^> A y . » • « , «^ g* *o *^!T. A /\ Z -J5&j ***** **. <* .A* V *^Vi» A v^V'* "v^ f y \/v #;; ^* *%- '«• ^ V ^ •.*«&• , * \^\o' V^^*\/ %^ f *V V*^\/ %^ f 'V V'— V^u %WS^* A»C„ ^^ v ^ y ^ ^0* W>*\ '^^" o*^ K- > oV v ;^^>*. *^d^ : .7* -G* V *^W A ^ • »• A / •* 0^ ••11: ♦ »••- **^ ' .-Jsa&i-. x*^' /jsk •. *^,** ' .-5 vv • ^. a* *V * A " '* '-^^", : * 4< ^ "•"SHIP'-' c >0, *-=- w /\. : -SR- ; ♦♦'x l ™ ; /\'wy^ "'™* t / ^ t _ .*^vi_ * V "" *\^^\ ' «ssA ' ^ *° A V *A sT^sftttf* V* ^ -^Js. (V r ° " ° ♦ V> (ft . *■ ' » .. ^^ ^q* & * ^ q*. *.-• a BUREAU OF MINES INFORMATION CIRCULAR/1989 310 Bureau of Mines Geotechnical Centrifuge Research-A Review By Paul C. McWilliams UNITED STATES DEPARTMENT OF THE INTERIOR Mission: Asthe Nation's principal conservation agency, the Department of the Interior has respon- sibility for most of our nationally-owned public lands and natural and cultural resources. This includes fostering wise use of our land and water resources, protecting our fish and wildlife, pre- serving the environmental and cultural values of our national parks and historical places, and pro- viding for the enjoyment of life through outdoor recreation. The Department assesses our energy and mineral resources and works to assure that their development is in the best interests of all our people. The Department also promotes the goals of the Take Pride in America campaign by encouraging stewardship and citizen responsibil- ity forthe public lands and promoting citizen par- ticipation in their care. The Department also has a major responsibility for American Indian reser- vation communities and for people who live in Island Territories under U.S. Administration. ( jjvJM &&* \ BjAfitMi tf / hh^d Information Circular 9218 n Bureau of Mines Geotechnical Centrifuge Research-A Review By Paul C. McWilliams UNITED STATES DEPARTMENT OF THE INTERIOR Manuel J. Lujan, Jr., Secretary BUREAU OF MINES T S Ary, Director Library of Congress Cataloging in Publication Data: McWilliams, P. C. (Paul C.) Bureau of Mines geotechnical centrifuge research— a review. Bureau of Mines information circular; 9218) Bibliography: p. 19. Supt. of Docs, no.: I 28.27:9218. 1. Tailings embankmemts— Testing. 2. Rock mechanics. 3. Centrifugation. I. Ti- tle. II. Series: Information circular (United States. Bureau of Mines); 9218. TN295.U4 [TN288] 622 s [622'.7] 88-607916 CONTENTS Page Abstract 1 Introduction 2 Acknowledgment 2 Brief history of geotechnical centrifuge testing 2 Rock mechanics testing 2 Soil mechanics testing 3 Current status, geotechnical centrifuging in United States I 4 Centrifuge and model testing 5 Similitude, scaling, and modeling-of-models 5 Bureau of Mines sponsored geotechnical centrifuge projects 6 First experimental series-University of Cambridge- 1977 6 Experimental goal and design 6 Test equipment 6 Experimental results 7 Second experimental series-Univefsity of Cambridge-1978 9 Experimental goal and design 9 Experimental results 10 First experimental series-Sandia National Laboratories-1981 11 Experimental goal and design 11 Test equipment 12 Experimental results 12 Second experimental series-Sandia National Laboratories- 1983 15 Experimental goal and design 15 Test equipment 15 Experimental results 15 Other Bureau of Mines projects 17 Grain-size mapping between prototypes and centrifuge models 17 Centrifuge usage to solve rock mechanics problems 17 Conclusions 18 References 19 ILLUSTRATIONS 1. University of Cambridge's 13-ft radius centrifuge 7 2. Cambridge experiment-embankment prior to testing 8 3. Cambridge experiment-embankment after testing 9 4. Sandia National Laboratories' 25-ft radius centrifuge 11 5. Sandia experiment-embankment prior to testing 13 6. Sandia experiment-embankment after testing 14 7. Sandia's first experimental series-steady-state phreatic surface at 90-g, 125-g, and 150-g scaling 14 8. Sandia's second experimental series-equipotential contours 16 UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT ft foot m meter h hour min minute in inch pet percent lb pound st short ton lb/st pound per short ton yr year BUREAU OF MINES GEOTECHNICAL CENTRIFUGE RESEARCH-A REVIEW By Paul C. McWilliams 1 ABSTRACT The U.S. Bureau of Mines has, primarily through its contract program, used large-scale centrifuges to determine design criteria for tailings embankments. The centrifuge runs were made at two instal- lations, the University of Cambridge, Cambridge, England and Sandia National Laboratories, Albuquer- que, NM. The major problems considered were as follows: slope stability of embankments, modeling erosion and seepage, use of the phreatic surface level to ascertain the validity of centrifuge modeling, and the effects of compaction and weathering on a tailings embankment. This report summarizes the results of the four test series conducted at University of Cambridge and Sandia National Laboratories. A review of prior centrifuge applications to mining problems is included. Consideration is given to future centrifuge application to mining problems in both soil and rock mechanics. Mathematical statistician, Spokane Research Center, U.S. Bureau of Mines, Spokane, WA. INTRODUCTION The prime motivation for writing this report is to pre- sent-in digest form-recent centrifuge work done relative to the safety of mine tailings embankments. It is hoped that this review will motivate the reader to consider the detailed reports themselves. These reports written at the University of Cambridge (10-11), 2 U.S. Army Waterways Experimental Station Vicksburg, MS, (40), and Sandia National Laboratories (37-38), detail the four major experimental tests. The Bureau of Mines has now been involved in centri- fuge testing in rock and soils mechanics for about 40 yr. Of particular interest is the 10 yr series of centrifuge ex- periments conducted by Panek (21-26) at College Park, MD, from 1952 to 1961. Panek's area of interest was to consider the effects of rock bolts on underground mine roofs. More detail on Panek's work is presented in the section on "Rock Mechanics Testing." ACKNOWLEDGMENT The author wishes to thank Bill Stewart, mining en- gineer, Bureau of Mines, Spokane, WA, who was the original project leader on the coal waste embankment centrifuge work done at the University of Cambridge in 1977 and 1978. BRIEF HISTORY OF GEOTECHNICAL CENTRIFUGE TESTING ROCK MECHANICS TESTING Many authors (1, 6-7, 32) have chronicled accounts of the use of centrifuge testing in geotechnical investigations. Of particular interest to this Bureau of Mines report are those works that apply to the mining industry. The most prominent pioneer in the use of centrifuge testing in rock mechanics is Bucky (3), who initiated such experimentation in this country at University of Columbia, New York, NY in 1931. Bucky studied model beams of various materials by increasing their self weight while rotating at increasing speeds in the centrifuge. It was concluded that: "If in the model the pull of gravity on each part can be increased in the same proportion as the linear scale is decreased, then the unit stress at similar points in the model and the prototype will be the same, and the displacement or deflection of any point in the model will represent to scale the displacement of the corresponding point in the prototype (3)." Bucky published several articles with mining applica- tions from 1931 to 1949. The first work for the Bureau in centrifuging was by Wright (43) in 1948. The objective of this work was to determine optimal pillar placements that would provide a safe working environment. For this purpose, a set of charts was produced from the centrifuge modeling