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Considerations on the design of flowthrough rockfill drains Garga, Vinod K. 2009
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Title | Considerations on the design of flowthrough rockfill drains |
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Garga, Vinod K. Hansen, D. (David) Townsend, R. D. |
Date Created | 2009-08-20T19:28:50Z |
Date Issued | 1990 |
Description | Up to the present time the main tool used in the hydraulic design of flowthrough rockfill drains appears to have been Wilkins' (1956) equation. In this Paper the assumptions associated with this equation are discussed in detail. The authors note that piezometers are sometimes installed in rockfill drains to permit mine operators to ensure that a drain is functioning as expected, yet little effort seems to have been expended in verifying whether the observed water levels are in agreement with levels which could be estimated using theoretical considerations. Such modelling can indicate whether the values of parameters assumed in Wilkins' equation were correct and may therefore also indicate whether appreciable clogging of the drain has occurred. This Paper discusses an adaptation of the theory of gradually varied flow for computing the phreatic surface within a rock drain. Wilkins' (1956) equation for non-Darcy flow through porous media utilizes the parameter known as the hydraulic mean radius. In this Paper a rationale is presented for estimating this important parameter. The effect of subzero temperatures on the hydraulic capacity of rockfill drains has been examined for the first time. The possibility of ice build-up within a flowthrough rockfill drain is discussed, including the main modes of heat loss and the role of the viscous dissipation of hydraulic energy. |
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Language | Eng |
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B.C. Mine Reclamation Symposium 1990 |
Series | British Columbia Mine Reclamation Symposium 1990 |
Date Available | 2009-08-20T19:28:50Z |
DOI | 10.14288/1.0042158 |
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Applied Science, Faculty of |
Peer Review Status | Unreviewed |
Scholarly Level | Other |
Copyright Holder | British Columbia Technical and Research Committee on Reclamation |
URI | http://hdl.handle.net/2429/12430 |
Digital Resource Original Record | https://open.library.ubc.ca/collections/9379/items/1.0042158/source |
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Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation CONSIDERATIONS ON THE DESIGN OF FLOWTHROUGH ROCKFILL DRAINS V.K. Garga, D. Hansen, and R.D. Townsend Department of Civil Engineering University of Ottawa ABSTRACT Up to the present time the main tool used in the hydraulic design of flowthrough rockfill drains appears to have been Wilkins' (1956) equation. In this Paper the assumptions associated with this equation are discussed in detail. The authors note that piezometers are sometimes installed in rockfill drains to permit mine operators to ensure that a drain is functioning as expected, yet little effort seems to have been expended in verifying whether the observed water levels are in agreement with levels which could be estimated using theoretical considerations. Such modelling can indicate whether the values of parameters assumed in Wilkins' equation were correct and may therefore also indicate whether appreciable clogging of the drain has occurred. This Paper discusses an adaptation of the theory of gradually varied flow for computing the phreatic surface within a rock drain. Wilkins' (1956) equation for non-Darcy flow through porous media utilizes the parameter known as the hydraulic mean radius. In this Paper a rationale is presented for estimating this important parameter. The effect of subzero temperatures on the hydraulic capacity of rockfill drains has been examined for the first time. The possibility of ice build-up within a flowthrough rockfill drain is discussed, including the main modes of heat loss and the role of the viscous dissipation of hydraulic energy. 