Applicability of Time Domain Reflectometry Water Content Measurements in Municipal Solid Waste
Applicability of Time Domain Reflectometry Water Content Measurements in Municipal Solid Waste O R Ma hias J Staub,* Jean-Paul Laurent, Jean-Pierre Gourc, and Christophe Morra Water content (θ) and distribu on are important parameters for landfill operators because θ is generally considered a key factor for the degrada on of municipal solid waste (MSW) in landfills This study inves gated the applicability of me domain reflectometry (TDR) for the determina on of θ Although TDR is commonly applied to soils, only a few researchers have explored the sensi vity of its measurements to various parameters in MSW, which is a heterogeneous and me-evolving material The aim of this study was to evaluate the calibra on of TDR probes in MSW and to quan fy the sensi vity of the method to the waste’s characteris cs and to the distribu on of water in the material The sensi vity of TDR was quan fied rela ve to MSW composi on and density, the ini al θ and θ distribu on, the electrical conduc vity (EC) of the fluid, and the rate of change in θ Experiments were conducted on two different waste materials and on a sand–gravel mixture in a small-scale laboratory cell The rela onship between TDR measurement and true θ was calibrated for all experiments The effect of waste composi on and density appeared to be minor compared with the effect of the ini al θ and the θ distribu on around the probes This research opens a way for an effec ve use of TDR in large-scale experiments with MSW A : EC, electrical conductivity; MSW, municipal solid waste; TDR, time domain reflectometry; TDT, time domain transmissivity D of new MSW treatment techniques and increased recycling rates, landilling is still the most common MSW treatment method used worldwide (Arigala et al., 1995; Durmusoglu et al., 2005; Bilgili et al., 2007) To accelerate stabilization of the waste and to mitigate the adverse impacts of landills, research has been conducted for several decades on bioreactor technology Bioreactor landills difer from conventional landills by attempting to control the kinetics of the biochemical processes occurring within the landill, potentially resulting in a reduction in its post-closure care period he operation of a landill as a bioreactor includes the addition of water to the waste, mainly in the form of leachate, to enhance natural biodegradation processes (e.g., Reinhart and Townsend, 1997; Imhof et al., 2007) Water availability is considered the limiting factor for M.J Staub, J.-P Laurent, J.-P Gourc, and C Morra, LTHE, Grenoble Univ., BP 53, 38041 Grenoble Cedex, France; M.J Staub, Veolia Environnement Recherche et Innovation, 291, avenue Dreyfous Ducas, Zone portuaire de Limay, 78520 Limay, France *Corresponding author (matthias.staub@grenoble-inp.fr) Vadose Zone J 9:160–171 doi:10.2136/vzj2009.0046 Received 15 Apr 2009 Published online 26 Jan 2010 © Soil Science Society of America 677 S Segoe Rd Madison, WI 53711 USA All rights reserved No part of this periodical may be reproduced or transmi ed in any form or by any means, electronic or mechanical, including photocopying, recording, or any informa on storage and retrieval system, without permission in wri ng from the publisher www.vadosezonejournal.org · Vol 9, No 1, February 2010 160 natural biological activity in landills (e.g., Reinhart and Townsend, 1997; Zhao et al., 2008, Mehta et al., 2002) Besides providing water, leachate recirculation ofers environmental and economic beneits in leachate treatment and disposal But the control of water distribution remains essential to successfully operate bioreactor landills Insuicient water addition will limit the biodegradation processes, while excess water may result in side seeps and geotechnical instability (Imhof et al., 2007) Khire and Mukherjee (2007) have shown that the landfill’s stability could be afected by reducing the factor of safety for slope stability and potential breakouts of leachate from the landill, especially if the liquid pressure on the liner increases signiicantly (Khire and Mukherjee, 2007) Water content measurements within MSW are hence necessary to monitor recirculation and to allow a more eicient landill operation Ideally, θ measurement techniques should include characteristics such as reliability, ease of measurement, nondestructiveness, repeatability, accuracy, and large sampling volume (Yuen et al., 2000) Gawande et al (2003) and Imhof et al (2007) proposed