Applicability of Time Domain Reflectometry Water Content Measurements in Municipal Solid Waste

Applicability of Time Domain Reflectometry Water Content Measurements in Municipal Solid Waste

D of new MSW

treatment techniques and increased recycling rates,

land-i llland-ing land-is stland-ill 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 landi lls, research has been conducted for

several decades on bioreactor technology Bioreactor landi lls dif er

from conventional landi lls by attempting to control the kinetics of

the biochemical processes occurring within the landi ll, potentially

resulting in a reduction in its post-closure care period h e

opera-tion of a landi ll as a bioreactor includes the addiopera-tion of water to

the waste, mainly in the form of leachate, to enhance natural

bio-degradation processes (e.g., Reinhart and Townsend, 1997; Imhof

et al., 2007) Water availability is considered the limiting factor for

natural biological activity in landi lls (e.g., Reinhart and Townsend, 1997; Zhao et al., 2008, Mehta et al., 2002)

Besides providing water, leachate recirculation of ers environ-mental and economic benei ts in leachate treatment and disposal But the control of water distribution remains essential to success-fully operate bioreactor landi lls Insui cient 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 af ected by reducing the factor of safety for slope stability and potential breakouts of leachate from the landi ll, especially if the liquid pressure on the liner increases signii cantly (Khire and Mukherjee, 2007) Water content measurements within MSW are hence necessary to monitor recirculation and to allow a more ei -cient landi ll operation

Ideally, θ measurement techniques should include character-istics 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 dif erent θ measurement techniques for MSW within landi lls Most of the techniques were material sensitive and the determination of the actual θ required accurate calibration h ere 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,

Applicability of Time Domain Refl ectometry Water Content Measurements in Municipal Solid Waste

Ma hias J Staub,* Jean-Paul Laurent, Jean-Pierre Gourc, and Christophe Morra

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

Envi-ronnement 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.

A : EC, electrical conductivity; MSW, municipal solid waste; TDR, time domain refl ectometry; TDT, time domain transmissivity.

Water content ( θ) and distribu on are important parameters for landfi ll operators because θ is generally considered

a key factor for the degrada on of municipal solid waste (MSW) in landfi lls This study inves gated the applicability

of me domain refl ectometry (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

sen-si vity of TDR was quan fi ed rela ve to MSW composen-si on and densen-sity, the ini al θ and θ distribu on, the electrical conduc vity (EC) of the fl uid, and the rate of change in θ Experiments were conducted on two diff erent 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 eff ect of waste composi on and density appeared to be minor compared with the eff ect of the ini al θ and the θ distribu on around the probes This research opens a way for an eff ec ve use of TDR

in large-scale experiments with MSW.

which is a heterogeneous and time-evolving material, is still missing,

however h is 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 l uid,

and the rate of change in θ h e results should be useful for

improv-ing water content monitorimprov-ing and bioreactor landi ll operation

Literature Summary on Water Content

Measurement and Time Domain Refl ectometry

Types of Water Measurement and Material Characteris cs

h e 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) h is

method is the only available direct method and is both time

con-suming 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

elec-trical permittivity (for the TDR method) Direct θ measurement

using the thermogravimetric method provides the gravimetric water

content, w, of the sample:

w

t

M

w

M

of water is determined from the evaporated water at a given

tempera-ture 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, dei ned by

w

t

V

V

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,

under compression were conducted to assess this specii c volumetric

increase in θ

To characterize the materials tested, three other parameters

are used (Stoltz, 2009):

(i) the material’s bulk density, dei ned as

t

h

t

M

V

(ii) the material’s dry density, dei ned as

d

t

V

−

and (iii) the material’s porosity, dei ned as

1

n

V

constitu-tive solid density of the particles

Principle of Time Domain Refl ectometry Measurement

h e TDR method was i rst applied to determine the θ of soils

for irrigation scheduling and hydrologic applications (Topp et al.,

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 landi ll-scale experiments (van Praagh

et al., 2007; Zhao et al., 2008; Breitmeyer et al., 2008)

