prediction of unconfined compressive strength of pulverized fuel ash–cement–sand mixture

ORIGINAL ARTICLE

Prediction of unconfined compressive strength of pulverizedfuel ash–cement–sand mixture

Shervin Motamedi • Ki-Il Song • Roslan Hashim

Received: 19 February 2013 / Accepted: 14 November 2013

� RILEM 2014

Abstract Recently, ground improvement has

become much more feasible. Chemical stabilization

is a quick and affordable approach to enhancing soil

characteristics. An important avenue of research is

discovering alternative materials for use in soil

enhancement. Pulverized fuel ash (PFA), which is a

waste byproduct of coal power plants, has been shown

to reduce the environmental risks and costs involved in

construction. In this study, a series of unconfined

compressive tests were performed for various mix-

tures of cement, PFA, and sand; the tests considered

both the curing period and the optimum moisture

content (OMC). In addition, multiple variable linear

regression was used to analyze laboratory data in order

to obtain an empirical relationship that can be used to

predict the unconfined compressive strength (UCS) of

a PFA–cement–sand mixture. The accuracy of the

model was verified using statistical indices. The first

objective of this study was to assess the effects of PFA

content on the UCS of the mixture. The second was to

investigate the impact of the OMC on the UCS. The

focal point of this study was its derivation of a

relationship that can be used to estimate the UCS on

the basis of existing variables. The results indicated

that PFA can strengthen sand in terms of the UCS and

that excessive PFA in a mixture may adversely affect

the UCS of a medium. Therefore, a mixture must have

an optimum proportion of compounds. The OMC

plays a vital role in enhancing UCS. The UCS of

different mixtures can be predicted with an acceptable

level of accuracy by using the relationship derived in

this study.

Keywords Pulverized fuel ash � Ground

improvement � Unconfined compressive

strength � Multiple linear regression �Enhancement � Admixture

1 Introduction

In the modern world, ground conditions have deteri-

orated owing to overpopulation and the scarcity of

land, energy, and material resources [1]. The excessive

costs of consultancies and project execution have

restrained the adoption of conventional construction

methods. In the construction industry, the concept of

adopting an alternative approach involving the use of

enhancement technologies is not new. Although such

S. Motamedi � R. Hashim

Department of Civil Engineering, Faculty of Engineering,

University of Malaya, 50603 Kuala Lumpur, Malaysia

e-mail: [email protected]

R. Hashim


K.-I. Song (&)

Department of Civil Engineering, Inha University, 100

Inha-ro, Nam-gu, Incheon 402-751, Korea


Materials and Structures

DOI 10.1617/s11527-013-0215-1

technologies have been used for years, advances in

machinery, computers, and complex instruments have

widened the scope of ground improvement methods

[2].

These alternative approaches also need to be

sustainable. Traditional construction practices not

only produce waste materials but also use a large

amount of available resources that should be con-

served for future use [3]. One of the most accessible

ways of saving resources is to substitute new materials

for old ones. Gue and Tan [4] elaborated various

ground improvement techniques that can be used to

enhance the geotechnical properties of problematic

soil. For example, chemical stabilization involves

mixing additives with soil to enhance several geo-

technical characteristics. The type of chemical soil

stabilization is defined according to the chemical

reactions involved [5]. Furthermore, there are differ-

ent types of chemical stabilization depending on the

construction technique used [6].

Coal combustion byproducts (CCBs) refer to fly

ash, bottom ash, boiler slag, and the byproducts of flue

gas desulfurization material and fluidized bed com-

bustion [7]. CCBs can be used in concrete or grout

products, structural fills, embankments, soil improve-

ment, road layers, and agriculture and cement pro-

duction [8–10]. In 2009, the USA produced an

estimated 125.5 million tons of CCBs. Unfortunately,

only about 56 million tons of the waste byproducts

were successfully employed in applications; the rest

remained untreated [7]. Tick [11] predicted that, in

2010, CCB production in Malaysia would exceed

22.5 million tons per year.

Fly ash, which is a type of CCB, is a fine powder

substance formed mostly of glassy spherical particles

[12]. Kim et al. [13] stated that about 70 % of the total

fly ash that is produced is untreated and disposed of in

landfills. Huang et al. [14] investigated the effect of fly

ash, synthetic fibers, and organic fibers on loose sand.

Their results indicated that an increase in fiber content

and a constant inclusion of 70 % silty sand and 30 %

fly ash increases the unconfined compressive strength

(UCS) of the medium. Naik et al. [15] and Siddique

[16] investigated the effect of fly ash on loose sand

when mixed with various additives. Despite the

differences between the results, both studies proved

the positive impact of fly ash on soil stabilization.

The present study aimed to evaluate the effect of

pulverized fuel ash (PFA) content on the UCS of a

PFA–cement–sand mixture and to assess the effects of

optimum moisture content (OMC) on the 28-day UCS.

The focal point of this study was its formulation of the

relationship among the UCS, PFA and cement

contents, curing period, and density of the sample

after different curing periods.

2 PFA versus class-F fly ash

PFA and class-F fly ash are two types of fly ash that are

widely used in applications. These two materials must

be compared according to different criteria.

