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By Cahit Helvaci, Robert B. Kistler

Borates are defined as ' 'salts or esters of boric acid; a compound containing the radical B203" (Bates and Jackson, 1987). Borates are defined by industry as any compound that contains or supplies boric oxide. A large number of minerals contain boric oxide, but the three that are the most important from a worldwide commercial standpoint are: borax, ulexite, and colemanite. These are produced in a limited number of countries (Fig. 1), dominated by the United States and Turkey, which together furnish about 90% of the world's borate supplies (Lyday, 1991). Production in the United States originates in the Mojave Desert of California; borax and kernite are mined by US Borax from its large deposit at Boron. Borate containing brines are pumped from Searles Lake by North American Chemical Co., and a limited amount of colemanite is mined by Newport Mineral Ventures from Death Valley. Turkish production is controlled by Etibank, the national mining enterprise, which supplies most of the commercially traded ulexite and colemanite from mines in the Bigadic and Emet Districts, plus borax from the huge deposit at Kirka. Borate minerals have been employed in a wide range of uses for many centuries, dating from at least the 8th century when they were used primarily as a flux for assaying and refining gold and silver. Their valuable properties and relative rarity soon stimulated international trade in borates; Marco Polo claimed to have trans- ported Chinese borate minerals from Tibet to Europe, and his home port of Venice was the center for borate imports and use throughout the Middle Ages (Travis and Cocks, 1984). Borates were traded at relatively high prices for highly specialized applications into the late years of the 19th century. At that time they were being used for medicines, food preservatives, ceramic glazes, and in expanded applications as metal fluxes. It was in that era that borax was discovered in Clear Lake, CA, and more significantly, the playa deposits of western Nevada were found and exploited by F.M. "Borax" Smith and others. Research and development by Smith's company began the evolution of borates from a high priced commodity with a few specialized uses to the relatively low priced chemical raw material used in large tonnages on a worldwide scale today. Borates are often defined and sold by their boric oxide or B,03 content, and most statistical data are listed in tons of B203. Of the products sold by the industry, borax pentahydrate or 5 mol and boric acid are the most commonly traded commodities. Boric acid plants are operated by all of the major borate producers. Glass fiber insulation is the major end use in the United States followed by textile glass fiber and borosilicate glass, detergents, and ceramics. Detergent usage continues to be a major end use in Europe.

Jan 1, 1994

By R. Schuerch, C. Cimiotti, M. Piemontese, N. Karlin, P. Perazzelli, P. Halton

The new Los Angeles, California JWPCP effluent outfall tunnel will transport secondary-treated effluent from the Joint Water Pollution Control Plant in Carson to White Point Manifold. The tunnel will be approximately 7 miles (11 km) long with a finished internal diameter of 18 ft (5.5 m). The TBM is designed to cope with high water pressure up to 10 bar. The geotechnical challenges are due to the heterogeneous subsurface conditions: in the first half of the alignment, the tunnel runs through soils with a low overburden under urban areas, and, in the second half, the tunnel runs through extremely weak, intensely faulted rock masses with high overburden. Following an overview of the project, this paper focuses on the northern portion of the alignment and presents a decision-making procedure developed during pre-excavation phase in order to cope with the expected heterogeneous conditions during mining. The risk assessment and the TBM operational design of the southern portion will be dealt with in a future paper.

Jun 13, 2023

By W. F. Cannon

Many high-grade manganese deposits of the world occur in marine transgressive sedimentary sequences deposited on stable platforms. These include the Nikopol and related deposits in the Soviet Union and Groote Eylandt, Australia, among others. We suggest that the Atlantic and Gulf Coastal Plains and the vast area of Cretaceous rocks in the middle of North America are favorable provinces for sedimentary manganese deposits because regionally transgressive units are widespread. North America has 16% of the world's land area but only about 0.2% of known high-grade manganese reserves. This disparity is difficult to reconcile in view of the fact that large areas of North America are underlain by rocks that we consider at least broadly favorable to contain manganese ores, and we suggest, therefore, that important high-grade deposits remain to be found in North America.

