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M. Aminul Haque*

A Statistical Comparison of Mathematical Modelsfor Heavy Metal Leaching Phenomena from

Solidified Landfill Waste MortarDOI 10.1515/cppm-2015-0046

Received October 28, 2015; revised December 30, 2015;

accepted December 30, 2015

Abstract:In this research, landfill solid waste was solidified

as cement-waste matrix to protect the environment from

excessive intrusive contaminants like Fe, Cu and Ni and

minimize the waste load. Within this context, ingredients

of cement-waste mortar were characterized to determine

their physical properties. Long-term feasibility study was

conducted to examine the metal contents stabilization by

employing the standard mass transfer-leaching test. The

cumulative leaching concentration of Fe, Cu and Ni were

found to be 1.29 mg/l, 0.18 mg/l and 0.63 mg/l respectively

up to 180 days static leaching test period that satisfied the

surface water quality standard. Mechanical strength test

was also conducted to characterize the solidification

technique. Five well-established non-linear mathematical

Models were conducted to evaluate the mechanisms of Fe,

Cu and Ni migration. Goodness of fit statistical parameter

analysis and visual examination indicated that polynomial

equation Model is better for explaining the experimentallygenerated data. Moreover, parameter of polynomial equa-

tion was extended from five to nine for examining the best

calibration profile to the observations. In context of slope-

intercept and visual observation analysis resulted that poly-

nomial equation based Model bearing five parameters with

0.5 power interval of each parameter describes the leaching

phenomena quite similar with the experimental observa-

tions whereas goodness of fit parameters and information

criterion shows reverse. It was found that the studied immo-

bilized landfill waste mortar have acceptable mechanical

performance that confirms to be used as construction

material.

Keywords: landfill waste mortar, leaching phenomena,

fitted models, statistical analysis, visual examination

1 Introduction

Landfill leachate is a significant source of ground water

pollution [1] that formed by decomposition of municipal

solid waste [2, 3] and excess rainwater percolating through

the waste layers [1, 2]. Leachates are highly concentrated

complex effluents which contain dissolved organic matters;

inorganic compounds, such as ammonium, calcium, mag-

nesium, sodium, potassium, iron, sulphates, chlorides andheavy metals such as cadmium, chromium, copper, lead,

nickel, zinc etc.; and xenobiotic organic substances [1, 46].

Especially presence of heavy metals in leachate have poten-

tial impact on human health and the quality of environment

having the greater possibility of surface and ground water

pollution [7].

The long-term safe landing of the solidified hazardous

waste is an important request for keeping the surrounding

environment more secure for the coming generations [8].

Therefore, solidification/stabilization (S/S) techniques

are used to minimize the immense pressure of waste load

in landfill sites and leachate production by reducing themobility as well as solubility of contaminants in wastes

and converts them into chemically inert form [9]. In S/S

process, the immobilization of the contaminants is achieved

by formation of chemical bonds and/or by physical encap-

sulation. This ensures the reduction of the quantity and

release speed of contaminants to the environment to a

large extent [10] and avoids a back release of contaminants

from the matrix during aggressive conditions of storage and

disposal [11]. Macroencapsulationworks in S/S by physically

entrapping contaminants within a large structural matrix

whereas microencapsulation entraps contaminants withinthe crystalline structure of solidified matrix at a microscopic

level [12] and incapable of chemical interactions [9].

Cementitious materials are widely used in waste man-

agement systems with different aims and requirements for

long-term performance. Both conventional and novel

cementitious materials are used to create reliable immobi-

lizing elements for safe storage and disposal of wastes.

Conventional cementitious materials such as Portland

cement and composite cements with supplementary cemen-

titious materials in the form of fly ash, iron blast furnace

*Corresponding author: M. Aminul Haque, Department of Civil

Engineering, Leading University, 5th Floor, Rangmahal, Bandar

bazar, Sylhet-3100, Bangladesh, E-mail: [email protected]

Chem. Prod. Process Model. 2016; aop

Authenticated | [email protected] author s copy

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added an additional conception of leaching phenomena.

The last stage of contaminant leaching mechanism

from waste matrix is the slow portion of dissolution

control the leaching phenomena. Moreover, the dissolu-

tion of materials from the surface proceeds faster that

the diffusion through the pores. Both the rapid and

slow portion of dissolution will result in the release ofhighly soluble materials but it will not cause depletion

of material.

