United Slates Environmental Protection Agency Office of Radiation Programs Las Vegas Facility P.O Box 15027 Las Vegas NV89114 Technical Note ORP/LV 78 8 September 1978 Radiation oEPA Water Movement in Uranium Mill Tailings Profiles ------- Technical Note ORP/LV-78-8 WATER MOVEMENT IN URANIUM MILL TAILINGS PROFILES by A. Klute and D. F. Heermann U. S. Department of Agriculture Science and Education Administration Agricultural Research Fort Collins, CO 80523 A report of research conducted under IAG - DG - H026 between USDA - SEA and the U.S. Environmental Protection Agency Project Officer Robert F. Kaufmann Field Studies Branch Office of Radiation Programs-Las Vegas Facility U.S. Environmental Protection Agency Las Vegas, Nevada 89114 ------- DISCLAIMER This report has been reviewed by the Office of Radiation Programs - Las Vegas Facility, U.S. Environmental Protection Agency, and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the EPA. Mention of trade names or commercial products does not constitute endorsement or recommendation for their use. Neither the United States nor the EPA makes any warranty, expressed or implied, or assume any legal liability or responsibility for any information, apparatus, product or process disclosed, or present that its use could not infringe on privately owned rights. ------- FOREWORD The Office of Radiation Programs of the U.S. Environmental Protection Agency carries out a national program designed to evaluate population exposure to ionizing and non-ionizing radiation, and promote the development of controls to protect the public health and safety. This report was prepared as an integral element of the overall program to control radiation from uranium mill tailings piles situated in the western United States. Such piles are composed of materials containing con- centrations of radium-226 two to three orders of magnitude more than back- ground rock and soil. Radon-222, the noble gas progeny of radium-226, is produced within the pile and diffuses to the atmosphere as a continuing long-term source resulting in radiation exposure of the surrounding populace. Pathways of exposure from uranium mill tailing piles include airborne particulates and contamination of surface or ground water. This report assists in understanding the impact of normal precipitation cycles on recharge of shallow ground water with contaminated leachate from tailings piles. Knowledge of the vertical distribution of soil moisture also assists in evaluating the magnitude of radon diffusion from a tailings pile. This study represents what we believe is the first application of digital modeling techniques to simulate the unsaturated or soil moisture regime in a uranium tailings pile under average and extreme precipitation and evaporation cycles typified by a climatologic setting in Salt Lake City, Utah. Beginning with initial gravity drainage of the saturated pile, long- term soil moisture variations as a function of time, depth, and tailings lithology are simulated. The results clearly indicate that long-term recharge to underlying ground water can occur and that the upper 10 to 20 centimeters of the profiles tend to dry out rapidly. The presence of vege- tation would increase the rate and probably the depth of dewatering. Clear- ly then, there is a tradeoff at least qualitatively identified between management/stabilization schemes calling for minimal recharge to ground water and reduction of radon diffusion by maintenance of relatively high water content in the very near surface tailings. Future studies will be needed for identification and analysis of the tradeoffs. This was well beyond the scope of the present study. iii ------- Readers of this report are encouraged to inform the Office of Radiation Programs - Las Vegas Facility of any omissions or errors. Requests for further information or comments concerning this report are also welcome. Donald W. Hendricks Director, Office of Radiation Programs, LVF iv ------- ABSTRACT The general objective of this study was to characterize the behavior of water in profiles of uranium mill tailings. The approach taken consisted of (1) measurement of the water retention and transmission properties of selected tailings materials, (2) numerical simulation of water flow in selected profiles of tailings subjected to specific boundary conditions, and (3) analysis and interpretation of the simulation results within the framework of unsaturated soil water flow theory. The sequence of flow events in a tailings profile without vegetation and with a water table at a given depth is: (1) an initial drainage from satura- tion, with evaporation at the surface, (2) infiltration of varying amounts of rain at irregular intervals, (3) and periods of evaporation and drainage from the profile, with redistribution within the profile, between infiltration events. The water flow regime in the upper 90 cm, particularly the upper 10- 20 cm is transient and dynamic. Rainfall events produce wetting, which lasts only a few days, in the upper portion of the profile. The wetted zone is dried by evaporation to depths of about 10-15 cm in evaporation periods lasting 15 to 30 days. Infiltrated water, which has penetrated to depths more than about 10 cm, continues to flow downward within the profile while evaporation is occurring from the surface. The lower part of the profile, below about 70-90 cm, tends to behave in a quasi-steady downward flow condition. The average flow rate in this portion of the profile is determined by the fraction of the rainfall trapped in the profile and not re-evaporated during the time interval of averaging. The water content of the profile at depths below 70-90 cm and at distances more than 50-70 cm above the water table is that corresponding to a hydraulic conductivity equal to the magnitude of the downward flux. ------- CONTENTS Page FOREWORD i13- ABSTRACT v FIGURES vlii TABLES • xii SYMBOLS xiii ACKNOWLEDGMENT xiv 1. INTRODUCTION i 2. CONCLUSIONS ..... 2 3. RECOMMENDATIONS 4 4. SOIL WATER FLOW CONCEPTS AND TERMINOLOGY 5 5. DETERMINATION OF THE HYDRAULIC PROPERTIES OF TAILINGS ... 12 Sampling and Basic Physical Characteristics 12 Water Retention Characteristics . . ...... 13 Sample Preparation 15 Method for Determination of Hysteresis 15 Hydraulic Conductivity-Water Relationships 20 6. SIMULATION OF WATER FLOW IN TAILINGS PROFILES 28 The Numerical Solution Process 28 7. ANALYSIS OF WATER FLOW IN TAILINGS PROFILES 34 The Sequence of Flow Events 34 Drainage of Initially Saturated Profiles 34 Drainage Without Evaporation 35 Drainage With Evaporation 40 Drainage of Layered Profiles with Evaporation .... 