WASTE CLAY DISPOSAL IN MINE CUTS FINAL REPORT. BY BROMWELL ENGINEERING, INC. 202 Lake Miriam Drive Lakeland, Florida

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2 WASTE CLAY DISPOSAL IN MINE CUTS FINAL REPORT BY BROMWELL ENGINEERING, INC. 202 Lake Miriam Drive Lakeland, Florida Principal Investigator: W. David Carrier, III Prepared for FLORIDA INSTITUTE OF PHOSPHATE RESEARCH 1855 West Main Street Bartow, Florida Project Manager: Henry L. Barwood October, 1982 PREPARED UNDER CONTRACT NO

3 DISCLAIMER The contents of this report are reproduced herein as received from the contractor. The opinions, findings, and conclusions expressed herein are not necessarily those of the Florida Institute of Phosphate Research, nor does mention of company names or products constitute endorsement by the Florida Institute of Phosphate Research.

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12 1.0 SUMMARY The four objectives of the research program were: 1. To evaluate field dewatering behavior in a mine cut; 2. To develop new computer programs to analyze twodimensional consolidation; 3. To obtain laboratory data regarding consolidation properties of the IMC clays; and 4. To study the field desiccation behavior of phosphatic clay in order to predict when capping and final reclamation of clay or sand-clay disposal areas can be conducted. The main objective was to develop the new computer programs. The results of the research program are presented in detail in this report. From these results, the following has been concluded. Accurate measurements of the field dewatering behavior in the test pit were made over a period of one and a half years. The dry weight of clay in the test pit calculated based on the sampling programs and based on IMC's pumping data are in good agreement. Also, the average solids content of the clay in the pit calculated based on the sampling programs and based on IMC pumping data and the tide gauge readings are in good agreement. Both measurements of the boundary pore water pressures and pore water pressure measurements within the clay show that there is a head difference between the phreatic surface of the water in the waste clay and the phreatic surface of the water outside the test pit. This head difference causes a downward seepage force which increases the effective stress on the clay

13 particles. This in turn results in a higher solids content than would occur if the boundary pore pressures were at the same elevation as the phreatic surface of the water in the waste clay. The average head difference measured was 13.4 feet. Index tests and mineralogical analysis of the test pit clay have shown that the clay is essentially homogeneous and that the index properties and mineralogy are within the typical range of other Florida phosphatic clays tested. However, the plasticity index is on the high side of the typical range, which suggests "poor" consolidation behavior in comparison with other Florida phosphatic clays tested. Field and laboratory measurements of the compressibility and permeability of the test pit clay are in good agreement. Compressibility developed from correlations based on the Atterberg limits of the clay is in good agreement with the field and laboratory data. Permeability developed from the correlations does not agree with the field and laboratory data nearly as well as with compressibility; however, it is a reasonable first approximation. Compared with other Florida phosphatic clays, the test pit has "poor" consolidation properties. A very useful and accurate numerical model has been developed for analyzing pseudo-two-dimensional large-strain consolidation problems for rectangular or triangular regions. Parametric variation studies show the consolidation rate depends greatly on the aspect ratio (width/height), particularly for narrow widths and anisotropic permeability. For the test pit, which has an aspect ratio of approximately 5, the rate of consolidation as a result of two-dimensional drainage is only

14 slightly greater than the rate of consolidation as a result of one-dimensional drainage. Hence, disposal of thickened clay in mine cuts does not offer a significant improvement in the rate of consolidation compared to placement of thickened clay in a large pond with the same depth. It was found that the trapezoidal shape of the test pit had little influence on the consolidation. However, this may be due to the high aspect ratio and small change in height of the clay during the monitoring period. In situations where there is a smaller aspect ratio and a larger change in height, and hence a significant change in the shape of the waste clay as consolidation occurs, the shape of the pit may need to be taken into account. Simulation of consolidation in the test pit has also shown that the average seepage head of 13.4 feet had a strong influence on consolidation. However, under full-scale field conditions, there would be little or no seepage head. Existing one-dimensional design techniques have been shown to be sufficiently accurate for evaluation of consolidation in a V-shaped mine cut. However, the two-dimensional program would still be essential for analysis of an actual test pit. This research has shown how to simulate consolidation of waste clay in mine cuts. However, due to the differences in clay properties, geometry, and other factors, the optimal disposal system must be evaluated individually for each mine situation. As predicted by comparing the flow rate of water to the clay surface vs. time with the average pan evaporation rate, little desiccation occurred in the test pit during the study period. However, some interesting observations of the progression of desiccation in a trapezoidal shaped pit and some 3

15 measurements of the physical behavior of the clay during desiccation were made. More measurements of both actual rates of desiccation and of the physical behavior of the clay during desiccation are desirable in order to develop guidelines for predicting desiccation rates. 4

16 2.0 PROJECT DESCRIPTION 2.1 Introduction Waste clay disposal is a major technical and environmental problem for the phosphate mining companies in Florida. The volume of clay slurry produced by ore beneficiation exceeds the volume of below-ground void created by ore removal. At the present time, approximately 150,000 acre-feet of storage volume must be provided each year for the waste clays produced. Traditional practice in the industry requires the construction of earthen impoundments to store the waste clay. These ponds have typically been constructed on an as-needed basis, with little advance planning. Until the late 1960's, the dams surrounding the disposal areas generally consisted of shaped overburden spoil piles which had been cast by the dragline during mining. The lack of engineering design and construction control on these structures led to a series of dam failures that resulted in off-property spills of the semi-fluid clays. Following the last dam failure in 1971, State regulations requiring stricter dam design and construction were adopted. In addition, Federal and State regulatory agencies have continued to press for elimination of conventional above-ground clay ponds and reclamation of the land at or near original ground surface. In response to increased public concern over the adverse impacts of waste clay impoundment, the phosphate industry, aided primarily by the U.S. Bureau of Mines, has searched for improved methods of clay dewatering and disposal (Staff, Bureau of Mines, 1975; Lamont, et al., 1975; Bromwell and Raden, 1979). Following extensive research on the geotechnical 5

17 behavior of waste clays and sand tailings/clay mixtures (Bromwell and Oxford, 1977; Keshian, et al., 1977; Martin, et al., 1977), Bromwell Engineering developed laboratory testing and computer modelling techniques to predict the time rate of consolidation (or dewatering) of waste clays and sand-clay mixtures under varying disposal and treatment conditions (Bromwell and Carrier, 1979). These techniques have been used to prepare life-of-mine waste disposal and reclamation plans for several proposed new phosphate mines, as well as to analyze specific impoundments at existing mines. For each mine considered, forecasts have been made for the capacity of the initial settling areas, the time required to begin and to complete reclamation, the consistency of the reclaimed ground, and the final ground surface elevations. Furthermore, these techniques have been used to make quantitative comparisons among alternative methods of clay dewatering and disposal. For example, it is possible to numerically evaluate the effect of varying the site geometry, the filling rate, or the sand-clay ratio, as well as other variables. Hence, it is possible to optimize the waste disposal plan in order to balance the height of the temporary dikes versus the time required for reclamation. Although significant progress has been made in the last few years in developing these advanced techniques, their applicability has been limited to cases in which consolidation of the waste clay is essentially one-dimensional; i.e., the lateral dimensions of the disposal area are large with respect to the depth. Some practical disposal situations, however, involve two-dimensional drainage; i.e., both laterally and 6

18 vertically. A new disposal method has been tested at IMC in which drainage boundary spacing allows two-dimensional consolidation. The purpose of this research is to evaluate IMC's field experiment and to develop new design techniques in order to apply this method to other mining situations which involve different clay properties, filling rates, pit depths, side slopes, sand-clay ratios, seepage conditions, etc. IMC's field experiment involved pumping thickened clay, which has been partially dewatered by gravity in a holding pond, adding dewatered tailings sand if required, and depositing the mixture in mine cuts between windrows of overburden. The overburden rows provide easy access to the interior of a waste disposal area, and thus this disposal method may facilitate placement of a soil cap after a crust has formed on the waste clay. IMC has experimented with different construction techniques to apply the cap without displacing the soft clay. The overburden rows may also strongly influence the consolidation of the clay. In one-dimensional consolidation, the draining water only moves vertically, either up or down. In a mine cut, the water can also seep laterally into the overburden rows. Hence, the consolidation is two-dimensional. Depending on the dimensions of the mine cut, the dewatering may occur significantly faster than will occur with only one-dimensional drainage. The IMC field test was under the direction of Dr. James E. Lawver; the work was jointly sponsored by IMC, Agrico, and Mobil Chemical Company. Considerable information and experience was gained regarding pumping, piping, depositing, decanting, capping, etc. Two small mine cuts were filled during preliminary testing. As a crucial part of the project, IMC 7

19 filled a large mine cut with thickened clay. This mine cut is approximately 40 feet deep, 250 feet wide, and 1,200 feet long. Bromwell Engineering instrumented this mine cut and collected field data regarding the amount and rate of consolidation of the clay. Desiccation of the clay surface was also studied. In addition, a new two-dimensional computer model was written, by extending the large-strain finite difference formulation which formerly was used, in order to analyze the behavior of the clay and to develop a design methodology for other mining situations. To assist in this research program, Bromwell Engineering enlisted the support of Prof. Frank Somogyi of Northwestern University (formerly of Wayne State University), who was instrumental in the development of the existing finite strain slurry consolidation computer programs. 2.2 Objectives There are four major objectives of the research program, as follows: o Evaluate field dewatering behavior in a mine cut; o Develop new computer programs to analyze twodimensional consolidation; o Obtain laboratory data regarding consolidation properties of the IMC clays; and 8

20 o Study the field desiccation behavior of phosphatic clay in order to predict when capping and final reclamation of clay or sand-clay disposal areas can be conducted. Each of these objectives is described below Field Evaluation The first major objective of the proposed research program was to measure field rates of consolidation at the IMC test mine cut and to correlate the results with laboratory test data and computer analyses. From the field measurements, the computer model has been validated Two-Dimensional Computer Model Background: One-Dimensional Consolidation. Traditional practice within the phosphate industry involves the use of rules-of-thumb to predict the rate of consolidation of waste clays. For example, it is typical to assume that the clay will reach an average solids content of 20% when a disposal area is full. Such values are based on actual operating experience in Polk County mines and do not reflect the fact that a different clay mineralogy, filling rate, pit depth, dam height, or drainage conditions will produce a different result. Furthermore, such rules-of-thumb cannot be used to predict the effects of pre-thickening or flocculating the clays, sand-clay mixing, or other potential treatments to improve dewatering behavior. In an effort to improve on the rule-of-thumb approach, static settling tests in graduated cylinders have been used to