Time domain rel ectometry 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 h e signal produced by the TDR generator is sent through the probe’s head inside the porous medium and is rel ected twice: once as it enters the rods of the probe and again as it reaches the end h e resulting waveform is collected and its travel time, Τ, along the waveguide

is calculated as the dif erence between the times of these two main rel ections

Basic Equa on of Time Domain Refl ectometry

h e corresponding wave propagation speed, v, is calculated as follows:

2L v T

where L is the probe’s length (the factor 2 accounts for a round trip)

h is propagation speed is related to the relative electrical

c v K

Combining Eq [6] and [7] leads to the TDR basic equation (Fellner-Feldegg, 1969):

2

2

cT K L

⎛ ⎞⎟

⎜

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 inl u-ence of the coating Hu-ence, an intermediate calibration between

was required For this calibration, the TDR probe was immersed

in media of known electrical permittivities h e procedure is not detailed here; however, the results of this calibration are presented briel y below because they are required to interpret our results in terms of the electrical permittivity

Calibra on between Rela ve Electrical Conduc vity and the Volumetric Water Content

To deduce the volumetric water content from the TDR-measured K value, physically based models or purely empirical formulas are applied (Weiler et al., 1998) Two dif erent approaches for correlating θ with measured electrical permittivities are consid-ered: 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 = 1 is the sum of the travel times in each phase of the material: solid particles (s), liquid solution (w), and gaseous phase (g) h is can be written as

s w g

permit-tivity of the gaseous phase Finally, since the contribution of the

et al (1998), Gong et al (2003), or Masbruch and Ferré (2003):

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

tempera-ture dependent Equation [9] can be generalized considering that

the K exponent can be dif erent from 0.5 (the square root) h is is

then called the α model (Ponizovsky et al., 1999):

By neglecting the gaseous-phase contribution, Eq [11] will thus

be reduced to

Most researchers have obtained α values ranging roughly from 0.4

to 0.7 when i tting 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

dielec-tric relaxation ellipsoids inside the material and therefore to its

structure (Zakri et al., 1998)

On the other hand, the empirical approach consists in i tting

parameters of mathematical expressions to calibrate the relationship

between θ and K h e 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):

2

3

0.0000043

K

When applying this model to MSW by simple humidii cation,

how-ever, Li and Zeiss (2001) found dif erent θ values that could be due

to the MSW’s mixed composition, which is signii cantly dif erent

from that of soil h e most commonly used functions for MSW are

0 0

(Masbruch and Ferré, 2003) in experiments performed with time

domain transmissivity (TDT) probes,

(van Praagh et al., 2007), and

(Li and Zeiss, 2001)

Literature Review on the SensiƟ vity of the Time Domain Refl ectometry Method

Time domain rel ectometry measurements are sensitive to many factors Changes in bulk EC inl uence the TDR measure-ments due to energy losses, which might attenuate the signal and eventually prevent detection of the second wave rel ection (Li and Zeiss, 2001; Staub et al., 2008) Concerning the liquid phase, its electrical permittivity is supposed to increase with its electrical

proposed the following calibration model, derived from Eq [10],

a

calibration curve is altered by an of set Temperature has an impact

(Grellier et al., 2006) To mitigate the EC ef ects, 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 l uid inl uences measurements even with coated probes,

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 signii cant inl uence on the TDR response when the probes are coated In soils, several researchers have shown experi-mentally that the soil texture inl uences 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 inl uence on the absolute measurement of θ, but it does not impact relative θ measurements

Other factors are also known to inl uence the electrical per-mittivity 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 mea-surements; nevertheless relative measurements with coated probes may of er a potential accuracy comparable to other nondestructive

θ determination techniques such as neutron scattering or geophysi-cal techniques (Imhof et al., 2007)