For interpreting the contaminants leaching mechan-

ism from waste matrix, some researchers have been used

different non-linear Models. To identify the long term

leaching phenomena, some researchers [1720] provided

a Fickian diffusion based equation that is,

f =

Pana0

=2S

ffiffiffiffiffiffiffiffiffiffiDetn

p

V

ffiffiffi

p (1)

Where f = Cumulative fraction leached of heavy metals. Decan be calculated from the slope of an/A0 versus tn

1/2,

according to the following relationship:

De=

4 m2 V

S

2(2)

Where, m=

Pana0ffiffiffitn

pFrom eqs (1) and (2),

f = m

ffiffiffiffiffitn

p (3)

To generalize the Model equation (3) can be expressed as,

f = A0 + A1t1=2 (4)

As the diffusion rate gradually slow down with the

leaching period elapsed. Therefore, if the diffusion

path becomes longer, diffusion rate is not a controlling

factor in any of the leaching intervals. Some researchers

[2123] adopted polynomial equation based a semi-

empirical method to overcome this problem because

polynomial equation describes the long-term leaching

characteristics of a waste component. In this Model,

the cumulative amount of contaminant leached isexpressed by:

f = A0+ A1t1=2 + A2t (5)

Plecas [24] applied polynomial equation based Model up

to its fourth terms of this Model to observe the leaching

behavior of 137Cs from radioactive waste formation,

f = A0+ A1t1=2 + A2t + A3t

3=2 (6)

Similarly, Plecas and Dimovic [25] and Plecas and

Dimovic [26] used same Model up to its fifth terms for

characterizing the immobilization of industrial waste within

cement-bentonite clay matrix and transport phenomena of60Co from radioactive material respectively,

f = A0+ A1t1=2

+ A2t + A3t3=2

+ A4t2

(7)

In the current study, concentration of five heavy

metals like Fe, Cu, Ni, Cr and Cd were examined in land-

fill decomposed solid waste and effluent leachate. It was

observed that concentration of Fe, Cu and Ni exceeded

the Bangladesh standard [27]. Therefore, the aims of

present work is oriented to characterize the leaching

phenomena of Fe, Cu and Ni from waste matrices with

controlling leaching mechanism and predict the long-

term leaching phenomena by applying various non-linear

mathematical Models such as diffusion, polynomial,

logarithmic, exponential and power based equations.The performance of the prediction Models were measured

based on some statistical goodness of fit indicators with

the accuracy of 95 % confidence interval of the estimated

Model parameters.

2 Materials and methods

2.1 Experimental approach

In the current study, solidified waste mortar (SWM) speci-

men was prepared using stabilizing binding materials

like Ordinary Portland cement (OPC) and fine aggregate

such as sand and landfill decomposed solid waste

(LDSW). OPC and sand were collected from locally avail-

able areas. LDSW was collected from Matuail Sanitary

Landfill Site (MSLS), Dhaka, Bangladesh and prepared

through air drying, blending and sieving at room

temperature (25 1 C). Concentration of selected heavy

metals in LDSW and effluent leachate samples were

determined using flame emission atomic absorption spec-

trophotometer (AAS) (Spectra AA Varian). Physical char-

acteristics of specimen ingredients were measured

following the ASTM standard methods that are men-

tioned in Figure 3. Cubical specimen having the mold

dimensions of 5cm5cm5cm was prepared whereas

in each specimen 30 % of the total volume of fine aggre-

gate was replaced by LDSW [28]. Standard leaching

test method ANS 16.1 was used to observe the Fe, Cu

and Ni leaching phenomena from solidified waste form.

M. A. Haque: Statistical Comparison of Mathematical Models 3



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Leaching tests were performed for 17, 14, 21, 28, 56, 90

and 180 days immersion period and results were recordedin terms of cumulative release in the curing leachant

versus curing ages. The compressive strength test, given

as applied maximum load divided by the cross-sectional

area of a specimen, was performed to confirm the struc-

tural integrity of solidified waste matrix. All tests were

performed three times to ensure the statistical signifi-

cance of the experimental data. Average value of each

test was presented in this study along with the standard

deviation. The overall experimental and analytical work-

ing steps are briefly depicted in Figure 3.

2.2 Fitting of the leachate Models

Five different well-known non-linear mathematical equa-

tion based Models were fitted as leachate Model to cali-

brate for demonstrating the leaching mechanism and

justify against the experimental observations showing

Collection of SWMBs

ingredients.

Collection of

effluent leachate

from landfill

leachate pond.

Measurement of heavy

metal concentration in

effluent leachate using

AAS.

Comparison of results

with the inland surface

water quality standard

[27].

Collection of

DSW

Digestion by

Aqua-regia

Solution (1:3).

Measurement of heavy

metal concentration in

LDSW sample using AAS.

Collection

MSLS

Sand and LDSW:

1. pH (Hevi-sand-TP283)

2. Dry density (ASTM-D2937-00)

3. Bulk density (ASTM C29)

4. Specific gravity (ASTM 128-15)

5. Porosity (Bowels, 1997)

6. Water content (ASTM D2216-80)

7. WAC (ASTM C 128-88)

8. FM (ASTM C136 96a)

OPC:

1. Fineness (ASTM C184-94)

2. Consistancy limit (ASTM C187)

3. Initial settting time (ASTM C150)

4. Final setting time (ASTM C150)

5. Specific gravity (IS -2720)Physical

property

analysis

1. Analysis of

oxides

2. Compressive

strength test at 3

and 7-day.