21 predict field dewatering behavior. Although such tests can be useful to correlate differences in clays from various areas, they cannot be used to predict the changes in clay consolidation that will result from varying the geometry of the disposal area, filling rate, drainage conditions, etc. In order to properly account for all of the significant factors that can influence the field dewatering behavior of a clay slurry, two conditions must be met: A laboratory test (or small-scale field test) must be performed that measures the basic consolidation properties of the material involved (dilute clay, flocculated clay, sand-clay mixture, or clay treated by any other method). A computer model must be used that correctly accounts for all of the site-specific variables (area, height, drainage conditions, filling rate, etc.). Bromwell Engineering has developed a laboratory test procedure and a family of eight finite difference computer programs specifically to analyze the one-dimensional consolidation of phosphatic clays. These programs were written under the sponsorship of ten mining companies within the Florida Phosphate Council. These computer programs are based on established geotechnical principles, and they use a sophisticated formulation of finite-strain, non-linear consolidation theory. Details of the mathematics and applications of the programs are documented in the literature (Bromwell Engineering, Inc., 1979; Carrier and Keshian, 1979; Bromwell and Carrier, 1979; Somogyi, 1980; 10

22 Carrier and Bromwell, 1980; Somogyi, et al., 1980). These programs also have important applications in related fields such as dredged spoil material, rapidly sedimenting clay in estuaries and ocean basins, and other fine-grained waste materials. The computer programs have been named: FLINITS FLCONTS QSNONUS QSUNIFS FLINITD FLCONTD QSNONUD QSUNIFD The "FL" programs analyze consolidation during filling for a given period of time, or until a specified height is reached. The "QS" programs analyze consolidation during quiescent settling for a specified period of time. The final letter "D" denotes those programs which permit double drainage through both the top and bottom surfaces of the clay. The final letter "S" denotes those programs which are restricted to single drainage through the top surface of the clay. The FLINIT programs are used to analyze consolidation during an initial filling period. The FLCONT programs are used to analyze consolidation during filling over an existing deposit. The FLCONT programs are used whenever a change in the filling rate occurs, or when filling is resumed after a period of quiescent settling. The QSNONU programs are used to analyze consolidation during quiescent settling of clay in which the solids content varies with depth. The QSNONU programs are utilized when filling is stopped, either permanently or temporarily. 11

23 The QSUNIF programs are used to analyze consolidation during quiescent settling of clay in which the initial solids content is uniform with depth. conducting parametric studies. This program is very useful for All of the programs allow application of a surcharge load to the top surface of the clay to simulate overburden capping. The output includes predicted settlement versus time and solids content versus depth and time. The output of one program becomes the input for the next program and virtually any sequence of filling and quiescent settling can be analyzed. A typical analysis may require first a FLINITS run, followed by QSNONUS, FLCONTS, QSNONUS, FLCONTS, etc. The computer programs have been verified in numerous one-dimensional situations, and full-size settling areas. including large standpipes, tanks, These programs have been used to prepare life-of-mine waste disposal plans for numerous proposed mines, including Duette (ESTECH), Pine Level (AMAX), Hardee County Mine (Mississippi Chemical Company), and South Rockland (U.S. Steel). New Two-Dimensional Computer Model. All of the above analyses have had one major point in common: the consolidation is primarily one-dimensional. For many mining areas, much of the overburden must be removed from the pit to construct the perimeter dikes, and a one-dimensional analysis is adequate (see Figure 2-l). However, in other mining areas, windrows of overburden remain in the pit, and two-dimensional consolidation obviously occurs (see Figure 2-l). Neglecting two-dimensional consolidation in these cases will lead to an underestimate of the rate of consolidation. The error will likely result in 12

24 planning for higher dikes than would actually be required. In addition, it may not be possible to predict final elevations accurately. Hence, the second objective of this research is to write new two-dimensional, finite-difference computer programs. Not only will two-dimensional analyses be useful for general phosphate mining situations, but the shape of the IMC test mine cut, described above, is such that it is essential to have this capability in order to evaluate its performance and thereby extrapolate the test results to full-scale mine operations. In addition, the existing one-dimensional programs do not consider seepage forces. For example, if the natural water table beneath the disposal area is below the water surface in the pond, downward seepage will occur. This seepage produces an additional stress which consolidates the clay more than would occur otherwise. (Note: Seepage force is not to be confused with double drainage. In the latter, water flows through the bottom of the disposal pond due to the dissipation of excess pore pressure; the outside water table is presumed to be equal to the inside water level.) Neglecting seepage forces also leads to an underestimate of the actual rate of consolidation, but the magnitude and effects on waste disposal planning are not known. Hence, also included in the programs are the following seepage alternatives: o Constant water level differential; o Variable water level differential, inside level coincidental with settling clay surface. These cases are likely to include any actual seepage situation and are essential to interpret the IMC test results. 13

25 2.2.3 Additional Consolidation Data In addition to the existing computer programs, a laboratory slurry consolidation test has also been developed and refined. This test is used to determine the compressibility and permeability properties of the phosphatic clay, which are used as input to the computer programs. Details of operation of the consolidometer are described in the literature (Bromwell and Carrier, 1979; Carrier and Keshian, 1979; and Section 4.3 of this report). The clay samples are obtained either from geologic cores for future mines or from active settling areas for existing mines. In addition, Prof. Robert L. Schiffman and his colleagues at the University of Colorado have developed a Constant Rate of Deformation Slurry Consolidometer (c.f., Znidarcic and Schiffman, 1981). The CRDSC represents a major breakthrough, as the testing time is greatly reduced and the permeability of the sediment is based on a more mathematically correct procedure than was formerly used. Based on numerous slurry consolidation tests on phosphatic clays from future and existing mines, it has been found that the compressibility and permeability can be conveniently expressed as: B Compressibility: e = A;; Permeability: k = Ce D 14

26 where e = void ratio of clay* z = effective stress imposed on clay element k = permeability of clay A,B,C,D = material property constants It has been found that the values of A, B, C, and D can vary widely from mine to mine and even within mine tracts. has also been found that the mineralogical composition of the clay strongly influences the values of these parameters. the mineralogy is also reflected in the liquid and plastic limits of the clay, correlations have been developed by It Since Bromwell Engineering in an effort to make preliminary estimates of consolidation parameters based on relatively simple laboratory tests (Carrier, et al., 1982). In preliminary work at the IMC test site, values for A and B were reasonably well established based on field and laboratory data; values for C and D were initially estimated based on limited laboratory data. Hence, representative samples of the test clay were obtained and the following data obtained: * e = volume of void volume of solid; for saturated conditions (i.e., no air in the slurry), the void ratio can be calculated as: where G sc = specific gravity of clay particles; = solids content (%) 15

27 0 Atterberg limits (liquid and plastic limits); o o o o o Specific gravity; Hydrometer analysis (particle size); X-Ray diffraction; Scanning electron microscope; and Slurry consolidation Desiccation Behavior As explained earlier, advanced techniques have been developed for analyzing and predicting one-dimensional consolidation of phosphatic clay and sand-clay mixes. In addition, the first three objectives of this research project are aimed at extending these techniques to include two-dimensional consolidation. With these tools, it will be possible to prepare a life-of-mine waste disposal plan for virtually any mining conditions. Once waste disposal can be handled effectively, the next major consideration is reclamation. It is well known that simply filling a disposal area with thickened clay or sand-clay mix will not produce reclaimed land. Even with a sand-clay mix, the surface will not have suitable mechanical and agronomic properties to restore the area to productive use, such as agriculture or wildlife sanctuary. Hence, the clay must be capped, either with overburden, tailings sand, or a sand-clay mix with a very high SCR of, say, 10. In order to apply this cap, the surface of the clay must first be desiccated to form a crust with sufficient thickness and shear strength to support the extra load. For a given height of capping material, it is a straightforward calculation to determine the required crust properties. What is not known is how much desiccation time 16

28 will be required to achieve the desired crust, nor what is the best construction method of applying the cap. Preliminary studies of crust formation on dredged materials have been performed by the Corps of Engineers (Haliburton, 1978). Based on these studies, the thickness of the crust, h, in inches, in given by: As an example, w u content of 15% is equal to 567%. taken equal to 1.2 x plastic limit, at a typical thickened clay solids The COE recommends that W C be which for a typical phosphatic clay = 1.2 x 40% = 48%; this corresponds to a solids content of nearly 68%. The average pan evaporation rate for central Florida is approximately 5.7 in./month. By substituting into the above expression, h is found to be about * Water content, w, is defined as weight of water weight of solid, usually expressed as a percentage. It can be calculated from the solids content, S C, according to: x 100% 17

29 3 in./month; thus, a l-foot crust could be established in about four months. The shear strength of the crust would be in excess of 500 psf, and this would be sufficient to support several feet of capping material. Now, the fact is that field observations of thickened phosphatic clay disposal areas demonstrate that a crust does not form this quickly. This is because as consolidation proceeds, excess water flows from the interior of the clay to the surface, at an ever-decreasing rate. Desiccation will not even begin until the water flow rate drops below the desiccation * rate. Since essentially no field data previously existed on the rate of crust development for phosphatic clays, field tests were performed to measured the growth and development of a crust on the IMC mine cut. Concurrently, IMC personnel have been studying construction methods (such as hydraulic) for applying the capping material in an efficient and economical manner. It is expected that general guidelines can be developed for predicting the time required for desiccation of a crust at any given phosphate mine. This is essential for planning future reclamation of clay and sand-clay disposal areas. * However, the amount of water that must be removed from thickened clay or a sand-clay mix before desiccation can begin is much less than with conventional disposal of dilute clay. 18

30 3.0 FIELD EVALUATION 3.1 Pit Geometry and Test and Instrument Locations Figures 3-1 and 3-2 present a plan view and cross sections of the test pit, indicating the pit geometry and the testing and instrument locations. Also shown on the plan view is the topography of the test pit. As can be seen, the test pit is approximately 272 feet wide and 1,190 feet long, or a surface area of 7.4 acres. The cross section of the pit is roughly trapezoidal in shape. A plot of storage volume vs. elevation for the test pit is shown on Figure 3-3. The clay inlet pipe is located at the eastern end of the pit and a spillway is located at the western end of the pit to keep the water level inside the pit drained down to the clay surface. A grid of nine testing stations was established. All sampling, pore pressure measurements, and permeability tests in the clay were conducted at these stations. Permanent instrumentation included tide gauges in the pit and piezometers installed in the soil surrounding the mine cut. Two tide gauges were installed in the test pit, one at each end of the pit. The tide gauges consisted of 24-inch diameter steel pipe embedded in the bottom of the pit so that no movement of the tide gauges would occur. Four hydraulic and six pneumatic piezometers were installed in the soil surrounding the mine cut. These piezometers permitted continuous monitoring of the boundary pore pressures. 3.2 Filling History The test pit was filled with gravity thickened clay. clay was discharged into the eastern end of the test pit. The The 19

