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SN Applied Sciences

, 1:1666 | Cite as

Modeling compressive strength of Moroccan fly ash–phosphogypsum geopolymer bricks

  • Mohamed Vadel Bebana
  • Khadija ZiatEmail author
  • Nawal Semlal
  • Mohamed Saidi
Research Article
  • 162 Downloads
Part of the following topical collections:
  1. 2. Earth and Environmental Sciences (general)

Abstract

Fly ash and phosphogypsum are industrial by-products requiring a cost to get rid of. Their potential use in the synthesis of geopolymer bricks provides great benefits such as the saving use of natural resources and the solid by-product waste management. Compressive strength is the most important parameter for geopolymer bricks design. In this study, two artificial neural networks, namely the multilayer perceptron (MLP) and the radial basis function (RBF) networks, have been investigated to predict the compressive strength. While developing the MLP or RBF models, 99 experimental observations were used for training and testing. Two evaluation steps were performed: The first step determined the effective number of hidden layers and neurons in each hidden layer as well as the appropriate activation function in predicting the compressive strength. The second evaluation step evaluated the accuracy with which the model would predict the compressive strength of geopolymers. The MLP neural network with two hidden layers having 8 and 10 neurons and the hyperbolic tangent activation function was the best model for predicting the compressive strength. Artificial neural networks can be used as a reliable and accurate technique for estimating the parameters of geopolymer materials.

Keywords

Phosphogypsum Fly ash Geopolymer bricks Modeling 

List of symbols

\(\bar{y}_{\text{prd}}\)

Mean of predicted values

\(\beta\)

Weight vector connecting the hidden neurons to the output neuron

\(\sigma\)

Impact factor of radial basis function

\(a_{j}\)

Weight vector connecting the jth hidden neuron

\(b_{j}\)

Threshold of the jth hidden neuron

c

Center of radial basis function

f

Output function

g

Activation function

N

Number of hidden neurons

n

Number of experimental data

\(R^{2}\)

Coefficient of determination

\(x_{i}\)

Vector of the ith input neuron

\(y_{\exp }\)

Experimental values

\(y_{\text{prd}}\)

Predicted values

Abbreviations

ANN

Artificial neural network

AT

Aging time

BP

Back-propagation

CS

Compressive strength (MPa)

CT

Curing temperature (°C)

FA

Fly ash

LM

Levenberg–Marquardt

MAE

Mean absolute of errors

MLP

Multilayer perceptron

PFA

Percentage of fly ash

PG

Phosphogypsum

PPG

Percentage of phosphogypsum

RBF

Radial basis function

RMSE

Root mean square errors

SHC

Sodium hydroxide concentration

W

Water

1 Introduction

Dumping or landfilling the solid by-product has a negative impact on the environment leading to many types of pollution. Therefore, the urgent investigation of the reuse of by-products is fundamental ensuring new materials to be safely and efficiently used in different applications. Fly ash (FA) is a solid waste generated from coal-fired electric power stations. The by-product phosphogypsum (PG) is obtained during the wet process phosphoric acid production by attacking phosphate rock by sulfuric acid. Many researchers have valorized these materials by their incorporating as a binder in cementitious materials [1, 2, 3, 4]. Altun and Sert [1] reported that phosphogypsum can be used in place of natural gypsum for Portland cement. The authors found that 3 wt% PG is the optimal content showing the highest mechanical property. Shen et al. [2] studied the effect of incorporating PG to improve the performances of lime–FA binder. The results showed that phosphogypsum promotes the binder action between lime and fly ash. Kumar [3] investigated the production of bricks from fly ash–lime–phosphogypsum. Outcomes indicate that these bricks are comparable with those of the ordinary burnt clay. Moreover, they are lighter and could be used for building construction. Shen et al. [4] reported that phosphogypsum can be used to produce the calcium sulfoaluminate cement with an optimal firing temperature between 1250 and 1300 °C.

Geopolymers, originally proposed by the French scientist Davidovits [5], designated a large range of materials characterized by chains or networks of inorganic molecules that can be used as a binder in concrete. Their main properties are quick compressive strength development, low permeability, resistance to acid attack and good resistance to freezing cycles [6]. The geopolymers were produced from a vast variety of raw materials such as metakaolin [7], clay [8] and other natural silica-aluminates [9] as well as industrial process wastes such as coal fly ash [10, 11], lignite bottom ash [12], metallurgical slag [13, 14] and phosphogypsum [15, 16].

