the determination of the moisture retention characteristics of waste ...
THE DETERMINATION OF THE MOISTURE RETENTION CHARACTERISTICS OF WASTE MATERIALS USING VERTICAL DRAINAGE EXPERIMENTS K. ZARDAVA AND W. POWRIE School of Civil Engineering and the Environment, University of Southampton, UK Email: [email protected]; [email protected] J. WHITE WJ Groundwater Limited, Hertfordshire, UK Email: [email protected]
SUMMARY: This paper describes an investigation into the extent to which a simple experiment involving the drainage of columns of waste materials can be used to determine the relationships between the capillary pressure, pc(θ) or ψ(θ), the liquid and gas relative permeabilities krL (θ ) and krG (θ ) ,and areas of gas and liquid flows, AG(θ) and AL(θ), and volumetric moisture content θ . Initial drainage experiments were carried out on fine sand for which many of the processes involved in two-phase flows are relatively well understood. The HYDRUS-1D model has been used to interpret the results from the drainage experiments. Initial experimental and modeling results are compared and further experimental plans are presented. The aim is to determine whether the functions k (θ ) and pC (θ ) can be deduced from the measured transient outflow data. 1. INTRODUCTION It is widely recognised that the polluting potential of landfills will continue for centuries rather than decades. Even the extensive adoption of strategies including recycling, incineration and waste pre-treatment will not overcome the need for final disposal of a significant amount of residual wastes in landfills. The overall purpose of the EPSRC project “Science and strategies for the management and remediation of landfills” is to help develop techniques (simulation and design tools) that could be used to shorten the length of time for which landfill sites pose a pollution risk. The research will be applicable to cleaning up the legacy of old landfill sites that exists across the UK and much of the developed world. The research will also be of use in predicting the potential impact that new types of waste may have in landfills, in advance of any wholesale adoption of the technologies that produce them. This will make a positive and essential contribution to waste management policy and strategic decision making. An objective of this project is to carry out experimental work and develop a numerical model
Third International Workshop “Hydro-Physico-Mechanics of Landfills” Braunschweig, Germany; 10 - 13 March 2009
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
to better our understanding of gas generation and movement in landfill waste, and to also investigate the interplay of mechanisms that control the simultaneous flow of leachate and gas in waste materials. It is intended that the current flow algorithm in the University of Southampton Landfill Degradation and Transport model (LDAT) will be extended to become more representative of the flow processes that take place in a landfill waste material and also be tested and calibrated by comparison with the results from a number of field and laboratory experiments. The experiments will focus on illuminating specific issues and uncertainties associated with the theoretical concepts of gas/liquid movement in porous media. LDAT does not at present cater for the two distinct pore-pressure fields, one for liquid and one for gas, that are present in partially saturated flows. Use of a capillary pressure function related to moisture contact, p C (θ ) , would be a straightforward way of doing this, and it could be incorporated as a parameter driven algebraic function such as those proposed by Richards (1967) and van Genuchten (1980). Similarly LDAT calculates the flow areas for liquid and gas from the volumes of liquids and gas in the element (Beaven and White, 2006). There is however no well established relationship between the pore volume occupied by either the gas or the leachate, and the corresponding area of flow, AL (θ ) and AG (θ ) . It is also proposed to use the experimental results to verify the expressions used in LDAT to calculate relative permeability krL (θ ) and krG (θ ) . These key model parameters which control the simultaneous flow of leachate and gas in waste material will be measured under laboratory conditions (two column experiments involving drainage and aeration are under way) and will be incorporated in LDAT numerical model to verify against experimental results. The results from the drainage experiments are interpreted using HYDRUS-1D model (Šimůnek et al., 2005). HYDRUS-1D numerically solves Richards' equation for saturated-unsaturated water flow using the van-Genuchten functions for k (θ ) and pC (θ ) . The aim is to determine whether the functions k (θ ) and pC (θ ) can be deduced from the measured transient outflow data, i.e. to determine how to back calculate k (θ ) and pC (θ ) from the experimental results
2. MOISTURE RETENTION CHARACTERISTIC CURVES OF WASTES Measurement of soil water content (θ) as a function of matric potential or suction (ψ) in unsaturated soil yields the water retention curve or moisture retention curve (SWCC). Here, the moisture retention curves of coarse sand, clay and of waste materials (from the literature) are plotted in one graph (Figure 1). • The moisture retentions curves of sand and clay derived from the van Genuchten model θs −θr (1980): θ = θ r + with θ r = 0.01, θ s = 0.395, α = 0.1596cm −1 , n = 1.727 n m 1 + (α ψ )
[
]
for sand and with θr = 0.2141, θs = 0.54, α = 0.0154 cm-1 and n = 1.145 for clay (Karvonev, 2001) • Korfiatis et al. (1984) constructed a laboratory column cell to investigate the behaviour of unsaturated flow through solid waste. The column was instrumented with two vertical lines of tensiometers to monitor the suction of the waste. The power law relationship proposed by Clapp and Hornberger (1978) was used to fit the data: ψ = ψs(θ/θs)-b with ψs=2.45, θs=0.55 and b=1.50. • Kazimoglu (2005) studied suction characteristics for MSW using a modified pressure plate apparatus and compared his measurements with the van Genuchten (1980) equation with
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
θ r = 0.14, θ s = 0.58, α = 1.5m −1 , n=1.6 and m = 0.375. • Munnich (2003) and Stoltz (2007) determined the water retention curve of MBT waste and drilled domestic waste respectively by placing the waste on a ceramic plate and applying a negative pressure. • Mansoor (2003) used the filter paper method for the determination of suction in a synthetic landfill waste with dry density 0.35 T/m3 and compared his measurements with the van Genuchten equation (1980) for θ r = 0.01 , θ s = 0.35, α = 0.49m −1 , n = 1.45 and m = 0.31. 10000
Suction (KPa)
1000
100
10 Coarse sand Korfiatis vanGenuchten-Kazimoglu Mansoor-vanGenuchten 0.35T/m3 Stoltz data 0.77T/m3 MBT Munich data 0.6T/m3 Sand data (soton)
1
0.1 0.0
0.1
0.01
0.2
0.3
Clay Kazimoglu data Mansoor data 0.35T/m3 Stoltz data 0.54T/m3 MBT Munich data 0.8T/m3 MBT Munich data 0.3T/m3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
degree of saturation
Figure 1. Moisture retention curves for coarse sand, clay and waste materials For reference indicative curves for coarse sand and clay derived by van Genuchten model are shown in Figure 1.Generally a curve will be expected to move to the right within this zone as the pore size is reduced either as a result of decreaseing particle size or increasing density.
