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By Wern-ping Chen, Jean Habimana, Jinyuan Liu, Mirza M. Rabbaig, Robert Barbour

To mitigate and control the combined sewer overflows from 17 outfalls in the City of Detroit, three outfalls in Dearborn Heights and eight outfalls in Redford Township, the Detroit Water and Sewerage Department has completed the preliminary design of a storage tunnel in 2005. In 2006, a final design has revised the alignments and the inside diameter (ID) of the tunnel. The revised tunnel system includes an 11.28-km(7-miles) 9.14-m (30-ft) ID tunnel, a 24.4-m (80-ft) ID pump station, two work shafts about 15.2-m (50-ft) ID each, and 14 drop shafts with various IDs. This paper discusses the latest development of this tunnel system.

Jan 1, 2007

By V. F. Hollister

Epithermal gold deposits occur in and near the marginal fault that circumscribes the Goldfield, Nevada, Tertiary caldera. The gold occurs disseminated in alunite, pyrite, and kaolin- bearing silicified zones that are controlled by the circular faults. Other Tertiary calderas (i.e., Summitville and Red Mountain No. 3) have epithermal disseminated gold deposits located in and near their marginal circular faults in settings that resemble the Goldfield example. These additional caldera- controlled epithermal gold deposits are also characterized by alunite, pyrite, and kaolin-bearing silicified rock that act as hosts for the gold disseminations. The Goldfield District is therefore an exploration model for those seeking disseminated epithermal gold deposits in a caldera setting.

Jan 1, 1986

By Ronald J. Riberich

The Mineral Economics and Management Society (MEMS) held its fifth annual conference in Montreal, Quebec, Canada earlier this year. “The Minerals Industry: Responding to the Global Challenge” was the first MEMS conference to be held outside of the United States. About 125 mining- and minerals-related professionals attended. The MEMS program included six sessions and three distinguished speaker addresses. The session topics included: “Minerals in the Macro economy: Development in Demand,” “Trends in Global Metals Supply: The Producers’ Challenge,” “Global Environmental Issues: Policy Perspectives,” “Global Environmental Issues: Quantitative Analysis” and “Minerals in the CIS: Phoenix or Albatross?” A student session was also offered. It provided a competition for monetary awards for outstanding papers.

Jan 1, 1996

By Stuart Ratcliffe, Denis Kidby

The development of Vitrokele™ Technology over the last 10 years is reviewed with reference to mine site piloting and com­mercial applications. The first mine site piloting was conducted in Australia in 1989 followed by a further six continuous site trials in Australia, Canada and the USA. These major pilot plant studies are complemented by over 50 laboratory scale batch and pilot testwork programmes. The first commercial plant using Vitrokele™ Technology was the Connemara project commissioned in Zimbabwe in 1995. Subsequent to this, three commercial scale projects have been designed using Vitrokele™ to recover precious metals, base met­als and cyanide. The various projects are discussed with relation to the differ­ing flowsheets applied to each particular case.

Jan 1, 1998

In analyzing cost performance, managers must initially consider the issue of scope. Is the analysis for a single responsibility center or multiple centers? For a single period or a number of periods? If multiple responsibility centers are being examined, how can managers compensate for differences in their sizes? Several techniques have been developed to analyze the relationships in a set of financial statements at a single point in time and the trends in these relationships over multiple periods. Cross-sectional techniques focus on the first of these, and time-series techniques look at the latter. Although this text focuses on cost performance, these methods also can be used for revenue-related analyses.

Jan 1, 1999

By Charles H. Arnold, Timothy Fallara, David A. Day, Paul H. Marshall

The Upper Scioto West Interceptor Sewer (USWIS), Parts 1 and 2, consists of approximately 7,128 meters (23,385 ft) of 328 cm (129 in.) diameter tunnel. The project ex-tends from the City of Dublin to Griggs Dam in the City of Columbus. The majority of the tunnel was designed for excavation in rock by TBM. The remaining portions span pre-glaciation formed valleys in-filled with glacially-derived sediments. Tunnel construction in one of the glacial till filled sections includes excavation by drilling and controlled blasting. The other section will be constructed by ground consolidation followed by excavation by TBM. This paper describes the methods employed to mine the glacial till filled valleys.