45 vi ------- Page Infiltration Events 51 Infiltration into a Uniform Coarse Profile 51 Infiltration into the M/F/M Profile 55 Evaporation Following a Rain 60 Uniform Coarse Profile 60 Evaporation from the M/F/M Profile 61 Discussion of the Flow in the Tailings Profile 70 The Development of the Quasi-Steady State Profile . . 72 REFERENCES 77 GLOSSARY 79 vii ------- Number FIGURES Page 1 A diagram of the relationships between hydraulic head, H, pressure head, h, and gravitational head, z ........ 6 2 Diagram of the hysteresis in the water content-pressure head relation, 6(h) ..................... 9 3 Diagram of the pressure chamber apparatus used to determine the water retention characteristics of the tailings materials .......................... 4 Water retention functions for the Coarse tailings ....... 17 5 Water retention functions for the Medium tailings ....... 18 6 Water retention functions for the Fine tailings ........ 19 7 Hydraulic conductivity-water content function for Coarse tailings .................. ......... 25 8 Hydraulic conductivity-water content function for Medium tailings ........................... 26 9 Hydraulic conductivity-water content function for Fine tailings ........................... 27 10 Diagram showing the division of the space-time domain into increments and the numbering of the nodes .......... 29 11 Expanded view of the nodes about the general node n, m showing the identification of the nodal values of pressure head ........................ 31 12 Water content profiles at several times during the drainage, without evaporation, of a uniform Coarse tailings profile . . 36 13 Water content profiles at several times during the drainage, without evaporation, of a uniform Fine tailings profile ... 36 14 Water content versus time at several depths in a uniform Coarse tailings profile draining without evaporation at the top ........................... 37 viii ------- Number Page 15 Water content versus time at several depths in a uniform Fine tailings profile draining without evaporation at the top ........................... 37 16 Flux across the water table (0 to 1 day) from uniform profiles of Coarse, Medium and Fine tailings, draining without evaporation at the upper end ....... . ..... 38 17 Flux across the water table (0 to 30 days) from uniform profiles of Coarse, Medium and Fine tailings, draining without evaporation at the upper end ............. 38 18 Water content profiles at several times in a uniform Coarse tailings profile draining with a 1 cm/day potential evaporation rate at the top ................. 41 19 Water content profiles at several times in a uniform Medium tailings profile draining with a 1 cm/day potential evaporation rate at the top ................. 41 20 Water content versus time at several depths in the uniform Coarse tailings profile of Fig. 18 .............. 42 21 Water content versus time at several depths in the uniform Medium tailings profile of Fig. 19 .............. 42 22 Flux versus depth in the upper 30 cm of the uniform Coarse profile of Fig. 18 ...................... 44 23 Flux versus depth in the upper 30 cm of the uniform Medium profile of Fig. 19 ...................... 44 24 Flux across the surface (actual evaporation rate) of the uniform Coarse and Medium profiles of Fig. 18, and 19 .... 45 25 Water content profiles at various times in a two-layer, Coarse over Medium, profile draining with a potential evaporation rate of 1 cm/day ................. 46 26 Pressure head distributions for the profile of Fig. 25 ..... 46 27 Flux across the water table (0 to 1 day) for draining profiles of uniform Coarse (Fig. 18), Coarse over Medium (Fig. 25), and Coarse over Fine (Fig. 29) ................ 48 28 Same as Fig. 27, except 0 to 15 days .............. 48 29 Water content profiles at several times in a two-layer, Coarse over Fine profile, draining with evaporation ..... 50 ix ------- Number Page 30 Pressure head distributions for the profile of Fig. 29 50 31 Flux across the surface (negative of the rainfall rate) of the uniform Coarse profile 52 32 Water content distributions in the uniform Coarse profile subjected to a 2.3 cm rainfall 53 33 Detail of water content distributions in the upper 30 cm of the profile of Fig. 32 54 34 Pressure head profiles corresponding to the water content profiles of Fig. 33 54 35 Flux versus depth in the upper 30 cm of the profile of Fig. 32 55 36 Flux across the surface (negative of the rainfall rate) of the layered M/F/M tailings profile 57 37 Water content distributions in a layered (M/F/M) profile at several times during a 12 cm rain 58 38 Flux versus depth at various times in the upper 90 cm of the M/F/M profile of Fig. 37 58 39 Detail of water content distributions in the upper 90 cm of the M/F/M profile of Fig. 37 59 40 Water content distributions in a uniform Coarse tailings profile subjected to a potential evaporation rate of 0.5 cm/day after a 2.3 cm rain 62 41 Detail of water content distributions in the upper 30 cm of the uniform Coarse profile of Fig. 40 62 42 Flux versus depth at various times during the evaporation from the profile of Fig. 40 63 43 Flux across the surface during evaporation from the uniform Coarse profile (Fig. 40), M/F/M profile, 12 cm rain (Fig. 44), and M/F/M profile, 6 cm rain (Fig. 47) 64 44 Water content distributions in the M/F/M profile subjected to a 0.5 cm/day potential following a 12 cm rain 65 45 Detail of water content distributions in the upper 90 cm of the M/F/M profile of Fig. 44 65 ------- Number ^£ 46 Flux versus depth at several times during evaporation from the M/F/M profile of Fig. 44 67 47 Water content distribution in the M/F/M profile with a 0.5 cm/day potential evaporation rate following a 6 cm rain 69 48 Detail of the upper 90 cm of the M/F/M profile of Fig. 47 69 49 Flux versus depth in the upper 90 cm of the M/F/M profile of Fig. 47 71 50 Water content distributions for two states of steady flow in a uniform Medium tailings profile 74 51 Water content distributions for two states of steady flow in a profile of Medium tailings with a Fine layer at 30 to 60 cm depth 75 52 Water content distributions for two states of steady flow in a profile composed of alternating 30 cm layers of Medium and Fine tailings 75 xi ------- TABLES Number Page 1 IN SITU BULK DENSITY AND PARTICLE DENSITY OF THE SELECTED FRACTIONS OF MILL TAILINGS, VITRO MILL SITE 12 2 PARTICLE SIZE DISTRIBUTION OF THE MILL TAILINGS FRACTIONS 13 3 PARAMETERS OF THE EMPIRICAL 6(h) AND K(6) FUNCTIONS OF THE COARSE