31 throughput solids content measured by IMC during filling varied from 13.8 to 17.4, with an average of 16.0%. The pit was filled to an average elevation of on 04/24/81. At this time, the difference in the elevation of the clay at the two ends of the pit was 0.7 feet, giving a slope of approximately 0.7 feet per 1,000 feet. The clay was then allowed to consolidate until 07/10/81, at which time additional clay was pumped into the test pit, raising the average elevation to After this second fill, the slope of the clay from one end of the pit to the other was approximately 1.2 feet per 1,000 feet. Figure 3-4 shows how the average elevation of the clay surface has varied with time. The corresponding variation in volume of clay is shown on Figure 3-5. The "sawtooth" pattern is due to alternating periods of filling and settling. Figure 3-6 presents the dry weight of clay -vs. time from throughput measurements made by IMC personnel. The amount of clay that was calculated based on the sampling programs is also shown. A comparison between the amount of clay calculated based on the sampling programs and the amount of clay based on IMC's pumping data is shown in Table 3-1. As can be seen, the data agree very well, with the largest difference being less than 4% and the average difference being 1.9%. A daily record of the IMC throughput measurements is shown in Appendix A. 3.3 Boundary Pore Water Pressures The boundary pore water pressures were monitored with four hydraulic and six pneumatic piezometers located in the soil on the sides and bottom of the test pit. The locations of the piezometers are shown on Figure 3-2. Measurements of pore water pressure vs. calendar time for the various piezometers is 20

32 shown on Figures 3-7 and 3-8. As can be seen, the boundary pore water pressures measured in these piezometers are less than the phreatic surface of the water in the waste clay. This head difference causes a downward seepage force which increases the effective stress on the clay particles. This in turn results in a higher solids content (lower void ratio) than would occur if the boundary pore pressures were at the same elevation as the phreatic surface of the water in the waste clay. Table 3-2 shows how the average boundary pore water pressures and head difference have varied with time. As can be seen, the boundary pore water pressures on the average had dropped nearly 3 feet by July 21, 1981, and have continued to drop slowly since then. The cause for the decrease in the boundary pore pressures may be that the area of infiltration was reduced once the pit was filled with clay as the water inside the pit was kept drained down to the clay surface. The head difference between the boundary pore water pressures and the phreatic surface of the water inside the pit has varied from a minimum of 11.8 feet to a maximum of 16.2 feet, with an average of 13.4 feet. The larger head difference of 16.2 feet was measured on July 21, 1981, and was caused partly by the additional clay that was pumped into the pit between the dates of July 10 and July 21, Hence, even though the phreatic surface inside the pit has dropped 5 feet, the boundary pore water pressures have also dropped, so that the head difference has not varied much. 21

33 3.4 Sampling Data Samples of the clay vs. depth were obtained with a piston tube sampler. A schematic of the sampler is shown on Figure This sampler has proven to be reliable in obtaining samples over a large range of solids concentration. In operation, the sampler is manually pushed into the soil to a specified depth, and a sample is taken by holding the piston stationary and advancing the sampler. The sample is then extruded into a jar, sealed, and returned to the laboratory for testing. The sample recovered is not undisturbed, but the water content is representative of the -- in situ condition. Hence, the total weight (saturated), dry unit weight, and void ratio can be determined with reasonable accuracy. The test pit was sampled five times at each of the nine sampling stations over a period of eight months. Samples were taken at the surface, one-foot depth, three-foot depth, and every three feet thereafter. The samples were returned to the Bromwell Engineering laboratory for determination of solids content and percent passing a U.S. Standard No. 140 mesh sieve. Solids content vs. depth at each test station for each field sampling is shown on Figures 3-10 to Tabulations of the sampling data are shown in Appendix B. Detailed evaluation of the sampling data indicates that the average solids content of the clay in the pit varied as shown in Table 3-3. As can be seen, the average solids content decreased between July 10 and July 21. This was due to the clay which was added between those two dates being at a lower solids content and thereby reducing the overall average. Also shown in Table 3-3 is the average solids content calculated from the IMC pumping 22

34 data and the tide gauge readings. As can be seen, these values agree very well with the values obtained from sampling the pit. 3.5 Pore Pressure Probe Data Pore water pressure measurements within the clay were made using the electrical pore pressure probe shown in Figure To obtain pore pressure measurements, the probe is manually pushed into the clay to a specified depth. The fluid pressure is transmitted through the porous tip and acts against the diaphragm of the electrical transducer. The output from the transducer in millivolts is then converted to pressure by means of a calibration curve. It is necessary to hold the probe in position until the electrical reading indicates equilibrium has been achieved, which may take up to sixty minutes. After a reading has been completed, the probe is pushed deeper into the soil to measure the pore pressure at the next specified depth. Piston tube samples of the clay are then taken immediately adjacent to the pore pressure probe location at the same depths. By measuring the total unit weight of the samples, it is possible to calculate the total stress vs. depth. Then, the effective stress vs. depth is calculated by subtracting the pore pressure from the total stress. Next, the void ratio of each sample is correlated with the effective stress in the soil at the same depth. Thus, by performing a pore pressure probe and recovering samples, it is possible to directly evaluate the compressibility of the clay. This procedure is repeated at different locations in the disposal area in order to investigate the variations in material properties. Pore pressure probe measurements were performed at the six test locations along cross sections 1 and 3 on 04/27/81, at 23

35 test location 3B on 07/10/81, and at the six test locations along cross sections 1 and 3 on 12/30/81. The results of the measurements are shown on Figures 3-20 to Tabulations of the pore water pressure measurements are shown in Appendix C. As can be seen, the measured pore water pressure at the bottom of the pit is less than the hydrostatic water pressure at the same depth. This is due to the water table in the overburden outside the pit being lower than the water table inside the pit, which results in a seepage force that has the effect of increasing the clay solids content. A compressibility curve of the clay has been developed from the pore pressure and sampling data and is discussed with laboratory measurements of compressibility in Section Field Permeability Measurements In situ permeability measurements were made by performing rising head tests with a permeability probe. A schematic of the probe is shown on Figure The test involves lowering the water-filled tube connected to the probe a few centimeters below the equilibrium reading and then measuring the rate at which the water level rises back to the equilibrium value. The in situ permeability of the clay can then be calculated by means of standard formulae. By taking measurements at different depths and at different times, a plot of in situ permeability vs. void ratio can be obtained. In situ permeability measurements were performed on 12/30/81 at test locations 1A and 3A. The results of these tests are shown in Appendix D and are discussed with laboratory measurements of permeability in Section

36 4.0 LABORATORY TESTING 4.1 Index Properties Index tests were performed on composites from different depths in the test pit from samples recovered on 04/29/81. The tests included Atterberg limits, hydrometer analysis, and specific gravity. The results of the tests are summarized in Table Atterberg Limits Atterberg limits are simple laboratory tests which provide an approximate indication of clay mineralogy and soil behavior. The test methods are described in ASTM D 423 and D 424. The liquid limit (LL) is defined as the water content above which the clay behaves essentially as a liquid and below which it behaves as a plastic material. The plastic limit (PL) is defined as the water content above which the clay is still plastic and below which it is a semi-solid. The plasticity index (PI) is defined as the liquid limit minus the plastic limit. In general, as the plasticity index increases, the consolidation properties become worse; that is, the compressibility increases and the permeability decreases. Recently methods have been developed for determining preliminary values of compressibility and permeability which are based solely on the Atterberg limits of the material (Carrier, et al., 1982). The results from using these methods for the clay in the test pit is discussed in Section 4.3. Referring to Table 4-1, it can be seen that there is a small range in the Atterberg limits for the clay in the test pit. The plasticity index varies from 164 to 177. The 25

37 Atterberg limits of the clay in the test pit plotted on the standard plasticity chart are shown on Figure 4-1. Also shown, for comparison, is the range for Florida phosphatic clay samples tested to date. It can be seen that the plasticity index of the test pit clay is on the high side, which indicates relatively poor consolidation properties compared to other phosphatic clays Hydrometer Analysis The hydrometer analysis is a laboratory test used to calculate the particle size distribution for soils finer than a No. 200 sieve. The technique is based on Stokes' law for spheres falling through a fluid. The test method is described in ASTM D 422. Of most interest is the percent by weight of the waste clay which is finer than 2 micrometers. Particles larger than 2µ are considered to be silt-sized; particles smaller than 2µ are clay-sized. Hence, it is the fraction finer than 2µ which causes the colloidal behavior of the waste clay. Referring to Table 4-1, it can be seen that this fraction varies little from a minimum of 76% to a maximum of 88%. The range in the fraction finer than 2µ for other samples of Florida phosphatic clay previously tested is 20% to 90%. Particle size distribution curves for the eleven hydrometer tests performed are included in Appendix E. Also tabulated in Table 4-1 is the clay activity, which is defined as the plasticity index divided by the fraction finer than 2µ. It can be seen that the activity ranges from 2.04 to This is considered a high activity compared to most naturally occurring clays in other parts of the world and indicates the presence of highly plastic clay minerals. The 26

38 range in activity for samples of other Florida phosphatic clay tested is 1.2 to Specific Gravity The specific gravity is used to calculate the void ratio, e, of the clay, which is defined as the volume of voids divided by the value of solids: where G sc = specific gravity = clay solids content (%) The test method is described in ASTM D 854. Referring to Table 4-1, it can be seen that the specific gravity of the test pit clay varies little from 2.70 to The range in the specific gravity for samples of other Florida phosphatic clay tested is 2.65 to Hence, the test pit clay has a specific gravity typical of most Florida phosphatic clays Summary of Index Properties In summary, the index properties show that the clay is essentially homogeneous throughout the test pit. The average index properties of the test pit clay are: 27

39 LL = 226 PL = 54 PI = 172 minus 2µ = 81 activity = 2.12 G = 2.71 These values are within the usual range of Florida phosphatic clays. However, the plasticity index is on the high side of the typical range, which indicates that the consolidation properties of the test pit clay are on the "poor" side of the typical range for Florida phosphatic clays. This is discussed further in Section Mineralogy Five of the composite samples were sent to Bromwell Engineering's consulting clay mineralogist, Dr. R. T. Martin, for mineralogical analysis by X-Ray diffraction. Dr. Martin's report is included in Appendix E. It was found that the samples were very similar. Approximately two-thirds to three-fourths of each sample consisted of clay minerals. Smectite (montmorillonite) is the dominant clay mineral, followed by illite, with minor amounts of kaolinite and palygorskite (attapulgite). 4.3 Consolidation Tests Two types of slurry consolidation tests were performed on a composite of samples taken from the test pit on 04/27/81: a stress-controlled consolidometer test and a constant rate of deformation slurry consolidometer (CRDSC) test. Bromwell 28