Jan 1, 1997

By Alan M. Muir Wood, Gerhard Sauer

There axe two essential features of administrative practices in tunnelling in order to provide proper encouragement to innovative and economic tunnelling: first, that there should be a continuity in the decision making at all stages so that the full implications of decisions in early stages of planning and design are understood; second, that there should be appropriate provision for variation so that the greatest possible benefit can be derived from modifying the working scheme in relation to the characteristics of the ground and from study of its behaviour during execution of the work. Examples are given from the Authors[?] experience as to the benefits to be derived from the application of such principles.

Jan 1, 1981

By David Jenkins

Grefco Inc. operates two diatomite mines in the western Santa Ynez Mountains. The larger of the two mines, the Palos Colorados Mine, is located approximately seven miles southeast of Lompoc. The Miguelito Mine is located about two miles south of Lompoc on the west side of the Miguelito Canyon. Diatomite from the Palos Colorados and Miguelito mines is trucked to the Grefco plant at Lompoc for processing (Figure 1). HISTORY Grefco, Inc. evolved from the originating Dicalite Company which in 1929 began operations at the Walteria plant in the Palos Verdes Hills south of Los Angeles. In 1942 Dicalite leased the Palos Colorados mine at Lompoc. In 1944 the Dicalite Company was purchased by Great Lakes Carbon Corporation.

Jan 1, 1995

By F. F. Aplan

Estimations have been made of the tonnage of raw ores and coal treated by various beneficiation processes. The amount treated by gravity concentration is substantially greater than that treated by flotation, with coal representing the bulk of the material treated by gravity means. A discussion is given of the trends and anticipated improvements in gravity methods. Except for the concentration of iron ores, magnetic and elec- trostatic separation processes find their greatest use in the beneficiation of non-sulfide ores. Exciting new developments in magnetic materials and separation process (and, to a lesser extent, in the electrostatic process) indicate a substantial increase in the application of such processes to ores and a broad variety of non-ore uses.

Jan 1, 1989

By D. R. Nagaraj

The practice of nonsulfide minerals flotation can be best characterized as an evolutionary blend of scientific theory and art. Although extensive fundamental studies have been carried out in the past several decades, and significant theoretical aspects have been developed, plant practice has developed the art form, often ahead of the theory, which is somewhat in contrast to sulfide minerals flotation. Several excellent review articles have been published in the past highlighting both the theoretical aspects and plant practice. An overview of nonsulfide flotation is presented here. Major differences in sulfide and nonsulfide flotation are highlighted. An assessment of the state of nonsulfide flotation, recent advances made in flotation processing, and industry needs are also given.

Jan 1, 1999

By B. Denby, R. Hollands, S. Cooper

Augmented Reality (AR) is a technology that can be used to mix computer-generated images of data with views of the real world. The University of Nottingham is developing AR technology in a major research project which can be used to assist mining companies in visualising complex mine data whilst out in the field. The technology comprises of integrated GPS surveying technology and electronic orientation devices to provide location and viewing information, video capture via digital camera and portable computing hardware to overlay 3D models on views of the real world. The paper describes the concepts of the technology in some detail and concentrates on the possible applications of this in the surface mining and exploration industries.

Jan 1, 2002

By Kostas Fytas, Sebastien Perreault

This paper presents EOLAVAL, an integrated mine ventilation design software. In its new expanded version it is a user friendly and fully interactive computer package. The features of the new version are a graphics interface fully compatible with Autocad files, an integrated database of fan characteristics and the optional use of the thermodynamic approach in carrying out network simulations. This software can be used in underground mine ventilation planning: mine ventilation network analysis and simulation, economic design of airways, auxiliary ventilation design, calculation of a mine air heating plant, and evaluation of the natural ventilation and pressure losses in a mine shaft. This paper presents a case study illustrating the use of the computer package in mine ventilation design.

Jan 1, 2002

By John Jonkman

Many companies in the mining and minerals processing industry are finding themselves in the transition stage from the Industrial Age to the Information Age and are trying to become prepared for the Knowledge Age. To remain competitive in the decades ahead, they are faced with integrating the enterprise through the use of computers and networks. This paper discusses some common human and organizational barriers to enter- prise integration. It proposes how to develop the organizational and human' networks to match the capabilities of the technical networks which are being' implemented. Ten practical considerations are then presented for consideration in the executive suite in addressing the human side of implementing the computer integrated enterprise.