TAILINGS 21 4 PARAMETERS OF THE EMPIRICAL 6(h) AND K(6) FUNCTIONS OF THE MEDIUM TAILINGS 21 5 PARAMETERS OF THE EMPIRICAL FUNCTIONS OF THE FINE TAILINGS 22 6 SUMMARY OF CONDITIONS FOR SIMULATIONS OF DRAINAGE WITHOUT EVAPORATION 39 7 SUMMARY OF CONDITIONS FOR SIMULATIONS OF DRAINAGE WITH EVAPORATION AT THE SURFACE 40 8 SUMMARY OF CONDITIONS FOR SIMULATION OF DRAINAGE WITH EVAPORATION OF A TWO-LAYER, COARSE OVER MEDIUM PROFILE 47 9 SUMMARY OF CONDITIONS FOR SIMULATION OF DRAINAGE WITH EVAPORATION OF A TWO-LAYER COARSE OVER FINE PROFILE 49 10 SUMMARY OF CONDITIONS FOR SIMULATION OF THE FILTRATION INTO A UNIFORM COARSE PROFILE 52 11 SUMMARY OF CONDITIONS FOR SIMULATION OF INFILTRATION OF 6 AND 12 CM RAINFALL INTO THE M/F/M PROFILE 56 12 SUMMARY OF CONDITIONS FOR SIMULATION OF EVAPORATION FOLLOWING A RAIN ON A UNIFORM COARSE TAILINGS PROFILE 60 13 SUMMARY OF CONDITIONS FOR SIMULATION OF EVAPORATION FOLLOWING A 12 CM RAIN ON THE M/F/M PROFILE 64 14 SUMMARY OF CONDITIONS FOR SIMULATION OF EVAPORATION FOLLOWING A 6 CM RAIN ON THE M/F/M PROFILE 68 ------- LIST OF SYMBOLS Symbol A B Definition Units d C h b e 0, K Empirical curve fitting parameter in the hydraulic conductivity function, K(0) = Aexp(B9), Eq. (18). Empirical curve fitting parameter in the hydraulic conductivity function, See A, above. Empirical curve fitting parameter in the relation 6(h) = (h/d)a, Eq. (11). Ditto. Water capacity, d9/dh Pressure head of the soil water Empirical curve fitting parameter in the water retention function, Eqs. (8), (9) and (10) Ditto. Volumetric water content Empirical curve fitting parameter in the water reten- tion function, Eqs. (8), (9) and (10). The water content at zero pressure head. Ditto. The water content limit as h ->• -°° . Volumetric water content at the intersection of the empirical 9(h) functions, Eq. (8) and Eq. (11). Pressure head at the intersection of the empirical 0(h) functions, Eq. (8) and Eq. (11). Hydraulic conductivity L/T, cm/day None None L, cm L-1, cm'1 L, cm L, cm None None None None None cm L/T, cm/day xiii ------- ACKNOWLEDGMENTS The United States Department of Agriculture, Science and Education Administration, Agricultural Research, and Colorado State University, carry out research on problems of mutual interest under a broad form cooperative agreement. The cooperation of the Department of Agronomy, Colorado State University, in this investigation is gratefully acknowledged. xiv ------- SECTION 1 INTRODUCTION The tailings materials which result from the extraction of uranium from ore are deposited in piles formed from a slurry containing up to 80-90% water. The piles consist of interbedded layers of materials ranging from clay to coarse sand in texture. The radionuclides in the tailings are a potential source of airborne, waterborne, and direct gamma radiation expo- sure to people. Radon-222, a noble gas daughter of radium-226 is formed within the pile and transported to the surface.!./ A primary variable affect- ing the diffusion of radon to the surface of a pile is the distribution of the water content of the tailings as a function of time and depth. It was the general objective of the study reported here to develop background information on the behavior of water in profiles of tailings materials. The specific objectives of this project were: 1. Characterize the movement and storage of water in tailings profiles consisting of clay, silt and sand-sized particles. 2. Estimate future moisture conditions under typical (average) and extreme precipitation, and evaporative conditions. A simulation approach to the objectives was taken, which involved: (1) the determination of the hydraulic conductivity and water retention functions for each tailings material of interest. (2) selection and mathe- matical description of the appropriate boundary and initial conditions to characterize specific flow problems, and (3) numerical solution of the equation of water movement. The numerical solutions gave the water content, and soil water flux distributions within the tailings profile subjected to specific boundary and initial conditions. The results from the numerical simulations were then interpreted and analyzed in the framework of the concepts of unsaturated flow theory. !/ Radon, in turn, decays by alpha emission to several daughters most notably lead-210 and polonium-210, both of which are particulates. Inhalation of radon and its daughters, therefore, results in exposure to alpha particles and is related to an increase in cancer incidence. ------- SECTION 2 CONCLUSIONS In a profile of tailings without vegetation and with a water table at a given depth, the sequence of water flow events may be described as: 1. An initial period of drainage from saturation, with evaporation at the surface. 2. Infiltration of varying amounts of rain at irregular intervals. 3. Periods of evaporation and drainage from the profile, and redistri- bution of water within the profile, between rainfall events. The initial drainage from saturation, if not disturbed by rainfall events, could last for several years. However, rain events will prevent the profile from attaining a steady state condition in the upper profile. The water flow regime in the upper profile (depths to about 90 cms) will be one of dynamic, transient fluctuations in water content and flux. The lower part of the profile will tend toward a quasi-steady state downward flow condition. Rainfall infiltration events will wet the upper profile to volumetric water contents, 9, on the order of 0.25 to 0.4 in the coarser fractions of tailings and to about 0.6 in the finer fractions. These levels of 6 will be maintained for only a short time (a fraction of a day) during and just after a rainfall. Infiltration produces a "wetting front" which moves down- ward into the profile. Above the front, the general level of 9 will be about as given above. Below the front the water content will not be affected during the period of infiltration. Wetting front penetration increases with the magnitude of the rainfall event and the initial level of water content in the profile. An approximation of the depth of wetting, d, can be obtained from d = r/(6u-9i), where 9U is the water content in the wetted zone, Q^ is the initial water content of the profile, and r is the depth of rainfall applied. This relation holds only if 9U and 9^ are constant with depth, and normally they are not. The level of water content reached in the wetted zone during a rain event will depend on the intensity of the rain — the higher the intensity, the higher the water content. In the