10 th International Symposium Topical Problems in the Field of Electrical and Power Engineering Pärnu, Estonia, January 10-15, 011 Hydraulic conductivity testing method for all-in aggregates and mining waste materials Julija Šommet, Jüri-Rivaldo Pastarus, Sergei Sabanov Department of Mining, Tallinn University of Technology julija@vaopaas.ee, pastarus@cc.ttu.ee, sergei.sabanov@ttu.ee Abstract The paper deals with the problems of aggregate testing and introduces first test results of all-in aggregates. Also it is expected that testing method is applicable for waste materials in mining. Currently, nowadays there is not enough experience in experimental methods for defining conductivity and its setting limits, which could be used anywhere in Europe. Vertical conductivity test method may be any indirect method and its requirements may be placed by the benefit rules. From the current thesis topic test results may be used for research in other EU countries. Used standards for test equipment are valid throughout the EU. Keywords All-in aggregate quality, experimental methods, filtration coefficient, vertical hydraulic conductivity, maximum grain-size Introduction The expected result of the study is to explore different vertical conductivity parameters and suit the measurement methodology for all-in aggregates and probably for the mining waste materials. With this new test system is planned to develop through a single system of parameters, by which the tested materials can be classified and find for them a new area of use, especially road building. The main idea for the work is that Darcy`s law is valid also for groundwater flow in any direction in space. When we decide to analyze water flow with the Darcian approach, it means, in effect, that we are going to replace the actual ensemble of grains (rock fragments) that make up the porous medium by a representative continuum for which we can define macroscopic parameters, such as the hydraulic conductivity, and utilize macroscopic laws, such as Darcy`s law, to provide macroscopically averaged descriptions of the microscopic behavior. This is a conceptually simple and logical step to take, but it rests on some knotty theoretical foundations. 1 My task is to determine the potential gradient that controls the water flow trough porous media in all-in road materials and in mining waste materials. To create the analogue (Darcy, Sojuzdornii) apparatus with the vertical cylinder (θ = 0 ), where flow would certainly occur down through the cylinder (from high evaluation to low) in response to gravity. If the cylinder placed in a horizontal position (θ = 90 ) so that gravity played no role, flow could presumably be induced by increasing the pressure at one end and decreasing it at the other. And the work done in moving a unit mass of fluid between any two points in a flow system is a measure of the energy loss of the unit mass. Chemical gradients can cause the water flow (as well as the movement of chemical constituents through the water) from regions where water has higher salinity to regions where it has lower salinity, even in the absence of other gradients. The role of chemical gradients in the production of water flow is relatively unimportant, but their direct influence on the movement of chemical constituents is of major importance in the analysis. [1] So the testing of apparatus with salt water is also necessary, taking into account a water temperature to measure the phenomenological coefficient. Testing with salt water is important for road building materials. The research should search for a parameter that can describe the conductive properties of a porous medium independently from the fluid flowing through the laboratory sample. It is necessary to use different rock samples and different fractions of all-in aggregate for different deposits to find out the true method. 1. Physical Properties and Principles 1.1 Hydraulic Conductivity It is pointed out, the constant of proportionality in Darcy`s law, which has been christened the hydraulic conductivity, is a function not only of the porous medium but also of the fluid. [1] Considering the theoretical apparatus it no surprise to measure the specific velocity value is very low. To accommodate this idea for the all-in aggregate and wastes materials it is necessary to use cylinders
with different diameters d and heights h, which are appropriative for maximum grains size according to the standard EVS-EN 1097-3 (for more see Table 1.). Table 1. Cylinder parameters and grain size. Grain size, mm Cylinders parameters, cm Size ratio d/h Permitted size ratio d/h by EVS-EN 1097-3 Cylinder volume V, ml 0 4 d 9,1 0,53 0,5...0,8 1118,7 h 17, L 8,6 d 14,9 0,51 0,5...0,8 516,4 h 9,4 0 16 L 46,8 d 19,5 0,58 0,5...0,8 10094,3 0 3 h 33,8 L 61,3 0 63 d 5 0,61 0,5...0,8 015,8 h 41 L 78,5 Used fluid of water should be with the same density ρ, hydraulic gradient dh/dl should be also constant. It is necessary to take into account the parameter C. C is a constant of proportionality, for example for soils it must include the influence of other media properties that could affect a water flow, apart from the mean grain diameter: for example, the distribution of grain sizes, the sphericity and roundness of the grains, and the nature of their packing. Comparison of Eq. (1) with the original Darcy equation shows that: K = (Cd ρg):µ (1) In this equation, ρ and µ are functions of the fluid alone and Cd is a function of the medium alone. If we define: k = Cd () then K = kρg:µ (3) The parameter k is known as the specific or intrinsic permeability. If K is always called hydraulic conductivity, it is safe to drop the adjectives and refer to k as simply the permeability. That is the convention that will be followed in this paper, but it can lead to some confusion, especially when dealing with older texts and reports where the hydraulic conductivity K is called coefficient permeability. For all equations C is emerges a dimensionless constant. When measured in m or cm, k is very small. It is sufficient to note that differences in the temperature of measurement between the field environment and laboratory environment can influence hydraulic conductivity values through the viscosity term (3). The effect is usually small, so correction factors are seldom introduced. It still makes good sense to report whether hydraulic conductivity measurement are very different and the interpretations placed on the values may be depend on the type of measurement. 