Jan 1, 1989

By Bruce Kennedy, Dan Nilsson

Mining means drilling and blasting in order to break down the rock, loading and transport, and often also crushing the ore down to a suitable size. These operations can be done in open pits or in underground mines, and also, to a lesser extent, in marine mining. The same operations are also used in various types of construction, i.e., for roads, water power stations, etc. Before beginning a detailed economic analysis of the factors which enter into deciding whether to mine by open-pit or underground mining, and at what point a change should be made from open-pit to underground mining, or vice versa, it is of interest to consider some general factors.

Jan 1, 1982

By Hans Skretting, Abraham A. Dor

This paper briefly reviews the historical development of the Rotary Kiln-Electric Furnace Process, which was first applied commercially to the treatment of qarnieritic ores in New Caledonia in the mid-fifties. It describes various technological improvements introduced, since, in industrial plants or developed in pilot facilities where a wide variety of nickel oxide ores has been treated success- fully over the years. Major categories of ores are characterized. The effect of their physical and chemical properties on their performance in the electric furnace is discussed. The relationships between ore composition, ferronickel grade and slag composition are analyzed and their effect on slag and metal tapping temperatures, nickel recovery, and electrode voltage are discussed.

Jan 1, 1979

By P. R. Desam, J. D. Miller, A. Datta

The flow behavior of bubble-particle aggregates in separation tanks is important for many flotation systems, particularly for wastewater treatment. These aggregates can be considered as the dispersed phase in a continuous liquid phase of water and the flow characteristics determine the efficiency of the bubble separation process. In this work, a general methodology for the computational fluid dynamics (CFD) simulation of a bubble separation tank is described. This system is analyzed by Eulerian-Lagrangian approach. The momentum transfer from the dispersed phase to the continuous phase is quantified using the Particle-Source-In Cell (PSI-Cell) method. With CFD simulations, the effectiveness of different tank design parameters are evaluated in terms of the extent of bubble separation.

Jan 1, 2000

By C. Pieper, J. B. Pateiro Fernandez, S. Möllerherm

"Since the United Nations conference on "environment and development" in Rio de Janeiro in 1992, the term "sustainable development" or short "sustainability" is used more and more in social-political discussions. Agenda 21 calls on the countries on national level as well as governmental and non-governmental organisations on international level to develop a concept of sustainability indicators to measure the progress towards sustainability. This paper deals with the development of an evaluation system for sustainability in the minerals extraction. By their application, aspects of sustainable development in the raw minerals industry are to be systematically conceived and assessed. This project has been carried out on behalf of the German Federal Ministry of Economics and Labour."