The prediction of the compressive strength is an essential parameter for successful geopolymer design. Indeed, several researchers have predicted the compressive strength using different methods such as the regression analysis, the genetic algorithm, the fuzzy logic and the artificial neural networks [17, 18, 19, 20]. ANN is one of the most commonly applied methods because of its effectiveness and large applicability [21, 22, 23]. Nazari and Torgal [24] have developed different models based on ANNs to predict the compressive strength of various types of geopolymers. Mansour et al. [25] built trained and tested ANNs to predict the ultimate shear strength of reinforced concrete beams with transverse reinforcements. Recently, Naderpour et al. [26] have predicted the compressive strength of recycled aggregate concrete using artificial neural networks.

The present study aims the prediction of the compressive strength of Moroccan fly ash–phosphogypsum geopolymer bricks by using radial basis function and multilayer perceptron neural networks. The effects of the number of hidden layers, the neurons in hidden layers as well as the activation functions on the prediction of the compressive strength were evaluated. Various input parameters of models are considered, whereas the compressive strength is used independently as the output parameter.

2 Materials and methods

2.1 Materials and sample preparation

Fly ash used in this study was from LafargeHolcim in the west of Morocco. Phosphogypsum is issued from phosphate rock original from Morocco. FA was used in its natural particle size distribution without further reduction through milling. PG was washed with tap water, filtered and dried in the oven at 60 °C for 24 h, then grounded and sieved through a sieve of 120 µm. Figure 1 shows the materials used for making geopolymer bricks at a laboratory scale. The chemical compositions of fly ash and phosphogypsum are shown in Table 1.
Fig. 1

Materials

Table 1

Chemical composition of fly ash and phosphogypsum in weight percentage of oxides

Composition (%)

SiO2

Al2O3

Fe2O3

CaO

MgO

SO3

P2O5

F

LOI

FA

50.85

26.55

3.69

5.45

1.56

0.46

1.16

6.89

PG

2.06

1.04

4.28

20

0.137

43.5

0.697

2.48

22

The sodium hydroxide NaOH (analytical reagent grade, Fluka) solution was obtained by dissolving sodium hydroxide pellets in bi-distilled water and allowed to cool to room temperature. The mixtures were obtained by hand mixing for 5 min.

Samples were prepared from fly ash, washed and sieved phosphogypsum, alkaline liquid and tap water. FA was partially replaced with PG at the level of, 0, 5, 10, 15, 20, 25 and 30% by weight. Four concentrations of NaOH 1, 5, 10 and 15 M were added to a different liquid ratio to form geopolymer pastes. The paste samples were cast in cylindrical plastic molds with a diameter of 20 mm and height of 30 mm and vibrated to remove entrapped air. The manufacturing process of FA–PG-based geopolymer bricks is shown in Fig. 2. The specimens were cured at a temperature of 60, 80 and 100 °C for 24 h in order to accelerate the geopolymer reaction and thus achieve the hardening of the structure. The bricks were placed in room temperature until the aging time test which was 3, 7 or 28 days.
Fig. 2

Flowchart of the experimental procedure of FA–PG geopolymer bricks synthesis

2.2 Compressive strength test

The compressive strengths of specimens at 3, 7 and 28 days were determined following the procedure described in BS EN 1961:2005 using an automatic compression test machine. Four compression strength tests were carried out for samples prepared with each ratio, and the values reported were the averages of the four compression strength values. Table 2 shows the details of the mixture proportions and the corresponding results under the considering experimental conditions. The specimens that contain FA, PG and NaOH solutions are abbreviated as FAPG1 to FAPG33.
Table 2

Details of mix proportions for different FA–PG-based geopolymer bricks

Samples

FA (%)

PG (%)

NaOH (M)

Added water (%)

Water solid ratio

Aging time (days)

Temperature (°C)