40 Engineering has used the stress-controlled slurry consolidometer since Similar slurry consolidometers have also been designed by other investigators (Salem and Krizek, 1973; Roma, 1976; Barvenik, 1977). In the stress-controlled test, vertical loads are applied to the sample in a series of increments by means of a piston. Measurements of the change in height of the sample with time are made as the sample consolidates under each load increment. The compressibility of the sample is determined by plotting the void ratio at the end of each loading increment versus the applied stress, as is generally done in the conventional oedometer test. The permeability is calculated according to an empirical procedure (Carrier and Keshian, 1979). This procedure uses elements of the classic Terzaghi consolidation theory, which has been modified based on finite strain computer simulations of the slurry consolidation test. Direct measurements of permeability using conventional constant head or falling head tests would be in error due to seepageinduced consolidation. Even the lowest gradients can cause significant seepage consolidation in the very soft sediments tested in the slurry consolidometer. The primary disadvantage of the stress-controlled slurry consolidometer is that it requires a considerable period of time to perform a test. For example, a test on Florida phosphatic clay will run four to six months. Recently, Bromwell Engineering has improved the stress-controlled slurry consolidometer so that tests on samples of Florida phosphatic clay can now be completed in less than six weeks, and accurate direct measurements of permeability can be made. The CRDSC test was performed by Bromwell Engineering's consultant, Prof. Robert L. Schiffman, and his colleagues at 29

41 the University of Colorado. In the CRDSC test, a piston squeezes the clay sample at a constant velocity, and the resulting total stress and pore pressure versus time are recorded. This operation is similar to that of constant rate of strain oedometers developed by other investigators (Smith and Wahls, 1969; Wissa, et al., 1971). However, interpretation of the test data is based on finite strain theory, rather than the infinitesimal strain Terzaghi theory (Znidarcic and Schiffman, 1981). This, of course, is a much more complicated analytical procedure. The CRDSC represents a major breakthrough, as the testing time is less than one week. Furthermore, evaluation of the permeability of the sediment is based on a more mathematically correct procedure than has previously been used. The results of the two consolidation tests are shown on Figures 4-1 and 4-2. Tabulated results of the consolidation tests are shown in Appendix G. As can be seen, the two tests agree extremely well. The compressibility and permeability can be conveniently expressed as: Compressibility: e = 23.0; Permeability: k x 10-6e4'1g where: e = void ratio of clay ';; = effective stress in psf k = permeability in ft/da Figures 4-4 and 4-5 show a comparison between the best fit curve of the CRDSC test, the results of field measurements, the relationships assumed for preliminary predictions of consolidation in the test pit, and relationships developed from

42 correlations based on the Atterberg limits of the clay (Carrier, et al., 1982). As can be seen, all of the compressibility data are in reasonable agreement. The field and laboratory measurements of permeability are also in reasonable agreement. However, the measured permeability is significantly less than had been assumed for the preliminary predictions. At any given void ratio, the measured permeability is one-fourth of the preliminary value. The correlation based on Atterberg limits predicted an even lower permeability. Figures 4-6 and 4-7 show the compressibility and permeability of the waste clay in the test pit compared with the typical range of these properties for Florida phosphatic clay. As can be seen, the clay in the test pit has "poor" consolidation properties compared with phosphatic clay from other mines. 31

43 5.0 MATHEMATICAL MODELLING OF TWO-DIMENSIONAL CONSOLIDATION 5.1. Introduction The problem being addressed is the prediction of the rate of quasi-two-dimensional self-weight consolidation of a uniform initial solids content slurry deposited into a rectangular cross section disposal area with frictionless sides. The term "quasi-two-dimensional" consolidation refers to an idealization of the actual process, whereby the soil particles are constrained to move in the vertical direction, while the pore fluid may move both vertically or horizontally. Utilizing this idealization, initially rectangular control volumes (or numerical mesh) remain rectangular throughout the consolidation process. While this avoids the need for, and mathematical complexities associated with, multi-dimensional constitutive relations and failure criteria, it precludes the ability to model lateral particle movements due to lateral seepage forces or the "self-levelling" flow near the surface of the consolidating deposit. The rectangular cross section was chosen for initial modelling because of computational ease. The assumption of frictionless vertical boundaries was introduced to again avoid the need for multi-dimensional constitutive relations and failure criteria Mathematical Derivation The mathematical formulation paralleled the basic formulation presented by Gibson, England, and Hussey (1967). The problem was initially formulated directly in terms of 32

44 material coordinates for both vertical and horizontal directions. Major difficulties were encountered in transforming solutions thus obtained to spatial coordinates. Therefore, the problem was re-formulated in terms of material coordinates in the vertical direction and spatial coordinates in the horizontal direction, thus taking full advantage of the idealization that particles are constrained to vertical movement. The equation describing the consolidation process is given by: 33

45 It should be noted that in Equation (5-1), the term (1 + e) appears in the denominator of the "diffusion coefficient" in the vertical direction (and must be differentiated) and in the numerator of the horizontal "diffusion coefficient". The numerical ramifications of this will be discussed later. After introducing the following relationships Somogyi, 1980): (as in 34

46 Equation (5-3) is the general equation describing the process and is to be solved numerically. It should be noted that the equation assumes constant submergence of the consolidating deposit. Details of the mathematical derivation are contained in Appendix H. Assuming perfect drainage all around, the boundary conditions are zero excess pore pressure (u) at all boundaries. In addition, the initial excess pore pressure distribution is identical to the buoyant stress distribution. It is of interest to compare Equation (5-1) with the classical linear small strain theory. The relationship between material and spatial vertical coordinates gives: 35

47 where a and b are the initial location of the point in question, which does not change with time in the classical formulation. If the void ratio is assumed constant in the horizontal (i.e., b) direction,, then the last term of Equation (5-5) vanishes. Furthermore, if very small changes in void ratio are assumed, then: Finally, if a homogeneous, isotropic, and constant permeability and linear void ratio vs. effective stress are assumed, Equation (5-5) becomes: (5-7) which is the standard linear two-dimensional heat conduction equation or the classical linear "pseudo-two-dimensional" consolidation equation. 5.3 Numerical Formulation A great variety of finite difference schemes can be, formulated for solving equations such as Equation (5-3). Richtmeyer and Morton (1967) presented thirteen different schemes for solving linear initial value problems. Somogyi 36

48 (1975) presented a summary of available techniques for solving linear multi-dimensional diffusion equations. Allada and Quon (1966) compared various algorithms for solving the linear problem and concluded that the alternating direction explicit procedure (ADEP) was superior since it combined the computational ease of explicit methods with the stability of implicit methods. ADEP was therefore the initial choice for the present work ADEP The alternating direction explicit procedure was first introduced by Saul'ev (1957), and its stability was analyzed by Larkin (1964). A forward difference is used to approximate the time derivative. The second derivatives in "space" are approximated by the combination of a forward difference at one time level and a backward difference at the other. By judicious choice of starting point and finite differencing, either known boundary values or previously calculated values at surrounding points can be employed to advance the solution point by point. Since errors are accumulated in the corner opposite the starting point, a reverse sweep is performed at the next time step (starting at the opposite corner), thus minimizing overall errors. The basic computational model is shown schematically in Figure 5-1. The basic ADEP scheme was slightly modified in order to handle the diffusion-convection equation given by Equation (5-3). The first derivatives in "spatial" coordinates were approximated using either forward or backward differences, depending on the direction of sweep. 37

49 The implications of this modification should be discussed. Equation (5-1) can be rewritten in self-adjoint form as: The D's are diffusion coefficients (or functions), and C's are convection coefficients (functions). If the diffusion functions are small in some region of "material-physical" space (3 - x space), then Equation (5-8) reduces to: Since the void ratio is a function of buoyant stress (which is independent of both x and t unless filling occurs) and excess pore pressure, Equation (5-9) can be written as: (5-10) 38

50 Thus the excess pore pressure u satisfies a nonlinear wave equation in regions where diffusion is small. The physical implications of the above observation suggests that the pressure "convects" in a nonlinear fashion in regions of small diffusion. According to Kriegsmanu (1982), the computational ramifications are equally as important. It has been established that ADEP yields unconditionally stable calculations for Equation (5-8) when C 2 = 0. That is, the spatial and temporal step sizes are independent. However, when C 2 # 0 and the diffusion is small in some region, this is no longer the case for Equation (5-10). This is because Equation (5-10) admits discontinuous solutions or "shock waves" which cannot be reproduced by a fixed grid situation. Such an attempt introduces errors which may propagate into other regions of the numerical domain. Another potential pitfall arises because it isn't clear the ADEP is unconditionally stable for Equation (5-10). If it were not, then a restriction such as: (5-11) must be made for stable calculations. Here A is some constant which can be definitely determined for linear problems, but not for nonlinear cases, for which it must be established by trial. In the numerical literature (as in Richtmyer and Morton, 1967), this restriction is called the Courant, Friedricks Levi condition. 39

51 5.3.2 Recurrence Formulae The numerical mesh and boundary conditions for the problem at hand are depicted in Figure 5-2. Advantage was taken of symmetry by imposing a no-flux boundary along the centerline of the region, thus halving the required number of calculations. As previously mentioned, the solution proceeds in two stages or sweeps. The first stage, or forward sweep, begins in the "southwest corner," or at i = 2, j = 2. The second stage or reverse sweep begins in the opposite, or "northeast" corner, at i = m - 1, j = n. The recurrence formulae for advancing the solution to Equation (5-3) using ADEP are as follows (detailed derivation in Appendix I): Stage I (Forward Sweep) at interior nodes (i = 2, m - 2, and j = 2, n): 40

52 Adjacent to the centerline (along i = m - l), Equation (5-12) can be used as is if the following is set immediately prior to computation: 41

53 At each time level "K," once the excess pore pressures have been computed (using Equations (5-12) and (5-13), or (5-14) and (5-15)), the corresponding effective stresses, void ratios and permeabilities must be calculated before the solution can proceed (in order to update e, s, k, and K). These are calculated from: 42

54 It should be noted that the effect of sand mixing (as well as the solids content and effective stress near the deposit surface) is handled in the same manner as has been previously for the one-dimensional situation, as described in Somogyi, et al. (1982). Whenever conditions along the centerline are desired, they are calculated using a parabolic interpolation between surrounding points, from: (5-17) Whenever the average height and solids contents (total and/or clay) are desired, the heights, H., at each vertical 1 strip (i = 1, m - 1, and centerline) are first computed from the corresponding void ratios. The average height is then computed as the total volume divided by the deposit width, the total volume being calculated from: (5-18) 43

55 5.4 Computer Program "TWODUN" A computer program, TWODUN, has been written for performing the computations described in the previous section. The complete listing is contained in Appendix J. The parameters used in the analysis can be broadly grouped into Input, Internal, and Output Parameters. The Input Parameters can be further subdivided into Site, Material, Numerical, and Print Control Parameters. The Internal and Output Parameters are in general identical to those described by Bromwell Engineering (1981), with the addition of the degree of consolidation, DEG, which is defined as: (5-19) The Input Parameters and their format requirements are presented below: 44