Jan 1, 1982

By V. C. Rogers, K. K. Nielson

INTRODUCTION An evaluation of the radiological health risks from uranium mining and milling requires the determination of several key parameters. As shown in Figure 1, the first step is the estimation of the radioactive source term. The radionuclides in the ore consist of the 238U decay series nuclides shown in Figure 2, the 235U series nuclides, and 40K. The 238U decay series isotopes dominate the source term, with the 235U series isotopes causing less concern and 40K remaining at background levels. [ ] Specifically, the risks from uranium mining and milling are mainly associated with 230Th, 226Ra, 222Rn, and its short-lived daughters. These radioisotopes are mainly alpha-particle emitters; hence, some dispersion mechanism is necessary to bring them into intimate contact with man so that they can be inhaled or ingested For water pathways, the leaching of the isotopes from [ ] the solid ore or tailings provides a measure of the amount of contaminant initially available to the environment. For the air pathway, dust-creation mechanisms such as blasting, crushing or general resuspension processes dominate for 226Ra and 230Th. However, 222Rn, being a chemically inert gas generated from the decay of 226Ra, can migrate through the ore, overburden and tailings over considerable distances. As shown in Figure 1, the next step in the pathway to man is environmental dilution and delay. For the water transport mechanism, the delay in the isotopes reaching an accessible water supply may be considerable (several thousand years or more), but for airborne nuclides the dispersion in the atmosphere is rapid and constitutes the main mitigating factor. Considerable ventilation is provided in underground mines to dilute and remove radon and its daughters in order to keep their concentrations low and thereby minimize their inhalation by miners. The rate of uptake by both the workers and the general public is often difficult to ascertain. It involves breathing rates, rates of water consumption and other poorly-defined parameters. The final steps are the risk estimators used to predict doses and cancer rates from the inhaled radon daughters and ingested or inhaled radium. Many

Jan 1, 1981

By Christof Brewka

Los Pelambres, 200 km north of Santiago, Chile, is the latest in a series of mega-projects developed in this part of the world. While most of its predecessors are spread over open desert, the Los Pelambres mine is nestled inside a narrow alpine valley high in the Andean Mountains. To handle the daunting task of transporting the mined copper ore more than 12 km and 1,400 vertical meters downhill to the concentrator plant, a gigantic belt conveyor system (capacity of 8700 mtph, 1800 mm wide ST 7800 steel cord belt, 2.5m diameter pulleys, an elaborate braking system including a mechanical failsafe and large reducers with a total installed drive power of 25,000 kW) has been employed. Many of these components have pushed the limits of conventional belt conveyor design.

Jan 1, 2000

By Wern-ping Chen, Joseph Pratt, Thomas G. Brueckner, Tracy K. Lundin

To address and mitigate discharges from combined sewer overflows in the Providence, Rhode Island area, the Narragansett Bay Commission completed a comprehensive Combined Sewer Overflow (CSO) Facilities Plan in 1993 which included a series of deep rock tunnels. Since completion of preliminary design of the program in 1994, the program has been reconfigured in response to the Environmental Protection Agency’s (EPA’s) new CSO policy. The currently proposed system consists of a deep rock tunnel with two tunnel stubs which will provide230,000 cu m (62 million gallons) of storage at depths of up to 90 m (300 ft). This paper discusses the revised 5 km (3 mile) long deep tunnel system.