Grinding

Sieve

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heavy metal migration phenomena from SLWM. Fitted

non-linear Models are presented below:

1. Diffusion equation based Model (Generalize form):

f = A0 + A1t1=2 (4)

2. Polynomial equation based Model:

f = A0+ A1t1=2 + A2t (5)

3. Logarithmic equation based Model:

f =a +b l n t (8)4. Exponential equation based Model:

f =aebt (9)

5. Power equation based Model:

f =atb (10)

2.3 Parameter extension of well-fittedleachate Model

In this study, parameter of polynomial equation based

Model was extended in different longer terms with 0.5

and 0.25 intervals as trial basis using the least squares

procedure for demonstrating the best fit Model of

metal leaching mechanism in a better way with high

accuracy. The study adopted the following fitted Model

options such as Polynomial extended model one (PEMO),Polynomial extended model two (PEMT), Polynomial

extended model three (PEMTh), Polynomial extended

model four (PEMF), Polynomial extended model five

(PEMFv) and Polynomial extended model six (PEMS) as

trial basis to well calibrate with the experimental obser-

vations of Fe, Cu and Ni releasing data from SWM with

curing ages:

f = A0+ A1t1=2 + A2t 5 PEMO

f = A0+ A1t1=2 + A2t + A3t

3=2 6 PEMT

f = A0+ A1t1=2 + A2t + A3t3=2 + A4t2 7 PEMThf = A0+ A1t

1=4 + A2t1=2 + A3t

3=4 + A4t1 11 PEMF

f = A0+ A1t1=4 + A2t

1=2 + A3t3=4 + A4t

1 + A5t5=4 + A6t

3=2

12 PEMFv

f = A0+ A1t1=4 + A2t

1=2 + A3t3=4 + A4t

1 + A5t5=4

+ A6t3=2 + A7t

7=4 + A8t2

13 PEMS

The estimation of Model parameters was done following

non-linear techniques using MATLAB (R2015a).

2.4 Evaluation of fitted leachate Modelscalibration

Well calibration between the simulated data from fitted

Models and experimentally generated data from leaching

(Fe, Cu and Ni) test were evaluated using the most commonly

used statistical parameters like goodness of fit indicators and

information criteria. These are presented in Table 2.

3 Results and discussions

3.1 Heavy metal concentration in DSWand leachate samples

In the current study, concentration of five heavy metals like

Fe, Cu, Cd, Ni and Cr in LDSW and effluent (Outflowing to

the surface water body) leachate samples collected from

MSLS were examined. The average concentration of tested

heavy metals are presented in Table 3. In DSW, the study

observed that Fe was the highest concentration about

11,233.35 mg/kg at MSLS. Similar results of Fe concentration

was observed in landfill waste by Oluyemi et al. [42],

Mamtaz and Chowdhury [43] and Esakku et al. [44] about

4,130.02 mg/kg, 9,600 mg/kg and 20,485 mg/kg respec-

tively. Cu content was found greater about 260.675 mg/kg

than the observation of Esakku et al. [44], almost 169.9 mg/

kg. Moreover, the study revealed the significant level of restof the three tested metals such as Ni, Cr and Cd contents in

DSW as compared to the observations of Adjia et al. [45],

Mamtaz and Chowdhury [43] and Esakku et al. [44].

Though the average concentration of Cd and Cr in

outflowing treated leachate samples were observed to be

safety limit (Table 3) according to the BECR [27], the

contents of Fe, Cu and Ni were found not safe for disposal

to the near surface water body at landfill site, since they

exceed the Bangladesh standards that may be pointed

out a potential risk of metals entrance into food chain

through overflow of landfill site due to heavy rainfall

and leachate disposal to the surrounding environment.

Therefore, solidification/stabilization of landfill waste

may be a promising solution to prevent the metal intru-

sion and contamination into the environmental cycle.

3.2 Characteristics of SWM ingredients

As the LDSW was used as the partial replacement of sand in

the mortar specimen, physical properties of sand and LDSW




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were analyzed in mix condition to measure the values withquality parameters and the level of effectiveness and effi-

ciency for using waste as fine aggregate in constructional

purposes. The study revealed that water absorption capa-

city and moisture content in mix condition of study sample

were slightly higher due to the presence of LDSW. Waste

sample was organic matter which generally absorbs higher

water amount than inert material like sand. Otherwise, rest

of the examined parameters showed quite similar results

with the reported studies. Experimental results of SWM

ingredients characteristics are represented in Table 4.

Table 3:Concentration of heavy metals in DSW and effluent leachateof MSLS.

Heavy

Metal

DSW (mg/kg) Effluent

leachate

(mg/l)

Inland surface water

quality standard

(mg/l) []

Fe ,. . . . .

Cu . . . . .