2.1 General classification of fly ash

There are two main chemical reactions that are

involved in mixing soil with additives. These reactions

are needed to induce bonding between soil particles

and additives, which eventually results in the forma-

tion of stiffer materials that can resist geotechnical

loads. Hydration and the pozzolanic reaction are

processes that take place after the mixing of binding

agents such as lime, cement, fly ash, gypsum, and rice

husk with water and soil [17].

Fly ash is a fine remnant of pulverized coal

combustion. ASTM C 618 [18] differentiates two

types of fly ash: classes F and C. Class-F fly ash is

generated from anthracite and bituminous coal,

whereas class-C fly ash is obtained from subbitumi-

nous and lignite coal [19]. Fly ash is primarily

classified according to its pozzolanic content (oxides

of aluminum, silicon, and iron) and then its calcium

content (CaO class). Class-F fly ash is a pozzolanic

material. It needs a cementation substance such as

lime or cement to activate the hydration process. On

the other hand, class-C fly ash exhibits cementation

and pozzolanic behavior owing to its available free

lime content, so activators may not need to be added

for enhancement [19, 20].

2.2 Chemical properties of fly ash

Fly ash types can be differentiated according to the

chemical properties. A Pozzolanic material is a

substance that has low lime content but a significant

amount of silica. This material needs to be mixed with

an external source of calcium oxide (CaO) or calcium

hydroxide (Ca(OH)2) to gain the required degree of


strength [21]. Class-F fly ash contains a low level of

lime. Although this material does not produce signif-

icant cementation effects, it has been observed to

produce cementation compounds in the presence of

moisture under normal temperatures [22, 23]. In

contrast, class-C fly ash is richer in lime, so it has

also been called ‘‘high-lime fly ash’’ [24–26].

PFA is a type of class-C fly ash [27]. PFA exhibits

pozzolanic behavior that produces self-hardening

matter, although the degree of self-cementation can

vary depending on the source of material and type of

coal [28]. X-ray studies have demonstrated the

complexity of PFA in terms of its chemical compo-

sition and crystallography. Although it generally

contains quartz (SiO2), mullite (2SiO2•3Al2O3),

hematite (Fe2O3), and magnetite (Fe3O4), it also

contains other minor minerals such as lime (CaO),

anhydrite (CaSO4), and gypsum (CaSO4•2H2O) [29].

Although PFA is categorized as a high-calcium

material, this calcium content is assumed to still be

insufficient to initiate the hydration process [30].

2.3 Physical properties of fly ash

Fly ash can be categorized on the basis of its physical

properties. Fineness and vitreosity are two vital factors

that are used for its categorization. Janz et al. [17]

reported that, the finer the material, the more it can

contribute to the strength gained in the hydration

process. Vitreosity also plays an important role;

amorphous materials are believed to be more active

than their crystalline counterparts in terms of pozzo-

lanic reactions [17]. Thus, class-F fly ash is generally

defined as being a coarser and more vitreous substance

than class-C fly ash [17]. Class-F fly ash has a

spherical shape and amorphous nature; moreover, its

formation involves high temperatures and quick

cooling. These factors make class-F fly ash a suitable

choice for facilitating a pozzolanic reaction.

2.4 Utilization of PFA in previous research

Yoon et al. [31] studied the effects of different

stabilization techniques by using various combined

materials, although PFA was not specifically an object

of direct study. Jo et al. [32] revealed the effects of

lime, cement, and PFA on the strengthening of a sand

composite material. Their results indicated that, when

the cement and lime content is fixed at 20 % of the

total weight of a mixture, the UCS increases by up to

50 % of its initial value with increasing PFA content.

However, their study failed to provide technical details

on other geotechnical parameters such as the moisture

content, sand characteristics, and curing period that

can readily be associated with UCS estimation. There

are few reports on the stabilization effects of PFA on

the geotechnical properties of sand mixtures, and the

existing literature does not offer the full technical

background of the procedures used in testing or details

on the materials. Thus, this paper provides the

technical details and relevant background of the

employed testing procedure.

3 Materials and methodology

3.1 PFA

PFA was used throughout this study. PFA is a class-C

fly ash [15] that is obtained from subbituminous and

lignite coal [27]. During the stabilization process,

class-C fly ash becomes involved in cementation and

pozzolanic reactions, depending on the available free

lime content. Therefore, the use of other hydrators to

activate chemical reactions may be avoided [33]. The

PFA used in this study was supplied by Tenaga

Nasional Bhd, Selangor, Malaysia; its physical prop-

erties are summarized in Table 1. The chemical

composition of PFA was assessed according to the

Standard Test Methods for Sampling and Testing Fly

Ash or Natural Pozzolans for Use in Portland Cement

Concrete (ASTM C 311) using X-ray fluorescence

(XRF); the results are presented in Table 2. Figure 1

shows the physical form of the PFA that was used in

this study.

Table 1 Physical properties of PFA used in this study

Physical property name Index properties

Color Whitish gray

Odor Odorless

Bulk density (g/cm3) 0.984

Specific gravity 2.293

Moisture content (%) 2.12

Average particle size (lm) 6.82

Fineness (m2/kg) 155


3.2 Cement

Cement is a synthetic material that is produced with

Portland clinker; it contains approximately 5 %

gypsum. It is ground until a particle size of

1–100 lm and specific surface area of 300–550 m2/

kg are obtained [34]. Cement is categorized into five

types (I–V). In practice, type I or II Portland cement

is utilized in construction [35, 36]. Type I Portland

cement was used throughout this study. Table 2 lists

details of the chemical composition of the cement

based on XRF performed in accordance with ASTM

C 311.