3. METHODOLOGY There are many laboratory methods for determining the water content-suction (θ(ψ)) and the hydraulic conductivity functions (k(ψ)). Popular techniques include one-step outflow (Parker et al., 1985; Kool et al., 1987; van Dam et al., 1992), multi-step outflow (van Dam et al., 1994; Eching and Hopmans, 1993; Eching et al., 1994), and evaporation (Wind, 1966; Schnindler and Muller, 2006; Šimůnek et al., 1998a). Parameter optimization offers an indirect approach to obtain θ(ψ) and k(ψ) simultaneously from transient flow data (Kool et al., 1987). A drainage test was developed to define the water retention curve (ψ vs θ) of a material. An experiment for defining the unsaturated conductivity is being studied. The transient outflow data, the measured water content and pressure heads from the drainage experiment will be used for the
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
inverse estimation of the unsaturated hydraulic properties. The van Genuchten model has been selected for describing the water retention and hydraulic conductivity functions. The experimental data are compared to simulations camed out using HYDRUS 1-D. The van Genuchten parameters (α, n, ks) describing the water retention and hydraulic conductivity functions can be estimated from the transient outflow data, the measured water contents and the pressure heads using the parameter estimation routine (inverse modelling) in HYDRUS 1-D. Further the experimental data could be fitted to the predicted data of other models (Brooks & Corey, 1964; modified van Genuchten, 1988) that are included in the HYDRUS 1-D program. 3.1 Description of the drainage experiment Scoping experiments using sand prior to the introduction of waste are being carried out in a clear Perspex cylinder with an inner diameter of 26cm and 1m in height. A photograph of the experimental set-up is shown in Figure 2 and the schematic diagram of the cell is shown in Figure 3. A 24 cm layer of gravel (particle size 10 to 20 mm) was installed at the bottom of the column. A geotextile filter (1 cm thickness) was installed above the gravel layer to prevent sand infiltration. Fine builder’s sand (47 kg) was deposited in 3 cm lifts above the saturated gravel underwater. The sand had been washed sieved and oven dried beforehand. The sand column (55 cm) was saturated by introducing approximately 10 litres of water into the cell upwards. It was left overnight to develop full saturation. The top of the cell was left open, at atmospheric pressure initially. The fully saturated column was then allowed to drain by opening the drainage tap located at the bottom of the cell. A fully saturated condition in the gravel layer at the bottom of the column was imposed using a U-tube outflow system. This arrangement prevents evaporation of the sand column from the bottom. Measurements of the volume of the water drained from the column were made using an electrical balance. The drainage experiment lasted for 10 days. Measurements of the pore water pressures in the sand at the four ports (4 cm, 19 cm, 25 cm and 39 cm from the bottom of the sand column) of the cell were made using manometers during that period. Vertical sand cores (at 5 cm intervals) were also removed from different points using a copper tube with a 13.5 cm inner diameter and 0.8 cm wall thickness and about 6° cutting-edge taper (Clayton & Siddique, 1999) to measure the moisture content of the sand.
Figure 2. Set-up for the drainage experiement
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
Figure 3. Schematic diagram of the cell
3.2 Properties of sand A particle-size distribution (PSD) curve for the sand was determined by sieve analysis (Figure 4). The porosity of the fine sand as placed in the column was estimated to be 40% and the dry density 1570kg/m3 (1540-1610kg/m3). The saturated permeability (ks) of the fine sand was measured as 5 × 10-5 m/s using the constant-head method in a 75 mm diameter permeameter.