FAPG1

100

0

1

39.6

0.396

3, 7, 28

60

FAPG2

95

5

1

39.1

0.391

3, 7, 28

60

FAPG3

90

10

1

38.6

0.386

3, 7, 28

60

FAPG4

85

15

1

38.1

0.381

3, 7, 28

60

FAPG5

80

20

1

37.6

0.376

3, 7, 28

60

FAPG6

75

25

1

37.1

0.371

3, 7, 28

60

FAPG7

70

30

1

36.6

0.366

3, 7, 28

60

FAPG8

100

0

1

39.6

0.396

3, 7, 28

80

FAPG9

95

5

1

39.1

0.391

3, 7, 28

80

FAPG 10

90

10

1

38.6

0.386

3, 7, 28

80

FAPG 11

85

15

1

38.1

0.381

3, 7, 28

80

FAPG 12

80

20

1

37.6

0.376

3, 7, 28

80

FAPG 13

75

25

1

37.1

0.371

3, 7, 28

80

FAPG 14

70

30

1

36.6

0.366

3, 7, 28

80

FAPG 15

100

0

1

39.6

0.396

3, 7, 28

100

FAPG 16

95

5

1

39.1

0.391

3, 7, 28

100

FAPG 17

90

10

1

38.6

0.386

3, 7, 28

100

FAPG 18

85

15

1

38.1

0.381

3, 7, 28

100

FAPG 19

80

20

1

37.6

0.376

3, 7, 28

100

FAPG 20

75

25

1

37.1

0.371

3, 7, 28

100

FAPG 21

70

30

1

36.6

0.366

3, 7, 28

100

FAPG 22

80

20

1

39.6

0.396

3, 7, 28

60

FAPG 23

80

20

1

39.4

0.394

3, 7, 28

60

FAPG 24

80

20

1

39.2

0.392

3, 7, 28

60

FAPG 25

80

20

5

38

0.38

3, 7, 28

60

FAPG 26

80

20

5

37

0.37

3, 7, 28

60

FAPG 27

80

20

5

36

0.36

3, 7, 28

60

FAPG 28

80

20

10

35.5

0.355

3, 7, 28

60

FAPG 29

80

20

10

34

0.34

3, 7, 28

60

FAPG 30

80

20

10

32

0.32

3, 7, 28

60

FAPG 31

80

20

15

33.5

0.335

3, 7, 28

60

FAPG 32

80

20

15

31

0.31

3, 7, 28

60

FAPG 33

80

20

15

28

0.28

3, 7, 28

60

2.3 Artificial neural network and performance of models

The artificial neural network is a system of data processing based on the working mechanism of the brain. The fundamental processing consists of a linear combination of input variables into a hidden layer of units where new combinations are created as final output variables. The architecture of ANN requires the knowledge of the number of network layers, the number of neurons in the layers as well as the learning algorithms and the neuron transfer functions. The theoretical backgrounds of neural network models can be found in [27, 28, 29, 30, 31].

The radial basis function network applies RBF neurons in its hidden layer. Each RBF node is composed of a centroid, an impact factor, and its output is a function with radial symmetry [27, 28].

The multilayer perceptron is a class of feedforward neural network that has been commonly used for the approximate function [28]. The MLP learns the information of the dataset pattern using an algorithm known as “training.” This algorithm modifies the weights of the neurons according to the error between the values of real output and target output, where it provides nonlinear regression between the input variables and the output variables [32]. The back-propagation (BP) with the gradient descent technique and Levenberg–Marquardt (LM) is the most well-known training algorithms for the multilayer perceptron [32]. Table 3 lists the output functions of the RBF and MLP network models and the used activation functions.
Table 3

Used activation functions and output functions

ANN type

Output function

Activation function

RBF [27]

\(f(x) = \sum\limits_{i = 1}^{N} {\beta_{i} g_{i} (x)}\)

\(g_{i} (x) = \exp \left( { - \frac{{\left\| {x - c_{i} } \right\|^{2} }}{{2\sigma_{i}^{2} }}} \right)\)

MLP [28]

\(f(x) = \sum\limits_{j = 1}^{N} {\beta_{j} } g\left( {\sum\limits_{i = 1}^{n} {a_{j} x_{i} + b_{j} } } \right)\)

\(g(x) = \frac{{{\text{e}}^{2x} - 1}}{{{\text{e}}^{2x} + 1}}\)

\(g(x) = \frac{1}{{1 + {\text{e}}^{ - x} }}\)

ci and \(\sigma_{i}\) are the center and impact factor of the ith RBF node, x is the input vector, and \(\left\| . \right\|\) denotes a norm that is usually Euclidean. \(\beta_{i}\) is the weight connecting the ith RBF hidden node to the output node, and g is the activation function. \(a_{j}\) is the weight vector connecting the jth hidden neuron and the input neurons, and \(b_{j}\) is the threshold of the jth hidden neuron. \(a_{j} x_{i}\) represents the inner product of \(a_{j}\) and \(x_{i}\), N is the number of hidden neurons, and n is the number of experimental data