Jan 1, 2005

By Harold R. Kokal, Madhu G. Ranade

A metallurgical/flux is a substance that is added to combine with gangue (unwanted minerals) during ore smelting, with impurities in a molten metal, or with other additives in metal refining processes to form a slag that can be separated from the metal. Because slags are immiscible with the metallic melt and are of lower density, a separation of the slag and metal occurs if the viscosity and surface tension are of the proper values. The chemistries of slags are adjusted to provide the proper melting point, viscosity, surface tension, conductivity, specific heat, density, or chemical properties to effect the desired task. In addition to absorbing impurities from the metal, the purposes of the slag are to thermally insulate the metal bath, protect the molten metal from the atmosphere, and control the chemical potential of the system. Several excellent references on slags and metallurgical fluxes are available (Boynton, 1980, Lankford, Jr., et al., 1985, Turkdogan, 1983, Rosenqvist, 1974, Fine and Gaskell, 1984). The function of the slag might vary at different stages within a process prior to final melting. For example, the slag composition and behavior will change as materials descend in the iron blast furnace, or as they melt in the early stages of formation of steel- making slags. Selection of the chemistry for a slag might be influenced by factors outside the primary function as when blast furnace slags are used to make cement, rock wool insulation, or fertilizer supplements. Sometimes slags contain a sufficient amount of valuable recoverable elements to be sold as raw materials for other processes. Fluxes are often referred to as acid, basic, or neutral. Acid fluxes are those that generally form acids in water and bases are those that would generally form bases in water. Typical acid fluxes are silica, alumina, and phosphorus, although alumina can function as either an acid or base. Typical basic fluxes are lime and magnesia. Fluorspar, or calcium fluoride, is a neutral substance because it can be viewed as the reaction product of a base and an acid. The degree of acidity (ratio of acids to bases) or basicity (ratio of bases to acids) is often specified to characterize the slag chemistry for a particular system. The system might also be referred to as acid or basic depending on the choice of slag, for example, basic steelmaking uses slags with more bases (lime and magnesia) than acids (silica and alumina). Many forms of minerals and compounds have been used as fluxes depending on the process requirements, availability, costs, requirements for recycling of intermediate products, and environmental concerns. Because slags are most often mixtures of oxides and silicates, fluxes are usually oxides, carbonates (which decompose to oxides) and silicates. Slags comprising phosphates, borates, sulfides, carbides, or halides have also been used (Rosenqvist, 1974, Moore, 1981, Szekely et al., 1989). In ironmaking and steelmaking, some acidic components are sometimes added. In nonferrous processes slags and fluxes are acidic with silica as the primary component, and although the use of basic flux such as limestone or lime is not extensive, some amount is used to modify slag properties and some refining slags are lime based. The production of iron is accomplished by smelting of ores, pellets, and sinter in blast furnaces with subsequent refining of molten iron and scrap in oxygen-blown processes. The electric furnace is used to make steel, stainless steels, ferroalloys, and special alloys, whereas ferromanganese is often made in blast furnaces. Fluxes are used in all of these processes, and either limestone or lime is the major flux component with some dolomite, dolomitic lime, silica, alumina, and fluorspar being used. In ironmaking, the flux is added either by direct charging or through sinter and fluxed pellets. In steel refining by the basic oxygen process, flux is added as lime and dolomitic lime that are either charged as lumps or injected as fines. Some small amount of limestone is sometimes used. Fluorspar is often added as lumps or mixed with other fine materials in briquettes. Alumina is sometimes added to blast furnaces either by direct charging of sized lumps or through sinter. Typical acid fluxes are sand, gravel, quartz rock, used silica brick, or raw siliceous ore (Lankford, Jr., et al., 1985). Olivine, which is a magnesium-silicate mineral, has been added to iron blast furnaces to enhance removal of alkalis (Lankford, Jr., et al., 1985). Alumina in the form of bauxite, aluminiferous clay, and recycled alumina brick has been used as flux. Alumina can function amphoterically as either an acid or base, for example it can form aluminum silicate in high silica slags or calcium aluminate in lime-bearing slags (Lankford, Jr., et al., 1985). Limestone (calcium carbonate) and dolomite (magnesium-calcium carbonate), or fluxstones as they are sometimes called (Boynton, 1980), and their calcined forms, lime and dolomitic lime are the major basic fluxes. In the latter cases, the carbonates are de- composed in a kiln-type process to drive off carbon dioxide that might otherwise interfere with the subsequent smelting or refining process or require expensive forms of energy to effect the decomposition (e.g., by combustion of coke in the iron blast furnace). Limestone is considerably less expensive than lime because it is not calcined; however, lime is far more difficult to handle and reacts readily with water. Dolomite and dolomitic lime are used for their magnesia content. Fluorspar is a neutral flux often used as an additive in steel- making slags to improve fluidity, but it has also been used in combination with lime as a primary slag in electroslag refining (Duckworth and Hoyle, 1969). Fluorspar is available in several grades, with the lowest grade often used for steelmaking. When the price of fluorspar has risen, substitutes including aluminum smelting dross, borax, manganese ore, titania, iron oxides, silica sand, and