Ni ,. . . . .

Cr . . . . .

Cd . . . . .

Table 2: Goodness of fit indicators for the selection of fitted model.

Parameter Expression Reference

Correlation coefficient (r) r= n

Pxy

Px Py ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

nP

x2 Px 2q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin Py2 Py 2q []

Coefficient of determination (R-squared) R2 =Pn

i=0 Oi

O pi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni=0

Oi O 2q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i=0 pi p 2

p0@ 1A2

; oi = Observed data pi = Predicted data [,]

Adjusted R-squared R2 = n 1 SSEn k SST; Here, n = Nos. of observations, k = Nos. parameter in model,

SSE = Sum of squares error; SST= Total sum of squares.

[]

NashSutcliffe efficiency(NSE) NSE = 1

PNi= 1

oi pi 2PNi =1

Oi O 2; = Mean of observed data [,]

Coefficient of persistence (cp) cp = 1

PNi= 2

oi pi 2PN 1i= 1

Oi +1 O 2 []

Index of Agreement (d) d= 1

PNi=1

Oi pi 2

PN

i=1 pi Oj j + Oi Oj j 2 [,]

Kling-Gupta Efficiency (KGE) KGE = 1 ED []

ED =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis 1 r 1 2 + s 2 vr 1 2 + s 3 1 2

qr = Person product moment correlation coefficient

= s=o

vr = , method= 2009, method=2012

= s=0

= CVsCV0

= s=s0=0

Root mean square error (RMSE) rmse =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

PNi= 1

Oipi 2s

[]

Percent bias (PBIAS) PBIAS= 100*PN

i=1 oipi

PNi=1 Oi []Weighted coefficient of determination (wr) wr2 = |b|R2, |b| 1; br2 = R

2

bj j, b>1; b = Slope of the regressionline between observed and predicted data

[,]

Akaike Information Criteria (AICc) (Second

order). Generally used when n/k < .

AICC = 2 ln L + 2K+ 2K K+ 1 n K 1 ; ln(L) = Likelihood function for the model,n = Number of observations, K = Number of estimated parameters

of the model.

[,]

Schwarz Bayesian Information Criteria (SBIC) SBIC = 2 ln L + Kln n [,]HannanQuinn information criterion(HQC) HQC = 2 ln L + 2Kln ln n []Mallows Cp Cp = RSS

2 n 2k; RSS = Residual sum of squares,

2 = Residual mean square error.

[]

6 M. A. Haque: Statistical Comparison of Mathematical Models


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In the study OPC was used as stabilizing agent. The

chemical compositions and different properties of OPC

are given in Table 5, which were analyzed in the labora-

tory. The examined results showed the quite well as

compared with the standard and reported studies that

ensured as a binding material to be used for the solidified

waste mortar.

3.3 Leaching characteristics of Fe, Cuand Ni ions

Leaching is generally considered as the basic criterion to

evaluate the safety, acceptability and the chemical beha-

vior of the final waste forms in the disposal site [52]. The

cumulative migration characteristics of Fe, Cu and Ni

from Solidified waste mortar block (SWMB) to curing

leachant with the increases of curing ages are shown in

Figure 4. It could be noticed clearly from Figure 4 that the

rate of Fe, Cu and Ni release contents were high at early

ages of leaching and then decreased with the increases in

leaching duration. The cumulative releasing behavioral

curves of Fe, Cu and Ni can be characterized by three

distinct regions. 1st region from 1 to 7 days, observed

highest leaching trend ranges from 0.483 mg/l to 0.951

mg/l, 0.039 mg/l to 0.108 mg/l and 0.166 mg/l to 0.416

mg/l for Fe, Cu and Ni respectively. 2nd region from 7 to56 days, slightly lower releasing content was found than

1st region whereas drastic reduction of metal releasing

Table 4: Physical characteristics of mixed MLSW and sand as fine

aggregate.

Parameters Experimental

values

References

Dry density (gm/cm) . . .[]

Bulk density (gm/cm) . . .[]Specific gravity . . .[, ]

Water absorption capacity (%) . . .[, ]

Moisture content (%) . .[]

Porosity (%) . []

Fineness modulus . . ..[]

pH . .

Table 5: Properties and chemical analysis of OPC.

Parameters Experimental values References

Physical property

Fineness (%) . . not less than % (ASTM standard)

Consistency Limit (%) . . % % by weight (ASTM standard)

Initial setting time (min.) not less than minutes (ASTM standard)

Final setting time (min.) not more than minutes (ASTM standard)

Specific Gravity . . .[IS: (Part -)]

Mechanical property

Compressive strength (MPa)

days . . Minimum .(ASTM standard)



Chemical composition (%)

Oxides

CaO . []

SiO . []

AlO . .[]

FeO . .[]

SO . Maximum .(ASTM standard)

MgO . Maximum .(ASTM standard)

Loss on Ignition (LOI) . Maximum .(ASTM standard)

Insoluble Residue (IR) . Maximum .(ASTM standard)

NaO + .KO . Maximum .(ASTM standard)

Free Lime (FCaO) .