Materials and Methods

Experimental Cell and Time Domain Refl ectometry Probe

h e 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

Experimental Cell

h e experimental cell consisted of a rigid transparent poly-methyl methacrylate (PMMA) cylinder of 20-cm inner diameter, D; the upper and lower cell supports were made of polyvinyl chlo-ride (PVC) h e inner volume of the cell ranged between 9.4 and 12.0 L depending on the vertical position of the upper cell support

along the threaded steel rods (h, ranging from 0.31–0.38 m) h e

two supports could be moved like a piston to allow modii cation of

the sample’s volume and density between two measurements h e

cylinder was i lled with the test medium and the coated TDR probe

was inserted h e schematic diagram of the cell is given in Fig 1

Time Domain Refl ectometry Probe

h e TDR probe used in this research was a commercially

avail-able CS605 three-rod probe (length L, 30 cm; rod diameter, 0.5

cm) from Campbell Scientii c (Logan, UT) h e distance between

the rods is 1.8 cm h ese 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 h e probes

were coated by hand with heat-shrinkable, initially 8-mm-diameter,

polyolei n tubing h e TDR probe’s measurement volume was

veri-i ed to be veri-included veri-in the cell’s volume (Fveri-ig 1)

Signal processing and collection was done with a TDR100

from Campbell Scientii c (Logan, UT) and distributed to the

probe by a i rst-level SDMX50 multiplexer (Campbell Scientii c)

A 10-m-long coaxial cable was used to connect the probe h e TDR

setup was managed by PCTDR sot ware (also from Campbell

Scientii c) via an RS232 interface connected to a computer h e

waveform collection and response time calculation were stored on

a CR1000 datalogger (Campbell Scientii c) during the experiments

h e probe was inserted at er 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 coni nement 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 inl uence 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

Characteris cs of the Tested Media

Two dif erent shredded fresh MSW materials, A and B,

col-lected from French sanitary landi ll 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 l uid used for calibration Figures 2

and 3 show the aspect of the materials; their characteristics and

composition are given in Tables 1 and 2 The waste fractions were sorted according to the waste categories given in the French MODECOM method (Ademe, 1993)

h e gravimetric water content, w, of the materials was deter-mined using the thermogravimetric method: samples of 2.5 kg each were oven dried at 105°C to constant mass h e 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 back-calculated at er each test

h e major dif erence between the two materials is that Sample

A was a coarse-graded typical French MSW, whereas Sample B was

F 1 Schema c diagram of the experimental me domain refl

ec-tometry (TDR) cell (not to scale).

F 3 Municipal solid waste Sample B.

F 2 Municipal solid waste Sample A.

T 1 Physical characteris cs of the tested materials.

Characteris c Sample A

waste

Sample B waste

Sand–gravel mixture

Maximum par cle size (dmax), mm 70 40 20 Ini al dry density (ρd), Mg m−3 0.41 0.39 1.55 Ini al cons tu ve solid density ( ρc),

Mg m−3

Ini al gravimetric water content

(w), kg kg−1

Ini al volumetric water content

i ne 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

Methodology

Each experiment with a MSW sample was conducted within

a maximum of 3 to 4 d to limit biochemical changes in the

mate-rial h e experiments were run between December 2007 and June

2008 with dif erent procedures to establish the TDR sensitivity

h e procedures are detailed below and summarized in Fig 4 and

Table 3 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 ef ect of their composition and

struc-ture According to Eq [5], comparing the materials on their dry

B were very close (see Table 1) Some of the tests also included a

spe-cii c evaluation of the bulk density’s inl uence on the measurements

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 homo-geneous h e ef ect of this heterogeneity is discussed below

h ree wetting processes were assessed, representing dif erent wetting conditions that may be found in landi lls: (i) gradual wet-ting, 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) Step-by-Step and Con nuous We ng by Upward

Infi ltra on under Constant Head

h e material was wetted with water and later drained through the drainage pipe to return to i eld capacity h is procedure was done in steps, and each step consisted in the addition (during wet-ting) or removal (during drainage) of 100 to 250 mL of liquid, depending on the sample h e addition and removal of liquid was made via the l exible pipe shown in Fig 1 At erward, the θ was kept constant for 15 min to enable a relatively homogenized water distribution, and TDR measurements were recorded every minute before a new step was started

h e arithmetic average of the last i ve readings was taken to represent the actual TDR measurement Given that the added or removed volume of l uid 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

T 2 Composi on of the municipal solid waste materials.