Jan 1, 1999

By Ireneusz Tomza, Jolanta Lebecka

INTRODUCTION Radioactive deposits were observed in 1972 in some of the Upper Silesian coal mines. They were located mainly in the drains in galeries and on the inside surfaces of water pipes. They also caused some problems by accumulating in water pumps. It has been postulated that the deposits are produced by natural radioactive waters seeping from the rocks. Investigations were initiated to answer the following questions: - What is the composition and the amount of radioactivity in the deposits? - What radioisotopes are present in the water? - How are the radioactive deposits formed? - Do the radioactive waters also occur in other mines? - How does the radioactivity of the water depend on chemical composition? - What is the origin of the radioactive water? - Does the water and the deposits cause radiation hazards for miners? -How can the radiation hazard be reduced? METHODS OF MEASUREMENT Determination of Radium Isotopes in Water The commonly used methods of radium determination in water are either based on measurements of the radioactivity of 222Rn which is in equilibrium with 226Ra, or on the detection of alpha particles of the radium radioisotopes after chemical separation of radium from the water sample. The method based on radon activity measurements is very sensitive and does not require any chemical Separation, but it can be used for determination of 226Ra from the uranium series only, because the thorium daughter 220Rn has too short a half-life (55s to yield the required accuracy. The method developed by Goldin, 1961 [2] involved alpha-particle measurements in thin layers of RaS04 and BaS04 separated from the water. This method is not convenient for saline water and water with high barium concentration because the amount of barium carrier in this case is too large to obtain a thin layer of precipitate with sufficient activity. The Upper Silesian carboniferous waters are often saline with high barium content, so the method described by Goldin was not convenient for this case and it was necessary to change the detection system and modify the chemical preparation. The procedure developed by the authors for the determination of radium isotopes in water was as follows: - Depending on the Ba2+ content and the required sensitivity of measurement, a water sample of 200 cm3 to 3 dm3 was taken. - 10 cm3 of 0.25 M citric acid and 5 cm3 15M ammonia was added to form complex Ba2+ ions and avoid the immediate precipitation of BaSO4. (This was repeated as long as the addition of BaC12 did not form a precipitate.) - 1 cm3 of 1N solution of Pb(N03)2 as a carrier for radioactive isotopes of lead and 10 cm3 of 0.1 N BaC12 as a carrier for radium were added. - The sample was heated to the boiling point and the precipitation of RaS04, BaSO4 and PbS04 with 50% H2SO4 was carried out. - After several hours the sample was centrifuged and the precipitate was purified by washing with nitric acid and distilled water. - The precipitate was then redisolved in 20 cm3 0.125 M Na2EDTA and 3 cm3 6M ammonia and reprecipitated from the solution by dropwise addition of acetic acid to d pH of 4.5. At this value of pH, precipitation occurs only for the barium and radium sulfates, while lead and all other radioactive elements remain in the solution. The date and time of deposit precipitation was recorded. - The final barium-radium sulfate mixture was washed with distilled water and transferred to standard measurement vials. - Each vial containing a deposit had 6 cm3 of distilled water added and was then shaken vigorously. 12 cm3 of liquid gelling scintillator (INSTA-GEL UNISOLV-1 type) was then added and the vi 1 was shaken again. After a while the scintillator turns into a milky gel in which the deposit is uniformly distributed. - The standard sample of 226Ra was prepared in the same way. - The activity of the samples was measured using a liquid scintillation spectrometer. (In this case the TRICARB 3320 produced by Packard Instruments, was used). Tests run on standard radium solutions provided by Amersham Radiochemical Centre indicated that this method of measurement enables one to achieve an efficiency of almost 100% (within measurement error). For alpha particles no quenching effect was observed for the BaS04 concentration in the range up to 80 mg of BaS04 per 1 cm3 of liquid scintillator coctail (Fig. 1). This provides a sensitive determination of radium in water with high barium content and also in saline water. In saline water the solubility of barium sulfate is much higher than in

Jan 1, 1981

By B. J. Scheiner, D. A. Stanly, P. M. Brown

The Bureau of Mines has developed an equation that describes the dewatering of clay slurries with poly- ethylene oxide. This dewatering equation is: A[ ] = KC + b where n, k, and h are empirical constants and C is the concentration of polymer solution used for dewatering. The minimum amount of polymer required for dewatering, A, is determined by titration of the clay slurry with a polymer solution. In this report, the dewatering equation is applied to data obtained for a polyacrylamide dewatering sequence. Fundamental similarities between the dewatering properties of clays and the viscosity of polymer solutions were observed. These similarities were explained by correlating an equation describing polymer configuration in solution with the dewatering equation. This correlation showed that the amount of polymer required for dewatering and polymer solution viscosity are both the consequences of the frictional interaction of entangled polymer coils.

Jan 1, 1991

By Yeonuk Choi, Gus Van Weert

cyanide control in effluents is becoming a critical environmental issue for the gold extraction industry. Silver impregnated carbon removes free cyanide effectively to the ppb level from solution in high throughput columns. By re-calcining the cyanide saturated carbon, the impregnated silver is restored to activity and the cyanide destroyed outside the effluent stream. Many gold mills already have an activation kiln on site, which could make retrofit relatively easy.

Jan 1, 1993

By M. D. McInnis

The Jualin Gold Prospect is centered on Johnson Creek, approximately 40 air miles north-west of Juneau, Alaska. The property is on the southern end of the Kakuhan Range with Berners Bay immediately to the south and Lynn Canal to the west. The property is accessible directly by helicopter from Juneau or by float plane to the head of a 5.5 mile gravel road that begins on the north side of Berners Bay and terminates at the old workings of the Jualin Mine near the center of the property.