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
100
Percentage passing (%)
90 80 70 60 50 40 30 20 10 0 0.01
0.1
1
10
Particle size (mm)
Figure 4. Particle size distribution curve for the fine sand
3.3 Interpretation of the experimental data with HYDRUS 1-D The experimental data were analyzed using the HYDRUS-1D program (Šimůnek et al., 2005), which numerically solves Richards' equation (eq.1) for saturated-unsaturated water flow. ∂θ ∂ ⎡ ⎛ ∂ψ ⎞⎤ = ⎢k (θ )⎜ + 1⎟⎥ (eq.1) ∂t ∂z ⎣ ⎝ ∂z ⎠⎦ ψ denotes the pressure head (L), t is time (T), z is the elevation head (L), θ is the volumetric water content (L3/L3) and k (θ ) is the hydraulic conductivity (L/T), which is a function of θ under unsaturated conditions. The HYDRUS-1D code describes the relationship between water content and pressure head and hydraulic conductivity using three models: van Genuchten (1980), Brooks and Corey (1964) and modified van Genuchten type equations (Vogel and Cislerova, 1988). In this study, the van Genuchten (1980) empirical equations were selected because they are commonly used by the soil mechanics ‘community’:
[
θ e = 1 + (aψ )n where:
θe =
]
−m
(eq.2)
θ −θr θs −θr
(eq.3)
Re-arranging equation (2) gives the water content, θ, as a function of matric suction head, equation (4).
θ = θr +
θs −θr
[1 + (α ψ ) ]
n m
(eq.4)
where θr represents the residual water content (dimensionless). The parameter α (L-1) is related
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
to the inverse of the value of the air-entry pressure, the n and m parameters (dimensionless) are related to the pore size distribution of the soil. For m=1-1/n the above equation reduces to the van Genuchten (1980) & Mualem (1976) equation. The hydraulic conductivity as a function of water content is given by equation m 2 k (θ ) k r (θ ) = = θ e0.5 1 − (1 − θ em /( n −1) ) (eq.5) ks The relative hydraulic conductivity (dimensionless) is denoted by k r (θ ) . k (θ ) is the unsaturated hydraulic conductivity (L/T), k s denotes the saturated conductivity (L/T), θ e is the effective saturation (dimensionless) and θ s is the saturated water content (dimensionless).
(
)
4. RESULTS AND DISCUSSION
Free gravity drainage of the sand column was allowed to continue for 10 days. A very rapid drawdown of the water table was achieved by opening the tap at the bottom of the cell. About 1.9 litres of water drained out, most of it within a few hours. Figure 5 shows the cumulative flow per unit cross-sectional area from the sand column during drainage measured by the electrical balance (dot points), and six cases of the simulated cumulative flow per unit cross-sectional area calculated by HYDRUS- 1D. Due to data logging problems, data gaps occurred in the night. More frequent measurement of the outflow transient data is required. Table 1 lists the van Genuchten parameter values for the six cases run in HYDRUS-1D program. Table 1: Fitted van Genuchten parameters Case 1 Case 2 Case 3 θr 0.034 0.034 0.04 (m3m-3) 0.35 0.35 0.38 θs (m3m-3) α 2 2 1.66 (m-1) n 2 4 1.51 ks 5E-5 5E-5 5E-5 (m/s)
Case 4 0.04
Case 5 0.034
Case 6 0.034
0.38
0.34
0.35
2
2
2.5
1.51 5E-5
1.51 5E-5
1.51 5E-5
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
Data Hydrus case 1 Hydrus case 2 Hydrus case 3 Hydrus case 4 Hydrus case 5 Hydrus case 6
Volume of water drained per unit cross-sectional area
Mass of water out (m)
0.03 0.025 0.02 0.015 0.01 0.005 0 0
10
20
30
40
50
60
Time (hrs)
Figure 5: Measured and modelled cumulative volume per unit area of water drained Sand cores were taken from the column 13, 17, 18 and 29 days after the start of the drainage experiment. In simulations, steady state conditions were achieved after 2-3 days; the profiles presented are at 10 days after equilibrium conditions had been achieved. Figure 6 shows the measured moisture profiles and and a number of simulated moisture profiles.
5
10
Vol.moisture content (%) 15 20 25 30
35
40
0
Depth (cm)
10 20 30 40 50 60
Data after 13days Data after 18days Hydrus case 1 Hydrus case 4 Hydrus case 6
Data after 17days Data after 29days Hydrus case 2 Hydrus case 5 Hydrus case 3
Figure 6: Measured and modelled moisture profiles after 10 days Figure 7 shows the measured suction profiles at selected times. After about 60 hours the suction
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
profile reaches the hydrostatic line. Also, the simulated suction profiles at two selected times are shown for case 1. measured
simulated
Figure 7: Measured and simulated suction profiles for case 1. The moisture retention (ψ vs θ) data from the drainage experiment are plotted and give close agreement with the sand SWCC (Figure 1). More precise measurement of suction heads, moisture content and outflow transient data will be achieved by the use of specific instruments. Four additional manometer ports (2mm diameter) have been fitted to the column to enable more points of suction measurent. The manometer readings will be compared with those from six mini tensiometers (Delta-T Devices, model SWT5) of 5mm diameter and 75mm length, which are able to measure both positive and negative pore water pressures (+100 to -85kPa). Six impedance probes (Delta-T Devices, model Theta probes ML2x ) of 40mm diameter and 105mm length will be installed in the column for moisture content measurements, under the following arrangements: o Theta probes will be located at 14, 34 and 54 cm from the bottom of the sand column. o Tensiometers will be located at 4, 25 and 45 cm from the bottom of the sand column. All instruments will be coupled to a data-logger system. The entire assembly will be placed onto three load cells for recording weight changes. Figure 8 presents the instrumentation layout for the experiment.