1. INTRODUCTION The use of engineered rockfill to pass seepage through it or over it has now been well established in practice. Some early examples of "self-spillway" rockfill dams without a conventional spillway were constructed in Mexico between 1939 and 1945, and have been documented by Weiss (1951). An impetus to use this technology was provided by Australian research conducted between 1955 and 1965, and the construction of the 109 m Cethana Dam in Tasmania (Wilkins Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation 1963; Parkin et al 1966). Indeed, even today, it is difficult to find a publication which does not make use of Wilkins' findings. Canadian examples of flowthrough structures are more common in the mining industry, one of which has been described by Lane et al (1986). The flowthrough rockfill structures can be particularly well-suited to the mining environment since many mines can provide large volumes of rockfill at low cost. Also, flowthrough rockfill structures such as dams or drains may require virtually no long term maintenance. Hence they become an attractive option for the abandonment stage of the mine. An innovative design of a flowthrough structure for the abandonment of acid generating metal tailings in Northern Canada has been described by Garga et al (1983) . The use of flowthrough rockfill can also be made to provide a relatively low cost containment structure for mini-hydro schemes for mining camps and other remote locations. Considerable research on the fundamental behaviour of flow through rockfill has been undertaken at the University of Ottawa over the last two years. The experimental work, comprising of 22 packed column tests with rockfill of different shapes and sizes, 52 instrumented flume tests (flume widths of 0.4 m and 1.4 m) with different dam configurations, and 3 flume tests in the low temperature laboratory to simulate winter flow conditions, has already been undertaken. The work has focussed on the estimation of discharges, phreatic surfaces, and the direct measurement of the destabilizing bursting forces on the downstream slope of the model dams. This Paper presents a brief discussion of some of the findings from this study which may influence the design of flowthrough drains for mining projects. 2. EXAMINATION OF WILKINS EQUATION Wilkins' (1956) original equation can be stated as: The reason for stating the exponent as 1/N pertains to a forthcoming explanations on how N relates to the level of turbulence and to how N is used in computing the phreatic surface. The average velocity in the voids VV, also known as the average linear velocity (Freeze and Cherry 1979) and the void velocity (Jain et al 1988), is related to the bulk velocity by: Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation where: V = bulk velocity (Q/A) n = porosity Wilkins equation is actually only one of many empirical equations which have appeared in the literature for non-Darcy flow through porous media. There are five factors which should be clearly understood before applying Wilkins' equation to practical problems. These are: 1. The flow is unidirectional with a nearly uniform velocity distribution. 2. A single value of the hydraulic gradient i applies throughout the flow field. Assumptions 1 and 2 warrant elaboration. Wilkins' equation was developed from column tests in which no phreatic surface was present. Therefore, as a corollary of assumptions (1) and (2), Wilkins equation should not be directly applied when a non-uniform velocity distribution is present in the flow field, such as in situations where the flow has a phreatic surface and the bed slope is not equal to slope of the phreatic surface. Figure 1(a) illustrates a situation where the flow is neither nonuniform nor does the same hydraulic gradient act throughout the flow field. Figure 1 (b) illustrates a case of uniform flow through porous media, wherein the phreatic surface is parallel to the bed and it is assumed that the velocity profile is uniform. Wilkins' equation may be applied to the case in Figure 1(b) but not to the case in Figure 1(a). 3. Wilkins empirical value for N of 0.54 implies that turbulence was not quite fully developed in his tests (Parkin 1963). Whether or not turbulence is fully developed depends on the velocity of the flow, the value of the hydraulic mean radius, and the kinematic viscosity. McCorquodale et al (1978) examined non-Darcy flow through porous media in great detail by bringing together the results of some 1250 column tests, including tests on crushed rock up to 6 inches diameter. It was found that if the pore Reynolds number was greater than 500, the flow was essentially turbulent. The pore Reynolds number is defined as: Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation a) Non-uniform flow. b) Uniform flow. Figure 1. Examples of flow fields for flow through porous media. Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation In general the value of N in equation [1] must be between the values 1 and 2. If the voids are relatively large (implying that m is also large) turbulence has greater freedom to develop and the value of N will tend toward its limiting upper value of 2. If the voids are small and the flow velocity is also small, such as for seepage flow through sand or clay, N tends toward its lower value of 1.0 (Parkin 1963). It is therefore recommended that if from observation of velocity and estimation of the hydraulic mean radius it is determined that ReP > 500, the value of N could be set to 2. An example of the effect of using N = 1.85 or N = 2 is given in Figure 2. The error can be as large as 20 percent for small hydraulic gradients. For the relatively small size of rock used in Wilkins' column tests (about 2 inches), the value of N achieved by Wilkins was 1.85 and not 2. The reason Wilkins was able to achieve a value as high as 1.85 was that high hydraulic gradients (up to 3.0) were used in his tests. Use of equation [3] requires knowledge of the hydraulic mean radius, m. A discussion of the determination of hydraulic mean radius is presented later in this Paper. Using the critical Reynolds number stated by McCorquodale (1978), Table 1 indicates of minimum velocities needed to achieve fully developed turbulence for water at 20°C for a porous media with porosity 0.40: Table 1 4. Most of Wilkins' experiments were performed on crushed dolerite about 51 mm (2 inches) in diameter in a column 222 mm (8.75 inches) in diameter. A wall effect was therefore introduced, an effect which was not corrected for in his analysis. The wall effect refers to the fact that the porosity of the media is lower next to the wall of the column, allowing the flow to move at higher velocity in a narrow zone next to the column wall. This lower porosity next to the wall is due to the absence of interlocking particles at the face of the container. According to Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation Dudgeon (1967) the zone of higher velocity is about one half the average particle diameter. Various guidelines have appeared in the literature regarding the magnitude of the wall effect, and are summarized in Table 2: Table 2 Reported Guidelines on the Wall Effect. Rose (1945) D/d = 10 about 6% error Franzini (1956) D/d = 40 negligable error Dudgeon (1967) D/d = 35 about 7% error Somerton and Wood (1988) D/d = 200 negligable error d = representative particle diameter D = column diameter In Wilkins work D/d =4.4, so that the bulk velocities measured by Wilkins (1956) can be expected to be at least 6% too small. Wilkins' equation should therefore not be expected to give estimates of velocity closer than perhaps 10% of actual bulk velocities, even if the flow regime (level of turbulence) is identical to that in Wilkins' tests, and even if assumptions 1 and 2 are not violated. It should be noted however, that some "wall effect" might also occur in field situations, such as at the base of a waste dump. In general this is probably much less than the wall effect present in column tests, since the ground beneath the waste dump can deform, permitting some degree of "interlocking" to take place between the sharp edges of the rock and the ground beneath. 5. Wilkins' equation does not take into account the effect of fluid viscosity. Fortunately this effect is not large. However, the work of Ergun (1952), Ward (1964) and McCorquodale et al (1978) all indicate that increased viscosity decreases the rate of flow for the same applied gradient, especially when turbulence is not fully developed. A common approach in characterising flow through porous media is to plot a friction factor versus Reynolds number curve on semilog paper. Although the ratio of the kinematic viscosity V of water at 20°C to "v" at 0°C is 1 to 1.8, this in fact has a relatively small effect on the flow because friction factor changes relatively slowly with Reynolds number for non-Darcy flow in porous media. In order to perform a simple investigation into the effect of fluid viscosity on the velocity computed from Wilkins' equation, a friction-factor (f ) versus pore Reynolds number diagram was generated using Wilkins' equation, and this is shown in Figure 3. The following equation was obtained for a hydraulic radius of 0.05 m and a kinematic viscosity of 1.003 • 10" m /s (2O0C). Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation At 2O0C with n = 0.40 and i = 0.2, Wilkins equation yields a bulk velocity of 0.20 m/s. At 0°C (v = 1.785 • 10-6 m /s) equation [4] was used to find that V is only reduced to 0.19 m/s, which represents a 5% reduction in velocity. It is therefore concluded that even though seasonal changes in temperature in Canada typically result in large changes in kinematic viscosity, this will not introduce large errors if Wilkins' equation is used to compute discharges through rock drains. In addition, conventional theory regarding flow through pipes and through porous media dictates that when fully developed turbulence is achieved, the hydraulic gradient associated with a given velocity is virtually independent of fluid viscosity. 