an extensive assessment of diferent θ measurement techniques for MSW within landills Most of the techniques were material sensitive and the determination of the actual θ required accurate calibration here are no commonly accepted ways of measuring the θ of MSW (Li and Zeiss, 2001) Numerous researchers have investigated the applicability of TDR to MSW to measure θ in a relatively inexpensive, nondestructive, and automated way at the laboratory scale (Li and Zeiss, 2001; Gawande et al., 2003; Laurent et al., 2005; Imhof et al., 2007; Staub et al., 2008) Investigation of the TDR measurements’ sensitivity to various properties of MSW, which is a heterogeneous and time-evolving material, is still missing, however his study contributes to the existing knowledge about TDR applicability by quantifying its sensitivity to the parameters of MSW: composition, density, initial θ, θ distribution, EC of the luid, and the rate of change in θ he results should be useful for improving water content monitoring and bioreactor landill operation 1980; Schmugge et al., 1980) Applications of TDR in soil science have been conducted at the site scale, whereas the research on TDR in MSW has focused for the most part on small-scale applications, with the exception of some landill-scale experiments (van Praagh et al., 2007; Zhao et al., 2008; Breitmeyer et al., 2008) Time domain relectometry is an electromagnetic technique that measures the travel time of a fast rise-time pulse traveling along a waveguide—the TDR probe—placed into a material he signal produced by the TDR generator is sent through the probe’s head inside the porous medium and is relected twice: once as it enters the rods of the probe and again as it reaches the end he resulting waveform is collected and its travel time, Τ, along the waveguide is calculated as the diference between the times of these two main relections Literature Summary on Water Content Measurement and Time Domain Reflectometry Types of Water Measurement and Material Characteris cs he standard method to determine the water content of a solid sample is the thermogravimetric method, which consists in oven drying given volumes of the material (Walker et al., 2004) his method is the only available direct method and is both time consuming and destructive Indirect methods provide information on a physical parameter that can be correlated to the medium’s water content An example of a physical parameter is the material’s electrical permittivity (for the TDR method) Direct θ measurement using the thermogravimetric method provides the gravimetric water content, w, of the sample: Basic Equa on of Time Domain Reflectometry he corresponding wave propagation speed, v, is calculated as follows: 2L [6] T where L is the probe’s length (the factor accounts for a round trip) his propagation speed is related to the relative electrical permittivity K (or εr) (oten called the dielectric constant) by v= Mw [1] Mt where Mw is the mass of water and Mt is the total dry mass he mass of water is determined from the evaporated water at a given temperature ranging from 60 to 105°C, depending on the study Most of the indirect water content measurements, including TDR, are correlated with the volumetric water content of waste, θ, deined by w= c [7] K where c is the speed of light (3 × 108 m s−1) Combining Eq [6] and [7] leads to the TDR basic equation (Fellner-Feldegg, 1969): v= Vw [2] Vt where Vw is the volume of water and Vt is the sampled volume he TDR method determines θ, which will be used below It must be noted here that θ may increase due to an increase in the volume (or mass) of water, but also due to a decrease in the total volume, Vt, for instance due to compression of the sample Speciic trials under compression were conducted to assess this speciic volumetric increase in θ To characterize the materials tested, three other parameters are used (Stoltz, 2009): (i) the material’s bulk density, deined as θ= ρh = Mt Vt ⎛ cT ⎞2 K = ⎜⎜⎜ ⎟⎟⎟ ⎝ 2L ⎠ In the current study, coated probes were used, which means that the electrical permittivity of the medium could not be directly determined from the travel time measurements due to the inluence of the coating Hence, an intermediate calibration between the medium electrical permittivity and the apparent time delay, Ta, was required For this calibration, the TDR probe was immersed in media of known electrical permittivities he procedure is not detailed here; however, the results of this calibration are presented briely