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
Theta probe 70 mm
Proposed manometer port
50 mm
70 mm
SWT 5 tensiometer 5 mm
Existing manometer port
40 mm
290 mm
390 mm
500 mm 440 mm
640 mm
590 mm
790 mm
700 mm
30 mm
SWT5 tensiometer frontview
Theta probe frontview Boss
Manometer port
Figure 8: Instrumentation set-up of the column In addition it is planned to estimate the moisture retention properties of waste samples using the pressure plate apparatus technique (for suctions 10-150 kPa) and the hanging water column method (for suctions 0-10 kPa). The moisture retention curves determining using the pressure plate apparatus/hanging column and those resulting from the instruments measurements will be fitted to different algebraic representations based on the van Genuchten and Brooks & Corey curves.
5. CONCLUSIONS
This paper has described the details of a column apparatus that has been developed to examine the moisture retention characteristics of waste materials. Initial drainage experiments have been carried out on fine sand for which many of the processes involved in two-phase flows
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
are relatively well understood. These experiments will act as a benchmark for subsequent tests on different types of waste materials. Following drainage, imbibition and infiltration experiments will be carried out. The application of a direct method/experiment to measure unsaturated hydraulic conductivity is currently being assessed.
REFERENCES
Beaven, R.P. (2000) The hydrogeological and geotechnical properties of household waste in relation to sustainable landfilling. PhD dissertation, Queen Marry and Westfield college, University of London Beaven, R.P. and White, J.K. (2006) A review of the theory relating to the evolution and movement of gas in waste materials and proposals for the design of laboratory experiments to investigate this theory. Science and strategies for the management and remediation of landfills. Sub-package funded by Onyx. Final report. December 2006. Brooks, R. H. and Corey, A. T. (1964). Hydraulic Properties of Porous Media. Hydrol. Pap. 3. Colorado State Univ. Fort Collins, CO. Brooks, R. H. and Corey, A. T. (1966). Properties of Porous Media Affecting Flow. J. Irr. Drain. Div., ASCE, 92, pp.61-87. Clapp, R. B., and Hornberger, G. M. (1978) Empirical equations for some soil hydraulic properties. Water resources research. 14(4), pp.601-604. Clayton & Siddique. (1999) Tube sampling disturbance-forgotten truths and new prospectives. Proceedings of Institution of Civil Engineering, 137, July, pp.127-135 Eching and Hopmans (1993) Optimazation of hydraulic functions from transient outflow and soil water pressure data, Soil Sci. Soc. Amer. J., 57 (5), pp.1167-1175 Eching et al. (1994) Unsaturated hydraulic conductivity from transient multi-step outflow and soil water pressure data, Soil Sci. Soc. Amer. J., 58, pp.687-695. Kazimoglu, Y. K., McDougall, J. R., and Pyrah, I. C., (2005) Moisture Retention and Movement in Landfilled Waste. Proceedings of the International Conference on Problematic Soils, Famagusta, Cyprus. Karvonen, T. (2001) Soil and groundwater hydrology: Basic theory and application of computational methods. Korfiatis, G. P., Demetracopoulos, A., C., Bourodimos, E. L., and Nawy, E. G. (1984) Moisture transport in a solid waste column. Journal of Environmental Engineering, ASCE, 110(4), pp. 789-796. Kool et al. (1987) Parameter estimation for unsaturated flow and transport models- A review, J. of Hydrol., 91, pp.255-293. Mansoor, I. (2003) Applications of soil mechanics principles to landfill waste. PhD thesis, School of Civil Engineering and the Environment Southampton University,UK. Mualem, Y. (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12, pp.513-522. Munich et al (2003) Hydraulic behaviour of mechanical biological pre-treated waste. Proceedings Sardinia 2003, Ninth International Waste Management and Landfill Symposium. S. Margherita di Pula, Cagliari, Italy; 6 - 10 October 2003. Parker et al. (1985) Determining soil properties from one-step outflow experiments by parameter estimation, II. Experimental studies, Soil Sci. Soc. Am. J., 49, pp.1354-1359.
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
Schnindler and Muller (2006) Simplifying the evaporation method for quantifying soil hydraulic properties, J. Plant Nutr. Soil Sci., 169, pp.623-629. Šimůnek et al. (1998a) A parameter estimation analysis of the evaporation method for determining soil hydraulic properties, Soil Sci. Soc. Am. J. 62, pp.894-905. Šimůnek et al. (2005) The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variablysaturated media. Version 3.0, HYDRUS Software Series 1, Department of Environmental Sciences, University of California Riverside, Riverside, CA, 270 Stolz, G. (2007) Influence of compressibility of domestic waste on fluid conductivity. 2nd International workshop Hydro-Physico-Mechanics of Wastes, Southampton, UK. van Dam et al. (1992) Inverse method for determining soil hydraulic functions from one-step outflow experiments, Soil Sci. Soc. Am. J., 56, pp.1042-1050. van Dam et al. (1994) Inverse method to determine soil hydraulic functions from multi-step outflw experiments, Soil Sci. Soc. Am. J., 58, pp.647-652. van Genuchten, M. T. (1980) A Closed Form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Soc. Of Am. J. 44, pp.892-898. Vogel and Cislerova (1988) On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport in Porous Media 3, pp.1-15 Warrick, A.W. (2002) Soil Physics Companion. CRC Press LLC, Florida. Wind, G.P. (1966) Capillary conductivity data estimated by a simple method, in proc. UNESCO/IASH Symp. Water in the unsaturated zone. Wageningen, The Netherland, pp.181191.