Waste component Composi on according to MODECOM

Sample A waste Sample B waste

———————— % by wet wt ——————

T 3 Summary of the diff erent we ng procedures for municipal solid waste (MSW) Samples A and B and a sand–gravel mixture.

Steps at constant water content

Dura on of each step 15 min at constant θ 1–2 h of con nuous we ng 15 min at constant θ 15 min at constant θ

Densi es tested per experiment 3 1 (middle value) 1 (middle value) 4 (density steps)

F 4 The diff erent we ng pro-cedures; θ is the water content.

Alternatively, a continuous wetting without steps was

consid-ered, simulating the fast wetting of the material due to a hydraulic

gradient h is shorter “continuous” trial was then compared to

the step-by-step wetting In total, 18 dif erent step-by-step

wet-ting–drainage cycles were performed on the MSW Samples A and

B corresponding to three dif erent densities of both materials (see

Table 3) Each test consisted of three successive wetting–drainage

cycles Continuous wetting tests were conducted for one dry

den-sity of each sample, with three successive wetting–drainage phases

h is 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

Sprinkling and Mixing We ng Procedure

A dif erent wetting method that guarantees a more

homoge-neous distribution of θ within the sample was tested h e material

was placed in the cell for a i rst series of initial measurements, and

then taken out to be saturated by sprinkling water on the material

in a tank h e sample was then mixed by hand to ensure a

homoge-neous distribution of water

As the material was removed and replaced at er every trial, its

structure was modii ed h erefore, the procedure was repeated three

times at the same θ to evaluate the inl uence of the structure of the

sample on the TDR measurement (see Table 3) Predetermined

vol-umes of liquid were added, ranging from 400 to 800 mL depending

on the tested medium h e TDR measurements were then recorded

every minute for 60 min before the material was mixed again h e

actual TDR measurement was represented by the arithmetic

aver-age of all the readings excluding the i rst i ve measurements to avoid

transient conditions Each experiment was completed within 4 d

while recording one θ value per day

We ng by Compressing the Sample

A specii c test with varying bulk density was also performed

on the MSW At er 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

Dif erent 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 4 and Table 3 summarize the dif erent wetting

proce-dures applied to all the tests in the experimental cell

Experiments with Diff erent Liquids

To investigate the ef ect of the l uid’s type and conductivity on

TDR measurements, an inert material (the sand–gravel mixture)

prepared by adding commercially available sea salt to tap water to

prepare approximately 3 L of salt water before each trial h e ef ect

of temperature on the EC was not considered, as the water used for

the tests was i rst warmed to 25°C and as the tests were performed

in a room with thermostatic regulation at 25°C h e calibration of

the linear relationship between NaCl salinity and the EC of the

l uid as well as the verii cation of the dependence of conductivity

on temperature were made separately, but are not presented here

Five dif erent upward wetting experiments were performed with

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

h e calibration results of the probe’s intrinsic relationship

second-order polynomial (Fig 5; Eq [18]):

2

h is experimental work was done separately (Laurent, unpublished data) h e coei cient of determination for this calibration was very

polynomi-als showed poorer correlation For instance, for a linear relationship,

times measured in the waste material ranged from 7 to 9 ns and hence fell into the range of calibration of Eq [18], which was there-fore applied to determine the electrical permittivity of the tested medium for all the following tests

Eff ect of the Fluid’s Conduc vity

h e ef ect of the l uid’s conductivity and type was evaluated

in the sand–gravel inert material In total, six dif erent trials were conducted with water at dif erent NaCl concentrations and

results indicate that for a given θ, the higher the EC, the higher the

F 5 Calibra on of the rela onship between the electrical permi

v-ity (K) and the apparent travel me (T) for the coated CS605 probe.