To evaluate the performances of models, three error functions, namely the coefficient of determination (R2) [33], the root mean square error (RMSE) and the mean absolute error (MAE) [34], are used. Their mathematical expressions are as follows:
$$R^{2} = \frac{{\sum\nolimits_{i = 1}^{n} {\left( {y_{\exp ,i} - \bar{y}_{\text{prd}} } \right)^{2} } }}{{\sum\nolimits_{i = 1}^{n} {\left( {y_{\exp ,i} - \bar{y}_{\text{prd}} } \right)^{2} } + \sum\nolimits_{i = 1}^{n} {\left( {y_{\exp ,i} - y_{{{\text{prd}},i}} } \right)^{2} } }}$$
(1)
$${\text{RMSE}} = \sqrt {\frac{1}{n}\sum\limits_{i = 1}^{n} {\left( {y_{\exp ,i} - y_{{{\text{prd}},i}} } \right)^{2} } }$$
(2)
$${\text{MAE}} = \frac{1}{n}\sum\limits_{i = 1}^{n} {\left| {\left( {y_{\exp ,i} - y_{{{\text{prd}},i}} } \right)} \right|}$$
(3)
where \(y_{\exp }\) and \(y_{\text{prd}}\) are the experimental and predicted output values and \(\bar{y}_{\text{prd}}\) is the mean of predicted values.

3 Results and discussion

The most difficult thing in artificial neural network studies is to find the appropriate network architecture, which is based on the determination of the number of optimal layers and neurons in the hidden layers as well as of the suitable activation function. In the present study, three- and four-layer perceptron was investigated by using IBM SPSS version 20 and MATLAB version R2015a software. For MLP-MATLAB, the number of hidden layers was limited to one layer with the sigmoid activation function. The optimal number of neurons was selected using the neural network toolbox. The RBF model was tested for the same version of IBM SPSS. The BP and LM training algorithms were used for IBM SPSS and MATLAB software, respectively. A total of 40 artificial networks were constructed using 99 experimental datasets. For all models, about 70% of samples were randomly assigned to the training phase and the remaining 30% of samples were allocated to the testing phase. The learning and momentum rates were 0.9 and 0.4, respectively. The maximum epoch of the network varied from 1000 to 2000.

The ANN’s architectures used in this work are composed of an input layer with six input parameters: percentage of phosphogypsum (PPG), percentage of fly ash (PFA), curing temperature (CT), aging time (AT), sodium hydroxide concentration (SHC) and water (W), one or two hidden layers, and an output layer (compressive strength). The input parameters are the various constituents of the geopolymer specimens as used in the laboratory experiments.

Table 4 lists the fitting values of error functions for single-layer feedforward (RBF) and multilayer perceptron models. Outcomes indicate that the number of neurons in the hidden layers and the activation function affect the performance of the model. Similar observations were reported in the literature [21, 24]. Also from Table 4, we can conclude that the MLP models are able to predict the compressive strength values more accurately than the RBF one. Among multilayer perceptron networks, the MLP-III with architecture 6–8–10–1 (six input neurons, two hidden layers having 8 and 10 neurons, and one output neuron) with the hyperbolic tangent activation function is the best model for predicting the compressive strength of FA–PG-based geopolymer bricks, as confirmed by its high R2 value and the lowest RMSE and MAE values. Figure 3a, b depicts the predictive performance of the MLP-III (6–8–10–1) model. From Fig. 3a, it can be seen that the predicted compressive strength values present better agreement with those of experimentally determined values. These results prove that the model was able to reproduce the experimental compressive strength results with high accuracy. The results of the regression analysis (Fig. 3b) show that the experimental and predicted compressive strengths are highly correlated, with a coefficient of determination close to 1.
Table 4

Best-fitting values of the compressive strength of FA–PG-based geopolymer bricks

Models

Hidden layer 1

Hidden layer 2

Activation function

Statistical parameters

R2

RMSE

MAE

Number of neurons

Number of neurons

MLP-I-MATLAB

12

0

Sigmoid

0.9608

0.7320

0.4968

MLP-I-SPSS

16

0

Hyperbolic tangent

0.9434

0.8877

0.6499

MLP-I-SPSS

16

0

Sigmoid

0.8952

1.2398

1.0245

RBF-SPSS

28

0

Gaussian

0.9487

0.8424

0.5963

MLP-II-SPSS

6

8

Hyperbolic tangent

0.9531

0.8037

0.5496

MLP-II-SPSS

6

8

Sigmoid

0.9367

0.9419

0.6861

MLP-III-SPSS

8

10

Hyperbolic tangent

0.9622

0.7185

0.4455

MLP-III-SPSS

8

10

Sigmoid

0.9394

0.9202

0.6742

MLP-IV-SPSS

10

12

Hyperbolic tangent

0.9517

0.8158

0.5576

MLP-IV-SPSS

10

12

Sigmoid

0.9350

0.9551

0.7148

Fig. 3

Predictive performance of the MLP-III (6–8–10–1) model

  1. (a)

    Comparison between measured and predicted compressive strength values for all samples.