Mineral composition (%)

CS . (Test results by ASTM C )

CS . (Test results by ASTM C )

CA . (Test results by ASTM C )

CAF . (Test results by ASTM C )

LSF . % []




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tendency or quite steady state condition observed in 3rd

region from 56 to 180 days curing ages.

The study revealed the cumulative leaching concentra-

tion of Fe, Cu and Ni were about 1.29 mg/l, 0.18 mg/l and

0.63 mg/l respectively up to 180 days static leaching testperiod that satisfied the surface water quality standard [27]

by using the mixing proportion of 1:2. These leaching results

ensured the potentiality of waste product as reusable with

environmental safety. The leach incremental rate of Fe, Cu

and Ni with the development of waste mortars compressive

strength over the examined period are graphically depicted

in Figure 5. Before the immersion of waste mortar block in

curing leachant, ionic species contents are fully encapsu-

lated or entrapped within the waste matrix. At the initial

contact time of curing, incremental rate of each ion release

was high. This trend could be attributed to the washout

of the loosely bounded surficial compounds of the waste

block [52]. When each ion has been leached out from the

surface of the block [16] incremental rate dramatically

reduced in release from 1st region to 2nd region that is

maintained over a longer period of curing time (Up to 180

days) by longer pathways from the bulk through diffusion-

controlled stage, which determines the long term leaching

behavior of the block [15, 16]. Even the study observed

that the rate is reduced to about zero in the 3rd region

from 56 to 180 days curing ages. Similar results were

observed in some reported studies in the literature [15, 53].

Moreover, a major reason of metal ion release rate

reduction is that compressive strength of waste mortar

block increases over the curing age due to the hydrationof binding material like OPC (Figure 5). Compressive

strength and structural integrity bond develops for the

hydration of OPC with the presence of water. The metal

ion species are strongly captured and pore spaces in

waste forms decreased day by day. Therefore, migration

rate of metal ion contents are impeded from SWMB

through diffusion.

3.4 Controlling leaching phenomenaof Fe, Cu and Ni

In some reported studies [1517, 54] the contaminant

content releasing phenomena from waste forms are char-

acterized by three distinct parts such as surface-wash off,

diffusion and dissolution. But under the which region

contaminants leachates from the waste matrices in the

duration of leaching, to determine it, some researchers

[53, 55, 56] indicated that controlling leaching mechanism

could be conducted based on the slope of the linear

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 20 40 60 80 100 120 140 160 180 200

Leaching

ofHeavymetal(mg/l)

Curing age (Day)

Fe (mg/l)

Cu (mg/l)

Ni (mg/l)

Figure 4: Cumulative leaching characteristics of Fe, Cu and Ni from SWMB.

0

5

10

15

20

25

30

0

0.03

0.06

0.09

0.12

0.15

0.18

0.210.24

0.27

0 20 40 60 80 100 120 140 160 180 200

CSofSWMB(MPa)

Incrementalrate(mg/d)

Curing age (Day)

Fe

Cu

Ni

CS

Figure 5: Leaching incremental rate of Fe, Cu and Ni with CS development and curing age.




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regression of the logarithm of CLF versus the logarithm of

time. If the slope is less than 0.35 the controlling leaching

mechanism will be the surface wash-off, for the slope

values ranging from 0.35 to 0.65 the controlling mechan-

ism will be the diffusion, and higher slope values repre-

sent the dissolution mechanism [10, 53, 57]. The plots of

the log(Fe, Cu and Ni concentration) versus log(Curingduration) are shown in Figure 6. From the result of the

linear regression for Fe, Cu and Ni leaching content using

logarithm, it can be clearly concluded that the values of

the correlation factor (R2) have high values for three

tested metal ions leaching. The values of the slopes for

Fe, Cu and Ni are less than 0.35 (Figure 6) which indicate

that surface wash-off govern the leaching phenomena.

That means Fe, Cu and Ni contents only migrated from

the surface of studied waste mortar during the whole

curing period that confirms the studied waste mortar

can be catalogued as sustainable potential re-usable

material in the construction field.

3.5 Calibration of fitted leachate Model

and parameter estimation

The prediction of Fe, Cu and Ni transport phenomena trend

(Figure 4) from the studied SWMB, the experimental lea-

chate data of Fe, Cu and Cu were fitted to the five non-

linear equation based Models such as diffusion equation

(DE), polynomial equation (PE), logarithmic equation (LE),

exponential equation (EE) and power equation (Power E) as

illustrated in Figures 79. From the visual observation of

Figures 79, it could be concluded that for the studied

y = 0.1807x 0.2118

R2= 0.8504

y = 0.299x 1.305

R2= 0.8862

y = 0.2601x 0.6794

R2= 0.8742

1.5

1.3

1.1

0.9

0.7

0.5

0.3

0.1

0.10.3

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

Log(Heavymetalcontent)

Log (Curing age)

Fe

Cu

Ni

Figure 6: Controlling leaching phenomena identification of Fe, Cu and Ni.