simulations. Italic numbers in parentheses refer to items in the list of references at the end of this report. The next notable works of this kind were conducted by Panek of the Bureau. An extensive series of tests was conducted in which models of layered, bolted roof beams were tested, resulting in several publications (21-26) over a 10-yr period. Panek's centrifuge work respresented a marked improvement over earlier designs, with strain gages being incorporatd for the first time. (To give the reader perspective of the state of the art in centrifuge modeling in 1952, Panek's centrifuge could carry a 90-lb payload at up to 2,600 gravity (g). The machine had a radius of 2 ft.) Of particular interest was the fact that Panek's work involved nondestructive testing. In a majority of other investigations, centrifuge testing was continued until failure occurred, thus Panek's work was novel from this point of view. Some more detail about Panek's work seems appro- priate. Panek enumerated six advantages to centrifuge testing: 1. The model can be made of a material different from that of the prototype (for experimental convenience, lime- stone was used as the test material). 2. The model need not be tested to destructive, hence variations in strength or other properties from one test specimen to another are not reflected in the results. 3. The effects of changes in one or more variables can be studied by performing a series of tests on a single model. 4. The state of strain in the test model can be determined. 5. By measuring the model strains corresponding to several load values a load-strain relation can be deter- mined from a single test. 6. The test results, which consist of quantitative relations between the load, the strain, and the dimensions and properties of the structural members, are directly applicable to any prototype that satisfies the simularity requirements, irrespective of its dimensions or component materials. Panek proceeded to show that for rockbolting problems, the laws of similitude 3 could be relaxed for the material properties of the bolt itself. Further, since plane-strain was used to model the action of the roof, one could also relax the similitude criteria for equality of Poisson's ratio between model and prototype. These arguments are de- tailed in the report "Theory of Model Testing as Applied to Roof Bolting" (22). In the last series of tests (23-26), Panek was concerned with modeling bolted bedded mine roofs. It was concluded that centrifuge results are con- sistent with theoretical calculations. Methodology of how to best space rockbolts is discussed (23-24). Panek consid- ered the problems of separated roof bedding-the suspen- sion problem-and the effect that friction between the beds has on this problem (25-26). Here one sees the researcher observing the mechanism of the action and reaction through centrifuge experimentation. At about the same time, Caudle (5) was also working with supported beam theory problems. In a later publi- cation, Clark (7) stated that: "A unique and vital charac- teristic of the centrifugal testing of beams and other struc- tures which has not been explored is the determination of the behavior of a beam after initial fracture takes place, and the stress can no longer be determined analytically. That is, after initial fracture has taken place, further defor- mation and failure due to body forces can be created and effects observed only in a centrifuge." Obviously Clark feels that, given a proper centrifuge for the situation, sig- nificant advances in the measuring of post-failure defor- mations can be made only through centrifuge work. In 1965, Hoek published an article "The Design of a Centrifuge for the Simulation of Gravitational Force Fields in Mine Models" (13). In this article the author discusses the 4-1/2-ft radius 1,000-g centrifuge designed and con- structed by the South African Council for Scientific and Industrial Research, Pretoria, South Africa. This machine was used for photoelastic stress determinations (at 100 g) and brittle fracture studies (at 600 g). Hoek like Clark (7), holds that a 2,000-g machine is desirable for future hard rock centrifuge work. Ramberg did extensive work in using the centrifuge to study domes, folds, gravity sliding, extrusion of lava, etc. This work was started by Ramberg at the University of Chicago, Chicago, IL in 1960 and was later switched to the Uppsala Centrifuge Laboratory in Uppsala, Sweden. In the test "Gravity, Deformation, and the Earth's Crust" (30), 3 See section, "Similitude, Scaling, and Modeling-of-Models." Ramberg stated: "The principle of centrifuged dynamic models is simply that the centrifugal force plays the same role in the models as does the force of gravity in geological structures. However, since the centrifugal force per unit mass, which in magnitude equals the centripetal acceler- ation, but is oppositely directed, may be made several thousand times stronger than the gravitational force per unit mass, model materials can be used that are several thousand times stronger and correspondingly more viscous than materials usable in noncentrifuged models of the same size." Thus, another centrifuge innovator states the advantage of using the centrifuge in lieu of other modeling. In the early 1980's, Sutherland of Sandia National Labo- ratories (34-36) conducted a series of subsidence tests on their 25-ft centrifuge. This machine— using a swing plat- form to position the model-is capable of carrying a pay- load of over 1,000 lb and attaining over 150-g acceleration. Use of this large-scale machine represents another mile- stone in centrifuge applications in this country; previously only smaller machines were available for geotechnical use here. Sutherland and associates developed finite-element computer models and discrete-element models for the rock rubble flow in a mine opening resulting from subsiding overburden ground. The centrifuge results were then com- pared with the analytic model calculations. Agreement between the centrifuge tests, the finite-element models, and the discrete-element models was quite good. SOIL MECHANICS TESTING Almost all the early soil mechanics centrifuge work was focused in the Soviet Union (1930's) and other European locations (1960's). In the mid-1930's, Pokrovsky and asso- ciates published articles concerned with modeling and cen- trifuge applications to problems in soil mechanics (27-28). Later Malushitsky (19) published a book on centrifuge model testing relative to slope stability in embankments. During the 1970's, several prominent European and Amer- ican soil mechanic engineers visited the Soviet Union installations. In mining, the Soviet Union is very reliant on centrifuge testing in designing and establishing slope sta- bility criteria for actual prototype waste disposal sites. The Soviet Union also used the centrifuge to "directly model" a variety of other geotechnical problems (29). This approach is in contrast to that of U.S. designers who rely primarily on computer models and calculation techniques to establish prototype design criteria. Malushitsky's book is effectively a user's guide for designing embankments on a geotechnical centrifuge. Beginning in the early 1960's, European usage of centri- fuges to study soil mechanics application became common practice. However, most of these early centrifuge appli- cations were not related to mining problems. The majority of the work was done in Sweden and England. Professors Roscoe and Schofield of the Engineering Department at the University of Cambridge became prominent practi- tioners of centrifuge soil