simulations conducted in this study a rainfall of 2.3 cm pene- trated 20 cm into coarse tailings (c.f. Fig. 33) and a rain of 5.5 cm pene- trated about 18 cm into medium tailings. The initial water content of the latter was lower than that of the coarse tailings. In view of the character- istics of the rainfall at a location such as the Vitro Mill site, Salt Lake City, Utah, where rains of greater than 2 cm occur several times a year, ------- and rains of 5 cm or more very infrequently, the depth of wetting during rainfall infiltration will usually be less than 20 cm. Layers of finer textured material at depths greater than about 30 cm will have no appreciable effect on the dynamic transient behavior of the water content profile above that depth. Evaporation at the surface of a profile following a rain event will dry only the upper 5 to 10 cm of the profile even when the evaporation period extends to 15 or more days. If the preceding rain has penetrated beyond this depth the water in the wetted zone will continue to move downward and eventually moves to the water table. The long term (e.g. annual) average flux in the lower part of the pro- file, which is in the quasi-steady state condition, will be downward and its magnitude will be between zero and R/At, where R is the amount of rainfall in the averaging time interval At. The water content distribution in the lower part of the profile when it is in quasi-steady state will be determined by the texture of the material in that region, the magnitude of the average downward flux, and the proximity to the water table. At depths below approximately 70-90 cm and at distances more than 50-70 cm above a water table the water content of such a profile approximates that corresponding to a hydraulic conductivity equal to the magnitude of the downward flux. For example, for a downward average flow rate of .05 cm/day (about 10 cm/year), the water content of coarse tailings would be about 0.3, that of the fine tailings about 0.5 to 0.6. Under limited rainfall conditions, such as at the Vitro Mill site in Salt Lake City, any significant vegetative cover on the tailings pile would use all the available precipitation, leaving little or no water to flow below the root zone to greater depths. ------- SECTION 3 RECOMMENDATIONS Many aspects of water movement in tailings profiles could not be adequately explored within the scope of the project. The simulations and analyses should be extended to include a series of rainfall and evaporation events with a fuller exploration of the effects of various rainfall intensi- ties and magnitudes on water flow within the profile. The extraction of water by plant root systems should be included in the simulations and its effect on the behavior of water in the profile determined. A more extensive and systematic examination should be made of the effect of profile layering on the water content distribution in the upper 30 to 60 cm of the tailings profile. Another factor that should be explored Is the effect of water table depth on the flow in the profile, including the case of a water table at great depth or the "no water table" case. A logical extension of the present work on simulation of water flow in tailings profiles would be the combination of a model for radon transport in the profile with the water transport model. Such a combination could provide a method of systematic examination of the effect of various profile layering sequences on radon transport to the pile surface. Also, a combination of the soil water flow model with a model for transport of dissolved chemical species would seem to be a possible method of examining transport of contam- inants to the ground water. ------- SECTION 4 SOIL WATER FLOW CONCEPTS AND TERMINOLOGY The salient features of the theory of flow of water in unsaturated porous materials, such as soils, will be outlined in order to provide the reader, who may be unfamiliar with this subject, with the essential concepts and definitions of terms required for the subsequent discussion and analysis of flow systems. For further, more detailed, background on the subject the reader is referred to the cited literature (Childs 1969, Klute 1973, Swartz- endruber 1969). Selected terms used in this report are defined in the Glossary of this report. Water movement in soil can occur in the liquid phase or the gas phase. In each phase water may be transported by convective motion or by diffusion processes. The convective motion of a phase is driven by mechanical forces such as gravity and pressure gradients. Movement by diffusion within a phase occurs in response to gradients of the thermodynamic chemical potential of the water within the phase. In many cases diffusion may be considered to be driven by the concentration gradients of the water. In a water saturated medium the water transport is of necessity solely in the liquid phase and is dominantly a process of convective transport driven by mechanical forces. These forces are given by the negative gradient of a potential function. A commonly used potential function is the energy per unit weight of soil water or the hydraulic head, H. The hydraulic head is made up of two components, the gravitational head and the pressure head. The gravitational head of the soil water at a point in the soil is the elevation of that point above an arbitrarily chosen reference and is a measure of the gravitational potential energy per unit weight of the soil water at a given point in the gravity force field of the earth. In saturated soils the pressure head, h, is related to the pressure in the soil water by the relation: P -P h = w atm (1) d g where d is the soil water density, g is the acceleration of gravity, P is the pressure of the soil water and Patm is atmospheric pressure. The W hydraulic head and its components may be measured in those cases where P > patm with a Piezometer, which is a cased well, usually of small diameter™ terminated at the point in the soil at which the head is to be measured. Fig. 1 shows a piezometer, and the interpretation from it, of the hydraulic head and its components. In reference to a piezometer, the hydraulic head is defined as the elevation of the free water surface in the piezometer tube relative to an arbitrarily chosen reference elevation. ------- SOIL-WATER SYSTEMS Saturated Piezometer Unsaturated Tensiometer Porous cup Reference level Fig. 1. A diagram of the relationships between hydraulic head, H, pressure head, h, and gravitational head, Z. The pressure head is measured from the level of termination of the piezometer or