Jan 1, 1989

By W. L. Hollinshead

For more effective and cost-saving production in tunnels, the machinery used on construction sites in the future will be equipped with guidance systems combined with working-procedure management systems. This paper describes sensors for these systems and vari¬ous system configurations. A project is described that uses a computerized guidance system on an underground mining machine for guidance and profile control.

Jan 1, 2000

By Johan Bosch, Wout Broere, Minh Ngan Vu

"INTRODUCTION Shield tunnelling is often used in constructing underground infrastructure in cities due to the ability to limit settlements and damage to existing buildings. However, in an urban environment with soft overburden and buildings on pile foundations such as the North-South Line project in Amsterdam, there is a tendency to design the tunnel well below the surface and below the pile tip level in order to reduce interaction between tunnelling process and piles. This results in deep tunnels and deep station boxes. When the tunnels are located close to the surface and above the pile tip level, this would reduce the required depth of the station boxes and the construction cost. Moreover, other benefits of shallow tunnels are the low operational cost in the long-term and shorter traveling time from the surface to the platforms. Still, the tunnels should be constructed in such a manner that existing buildings are not structurally damaged, which results in a minimum required distance between tunnelling process and existing buildings. In this paper, the extent of the area that is influenced by tunnelling will be investigated in order to determine the limit distance from tunnelling to existing foundations without inducing too large building deformation. From analysing empirical data of many shield tunnels, Peck (1969) firstly presented the settlement trough on the surface induced by tunnelling in soft soil as a Gaussian distribution. This is also confirmed by other authors (Cording and Hansmire, 1975; Mair et al., 1993; Ahmed and Iskander, 2010). In this study, the Gaussian curve is used to investigate the ground movement when tunnelling in order to find the effects on existing structures. Based on the results from centrifuge test and empirical data, Mair et al. (1993) showed that the subsurface settlement profile distributes as the Gaussian curve also. The width of settlement trough at the depth z depends on the depth of the tunnel z0 and a coefficient K depending on depth. Other studies by Moh et al. (1996), Grant and Taylor (2000) and Jacobsz (2003) based on Mair et al. (1993) proposed a limited change of K in various kinds of soil."

Jan 1, 2016

By Shuang Shuang Huang, John Fillos

Ozonation was evaluated as an alternative treatment process for leachates of municipal landfills. The study was carried out on leachate from the Fresh Kills Landfill, New York City. The leachate has strong tea color and BOD5 ranging between 90 mg/L and 130 mg/L. The average COD, TOC and NH3-N concentrations were 1800 mg/L , 550 mg/L, and 665 mg/L, respectively. The kinetics of the process were studied in a sparged batch reactor by developing concentration- time profiles for residual color and TOC. Continuous flow experiments were then carried out at two selected contact times. The process was found to be effective in the treatment of leachates for color and TOC removal.

Jan 1, 1992

By Douglas M. Deason

Swelling clays, such as montmorillonite, contribute significantly to the poor dewatering and consolidation behavior of the Florida phosphate clay wastes. Understanding and to a degree, control of the forces which cause the swelling behavior may aid in supplying a solution to this problem. The technical feasibility of utilizing control- led dispersion for aiding dewatering of phosphatic slimes was investigated. This technique is based upon inhibition of swelling and self-dispersing tendencies of the montmorillonite clays by dispersing the solids in electrolyte solutions. Through this process, significant improvements in settling rates and sediment solids content were achieved in both pure clay systems and on simulated phosphate slimes.

Jan 1, 1983

By H. F. Haller, H. C. Pattison

The research program described in this paper is sponsored by the Advanced Research Projects Agency of the Department of Defense and monitored by the Bureau of Mines, United States Department of the Interior. PROGRAM DEVELOPMENT While Holmes & Narver is better known in other fields, the company has been active in many phases of underground excavation for over twenty years. In the 1950's, H&N participated in design and construction of nearly twenty miles of waste disposal tunnels in Southern California. As Architect-Engineer for the Atomic Energy Commission, we had design and management responsibility for many miles of tunnels and for thousands of feet of exploration and big hole drilling, from coast to coast in the States, and for gas well completions and exploration drilling for the Navy and the National Science Foundation from Pt. Barrow to Byrd Station in Antarctica. In my ten years with the company, we contributed to the development of big hole drilling techniques at a number of sites and analyzed the capability of boring machines for many of the tunnel projects. In a 1965 engineering study of a hundred miles of vehicular tunnels in rock under New York City, we investigated