F 6 Infl uence of liquid electrical conduc vity (EC) on the me domain refl ectometry 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.

travel time h e EC curves for values ≤10 mS cm−1 were grouped,

however; there seemed to be no major inl uence of EC beyond the

permittivity h is ef ect was also described by Li and Zeiss (2001),

uncoated probes, a high EC of the l uid 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

h e results in Fig 6 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 coni rming the results of other

researchers (Bouyé et al., 2005) Salt water was also used for

cali-bration 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

Compara ve Results for the Municipal Solid Waste Materials

Global Calibra on for Municipal Solid Waste

The results of the different trials are shown in Fig 7 For

the upward wetting procedures (step-by-step and continuous

wettings), the average measurements of the second and third

wet-ting–drainage cycles were considered to avoid the ef ects of the

material’s wetting history (see below) Each data point for the

sprin-kling and mixing tests represented the average of three replicates

Compression trials were performed only once, so the corresponding

data points were not replicated h e 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

i rst wetting–drainage cycle did not drain the sample completely,

as water was held by capillary retention

h e model proposed by Topp et al (1980) was also included

for comparison purposes h e 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 specii c 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

cali-bration points A similar regression with a third-order polynomial

third-order polynomial found for MSW:

2

3

0.066 0.0301 0.00085 0.0000094

K

+

[19]

with the polynomial of Topp et al (1980) (Eq [13]) h e RMSE

estimation using Topp’s polynomial for MSW could lead to an under-estimation of the true θ in the low and high range of permittivities

h is means that Eq [19] may be used within our calibration range,

compa-rable 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 ef ects on the calibration equations (below)

Calibra on for the Diff erent Experiments and Comparison with Previous Work

To compare the calibration functions for each wetting condi-tion, dif erent regressions were performed, including square-root,

(square-root regression), [15], and [16] (third- and fourth-order polynomials, respectively) and additionally to

1 1

first-order linear regression: θ = +a b K [20]

2

second-order polynomial: θ = +a b K+c K [21]

experi-ments, which indicates signii cant i ts for all wetting conditions (Table 4) h e consistency of the results is systematically evaluated

by calculating the CV, which gives a normalized measure of disper-sion (CV = SD/m, where SD is the standard deviation and m is the average of the regression parameters)

For the square-root and linear regressions, the i tting

another, and it seems impossible to propose a unique value h is may suggest that TDR measurements are able to quantify variations in θ but fail to accurately determine the absolute θ For regressions with

a second-order polynomial or above, the variability of the i tting parameters was too high to enable interpretation of the consistency

of the results h is is why reference is made below to the parameters

to best represent the shape of the calibration curves

For the square-root and some polynomial regressions on each series of calibration data for the respective wettings, some param-eters were compared with previous literature data h e results of

0.045 to 0.156 and showed relatively consistent values It was not

variability of the results is large In fact, Masbruch and Ferré (2003)

F 7 Overall results of me domain refl ectometry measurements,

water content θ vs electrical permi vity K, in municipal solid

waste (MSW) Samples A and B using upward step-by-step we ng,

con nuous we ng under constant head, sprinkling and mixing

we ng, and compression (we ng by increasing the sample’s

density); ρd is dry density.

performed a square-root regression under upward controlled ini ltration, and therefore the constant head wetting results obtained here could be compared to their results using TDT

2003) h ese values are consistent with the upward wetting results presented in Table 4 When modeled by a third-order polynomial, the relationship between K and θ becomes

high for comparison, and the increased number of i tted parameters contributed to the

parameters Similarly, Li and Zeiss (2001) found values ranging from 0.99 to 1.00 based on TDR measurements in the dif erent constituents of MSW As mentioned above, it is

variability, ot en >100% What is more, the higher order polynomials lack the physical basis that can be assigned to the square-root model (see above) h e fourth-order polynomial should be used, however, if one unique calibration function is to be used for all the tests