1. Range of Porosity The porosity ranges for various geologic materials. I general rocks have lower porosities than soils; gravels, sands, and silts, which are made up of angular and rounded particles, have lower porosities than soils rich in platy clay minerals. The porosity n can be an important controlling influence on hydraulic conductivity K. Range of values of porosity see in Table. In sampling programs carried out within deposits of well-sorted sand or in facturated rock formations, samples with higher n generally also have higher K. [1] Table. Range of Values of Porosity Unconsolidated Deposits n, % Gravel 5-40 Sand 5-50 Silt 35-50 Clay 40-70 Rocks n, % Karst limestone Sandstone Limestone, dolomite Shale Dense crystalline rock 5-50 5-30 0-0 0-10 0-5 In the next paragraphs you may find the dependence between different components in graphical view. The first test results data with apparatus shows that hydraulic conductivity varies over wide range if we apply different diameters, but when it is permitted the range is not so wide (see Table 3. and Table 4.). Table 3. Hydraulic Conductivity by Different Estimation Sample h, m Hvorslev Hazen Hassen 0,17540 0,00004 0,00010 30,39007 0,1800 0,00003 0,00010 30,39007 0,18100 0,00001 0,00510 15699,13355 0,19300 0,00005 0,00510 15699,13355 0,18600 0,00006 0,000 60,7565 0,17830 0,00004 0,0003 70,87773 0,17490 0,00010 0,0003 70,87773 0,07450-0,00001 0,00135 415,5760 0,8430 0,00108 0,00135 415,5760 0,9550 0,000 1,9667 5959,38011 0,6640 0,0005 0,84375 5951,6100 13
Table 4. Hydraulic Conductivity by Different Estimation (II). Sample h, m Kozeny Carmen Fair- Hatch K 10 by Sojuzdornii Simplest K 0,1754 0,1105 843418,184 5,05764 0,00131 0,180 0,1105 843418,184 416,35673 0,0000 0,1810 0,118 18367773,8 784,80759 0,0043 0,1930 0,118 18367773,8 40,50381 0,0013 0,1860 0,1105 7590763,66 489,8050 0,00175 0,1783 0,0359 1653099,64 636,073 0,00 0,1749 0,0359 1653099,64 30,56694 0,00089 0,0745 0,0798 5811678,43 374,099 0,00057 0,843 0,0798 5811678,43 30,65097 0,00054 0,955 0,1105 346713,7 1417,37737 0,00303 0,664 0,485 14877896,8 856,8748 0,00179 The approaches to the measurement of hydraulic conductivity in the laboratory with the limestone allin aggregates are described in the next paragraph. 1.3 Measurement of Parameters First laboratory tests described in this paper can be considered as providing values of the basic parameters. They are carried out on samples that are collected from Tondi-Väo deposit. For samples with disturbed structure is expected to yield useful values. Testing method description for the determination of hydraulic conductivity in saturated and unsaturated state will be given below. Method is related to extracted rock mass: all-in aggregate and mining waste aggregates. Tests are initiated by causing an instantaneous change in the water level through a sudden introduction or removal of a known volume of water. The recovery of the water level with time is then observed. The method is interpreting the water versus time data. In a constant-head test, a sample of length L and crosssectional area A is enclosed in a cylindrical tube. A simple application of Darcy s leads to the expression, where Q is the steady volumetric discharge trough the system [1] K= QL:AH (4) In extracted rock mass case it is necessary to choose the stand tube diameter with regard to the grain size material being tested. Disturbed samples are tested four times: with natural moisture content, 30 min moisture, 4 h moisture and finally saturated in oven to constant weight at 105 C. The simplest interpretation of piezometer-recovery data is that of Hvoroslev. His analysis assumed a homogeneous, isotropic, infinite medium in which sample and water are incompressible. Hvoroslev defined the basic time lag T o, which could be measured graphically or by differential equation. [1] Similar to principle to the Hvoroslev method but differing in detail have been developed for the measurement of saturated hydraulic conductivity 14 K=r ln(l/r): LT o (5) Hassen has worked out the simplest and most wellknown formula for hydraulic conductivity: ( 0,7 0, t) 10 + k = cd 03 (6) where c - describes a aggregate permeability c = 400 + 40(n - 6) (7) where n is porosity in percents, t-water temperature, d 10 - effective grain size, which could be find from sieve analyze. It is the grain-size at which 10 % by weight of the sample particles are finer and 90 % are coarser. Hydraulic conductivity is compared in temperature of 10 ºC. It has long been recognized that hydraulic conductivity is related to the grain-size distribution of granular porous media. Next estimation techniques based on grain size analyses and porosity determinations. The determination of a relation between conductivity and soil texture requires the choice of a representative grain-size diameter. A simple and apparently durable empirical relation due to Hazen in the latter part of the last century, relies on the effective grain size, d 10, and predicts a power-law relation with K: K=Ad 10 (8) The d 10 value can be taken directly from grain-size gradation curve as determined by sieve analysis. For K in sm/s and d 10 in mm the coefficient A in Eq. (8) is equal to 1.0. Hazen s approximation was originally determined for uniformly graded sands, but it can provide rough but useful estimates for most soils in the fine sand to gravel range.