tensiometer in the soil to the water level in the manometer and is negative in the unsaturated soil. ------- In unsaturated soils the pressure in the liquid phase PW is usually less than atmospheric, and the piezometer cannot be used to measure the hydraulic head. A. tensiometer, which consists of a porous permeable membrane or cup connected to a manometer or other pressure measuring device (See Fig. 1), is used to extend the measurement of hydraulic head to unsaturated soils. The pressure of the water inside the "cup" when the water in the tensiometer is in equilibrium with the soil water is then used in equation (1) to obtain the pressure head. The pressure that must be applied to the tensiometer water to establish equilibrium between it and the soil water is determined by the water content of the soil which in turn is related to factors such as the curvature and surface tension of the air water interface within the soil water system, and the magnitude and extent of the adsorptive forces between the soil solid matrix and the soil water. The equation of soil water transport, which was used in the simulations and analyses described in this report, is developed by combining a mass bal- ance for the soil water with a flux equation. The mass balance equation relates the time rate of change of water content of a differential volume element of soil to the excess of inflow over outflow from the element and to the time rate of production of soil water within the element. If it is assumed that the soil water is of constant density, the mass balance may be written as a volume balance, which for one dimensional flow becomes: £--£*« (2> In equation (2) 9 is the volumetric water content, z is the vertical space coordinate taken as positive upward, t is the time, Q is the soil water flux and S is a source term or the time rate of production of soil water per unit soil volume. The latter may be used to represent the extraction of water from soil by plant roots in which case the production rate is generally nega- tive. Equation (2) expresses the fact that there are two reasons for the change in water content of a differential soil volume element at a point in the flow system, (1) the excess of inflow to the element over outflow from the element, which is mathematically described by - 9Q/(Dz), and (2) the production (positive or negative) of water by any processes or reactions in the soil within the element. In the simulations described in this report we have not considered extraction of water by plant roots, and have set the source function S equal to zero. The soil water flux is assumed to be given by the Darcy equation which is the product of the hydraulic conductivity, k, and a driving force express- ed as the negative gradient of the hydraulic head. For a saturated soil the hydraulic conductivity is a maximum for the given soil. As the water content of the soil decreases from saturation the ability.of the soil to transmit water, which is measured by the hydraulic conductivity, decreases very strongly. The Darcy equation has been extended to unsaturated soils by con- sidering the conductivity to be a function of the water content. The primary reasons for the decrease of K as 9 decreases are (1) the decrease in effec- tive cross section of the soil which is available for liquid flow, (2) the drainage of water from the largest pores, which contribute strongly to the conductivity, and a decrease in the average size of the liquid-filled flow ------- channels and, (3) the increase in tortuosity (crookedness) of the liquid flow path. In one dimension the Darcy equation or flux equation may be written as: 3H Q - - K(6)ff (3) where K(6) is the hydraulic conductivity water content function. The con- ductivity is a positive quantity, and since the hydraulic gradient may in a given case be either positive or negative, the flux Q may be either positive or negative. The algebraic sign of the flux indicates the direction of the flow with respect to the chosen coordinate axis, a positive flux being in the positive z axis direction, and vice versa for a negative flux. Since the hydraulic head is the sum of the pressure and gravitational heads, equa- tion (3) may be written: Q - - K (e)<|£+ 1) (4) where 3h/3z is the pressure head gradient. Combining equation (4) with (2) with S = 0 yields: + 1) ) (5) dt dZ dZ Equation (5) is a partial differential equation in two dependent variables, 6 and h. In order to obtain an equation for water flow in one dependent variable, another relation between 6 and h is required. This relationship is the water retention function, 8(h). The schematic form of this function is shown in Fig. 2. In general, the water content decreases as the pressure head decreases (becomes more negative). The retention function displays a phenomenon called hysteresis, i.e., the water content at a given pressure head depends on the historical sequence of pressure heads which has been imposed on the soil. If the flow process is entirely one of drainage from saturation or of wetting from a given initial water content, the relation between 9 and h is single valued and non-hysteretic. If, however, the flow process involves sequences of wetting and drying the water content-pressure head relation is multi-valued and hysteretic. There is an infinite number of possible 6(h) relationships or scanning curves lying between the initial drainage curve and the main wetting curve (See Fig. 2). The scanning curve to be applied at any time and place in a flow process depends on the sequence of reversal points that have occurred at that place. A reversal point is described by the paired values of pressure head and water content (such as nl» ®1 or ^2» ®2 *n ^-8' 2} at which a reversal in the time-trend of water content change has taken place. In non-hysteretic flow simulation the func- tion 9(h) is single valued and may easily be represented empirically. In hysteretic flow simulation the 6(h) relation is much more complicated because some method must be devised to keep account of the necessary reversal points and select the appropriate scanning curve. We have devised procedures to treat the hysteresis in the 6(h) relation that can be used in the numerical solution process for the flow equation to be described in another section of this report. ------- (-) PRESSURE HEAD Fig. 2. Diagram of the hysteresis in the water content-pressure head relation, 0(h). IDC - initial drainage curve. MDC - main drainage curve. MWC- main wetting curve. a and b - primary wetting scanning curves, c - primary drying scanning curve. Higher order (e.g., secondary, etc.) are possible and reverse from lower order scanning curves. ------- Assuming that proper mathematical description of the 6(h) relation and its hysteresis is available, the time derivative term in equation (5) can be transformed to li _ !