Eff ect of the Waste Composi on

It can be inferred from Table 4 that for all square-root and linear regressions, the parameter b, which characterizes the general shape of the curves, is smaller for Sample B than for Sample A h is tends to indicate that Sample B shows more sensitivity than Sample

from Samples A and B range from 1.19 to 1.76, indicating that waste characteristics did

af ect the TDR measurements

h e dif erence may be explained by the high organic content of Sample B, as organic matter usually lowers the electrical permittivity As θ increases, the dif erence in electrical permittivity also increases, thus resulting in a higher slope for Sample B When considering only the upward wetting trials, two distinct groups corresponding to each sample can be inferred (Fig 8), the main dif erence being the dif erent initial θ of each sample, result-ing in a dif erent of set in the curves h is suggests again that TDR is not believed to be relevant for absolute θ measurements in MSW, and the dif erences in intercepts cannot be correlated to the dif erent densities of the samples Waste composition has an inl uence on TDR response, as dif erent materials may have dif erent electrical permittivities; however,

it may be dii cult to conclude from only two dif erent MSW compositions Comparative tests with other types of waste should be conducted to investigate the inl uence of waste composition on TDR measurements, as suggested by others (Li and Zeiss, 2001)

a0

b0

a1

b1

a2

b2

c2

a3

b3

c3

d3

a4

b4

c4

d4

e4

3 m

3 m

3 m

3 m

3 m

F 8 Infl uence of dry density ( ρd) and municipal solid waste composi on on me domain refl ectometry measurements, water content θ vs electrical permi vity K, in municipal solid

waste Samples A and B.

Eff ect of the Diff erent We ng Procedures

h e ef ect of the dif erent wetting procedures can be inferred from Table 4 A

some-what 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

experi-ments, which are called homogeneous wetting procedures in the table Values of the slope

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

h ese two wetting procedures dif er in the distribution of the water around the

probe’s rods In upward wetting trials, the water is “pushed up” in large macropores that

of er the least hydraulic resistance h e back-pressure applied, however, is low (<1 m

water column or 10 kPa), and the liquid stays mostly in the large pores without i lling

the small pores When the sample is wetted by hand or compressed from i eld capacity, it

can be assumed that some of the water might reach very small pores as a result of a more

ef ective wetting of the waste particles’ surface (when the sample is mixed and sprinkled)

or of local compressions (when the sample’s density is increased) h e two procedures do

not wet the waste medium in the same way: when the sample is wetted homogeneously,

the water distribution is supposedly homogeneous, whereas a discontinuity of water

phase may exist when the sample is ini ltrated upward with a constant head (Fig 9)

h e dif erence in TDR response for these two wetting procedures is rather

unex-pected for TDR measurements because the water distribution in soils is shown not to

inl uence the TDR response (Topp et al., 1980; Gong et al., 2003) Yet this discrepancy

cannot be explained by the bound water ef ect, described for clayey soils by Gong et al

(2003) Indeed, the presence of bound water can lead to lower K values and an

underes-timation of the sample’s θ h is has been demonstrated with clay particles, which, unlike

MSW particles, have very small diameters and an electrically charged surface It is

sup-posed that this discrepancy here comes from the dif erent lubrication of the waste’s i ne

materials around the TDR rods h e electrical connection between the rods and the

homogeneously wetted medium can be assumed to be better all along the rods, and the

relative contribution of the dif erent phases’ electrical permittivity is hence altered (Eq

[9]) h is aspect is addressed below when discussing how water distribution and the

wetting history of the sample inl uence the measurements

Infl uence of Density, Ini al Water Content, and Rate of Water Content

Changes

Eff ect of Density

A separate evaluation of the influence of the materials’ density was made on

the upward wetting tests h ree dif erent densities were considered for each sample