3.3 Sand

Sand was an essential material in this research; it was

imperative to identify the type of sand that was used.

Stevens [37] introduced a classification method for

soil that is based on dry sieving. In this study, the sand

was thus categorized according to the Standard

Practice for Classification of Soils for Engineering

Purposes (ASTM D 2487) and Stevens’ method [37]

as poorly graded sand (SP). Figure 2 shows the

particle size distribution of the sand, and Table 3

summarizes its physical properties. The sand deposit

was collected from Selangor, Malaysia.

3.4 Methods

A multidisciplinary approach was employed in this

study, which included laboratory tests, statistical

analysis, and computer programming. Samples were

Table 2 Chemical composition for cement and PFA used in

this study

Component Cement

(%)

PFA

(%)

ASTM C 618

requirement

for PFA (%)

Silica (SiO2) 20.65 58.00 –

Alumina (Al2O3) 5.87 22.00 –

Iron oxide (Fe2O3) 2.52 3.80 –

SiO2 ? Al2O3 ? Fe2O3 – 83.80 50.00 min

Calcium oxide (CaO) 63.55 6.80 –

Magnesium oxide (MgO) 2.79 1.30 –

Sulphur trioxide (SO3) 1.62 1.10 5.00 max

Sodium oxide (Na2O) 0.85 1.30 –

Potassium oxide (K2O) 0.63 0.80 –

LOI 1.54 4.65 6.00 max

Fig. 1 Physical form of PFA at the laboratory condition

0

10

20

30

40

50

60

70

80

90

100

0.01 0.1 1 10

Per

cent

Fin

er (

%)

Grain Size (mm)

Fig. 2 Particle size

distribution of sand used in

this study


prepared in accordance with the Standard Test Meth-

ods for Laboratory Compaction Characteristics of Soil

Using Standard Effort (ASTM D 698) and cured for 1,

7, 14, and 28 days. Unconfined compression testing

(UCT) was performed in compliance with the Stan-

dard Test Method for Unconfined Compressive

Strength of Cohesive Soil (ASTM D 2166). Before

loading, samples were weighed to a precision of

0.01 g. The diameter and length were also measured to

a precision of 0.1 cm. To summarize the data, the UCT

results were analyzed using an automatic coded

system written in VB.NET. Diagrams are presented

to assess the impact of PFA and cement in case when

the two are mixed with sand. The results were

analyzed using multiple variable linear regression

[38, 39]. An empirical relationship was introduced to

predict the UCS of a PFA–cement–sand mixture. The

accuracy of the model was tested using statistical

parameters, and the regression line was verified in

terms of the estimation accuracy.

4 Test results

A total of 480 cylindrical samples, each 5 cm in

diameter and 10 cm in height, were compressed in

accordance with ASTM D 698 to ensure sufficient

compaction. The samples were also tested in compli-

ance with ASTM D 2166. Figure 3 shows the samples

that were prepared before performing UCT. The

samples contained 5–40 % PFA and 5–25 % cement

(Table 4). The cement and PFA contents were varied

in steps of 5 %. The curing period was used as a

parameter for determining the strength of the mixture

after 1, 7, 14, and 28 days. Three samples were tested,

and the results were averaged to avoid the impact of

any relevant errors. The densities of the samples were

measured prior to testing. The results were analyzed

using a multiple linear regression technique [38, 39].

4.1 Effect of cement content on strength of PFA–

cement–sand mixture

As shown in Fig. 4, the UCS increased nonlinearly

with increasing cement content. As the samples aged,

the UCS increased as well. For example, when the

PFA content was 30 % and the cement content was

15 %, the UCS on day 1 was 4.23 MPa. On days 7, 14,

and 28, the UCS for the same material contents

increased to 6.94, 8.06, and 9.14 MPa, respectively.

The UCS reached its highest value of 13.22 MPa when

the PFA content was 30 % and the cement content was

25 % of the total weight of a specimen. The lowest

UCS value of only 1.2 MPa was recorded on the first

day of the curing period, for a PFA content of 30 %

and cement content of 5 %.

4.2 Effect of PFA content on strength of PFA–


According to Fig. 5, sample with 0 % PFA provides a

control condition for evaluating how PFA can enhance

the strength of PFA–cement–sand mixture. As shown

in Fig. 5, if PFA is added to the mixture, the UCS of

Table 3 Physical properties of sand used in this study

Physical property name Index properties

Dry bulk density (kg/m3) 1,928

Dry compacted bulk density (kg/m3) 2,035

Relative density 1.47

Specific gravity 2.63

Fineness modulus 2.84

24-h water absorption (%) 25.12

Fig. 3 The UCT samples of 5 cm in diameter and 10 cm in

height prepared prior to testing

Table 4 Percentage of PFA and cement in samples

Material Percentage

PFA 5, 10, 15, 20, 25, 30, 35, 40

Cement 5, 10, 15, 20, 25


PFA–cement–sand mixture is higher than that of

cement–sand mixture. Interestingly, the UCS gradu-

ally decreased after the PFA content exceeded 20 %.