Jan 1, 1994

By William Lyman

GENERAL DESCRIPTION Shrinkage or shrinkage stoping refers to any mining method in which broken ore is temporarily retained in the stope to provide a working platform and/or to offer temporary support to the stope walls during active mining. Since ore "swells" when broken, it is necessary to shrink the muck pile a corresponding amount by draw¬ing some of the broken ore out as the stope is advanced-hence the name. Broken ore retained during stoping is drawn out after the stope has reached its limits. The stope may be left empty or may be filled with waste contemporaneous with, or subsequent to, the final draw. Traditionally the method implies conventional overhand stoping methods with miners working between the muck pile and the stope back, in a space which advances updip with mining and is maintained by balanc¬ing "swell" with "shrink." The shrinkage classification is also applicable to so-called "semishrinkage" methods in open pillar-supported stopes where broken ore is temporarily retained as a working platform but offers no wall support; and to various blasthole shrinkage methods which utilize broken ore temporarily retained in the stope for wall support, but which do not require miners to work from muck pile in the stope. The method is generally applied to steeply dipping veins of strong ore between strong walls. APPLICATION Geometry The geometry of a shrinkable vein is described in terms of dip, width, and regularity along dip. Overall strike and dip dimensions and irregularities along the strike generally impose no restrictions on the method. Dip is ideally 1.2 to 1.5 rad (70 to 90°). As dip falls below 1.2 rad (70°), the shrinkage draw begins to strongly favor the hanging wall side, thus leaving a poor working platform for conventional overhand work. This is particularly true in relatively wide stopes. The sup¬port afforded to the hanging wall also diminishes with decreasing dip, reaching nil as the dip approaches the repose angle of broken ore. Dips below 0.78 to 0.87 rad (45 to 50°) are not generally shrinkable except by open stope "seinishrinkage" methods. Minimum mining width is fixed by working space requirements in the stope-generally about 1 m. Shrink¬age in narrower veins requires that waste rock from one or both walls be broken with the ore and the attendant dilution accepted to achieve the minimum width. Nar¬row stopes are less suitable, encouraging hang-ups and bridging of broken ore, with the attendant problems of erratic draw and incomplete recovery of broken ore. Maximum practical width may be 3 m or less to over 30 m, depending upon the competency of the ore and its ability to stand unsupported across the stope back. This is a vital safety consideration in conventional over¬hand stopes, but is much less of a factor in blasthole shrinkage methods. Very wide veins and massive ore bodies have been mined by transverse vertical shrinkage panels separated by transverse vertical pillars which are either abandoned or recovered later by other methods. Regularity along the dip is a prerequisite of shrink¬age as there must be no serious obstruction to the flow of broken ore downward through the stope to the sill level. Gentle rolls along the dip are acceptable if the local footwall dip everywhere exceeds 0.78 to 0.87 rad (45 to 50°). Off-dip hanging wall and/or footwall splits can generally be mined selectively from a conventional shrink stope as they are encountered without ad¬versely affecting subsequent continuation of shrinkage mining updip on the main vein. Vertical offsets or major rolls along the dip which cannot be "smoothed over" generally require that a sublevel be established with new draw control development. Blasthole shrinkage methods are much less flexible (and thus less selective) in their ability to accommodate any of these irregularities. Ground Conditions The wall rock must be strong enough to stand with the minimal support afforded by the dynamic mass of broken ore in the stope. During active mining, local sloughing from the walls is restrained, but the broken ore affords little, if any, useful resistance to closure of the stope walls. Such squeezing, if present, may bind up the stope and cause the loss of much ore. Pillars left between and/or within stopes are effective in preventing closure but reduce overall recovery. Walls may be re¬inforced by bolting after each stope cut in conventional shrinkage but not in blasthole shrinkage. Ore in place must be strong enough to stand with no natural support across the stope width, although tem¬porary artificial support or reinforcement may be used locally in conventional stopes. Some spalling or sloughing is permissible in blasthole shrinkage as men are never present in the stope. Physical and/or mineralogical characteristics of the broken ore may impose restrictions on stope design and/or operational plan¬ning, and may even preclude the use of shrinkage al¬together. Examples include: ores which, when broken, are cohesive or which tend to pack or cement together under the influence of ground water, wall pressure, and/ or chemical reaction. Such conditions precipitate er¬ratic draw during mining and often result in difficult and/or incomplete final draw; pyritic ores which oxidize very rapidly in the stopes and may generate heat, imposing a fire hazard by spontaneous combustion; sulfide ores which oxidize sufficiently in the stopes to adversely affect mill recovery by flotation; and ores (es¬pecially those containing uranium minerals) which ex¬ude radon gas and thereby impose ventilation constraints on stope design. In most cases these problems can be minimized by limiting the size of stopes, by minimizing the duration of mining activity in each stope, and by promptly drawing each stope empty following comple¬tion of mining.