F 9 Water distribu on in homogeneous and upward we ng T

a0

b0

a1

b1

a2

b2

c2

a3

b3

c3

d3

a4

b4

c4

d4

e4

3 m

3 m

3 m

3 m

3 m

Calibration curves appear on Fig 8, and Table 5

sum-marizes the regression results To compare the results,

regressions obtained for dif erent densities were again

compared None of the tests showed a clear trend for

Masbruch and Ferré (2003) found that the density and

results also showed poor correlation Correlation was

shown here) h ese results indicate that dry density seems

more reliable than bulk density to evaluate the behavior

of the sample, as it is more representative of its porosity

h e theoretical inl uence of bulk density on the

inter-cept of the square-root calibration function, as described

by Gong et al (2003) for soils, was not perceived here, as

low In agreement with our results, other researchers have stated

that the inl uence of density was relatively small for soils (Ledieu

et al., 1986) Waste density did not appear to drastically af ect the

TDR response Indeed, there was no clear trend concerning the

inl uence of density with these data Given that the range of tested

stud-ies are necessary to coni rm the independence of density for relative

TDR measurements in MSW

Eff ect of the Material’s Structure

h e sprinkling and mixing tests were repeated three times

at the same θ value Since the sample was taken out, mixed, and

replaced in the cell repeatedly, this would eventually result in a

modii ed structure h e variation in the TDR response due to this

change in structure was relatively low; the CVs of the electrical

permittivities found for the three replicates at each θ did not exceed

5% h is agrees with the fact that dry density was not found to have

a signii cant inl uence on the measurements (see above), as dry

den-sity was directly correlated to the material’s poroden-sity (both materials

state whether structure has an inl uence on TDR measurements or

not, as both MSW materials considered here were shredded wastes

h e waste’s structure could have a great inl uence on measurements

when considering raw MSW, which has a very wide range of pore

diameters h e probe’s relatively small dimensions may hinder

mea-surements in raw MSW, making the demonstration of the inl uence

of macroscopic elements on TDR measurements more dii cult

Eff ect of the Material’s We ng History

For the upward wetting experiments, three wetting–drainage

cycles were completed for each test (see above) At er the i rst

wet-ting from the original state, the sample was drained; however, some

water was retained due to capillary ef ects in the waste material and

also due to the transfer of water to the micropores Subsequent

wet-ting–drainage cycles therefore had a dif erent initial θ h is allowed

comparing the measurements made on an initially dry sample to

those made on wetter materials Figure 10 shows the corresponding

calibration curves, where only two dif erent trials are shown

h ere were two dif erent trends: the i rst wetting was detected

dif erently by the TDR than the next wetting–drainage cycles (Fig

10) From the second wetting on, the TDR measurements were very consistent (including the third cycle, not shown on the graph) h e regression results (not shown here) also showed dif erent behavior for the i rst wetting and for all following drainages and wettings,

the regression results given in Tables 4 and 5 for upward wetting procedures correspond to the averages of the second and third wet-ting–drainage cycles For the square-root regression, the ratios of the slopes of the i rst to the following wettings were 0.61 and 0.74 for Samples A and B, respectively (Fig 10), i.e., the slopes of the second and third wettings were 26 to 39% lower

This could be explained by the fact that the first wetting resulted in shorter apparent wave travel times (and hence electri-cal permittivities) because part of the energy was rel ected by the wet–dry interface very quickly In fact, it was during the i rst wet-ting that the contrast in θ below and above the ini ltrawet-ting front was the highest Later on, during the i rst drainage and the follow-ing cycles, the medium was already partially wetted and a certain quantity of water could not be drained by gravity, being absorbed

by the medium as indicated in the curves in Fig 10

Eff ect of the Rate of We ng for Upward We ngs

h e ef ect of the rate of water ini ltration was investigated by comparing the results obtained for step-by-step wetting and con-tinuous wetting tests under constant head (see above) Except for

a clear vertical shit when comparing both curves, which can be explained by the dii culty of TDR to measure absolute θ values, there was no obvious dif erence between the calibration curves (Fig

F 10 Infl uence of the number of we ng cycles on me domain refl ectometry measurements, water content θ vs electrical permi vity K, in municipal solid

waste Samples A and B; S1 and S2 refer to the fi rst and second we ngs, and D1 and D2 to the fi rst and second drainages; ρd is the dry density.

F 11 Infl uence of the we ng rate on me domain refl ectometry measurements in municipal solid waste Samples A and B using upward step-by-step we ng and con nuous upward we ng.