The decrease is generally related to the low pozzolanic

activity of PFA, which delays the development of

strength. The low pozzolanic activity is associated

with the high amount of insoluble silica content (SiO2)

and high organic content due to the high loss on

ignition (LOI) value (4.65 %). This result is consistent

with the results of Openshaw [40]. Similar reductions

in strength have been previously observed in mortar

using PFA [41]. According to Larsen [42], fly ash

should make up\20 % of the total weight of concrete;

the specification is based on Florida Department of

Transportation practice.

Camilleri et al. [43] observed a considerable drop in

compressive strength of PFA–cement –sand mixtures

when PFA exceeds 20 % of the total weight. For

example, after 28 days, the sample with 40 % PFA

and 25 % cement had a UCS of 13.03 MPa, whereas

the sample with 30 % PFA and 25 % cement showed

an increased UCS of 13.22 MPa. Consequently, a

sample with 25 % PFA and 25 % cement had a UCS

of 13.48 MPa; the highest UCS of 13.6 MPa was

obtained with 20 % PFA and 25 % cement. In general,

a longer curing period increases the UCS irrespective

of the material content (Figs. 4, 5). Moreover, the

addition of PFA to the medium was found to have a

substantially smaller effect than increasing the cement

content. In summary, for the range in which the PFA

content was increased in this study, the optimum PFA

content for producing greater strength gain can be

concluded to be 20 %.

4.3 Effect of OMC on the integrity of a PFA–


To evaluate the effect of moisture content on the

28-day UCS, we prepared three classes of samples:

OMC samples, samples with 15 % moisture content,

and samples with 5 % moisture content. The 5 and

15 % moisture contents were selected to avoid

extremely soft and extremely solid textures for the

specimens. The effects of moisture content on UCS are

shown in Figs. 6 and 7.

Figure 6 shows the 28-day UCS with 30 % PFA

and various values of cement content. For example,

the sample with 30 % PFA and 15 % cement had a

UCS of 9.14 MPa under OMC conditions (i.e.,

11.42 % moisture content). With the same mixture

composition, the UCS decreased to 6.1 MPa with

15 % moisture content. When the sample had 5 %

moisture content and the same mixture composition,

the UCS decreased to 7.09 MPa. The 28-day UCS

increased with the increase in cement content. A

composition of 30 % PFA and 25 % cement with

OMC yielded the maximum UCS of 13.22 MPa,

which was approximately 30 % higher than the values

10

12

14

UC

S (M

Pa)

0

2

4

6

8

0 7 14

Day21 28

PF

PF

PF

PF

PF

A 30% - CEME

A 30% - CEME

A 30% - CEME

A 30% - CEME

A 30% - CEME

NT 5%

NT 10%

NT 15%

NT 20%

NT 25%

Fig. 4 Effect of cement content on UCS with 30 % of PFA

inclusion

5

6

7

8

9

10

11

12

13

14

0 7 14 21 28

UC

S (M

Pa)

Day

PFA 0% - CEMENT 25%PFA 20% - CEMENT 25%PFA 25% - CEMENT 25%PFA 30% - CEMENT 25%PFA 35% - CEMENT 25%PFA 40% - CEMENT 25%

Fig. 5 Effect of PFA content on UCS with 25 % of cement

inclusion


obtained with 15 % and 5 % moisture content. OMC

clearly yielded the maximum UCS with a fixed PFA

and cement content. A lower moisture content can be

inferred to be more favorable than a higher moisture

content.

Figure 7 shows the 28-day UCS with 25 % cement

and various values of PFA content. For example, the

samples with 25 % cement and 30 % PFA had a UCS

of 13.22 MPa under OMC conditions (i.e., 11.42 %

moisture content). For the same mixture composition,

the UCS dropped 22.7 % to 10.22 MPa with 15 %

moisture content. On the other hand, for the condition

of 5 % moisture content and the same mixture

composition, the UCS decreased 15.1 % to

11.22 MPa. The highest UCS (i.e., 13.6 MPa), which

was 22 % higher than that obtained in the case of 15 %

moisture content and 14 % higher than that obtained in

the case of 5 % moisture content, was observed under

OMC conditions with 25 % cement and 20 % PFA.

Thus, the OMC should be maintained to secure the

integrity of a PFA–cement–sand mixture with a high

UCS.

5 Predicted UCS of PFA–cement–sand mixture

5.1 Multiple linear regression

Multiple linear regression is a direct general form of

simple regression analysis. The difference is that, in

multiple regression analysis, the value of a response

depends on more than one predictor. Multiple linear

regression can be used to evaluate the relative

importance of each predictor. Prior to analysis, the

correlation coefficient must be checked to ensure that

there is adequate interdependency between the pre-

dictors and outcome. Table 5, which lists the analysis

results, indicates that there is a strong correlation

between each variable and response.

The Pearson correlation coefficient is considered

fair if it lies within -1 \ R \ -0.7 and 0.7 \ R \ 1.

For all three variables, the calculated R yielded an

acceptable correlation with the UCS. The results

indicated that C/10 has a positive correlation with the

UCS at R = 0.844. The second variable [ln (107 c4/

AC)] had a negative correlation with the UCS at

R = -0.723. The third variable of |ln (10P/AC4)| also

showed a positive correlation with the UCS at

R = 0.877. Based on the Pearson correlation coeffi-

cient, this dataset showed an acceptable level of

interdependency between the predictors and the

expected outcome.