mechanics work in the late 1960's. Many of the current centrifuge-oriented engineers in the United States studied at the University of Cambridge dur- ing the 1970's. The work discussed hereafter was done in the last 15 yr. One of the centrifuge applications in mining was funded by the Bureau, with the work being done at the University of Cambridge in 1977 (10-11). Waterways Experimental Station, U.S. Corp. of Engineers, Vicksburg, MS, was also involved as the primary contractor (40). The objective of these government funded studies was to establish design criteria for slope stability of coal waste embankments. Motivation for the slope stability question was due to the 1972 Buffalo Creek disaster in West Virginia when a coal refuge retaining dam failed, killing 116 people. The Bu- reau's centrifuge work was continued at Sandia National Laboratories by Sutherland in the early 1980's (37-38). These projects are described in detail in this report. There was other centrifuge work in soils that is of interest to the mining industry. The University of Florida, Gainesville, FL, has studied problems in evaluating the sedimentation and consolidation characteristics of phosphatic waste clays (2, 18). The Japanese, Scott at California Institute of Technology, Pasadena, CA, and Ko at the University of Colorado, Boulder, CO have addressed problems involving underground tunnel construction. Ko has also investigated many other topics; of particular interest is that of cone penetrometers, slope stability of embankments, and overtopping earth dams (9, 14-15). Goodings of the University of Maryland, College Park, MD (12) has work relative to erosion and seepage modeling in a tailings embankment. This work is derivative from the aforementioned work in embankments by Schofield and Goodings at the University of Cambridge (10-11). In addition, Goodings is currently doing research on reinforced soil walls and particle scale effect in modeling slope stability. Certainly, there are other works in soil and rock mechanics not discussed herein. Although not a mining problem per se, the work of Schmidt and Holsapple at Boeing Co., Seattle, WA is held in high esteem. They use centrifuge testing to simulate the effects of cratering. An example problem would be to predict the resulting crater size formed from the detonation of a high-explosive device. Some 40 publications by Schmidt and/or Holsapple are enumerated in Cheney's biography of centrifuge paper (6, pp. 10-22). To paraphrase Cheney's appraisal of this work (6, p. 2): "The work of Schmidt and Holsapple has revolu- tionized the science of crater prediction at nuclear explosive levels and was accomplished by a scale test at Boeing Co. in Seattle, WA, using small chemical explosives and impact of small projectiles at high velocities. The results dramatically reduce the size estimates for craters formed by near-surface large- yield nuclear explosives and by planetary impact of large bodies." In a recent experiment (6, p. 256), Schmidt and Holsapple were able to model a 40-ton 4 explosive event of their centrifuge. The authors state that: "The results were gratifying. In contrast to the "state-of-the-art" numerical prediction, which proved to be in error by over 100 pet in volume of the crater, the single-shot centrifuge prediction was accurate to within 12 pet. Subsequent refinement of the model gave even better accuracy." From the preceding discussion of the history of geo- technical centrifuge applications, it would seem justifiable to conclude that these are exciting times for centrifuge users in the areas of soils and rock mechanics. CURRENT STATUS, GEOTECHNICAL CENTRIFUGING IN UNITED STATES Currently there is considerable momentum towards geotechnical usage of centrifuges in this country. Cheney (6) has printed an extensive bibliography of centrifuge publications. There were 37 publications listed between 1931 to 1977, but in 1983 alone there were 32 publications. If the number of publications represents some measure of growth, then one can conclude that the amount of geotech- nical centrifuge work is increasing at an almost exponential rate. Three large-scale geotechnical centrifuges are avail- able in this country-at Sandia National Laboratories, at the University of California at Davis, and at the University of Colorado. In addition, there are several smaller instal- lations being used: again at Davis and Colorado, Cali- fornia Institute of Technology, University of Maryland, University of Princeton, Princeton, NJ, University of Ken- tucky, Lexington, KY, Boeing Co., Massachusetts Institute of Technology, Cambridge, MA, New Jersey Institute of Technology, Newark, NJ, Ohio State University, Colum- bus, OH, and University of Florida. This list is by no means complete; there may be other academic and com- mercial installations that are not included herein. Several centrifuge users, notably Scott at California Institute of Technology (8, 33), Schofield (31) at University of Cam- bridge, Ko at the University of Colorado, and Kutter (16) now at the University of California, Davis, have incorpo- rated dynamic effects into their centrifuge modeling. Sim- ulation of earthquakes and other ground movement is now incorporated into current centrifuge testing. 4 In this report, "ton" indicates 2,000 lbf. CENTRIFUGE AND MODEL TESTING A very logical question that might be asked is: why is it necessary to use a centrifuge for model testing? Tradi- tionally, laboratory scientists conduct a small-scale exper- iment of some kind prior to large-scale involvement. In more recent times, mathematical models are often substi- tuted for (or are complementary to) laboratory scale mod- els. Certainly centrifuges are not commonplace instru- ments in most laboratories. Further, the cost in both money and time for running centrifuge experiments is not cheap. Thus, argumentation must be provided to justify using a centrifuge to model prototype situation. Proponents of centrifuge usage (6-7, 32) provide a vari- ety of reasons why a centrifuge is a very good modeling tool. The following is a synopsis of some of their major ideas: 1. One can directly model prototype situations. Par- ticularly in soils, the same material can be used in the model as exists in the prototype. In many cases, a centri- fuge model better satisfies the laws of similitude between model and prototype than does the corresponding 1-g model. 5 For example, since the stress field functions exactly the same on the centrifuge and the prototype, gravity load situations can be simulated easily on the centrifuge (assuming identical friction, cohesion, and den- sity properties exists between the model and prototype (40, p. 14)). Further, time-sequenced events can be forecasted on the centrifuge; a decided advantage over most 1-g models. 2. Sophisticated computer models can be verified via centrifuge experimentation. Many centrifuge advocates consider this to be the prime use of their experimentation. 3. It can be used as an educational aid. Insight as to the mechanism of failure is often cited as a reason for cen- trifuge testing. Visually seeing how a structure reacts to various loading conditions without actual failure is also quite useful. 