[1] Another textural determination of hydraulic conductivity becomes more powerful when some measure of spread of the gradation curve is taken into account. It is Masch and Denny recommended curve, but unfortunately it suits for unconsolidated sands and no uniform soils. The fact that the porosity n, represents an integrated measure of the packing arrangement has led many investigators to carry out experimental studies of the relationship between C and n. The best known of the resulting predictive equations for hydraulic conductivity is the Kozeny-Carmen equation, which takes the form: 3 ρg n K = µ (1 n) d m 180 (9) In most formulas of this type, the porosity term is identical to the central element of equation, but the grain-size term can take many forms. For example Fair-Hatch equation take form: 3 ρ g n 1 K = (10) µ (1 n) θ P m 100 d m
where m is a packing factor found experimentally to be about 5; θ is a shape factor; P is the percentage of fines held between adjacent sieves; and d m is geometric mean of the rated sizes of adjacent sieves. Both Eqs. (9) and (10) are dimensionally correct. They are suitable for application with any consistent dimensions. [1] The last possibility which will be presented in this paper is another laboratory method for determination of filtration factor, which is described in the standard ГОСТ 5584-90. It is widely used in Russia for sands, clay and gravel and could be named also Sojuzdornii method. Most disadvantage of this method is that sample maximum allowed grain size is only 5 mm. If disregard this rule it is possible to get a presented data in Table 4. using next equation: К 10 V 864 ω (11) = t m ATJ where K 10 is filtration coefficient, m/day, reduced to the filtration conditions at 10 C, V ω volume of filtered water at a single testing, t m average duration of filtration (for measurements at the same volume of water), A cross-sectional area of the cylinder tube filtration, J pressure gradient (in this testing J is equal to 1); T an amendment to bring the values of the coefficients cient filtering in terms of water filtration at 10 C, where the Т ф -water temperature during the test, C: Т = (0,7+0,03 Т ф ) (1) and 864 is conversion factor (in cm/s in m/day). [] Chart. K dependence from h by Simplest Hydraulic Conductivity system. Chart 3. K dependence from h by Different Measurement Methods in m/day.. Tests Results Tests results could be found at the Table 3. and Table 4. for all described measurements. For easiest comparison all results are given in meter per day units. As it can be seen from the tables all results are different. Some of them are non realistic ( Fair- Hatch). Correlation analysis of data and test results have shown that minimal regression is valid for Simplest Hydraulic Conductivity-time versus sample h (R =0.03) and Kozeny-Carmen system (R =0,05) as it might be seen from the Chart 1. and Chart. All dependencies are shown on the Chart 3. Chart 1. K dependence from h by Kozeny-Carmen system. Conclusion Factual situation is quite complicated- seven different measurements are available. As it could be seen from the tables below that possible results calculated by the described systems are very different and in some calculation cases deviations are too large. It was only introduced data dependence by h versus K. Rational research will continue to improve data with other measured parameters like water content, porosity, shape index and fines content at the samples sieve grain-size analyze with salty and insipid water in order to find better measurement for testing all-in aggregates and oil shale waste materials. 15
The main task of this research is to develop a system, which suits and gives a real result for all-in aggregates and waste materials. As the analyze have shown more efficient methods are Kozeny-Carmen and Simplest Hydraulic Conductivity system. It is still necessary to continue testing with this appropriate methods. When a testing system is finely worked out next step of the research is to create a values matrix, where all dependencies could be calculated or traceable. A new traceable system in this case will be as a classification system - if all parameters are ranked out it is easier to find a new consumption area for the material. Described measurements for conductivity determinations could be used in laboratory and also on field. Delivered test system is simple and cheap and can provide adequate data in many cases where other tests are not justified. The work would be also to develop the scientific output of the optimal excavation specific for different geological conditions, which can also be used in other EU countries, and the ballast testing methodology, based on the particular intended use. Work is to ensure the practical output of the company's competitiveness in Estonia on the basis of the consumer's wishes and needs (quality). To provide an optimal assessment of the capacities of different groups based on the market needs. Acknowledgment The research was supported by Estonian Science Foundation (Grant Backfilling and waste management in Estonian oil shale industry No ETF813) and by the project DAR8130 Doctoral School of Energy and Geotechnology II for interdisciplinary research topic Sustainable mining: key challenges and opportunities to economic growth of mining waste management and innovative mining technologies supervised by Dr. Sergei Sabanov. References 1. R. Allan Freeze, John A. Cherry Groundwater, Prentice hall, Englewood Cliffs, NJ0763. Laboratory methods for determination of filtration factor, ГОСТ 5584-90 16