3. USE OF A FRICTION SLOPE EQUATION WITH THE THEORY OF GRADUALLY VARIED FLOW. In the design of flowthrough rockfill structures it is often of interest to determine the location of the phreatic surface within the porous media. One convenient method is the application of the theory of gradually varied flow (GVF), commonly applied to flow in open channels. It is of interest to note that while virtually all papers related to flow through rockfill refer to equation [1] by Wilkins (1956), there has been little use made the GVF theory which he also suggested in the same publication. It is important to understand the basic concepts related to GVF theory before attempting to apply it to flow through porous media. The ordinary differential equation for steady gradually varied flow in open channels is: So = Sf = Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation α2 = energy coefficient, typically 1.1 to 1.2 for turbulent flow, V2 /2g = velocity head, based on the average velocity, V = Q/A. Clearly, in any open channel flow, a velocity distribution exists in the vertical in which horizontal velocities near the bed are smaller than the velocities elsewhere. The energy correction coefficient, α, is included in equation [5] because the total velocity head, computed on the basis of the average velocity, is not equal to the total velocity head computed by integrating the local velocity head through the vertical. In order to determine the water surface profile for gradually varied flow in an open channel, equation [5] can be numerically integrated. One such method of numerical integration is known as the direct step method. Under the direct step method a difference in depth ∆y between two cross sections (denoted by subscripts 1 and 2) is assumed. The distance between the two sections, ∆x is then computed from equation [6] following. This is done iteratively for a number of sections upstream (or downstream) of the section where the depth and velocity are known a priori. The procedure can be performed in a table and is described by Chow (1959) The expression used in the direct step method is: Equation [6] only applies to prismatic channels, in which the cross sectional shape is the same at all cross sections. Wilkins (1956) first suggested the use of GVF theory for non-Darcy flow through porous media, however, comparisons between observed and computed phreatic surfaces were not presented in his work. Parkin (1963) tested the method and found fair agreement between observed and computed phreatic surfaces for three cases. The only modification suggested by these two authors was replacement of the expression for friction slope in an open channel with the expression for "friction slope" for flow through a porous media. In the context of open channel flow the friction slope is generally found from rearranging either the Manning or Chézy equation. In the context of non-Darcy flow through porous media the friction slope can be evaluated using a power-type equation of the following type: Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation where: i = hydraulic gradient (dimensionless), a = empirically determined coefficient, N = empirically determined exponent, equal to 2 for fully developed turbulence, V = bulk velocity (not the void velocity). Equation [7] can be considered a rearrangement of Wilkins' equation [1], except that the hydraulic mean radius and the value of W are both inherent in the parameter "a". For a column test performed in the present study on 24.6 mm (nominal -1" to +3/4" sieved) crushed limestone at a porosity of 47.4% with m = 2.35 mm, it was found that a = 50.76 and N = 1.879 (m-sec units). Figure 4(a) shows the column apparatus. Using Wilkins' form of non-Darcy flow equation, this result from a single column test, with no correction for the wall effect, can be expressed as: This result for the coefficient W, as defined in equation [1], is only 3% different than Wilkins' original result. As was noted for the assumptions associated with Wilkins'' equation, equations [7] and [8] (and like equations) are for unidirectional flow and are generally determined in an apparatus having no phreatic surface. In this sense equation [7] is not a friction slope equation for open channel flow, but rather expresses the rate of change of piezometric head with distance for any given bulk velocity. In the present study it was found that straight-forward application of the direct step method did not accurately estimate the position of the phreatic surface, except when the slope of the observed phreatic surface was very gradual (nearly horizontal). It was found that the discrepancy