4. Tests can be replication of testing. Often laboratory models are destroyed during testing, and are thus, one shot by nature. In contrast, many centrifuge models can be constructed within a reasonable time span. For example, a centrifuge model of a tailings embankment may be con- structed in 2-3 h and a complete parameter study of a problem could be conducted in a few days. There are, of course, centrifuge modeling problems that do require time and care in preparation, particularly those in rock mechan- ics. Nonetheless, replication of testing via centrifuge mod- eling is very important, yet advocates of centrifuge use often fail to adequately emphasize this point. Although the preceding list is not exhaustive, it does give some indi- cations why modelers are turning to the centrifuge more frequently than before. SIMILITUDE, SCALING, AND MODELING-OF-MODELS For any small-scale model to be representative of a corresponding prototype situation, the model ideally should possess all the important characteristics of the prototype. In the book, "Dimensional Analysis and Theory of Models" (17), Langhaar differentiates between desirable kinds of similarity. Geometric similarity is usually easiest to obtain; in a centrifuge, geometric dimensions scale in proportion to the number of gravities (N) transmitted to the model. Kinetic and dynamic similarities are also desirable. As stated previously, one of the chief advantages of using a centrifuge is that the stress fields in is exact correspon- dence between the model and the prototype. However, many other pertinent variables have laws of correspon- dence of their own. For example, in soil applications on a centrifuge, time scales as follows: proportionate to N in dynamic terms, proportionate to N 2 inthe case of diffusion, and identically scaled in the case of viscous flow (40, p. 15). Ideally, one would strive for complete similarity, in which all the variables of interest would scale in the same 1-g modeling refers to doing the work under influence of the earth's gravity, i.e., normal laboratory modeling. manner. Practical considerations may require the modeler to be less stringent, relaxing similarity requisites on vari- ables of lesser importance. The previous referenced work of Panek (22-26) shows the skill of the researcher in being able to relax some relatively unimportant similarity requirements in order to proceed with the research. There are two approaches taken by centrifuge users in evolving the laws of similitude: 1. Scaling relationships are derived using the basic laws of physics. Two basic "truisms" are predicated; namely that the centrifuge's acceleration is N times that of the prototype and that the physical dimensions of the prototype are N times those of the centrifuge model. Given those as a basis, one can derive relationships between prototype and the centrifuge's stresses, time relationships, erosion equations, capillary rise, etc. 2. Dimensional analysis provides another approach to the problem. Here similitude relationships evolved by establishing dimensionless products involving pertinent parameters of the scientific phenomena being investigated. Again, the tenets involving accelerations and physical dimensions are involved in evolving the resulting similitude statements. This approach uses Buckingham's Pi theorem, which states: "If an equation is dimensionallly homogen- eous, it can be reduced to a relationship among a complete set of dimensionless products." A noteworthy consideration in soil work is that centri- fuge models are often more favorable in terms of similarity than are 1-g models. Using dimensional analysis, Overson (6) derives six important variable relationships needed to model the settling of footings on a dry sand surface. Con- ventional (1-g) modeling is compared with centrifuge mod- eling. Of the six relationships, the conventional modeling preserves similarity in two of the relationships, while the centrifuge modeling preserves similarity in five of the rela- tionships. Hence, the modeler chose to use the centrifuge for the work. The scaling process is both interesting and complex, and therefore deserves more detailed consideration than provided herein. An article by Cargill (4) is recommended for a straightforward look at scaling centrifuge modeling of transient waterflow. The preceding is a very brief sketch of the topic of similitude. To comply with the intent of this paper, con- sideration was restricted to comparisons between the cen- trifuge and the prototype. Thus, centrifuge similitude represents a subset of the general topic, and the interested reader is invited to consider more detailed explanations as found in the books of Langhaar (17) and Ramberg (30). Another concept of importance is the so-called mod- eling-of-models. Cargill (4) provides this definition: "To test the scaling laws which relate prototype and its centri- fuge model, a series of reduced scale models can be tested at the necessary increased gravity ratios so that they all represent the same hypothetical prototype." This tech- nique is often used as a first step when introducing a new problem to the centrifuge. BUREAU OF MINES SPONSORED GEOTECHNICAL CENTRIFUGE PROJECTS The following is an attempt to put into summary form the results of the contract program which the Bureau has funded in centrifuge research. Five detailed reports have been previously published: three on the Cambridge work (10-11, 40), and two on the Sandia work (37-38). All of this work was done for the Bureau during the years 1977 to 1984. Coal waste was chosen as the material of interest. This was quite logical at the time, for there had been two recent disastrous coal waste failures, one at Buffalo Creek, WV, and another at Aberfan, Wales. Coal waste material is hard to work with as a modeling material. The basic problem encountered was the difficulty in making the sample representative of the prototype while still adhering to grain-size reduction demands of centrifuge testing. Deterioration of coal waste fines with time was an addi- tional problem. Since it was deemed prudent to use a reasonably large- scale model, the geotechnical centrifuge at the University of Cambridge was selected for use on our first project in 1977. At that time, use of the large-scale Cambridge machine (13-ft working radius) was the most logical op- tion. The U.S. Army Waterways Experimental Station (Townsend) 6 was the prime contractor, subcontracting the actual centrifuge runs to Cambridge (Goodings, Scho- field). 6 After 1980, Sandia National Laboratories (Suther- land) 6 made its 25-ft-radius machine available to the Bu- reau on a governmental interagency basis. Since 1980, all of the Bureau's centrifuge work was done at Sandia. FIRST EXPERIMENTAL SERIES-UNIVERSITY OF CAMBRIDGE-1977 EXPERIMENTAL GOAL AND DESIGN TEST EQUIPMENT Since this series of mine waste embankment tests as the first of its kind in the Western world, this was truly an orientation set of experiments. Slope stability analysis was of first order of interest. As the test series contin- ued, emphasis switched to consideration of erosion and seepage problems. In this series, 13 experimental tests were conducted. The University of Cambridge's geotechnical centrifuge (fig. 1) has a working radius of 13 ft from the center of the rotor to the mid-depth of the soil in a model on the swing- ing platform. The soil is enclosed in a strong box. The centrifuge was capable of attaining 150 g. The maximum Principal investigators. Figure 1 .