SUMMARY: This paper describes an investigation into the extent to which a simple experiment involving the drainage of columns of waste materials can be used to determine the relationships between the capillary pressure, pc(θ) or ψ(θ), the liquid and gas relative permeabilities krL (θ ) and krG (θ ) ,and areas of gas and liquid flows, AG(θ) and AL(θ), and volumetric moisture content θ . Initial drainage experiments were carried out on fine sand for which many of the processes involved in two-phase flows are relatively well understood. The HYDRUS-1D model has been used to interpret the results from the drainage experiments. Initial experimental and modeling results are compared and further experimental plans are presented. The aim is to determine whether the functions k (θ ) and pC (θ ) can be deduced from the measured transient outflow data. 1. INTRODUCTION It is widely recognised that the polluting potential of landfills will continue for centuries rather than decades. Even the extensive adoption of strategies including recycling, incineration and waste pre-treatment will not overcome the need for final disposal of a significant amount of residual wastes in landfills. The overall purpose of the EPSRC project “Science and strategies for the management and remediation of landfills” is to help develop techniques (simulation and design tools) that could be used to shorten the length of time for which landfill sites pose a pollution risk. The research will be applicable to cleaning up the legacy of old landfill sites that exists across the UK and much of the developed world. The research will also be of use in predicting the potential impact that new types of waste may have in landfills, in advance of any wholesale adoption of the technologies that produce them. This will make a positive and essential contribution to waste management policy and strategic decision making. An objective of this project is to carry out experimental work and develop a numerical model
Third International Workshop “Hydro-Physico-Mechanics of Landfills” Braunschweig, Germany; 10 - 13 March 2009
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
to better our understanding of gas generation and movement in landfill waste, and to also investigate the interplay of mechanisms that control the simultaneous flow of leachate and gas in waste materials. It is intended that the current flow algorithm in the University of Southampton Landfill Degradation and Transport model (LDAT) will be extended to become more representative of the flow processes that take place in a landfill waste material and also be tested and calibrated by comparison with the results from a number of field and laboratory experiments. The experiments will focus on illuminating specific issues and uncertainties associated with the theoretical concepts of gas/liquid movement in porous media. LDAT does not at present cater for the two distinct pore-pressure fields, one for liquid and one for gas, that are present in partially saturated flows. Use of a capillary pressure function related to moisture contact, p C (θ ) , would be a straightforward way of doing this, and it could be incorporated as a parameter driven algebraic function such as those proposed by Richards (1967) and van Genuchten (1980). Similarly LDAT calculates the flow areas for liquid and gas from the volumes of liquids and gas in the element (Beaven and White, 2006). There is however no well established relationship between the pore volume occupied by either the gas or the leachate, and the corresponding area of flow, AL (θ ) and AG (θ ) . It is also proposed to use the experimental results to verify the expressions used in LDAT to calculate relative permeability krL (θ ) and krG (θ ) . These key model parameters which control the simultaneous flow of leachate and gas in waste material will be measured under laboratory conditions (two column experiments involving drainage and aeration are under way) and will be incorporated in LDAT numerical model to verify against experimental results. The results from the drainage experiments are interpreted using HYDRUS-1D model (Šimůnek et al., 2005). HYDRUS-1D numerically solves Richards' equation for saturated-unsaturated water flow using the van-Genuchten functions for k (θ ) and pC (θ ) . The aim is to determine whether the functions k (θ ) and pC (θ ) can be deduced from the measured transient outflow data, i.e. to determine how to back calculate k (θ ) and pC (θ ) from the experimental results
2. MOISTURE RETENTION CHARACTERISTIC CURVES OF WASTES Measurement of soil water content (θ) as a function of matric potential or suction (ψ) in unsaturated soil yields the water retention curve or moisture retention curve (SWCC). Here, the moisture retention curves of coarse sand, clay and of waste materials (from the literature) are plotted in one graph (Figure 1). • The moisture retentions curves of sand and clay derived from the van Genuchten model θs −θr (1980): θ = θ r + with θ r = 0.01, θ s = 0.395, α = 0.1596cm −1 , n = 1.727 n m 1 + (α ψ )
[
]
for sand and with θr = 0.2141, θs = 0.54, α = 0.0154 cm-1 and n = 1.145 for clay (Karvonev, 2001) • Korfiatis et al. (1984) constructed a laboratory column cell to investigate the behaviour of unsaturated flow through solid waste. The column was instrumented with two vertical lines of tensiometers to monitor the suction of the waste. The power law relationship proposed by Clapp and Hornberger (1978) was used to fit the data: ψ = ψs(θ/θs)-b with ψs=2.45, θs=0.55 and b=1.50. • Kazimoglu (2005) studied suction characteristics for MSW using a modified pressure plate apparatus and compared his measurements with the van Genuchten (1980) equation with
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
θ r = 0.14, θ s = 0.58, α = 1.5m −1 , n=1.6 and m = 0.375. • Munnich (2003) and Stoltz (2007) determined the water retention curve of MBT waste and drilled domestic waste respectively by placing the waste on a ceramic plate and applying a negative pressure. • Mansoor (2003) used the filter paper method for the determination of suction in a synthetic landfill waste with dry density 0.35 T/m3 and compared his measurements with the van Genuchten equation (1980) for θ r = 0.01 , θ s = 0.35, α = 0.49m −1 , n = 1.45 and m = 0.31. 10000
Suction (KPa)
1000
100
10 Coarse sand Korfiatis vanGenuchten-Kazimoglu Mansoor-vanGenuchten 0.35T/m3 Stoltz data 0.77T/m3 MBT Munich data 0.6T/m3 Sand data (soton)
1
0.1 0.0
0.1
0.01
0.2
0.3
Clay Kazimoglu data Mansoor data 0.35T/m3 Stoltz data 0.54T/m3 MBT Munich data 0.8T/m3 MBT Munich data 0.3T/m3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
degree of saturation
Figure 1. Moisture retention curves for coarse sand, clay and waste materials For reference indicative curves for coarse sand and clay derived by van Genuchten model are shown in Figure 1.Generally a curve will be expected to move to the right within this zone as the pore size is reduced either as a result of decreaseing particle size or increasing density.