below because they are required to interpret our results in terms of the electrical permittivity [3] Calibra on between Rela ve Electrical Conduc vity and the Volumetric Water Content (ii) the material’s dry density, deined as Mt − M w Vt and (iii) the material’s porosity, deined as ρd = To deduce the volumetric water content from the TDRmeasured K value, physically based models or purely empirical formulas are applied (Weiler et al., 1998) Two diferent approaches for correlating θ with measured electrical permittivities are considered: a semitheoretical method described by Gong et al (2003) and the empirical formula from Weiler et al (1998) On the one hand, the semitheoretical approach proposed by Gong et al (2003) is derived from the Complex Refractive Index Model (CRIM) (van Dam et al., 2005) Initially developed for soils, it is based on the assumption that the total TDR waveform travel time along an elementary volume with length = is the sum of the travel times in each phase of the material: solid particles (s), liquid solution (w), and gaseous phase (g) his can be written as [4] ρ [5] = 1− d Vt ρc where Vg is the volume of gas in the material and ρc is the constitutive solid density of the particles n= V w +Vg Principle of Time Domain Reflectometry Measurement he TDR method was irst applied to determine the θ of soils for irrigation scheduling and hydrologic applications (Topp et al., www.vadosezonejournal.org · Vol 9, No 1, February 2010 [8] 161 K 1− n θ n−θ = = Ks + Kw + Kg v c c c c Literature Review on the SensiƟvity of the Time Domain Reflectometry Method [9] where n is the porosity of the material, Ks is the relative permittivity of the solid material, Kw is the relative permittivity of water (inversely temperature dependent), and Kg is the relative permittivity of the gaseous phase Finally, since the contribution of the gaseous phase can be generally neglected (Kg ∼ when Kw ∼ 80 and Ks ∼ 4–10), Eq [9] is reduced to the expression used by Weiler et al (1998), Gong et al (2003), or Masbruch and Ferré (2003): K = a + bθ Time domain relectometry measurements are sensitive to many factors Changes in bulk EC inluence the TDR measurements due to energy losses, which might attenuate the signal and eventually prevent detection of the second wave relection (Li and Zeiss, 2001; Staub et al., 2008) Concerning the liquid phase, its electrical permittivity is supposed to increase with its electrical conductivity (EC or σa) Robinson et al (2003) and Evett et al (2005) proposed the following calibration model, derived from Eq [10], taking into account changes in the bulk EC, σa, of the medium: [10] K = a + bθ + c σa where a and b are constants for each material One can infer from Eq [9] that the parameter a is porosity dependent and b is temperature dependent Equation [9] can be generalized considering that the K exponent can be diferent from 0.5 (the square root) his is then called the α model (Ponizovsky et al., 1999): K α = (1 − n ) K sα + θ K wα + ( n − θ ) K gα where a, b, and c are itted parameters Hence, for a constant σa, the calibration curve is altered by an ofset Temperature has an impact both on the σa and on the liquid and solid electrical permittivity (Grellier et al., 2006) To mitigate the EC efects, it is possible to coat the probes with a nonconductive layer (Li and Zeiss, 2001; Imhof et al., 2007) It should be noted, however, that the EC of the luid inluences measurements even with coated probes, especially in the “low” range (σa < 10 mS cm−1, which is a low value compared with that of the MSW leachate) Besides, coating the probes reduces the sensitivity of the method (Laurent et al., 2005) Li and Zeiss (2001) found that the waste composition does not have a signiicant inluence on the TDR response when the probes are coated In soils, several researchers have shown experimentally that the soil texture inluences TDR readings (e.g., Topp et al., 1980; Ponizovsky et al., 1999) Tabbagh et al (2000), as well as Jones and Friedman (2000), demonstrated that changes in the distribution of the three phases (air, water, and solids) alter the medium’s apparent permittivity By analyzing the semitheoretical approach for soils, Gong et al (2003) have shown that bulk density has an inluence on the absolute measurement of θ, but it does not impact relative θ measurements Other factors are also known to inluence the electrical permittivity of a given material, including the water status (bound or free), porosity, organic matter content, and