their good features as well as their limitations. Hence, some of the principal theories and classification systems used for design of roof bolting systems are discussed first.

Jan 1, 1982

By Best R. J, Poulos H. G

The method for design of primary roof support for the large todoidal cavern constructed to house the Sydney Opera House parking station is presented. The cavern was constructed with 5 m of rock cover beneath Sydney's Royal Botanic Gardens. Design of rock reinfonnent using a combination of fully grouted rock dowels and Macalloy bars was based on control of horizontal shear movement along bedding features in the roof. A combination of linear arch type analyses and non-linear jointed finite element analyses were used in the design study together with an analysis of the shear resistance offered by fully grouted bolts under shear deformation.

Jan 1, 1993

The basic rule for correct design of a sample plant is that all parts of the material being sampled must have an equal probability of being collected and becoming part of the final sample for analysis. However, this rule is often ignored in the design of sample plants to save capital costs. This is false economy, because the samples taken are likely to be seriously biased and the precision may be compromised. The introduction of bias is particularly serious, because no amount of replicate sampling and analysis will reduce bias once it is present and it is often quite difficult and expensive to subsequently rectify the problem due to space limitations around the primary sampling location. This is also true of secondary and tertiary sampling stages, particularly in terms of the relationship between particle size and retained sample mass. The best strategy is to seek expert sampling advice and design the sample plant correctly at the outset.

Jan 1, 2005

By Howard I. Epstein, John R. Buzek

Thickeners are simply large tanks, usually circular in shape, which are designed to allow settling of solids and to operate with continuous overflow of clear water and underflow of thick pulp. The dimensions of the thickener are usually such that dewatering of very fine pulps may be accomplished while still overflowing clear water. Some thickeners such as the Center, Hardinge and Hydrotator types combine thickening with filtering2 while others such as the Dorr type are pure thickeners. l .2 , 3 A schematic diagram of the traction type Dorr thickener is shown in [Fig 1]. This type is appropriate for tanks over 15 m (50 ft) in diameter. This tank employs a rotating raking mechanism which moves the settled material toward the central discharge. For this and other thickeners, it is common to have a shallow conical tank bottom in order to conform to the geometry of the raking mechanism, and it is often desirable to elevate the tank for ease of access to the product. When the tank does not rest on the ground, the forces resisted by the cone are large, and thick plates must be employed. The fabrication of these tanks requires temporary supports in order to erect the cone. A flat-bottomed tank could also be used because the settled material would soon form a hardened conical surface. However, because of the presence of large bending forces, even larger plate thicknesses are required than for the conical bottom. Significant cost savings often can be realized by the use of a scalloped-bottomed tank such as the one partially shown in [Fig. 2]. The particular scalloped bottom discussed in this paper employs radial beams forming the outline of the cone-shaped bottom. These beams are supported directly by columns. Cone segments are hung between adjacent beams. The exact geometry of these segments depends upon the cone angle and radius, the number of radial beams, and their inclination. The geometry is chosen to satisfy certain clearance restraints and to utilize the material as efficiently as possible. The resulting thickness of these segments is significantly less than that of the equivalent plate for the tank with a conical bottom. This result, along with the simpler fabrication procedures required, accounts for the cost savings associated with this design. The raking mechanism employed may be the same as for the conventional conical bottom since the settled material soon forms a conical surface. Determination of the internal force mechanism for the scalloped bottom leads to designs that utilized material efficiently and thus maximize the cost savings. The complicated geometry of these bottoms along with the difficulty in analyzing the structure are factors which may have limited the use of scalloped-bottomed tanks to date. When such tanks have been built, the uncertainties associated with the internal forces have led to designs that are somewhat inefficient. In this paper, equations relating the geometric parameters are presented along with simplified closed-form solutions for the internal forces in the cone segments, from which the loads applied to the beams and the loads carried to the cylindrical tank shell can be deduced. An example is presented to show the magnitude of the savings which may be realized with this configuration.

Jan 1, 1979