—University of Cambridge's 13-ft radius centrifuge. weight (both soil and strong box) that can be carried is slightly over 400 lb. Transducers are available to monitor displacements in the embankment. A system that allows the flow of water through the embankment is aboard. Manometers were used to measure phreatic height. Via a mirror system, video pictures documented the centrifuge runs. Instant still photography was also available. EXPERIMENTAL RESULTS Two reports (10, 40) detail results of this experimental series. A few highlights of these reports are of interest here. The material used was coal waste taken from an embankment in the southwest United States. Figure 2 illustrates a typical centrifuge model embankment prior to testing. To make the modeling realistic with prototype situations, flow of water through the embankment soil is a requisite. There are problems and ensuing constraints imposed on the experiment due to accommodating water- flow. The laws of similitude were examined to determine proper model scaling. It was necessary to make adjust- ments in the coal waste material's particle size distribu- tions for two reasons: 1. Very large particles were eliminated to accommodate the small size of the centrifuge models (typically 10 in high, 30 in long, 6 in deep). 2. Permeabilities had to be adjusted to accommodate the waterflow problems (11, pp. 27-31). Figure 2.— Cambridge experiment— embankment prior to testing. By running the centrifuge at high accelerations, slope failures were induced. Undesirable seepage conditions, which caused failures at the embankment's toe, were reme- died by using coarse waste at the toe as is done in many southwestern tailings embankments. Figure 2 is a model embankment prior to running, while figure 3 is a post-run view of a failed embankment. Note the classic slip circle failure situation here. The final runs of this series of experiments were concerned with the seepage-erosion problem which is the focus of the next Cambridge series. Major conclusions from this experiment were as follows: 1. The experimental nuances of modeling coal waste were solvable, and a 100-ft prototype could be modeled. These experiments indicated that compaction of material is not required for modeling. 2. The tested material was highly susceptible to both surface erosion and seepage failure problems. There are both modeling and real-world difficulties in this regard; in this and the next test series the authors address both of these problems. 3. Centrifuge modeling techniques are adaptable and flexible for coal waste embankments. In addition to the preceding, there are other points of consideration: 1. The research was new in that the previous Soviet work of Malushitsky (19) in 1975 was of different grain size and focused on the rate-of-construction failures. 2. The embankments behaved (except in one case which, unfortunately, was in sharp divergence) as predicted in regard to slope stability calculations. 3. The addition of toe-drains improved mass slope stability greatly. Also, sealing the upstream face with a slurry of low permeability improved the stability of the downstream face. However, inclusion of an undrained, but a highly permeable soil key was found to reduce embankment stability. Figure 3.-Cambridge experiment-embankment after testing. 4. Both the finite-element phreatic surface and the factor of safety calculation methods matched nicely with the test results in the runs. Major problems encountered in this experiment were as follows: 1. A practical problem was how to provide and control sufficient water to the model. 2. There was, in fact, no real prototype to scale to. Size limitations of the centrifuge box was a problem in constructing models of prototypical heights. 3. Trying to reconsile the divergence between seepage- erosion effects were primary motivators in having a second Cambridge test. SECOND EXPERIMENTAL SERIES-UNIVERSITY OF CAMBRIDGE-1978 EXPERIMENTAL GOAL AND DESIGN "The objective of the investigations in this research was basically modeling of models; it set out to examine effects on model behavior due to the changes in model scale and particle size distributions, with special attention given to changes in slope stability, permeability, and rate of embankment up. retrogression" (ll). 7 Six experimental models were tested in this series. The experimental setup for this series of tests was effectively the same as described for the first 7 Rate of retrogression refers to embankment failures induced by successive slides of the downstream face emitting from the toe of the 10 series. Many complex problems were addressed, including the effects of compaction and the modeling of seepage- erosion effects. EXPERIMENTAL RESULTS Two reports (11, 40) describe this experimental series in detail. Owing primarily to permeability considerations (also owing to the physical size of the sample container), particle size adjustments were required for this analysis. In deriving the scaling laws for waterflow, Darcy's law (11, p. 3) gives as the velocity of flow in the centrifuge: = kNi (1) where v = flow velocity, k = permeability, i = hydraulic gradient, and N = number of gravities. This scaling law is significant in that the waterflow in the model is quite rapid, being in proportion to the accel- eration of the centrifuge. Therefore, providing an ade- quate amount of water for the centrifuge is a practical concern. Slip circle analysis was again applied to all model runs. While scaled down particle size did not effect the stress relationships between model and a hypothetical prototype, such scaling is very important in establishing laws of similitude regarding permeability. The permeability relationship between model and pro- totype reduces to the following effective particle size relationship (11, p. 13): D io. = D ■*' (2) where D, 10% cumulative distribution point from the model, 8 and D 10 = 10% cumulative distribution point from p the prototype, N = number of gravities centrifuge attains. D is the diameter of the soil particles. D 10 indicates that 10% of the soil sample is of this diameter or less, D^ indicates that 50% of the soil is of this diameter or less. The experiments found a conflict between the above results and that obtained when modeling surface erosion. The appropriate scaling law for erosion is (12, p. 152): D 50 r , = D 50 p / N (3) where D^ = 50% cumulative distribution points. Since equations 2 and 3 cannot both be satisfied for var- ious values of "N", this demonstrates that one cannot con- currently model seepage and erosion effects simultaneously on the centrifuge. Major experimental results were as follows: 1. The particle size problems that evolved during the modeling-necessitating parameter changes as required- negated the modeling-of-models effort. 2. One can model either mass instability (induced by waterflow through the embankment) or surface erosion effects separately. Since different particle size alterations are requisite for each of these efforts, it is not possible to concurrently model both of these effects. 3. The critical type of failure is very dependent on the permeability of the material. For low permeability situa- tions, rate of embankment constructions may be a critical parameter. Intermediate permeability provides potential slope stability failure because of pore pressures resulting from the throughflow. Finally, high permeability present problems in regard to erosion effects. 4. Compaction of material in lifts may aggravate the tendency for erosion problems so that the possible bene- ficial effects on mass slope stability due to increased mate- rial strength are sacrificed to the increased permeability and throughflow (11, p. 32). Other points of consideration include- 1. The experiments moved quite quickly from the basic concepts of the first series of runs (Cambridge, 1977) to problems of considerable scientific depth. This necessi- tated using more sophisticated theoretical research design and running of the experiments. Particular reference is to the problems of seepage, erosion, and compactness. 