Equation (1) shows the regression relationship

between the variables and the expected outcome. C,

P, A, and c represent the cement content (%), PFA

0

2

4

6

8

10

12

14

0 5 10 15 20 25

UC

S (M

Pa)

Cement

OMC - PFA 30%

MC 15% - PFA 30%

MC 5% - PFA 30%

Fig. 6 Effect of moisture content on UCS with 30 % PFA and

various cement content after 28 days

5

6

7

8

9

10

11

12

13

14

20 25 30 35 40

UC

S (M

Pa)

PFA

OMC - CEMENT 25%

MC 15% - CEMENT 25%

MC 5% - CEMENT 25%

Fig. 7 Effect of moisture content on UCS with 25 % cement

and various PFA content after 28 days

Table 5 Pearson correlation coefficient (R value) table

Variables C10 ln 107 �c4

A�C

� �ln 10P

A�C4

� ��

ln 107 �c4

A�C

� �-0.431 1 -0.708

ln 10PA�C4

� �� 0.764 -0.708 1

UCS 0.844 -0.723 0.877


content (%), curing period (in days), and density of the

specimen at a given age (kg/cm3), respectively.

UCS ¼ 1:29þ 2:82C

10

� �� 0:887 ln

107 � c4

A � C

� ��

þ 0:54 ln10P

A � C4

� �� ð1Þ

Although OMC has been demonstrated to have a

vital role for maximum UCS, the OMC is not

considered as a predictor in Eq. (1). The proposed

model was verified under the assumption that the

samples were prepared with OMC in accordance with

ASTM D 698, as this standard was consistently

employed throughout this study. The OMC condition

is equal to the attainment of maximum dry density.

This minimizes the porosity within the sample. The

mean OMC for various mixture compositions was

11.42 ± 0.89 %. Therefore, the samples contained

almost the same OMC. If the OMC condition is not

met, the maximum UCS cannot be obtained and the

UCS will decrease.

5.2 Regression diagnostics

Diagnostic procedures verify how well the prerequi-

sites for multiple linear regression are satisfied. A

number of tests were carried out to ensure that the

analysis was set within the range of the basic

assumptions for multiple linear regression validity. If

these tests produce false results, the conclusions drawn

on the basis of the model are cast in doubt.

One technique used to validate the basic assump-

tions is to check the pattern of the residuals of the

UCS. Conceptually, residuals are defined as the

algebraic difference between the actual observed

value and the calculated mean value of a dependent

variable.

5.2.1 Normal probability plot of UCS residuals

A normal probability plot (NPP) of the residuals

helped confirm a normal distribution of residuals in

the UCS. Figure 8 shows the correct skew of the

distribution.

The mean value (Mean) was calculated as

-4.61467E-15. The standard deviation (StDev),

which expresses the spread of the data around the

mean value, was calculated as 1.292. Theodorsson

[44] noted that if the Anderson–Darling statistic (AD)

is [0.753, there is a 95 % level of confidence that a

dataset was drawn from a non-normal distribution.

Otherwise, the collection of data should be monitored

more delicately as the sampling progresses. In this

analysis, the AD was 1.208, which is far[0.753. This

demonstrates the randomness of the sample. The

P value represents the probability that the null

hypothesis is correct.

5.2.2 Residuals versus fitted values by the order

of data

A plot of the residuals versus the fitted values by the

order in which the data were entered may help in

identifying outliers in the data. Figure 9 shows the

presence of outliers in the dataset. These may be

attributed to the available measurement errors and to

the nonlinear nature of the chemical reaction during

the curing period. Fitted values were the output

variables that were estimated by the fitted model to

the dataset. The fitted values are also known as

predicted values.

5.2.3 Residuals versus fitted values

Another useful diagnostic tool is to consider the

residual plots versus the fitted values. This is done with

a simple scatter plot that represents a rectangular cloud

with no apparent general trend. Figure 10 shows that

the dataset for this analysis did not represent any

particular distinguishable trend. This demonstrates

543210-1-2-3-4

99.9

99

9590

80706050403020

105

1

0.1

UCS residuals (MPa)

Per

cent

( %

)

AD 1.208

Mean -4.61467E-15

StDev 1.292

N 92

P-Value <0.005

Fig. 8 Normal probability plot of UCS residuals


that the assumptions used for the multiple linear

regression were valid.

5.3 Predicted UCS versus observed UCS

Figure 11 shows a plot of the observed UCS and

predicted UCS versus the residuals. Figure 12 shows a

plot of the predicted UCS versus the observed UCS. The

figure clearly shows that the model can present a better

estimation where the observed UCS values are higher.

According to the reliability-based concept of statistical

analysis, it is natural that the two values do not perfectly

coincide. The role of an analyst is to determine the level

of accuracy and the power of estimation for a particular

model. This can be done by using statistical indices

such as the R2 value and null-test method [45].

5.4 Verification of model

The accuracy of a model must be verified using

statistical indices. For this purpose, two criteria must be checked: the regression statistic must be calculated

and second, an analysis of the variance needs to be

performed. Once these are checked, the estimation

accuracy of the model has been verified.