Jan 1, 1997

By Robert W. Lawson

INTRODUCTION Prior to 1705, underground mining was limited to mineral deposits located above or a very small distance below the water table. The development of the steamdriven mining pump was motivated by the need to extract minerals from deposits considerably lower than the water table. Today, the majority of mine pumps are driven by electric motors, although some small utility pumps are driven by compressed air. Of the numerous types of pumps that might be applied to mine service, the two types used most frequently underground are the centrifugal and plunger pumps. Each of these types has its proper application. In most instances, plunger pumps are best for handling low water volumes against high heads, while centrifugal pumps effectively handle either low or high water volumes against low heads or high water volumes against high heads. This chapter describes pumps applied to underground mine service, where the mine service consists of mine drainage (removing mine water as it accumulates), mine dewatering (removing water from a flooded mine), and pumping for special applications such as hydraulic mining and hydraulic hoisting. CENTRIFUGAL AND PLUNGER PUMPS Modern mine pumps are classified as either centrifugal (kinetic) or plunger (positive-displacement) pumps. The following paragraphs describe each of these classifications. Centrifugal Pumps Centrifugal pumps may be grouped into various types, depending upon their various features: Number of Stages: In a single-stage pump, the total head is developed by one impeller, while a multi¬stage pump utilizes two or more impellers acting in one casing to develop the total head. Fig. I shows a cutaway view of a single-stage horizontal split-case double -section centrifugal pump. Fig. 2 shows a cutaway view of a six-stage medium-pressure split-case diffuser-type centrifugal pump. Type of Casing: A volute pump has a casing in the form of a spiral or volute. A circular-casing pump has a casing of constant cross section concentric with the impeller. A diffuser pump is equipped with a diffuser that converts velocity head to pressure head. Shaft Position: A horizontal pump normally has the shaft in a horizontal position, while a vertical pump normally has the shaft in a vertical position. Fig. 3 illustrates a vertical turbine-type slurry pump. Suction: A single-suction pump equips the first stage with a single-suction impeller, with fluid entering the impeller on only one side. A double-suction pump equips

Jan 1, 1982

By Charles B. Dugger

Sacrificial linings for grinding mills have been a necessary state of the art of mineral dressing since the inception of comminution. Long recognized as the final link in energy transmission from power line to ore, mill liners as a scientific endeavor have not expanded as rapidly as other branches of mineral dressing engineering. Several reasons for this technological lag are apparent. Typically in the past, labor intensive foundries were freely located geographically, at a time when transportation charges made up a significant portion of the casting cost. Alloying agents had not gained their current level of sophistication and were relatively inexpensive in the quantities required. Precise foundry controls were not economically justified, or totally understood. Coincidental to these elements, liner consumption per unit processed did not categorically contribute as a major cost item to the mill operator. Grinding equipment was small, and many times lining life exceeded that of the promoter. These unique conditions no longer exist. Ore dressing equipment has grown to meet modern mining demands. Larger processing facilities, utilizing fewer pieces of equipment, have replaced operations of the past. Emphasis today and tomorrow is on larger and larger equipment, with an eye on lower and lower unit processing costs.

Jan 1, 1979

By W. H. Langer

The U.S. Geological Survey (USGS) in cooperation with the New Mexico Bureau of Mines is conducting an assessment of mineral resources in the 36,800 km2 Mimbres Resource Area, southwestern New Mexico. Included in the assessment is a literature-based evaluation of sand and gravel that utilizes third party geologic information. The USGS has developed a method based on existing 1:500,000 scale geologic maps supplemented by remote sensing, statistical models, and point data such as test hole or pit records. The method defines the areal extent, quality, and quantity of aggregate.

Jan 1, 1996

By Steven W. Hunt, Ronald E. Heuer, Safdar A. Gill

A 3.3 m (11 feet) diameter, 51 m (168 feet) deep temporary steel casing which had been sunk within glacial soils buckled and collapsed on July 29, 1985. The collapse occurred at the CT-8 Dropshaft site in Milwaukee while two workmen were contact grouting outside the casing in an attempt to stop groundwater inflows through a bottom plug. This paper describes the soil and groundwater conditions at the site, the casing design, the method of shaft construction, and probable causes of the buckling failure. Specific aspects of the paper include: slurry method of shaft excavation and casing installation, soil creep, earth pressure due to three dimensional arching, and buckling strength of a casing surrounded by slurry rather than grout and firm soil. The paper should be of interest to designers and constructors of temporary ground support systems for deep shafts.

Jan 1, 1995

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