56 45

57 5.4.1 Example An example will be presented in order to illustrate the usage of the program "TWODUN". The problem involves the prediction of the self-weight consolidation of 10.0 feet of clay slurry placed into a 10.0-foot wide containment area at a clay solids content of 16.0%. The void ratio-effective stress 46

58 and vertical permeability-void ratio relationships of the clay are as follows: The permeability is assumed isotropic (KRATIO = 1.0), and no seepage exists in the disposal area (UTOP = UBOT = 0.0). It is desired to perform the analysis for a maximum (TMAX) of one year. Two thousand iterations (NDT) are to be utilized (i.e., 1,000 two-stage calculation cycles), and therefore the size of each time-step is 365/2,000 = days. Since 20 printouts are desired for the year (i.e., after every 100th time step or 50th cycle), KPR is set at 50. The numerical grid is set up with 20 layers (N) and 10 nodes (M) along the halfwidth of 5.0 feet. Since only the excess pore pressures are desired to be printed, KU =l, and KEC...KSIG = 0. The required input file is discussed below, followed by key portions of the output. The entire input and output files for this problem have been included in Appendix K Tests of Stability and Convergence As previously discussed, ADEP is not necessarily unconditionally stable for the problem being solved. Tests were performed to assess the effect of mesh size on results. In no cases were instabilities encountered. However, the results were affected by the relative size of the grid. The basic problem used in these tests was the 10.0 by 10.0 region previously discussed. The basis for comparison is the 47

59 degree of consolidation (DEG) at 0.2 yr. The results of these tests are presented in Table 5-1. It can be seen that the results vary between 30.5% and 40.1% degree of consolidation. If the first run, utilizing 100 iterations per year, is ignored, the range is 36.7% to 40.1%. While this may seem substantial, it should be noted that the corresponding average solids contents are 17.4% and 17.6%, respectively. In general, it is recommended that the numerical grid be chosen so that: s (preferably < 1.0) DT - < 20.0 DX 2 - It should be emphasized that these are preliminary recommendations and may not be valid for large areas or low permeabilities. It is strongly recommended that tests of grid size be performed for all problems to be analyzed Effects of Aspect Ratio and Anisotropic Permeability A parametric variation was performed in order to assess the effects of disposal area width and horizontal permeability on the rate of consolidation. The basic problem involves a lo-foot height with initial solids content of 16% and material properties as given in the example previously presented. 48

60 The width of the disposal area was varied from 1.0 feet to 50.0 feet. The results of these analyses are presented in Figure 5-3. As expected, the width of the disposal area has a much greater effect on settlement rate for narrow areas than wide ones. Doubling the width from 1.0 feet to 2.0 feet produces a 350% increase in the time to attain 50% consolidation (from 3.6 to 12.8 days) and a 370% increase in the time to 90% consolidation. However, doubling the width from 10.0 feet to 20.0 feet causes only a 160% increase (from 108 to 170 days) for 50% consolidation and a similar amount for 90%. Coincidentally, the time for 50% consolidation doubles (55 to 110 days) when the width is increased from 5 to 10 feet, but the time for 90% consolidation increases 260%. The case with 50.0-foot width is also of interest because the aspect ratio (5:l) is quite similar to that in Pit 3, which will be presented later. Since Pit 3 is more than three times the size of this case, its consolidation rate can be expected to be 5 to 10 times slower. It should be noted that the cost of these runs, processed on-line, varied from about $12.00 for the l-foot width to $ for the 50-foot width (which involved 1,000 time steps per year for 2.5 years). The cost can be expected to increase linearly with number of iterations and exponentially as the spatial grid increases. The effect of possible anisotropic permeability, with horizontal permeability greater than the vertical, was also investigated for the basic 10.0-foot by 10.0-foot area. The results are shown in Figure 5-4. The time for 50% consolidation decreases from 110 days to 80 days if the horizontal 49

61 permeability is twice the vertical and 55 days (half) if the horizontal is four times the vertical. Somewhat unexpectedly, it was observed that the effect of halving the width was identical to quadrupling the ratio of horizontal to vertical permeability. This is demonstrated in Figure 5-5 for the 2.0-foot and 10.0-foot deposit widths. If this finding is valid regardless of actual geometry for all cases, it may have significant computational as well as physical implications. Referring again to Table 5-1, it seems that the accuracy of the solution is more dependent on the ratio (DT/DX0 than (DT/DX 2 ). Assuming this to be the case, then halving the width and quartering the permeability would increase the solution accuracy, since the (DT/DX 2 ) coefficient is unaffected, while the (DT/DX) one is halved, as shown below. If AX2 = 0.5AX, and K 2 = 0.25K, then: Prediction of Pit 3 Behavior 1. Preliminary Studies Preliminary numerical analyses were conducted to model the initial filling period, which ended in April of The actual cross section was idealized as a rectangle 34.4 feet high and feet wide. These equivalent dimensions represent an average cross-sectional area of 5,275 square feet 50

62 (equal to the actual). The filling history was idealized as having occurred instantaneously, at a uniform initial solids content of 16%. The measured clay properties, as discussed in Section 4.3, are as follows: A one-dimensional analysis was first performed, using program QSUDI (Bromwell Engineering, 1981). The results for five years are shown in Figure 5-6. The predicted equilibrium conditions were a height of 20.5 feet, at an average solids content of 25.1%. The results in Figure 5-6 indicate that the 1-D solution greatly underestimates the actual performance. Because of the large storage requirement and expense of "TWODUN," preliminary analyses were performed in an attempt to optimize grid size and time steps and maintain on-line processing capabilities. The largest mesh size for which reliable results could be obtained were as follows: DT = 0.73 days, DX = 1.58 feet, and DZ = 0.09 feet (corresponding to a "real" thickness of 1.38 feet). The results of a preliminary analysis conducted for 0.5 years are shown in Figure 5-6. The change in predicted behavior is not dramatic, as anticipated for an aspect ratio of 5 based on Figure 5-3. The obvious discrepancy between the analytical results and observed performance can be attributable to three physical phenomena. First, the horizontal permeability is greater than the vertical; second, the trapezoidal (or triangular) actual cross section of the pit; and third, the existence of seepage 51

63 out of the pit. Since no experimental data on the magnitude of anisotropy in permeability is available, and its existence has been questioned for pre-thickened clays, the first explanation will be avoided at present. Inspection of the actual cross sections of Pit 3 indicate it to be much more triangular (or trapezoidal) than rectangular. A triangular geometry can be expected to produce faster consolidation for three reasons. First, more drainage surface exists; second, the length of the drainage paths are substantially reduced over much of the area; and third, the magnitude and effect of caking along the sloping surface is greatly reduced. A width of 270 feet, very similar to Pit 3, was used to determine the equivalent triangular cross section. The depth required to contain 5,275 ft 2 was calculated to be 39.1 ft (it should be noted that this produced 281 feet of drainage boundary, as opposed to 222 for the equivalent rectangle). This depth corresponds to a "material depth" of feet, as shown in Figure 5-7(b). In order to facilitate computations, a side slope of 50:1 was selected, the depth rounded to 2.6 feet, and the width appropriately modified to 260 feet. In order to accommodate the half "DX" width required by ADEP along the centerline, the region was further modified to a 265-foot wide "trapezoid" as shown in Figure 5-7(d). The actual area contained is 5,328 ft 2 (as compared to 5,277 ft 2 ). A computer program, "TRIAG," was written to analyze this geometry. The program was written to accommodate very specific geometries and is not included herein because of insufficient documentation. Results of this analysis are shown in Figure 5-6 and indicate almost no difference in consolidation 52

64 rate, at least for the half-year period analyzed. This is again probably because of the very shallow pit (relative to its width). Underseepage was actually observed and monitored, as has been discussed in Sections 3-3 and 3-5. As a first attempt at modelling this phenomenon, a constant seepage head was imposed across the deposit. While this cannot physically occur for long-term conditions, it is reasonable for relatively short times (perhaps a few years), especially in light of the caking or sealing at the boundaries that is predicted and has been observed. The results obtained when a 13.4-foot seepage head was imposed across the deposit are plotted on Figure 5-8. Excellent agreement with measured results can be seen, with the predicted solids contents being 19.1% and 19.7% at 0.4 and 0.5 years, as compared to the actual 18.8% and 19.6% at 0.38 and.60 years. In order to check whether post-filling consolidation behavior is independent of filling history (for rapid filling), as has been proposed for the one-dimensional case, an attempt was made to predict the solids content at the end of the second filling period, by beginning with an appropriate height of 16% solids material at the start of the initial filling. The dimensions of the equivalent rectangle are 43.3 feet by feet. The increased width (over feet) is indicative of the sloping sides of the actual pit. The results, plotted on Figure 5-8, indicate a predicted solids content of 19.1% at 0.6 years, as compared with the actual 18.9% at 0.63 years. 53

65 The analysis was continued for longer times by assuming as initial conditions a uniform deposit 35.9 feet high with solids content of 18.9%. These were the measured values on July 21, 1981, after the second filling had been completed. The equivalent width of feet was again used. The results for one year are presented in Figure 5-9 and also show excellent agreement. The results are re-plotted in Figure Conclusions A very useful and accurate numerical model has been depseudo-two-dimensional veloped for analyzing large strain consolidation problems for rectangular or triangular regions. Parametric variation studies show the consolidation rate depends greatly on the aspect ratio (width/height), particularly for narrow widths, and anisotropic permeability. Similar to linear 2-D seepage problems, the effect of quadrupling horizontal permeability is identical to halving width. The model is an accurate predictor of full-scale field situations, but will probably find greatest utility in analyzing smaller-scale pit tests. As with most studies, this one also uncovered additional areas of needed research or improvements. These include: 1) an attempt to non-dimensionalize, or at least scale, Equation (5-3) in order to facilitate evaluation of convergence criteria 2) more computationally efficient numerical methods for solving Equation (5-3) or its self-adjoint form, Equation (5-8) 54

66 3) a program to model the filling process, which would include a description of the "flow" process 4) a more realistic numerical model of seepage, in which time-dependent boundary pore pressures and fluid levels could be accommodated 5) a parametric variation study to investigate effect of side slopes and gradient control on dewatering rate 6) an experimental investigation, in lab and/or field, of possible anisotropic permeability 55

67 6.0 ENGINEERING APPROXIMATIONS FOR PREDICTION OF CONSOLIDATION As discussed earlier in this report, conventional disposal of phosphatic clay involves deposition in settling areas in which the lateral dimensions are many times greater than the vertical dimension. As a result, the consolidation of the clay is primarily one-dimensional; that is, the excess water flows * vertically either upward or downward. Most of the flow is upward, because a "cake" on the bottom of the settling area. of low permeability clay rapidly forms A small amount of water flows horizontally into the embankment surrounding the settling area, but this is an "edge effect" In contrast, and is usually neglected. Test Pit 3 occupies a long, narrow mine cut, and, as a result, the ratio of the short axis to the depth is much smaller than in a conventional pond (see Figure 2-1). Hence, the clay is much more subject to two-dimensional consolidation. the The main objective of this project has been to evaluate significance of this two-dimensional consolidation. In particular, it is important to determine if the difference in the geometry of the drainage boundary leads to rapid dewatering. For comparison purposes, predictions of consolidation in Test Pit 3 have been made which are based on engineering approximations utilizing one-dimensional analyses. consolidation computer The objective of this portion of the project has * Downward flow of excess water can occur even if the water table outside the disposal area is at the same level as the water table inside the disposal area. If the outside water table is lower than inside, then downward seepage forces will be generated which result in more and faster consolidation. Seepage forces are usually ignored in design cases. 56