Jan 1, 1982

By W. M. Ma, Daniel W. H. Su, K. Centofanti, Yi Luo, W. L. Zhong, Syd S. Peng

2.1 INTRODUCTION When total extraction of an opening of sufficient size is reached in a horizontal coal seam, the roof strata in the overburden deform continuously to reach a new equilibrium condition. The severity of deformation decreases upward toward the surface. As the downward saggings of the strata propagate and reach the surface, there will be a depression zone on the surface directly above, but extending beyond the edges of the underground opening. This is the surface subsidence basin or surface subsidence trough. The surface subsidence basin is circular in plan view, if the coal seam is horizontal and the mined-out opening is square in shape. But it is rectangular with rounded corners or elliptical if the coal seam is horizontal and the mined-out opening is a long- and thin rectangle or a short-rectangular, respectively (Fig. 2.1). Most underground openings (e.g., longwall panel) assume rectangular shape when total extraction has been completed. Theoretically the edges of the subsidence basin are the points of zero subsidence. But it is difficult to exactly locate the points of zero subsidence. Therefore in practice the points with vertical subsidence of 0.4 in. (10 mm) are used. The final subsidence basin is that which exists long after the mining has been completed, because its magnitude and shape are quite different from the dynamic subsidence basin formed while the face is moving. 2.2 CHARACTERISTICS AND TYPES OF DEFORMATION IN THE FINAL SUBSIDENCE BASIN For a horizontal coal seam, every point in the subsidence basin moves toward the center of the basin. Subsidence is maximum at the center of the basin. Any cross-section that passes through the point of maximum subsidence and either parallel to AB or CD line (Fig. 2.1) is a major cross-section along which principal directions of surface movements occur. However among those infinite numbers of major cross-sections, two specific ones are of special significance, not only because the magnitudes of surface movements are the largest, but also because they are the most easily identifiable directions, i.e., one that is parallel to the faceline at the center of the basin (CD in Fig. 2.1) and' the other is that perpendicular to the faceline but parallel to the diction of face advance (AB in Fig. 2.1). Nearly all the subsidence data obtained in the US have been derived from these two cross-sections, although some cross- sections parallel to CD but near the edges of the panel have also been included. In addition to moving horizontally toward the center of the basin, every point in the basin also subsides vertically. The magnitude of subsidence increases toward the center of the basin. Therefore surface subsidence is a three-dimensional problem and should be treated so in all cases. On all the major cross-sections, only principal subsidence and principal displacement occur. Since subsidence and displacement vary continuously in every major cross-section, three additional deformation components are de- rived, i.e., slope, curvature, and strain. On all other non-major cross-sections on the other hand the five components are accompanied by two additional components, i.e., twisting and shear strain. The seven components of the surface movement are defined as follows (Fig. 2.2): 1. Subsidence, S. On any cross-section, the vertical component of the surface movement vector is called surface subsidence. It generally points downward. But sometimes it points upward in areas ahead of the faceline or beyond the edges of the opening. In such cases it is a surface heave which is usually less than 6 in. 2. Displacement, U. On any cross-section, the horizontal component of the surface movement vector is called surface horizontal displacement. It generally points toward the center of the subsidence basin. But in steep terrain, it moves along the downdip direction 3. Slope, i. On any cross-section, the difference in surface subsidence between the two end points of a line section divided by the horizontal distance between the two points is called the surface slope of the section. 4. Curvature, K. On any cross-section, the difference in surface slope between two adjacent line sections divided by the average length of the two line sections is called the surface curvature of those two line sections. There are two types of curvature: con- vex or positive curvature and concave or negative curvature. 5. Horizontal strain, e. On any cross-section, the difference in horizontal displacement between any two points divided by the distance between the two points is called horizontal strain. If the distance between the two points is lengthening, it is tensile strain with positive sign. Conversely, if it is shortening, it is compressive strain with negative sign 6. Twisting, T. On the surface of the subsidence basin, the difference in slope between two parallel line sections divided by the distance between the two line sections is called twisting. 7. Shear strain, y. Shear strain is the changes in internal angles of a square on the surface of the subsidence basin or on any major cross-section. It is the summation of the differences in incremental (or decremental) lengths between the two opposite sides divided by the original distance between the two opposite sides. More precisely, the surface deformation indices (i.e., slope, strain, curvature, twisting and shear) are defined by derivatives of surface movement components. For simplicity, the x- and y-axes of the cartesian coordinate system are set to be parallel and perpendicular to the cross-section of interest, respectively. In such a coordinate system, slope and curvature along x direction are the first and the second derivatives of the vertical components (S) of surface movement with respect to x, respectively, or i, = ds/dx and kx = d2s/dx2. Horizontal strain along x direction is the first derivative of the component along x direction of the horizontal displacement,

Jan 1, 1992