3. METHODOLOGY There are many laboratory methods for determining the water content-suction (θ(ψ)) and the hydraulic conductivity functions (k(ψ)). Popular techniques include one-step outflow (Parker et al., 1985; Kool et al., 1987; van Dam et al., 1992), multi-step outflow (van Dam et al., 1994; Eching and Hopmans, 1993; Eching et al., 1994), and evaporation (Wind, 1966; Schnindler and Muller, 2006; Šimůnek et al., 1998a). Parameter optimization offers an indirect approach to obtain θ(ψ) and k(ψ) simultaneously from transient flow data (Kool et al., 1987). A drainage test was developed to define the water retention curve (ψ vs θ) of a material. An experiment for defining the unsaturated conductivity is being studied. The transient outflow data, the measured water content and pressure heads from the drainage experiment will be used for the
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
inverse estimation of the unsaturated hydraulic properties. The van Genuchten model has been selected for describing the water retention and hydraulic conductivity functions. The experimental data are compared to simulations camed out using HYDRUS 1-D. The van Genuchten parameters (α, n, ks) describing the water retention and hydraulic conductivity functions can be estimated from the transient outflow data, the measured water contents and the pressure heads using the parameter estimation routine (inverse modelling) in HYDRUS 1-D. Further the experimental data could be fitted to the predicted data of other models (Brooks & Corey, 1964; modified van Genuchten, 1988) that are included in the HYDRUS 1-D program. 3.1 Description of the drainage experiment Scoping experiments using sand prior to the introduction of waste are being carried out in a clear Perspex cylinder with an inner diameter of 26cm and 1m in height. A photograph of the experimental set-up is shown in Figure 2 and the schematic diagram of the cell is shown in Figure 3. A 24 cm layer of gravel (particle size 10 to 20 mm) was installed at the bottom of the column. A geotextile filter (1 cm thickness) was installed above the gravel layer to prevent sand infiltration. Fine builder’s sand (47 kg) was deposited in 3 cm lifts above the saturated gravel underwater. The sand had been washed sieved and oven dried beforehand. The sand column (55 cm) was saturated by introducing approximately 10 litres of water into the cell upwards. It was left overnight to develop full saturation. The top of the cell was left open, at atmospheric pressure initially. The fully saturated column was then allowed to drain by opening the drainage tap located at the bottom of the cell. A fully saturated condition in the gravel layer at the bottom of the column was imposed using a U-tube outflow system. This arrangement prevents evaporation of the sand column from the bottom. Measurements of the volume of the water drained from the column were made using an electrical balance. The drainage experiment lasted for 10 days. Measurements of the pore water pressures in the sand at the four ports (4 cm, 19 cm, 25 cm and 39 cm from the bottom of the sand column) of the cell were made using manometers during that period. Vertical sand cores (at 5 cm intervals) were also removed from different points using a copper tube with a 13.5 cm inner diameter and 0.8 cm wall thickness and about 6° cutting-edge taper (Clayton & Siddique, 1999) to measure the moisture content of the sand.
Figure 2. Set-up for the drainage experiement
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
Figure 3. Schematic diagram of the cell
3.2 Properties of sand A particle-size distribution (PSD) curve for the sand was determined by sieve analysis (Figure 4). The porosity of the fine sand as placed in the column was estimated to be 40% and the dry density 1570kg/m3 (1540-1610kg/m3). The saturated permeability (ks) of the fine sand was measured as 5 × 10-5 m/s using the constant-head method in a 75 mm diameter permeameter.
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100
Percentage passing (%)
90 80 70 60 50 40 30 20 10 0 0.01
0.1
1
10
Particle size (mm)
Figure 4. Particle size distribution curve for the fine sand
3.3 Interpretation of the experimental data with HYDRUS 1-D The experimental data were analyzed using the HYDRUS-1D program (Šimůnek et al., 2005), which numerically solves Richards' equation (eq.1) for saturated-unsaturated water flow. ∂θ ∂ ⎡ ⎛ ∂ψ ⎞⎤ = ⎢k (θ )⎜ + 1⎟⎥ (eq.1) ∂t ∂z ⎣ ⎝ ∂z ⎠⎦ ψ denotes the pressure head (L), t is time (T), z is the elevation head (L), θ is the volumetric water content (L3/L3) and k (θ ) is the hydraulic conductivity (L/T), which is a function of θ under unsaturated conditions. The HYDRUS-1D code describes the relationship between water content and pressure head and hydraulic conductivity using three models: van Genuchten (1980), Brooks and Corey (1964) and modified van Genuchten type equations (Vogel and Cislerova, 1988). In this study, the van Genuchten (1980) empirical equations were selected because they are commonly used by the soil mechanics ‘community’:
[
θ e = 1 + (aψ )n where:
θe =
]
−m
(eq.2)
θ −θr θs −θr
(eq.3)
Re-arranging equation (2) gives the water content, θ, as a function of matric suction head, equation (4).