between observed and computed surfaces increased as the exit height h increased, where h is defined in Figure 5. The need to introduce a correction was illustrated in Figure 1 (a). It is clear that the velocity distribution in the vertical at any given cross section in Figure 1 (a) is not uniform. Moreover, as the distance from the bed increases, the local velocity has an increasingly downward component. Hence, a correction is needed to account for these two effects. It was also found that adjustments to the value of a could not be used to achieve agreement between observed and computed phreatic surfaces. This is consistent with the fact that the phreatic surface through the porous media was typically associated with relatively high hydraulic gradients and low flow velocities in the laboratory, as compared to ordinary open channel flow. Changes in velocity head between cross sections are therefore relatively small compared to S (S = i) . This means that changing a will indeed have little effect on the computed values of ∆x. Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation a) Packed column apparatus. b) Small flume with model embankment. Figure 4. University of Ottawa packed column and small flume apparatus. Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation In order to accurately estimate the location of the phreatic surface, the parameter "a" for unidirectional non-Darcy flow required downward adjustment as h increased. The equation for adjusting "a", based on experiments performed in a glass-walled flume was found to be: where : Wilkins' equation (1956) can be written in m-sec units as: where V is the bulk velocity. This can be rearranged to the form of equation [7] Rearranging equation [8] (which was determined experimentally' by the authors) to the form of equation [7] yields an equation quite close to equation [12]. Therefore, combination of equation [9] and equation [12] gives: Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation The following table shows how the value of "a" in equation [13] changes as h /H increases: Table 3 coefficient he/H a/ao a in [13] 0.00 1.00 1.72 0.10 1.05 1.81 0.20 1.11 1.91 0.30 1.16 2.00 0.40 1.22 2.10 0.50 1.27 2.19 Porosity n = 0.45 Hydraulic mean radius m = 0.1 m Laboratory measurements of the phreatic surface consisted 20 water surface profiles in three model dams. Figure 4 (b) shows one of these model dams. Using equation [13] and the direct step method, the position of the phreatic surface was estimated upstream of the exit point h . Figure 5 presents a comparison between observed and computed phreatic surfaces for one of these model dams. Data associated with the near-overflow condition seen in the laboratory are not included in Figure 5, in keeping with the unlikelihood of such an occurence at a mine waste dump. While the above computational method was developed from tests on relatively small crushed rock, the following observations can be made: 1. The value of N = 1.88 (obtained from a column test) indicates a slightly higher level of turbulence than that achieved in Wilkins' tests. The maximum pore Reynolds number for the column test was about 510, indicating fully developed turbulence. 2. It is not known at this point whether the adjustment to the value of "a", suggested above, is of general applicability in full-scale field conditions. Both the aspect ratio of the drain and the bed slope of full-scale rock drains are different from the Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation model drains tested in the laboratory. However, calibration of this method against observed piezometric data under various flow conditions would indicate how "a" should be adjusted downward at the prototype scale in order to achieve a match between computed and observed water levels. This would permit determination of the variation in hydraulic mean radius over time, which would indicate whether or not the drain is clogging. For flowthrough rockfill dams the position of the phreatic surface is of interest partly because the exit height (where calculation of the phreatic surface begins) indicates the extent of the downstream face which will be submerged by emergent seepage. This fraction of the downstream slope beneath the seepage surface is the area most likely to fail by erosion. A discussion of the downstream stability of flowthrough rockfill has not been presented since most drains for mining projects are not subject to appreciable upstream heads, so that the possibility of overtopping is remote. The stability considerations become important in the case of water storage dams and spillways. Research involving physical measurement of the destabilizing bursting forces is currently being undertaken. These measurements would provide a rational methodology for evaluating the stability of such slopes. 