# Modeling compressive strength of Moroccan fly ash–phosphogypsum geopolymer bricks

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## 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

*j*th hidden neuron- \(b_{j}\)
Threshold of the

*j*th 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

*i*th 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

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

Composition (%) | SiO | Al | Fe | CaO | MgO | SO | P | 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.

### 2.2 Compressive strength test

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].

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] | \(f(x) = \sum\limits_{j = 1}^{N} {\beta_{j} } g\left( {\sum\limits_{i = 1}^{n} {a_{j} x_{i} + b_{j} } } \right)\) | \(g(x) = \frac{{{\text{e}}^{2x} - 1}}{{{\text{e}}^{2x} + 1}}\) \(g(x) = \frac{1}{{1 + {\text{e}}^{ - x} }}\) |

*R*

^{2}) [33], the root mean square error (RMSE) and the mean absolute error (MAE) [34], are used. Their mathematical expressions are as follows:

## 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.

^{2}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.

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

Models | Hidden layer 1 | Hidden layer 2 | Activation function | Statistical parameters | ||
---|---|---|---|---|---|---|

| 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 |

- (a)
Comparison between measured and predicted compressive strength values for all samples.

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

^{4+}and Al

^{3+}ions from fly ash, caused by the increase in NaOH concentration [37].

^{2}, 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.

## 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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