θ = θr +
θs −θr
[1 + (α ψ ) ]
n m
(eq.4)
where θr represents the residual water content (dimensionless). The parameter α (L-1) is related
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
to the inverse of the value of the air-entry pressure, the n and m parameters (dimensionless) are related to the pore size distribution of the soil. For m=1-1/n the above equation reduces to the van Genuchten (1980) & Mualem (1976) equation. The hydraulic conductivity as a function of water content is given by equation m 2 k (θ ) k r (θ ) = = θ e0.5 1 − (1 − θ em /( n −1) ) (eq.5) ks The relative hydraulic conductivity (dimensionless) is denoted by k r (θ ) . k (θ ) is the unsaturated hydraulic conductivity (L/T), k s denotes the saturated conductivity (L/T), θ e is the effective saturation (dimensionless) and θ s is the saturated water content (dimensionless).
(
)
4. RESULTS AND DISCUSSION
Free gravity drainage of the sand column was allowed to continue for 10 days. A very rapid drawdown of the water table was achieved by opening the tap at the bottom of the cell. About 1.9 litres of water drained out, most of it within a few hours. Figure 5 shows the cumulative flow per unit cross-sectional area from the sand column during drainage measured by the electrical balance (dot points), and six cases of the simulated cumulative flow per unit cross-sectional area calculated by HYDRUS- 1D. Due to data logging problems, data gaps occurred in the night. More frequent measurement of the outflow transient data is required. Table 1 lists the van Genuchten parameter values for the six cases run in HYDRUS-1D program. Table 1: Fitted van Genuchten parameters Case 1 Case 2 Case 3 θr 0.034 0.034 0.04 (m3m-3) 0.35 0.35 0.38 θs (m3m-3) α 2 2 1.66 (m-1) n 2 4 1.51 ks 5E-5 5E-5 5E-5 (m/s)
Case 4 0.04
Case 5 0.034
Case 6 0.034
0.38
0.34
0.35
2
2
2.5
1.51 5E-5
1.51 5E-5
1.51 5E-5
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Data Hydrus case 1 Hydrus case 2 Hydrus case 3 Hydrus case 4 Hydrus case 5 Hydrus case 6
Volume of water drained per unit cross-sectional area
Mass of water out (m)
0.03 0.025 0.02 0.015 0.01 0.005 0 0
10
20
30
40
50
60
Time (hrs)
Figure 5: Measured and modelled cumulative volume per unit area of water drained Sand cores were taken from the column 13, 17, 18 and 29 days after the start of the drainage experiment. In simulations, steady state conditions were achieved after 2-3 days; the profiles presented are at 10 days after equilibrium conditions had been achieved. Figure 6 shows the measured moisture profiles and and a number of simulated moisture profiles.
5
10
Vol.moisture content (%) 15 20 25 30
35
40
0
Depth (cm)
10 20 30 40 50 60
Data after 13days Data after 18days Hydrus case 1 Hydrus case 4 Hydrus case 6
Data after 17days Data after 29days Hydrus case 2 Hydrus case 5 Hydrus case 3
Figure 6: Measured and modelled moisture profiles after 10 days Figure 7 shows the measured suction profiles at selected times. After about 60 hours the suction
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
profile reaches the hydrostatic line. Also, the simulated suction profiles at two selected times are shown for case 1. measured
simulated
Figure 7: Measured and simulated suction profiles for case 1. The moisture retention (ψ vs θ) data from the drainage experiment are plotted and give close agreement with the sand SWCC (Figure 1). More precise measurement of suction heads, moisture content and outflow transient data will be achieved by the use of specific instruments. Four additional manometer ports (2mm diameter) have been fitted to the column to enable more points of suction measurent. The manometer readings will be compared with those from six mini tensiometers (Delta-T Devices, model SWT5) of 5mm diameter and 75mm length, which are able to measure both positive and negative pore water pressures (+100 to -85kPa). Six impedance probes (Delta-T Devices, model Theta probes ML2x ) of 40mm diameter and 105mm length will be installed in the column for moisture content measurements, under the following arrangements: o Theta probes will be located at 14, 34 and 54 cm from the bottom of the sand column. o Tensiometers will be located at 4, 25 and 45 cm from the bottom of the sand column. All instruments will be coupled to a data-logger system. The entire assembly will be placed onto three load cells for recording weight changes. Figure 8 presents the instrumentation layout for the experiment.