68 been to determine if an engineering approximation can be used to obtain a satisfactory prediction of consolidation, in lieu of sophisticated (expensive-to-run) two-dimensional computer programs. Two classes of prediction were made: 1) preliminary, which was made prior to obtaining clay consolidation properties or boundary pore pressure data; and 2) final, which was made at the conclusion of the project. In both cases, the same engineering assumptions were made regarding the effects of the test pit geometry. 6.1 Preliminary Predictions Computer programs have previously been written specifically to analyze the one-dimensional consolidation of phosphatic clays. These programs are based on non-linear finite strain consolidation theory and utilize a finite-difference solution technique. The theory of finite strain consolidation is well established: c.f., McNabb, 1960; Mikasa, 1965; Gibson, et al., 1967; De Simone and Viggiani, 1976; Bromwell and Carrier, 1979; Gibson, et al., 1980; Sills and Lee, 1980; Schiffman, 1980; Somogyi, 1980; Schiffman and Cargill, 1981; Pane and Schiffman, 1981; Znidarcic and Schiffman, 1981; Somogyi, et al., Furthermore, the details of the computer programs have been documented elsewhere (Bromwell Engineering, 1979; Somogyi, 1980; Somogyi, et al., 1981). Suffice it to say that the programs require the following input: 0 Compressibility and permeability of clay 0 Initial solids content of clay 0 Size of disposal area 0 Filling rate of dry solids 57

69 0 Surcharge (if any) 0 Boundary drainage conditions The output from the programs include: 0 Settlement vs. time 0 Solids content vs. depth and time 0 Pore pressure within clay vs. depth and time The output from one program becomes the input for the next program, and virtually any sequence of filling and quiescent consolidation can be analyzed. It has been found that the compressibility of phosphatic clay can be reasonably expressed according to the following empirical relationship: * For saturated conditions, given by: the clay solids content, S, is s = 100% where G is the specific gravity of the clay particles, typically

70 where k = permeability (ft/day) C,D = material property constants The compressibility controls the amount of consolidation; the permeability controls the rate of consolidation. Based on earlier studies performed in the vicinity of Test Pit 3 (but not necessarily the same clay), the following material property constants had been developed: A = B = c = 4.0 x 10-6 D = 4.11 These values were presumed to be applicable to Test Pit 3 as well and were used in the preliminary predictions of consolidation One-Dimensional: Single Drainage It has been found that the height of the clay in a disposal area during filling at a constant rate is given by (c.f. Carrier, et al., 1982): 59

71 Briefly, a, b, and c is as follows: the general procedure to determine the values of (1) Three or four computer runs are made in which the filling rate is varied over the range of interest; (2) Curves are calculated in the form of Equation (6-3) which give virtually exact fits to the individual computer analyses; (3) The empirical coefficients a, b, and c are selected which give the best overall fit over the range of Q. The specific steps taken to predict the consolidation of Test Pit 3 under one-dimensional, single drainage conditions were as follows: (1) Equation (6-3) was re-written in terms of the dry weight of clay, since, where W = dry weight of clay (tons) A = size of disposal area (acres) then, b h= & tc 60

72 b h = a(e) tceb (6-4) Hence, given the dry weight of clay, W, at time t during or after filling, the height of clay, h, can be calculated. Furthermore, the solution is essentially independent of the filling history; i.e., Equation (6-4) can be used to calculate clay height for nearly any sequence of filling and quiescent consolidation. (2) The maximum storage volume of Test Pit 3 is approximately ac-ft (see Sec. 3.1), and the average maximum depth is 34.4 feet. Thus, the effective area of the "rectangularized" test pit is given by A = = 4.66 acres. (3) Sampling data indicated that the initial solids content of the clay as it flowed into Test Pit 3 was 16%. Hence, this value was used in a series of computer runs in which the filling rate was varied as follows: 5,000, 10,000, 18,000, 28,000, and 40,000 tons/yr/acre. All runs assumed the single drainage condition; that is, the excess water was only allowed to move upward. This is a conservative assumption, as it neglects the downward component. Single drainage is used in virtually all design studies of full-scale disposal areas. 61

73 (4) Based on these computer runs, values for a and b were selected: a = 9.77 x 10-4 b = However, the value of c was found to be too variable, and it was necessary to express it as a function: C = I- 54r (5) The sampling data for late April, 1981 (see Sec. 3.4), indicated that Test Pit 3 contained W = 46,477 tons of clay. (6) Hence, for times greater than or equal to the filling period, Equation (6-4) can be expressed as: h= or h= (6-5) For example, if t = 0.36 yr (the time required to fill Test Pit 3), h = 38.6 ft, corresponding to a clay solids con- tent of 17%. 62

74 Equation (6-5) was used to calculate one-dimensional single drainage consolidation of Test Pit 3. Shortly thereafter, IMC deposited more clay, and the expression was modified to take this additional tonnage into account. The resulting prediction is shown in Figures 6-1 and One-Dimensional: Double Drainage The double drainage condition allows downward movement of the excess water, as well as upward. As a result, the computer runs yielded slightly different values from the single drainage case: a = 8.77 x 10-4 b = C = gr When substituted into Equation (6-4), these values yield a clay height of 35.8 ft at the end of filling vs f-t for single drainage, or about 8% lower (resulting in a very slightly increased clay solids content of 18%). The prediction for one-dimensional, double drainage consolidation is also shown in Figures 6-1 and 6-2, including the effect of the additional clay tonnage Pseudo-Three-Dimensional: Single Drainage "Rectangularizing" the disposal area, as was done above, is a simple engineering approximation. However, Test Pit 3 is 63

75 rather trapezoidal in shape, was developed (c.f. Carrier, et al., 1982): and so the following expression w = t%)ywl + +$ (w + L + E) a I (6-6) where w = base width L = base length m = inside slope of disposal area (see Figure 3-2) This expression assumes that the clay behaves in accordance with Equations (6-3) and (6-4); furthermore, the distribution of clay solids within the area is allowed to vary such that the surface of the clay is always level. This engineering approximation ignores drainage along the lateral boundaries, but does account for the geometry in the test pit in a more accurate fashion than the one-dimensional assumption. Note that if m = 0 (vertical walls), then Equation (6-6) reduces to Equation (6-4). For Test Pit 3, w = 130 ft L = 1,080 ft m = 1.47 For single drainage, the same values of a, b, and c were used as in Section The resulting expression is rather complex and must be solved iteratively. The prediction of consolidation thus obtained is shown in Figures 6-1 and

76 6.1.4 Pseudo-Three-Dimensional: Double Drainage This prediction method is the same as the last, except that double drainage conditions are assumed and the values for a, b, and c were used as in Section The prediction of consolidation in Test Pit 3 thus obtained is also shown in Figures 6-1 and 6-2. It may be seen that these four engineering approximations are in fact not very different. Even after two years of consolidation, the predicted average clay solids content only varies from 22% to 26%, which would not be considered a very wide range. Still, the last approximation, pseudo-threedimensional with double drainage, was considered to be the best possible estimate without recourse to a more sophisticated computer program. Furthermore, the field measurements seemed to agree very closely with the latter prediction: in all cases, the measured clay solids content was within 1% of the predicted value and in most cases within 0.5% (see Figure 6-1). Even one year after filling, the actual and predicted values were still very close together. 6.2 Final Prediction Subsequent to making the preliminary predictions discussed in Section 6.1, field and laboratory tests were performed on the clay in Test Pit 3. As discussed in Section 4-3, these tests showed the following: 1. The field and laboratory bility were in reasonable larly different from the preliminary predictions. measurements of compressiagreement and not particuvalues assumed for the Furthermore, the measured 65

77 compressibility agreed well with correlations based on the Atterberg limits of the clay (c.f., Carrier, et al., 1982). 2. The field and laboratory measurements of permeability were also in reasonable agreement. However, the measured permeability was significantly less than had been assumed for the preliminary predictions. At any given clay solids content, the measured permeability was one-fourth of the preliminary value. Interestingly, the correlation based on Atterberg limits would have predicted an even lower permeability. 3. On the other hand, analysis of the piezometric data at Test Pit 3 showed that there was a downward seepage force averaging 13.4 feet of hydraulic head, whereas the preliminary predictions had assumed there was zero seepage force. At the present time, an engineering approximation has not been devised which takes into account the trapezoidal shape of the test pit in conjunction with seepage head. Hence, the final prediction is based solely on a one-dimensional approximation. However, as shown in Section 6.1.4, the shape of Test Pit 3 does not have a strong influence on the predictions. For the final prediction, the compressibility and permeability parameters are based on the results of the CRDSC laboratory test: 66

78 A = 23.0 B = C = 1.03 x 10-6 D = 4.19 First, consider the case of double drainage with no seepage head. At the end of July, 1981, after the second filling of the test pit, the average clay solids content was measured to be 18.9%, and the depth of the clay was approximately 36 feet. Starting from this point, a double drainage analysis was run using the above parameters, and the results are presented in Figure 6-3. It can be seen that the clay solids content rises very slowly: at the end of one year, it has reached 20.8% and after two years 22.0%. Referring back to Figure 6-1, it can be seen that this analysis results in clay solids contents which are significantly less than the preliminary prediction and, more importantly, much less than values measured in the field. This is, of course, attributable to the lower value of permeability. Next, consider the case of double drainage with a constant seepage head of 13.4 feet. This increases the effective stress on the clay considerably beyond what would occur under hydrostatic conditions. As a result, the rate of consolidation is much more rapid, as shown in Figure 6-3. Starting at the same clay solids content as before, after one year it has risen to 23.6% and after two years 27.7%. These results are in much better agreement with the preliminary prediction and the field measurements. 67

79 The following conclusions can be drawn: 1. The good agreement between the preliminary prediction and the field measurements was due to a cancellation of assumptions: initially, the permeability was assumed to be too high, but the seepage force was neglected. When both factors are considered, good agreement is again achieved. 2. An engineering approximation based on one-dimensional consolidation, with double drainage and constant seepage head, yields good agreement with the field measurements. Thus, this method can be used for design purposes in lieu of a more sophisticated computer program. 3. It is very important to note that under full-scale field conditions, there would be little or no seepage head. Hence, the consolidation performance of this isolated test pit has been considerably better than could be expected under normal operating conditions. On the other hand, this particular clay has "poor" consolidation properties compared with phosphatic clay from other mines. Hence, the optimal disposal system must be evaluated individually for each mine situation. 68