0

0.5

1

1.5

2

0 20 40 60 80 100 120 140 160 180 200

LeachingofFe(mg/l)

Curing age (day)

Fe

DE

PE

LE

EE

Power E

Figure 7: Calibration of non-linear models with the Fe leaching concentration.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 20 40 60 80 100 120 140 160 180 200

LeachingofCu(mg/l)

Curing age (day)

Cu

DE

PE

LE

EE

Power E

Figure 8: Calibration of non-linear models with the Cu leaching concentration.




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waste matrix, the DE, LE, EE and power E Model cannot

represent the experimental observations adequately during

the whole examined curing period. In every cases, the

polynomial equation based Model were found to be suc-

cessful and quite good for demonstrating the experimental

releasing behavior of metal ion contents from the wastematrix. Although metal ion species releasing phenomena

associated with the matter of diffusion based, diffusion rate

is not a controlling factor because the diffusion path was

longer. The reason is that diffusion rate rapidly occur at the

initial period but gradually slow down with the leaching

time elapsed. Moreover, LE, EE and power E Model under-

estimates the releasing profile of Fe, Cu and Ni that shows

unrealistic leaching pattern (Figures 79). In order to assess

the better calibration statistically of the leachate Models to

the experimental observations, goodness of fit indicators

like R2 and RMSE values were calculated which are shown

in Table 6. Statistical analysis shows that polynomial equa-tion Model have ability to explain each data point for that

matter R2 was found greater and RMSE also lower as com-

pared to the other fitted Models.

3.6 Statistical comparison of fitted PEModels for well calibration

Several techniques have been used by the previous

researchers to provide a comparison between the simulated

and measured data. In the study, quantitative and graphical

technique were used to evaluate the better demonstrating

leachate Model of Fe, Cu and Ni from the SWMB. Graphical

technique provide a visual comparison and a first overview

of Model performance [33, 58] and are essential to appro-

priate Model evaluation [29, 31].

3.6.1 Goodness of fit indicators

The number parameters of the fitted PE Model were

extended in different terms as trial basis for the well cali-

bration to the experimentally generated leaching data of Fe,

Cu and Ni (Figure 4). From the visual examination of

Figures 1012, it is clearly seen that PE Models shows

comparatively better calibration with the increases of para-

meter from 3 to 5 (From PEMO to PEMTh). But reverse result

is seen for further extension of parameters. PE Model with 7

and 9 parameters (PEMTFv and PEMS) are shown deviated

profile with the experimental metal release contents. The

visual analysis revealed that PEMTh and PEMF with 5 para-

meters shows well calibration by comparison whereas

PEMTS with 9 parameters cannot represent the experimen-

tal data adequately (Figures 1012) that describes the most

unrealistic predicted pattern. For the selection of PE based

well calibrate leachate Model among the six fitted, the

statistical analysis using goodness of fit parameters are

shown in Table 6 that measure the how well the experi-

mental data points fit the PE based regression Models. Inthe study, goodness of fit parameters are calculated using

the simulated data predicted from PEMO to PEMTS and

experimental observed data. The analysis shows a specific

trend that is, fitting the experimental leaching data of Fe, Cu

and Ni to the fitted PE Modelsresulting in a high accuracy of

each statistical parameter with the increases of parameters

from PEMO to PEMTS, which confirm that PEMTS is better

than other Models to represent the leaching data (Table 7).

However, it is quite reverse result than visual examination.

The reason behind that if the parameter of PE based Model

Table 6: Statistical evaluation of fitted leachate models for Fe, Cu

and Ni.

Heavy

metal

Parameter DE PE LE EE Power E

Fe R . . . . .

RMSE

.

.

.

.

.

Cu R . . . . .

RMSE . . . . .

Ni R . . . . .

RMSE . . . . .

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100 120 140 160 180 200

LeachingofNi(mg/l)

Curing age (Day)

Ni

DE

PE

LE

EE

Power E

Figure 9: Calibration of non-linear models with the Ni leaching concentration.




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increases, it explainsor touch the each data point in a better

way but deviates from the original smooth curve line of

experimental data. As the simulated data predicted by

PEMTS are almost near to experimental observations, there-fore goodness fit parameters of PEMTS shows better results

than other fitted Models.