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
Theta probe 70 mm
Proposed manometer port
50 mm
70 mm
SWT 5 tensiometer 5 mm
Existing manometer port
40 mm
290 mm
390 mm
500 mm 440 mm
640 mm
590 mm
790 mm
700 mm
30 mm
SWT5 tensiometer frontview
Theta probe frontview Boss
Manometer port
Figure 8: Instrumentation set-up of the column In addition it is planned to estimate the moisture retention properties of waste samples using the pressure plate apparatus technique (for suctions 10-150 kPa) and the hanging water column method (for suctions 0-10 kPa). The moisture retention curves determining using the pressure plate apparatus/hanging column and those resulting from the instruments measurements will be fitted to different algebraic representations based on the van Genuchten and Brooks & Corey curves.
5. CONCLUSIONS
This paper has described the details of a column apparatus that has been developed to examine the moisture retention characteristics of waste materials. Initial drainage experiments have been carried out on fine sand for which many of the processes involved in two-phase flows
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
are relatively well understood. These experiments will act as a benchmark for subsequent tests on different types of waste materials. Following drainage, imbibition and infiltration experiments will be carried out. The application of a direct method/experiment to measure unsaturated hydraulic conductivity is currently being assessed.
REFERENCES
Beaven, R.P. (2000) The hydrogeological and geotechnical properties of household waste in relation to sustainable landfilling. PhD dissertation, Queen Marry and Westfield college, University of London Beaven, R.P. and White, J.K. (2006) A review of the theory relating to the evolution and movement of gas in waste materials and proposals for the design of laboratory experiments to investigate this theory. Science and strategies for the management and remediation of landfills. Sub-package funded by Onyx. Final report. December 2006. Brooks, R. H. and Corey, A. T. (1964). Hydraulic Properties of Porous Media. Hydrol. Pap. 3. Colorado State Univ. Fort Collins, CO. Brooks, R. H. and Corey, A. T. (1966). Properties of Porous Media Affecting Flow. J. Irr. Drain. Div., ASCE, 92, pp.61-87. Clapp, R. B., and Hornberger, G. M. (1978) Empirical equations for some soil hydraulic properties. Water resources research. 14(4), pp.601-604. Clayton & Siddique. (1999) Tube sampling disturbance-forgotten truths and new prospectives. Proceedings of Institution of Civil Engineering, 137, July, pp.127-135 Eching and Hopmans (1993) Optimazation of hydraulic functions from transient outflow and soil water pressure data, Soil Sci. Soc. Amer. J., 57 (5), pp.1167-1175 Eching et al. (1994) Unsaturated hydraulic conductivity from transient multi-step outflow and soil water pressure data, Soil Sci. Soc. Amer. J., 58, pp.687-695. Kazimoglu, Y. K., McDougall, J. R., and Pyrah, I. C., (2005) Moisture Retention and Movement in Landfilled Waste. Proceedings of the International Conference on Problematic Soils, Famagusta, Cyprus. Karvonen, T. (2001) Soil and groundwater hydrology: Basic theory and application of computational methods. Korfiatis, G. P., Demetracopoulos, A., C., Bourodimos, E. L., and Nawy, E. G. (1984) Moisture transport in a solid waste column. Journal of Environmental Engineering, ASCE, 110(4), pp. 789-796. Kool et al. (1987) Parameter estimation for unsaturated flow and transport models- A review, J. of Hydrol., 91, pp.255-293. Mansoor, I. (2003) Applications of soil mechanics principles to landfill waste. PhD thesis, School of Civil Engineering and the Environment Southampton University,UK. Mualem, Y. (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12, pp.513-522. Munich et al (2003) Hydraulic behaviour of mechanical biological pre-treated waste. Proceedings Sardinia 2003, Ninth International Waste Management and Landfill Symposium. S. Margherita di Pula, Cagliari, Italy; 6 - 10 October 2003. Parker et al. (1985) Determining soil properties from one-step outflow experiments by parameter estimation, II. Experimental studies, Soil Sci. Soc. Am. J., 49, pp.1354-1359.
Third International Workshop “Hydro-Physico-Mechanics of Landfills”, 2009
Schnindler and Muller (2006) Simplifying the evaporation method for quantifying soil hydraulic properties, J. Plant Nutr. Soil Sci., 169, pp.623-629. Šimůnek et al. (1998a) A parameter estimation analysis of the evaporation method for determining soil hydraulic properties, Soil Sci. Soc. Am. J. 62, pp.894-905. Šimůnek et al. (2005) The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variablysaturated media. Version 3.0, HYDRUS Software Series 1, Department of Environmental Sciences, University of California Riverside, Riverside, CA, 270 Stolz, G. (2007) Influence of compressibility of domestic waste on fluid conductivity. 2nd International workshop Hydro-Physico-Mechanics of Wastes, Southampton, UK. van Dam et al. (1992) Inverse method for determining soil hydraulic functions from one-step outflow experiments, Soil Sci. Soc. Am. J., 56, pp.1042-1050. van Dam et al. (1994) Inverse method to determine soil hydraulic functions from multi-step outflw experiments, Soil Sci. Soc. Am. J., 58, pp.647-652. van Genuchten, M. T. (1980) A Closed Form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Soc. Of Am. J. 44, pp.892-898. Vogel and Cislerova (1988) On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport in Porous Media 3, pp.1-15 Warrick, A.W. (2002) Soil Physics Companion. CRC Press LLC, Florida. Wind, G.P. (1966) Capillary conductivity data estimated by a simple method, in proc. UNESCO/IASH Symp. Water in the unsaturated zone. Wageningen, The Netherland, pp.181191.