4. RATIONAL DETERMINATION OF THE HYDRAULIC MEAN RADIUS. In addition to keeping in mind the assumptions inherent in Wilkins equation, the design engineer is faced with the evaluation of m, the hydraulic mean radius. This parameter is a measure of the average pore size through which flow takes place. Little information appears to have been published on this parameter. As part of the present research program a detailed investigation was undertaken and procedural details on the determination of surface area and hydraulic mean radius are presented elsewhere (Garga et al 1990). The fundamental definition of hydraulic mean radius is: m= νvoids SAvoids Assuming that the surface area of the voids is equal to the surface area of the rocks, the following identity may be stated: [14] Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation It is further noted that: where : ρ = density of the rock, in units such as kg/m3, AMS = mass-specific surface area, units of area/mass. Determination of the mass-specific (or volume specific) surface area of a particle presents the difficult problem of estimating the surface area of the irregular rock particle. This problem was the subject of a special study at the University of Ottawa as part of continuing work on non-Darcy flow through porous media. Through use of a nickel coating technique, the mass-specific surface area of four sizes of rock was estimated, and these results are summarized in Figure 6(a). A total of 273 rocks were analyzed in order to produce the four points in Figure 6 (a), so that each point in Figure 6 (a) represents the average mass- specific surface area of at least 49 rocks. The dashed line through these points is similar to the results Wilkins (1956) for the same parameters, summarized in Figure 6 (b). Similar data regarding sample size and the procedure for determining surface area for the data in Figure 6(b) were not stated in Wilkins (1956) work. It should be noted that the position of the solid lines for spheres in Figures 6(a) and (b) depend on the density of the rock. The volume-specific surface area of perfect spheres is given by the following identity: where d is the diameter of the sphere. The degree of departure of a given rock type from the curve for perfect spheres is a matter of engineering judgement. Highly angular rocks with many sharp and jutting edges are relatively inefficient with respect to surface area per unit mass and will have correspondingly higher values of A . Very plate-like rocks such as shale will also have relatively high values of Avs. It should be noted that equations [14] and [15] should not be used with porous media made up of plate-like rocks because significant particle area is lost to inter-particle contact. When the amount of interparticle contact is large the assumption that the surface area of the voids is equal to the surface area of the rocks is not valid. Smoother and rounder rocks will approach the value of A of spheres. Equation [17] can be restated as: Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation Figure 6. Comparison of mass-specific surface area results for crushed rock. Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation where J = 6 for spheres. The extent to which the value J for a particle exceeds the value of J for spheres indicates the degree of surface area efficiency of the particle. The relative surface area efficiency can be stated as: The following equation is therefore presented: AVS = RSAE JSPHERE [20] d Therefore: m = e d [21] 6 RSAE A comparison of Wilkins results with the results of surface area analyses performed in this study is summarized in Table 4. The points for mass-specific surface area were determined from Wilkins work by abstracting the points of inflection from figure 2 in Wilkins (1956). By performing ordinary least squares linear regression on the data for rocks shown in Figure 6 it was found that: Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation The presence of a graded rockfill requires special consideration. The following steps are suggested: 1. Obtain the grain size distribution by weight in the form of a histogram. 2. Estimate RSAE for each size class and apply equation [21] to each size class. (If Figure 6 (a) is used, this implies an RSAE of 1.22). 