5.4.1 Regression statistics

Table 6 lists the regression statistics. The adjusted R2

value was calculated to be 0.886. The adjusted R2

value replicates the wellness of the independent

variable estimation. In this case, it indicated that

88.6 % of the observed UCS can be predicted using

this model. This criterion is preferable to the R2 value

that is commonly used in simple linear regression. It

adjusts the R2 value to consider both the sample size

and the number of predictors. In this analysis, the

9080706050403020101

3

2

1

0

-1

-2

-3

-4

Observation Order

UC

S R

esid

ual (

MP

a )

Fig. 9 Residuals versus fitted values by order of data

14121086420

3

2

1

0

-1

-2

-3

-4

Fitted Value ( MPa )

UC

S re

sidu

al (

MP

a )

Fig. 10 UCS residuals against fitted values

3210-1-2-3-4

14

12

10

8

6

4

2

0

UCS residuals (MPa)

UC

S (M

Pa)

Observed UCS

Predicted UCS

Fig. 11 Observed UCS and predicted UCS versus UCS

residuals

14121086420

14

12

10

8

6

4

2

0

Observed UCS ( MPa )

Pre

dict

ed U

CS

( M

Pa

)

Fig. 12 Predicted UCS versus observed UCS


adjusted R2 value represented significant regression.

There were 91 observations; hence, the analysis

involved 91 data points.

5.4.2 Analysis of variance (ANOVA)

Table 7 shows the ANOVA. DF denotes the degrees of

freedom, SS denotes the sum of squares, MS denotes

the mean square, F value is the ratio of the regression

mean square to the residual mean square, and P value

is the null hypothesis key. Assuming that the null

hypothesis is true, the hypothesis can be rejected if the

P value of a given analysis is less than the significance

level a, which is often 0.05. In the present analysis, the

P value (6.35492E-42) was significantly smaller than

the significance level. This proved that the null

hypothesis was false, which means that there was a

significant relationship among all of the independent

variables and the dependent variable.

5.4.3 T test analysis

Table 8 lists the statistics for the parameter estimates.

Coef denotes the Bj coefficients for the regression

relationship using the general form of Eq. (2):

Y ¼ B0 þ B1X1 þ B2X2 þ B3X3 þ � � � þ BjXj; ð2Þ

where j = 0, 1, 2, 3, …, (number of parameters).

t-Stat is the ratio of the predictors’ coefficient to the

standard error. The P value is the probability that the

null hypothesis is correct. If the corresponding P value

for each independent variable is less than an arbitrary

value of 0.05, the null hypothesis is rejected.

The P value is the probability that the null

hypothesis is correct. Therefore, the null hypothesis

has a \5 % chance of being true if the P value is

\0.05. In this series of analyses, the null hypothesis

was defined as the absence of a significant relationship

between the independent variable and dependent

variable. In this analysis, all the predictors had a

P value of \0.05; hence, the null hypothesis was

rejected for each predictor. Thus, all of the predictors

affected the response.

Table 6 Regression statistics table

Regression statistics

Multiple R 0.94

R2 0.889

Adjusted R2 0.886

Standard error 1.31

Observations 91

Table 7 Analysis of variance (ANOVA)

Source DF SS MS F-value P-value

Regression 3 1,219.948976 406.6496587 235.5411 6.35492E-42

Residual error 88 151.9275082 1.726448956 – –

Total 91 1,371.876484 – – –

DF degree of freedom, SS sum of squares, MS mean square, F-value ratio of regression mean square over residual mean square, P-

value null hypothesis key

Table 8 Parameter estimates table

Predictor Coef SE t-Stat P-value

Intercept 1.285653711 0.489224587 2.627941738 0.010135

C10

2.824793894 0.320687509 8.808556024 1.02E-13

ln 107 �c4

A�C

� �-0.887057725 0.146382386 -6.05986655 3.3E-08

ln 10PA�C4

� �� 0.539828131 0.141919 3.803776331 0.000263

Coef coefficients for regression relationship, SE standard error, t-Stat the ratio of predictors’ coefficient over standard error, P-value

null hypothesis key


5.5 Confidence intervals

Once all of the predictors are concluded to affect the

final response, the confidence intervals for the model

can be defined. Confidence intervals include the range

of values that serve as good estimates of unknown

independent variables.

Vining et al. [46] reported that, if x0 denotes the

true unknown parameters of the sample size and

yðx0Þis the estimated value of the response using the

model, then

yðx0Þ ¼ b0 þ b1x0 þ b2x0 þ � � � þ bjxj; ð3Þ

where j = 0, 1, 2, 3, …, (number of parameters).

A confidence interval of 100(1 - a) for a given

response is given below. Here, x0 is the independent

variable.

yðx0Þ � tn�2;a=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiMSres 1þ 1

n

� �þ ðx0 � �xÞ2

SSX

! !vuut ;

ð4Þ

where yðx0Þis the response, tn-2, a/2 is the t-distribution

associated with the sample size and significance level,

n is the sample size, a is the significance level, x0 is the

predictor, MSres is the mean square of the residuals, �x is

the mean value of the sample, and SSx is the sum of

squares for x values.