particle and pore shapes ( Jones and Friedman, 2000; van Dam et al., 2005) Most of the factors cited above can potentially alter the measurements; nevertheless relative measurements with coated probes may ofer a potential accuracy comparable to other nondestructive θ determination techniques such as neutron scattering or geophysical techniques (Imhof et al., 2007) [11] By neglecting the gaseous-phase contribution, Eq [11] will thus be reduced to K α = aα + bα θ [12] Most researchers have obtained α values ranging roughly from 0.4 to 0.7 when itting this model on experimental data (Ponizovsky et al., 1999); a value of 0.5 has been commonly used It has been proved that the parameter α is related to the distribution of dielectric relaxation ellipsoids inside the material and therefore to its structure (Zakri et al., 1998) On the other hand, the empirical approach consists in itting parameters of mathematical expressions to calibrate the relationship between θ and K he empirical polynomial relationship of Topp et al (1980) between K and θ is well known for soils (Topp et al., 1980; Ledieu et al., 1986; Weiler et al., 1998; Walker et al., 2004): θ = − 0.053 + 0.0292 K − 0.00055K + 0.0000043 K [13] When applying this model to MSW by simple humidiication, however, Li and Zeiss (2001) found diferent θ values that could be due to the MSW’s mixed composition, which is signiicantly diferent from that of soil he most commonly used functions for MSW are θ = a0 + b0 K Materials and Methods [14] Experimental Cell and Time Domain Reflectometry Probe (Masbruch and Ferré, 2003) in experiments performed with time domain transmissivity (TDT) probes, θ = a3 + b3 K + c K + d K he experimental setup consisted of a cylindrical experimental cell, a coated three-rod-type TDR probe, and an automatic data acquisition system connected to a computer [15] Experimental Cell (van Praagh et al., 2007), and θ = a + b4 K + c K + d K + e K he experimental cell consisted of a rigid transparent polymethyl methacrylate (PMMA) cylinder of 20-cm inner diameter, D; the upper and lower cell supports were made of polyvinyl chloride (PVC) he inner volume of the cell ranged between 9.4 and 12.0 L depending on the vertical position of the upper cell support [16] (Li and Zeiss, 2001) www.vadosezonejournal.org · Vol 9, No 1, February 2010 [17] 162 F Schema c diagram of the experimental me domain reflectometry (TDR) cell (not to scale) F Municipal solid waste Sample A along the threaded steel rods (h, ranging from 0.31–0.38 m) he two supports could be moved like a piston to allow modiication of the sample’s volume and density between two measurements he cylinder was illed with the test medium and the coated TDR probe was inserted he schematic diagram of the cell is given in Fig Time Domain Reflectometry Probe he TDR probe used in this research was a commercially available CS605 three-rod probe (length L, 30 cm; rod diameter, 0.5 cm) from Campbell Scientiic (Logan, UT) he distance between the rods is 1.8 cm hese probes have also been used in MSW by other researchers (Laurent et al., 2005; van Praagh et al., 2007) and provided good response in high-conductivity media he probes were coated by hand with heat-shrinkable, initially 8-mm-diameter, polyolein tubing he TDR probe’s measurement volume was veriied to be included in the cell’s volume (Fig 1) Signal processing and collection was done with a TDR100 from Campbell Scientiic (Logan, UT) and distributed to the probe by a irst-level SDMX50 multiplexer (Campbell Scientiic) A 10-m-long coaxial cable was used to connect the probe he TDR setup was managed by PCTDR sotware (also from Campbell Scientiic) via an RS232 interface connected to a computer he waveform collection and response time calculation were stored on a CR1000 datalogger (Campbell Scientiic) during the experiments he probe was inserted ater the waste was packed to avoid damage to the rods A 30-cm-long drilling rod of 0.4-cm diameter was used to make three holes in the waste, and the TDR sensor was placed in these holes As MSW is a visco-elastic material, it is supposed that the contact between the rods and the medium was good due to the lateral coninement of the waste toward the probe’s rods As the TDR probe’s steel rods measured only 30 cm in length, the θ was calculated only in the zone of inluence of the probe (dashed surface on Fig 1) thus the volume below the rods was not considered in the calculation of θ by mass balance F Municipal solid waste Sample B composition are given