3. The value of the hydraulic mean radius may then be computed as a weighted mean using equation [21]. Campbell (1989) suggests a value of J of 7.5 (RSAE = 1.25) as an inherent part of Wilkins' equation, and that the mean stone size be used for d. The authors do not recommend this because the RSAE of each size class of rock should be evaluated using engineering judgement regarding the relative shape and angularity of the rock in each class as compared to spheres having the same nominal diameter. This will indicate the degree of departure from the AMS curve for perfect spheres. Further, Campbell's approach requires the assumption that all types of rocks have the same value for RSAE , and that this value is L.25. 4. Behaviour of Rock Fill in Sub-zero Temperatures As water flows through a rockfill embankment three heat exchange phenomena may occur: 1. If the rock particles are at a different temperature than the water, heat transfer will occur. 2. The water/rock matrix making up the embankment may exchange heat with the air and the underlying ground. 3. As water moves between the voids in a turbulent fashion some of its hydraulic energy is converted to heat by viscous dissipation. Phenomena 1 is probably the least important since the thermal inertia of the rock would only come into play if the. ambient temperature changed very suddenly. For phenomenon 2 it is expected that the phreatic surface will be subject to freezing for the same reasons that a reservoir is subject to freezing in winter: it is a water surface exposed to the atmosphere. The following factors affect the net heat exchange between a water surface and the environment (Tsang 1982): 1. Shortwave insolation (a heat gain mainly via sunshine), 2. Net long wave radiation (which is affected by air temperature, cloud cover, cloud elevation, and albedo), Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation 3. Evaporative hear loss (affected by relative humidity), 4. Convective heat loss (affected by wind speed), 5. Snowfall (a heat loss). Of the five above-mentioned factors affecting heat exchange, convective heat loss is usually the most important in determining the net heat loss coefficient. However, this component would be negligible for rockfill drains since the phreatic surface is not exposed to moving air. Phenomena 3, viscous dissipation, is a quantity of heat which can be directly computed (Tsang 1982) from: ∆T = 0.002342 Ah [23] where : ∆T = increase in temperature (°C) , ∆h = drop in elevation (m). The difference in height of a flowthrough rockfill drain between inlet and outlet therefore determines the rise in temperature due to viscous dissipation. This phenomenon will mitigate against the formation of ice in the voids within a flowthrough rockfill structure due to the following reasons: 1. The temperature of the water below the ice cover in the upstream pool is at or above 0°C. 2. The phreatic surface is exposed to the air. Therefore sheet-like ice can be expected to form first at the phreatic surface. This then prevents any convective and evaporative heat losses, which are usually the largest mechanisms of heat loss (Tsang 1982). 3. The passage of water through the voids causes a slight temperature rise in the water, bringing it above 0°C and thereby preventing ice formation. The phenomenon of viscous dissipation may be relatively important in cases where the hydraulic gradient is steep and the time of passage through the porous media is short. Under such conditions Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation of short travel-time the opportunity for heat loss to the environment is limited, and the associated rapid drop in piezometric potential represents the addition of a small but relatively important amount of heat via viscous dissipation. In order to examine the growth of ice in (or on) a flowthrough rockfill embankment a series of tests were conducted in the Low Temperature Laboratory of the National Research Council. Figure 7 shows the flume and model embankment which were constructed. The flume was 1.2 m wide and 4.8 m long. Rock of nominal diameter of 130 mm was used to build a model flowthrough structure 0.7 m high and 2.7 m long. The model was instrumented with thermocouples connected to an automatic data logger. Tests typically ran for 3 days at an average temperature of about -16°C. Temperature data and visual observations indicated that ice generally formed only at the free surface. This tends to confirm that viscous dissipation plays an important role if the travel time through the media is short. The data from these tests is still being analysed and will be presented at a later date. 5. CONCLUDING REMARKS 1. Wilkins' (1956) equation is strictly valid for unidirectional flow and should not be directly applied to conditions in which a phreatic surface for non uniform flow conditions is present. Inherent in Wilkins' equation are assumptions regarding the flow regime, the magnitude of the wall effect, and the role of fluid viscosity. Under certain conditions the errors associated with these assumptions may be significant. 