§. lh _ _3h 9t ~ dh 3t ~ 9t (6) In equation (6) the water capacity function, C, is the rate of change of water content with pressure head, d6/dh, and is the derivative of the appro- priate applicable drying or wetting scanning curve of the 9(h) relationship. The water capacity is a function of the water content. It may be seen from the general shape of the 6(h) function (Fig. 2) that the water capacity will have a maximum at some pressure head less than zero. Using equation (6) in (5) yields C (9)f = fe(K(9)(f +1) > <7> which is the one-dimensional soil water flow equation used as a basis for the simulations described in this report. Particular solutions of equation (7), subject to given initial and boundary conditions, predict and describe the dependence of the pressure head, h, upon position and time. An initial condition is a mathematical statement of the spatial distribution of pressure head at the time arbitrarily designated as zero time. Boundary conditions are mathematical statements that specify either the pressure head or the soil water flux at the boundaries of the flow region. The functions C(0) and K(0) are the hydraulic functions or properties of the soil in the region of flow, and are the avenue by which the soil affects the flow behavior. A solution of equation (7), viz, the function h(z, t), may be used to obtain the water content position-time function, 6(z, t), by using the water retention func- tion 9(h). The soil water flux distribution, Q(z, t), may also be obtained by using h(z, t) in the Darcy law, equation (4). The assumptions implicit in equation (7) have been summarized by Klute (1973). One of these assump- tions is that the air phase is at atmospheric pressure, and has essentially a zero pressure gradient. This assumption is sometimes not well satisfied in practice. For various reasons it is not possible to give a complete as- sessment of the errors introduced by this assumption. Some qualitative statements may be made, however. Air pressure build up may occur during rapid infiltration from ponded water into a soil profile bounded at its lower end by a water table or a soil layer of low air permeability. The qualitative effect in this case is to decrease the rate of infiltration and the extent of penetration of the infiltrating water. Conversely, drainage of a layered soil profile, when air access to the soil layers is restricted, will not occur as rapidly as would be predicted from theory based on the assumption of constant atmospheric pressure within the gas phase. In general, a more correct approach to water flow in unsaturated soils would involve a two-phase flow treatment, and a flow equation for each phase (gas and water) would have to be solved. Such an approach is inherently more complex than the one-phase approach used in this study. We do not feel that the errors introduced in the analyses described herein due to neglect of the air phase flow are extremely significant. In the infiltration cases that were studied herein, no ponding occurred on the soil surface, hence, the situation of a 10 ------- pressure build-up in a gas phase trapped between a water table and overlying ponded water could not occur. Simulations of drainage of an initially satu- rated layered soil column may be significantly in error when a fine textured layer overlies a coarser textured layer and air must enter the coarse layer through the overlying wetter fine material, which may have a low air perme- ability. The error would be greatest during the initial (first one or two days) rapid drainage of the layered profile. The water content of a coarse layer under a finer textured layer would be higher than predicted by the method of simulation used in this study. However, after a few days, there is an increased probability of leakage or access of air to the buried coarse layers, and furthermore, the rate of flow and drainage would be decreasing. Both of these factors suggest that the error due to neglect of air flow would decrease in significance with time of drainage. The conductivity water content relationship K(6) has been found not to be very much hysteretic. In many cases the hysteresis in K(6) if it exists is hidden within the uncertainty of determination of the relationship. For the purpose of the analyses described in this report, it was assumed that K(6) is not hysteretic. However, the K(h) function will be hysteretic be- cause of the hysteresis in the 9(h) function. 11 ------- SECTION 5 DETERMINATION OF THE HYDRAULIC PROPERTIES OF TAILINGS SAMPLING AND BASIC PHYSICAL CHARACTERISTICS Upon consultation with representatives of the Office of Radiation Programs, U. S. Environmental Protection Agency, Las Vegas, Nevada, the tailings pile at the Vitro Mill site in Salt Lake City, Utah was selected as a test area. A visit to the site was made in April, 1976, to become famil- iar with the general features and characteristics of tailings materials. Three size fractions of tailings material were selected for characterization. These are hereafter designated as Coarse, Medium and Fine. A second trip to the site was made in June, 1976, to collect bulk samples of these fractions. Due to the generally single-grain structure of the tailings material in situ, it was decided to use core samples which were packed in the laboratory from bulk material for the determination of hydraulic properties. A limited number of core samples was taken at the site for the purpose of establishing the general level of in situ bulk density of the selected tailings fractions. These results are summarized in Table 1. TABLE 1. IN SITU BULK DENSITY AND PARTICLE DENSITY OF THE SELECTED FRACTIONS OF MILL TAILINGS. VITRO MILL SITE Fraction Bulk Density Particle Density Coarse Medium Fine g/cm 1.48 to 1.57 1.28 to 1.50 0.9 to 1.1 g/cnH 2.70 2.71 2.89 12 ------- The bulk samples were packed in drums, with plastic liners, and transported to the laboratory. Particle size distributions were determined by sieving and by the hydrometer method (Day, 1965). Table 2 lists the sum- mation percentage for each of the fractions. The particle density of each fraction was determined by the picnometer method (Blake, 1965). The results are shown in Table 1. TABLE 2. PARTICLE SIZE DISTRIBUTION OF MILL TAILINGS FRACTIONS SUMMATION PERCENTAGES^' I/ Particle Diameter 1000 pm 500 