in Tables and The waste fractions were sorted according to the waste categories given in the French MODECOM method (Ademe, 1993) he gravimetric water content, w, of the materials was determined using the thermogravimetric method: samples of 2.5 kg each were oven dried at 105°C to constant mass he volumetric θ was later deduced from the sample’s density Knowing the amount of water added and drained from each sample, the initial θ was backcalculated ater each test he major diference between the two materials is that Sample A was a coarse-graded typical French MSW, whereas Sample B was T Sample A waste Maximum par cle size (dmax), mm 70 0.41 Ini al dry density (ρ d), Mg m−3 1.65 Ini al cons tu ve solid density (ρ c), Mg m−3 Ini al gravimetric water content 30.7 (w), kg kg−1 Ini al volumetric water content 21.5 (θ), L L−1 Ini al porosity (n), L L−1 75 Characteris c Characteris cs of the Tested Media Two diferent shredded fresh MSW materials, A and B, collected from French sanitary landill sites were tested In addition, a sand–gravel mixture was used as a means to investigate the impact of the type and EC of the luid used for calibration Figures and show the aspect of the materials; their characteristics and www.vadosezonejournal.org · Vol 9, No 1, February 2010 Physical characteris cs of the tested materials 163 Sample B waste 40 0.39 1.62 Sand–gravel mixture 20 1.55 2.65 50.2 2.2 39.2 3.5 75 41 T Composi on of the municipal solid waste materials As a local determination of mass balance was not possible, the overall θ in the cell was used and supposed to be representative of the sample’s actual θ, although it might vary locally Because the sample was wetted from the bottom, it is clear that θ was not homogeneous he efect of this heterogeneity is discussed below hree wetting processes were assessed, representing diferent wetting conditions that may be found in landills: (i) gradual wetting, which occurs when rainwater or a leachate front is percolating downward through the waste material; (ii) natural homogeneous increase or decrease of water in the long term; and (iii) increase in θ due to waste settling To assess these three wetting processes, constant-head wetting, sprinkling and mixing, and compression tests were performed (Fig 4) Composi on according to MODECOM Waste component Putrescible waste Paper and cardboard Plas c Glass Metal Tex les and medical tex les Miscellaneous Sample A waste Sample B waste ———————— % by wet wt —————— 36.6 58.1 26.1 13.3 14.0 9.5 6.1 5.4 5.7 0.4 5.5 2.1 6.0 11.2 ine graded and mainly composed of organic material As for the tested sand–gravel mixture, it was composed of 67% sand and 33% gravel by weight Step-by-Step and Con nuous We ng by Upward Infiltra on under Constant Head Methodology he material was wetted with water and later drained through the drainage pipe to return to ield capacity his procedure was done in steps, and each step consisted in the addition (during wetting) or removal (during drainage) of 100 to 250 mL of liquid, depending on the sample he addition and removal of liquid was made via the lexible pipe shown in Fig Aterward, the θ was kept constant for 15 to enable a relatively homogenized water distribution, and TDR measurements were recorded every minute before a new step was started he arithmetic average of the last ive readings was taken to represent the actual TDR measurement Given that the added or removed volume of luid was known, the recorded measurement could be compared with the actual average θ of the sample Each wetting–drainage cycle was completed within the same day Each experiment with a MSW sample was conducted within a maximum of to d to limit biochemical changes in the material he experiments were run between December 2007 and June 2008 with diferent procedures to establish the TDR sensitivity he procedures are detailed below and summarized in Fig and Table Dry densities were calculated using the average gravimetric w determined by oven drying at the end of each trial Materials were compared on the basis of their dry densities rather than on their bulk densities to analyze the efect of their composition and structure According to Eq [5], comparing the materials on their dry densities (ρd) is equivalent to assessing the inluence of their porosity, given that the constitutive densities (ρc) of both Samples A and B were very close (see Table 1) Some of the tests also included a speciic evaluation of the bulk density’s inluence on the measurements F The different we ng procedures; θ is the water content T Summary of the different we ng procedures for municipal solid waste (MSW) Samples A and B and a sand–gravel mixture Upward we ng Cell volume, L Materials tested Steps at constant water content (θ) Dura on of each step Repe ons for each MSW Densi es tested per experiment Homogeneous we ng Step-by-step Con nuous 9.4 9.4 MSW A, B, sand–gravel mixture MSW A, B 10–15 (con nuous increase of θ) 15 at constant θ 3 www.vadosezonejournal.org · Vol 9, No 1, February 2010 1–2 h of nuous we ng (middle value) 164 Sprinkling and mixing 9.4 MSW A, B Compression 12.0–9.4 in volume steps MSW A, B 15 at constant θ (middle value) 15 at constant θ (density steps) Alternatively, a continuous wetting without steps was considered, simulating the fast wetting of the material due to a hydraulic gradient his shorter “continuous” trial was then compared to the step-by-step wetting In total, 18 diferent step-by-step wetting–drainage cycles were performed on the MSW Samples A and B corresponding to three diferent densities of both materials (see Table 3) Each test consisted of three successive wetting–drainage cycles Continuous wetting tests were conducted for one dry density of each sample, with three successive wetting–drainage phases his wetting procedure was generally used in previous published work (Li and Zeiss, 2001; Masbruch and Ferré, 2003; van Praagh et al., 2007; Staub et al., 2008) It is important to note that for the sand–gravel mixture, only this wetting procedure was used Five diferent upward wetting experiments were performed with ECs of 0, 5, 10, 20, and 40 mS cm−1 and compared with the results with leachate taken directly from a French landill site (σa = 30 mS cm−1) he procedure during the test was the same as previously described for step-by-step upward wetting Results and Discussion Calibra on of the Probe’s Intrinsic Rela onship between Electrical Permi vity and Apparent Wave Propaga on Time he calibration results of the probe’s intrinsic relationship between Ta and K in various media of known permittivities is a second-order polynomial (Fig 5; Eq [18]): Sprinkling and Mixing We ng Procedure K = 394.98 −114.25Ta + 8.4801Ta2 [18] his experimental work was done separately (Laurent, unpublished data) he coeicient of determination for this calibration was very high (r2 = 0.9955) and the RMSE was low (2.4) Other polynomials showed poorer correlation For instance, for a linear relationship, the values were r2 = 0.9122 and RMSE = 47.9 he typical travel times measured in the waste material ranged from to ns and hence fell into the range of calibration of Eq [18], which was therefore applied to determine the electrical permittivity of the tested medium for all the following tests A diferent wetting method that guarantees a more homogeneous distribution of θ within the sample was tested he material was placed in the cell for a irst series of initial measurements, and then taken out to be saturated by sprinkling water on the material in a tank he sample was then mixed by hand to ensure a homogeneous distribution of water As the material was removed and replaced ater every trial, its structure was modiied herefore, the procedure was repeated three times at the same θ to evaluate the inluence of the structure of the sample on the TDR measurement (see Table 3) Predetermined volumes of liquid were added, ranging from 400 to 800 mL depending on the tested medium he TDR measurements were then recorded every minute for 60 before the material was mixed again he actual TDR measurement was represented by the arithmetic average of all the readings excluding the irst ive measurements to avoid transient conditions Each experiment was completed within d while recording one θ value per day Effect of the Fluid’s Conduc vity he efect of the luid’s conductivity and type was evaluated in the sand–gravel inert material In total, six diferent trials were conducted with water at diferent NaCl concentrations and landill leachate he TDR measured the Ta presented in Fig he results indicate that for a given θ, the higher the EC, the higher the We ng by Compressing the Sample A speciic test with varying bulk density was also performed on the MSW Ater the sample was wetted under constant head, it was drained until free drainage ceased, and then the upper cell support was lowered in four steps to increase the bulk density of the sample, the volume of the sample being reduced from 12.0 to 9.4 L During this procedure, water was forced out at each step Diferent