     
  2. (b)

    Regression analysis of the MLP-III (6–8–10–1) model.

     
The reliability of the model was tested for different experimental conditions. The predicted and experimental values of CS, as a function of the percentage of phosphogypsum, for NaOH (1 M), at different curing temperatures and aging times based on MLP-III (6–8–10–1) neural network, are depicted in Fig. 4. The plots indicate that the MLP-III (6–8–10–1) model fits well the experimental data of the compressive strength of FA–PG-based geopolymer bricks. Also from Fig. 4, we can see that by increasing the curing temperature from 60 to 100 °C, the compressive strength decreases from 8.91 to 7.14 MPa. Similar observations were reported in other researches [35, 36]. On the other hand, the rise in aging time beyond 7 days had not a beneficial effect on the compressive strength. In addition, the optimal percentage found of phosphogypsum replacement is 10%. Therefore, the best conditions for Moroccan FA–PG-based geopolymer bricks are 60 °C, 28 days and 10% for curing temperature, aging time and phosphogypsum percentage, respectively.
Fig. 4

Compressive strength plots as a function of phosphogypsum percentage, at different curing temperatures and aging times. The symbols and dashed lines are the experimental and predicted values based on MLP-III (6–8–10–1) neural network

The effect of sodium hydroxide concentration on the compressive strength, at various aging times, is presented in Fig. 5. The increase in NaOH concentration and aging time leads to the rise in the compressive strength. Indeed, the CS was varied from 8 to 17.4 MPa with the variation of sodium hydroxide from 1 to 15 M. This was ascribed to the formation of sodium aluminosilicate, obtained from the dissolution of Si4+ and Al3+ ions from fly ash, caused by the increase in NaOH concentration [37].
Fig. 5

Effect of NaOH concentration on the compressive strength at various aging times. The symbols and dashed lines are the experimental and predicted values based on MLP-III (6–8–10–1) neural network model

Figure 6 depicts the relative importance of input parameters on the prediction of the compressive strength of FA–PG geopolymer bricks based on the MLP-III (6–8–10–1) model. The results clearly show that the concentration of sodium hydroxide is the most significant parameter for the compressive strength prediction.
Fig. 6

Relative importance of input parameters for the prediction of the compressive strength of FA–PG geopolymer bricks based on the MLP-III (6–8–10–1) model

The predictive performance of the MLP-III (6–8–10–1) model was tested on four data from the literature [17, 38, 39, 40]. The results are evaluated based on three mathematical error functions: R2, RMSE and MAE. The obtained values of the fitting error functions are summarized in Table 5. Outcomes indicate that the MLP-III (6–8–10–1) model can fit the experimental data very well.
Table 5

Fitting error functions values obtained by applying the MLP-III (6–8–10–1) model to data from the literature

 

MLP-III (6-8-10-1) 

R2

RMSE

MAE

Nazari [17]

0.9903

0.7361

0.3632

Ghezal and Khayat [38]

0.9918

0.7225

0.5644

Nazari and Riahi [39]

0.9806

0.0012

0.00086

Soudki et al. [40]

0.9811

0.9688

0.6848

4 Conclusion

Fly ash and phosphogypsum can be used as alternate binders for the synthesis of geopolymer bricks. The best geopolymerization process was obtained for 60 °C, 28 days and 10% for curing temperature, aging time and phosphogypsum percentage, respectively.

The artificial neural network was tested as an alternative to experimental tests for simulating the compressive strength of FA–PG-based geopolymers. The results show that the ANN technique may be a promising method for rapid and accurate estimation of the compressive strength of FA–PG-based geopolymer bricks.

This study contributes to a better understanding of the synthesis of geopolymer bricks based on fly ash and phosphogypsum and enables the prediction of the compressive strength using the ANN technique.

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laboratoire Physico-Chimie des Matériaux, Substances Naturelles et Environnement, Faculty of Sciences and TechniquesAbdelmalek Essaâdi UniversityTangierMorocco
  2. 2.OCP S.AJorf LasfarMorocco

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