3.6.2 Model selection based on information criteria

The Model selection problem can be tackled using a tradi-

tional approach in which parameter learning is repeated on

a set of candidate Model scales among which one is selected

by a Model selection criterion [39] like AIC, SBIC, HQC and

Mallows cp. AIC means the Akaike Information Criterion

that is useful in selecting the best Model in the set [36]. In

addition, AIC is designed to select the Model that will pre-

dict best and is less concerned with having a few too manyparameters. Schwarz Bayesian Information Criterion (SBIC)

is designed to select the true values of parameters exactly

like AIC. SBIC can be used to compare in sample or out

of sample predicting performance of a Model. The

Hannan-Quinn Criterion (HQC) for identifying an autore-

gressive Model denoted by HQ (p) was introduced by

Hannan and Quinn (1979). The best Model is the Model

that corresponds to minimum HQC [59]. These criteria

attempt to select a Model with small generalization error,

by trading off between the likelihood-based goodness of fit

0.5

0.7

0.9

1.1

1.3

1.5

0 20 40 60 80 100 120 140 160 180 200

Con

centrationofFe(mg/l)

Curing age (Day)

Fe

PEMO

PEMT

PEMTh

PEMF

PEMFv

PEMS

Figure 10: Calibration of PE Models for demonstrating the Fe migration phenomena.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 20 40 60 80 100 120 140 160 180 200

ConcentrationofCu(mg/l)

Curing age (Day)

Cu

PEMO

PEMT

PEMTh

PEMF

PEMFv

PEMS

Figure 11: Calibration of PE Models for demonstrating the Cu migration phenomena.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 20 40 60 80 100 120 140 160 180 200

Concentra

tionofNi(mg/l)

Curing age (Day)

Ni

PEMO

PEMT

PEMTh

PEMF

PEMFv

PEMS

Figure 12: Calibration of PE Models for demonstrating the Ni migration phenomena.




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and Model complexity subject to noise and uncertainty in a

finite number of observations [39]. In the current study,

statistical analysis using information criterion including

AIC, SBIC, HQC and Mallows cp for Model selection

shows the similar results with the goodness of fit para-

meters and contrast with visual observation. In addition,

the study found a trend for PE Models that is, the lowernumber of parameters the lower value of AIC, SBIC, HQC

and Mallows cp. Generally, the Model bear the compara-

tively lower value of AIC, SBIC, HQC and Mallows cp is

selected as the better Model. The calculated values from the

analysis of AIC, SBIC, HQC and Mallows cp (Table 8), it is

clearly seen that PEMO shows the lowest values. Therefore,

according to the principle, PEMO is better Model to repre-

sent the Fe, Cu and Ni leaching data than other fitted

Models that is opposite result of visual examination.

3.6.3 Slope and y-intercept

The slope and y-intercept of the best-fit regression line can

indicate howwellsimulateddata match with measured data.

The slope indicates the relative relationship between the

simulated and measured data. The y-intercept indicates the

presence of a lag or lead between Model predictions andmeasured data, or that the data sets are not perfectly aligned

[29, 60]. The current study compared the well calibration

between the simulated PE Models curves to the experimen-

tally measured data of Fe, Cu and Ni ion leaching curves

(Figures 1012) using slope and y-intercept of the best-fit

regression line which are shown in Table 9. The slope and

y-intercept of the simulated curves were calculated by three

distinct parts based on the three regions which is already

mentioned in Section 3.3. The comparative analysis shows

Table 7: Model evaluation based on goodness of fit parameters.

Parameter Heavy metal PEMO PEMT PEMTh PEMF PEMFv PEMS Standard range

r Fe . . . . . . [, + ]

Cu . . . . . .

Ni . . . . . .

R-squared Fe . . . . . . to

Cu . . . . . .

Ni . . . . . .

Adjusted R-squared Fe . . . . . . to

Cu . . . . . .

Ni . . . . . .

NSE Fe . . . . . . and .

Cu . . . . . .

Ni . . . . . .

cp Fe . . . . . . to

Cu . . . . . .

Ni . . . . . .

d Fe . . . . . . to Cu . . . . . .

Ni . . . . . .

KGE Fe . . . . . . and .

Cu . . . . . .

Ni . . . . . .

rmse Fe . . . . . . Minimum value is taken.

Cu . . . . . .

Ni . . . . . .

pbias Fe . Optimal value is

Cu . . .

Ni

br Fe . . . . . . Maximum value is

Cu . . . . . .

Ni . . . . . .




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that slope and y-intercept values of simulated curve by

PEMTh are quite similar with the Fe, Cu and Ni ion leaching

curves (Table 8). Moreover, it can be concluded that PEMTh

can demonstrate the experimental metal ion leaching con-tents profile with curing ages quite well than other five fitted

PE Models. Although PEMTF can explain approximately

the phenomena but PEMTh can better that result shows

similar with the visual examination of the figures whereas

the goodness of fit parameters and information criterion

measures opposite results. So, the study suggests based on

the visual examination and comparison results using slope

andy-intercept,PEMThcanbe used to represent the leaching

phenomena.

The accuracy of the PE Models calibration result was

justified through statistical comparison. Goodness of fit

parameters and information criterion were calculated

using the statistical software R.