measurements with the same w but increasing θ could be obtained from this experiment, and the impact of the increase in density could be monitored Figure and Table summarize the diferent wetting procedures applied to all the tests in the experimental cell F Calibra on of the rela onship between the electrical permi vity (K) and the apparent travel me (T) for the coated CS605 probe Experiments with Different Liquids To investigate the efect of the luid’s type and conductivity on TDR measurements, an inert material (the sand–gravel mixture) was wetted with salt water having ECs ranging from mS cm−1 (tap water with σa < 0.3 mS cm−1) to 40 mS cm−1 Salt water was prepared by adding commercially available sea salt to tap water to prepare approximately L of salt water before each trial he efect of temperature on the EC was not considered, as the water used for the tests was irst warmed to 25°C and as the tests were performed in a room with thermostatic regulation at 25°C he calibration of the linear relationship between NaCl salinity and the EC of the luid as well as the veriication of the dependence of conductivity on temperature were made separately, but are not presented here www.vadosezonejournal.org · Vol 9, No 1, February 2010 F Influence of liquid electrical conduc vity (EC) on the me domain reflectometry calibra on of water content (θ) vs apparent travel me (T) in the sand–gravel mixture The bold dashed line for bulk EC (σa) = 30 mS cm−1 corresponds to the trial with leachate 165 travel time he EC curves for values ≤10 mS cm−1 were grouped, however; there seemed to be no major inluence of EC beyond the threshold of 10 mS cm−1 on the travel time and hence the electrical permittivity his efect was also described by Li and Zeiss (2001), who found no inluence of EC when it was >10 mS cm−1 For uncoated probes, a high EC of the luid results in an increase in K because the medium is more conductive (Robinson et al., 2003; Evett et al., 2005), but due to the coating, K is roughly constant for a given θ, except for low ECs he results in Fig also show that the dielectric behavior of the tested leachate was very close to that of salt water, despite the former’s suspended solids charge, chemical composition, and biological constitution, therefore conirming the results of other researchers (Bouyé et al., 2005) Salt water was also used for calibration of TDR probes in MSW by Zhao et al (2008) Salt water was hence preferred for all the tests with MSW to simulate a highly conductive leachate (σa = 30 mS cm−1) was made on all experimental points (r2 = 0.84) to compare the third-order polynomial found for MSW: θ = 0.066 + 0.0301K − 0.00085K + 0.0000094 K with the polynomial of Topp et al (1980) (Eq [13]) he RMSE of the regression polynomial Eq [19] was 0.030 m3 m−3, whereas Topp’s polynomial Eq [13] yielded an RMSE of 0.046 m3 m−3 he θ estimation using Topp’s polynomial for MSW could lead to an underestimation of the true θ in the low and high range of permittivities his means that Eq [19] may be used within our calibration range, i.e., for θ between 0.3 and 0.6 m3 m−3, and for MSW with a comparable composition When precise TDR measurement is required, it may not be very accurate to use Topp’s model for MSW, which gives a rough estimate of the θ Some points fall out of the range of either global calibration function, and a detailed analysis of the calibration functions is provided for each wetting procedure to identify material and liquid efects on the calibration equations (below) Compara ve Results for the Municipal Solid Waste Materials Calibra on for the Different Experiments and Comparison with Previous Work To compare the calibration functions for each wetting condition, diferent regressions were performed, including square-root, linear, and polynomial regressions he diferent parameters an to en (n being the degree of the polynomial) refer to Eq [14] (square-root regression), [15], and [16] (third- and fourth-order polynomials, respectively) and additionally to Global Calibra on for Municipal Solid Waste The results of the different trials are shown in Fig For the upward wetting procedures (step-by-step and continuous wettings), the average measurements of the second and third wetting–drainage cycles were considered to avoid the efects of the material’s wetting history (see below) Each data point for the sprinkling and mixing tests represented the average of three replicates Compression trials were performed only once, so the corresponding data points