250 125 63 48 25 16 9 7 3 Coarse 92 % 76 41 22 15 10 7.5 5 3.4 - - Tailings Fraction Medium 98 % 95 81 55 33 24.4 4.2 2.1 1.3 - - Fine - - - 100 % 95 92 84 80 57 42 5.9 — Percent of the fraction with particle diameters less than or equal to the indicated diameter. WATER RETENTION CHARACTERISTICS The 0(h) relationship for each fraction was determined using a combina- tion of pressure chamber apparatus or suction apparatus (Rose, 1966; Taylor and Ashcroft, 1972). Fig. 3 illustrates the pressure apparatus. The suction apparatus was similar, except that the chamber enclosing the samples was maintained at atmospheric pressure, and suction was applied to the samples by lowering the water bottle relative to the porous plate to an appropriate distance. Generally, pressure chamber apparatus was used to obtain data in 13 ------- To Regulated Air Pressure (Pressure Chamber . I Air Trap Porous Ceramic Plate Plastic Screen 4 4 Roller Rubber Backing Sheet Water-filled Tubing Fig. 3 Diagram of the pressure chamber apparatus used to determine the water retention characteristics of the tailings materials. ------- the range of pressure heads less than -60 cm of water, and suction apparatus for h > -60 cm. Sample Preparation It was desired to pack core samples to the field value of bulk density. The following procedure was used for the Coarse and Medium fractions. A bulk quantity of a given fraction was thoroughly mixed with sufficient water to bring it to a water content of 6 - 10% by weight, and placed in a plastic bag to prevent loss of water. Sub-samples were taken to determine the actual weight percentage of water. The weight of moist material to be packed in a sample ring (volume 48.3 cm3, height 2.5 cm) to obtain the desired bulk density was calculated. A hydraulic press was used to pack the desired weight of moist tailings material into the sample rings. Cores were packed to bulk densities of 1.53 and 1.47 g/cm3 for the Coarse and Medium fractions, respectively. Cores of the Fine fraction were prepared by a filtration procedure, in which a filter cake of the material was formed in the sample ring by suction filtration from a slurry of the Fine material. Cores with bulk densities in the range 0.95 to 0.99 g/cm3 were obtained by this technique. After packing the cores, a piece of cheesecloth held in place by a rubber band, was placed over the lower end of the core to prevent loss of material from the core in subsequent handling. Method for Determination of Hysteresis In the simulation procedure the main drainage and main wetting curves for each fraction were required. Because any rewet curve of 6(h) starting at pressure heads less (i.e., more negative) than -7000 cm does not differ much from the rewet curve starting at -7000 cm, it was arbitrarily decided to determine the "main" wetting curve starting at h = -7000 cm and neglect any hysteresis at lower pressure heads. Pressure heads of -2, -7.5, -15, -30, -60, -120, -250, -500, -1000, -3000, and -7000 cms of water were select- ed as the standard points of measurement on the 6(h) curves. To determine the main wetting curve (MWC) beginning at h = -7000 cm, a large number of core samples (30 or more) was packed and soaked in water for at least 24 hours. They were then placed on a porous plate in a pressure chamber at a gas phase pressure of 7000 cm of water (corresponding to h = -7000 cm) and brought to hydraulic equilibrium. Equilibrium was determined by removal of the cores from the porous plate and weighing them. When the weight of the core remained constant (within approximately .05 gm, corres- ponding to an uncertainty in 9 of about 0.001) the cores were distributed to a series of pressure chambers at gas phase pressures of 3000, 1000, 500, 250, and 120 cms of water and to suction plates at pressure heads of -60, -30, -15, -7.5 and -2 cms of water, and allowed to take up water until they were at equilibrium. Gas bubbles tend to accumulate in the water beneath the porous plate and in the connecting tubing to the water bottle. These bubbles may block the flow of water to the ceramic plate and the core samples. Periodically, the gas bubbles were removed to the air trap by closing 15 ------- stopcock S~ (See Fig. 3) and circulating the water in the closed loop consisting of the air trap, the space below the ceramic plate and the connect- ing tubing, using a roller on one of the tubes. This modification of the apparatus allowed us to determine the wetting 9 (h) curve. After equilibrium was reached the water content of each core was deter- mined by standard gravimetric procedures. The data thus obtained were used to develop the MWC. The main drying curve MDC was determined by preparing a large number of cores, which were soaked for 24 hours or more, equilibrated in a pressure apparatus at h = -7000 cm, and then on a suction apparatus at h = -2 cm. This sequence was necessary to establish the rewet saturation at h = -2 cm so that the main drainage curve would be properly determined. After equili- bration at h = -2 cm, the cores were distributed to a series of suction plates at pressure heads of -7.5, -15, -30, and -60 cms of water, and to a series of pressure chambers at pressure heads of -120, -250, -500, -1000, -3000, and -7000 cms of water. After equilibration the water content of each core was obtained. The data thus obtained were used to develop the MDC. The water content-pressure head relation for the Coarse and Medium frac- tions was determined in the range of pressure heads less than -7000 cm water (-7 bars) by a vapor pressure technique (Croney, et al., 1952). Samples of the materials were equilibrated in vacuum dessicators over saturated salt solutions with relative humidities corresponding to water potentials of -71, -145, -290, -900, and -1,568 bars. The weight percentage water contents were determined at equilibrium and converted to the volumetric basis by multiply- ing by the bulk density of the cores packed for the 0(h) determination at pressure heads greater than -7 bars. Due to experimental difficulties (e.g. shrinkage at high suction) with the Fine fraction of tailings, it was decided to limit this study to simulations where the Fine fraction would not be exposed at the profile surface, and therefore, retention data at pressure heads less than -7 bars would not be needed for this fraction. The water retention data obtained from the measurements described above were represented by empirical functions for use in the numerical simulation. In the range of pressure head, -7000 cm <_ h <_ o, the following function was used (Gillham, et