Table 9 presents the coefficient of regression as

introduced in Eq. (2). In this analysis, since a was

defined as 0.05, the confidence interval domain was

considered to be 95 %. With these defined intervals,

95 % of the data points can be expected to lie

between the upper and lower bounds of the predic-

tion. However, increasing the vertical distance from

the model, as expressed in Eq. (1), will cause the

confidence in the prediction of data to become

lower.

6 Conclusion

The aim of this study was to seek possible solutions to

facilitate the utilization of PFA in construction.

Mixtures with various levels of PFA, cement, sand,

and moisture were prepared and subjected to UCT.

The cement content, PFA content, and density were

measured for 91 samples. The samples were each

10 cm long and 5 cm in diameter. The specimens were

cured for 1, 7, 14, and 28 days before testing. The PFA

content was 5–40 % of the total weight of the sample,

whereas the cement content was 5–25 %. The follow-

ing observations and conclusions are based on the

findings of this research.

The cement content has a significant effect on the

UCS of specimens. When the PFA content was fixed at

30 %, increasing the cement content increased the

UCS to 13.22 MPa after a curing period of 28 days.

The PFA content had an optimum value. An excessive

amount of PFA in a medium could decrease the UCS

under negative circumstances. When the cement

content was 25 % of the total weight of the medium,

the optimum content of PFA was 20 %. The OMC also

plays a vital role in obtaining higher UCS values.

A statistical model was introduced to predict the

UCS of a PFA–cement–sand mixture. The results

showed a strong correlation between each variable and

response. The findings indicated that, for the proposed

model, the assumptions made for multiple regression

were valid. The adjusted R2 value of 88.6 % that was

obtained indicated the good fit of the model with

observed data. In conclusion, the analysis results

proved that the model can estimate PFA mixtures with

a considerable level of accuracy.

Acknowledgments The authors are very grateful for the

valuable comments and suggestions of the reviewers. The

authors express their sincere thanks for the funding support they

received from HIR-MOHE University of Malaya under Grant

Table 9 Confidence intervals for statistical model

Predictors Lower 95 % mean Upper 95 % mean Lower 95.0 % prediction Upper 95.0 % prediction

Intercept 0.313422668 2.257885 0.313423 2.257885

C10

2.18749487 3.462093 2.187495 3.462093

ln 107 �c4

A�C

� �-1.177961951 -0.59615 -1.17796 -0.59615

ln 10PA�C4

� �� 0.257793948 0.821862 0.257794 0.821862


No. UM.C/HIR/MOHE/ENG/34. This research was supported

by Basic Science Research Program through the National

Research Foundation of Korea (NRF) funded by the Ministry of

Science, ICT & Future Planning (No. NRF-2013R1A1A1

060052). They also express their warm gratitude to the IEOS

at the University of Malaya for their help in providing facilities.

References

1. Bergen SD, Bolton SM, Fridley JL (2001) Design principles

for ecological engineering. Ecol Eng 18:201–210

2. Terashi M, Juran I (2000) Ground improvement—state of

the art. GeoEng 2000. Technomic, Lancaster, pp 461–519

3. Castro J, Sagaseta C (2011) Deformation and consolidation

around encased stone columns. Geotext Geomembr

29:268–276

4. Gue SS, Tan YC (20005) Chapter 23: failures of ground

improvement works in soft ground. In: Indraratna B, Chu J,

(eds) Ground improvement—case histories. Elsevier,

Amsterdam, pp 665–680

5. Ea Basha, Hashim R, Mahmud HB, Muntohar aS (2005)

Stabilization of residual soil with rice husk ash and cement.

Constr Build Mater 19:448–453

6. Larsson S (2005) State of practice report—execution,

monitoring and quality control. In: Proceedings of the

international conference on deep mixing, best practice and

recent advances. Stockholm, pp 732–786

7. Vories KC, Throgmorton D (2000) Proceedings of the use

and disposal of coal combustion by-products at coal mines:

a technical interactive forum at the US Department of

Energy, National Energy Technology Laboratory, Mor-

gantown: US Department of Interior, Office of Surface

Mining

8. Prabakar J, Dendorkar N, Morchhale R (2004) Influence of

fly ash on strength behavior of typical soils. Constr Build

Mater 18(4):263–267

9. Guleria SP (2011) Unconfined compressive strength of fly

ash-lime-gypsum composite mixed with treated tire chips.

J Mater Civ Eng 23(8):1255

10. Pone JDN, Hein Kaa, Stracher GB, Annegarn HJ, Finkl-

eman RB, Blake DR et al (2007) The spontaneous com-

bustion of coal and its by-products in the Witbank and

Sasolburg coalfields of South Africa. Int J Coal Geol

72:124–140

11. Tick HO (2010) Carbon capture and storage potential in

coal-fired plant in Malaysia—a review. Renew Sustain

Energy Rev 14(9):2697–2709

12. Okyay US, Dias D (2010) Use of lime and cement treated

soils as pile supported load transfer platform. Eng Geol

114:34–44

13. Kim B, Prezzi M, Salgado R (2005) Geotechnical properties

of fly and bottom ash mixtures for use in highway

embankments. J Geotech Geoenviron Eng 131:914–924

14. Huang Y, Bird RN, Heidrich O (2007) A review of the use of

recycled solid waste materials in asphalt pavements. Resour

Conserv Recycl 52:58–73

15. Naik TR, Singh SS, Hossain MM (1995) Abrasion resis-

tance of high-strength concrete made with class C fly ash.