were not replicated he range of θ tested depended on the trial and on the material Initial θ values for the upward wettings were larger than the initial θ of the samples (Table 1) because the irst wetting–drainage cycle did not drain the sample completely, as water was held by capillary retention he model proposed by Topp et al (1980) was also included for comparison purposes he values for electrical permittivities ranged from 10 to 50, with values ranging from 10 to 30 for waste material in its initial state In some speciic trials, values around 60 were obtained Most of the data points fell into the range of the polynomial proposed by Topp et al (1980) (Fig 7); however, a discrepancy of about 0.10 m3 m−3 in θ was observed for some calibration points A similar regression with a third-order polynomial first-order linear regression: θ = a1 + b1 K [20] second-order polynomial: θ = a2 + b2 K + c K [21] he overall results show r2 values >0.94 and RMSE values 100% What is more, the higher order polynomials lack the physical basis that can be assigned to the square-root model (see above) he fourth-order polynomial should be used, however, if one unique calibration function is to be used for all the tests F Influence of dry density (ρd) and municipal solid waste composi on on me domain reflectometry measurements, water content θ vs electrical permi vity K, in municipal solid waste Samples A and B www.vadosezonejournal.org · Vol 9, No 1, February 2010 167 www.vadosezonejournal.org · Vol 9, No 1, February 2010 168 188.1 −106.0 19.44 620 −13.88 8.328 −1.631 557 0.383 −0.245 0.052 491 −4.226 0.003 0.979 0.000 −0.005 −7.853 0.005 0.976 0.000 0.003 1.994 0.005 0.990 0.000 −0.001 – – 385 434 0.44 0.003 0.954 −0.296 0.112 0.003 0.950 0.121 0.008 0.003 0.972 0.000 0.046 −0.919 0.003 0.973 0.000 −0.004 0.228 0.47 0.007 0.940 −0.218 0.116 0.007 0.934 0.194 0.008 0.005 0.971 −0.001 0.062 −1.147 0.005 0.974 0.000 −0.008 0.461 0.51 0.007 0.987 −0.250 0.122 0.007 0.988 0.162 0.009 0.005 0.990 0.000 −0.003 0.446 0.005 0.990 0.000 0.002 −0.105 CV(B), % – – 13 – – 18 – – 208 815 158 – – 173 187 221 4.150 −279.3 79.55 237 −0.720 42.38 −11.20 228 0.049 −2.407 0.590 221 −1.828 0.003 0.995 0.000 −0.001 10.574 0.002 0.992 −0.001 0.061 −4.824 0.003 0.986 0.000 −0.014 510 – – 208 214 e4 d4 c4 b4 a4 Fourth-Order Polynomial r2 RMSE m3 m−3 Third-Order Polynomial d3 b2 a2 r2 RMSE m3 m−3 a1 r2 Linear regression b1 Second-Order Polynomial c2 RMSE r2 a3 b3 c3 m3 m−3 Sample A 0.44 0.007 0.965 −0.091 0.122 0.008 0.955 0.217 0.012 0.004 0.991 −0.001 0.056 −0.329 0.003 0.995 0.000 −0.008 0.234 0.51 0.003 0.974 −0.287 0.147 0.003 0.971 0.093 0.014 0.002 0.986 −0.001 0.082 −0.812 0.002 0.990 −0.001 0.046 −1.194 0.61 0.007 0.943 −0.310 0.141 0.007 0.937 0.072 0.013 0.004 0.983 −0.002 0.101 −1.206 0.004 0.985 0.000 −0.014 0.477 CV(A), % – – 43 – – 50 – – 23 24 46 – – 288 341 458 Sample B T F Water distribu on in homogeneous and upward we ng RMSE m3 m−3 Effect of Density A separate evaluation of the influence of the materials’ density was made on the upward wetting tests hree diferent densities were considered for each sample Square-Root Regression Dry density RMSE r2 a0 b0 Mg m−3 m3 m−3 Influence of Density, Ini al Water Content, and Rate of Water Content Changes Regression results for trials with step-by-step upward we ng of municipal solid waste Samples A and B at different dry densi es These results correspond to Fig Effect of the Different We ng Procedures he efect of the diferent wetting procedures can be inferred from Table A somewhat surprising result is that for all square-root and linear regressions, the parameter b was systematically lower for the sprinkling and mixing and the density increase experiments, which are called homogeneous wetting procedures in the table Values of the slope b0 of the square-root regression were more than doubled for saturation by upward wetting compared with homogeneous wetting methods (the ratios of slopes b0 found for upward wetting and homogeneous wetting range from 1.97–2.91) In other words, the probe was far more sensitive to θ changes when the sample was wetted homogeneously, indicating that TDR may be used to investigate settling if the only reason for volumetric θ increase is a change in density hese two wetting procedures difer in the distribution of the water around the probe’s rods In upward wetting trials, the water is “pushed up” in large macropores that ofer the least hydraulic resistance he back-pressure applied, however, is low (