80 7.0 DESICCATION BEHAVIOR 7.1 Introduction Once waste disposal can be handled effectively, the next major consideration is reclamation. It is well known that simply filling a disposal area with thickened clay or sand-clay mix will not produce reclaimed land. Even with a sand-clay mix, the surface will not have suitable mechanical and agronomic properties to restore the area to productive use, such as agriculture or wildlife sanctuary. Hence, the clay must be capped, either with overburden or a sand-clay mix with a very high sand to clay ratio, or the physical properties must be improved by establishing drainage ditches and desirable vegetation. In order to apply this cap or manipulate the surface clay, a crust must be formed with sufficient thickness and shear strength to support the loads involved. Hence, it is essential for planning reclamation of clay and sand-clay disposal areas to develop general guidelines for predicting the time required for desiccation of a crust. 7.2 Desiccation of Waste Clay in a Disposal Area Evaporation of water from the clay can occur directly from the soil surface or through extraction and transpiration by plants. When the two processes are concurrent, they are treated as a single process called evapotranspiration. When the clay surface is covered entirely by active vegetation, transpiration predominates over direct evaporation. In the absence of vegetation, evaporation takes place entirely from the clay surface. As a first approximation, potential transpiration can be taken as equal to potential direct evaporation 69

81 early in the desiccation process when evaporation from the clay surface does not differ greatly from the evaporation rate of a free water surface. However, whether there is a significant difference in the evaporation rate due to direct evaporation or transpiration as a surface crust develops is not known. It is well known that cattails will cover a Florida phosphatic waste clay disposal area rather quickly. Therefore, guidelines for predicting evaporation desiccation from both clay surfaces and vegetated clay surfaces are needed. In order for desiccation to occur, the outflux of water from the zone of extraction must be greater than the influx of water due to the flow of water caused by consolidation. As consolidation proceeds, excess water flows from the interior of the clay to the surface at an ever-decreasing rate. Desiccation will not even begin until the water flow rate drops below the evaporation rate. Hence, simulation of the consolidation of the clay is a necessary first step in predicting the rate of desiccation. 7.3 Vegetation Growth in the Test Pit Scattered cattails became established. at the west end of the pit even before the final filling of the test pit. By May, 1981, the western half of the pit was covered with cattails, and by December, 1981, the entire test pit was covered with cattails. 7.4 Rate of Crust Development in the Test Pit Very little desiccation around the edges of the pit occurred during the study period. As explained in Section 7.2, 70

82 desiccation will not even begin until the flow rate of water to the clay surface due to consolidation drops below the evaporation rate. The average pan evaporation rate for central Florida is approximately 5.7 inches per month. Figure 7-1 shows the simulated change in height of the clay in an equivalent rectangular pit. Since most of the water flow caused by consolidation moves upward due to the high solids content cake that forms at the bottom of the pit, the rate of change in the height of the clay can be taken as equal to the rate of flow of water to the clay surface. Referring to Figure 7-1, it can be seen that the rate of flow of water to the surface of the clay dropped below 5.7 inches per month within approximately six months after the final filling of the pit. However, two years after the final filling, the rate of flow of water to the surface was only slightly less than the average pan evaporation rate. Hence, very little desiccation should have occurred, as has been verified by field measurements. This prediction was made considering consolidation in a rectangularized pit where the depth of the clay is the same across the pit. If lateral seepage is considered negligible, then the rate and amount of consolidation of the clay across the pit will be equal and the clay surface will remain level. However, the test pit is trapezoidal in shape, and hence the height of the clay varies across the pit. The deeper clay in the middle of the pit will settle more than the shallower clay closer to the sides of the pit, which results in the surface of the clay assuming a concave shape, unless lateral movement of the clay occurs to keep the surface level. Observations of consolidation of clay in other trapezoidal shaped pits has 71

83 shown that eventually the clay surface does take a concave shape, but not nearly as concave as would occur if there were no lateral movement of clay. Hence, it is apparent that when the clay is at a low solids content and has essentially no strength, lateral movement of the clay occurs during differential consolidation and the clay surface remains essentially flat. However, as consolidation proceeds, the clay gradually becomes stronger, lateral movement of the clay is impeded, and the clay surface becomes gradually more concave in shape. Since the shallower depth of clay near the sides of the pit will reach a certain degree of consolidation more quickly than the greater depth of clay at the middle of the pit, and the concave shape of the clay surface will keep the clay surface closer to the sides of the pit drained of surface water, it appears that desiccation should first begin at the edges of a trapezoidal shaped pit and gradually move toward the center of the pit. Observations of consolidation and desiccation in trapezoidal shaped pits other than Pit 3 have shown that this is in fact how desiccation proceeds. 7.5 Physical Behavior of Clay During Desiccation The following measurements were made in bare desiccated clay around the edges of the test pit in order to characterize the behavior of the clay during desiccation: Solids Content Pore Water Suction Degree of Saturation Undrained Shear Strength 72

84 7.5.1 Solids Content Measurements of solids content vs. depth in the desic- - cated clay are shown in Table 7-1. As can be seen, there is a rather sudden decrease in the solids content with depth. It can also be seen that at depths below the phreatic water sur- face (below the zone of negative pore pressures), the clay had solids contents larger than at the same depth in areas of the pit where no desiccation had occurred. This happens because the increased effective stress caused by the water table low- ering and the removal of buoyant force causes additional con- solidation of the clay beneath the surface crust Pore Water Suction As desiccation less than atmospheric occurs, negative pore pressure (pressure pressure) or suction is produced in the soil due to capillary equation, action. The Terzaghi effective stress u=u-u where u = effective stress u = total stress u = pore water pressure, is valid for negative pore water pressure provided the system remains saturated (Aitchison, 1961). Thus, a negative pore water pressure contributes positively to the effective stress in the clay and is equivalent to a mechanically applied com- pressive stress. Hence, under saturated conditions, the only difference in compression due to suction and the self-weight of 73

85 the clay is that compression due to suction is isotropic, whereas compression due to self-weight is almost entirely one-dimensional. Isotropic compression results in horizontal strains as well as vertical strains, which is the cause for cracks that occur in the clay during desiccation. Measurements of suction in the desiccating clay were made with tensiometers. A schematic of the tensiometer is shown in Figure 7-2. The suction is transmitted through the porous tip of the device, and a reading of the negative pressure is indicated on the dial. Results of the suction measurements are shown on Table 7-1. Compressibility data developed from the suction measurements and corresponding measurements of the solids content are shown on Figure 7-3. Also shown is the compressibility curve from the CRDSC test. As can be seen, the two sets of data are in good agreement. The measurements of suction and solids content were made well after any rainfall, so that the desiccating clay was undergoing virgin consolidation. When rainfall or flooding occurs on desiccated clay, the clay absorbs water, which decreases the suction and hence the effective stress in the clay. This results in swelling of the clay. However, consolidation of the desiccated clay is largely irreversible. For the same change in effective stress, the volume change of the clay due to swelling is probably on the order of one-tenth of the volume change due to virgin consolidation. Hence, the relationship between effective stress and void ratio is not unique, as it is with self-weight consolidation, because of the swelling and reconsolidation that occur with cycles of wetting and drying. 74

86 7.5.3 Degree of Saturation The degree of saturation was determined on undisturbed samples of the clay obtained at the same locations and depths where the water suction measurements were made. The degree of saturation, S, is defined as the volume of water divided by volume of void. It can be calculated according to: S = W z(l % G where: w= water content of undisturbed sample (%) yt = unit weight of undisturbed sample (PCF) yw = unit weight of water (= 62.4 PCF) G = specific gravity of clay particles If the clay is completely dry, S = 0%. If the void space is completely full of water, S = 100%. Measurements of the degree of saturation are shown in Table 7-1. As can be seen, the test pit clay remains essentially saturated when dried to a solids content at least as high as 50%. This is due to the high compressibility of the clay. The degree of saturation has a large influence on the permeability of the clay, as the permeability of any soil at a given void ratio decreases rapidly as the degree of saturation decreases. 75

87 7.5.4 Undrained Shear Strength Measurements of undrained shear strength were made using a hand operated vane shear device. The results of the measurements are presented in Table 7-1 and on Figure 7-4. As expected, there is an increase in strength with solids content. 7.6 Summary As predicted by comparing the flow rate of water to the clay surface vs. time with the average pan evaporation rate, little desiccation occurred in the test pit during the study period. However, some interesting observations of the progression of desiccation in a trapezoidal shaped pit and some measurements of the physical behavior of bare clay during desiccation were made. More measurements of both actual rates of desiccation and of the physical behavior of the clay during desiccation are needed in order to develop guidelines for predicting desiccation rates. 76

88 8.0 CONCLUSIONS Based on the results of this investigation, the following conclusions can be made: 1) Accurate measurements of the field dewatering behavior in the test pit were made over a period of 1.5 years. The dry weight of clay in the test pit calculated based on the sampling programs, and based on IMC's pumping data, are in good agreement. Also, the average solids content of the clay in the pit calculated based on the sampling programs, and based on IMC's pumping data and the tide gauge readings, are in good agreement. 2) Both measurements of the boundary pore water pressures and pore water pressure measurements within the clay show that there is a head difference between the phreatic surface of the water in the waste clay and the phreatic surface of the water outside the test pit. This head difference causes a downward seepage force which increases the effective stress on the clay particles. This in turn results in a higher solids content than would occur if the boundary pore pressures were at the same elevation as the phreatic surface of the water in the waste clay. The average head difference measured was 13.4 feet. 3) Index tests and mineralogical analysis of the test pit clay have shown that the clay is essentially homogeneous and that the index properties and 77

89 mineralogy are within the typical range of other Florida phosphatic clays tested. However, the plasticity index is on the high side of the typical range, which suggests "poor" consolidation behavior in comparison with other Florida phosphatic clays tested. 4) Field and laboratory measurements of the compressibility and permeability of the test pit clay are in good agreement. Compressibility developed from correlations based on the Atterberg limits of the clay is in good agreement with the field and laboratory data. Permeability developed from the correlations does not agree with the field and laboratory data nearly as well as with compressibility; however, it is a reasonable first approximation. Compared with other Florida phosphatic clays, the test pit clay has "poor" consolidation properties. 5) A very useful and accurate numerical model has been developed for analyzing pseudo-two-dimensional largestrain consolidation problems for rectangular or triangular regions. 6) Parametric variation studies show that the consolidation rate depends greatly on the aspect ratio (width/height), particularly for narrow widths, and anisotropic permeability. For the test pit, which has an aspect ratio of approximately 5, the rate of consolidation as a result of two-dimensional drainage 78