2. Throughout all three reports on the two Cambridge experiments (10-11, 40), the authors present, on a model by model basis, interesting scenarios as to an analogous prototype situation. A word of caution-these portrayals should not be taken too literally, for there is not enough experimental replication to ascertain their results. 11 Major problems encountered in this experiment were as follows: 1. Questions exist involving capillary tension in slope stability and scaling the capillary tension to the prototype. These considerations were primarily due to the necessary reduction of particle size for modeling. 2. Of most importance was the incompatibility of mod- eling permeability (which model proportional to D 10 / J~N grain size) and resistance to erosion (which model propor- tional to D 50 / N grain size) simultaneously. 3. The compaction result is counter to the usual think- ing of the mining industry and certainly warrants more through investigation. 9 FIRST EXPERIMENTAL SERIES-SANDIA NATIONAL LABORATORIES-1981 EXPERIMENTAL GOAL AND DESIGN In 1980, Sandia National Laboratories decided to ex- pand usage of their large centrifuge facility to accommo- date geotechnical applications. In accordance, the Bureau and Sandia signed a series of interagency agreements to provide continuation of the waste embankment design series of centrifuge tests. The researcher's tests were the initial runs of this kind on Sandia's 25-ft centrifuge, in a sense, they were starting anew, and an orientation series of experiments seemed to be appropriate. 9 Soil engineers have long recognized the value of compacting soil to produce a strong, settlement-free, water-resistant mass. ////////////# 1 1 1 1 » » ' ,U Figure 4.— Sandia National Laboratories' 25-ft radius centrifuge. 12 Thus, the goals of the series were defined as follows: "The objective of this test series was to investigate the development of the phreatic surface and the scaling rela- tions associated with it. To accomplish this objective, a "modeling-of-models" approach (i.e., variation of model scale) was used. A single prototype embankment was scaled at three levels (90, 125, and 150 g) with 3 different embankment configurations being tested at each of the lev- els. The embankment was designed to be stable for all cases. The results illustrated the scaling phenomenon associated with the phreatic surface (37, pp. 2-3)." TEST EQUIPMENT Sandia's machine, with the specimen box aboard, is shown in figure 4. This 25-ft-radius machine is capable of attaining 240 g with a payload of about 8 st (2,000 lb/st). When the geotechnical swing bucket configuration is used, the machine is capable of 150 g with a payload of 2 st. A specimen box, specially constructed for the geotechnical series of experiments, had dimensions of 2.7 ft high, 3.7 ft long, and 8 in deep. Provisions are made to accommodate up to 12 transducers for the Bureau experiments. A means was provided to attain necessary waterflow levels throughout the embankment. Three types of cameras were available: video, movie, and still. EXPERIMENTAL RESULTS Three model configurations were used. One configu- ration represented a full-size embankment, while in the other two configurations the upstream face was sliced off just behind the embankment's crest. This style of model configuration was also used at the University of Cam- bridge. The advantage of aborting the upstream face is that a physically larger embankment can then be con- structed. To achieve the modeling-of-models effect, three acceleration levels (90, 125, and 150 g) were run on each model. The models were scaled in accordance with a fixed prototype geometry. This can be visualized by considering model height-the prototype height was 75 ft, the 90-g model height was 10 in, the 120-g model height was 7.5 in, while the 150-g model height was 6 in. Other dimensions were adjusted in a similar fashion. The experimental design was such that if the modeling-of-models concept was valid, all three phreatic surfaces would ideally map onto themselves when related to the prototype. To mea- sure the height of the phreatic surface in the experimental runs, a transducer system was installed; unfortunately, this system did not function properly. Instead, the experi- mental data was obtained by taking manual readings from video pictures of the centrifuge runs. Minor adjustment in particle size was necessary to meet permeability goals. Although slope stability failure calculations were made and compared with the results of the preliminary runs, this series was not designed for slope failures. Extensive ana- lytic techniques were used in both of the Sandia series of experiments. Several slope stability prediction methods were employed, while the automatic dynamic incremental nonlinear analysis of temperatures (ADINAT) finite- element program was used to predict the expected phreatic surface. The coal waste used was from the same southwestern site used for the two Cambridge series. Sandia performed extensive material properties test both prior and post to the centrifuge runs. Figure 5 shows a typical Sandia constructed embankment prior to running, while figure 6 illustrates an embankment after the centri- fuge run is completed. These Sandia centrifuge tests produced three conclusions: 1. The shape of the phreatic surface was not parabolic concave downward, as was predicted by the finite-element programs. 2. While the 90- and 125-g models map rather nicely, the 150-g model did not congrue with the other two. In fact, the phreatic surface is appreciably higher in all cases for the 150-g runs. Figure 7 illustrates this phenomenon. 3. Since all three model geometries performed in a similar manner, it is not necessary to have a full-scale model, allowing the experiments to expand the dimensions of the critical part of the embankment only. 13 Figure 5.-Sandia experiment-embankment prior to testing. 14 Figure 6— Sandia experiment— embankment after testing. . 30 30 40 50 60 70 HORIZONTAL DISTANCE, m 1 00 Figure 7— Sandia's first experimental series— steady-state phreatic surface at 90-g, 125-g, and 150-g scaling. 15 Other points of consideration include- 1. The centrifuge modeling adversely affected the phre- atic surface. The phreatic surface in the model clearly rises as the gravity-loading increases beyond 100 g. Pos- sible causes for this discrepancy include water seepage around the embankment, high-velocity fields in the embankment, and a curved gravitational field. Until resolved, care should be taken when modeling above 100 g. 2. The numerical and experimental phreatic surface results up to about 100-g loading compare quite favorably. At 90- to 100-g loadings, the centrifuge results on slope failures involving seepage flow should closely resemble failures in the prototype. 3. The slope stability conclusions were consistent with that obtained previously at Cambridge. 4. The Sandia authors are of the opinion that the pri- mary use of centrifuge modeling is as a complementary tool to analytic modeling of phenomena. Major problems encountered in this experiment were as follows: 1. The divergence between the three acceleration levels' phreatic surface is, of course, of primary concern. Explanations other than those offered by the authors have been expressed since completion of this work. An alternate hypothesis is that migration of fines within the embankment is responsible for the phreatic modeling-of- models discrepancies. 