al., 1976): where 3 = (h/h )b b < o (9) o r = (eo - er) / ------- T - 1 - 1 1 - 1 - 1 -f 1 - 1 - 1 COARSE TAILINGS Bulk Density 1.53 g/cc Total Porosity 0.433 1 - 1 1 - 1 — r IDC I I 0.5 0.4 0.3 M CJ s E9 0.2 8 0.1 -10* -1000 -100 -50 -20 -10 -5 PRESSURE HEAD, CM -2 -r Fig. 4, Water retention functions for the Coarse tailings. Each point is an average of 3 to 15 determinations. The vertical lines represent jK 1 standard deviation from the mean. The curves are the empirical functions used in the simulations of water flow. The IDC was calculated from the MDC by the theory of Mualem, ------- 00 I 1 1 I 1 1 r 1 1 MEDIUM TAILINGS Bulk Density 1.47 g/cc Total Porosity 0.458 -10* -1000 -100 -50 PRESSURE HEAD, CM -20 -10 -5 g O -2 -1 Fig. 5. Water retention functions for the Medium tailings. Each point is an average of 6 to 9 individual measurements. The vertical lines represent + 1 standard deviation from the mean. The curves are the empirical functions used in the simulations of water flow. The IDC was calculated from the MDC by the theory of Mualem. ------- T T 1 T T T 1 T FINE TAILINGS Bulk Density 0.986 g/cc Total Porosity 0.66 IDC & MDC t L J L- -10* _L JL _L _L _L 0.7 0.6 M O 0.4 § 0.3 -1000 -100 -50 PRESSURE HEAD, CM -20 -10 -5 -2 -1 Fig. 6. Water retention functions for the Fine tailings. Each point is an average of 4 to 12 individual determinations. The vertical lines represent + 1 standard deviation from the mean. The solid lines are the empirical functions used in the simulations of water flow. ------- the constraint that the MDC and MWC should intersect at (&it h-^), with h± about -7000 cm. The empirical functions for the MWC and MDC were used to generate the scanning curves interior to the MWC and MDC. A theory developed and tested by Mualem (1974) was used for this purpose. The initial drainage curve (IDC) was generated by his theory from the MDC. Scanning curves interi- or to the IDC and MWC were also obtained by his theory. Mualem's theory pro- vides a reasonably accurate method of obtaining scanning curves, which is suited to use in the numerical simulation process, and greatly reduces the necessary amount of experimental measurement required. At pressure heads more negative than about -7000 cm the 9(h) data were represented by the empirical form: 0(h) = &a (ID d where a and d are parameters which were selected to fit the data, and with the constraint that the function of Eq. (11) should pass through the inter- section point (Gj, hj) of the MDC and MWC (see above). Figs. 4, 5 and 6 show the empirical 9(h) functions obtained for the Coarse, Medium, and Fine fractions, respectively. The solid curves in these figures are plots of Eq. (8) subject to Eqs. (9) and (10). The dashed line in Figs. 4 and 5 is a plot of Eq. (11). The parameters of the functions are given in Tables 3, 4 and 5. HYDRAULIC CONDUCTIVITY - WATER CONTENT RELATIONSHIPS The measurement of the K(9) relation may be accomplished by a number of methods (Klute, 1972). All of the available methods require a substantial amount of time and in some cases the methods are rather difficult. Because of these and other difficulties encountered in the direct measurement of the K(6) function there has been considerable interest in schemes for the calcu- lation of hydraulic conductivity from pore size distribution data (Jackson, et al., 1965; Kunze, et al., 1968). The latter may be obtained from the water content - pressure head relation. Lalibertie, et al. (1968) described a method of using water content- pressure head data to calculate the conductivity-water content function. These authors developed an integral equation for the conductivity, which may be written as: 9 - 9 . r / J In Eq. (12), p is the density of the soil water, n is its viscosity, a is its surface tension, g is the acceleration of gravity, and 9g and 9 are param- eters of the 9(h) function. To evaluate the integral, and obtain K(9), a functional relation between h and 9 is needed. 20 ------- TABLE 3. PARAMETERS OF THE EMPIRICAL HYDRAULIC FUNCTIONS OF THE COARSE TAILINGS Function and Parameter Equation No. Symbol Water Retention Eq. (10) Eq. (9) Eq. (11) Intersection Point Hydraulic Conductivity Eq. (18) IDC 6 0.433 6r 0.076 h0, cm - 131 b -0.468 d, cm a h.£, cm ei A, cm/ day B Value MDC 0.385 0.0763 - 131 -0.468 -1.71 x 10~2 -0.1964 -7320 0.07842 5.40 x 10~8 54.29 MWC 0.385 0.0776 - 67.4 -0.504 TABLE 4. PARAMETERS OF THE EMPIRICAL HYDRAULIC FUNCTIONS OF THE MEDIUM TAILINGS Function and Parameter Equation No. Symbol Water Retention Eq. (10) Eq. (9) Eq. (11) Intersection Point Hydraulic Conductivity Eq. (18) IDC 60 0.458 er 0.090 h0> cm - 281 b -0.451 d, cm a h.£ , cm ei A, cm/ day B Value MDC 0.401 0.0959 - 281 -0.451 -1.102 x ID'2 -0.1749 -7121 -.09589 1.99 x 10~8 50.0 MWC 0.401 0.0939 - 166 -0.503 21 ------- TABLE 5. PARAMETERS OF THE EMPIRICAL HYDRAULIC FUNCTIONS FOR THE FINE TAILINGS Function and Equation No. Water Retention Eq. (10) Eq. (9) Eq. (11) Symbol 9o e r h , cm b d, cm a Parameter Value IDC & MDC 0.66 0.31 -2500 -0.28 — ^^ MWC 0.66 0.35 -400 -0.28 Intersection Point Hydraulic Conductivity Eq. .(18) cm 9i -6982 0.3727 A, cm/day B 5.38 x 10 45.1 -12 In application of most of the theories which have been developed to calculate K(9) from 9(h), it has been found that the calculated K(9) function can be brought into reasonable agreement with measured K(6) data by the use of a matching factor. The matching factor M is defined as: -ft] (13) where KM is a measured conductivity at some known water content, Qit and KC is the calculated conductivity at that water content. If Kc(9) is the calcu- lated conductivity function, the matched, calculated function ^(9) is obtained from Kmc(9) M K (9) c (14) Nielsen, et al. (1973) conclude that the procedure of calculating K(6) from 9(h), with a matching factor, is a satisfactory method of evaluating the hydraulic conductivity of a field soil, especially when one considers the spatial variability of the hydraulic conductivity. To avoid the time consuming procedure of determining K(9) by one of the available methods of direct measurement (Klute, 1972), and in view of Nielsen's conclusion cited above, as well as the experience of others, I decided to calculate K(9) from Eq. (12) and use a matching factor to adjust the calculated function as described above. For this purpose, the h(6) function obtained by solving equation (8) (with Eqs. 9 and 10) for h was used in the integral of Eq. (12). The result is: 22 ------- c K_(9) = TE7TT—o l«—z-) I (In (v + (v-lV) d9 (15) where e + e (e - e ) v = r (_2 ) r = _o r' 7 VV |