ACI Mater J 92:649–659

16. Siddique R (2003) Effect of fine aggregate replacement with

Class F fly ash on the mechanical properties of concrete.

Cem Concr Res 33:539–547

17. Janz M, Johansson SE. The function of different binding

agents in deep stabilization. Report 9. Swedish Deep Sta-

bilization Research Center, Linkoping: SGI. Linkoping,

Sweden2002

18. ASTM C (2008) Standard specification for coal fly ash and

raw or calcined natural pozzolan for use in concrete. Annual

Book of ASTM Standards: American Society for Testing

and Materials, West Conshohocken, pp 1–4

19. Cokca E, Cokca E (2001) Use of class C Fly ashes for the

stabilization of an expansive soil. J Geotech Geoenviron

Eng 127:568–573

20. Nalbantoglu Z, Nalbantoglu Z (2004) Effectiveness of class

C fly ash as an expansive soil stabilizer. Constr Build Mater

18:377–381

21. Zhang M, Javadi A, Min X (2006) Triaxial tests of sand

reinforced with 3D inclusions. Geotext Geomembr

24:201–209

22. Bakharev T (2005) Geopolymeric materials prepared using

class F fly ash and elevated temperature curing. Cem Concr

Res 35:1224–1232

23. Xie Z, Xi Y (2001) Hardening mechanisms of an alkaline-

activated class F fly ash. Cem Concr Res 31:1245–1249

24. Bouzoubaa N, Lachemi M (2001) Self-compacting concrete

incorporating high volumes of class F fly ash: preliminary

results. Cem Concr Res 31:413–420

25. LaRosa JL, Kwan S, Grutzeck MW (1992) Zeolite forma-

tion in class F fly ash blended cement pastes. J Am Ceram

Soc 75:1574–1580

26. Sezer A, Inan G, Yilmaz H, Ramyar K (2006) Utilization of

a very high lime fly ash for improvement of Izmir clay.

Build Environ 41(2):150–155

27. Poon CS, Boost M (1996) The stabilization of sewage

sludge by pulverized fuel ash and related materials. Environ

Int 22:705–710

28. Asavapisit S, Chotklang D (2004) Solidification of elec-

troplating sludge using alkali-activated pulverized fuel ash

as cementitious binder. Cem Concr Res 34:349–353

29. Goodarzi F (2006) Characteristics and composition of fly

ash from Canadian coal-fired power plants. Fuel

85:1418–1427

30. Fraay ALA, Bijen JM, de Haan YM (1989) The reaction of

fly ash in concrete a critical examination. Cem Concr Res

19(2):235–246

31. Yoon YW, Cheon SH, Kang DS (2004) Bearing capacity

and settlement of tire-reinforced sands. Geotext Geomembr

22:439–453

32. Jo AN, Hafez MA, Norbaya S (2011) Study of bearing

capacity of lime–cement columns with pulverized fuel ash

for soil stabilization using laboratory model. Electr J Geo-

tech Eng 16:1595–1605

33. Demir I, Hughes RE, DeMaris PJ (2001) Formation and use

of coal combustion residues from three types of power

plants burning Illinois coals. Fuel 80:1659–1673

34. ASTM (2004). Standard practice for characterizing fly ash

for use in soil stabilization. D5239

35. Wayne G, Iwabuchi J, Shaffie R (1989) Influence of

cementation on liquefaction of sands. J Geotech Eng

115(8):1102–1117


36. Kolias S, Kasselouri-Rigopoulou V, Karahalios A (2005)

Stabilisation of clayey soils with high calcium fly ash and

cement. Cem Concr Compos 27(2):301–313

37. Stevens J (1982) Unified soil classification system. Civ Eng

ASCE 52(12):61–62

38. Devore JL (2011) Probability and statistics for engineering

and the sciences. Thomson Brooks/Cole, Belmont

39. Chatterjee S, Hadi AS (2006) Regression analysis by

example. Wiley, New York, p 607

40. Openshaw S (1992) Utilization of coal fly ash. M.Sc Thesis,

Florida University, p 36

41. Snelson DG, Kinuthia JM, Davies PA, Chang SR (2009)

Sustainable construction: composite use of tyres and ash in

concrete. Waste Manag 29:360–367

42. Larsen T (1985) Use of fly ash in structural concrete.

In: Florida in seminar proceedings: fly ash in highway

construction, Demonstration Project No. 59, November

1985, U.S. Department of Transportation and Federal

Highway Administration, NTIS: PB86186079XSP.1985

43. Camilleri J, Sammut M, Montesin FE (2006) Utilization of

pulverized fuel ash in Malta. Waste Manag 26:853–860

44. Theodorsson E (1988) BASIC computer program to sum-

marize data using nonparametric and parametric statistics

including Anderson–Darling test for normality. Comput

Methods Progr Biomed 26(2):207–213

45. Kamps U (1995) A concept of generalized order statistics.

J Stat Plan Inference 48(1):1–23

46. Vining G, Kowalski S (2010) Statistical methods for engi-

neers. Duxbury Press, Pacific Grove


prediction of unconfined compressive strength of pulverized fuel ash–cement–sand mixture

Documents