2. Inverted curvature of the phreatic surface, also present to some degree in the Cambridge work, is still troublesome (37, pp. 39-40). SECOND EXPERIMENTAL SERIES-SANDIA NATIONAL LABORATORIES-1983 EXPERIMENTAL GOAL AND DESIGN The basic goal of this experiment was to "determine the influence of packing density and material gradation (by the addition of slurried fines from the washing plant) on the embankment's stability" (38, p. 4). These concepts were suggested to the Bureau by Mining Health and Safety Administration (MSHA) as being practical field considerations. In this series of tests, slope stability is used as a mea- sure of success. The eight embankments models tested were all constructed marginally stable; thus, the introduc- tion of waterflow would then drive the embankment close to failure. The material was again taken from the same southwest mine as in the previously mentioned tests. Unfortunately, the material was quite different from previ- ous batches. It was quite "slakey" 10 in content which pro- vided the experimenter with many undesirable problems. The logistics of the situation was such that it was not pos- sible to start over with new material. Four different grada- tions of the material were used in this test series. TEST EQUIPMENT The basic experimental setup was the same as in the previous Sandia experiment. The transducers used to measure head pressure were operative and provided the basic data set for analysis. Video and still photography were also used to document the experiments. EXPERIMENTAL RESULTS As before, the finite-element code ADINAT was used for predicting the phreatic surface, while a computer pro- gram using the modified Bishop method of slices was used for slope stability analysis. In order to best display the transient waterflow through the embankment, equipotential contours of total head are used throughout the Sandia report (38). See figure 8 for typical test results. In this series of tests, the centrifuge was accelerated to 100 g and held there for the duration of the test. Slope stability pre- dictions are again consistent with the test results. The first two tests were run for calibration purposes, so there were six actual experimental tests of interest. As predicted by the slope stability computations, four of these failed, one of which failed due to piping. 11 A typical failed embank- ment is shown in figure 6. Of most interest were the two embankments that did not fail. In the first case the objective was to significantly increase the compaction state of the embankment. Having done this, this embankment was stable for the 34.7 time- equivalent days (a 5-min real-time centrifuge run) that it Slaking refers to the disintegration or loss of physical integrity of the material when re-wetted after drying. n Piping means that failure is induced on the downstream slope due to severe internal erosion. 16 2 1.7m 18.5 12.011.5 8.7 A- Test 1 , phreatic surface contours 12.2 12.0 9.0 B-Test 2, phreatic surface contours KEY ▼ Phreatic surface 33.4 m height Photographic Inferred from pressure data 7 . 3 6.0 6.2 4.4 C-Test 6, illustrates difference between photographic and pressure transducer results Figure 8.— Sandia's second experimental series— equipotential contours. was run. The second embankment that did not fail was also heavily compacted. In addition, the reservoir was filled with slurried fines from the washing plant rather than with pea gravel. The water was introduced into the reser- voir only at the top of the fine-filled reservoir. This em- bankment was stable for the 69 time-equivalent days that it was run. There were some experimental difficulties which should be noted (38, pp. 34-35). To quote the authors: "The accumulated evidence from the entire series of tests iden- tified the photographic measurements of the phreatic sur- face as questionable." The primary explanation offered for this situation suggests that the embankment material may adhere to the surface of the viewing plate. Other possibilities for these major and local perturbations are presented. The authors feel that the transducers present more reliable information, because the transducer readings are more consistent with the theoretical calculations. 17 Figure 8C illustrates the discrepancies between the trans- ducer readings and the photographic results. A final note as to the philosophy of the Sandia experi- menters. They felt that a positive use of centrifuge modeling is the verification of computer modeling programs which predict slope stability and waterflow through the embankment (38, pp. 10-11). Therefore, computer modeling essentially represents the prototype in the Sandia experiments. This posture stands in strong contrast with the earlier soils centrifuge work of the Soviets (19, 26-29). The Soviets were concerned with directly designing a prototype embankment using the centrifuge as the analytic design tool. Major conclusions from this experiment were as follows: 1. This test series again confirms the reliability of slope stability calculations. Generally speaking, failure occurs as predicted, but the physical failure pattern does not nec- essarily follow the assumed classical slip circle shape, as witnessed by the failure shown in figure 6. 2. Several improvements are required for future exper- imental technique. In particular, the surface that mates the embankment to the viewplate must be disturbed as lit- tle as possible, and a construction technique must be developed to restrict the flow along this surface. 3. For the material investigated, an increase in packing density can increase the stability of the embankment. The effects of gradation are more complicated. Although in- creasing the amount of fines in the reservoir increased the stability of the structure, these same fines restrict the flow of water through the embankment, thus limiting the dis- charge from the reservoir. Obviously, this presents other problems, e.g., increasing the probability of overtopping the reservoir. A similar problem exists for putting fines in the slurry behind the embankment. OTHER BUREAU OF MINES PROJECTS In addition to the four major centrifuge simulation test series, the following work has also been sponsored by the Bureau. GRAIN-SIZE MAPPING BETWEEN PROTOTYPES AND CENTRIFUGE MODELS As a result of conducting the four centrifuge test series, several problems evolved. One of the more interesting can be stated as follows: it is all well and good that the geometric dimensions scale between a model and its proto- type. Thus, a 1-ft-high centrifuge model may indeed rep- resent a 100-ft-high prototype. It is convenient that the same material may be used in model and prototype. This preserves many desirable features especially for estab- lishing similitude between the model and prototype. The question is whether one should also scale the grain-size distribution, for if one does not, is there not an imbalance? For example, wouldn't a grain of sand in a centrifuge model map into a boulder in the corresponding prototype? In collaboration with Deborah Goodings (Associate Professor of Civil Engineering, University of Maryland), the preceding problem was formulated as follows: investi- gate the influence of particle size relative to geotechnical centrifuge modeling. A most desirable feature of centri- fuge modeling is the use of prototype soil in the centrifuge test. As stated previously, the scientist strives for compli- ance with the laws of similitude whenever possible. The question is: should the soil's grain size also be scaled for similitude? Such scaling presents problems because scaling means that one is no longer working with the true proto- type soil. Thus, important inherent characteristics of the soil would necessarily be changed. It is not surprising that this question has been deemed important by many centrifuge