90 is only slightly greater than the rate of consolidation as a result of one-dimensional drainage. Hence, disposal of thickened clay in mine cuts does not offer a significant improvement in the rate of consolidation compared to placement of thickened clay in a large pond with the same depth. It was found that the trapezoidal shape of the test pit had little influence on the consolidation. However, this may be due to the high aspect ratio and small change in height of the clay during the monitoring period. In situations where there is a small aspect ratio and a large change in height, and hence a significant change in the shape of the waste clay as consolidation occurs, the shape of the pit may need to be taken into account. Simulation of consolidation in the test pit has also shown that the average seepage head of 13.4 feet had a strong influence on consolidation. However, under full-scale field conditions, there would be little or no seepage head. 7) Existing one-dimensional design techniques have been shown to be sufficiently accurate for evaluation of consolidation in a V-shaped mine cut. However, the two-dimensional program would still be essential for analysis of a smaller test pit. 8) This research has shown how to simulate consolidation of waste clay in mine cuts. However, due to the differences in clay properties, geometry, and other 79

91 factors, the optimal disposal system must be evaluated individually for each mine situation. 9) As predicted by comparing the flow rate of water to the clay surface vs. time with the average pan evaporation rate, little desiccation occurred in the test pit during the study period. However, some interesting observations of the progression of desiccation in a trapezoidal shaped pit and some measurements of the physical behavior of bare clay during desiccation were made. More measurements of both actual rates of desiccation and of the physical behavior of the clay during desiccation are needed in order to develop guidelines for predicting desiccation rates. 80

92 REFERENCES Aitchison, G. D. (1961), "Relationships of Moisture Stress and Effective Stress Functions in Unsaturated Soils," in Pore Pressure and Suction in Soils, Butterworth, London, pp Allada, S. R. and Quon, D. (1966), "A Stable, Explicit Numerical Solution of the Conduction Equation for Multidimensional Nonhomogeneous Media," Chemical Engineering Progress, Symposium Series, Vol. 62, No. 64, pp Bromwell, L. G. (1967), "Soil Engineering Studies for Future Foundation Construction," report prepared for Climax Molybdenum N.V., Rotterdam, Holland, by T. William Lambe & Associates, Consultants in Soil Mechanics, Cambridge, Massachusetts. Bromwell, L. G., and Oxford, T. P. (1977), "Waste Clay Dewatering and Disposal,' Geotechnical Practice for Disposal of Solid Waste Materials, ASCE Geotechnical Division Specialty Conference, Ann Arbor, pp Bromwell, L. G., and Carrier, W. D., III (1979), "Consolidation of Fine-Grained Mining Wastes," Proceedings, Sixth Panamerican Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Lima, Peru, pp Bromwell, L. G., and Raden, D. J. (1979), "Disposal of Phosphate Mining Wastes," Current Geotechnical Practice in Mine Waste Disposal, ASCE Geotechnical Division Special Publication, New York, pp Bromwell Engineering, Inc. (1979), "Analysis and Prediction of Phosphatic Clay Consolidation: Implementation Package," Lakeland, Florida. "FSCON (Finite-Strain Con- Bromwell Engineering, Inc. (1981), solidation) Users Manual." Carrier, W. D., III, and Keshian, B., Jr. (1979), "Measurement and Prediction of Consolidation of Dredged Material," presented at Twelfth Annual Dredging Seminar, Houston, Texas. 81

93 Carrier, W. D., III, and Bromwell, L. G. (1980), "Geotechnical Analysis of Confined Spoil Disposal," Proceedings, Ninth World Dredging Conference, Vancouver, British Columbia, Canada. Carrier, W. D., III, Bromwell, L. G., and Somogyi, F. (1982), "Design Capacity of Slurried Mineral Waste Ponds," submitted to Journal of the Geotechnical Engineering Division, ASCE. Gibson, R. E., England, G. L., and Hussey, J. J. L. (1967), "The Theory of One-Dimensional Consolidation of Saturated Clays," Geotechnique, Vol. 17, pp Haliburton, T. A. (1978), "Guidelines for Dewatering/Densifying Confined Dredged Material," Dredged Material Research Program Technical Report DS-78-11, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Mississippi. Keshian, B., Jr., Ladd, C. C., and Olson, R. E. (1977), "Sedimentation-Consolidation Behavior of Phosphatic Clays," Geotechnical Practice for Disposal of Solid Waste Materials, ASCE Geotechnical Division Specialty Conference, Ann Arbor, pp Koppula, S. D. (1970), "The Consolidation of Soil in Two Dimensions and with Moving Boundaries," thesis submitted in partial fulfillment of the requirements for the degree of Ph.D., University of Alberta at Edmonton, Alberta, Canada. Kriegsmann, G. A. (1982), personal communication. Lamont, W. D., McLendon, J. T., Clements, L. W., Jr., and Feld, I. L. (1975), "Characterization Studies of Florida Phosphate Slimes," U.S. Bureau of Mines Report of Investigations No Larkin, B. K. (1965), "Some Finite Difference Methods for Problems in Transient Heat Flow," Chemical Engineering Progress, Symposium Series, Vol. 61, No. 59, pp

94 Martin, R. T., Bromwell, L. G., and Sholine, J. H. (1977), "Field Tests of Phosphatic Clay Dewatering," Geotechnical Practice for Disposal of Solid Waste Materials, ASCE Geotechnical Division Specialty Conference, Ann Arbor, pp Olson, R. E., and Ladd, C. C. (1979), "One-Dimensional Consolidation Problems," Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GTl, pp Richtmyer, R. D., and Morton, K. W. (1967), Difference Methods For Initial Value Problems, Interscience, New York. Schiffman, R. L. (1980), "Finite and Infinitesimal Strain Consolidation," Technical Note, Journal of the Geotechnical Engineering Division, ASCE, Vol. 106, No. GT2, pp Sills, G. C., and Lee, K. (1980), Discussion of "One-Dimensional Consolidation Problems" by Olson and Ladd, Journal of the Geotechnical Engineering Division, ASCE, Vol. 106, No. GT7, pp Somogyi, F. (1975), "Dewatering and Drainage of Red Mud Tailings," Ph.D. thesis, University of Michigan. Somogyi, F. (1980), "Large Strain Consolidation of Fine-Grained Slurries," presented at Canadian Society for Civil Engineering 1980 Annual Conference, Winnipeg, Manitoba, Canada. Somogyi, F., Keshian, B., Jr., Bromwell, L. G., and Carrier, W. D., III (1982), "Consolidation Behavior of Impounded Slurries," submitted for publication to A.S.C.E., Journal of the Geotechnical Division. Staff, Bureau of Mines (1975), "The Florida Phosphate Slimes Problem: A Review and a Bibliography," U.S. Bureau of Mines Information Circular No Wissa, A. E. Z., Martin, R. T., and Garlanger, J. E. (1975), The Piezometer Probe," In Situ Measurement of Soil Properties, Vol. 1, ASCE Specialty Conference, North Carolina State University, Raleigh, North Carolina. 83

95 Znidarcic, D., and Schiffman, R. L. (1981), "Finite Strain Consolidation: Test Conditions," Technical Note, Journal of the Geotechnical Engineering Division, ASCE, Vol. 107, pp

96 TABLES

97 85

98 86

99 87

100 88

101 89

102

103 91

104

105

106

107

108

109

110

111

112

113

114

115

116 104

117

118

119

120

121

122 110

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138 126

139

140

141 129

142

143

144

145

146

147

148

149

150

151 139

152 140

153

154 142

155

156

157

158 146

159

160 148

161 APPENDIX A IMC THROUGHPUT MEASUREMENTS

162 150

163 APPENDIX B SAMPLING DATA

164 151

165 152

166 153

167 154

168 155

169 156

170 157

171 158

172 159

173 160

174 161

175

176 163

177 164

178 165

179 166

180 APPENDIX C PORE WATER PRESSURE MEASUREMENTS IN THE CLAY

181 167

182 168

183 169

184 170

185 171

186 172

187 APPENDIX D PERMEABILITY PROBE MEASUREMENTS

188 173

189 174

190 APPENDIX E PARTICLE SIZE DISTRIBUTION CURVES

191 175

192 176

193

194

195 179

196

197

198

199 183

200

201

202

203 APPENDIX F MINERALOGY REPORT

204 R. TORRENCE MARTIN Clay Mineralogist CHIPMUNK CROSSING LINCOLN MA Mineralogy of IMC Test Pit No. 3 Clay Materials Five samples of phosphatic waste clay received from Bromwell Engineering have been examined by X-Ray diffraction, XRD. Using reference minerals that have been obtained specifically for application to Florida phosphatic clay waste, the relative amount of detectable crystalline species present in the samples are summarized in Table 1. The relative peak amplitude, R, of a given species is the net amplitude of a specific XRD peak in the unknown divided by the net amplitude of that same XRD peak taken from the appropriate reference mineral. The sample to be analyzed and the reference mineral data were all collected on specimens uniformly prepared so that the R values reasonably reflect relative changes of a given mineral phase within the sample suite. To facilitate handling the numbers, the data were tabulated as 100R. The 100R values are not weight percent. The samples were remarkably similar and were typical of phosphatic waste clay from central Florida. Wavellite R values were given only for two samples because the amount of wavellite was about at the detection limit. Sample A was the only sample with enough palygorskite to yield an R value. Again, this R value is near the palygorskite detection limit. The zero palygorskite in samples F and. I means that palygorskite, if present, was below the XRD detection limit (approximately 5wt%). Samples K and A contained enough interstratified expandable clay, other than the clear smectite phase, to be evident in the XRD data on hydrated specimens. An interstratified phase was present in all samples, Small differences 187

205 IMC Test Pit No in the interstratified phase were evident from XRD data on heated specimens. Based upon all available data, the amount of interstratified phase in the samples was K>A>C>F>I. The kaolin phase showed variation between the different samples. Samples K and I contained the most stable kaolin and samples A and F the most unstable. The kaolin phase stability for sample C was intermediate. 188

206 APPENDIX G CONSOLIDATION TEST RESULTS

207 189

208

209 191

210 APPENDIX H DERIVATION OF PARTIAL DIFFERENTIAL EQUATION

211 The following derivation of the partial differential equation describing "pseudo two-dimensional" large-strain consolidation parallels the 1-D derivation as presented by Koppula* (1970): Coordinate System: 192

212 193

213 194

214 195

215 196

216 Combining (4') and (5'): which is the general equation describing "pseudo two-dimensional consolidation". 197

217 APPENDIX I DERIVATION OF RECURRENCE FORMULAE

218 198

219 199

220 200

221

222

223 203

224 204

225 205

226 APPENDIX J LISTING OF THE COMPUTER PROGRAM "TWODUN"

227

228

229

230

231

232

233

234 APPENDIX K OUTPUT FILE FOR AN EXAMPLE OF THE USAGE OF THE PROGRAM "TWODUN"

235 213

236 21.4

237 215

238

239 217

240

241

242