3.7 Statistical significance test ofwell-calibrated PE Model parameters

The parameter estimation outcomes of well-calibrated

PEMTh for Fe, Cu and Ni are presented in the Table 10.

Parameters were calculated with their 95 % confidence

Table 8: Model selection based on statistical information criteria.

Parameter Heavy metal PEMO PEMT PEMTh PEMF PEMFv PEMS Standard value

AIC Fe . . . . . . Minimum value is taken

Cu . . . . . .

Ni . . . . . .

SBIC Fe . . . . . .Cu . . . . . .

Ni . . . . . .

HQC Fe . . . . . .

Cu . . . . . .

Ni . . . . . .

Mallows cp Fe . . . .

Cu . . . . . .

Ni . . . . . .

Table 9: Comparison of slope and intercept between the experimental observations and fitted PE models.

Parameter Heavy metal Curing days Experimental observation PEMO PEMT PEMTh PEMF PEMFv PEMS

Slope Fe to . . . . . . .

to . . . . . . .

to . . . . . .

Cu to . . . . . . .

to . . . . . . .

to .

Ni to . . . . . . .

to . . . . . . .

to . . . . .

Intercept Fe to . . . . . . .

to . . . . . . .

to

.

.

.

.

.

.

.

Cu to . . . . . . .

to . . . . . . .

to . . . . . . .

Ni to . . . . . . .

to . . . . . . .

to . . . . . . .




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interval. The study tested the statistical significance level

of each parameter using t and p-value statistics. The t-

value measures the ratio between the coefficient and its

standard error whereas p-value quantify the statistical

significance level of parameter. If the p-value of each

parameter is less than the significance level (e. g., p A3 >

A4 > A1 > A5.

3.8 Statistical prediction boundsof well-calibrated PE Model

Statistical prediction bounds of PEMTh with 95 % confi-

dence intervals for Fe, Cu and Ni are presented in the

Figures 1315 respectively. Each figure contains the three

curves such as the fit, the lower confidence bounds, and the

upper confidence bounds. The confidence interval consists

of the space between the two curves (dotted lines).The fit

means fitted of PEMTh to the experimentally generated data

and the bounds reflect a 95 % confidence level. Confidence

interval with 95% means there is a 95% probability that the

fitted line of PEMTh for the Fe, Cu and Ni leaching data will

lie within the confidence interval.

Table 10: Estimated parameters of model 03 with statistical significant test.

Heavy metal Parameter Estimate Std. Error t-stat p-value Range of p-value

Fe A . . . . Significance level ifp < .

A . . . and

A . . . . Insignificance level ifp > .

A . . . .A . . . .

Cu A . . . .

A . . . .

A . . . .

A . . . .

A . . . .

Ni A . . . .

A . . . .

A . . . .

A . . . .

A . . . .

Figure 13: Fitted prediction PEMTh for Fe leaching contents with 95 % prediction bounds.




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4 Conclusion

Fe, Cu and Ni leaching phenomena from solidified landfill

waste matrices were evaluated by performing static leach-

ing tests. The major conclusions pertaining to the findings

presented herein may be drawn from this research:

(1) The leaching contents of studied metal ions were

substantially reduced from waste matrices at

28 days curing age and similar result observed up

to 180 days that confirms the waste mortar block

to be used as an environmental friendly re-usable

product.

(2) Compressive strength test result was found quite satis-factory value 19.1 MPa at 28 days curing age that fulfill

the paving block standard (15 Mpa) in Bangladesh.

(3) The only surface wash off leaching phenomena was

found to control Fe, Cu and Ni leaching contents

that ensure the safe disposal of the product.

(4) By fitting the experimentally generated data to some

well-established non-linear models, it was revealed by

the visual examination and statistical analysis that the

migration phenomena of the studied metal ions from

landfill waste mortar block can be represented quite

well by semi-empirical Model PE for longer period.(5) From the statistical analysis, it was found that PE

Model bearing five parameters (PEMTh) with 0.5

power interval with each parameter can well explain

the leaching phenomena during the whole immersion

period in leachant that fails to prove using goodness of

fit indicators and information criteria like AIC, SBIC,

HQC and Mallows cp.

(6) Experimental leaching behavior of Fe, Cu and Ni

versus curing age can quite describe using slope

and intercept of the fitted PEMTh curves.

(7) It is recommended that the outcome of the study may

be a potential solution to recycle the landfill waste as

re-usable by product like paving blocks, road construc-

tion materials, etc. using S/S process.

Acknowledgements: The Author would like to acknowl-

edge the authority of Dhaka City Corporations for the

permission to collect the decomposed solid waste and

leachate samples from Matuail Sanitary Landfill Site.

Figure 14: Fitted prediction PEMTh for Cu leaching contents with 95 % prediction bounds.

Figure 15: Fitted prediction PEMTh for Ni leaching contents with 95 % prediction bounds.




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