2. An application of gradually varied flow theory is presented which can be used to calculate the position of the phreatic surface. A correction for determining the phreatic surface to account for the non-uniformity of the flow field is suggested. Since the hydraulic mean radius appears in the suggested formulation for the friction slope, it is possible to monitor changes in the hydraulic mean radius by applying the method to observed piezometric data at regular intervals. This would then indicate whether or not a rock drain is clogging. 3. A rationale for determining the hydraulic mean radius has been presented. Although little published information exists on the surface area of irregular rock particles, engineering judgement can be applied by considering the surface area efficiency ratio R for rocks of similar shape and angularity. SAE 4. The formation of ice in flowthrough rock drains and embankments is influenced by the phenomenon of viscous dissipation of hydraulic energy. The rate of heat loss to the environment must exceed this input of heat in order for ice to form. Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation Figure 7. Flume in low temperature laboratory of the National Research Council. Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation ACKNOWLEDGEMENTS The work described in this Paper has been financially supported by Energy Mines and Resources Canada, Hydraulic Energy Research and Development Program, through a Research Contract with the University of Ottawa. The Authors are grateful to Mr. Tony. Tung for his enthusiastic support. REFERENCES Campbell, D.B., 1989. Some observations relative to the performance of flow-through rock drains. 13th Annual British Columbia Mine Reclamation Symposium, June 7-9, pp.119-128 Chow, V.T. 1959. Open channel hydraulics. McGraw-Hill, NY, 680 p. Dudgeon, C.R. 1966. Wall effects in permeameters. ASCE Journal of the Hydraulics Division, vol.93, HY5, Sept., pp.137-148. Ergun, S., 1952. Fluid flow through packed columns. Chemical Engineering Progress, vol.48 no.2, p.89. Franzini, J.B., 1956. Permeameter wall effect. Transactions American Geophysical Union, vol.37, no.6, Dec., pp.735-737. Freeze, R.A. and Cherry, J.A., 1979. Groundwater. Prentice-Hall, Englewood Cliffs, NJ, 640 p. Garga V.K., Smith H.R., and Scharer, J., 1983. Abandonment of acid-generating mine tailings. VII Pan American Conference on Soil Mechanics and Foundation Engineering, Vancouver, BC, vol.2, pp.613-626. Garga, V.K., Townsend, R.D., and Hansen, D. 1990. A method for determining the surface area of quarried rocks. Submitted for publication to the ASTM Geotechnical Testing Journal. Jain, S., Holly, F.M., Lee, T., 1988. Head loss through porous dikes. Canadian Journal of Civil Engineering, Oct., vol.15, pp.766-775. Lane, D., Berdusco, R., and Jones, R., 1986. Five years experience with the Swift Creek rock drain at Fording Coal Ltd. Proc. of International Symposium on Flowthrough Rockfill Crains, Cranbrook BC, Sept.8-11, pp.7-17. McCorquodale J.A., Hannoura, A.A. and Nasser, M.S. 1978. Hydraulic conductivity of rockfill. Journal of Hydraulic Research, vol.16, no. 2, pp.123-137. Parkin, A.K., 1963. Rockfill dams with inbuilt spillways. Part I, Hydraulic Characteristics. Bull. 6, University of Melbourne and Water Res. Found, of Australia. March, 88 p. Proceedings of the 14th Annual British Columbia Mine Reclamation Symposium in Cranbrook, BC, 1990. The Technical and Research Committee on Reclamation Parkin, A.K., Trollope, D.H., and Lawson, J.D., 1966. Rockfill structures subjected to water flow. ASCE Journal of the Soil Mechanics and Foundations Division, vol.92, SM6, pp.135-151. Rose H. E., 1945a. An investigation into the laws of flow of fluids through beds of granular materials. Proceedings of the Institute of Mechanical Engineers, War Emergency Issues 1-12, pp.141-147. Somerton, C.W., and Wood, P., 1988. Effect of walls in modelling flow through porous media. ASCE Journal of the Hydraulics Division, vol.114, no.12, Dec., pp.1431-1447. Tsang, G. 1982. Frazil and Anchor Ice, a Monograph. Canada Centre for Inland Waters, NRC Assoc. Comm. on Hydrology, Ottawa, Ont., 89 p. Ward, J.C., 1964. Turbulent flow in porous media. Journal of the Hydraulics Division, ASCE, vol.92, HY4, Sept., pp.1-12. Wilkins, J.K., 1956. The flow of water through rockfill and its application to the design of dams. Proc. 2nd Australia-New Zealand Conference on Soil Mechanics and Foundation Engineering, pp.141-149. Weiss, A. 1951. Construction technique of passing floods over earth dams. Transactions of ASCE, vol.116, paper 2461, pp.1158-1178.
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