users. Several publications were critiqued in which experiments discussed the effects of grain-size distribution on particular centrifuge modeling problems. Consensus seems to be that finely grained soils can be viewed as reacting as a continuum, thus there is no reason for grain-size scaling. However, coarser materials present more difficult problems. Some investigators have established workable bounds for making decisions on scal- ing grain size. Overson (20) concludes that there is no scale effect in modeling piling footings when the ratio of model diameter to average grain size lies between 30 and 180. Other experimental rules exist for a variety of mod- eling situations. It is apparent that the grain-size ques- tion is an ongoing unresolved problem for centrifuge experiments. CENTRIFUGE USAGE TO SOLVE ROCK MECHANICS PROBLEMS Rock mechanics problems are certainly of prime inter- est to Bureau Research Centers. There are many unre- solved problems in theoretical rock mechanics that require solutions. For example, a classic dilemma is the incompat- ibility between physical properties measured in the labo- ratory and measured in situ. As outlined previously in the section on Rock Mechanics Centrifuge Testing, there have been several projects in which experiments used centri- fuges to explore rock mechanics problems. However, the number of rock mechanics centrifuge studies are certainly far less than that in soils. This is not surprising, for the problems in using a centrifuge for investigating rock mechanics theory are formidable. The most obvious stum- bling block is the strength of the rock. To do destructive testing of any kind, a large centrifuge capable of attaining 2,000 g carrying a payload of several short tons is recom- mended. Such a machine does not exist today in the West- ern world. 18 For the preceding reasons, the Bureau decided to work in conjunction with Bill Pariseau, professor of mining engineering, University of Utah, Salt Lake City, UT. The goal of this effort was to investigate usage of a centrifuge to enhance rock mechanics theory. A first point of consideration is that 1-g models- prevalent in Europe and Australia, but not used in the United States-often require modification of materials to meet the scaling law requirements. Further, to simulate the underground environment properly, a model of 10 ft in height is in order. The cost of building such a model, plus that of constructing the necessary test frame, is deemed virtually prohibitive. The lack of such a facility explains to some degree the heavy reliance of researchers on theoretical calculations in rock mechanics. In spite of the difficulties, there are two theoretical rock mechanics problems that could be amenable to centrifuge solutions. The strength of centrifuge testing is highlighted when gravity stresses are roughly equivalent to the stresses of the material being tested. This is why, in soil mechan- ics, where the strength of sand and soils meet this requi- site, centrifuge testing is much simpler. In mining, one can also match this condition when addressing problems such as the flow of rock rubble, broken ore, and waste rock. Block cave mining is predicted on breaking the rock and then allowing gravity flow to move the rock to the miner's advantage. Thus, interesting problems of this kind could be simulated by centrifuge experimentation. Another centrifuge test series would aid in under- standing the role of joint continuity and spacing in caving mechanics in particular and rock mass mechanics in gen- eral. The basic idea is to fabricate a jointed roof and then increase the mine width until failure occurs, thus establish- ing a relationship between jointing and mining opening width. Both of the ideas discussed could be investigated with the centrifuges currently available. CONCLUSIONS The Bureau's sponsorship of large-scale centrifuge research has played an important role in the current renaissance of centrifuge applications in the geotechnical sciences in this country. Advantages and disadvantages of centrifuge modeling include- 1. Capitalizing on the theoretical advantage of centri- fuge modeling-the exact mapping of stress and strain between the centrifuge model and the prototype-has been reasonably substantiated by these two test series. Use of the actual material of the embankment provides a realistic basis for modeling. 2. All four test series showed a consistency between slope stability predictions of failure and actual model fail- ure. The Cambridge test series often produced the classi- cal failure slip surface. 3. Although the theoretical laws of similitude are quite favorable for centrifuge modeling, in practice, many of the pertinent variables provide provocating results. Of par- ticular concern is the inability to model combinations of variables, such as erosion and mass instability. To truly simulate a prototype embankment, modeling should account for the interactions between the variables of concern. 4. A positive result of centrifuge testing is the ability to simulate a variety of situations in a short time span. Con- struction of a model in a few hours is ideal for experi- ments that require destructive testing. However, centrifuge research and testing is very expensive and primarily con- fined to research environments. For the present, it is hard to envision the mining industry routinely using centrifuge modeling of tailings embankments as a practical design tool. In fairness to the potential of centrifuge testing in geo- technical work, the above conclusions certainly are not the final word on the subject. The four test series conducted at Cambridge and Sandia represent just a beginning in analyzing the advantage of centrifuge modeling. Unfortunately, the coal waste used provided varying de- grees of difficulty for the experimenters. Waste from metal mines may be a more fair material of consideration. In regard to tailings embankments, it is felt the classical slope stability problem has been sufficiently considered by both the Bureau's work and the work of others. Recommendations for future centrifuge testing of tail- ings embankments include- 1. Better resolution of the compaction-erosion problem discussed in the second Cambridge experiment (72). 2. Horizontal drain design theory of embankments has been a topic of interest for the Bureau (39). Computer program output for analytical calculations (41-42) could be compared with centrifuge modeling results. In addition, rock mechanics work would, of course, also be exciting and potentially rewarding to the mining indus- try and the rock mechanics community. Present accelera- tion limits on large-scale centrifuge in the United States provide a constraint to doing rock mechanics work. 19 REFERENCES 1. Al-Hussaini, M. M. Centrifuge Model Testing of Soils: A Literature Review. U.S. Army Waterways Exp. Sta., Vicksburg, MS, Misc. 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Centrifugal Model Analysis of Coal Waste Embankment Stability (contract H0282018, U.S. Army Eng. Waterways Exp. Sta.). BuMines OFR 43-81, 1980, 118 pp.; NTIS PB 81-194524. 41. Tracy, F. T. A Three-Dimensional Finite-Element Program for Steady-State and Transient Seepage Problems. U.S. Army Eng. Water- ways Exp. Sta., Vicksburg, MS, Misc. paper K-73-3, May 1973, 20 pp. 42. Wang, F. F., and M. P. Anderson. Introduction to Groundwater Modeling. Freeman, 1982, 237 pp. 43. Wright, F. D., and P. B. Bucky. Determination of Room-and- Pillar Dimensions for the Soil-Shale Mines at Rifle, Colorado. Trans, of AIME, v. 181, 1949, pp. 352-359. 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