Prediction performance of compressive strength of cementitious

Multidiscipline Modeling in Materials and Structures Prediction performance of compressive strength of cementitious materials containing rubber aggregates and filler using fuzzy logic method Mohamed Turki, Ines Zarrad, Michéle Quéneudec, Jamel Bouaziz,

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Article information: To cite this document: Mohamed Turki, Ines Zarrad, Michéle Quéneudec, Jamel Bouaziz, (2017) "Prediction performance of compressive strength of cementitious materials containing rubber aggregates and filler using fuzzy logic method", Multidiscipline Modeling in Materials and Structures, Vol. 13 Issue: 2, pp.284-296, https://doi.org/10.1108/MMMS-12-2016-0066 Permanent link to this document: https://doi.org/10.1108/MMMS-12-2016-0066 Downloaded on: 13 August 2017, At: 06:22 (PT) References: this document contains references to 25 other documents. To copy this document: [email protected] The fulltext of this document has been downloaded 11 times since 2017* Access to this document was granted through an Emerald subscription provided by Token:Eprints:BF8VTZXUMWWMDCKCCFX4:

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MMMS 13,2

284 Received 25 December 2016 Revised 13 February 2017 20 March 2017 Accepted 10 April 2017

Prediction performance of compressive strength of cementitious materials containing rubber aggregates and filler using fuzzy logic method Mohamed Turki, Ines Zarrad, Michéle Quéneudec and Jamel Bouaziz


Department of Material Engineering, National School of Engineers of Sfax, Sfax, Tunisia and University of Picardie Jules Verne, Amiens, France Abstract Purpose – The purpose of this paper is to focus on compressive strength modelling of cementitious mixtures like mortar and Roller-compacted concrete (RCC) containing rubber aggregates from shredded worn tires and filler using adaptive neuro fuzzy inference systems (ANFIS). Design/methodology/approach – The volume substitution contains a ratio of rubber aggregates vs sand in mortar and with crushed sand in RCC and ranges from 0 to 50 per cent. As for the filler, they are substituted with sand by 5 per cent in mortar mixture. The methodology consists of optimizing the percentage of substitution in cementitious mixtures to ensure better mechanical properties of materials like compressive strength. The prediction of compressive strength and the optimization of cementitious mixtures encourage their uses in such construction pavements, in area games or in other special constructions. These cementitious materials are considered as friendly to the environment by focussing on their improved deformability. Findings – The results of this paper show that the performance of the constructed fuzzy method was measured by correlation of experimental and model results of mortar and RCC mixtures containing both rubber aggregates and filler. The comparison between elaborated models through the error and the accuracy calculations confirms the reliability of the ANFIS method. Originality/value – The purpose of this paper is to assess the performance of the constructed fuzzy model by the ANFIS method for two types of cementitious materials like mortar and RCC containing rubber aggregates and filler. The fuzzy method could predict the compressive strength based on the limited measurement values in the mechanical experiment. Furthermore, the comparison between the elaborated models confirms the reliability of the ANFIS method through the error and the accuracy calculations for the best cementitious material mixtures. Keywords Compressive strength, ANFIS, Rubber, Cementitious materials, Filler, Performance modelling Paper type Research paper

Multidiscipline Modeling in Materials and Structures Vol. 13 No. 2, 2017 pp. 284-296 © Emerald Publishing Limited 1573-6105 DOI 10.1108/MMMS-12-2016-0066

1. Introduction Roller-compacted concrete (RCC) is recognized as a durable material in pavements. It can also be used in urban street reconstruction, residential subdivision roads, industrial and commercial sites, hard stands, automobile manufacturing facilities, etc. In addition, it is quite economical because of its low production cost in comparison with bituminous binder, and develops high coverage on roadways. Pavement surfaces coated with RCC are considered as rigid pavements. In fact, the bituminous flexible pavements suffer from the disadvantage of their suppleness under the effect of heavy traffic. This high tonnage causes the development of ruts and ridges. Nowadays, the increase in worn tyres each year introduces a strong negative impact on the environment. Rubber shredded from worn tyres is a mixture of different proportions of The authors would like to thank the research Group REGIM at the National School of Engineering of Sfax in TUNISIA for their technical support during the modelling work using the fuzzy logic method.


natural and synthetic rubber, carbon black, sulfur, and other chemicals. Several studies have been carried out to reuse rubber aggregates in cementitious composites and solve the waste tires problem (Benazzouk et al., 2003; Labani et al., 2004; Turki, Ben Naceur, Makni, Rouis and Sai, 2009). Benazzouk et al. (2003) have investigated the influence of the alveolar texture of rubber aggregates on the physico-mechanical behaviour of cement-rubber composites. Labani et al. (2004) have reused rubber aggregates in cementitious composites to evaluate their hydrothermal behaviour. Turki, Zarrad, Mollines, Rouis and Queneudec (2009) and Turki, Ben Naceur, Makni, Rouis and Sai (2009) have focused on microstructure of rubberized-mortar mixtures and their influence on the specimens physico-mechanical properties. In other cases, the effect of rubber increases the concrete deformability remarkably without facing the rutting problem of RCC pavements. For instance, the research of Patell and Pitroda (2015) focused on crumb rubber with various proportions for mixing of bituminous pavements to optimize rubber percentage that can be used to obtain the desired strength. In addition, it revealed that rubberized concrete had the ability to absorb a large amount of plastic energy under compressive and tensile loads. Other related studies ( Jingfu et al., 2009) revealed the inferred mechanical properties with shrinkage behaviour of RCC containing rubber additives. It did not demonstrate the typical brittle failure, but rather a ductile, plastic failure mode (Neil and Senouci, 1994). According to Shafieyzadeh (2013), styrene-butadiene rubber in concrete can reduce water binder ratio effectively and slightly enhance both flexural and compressive strengths in the presence of silica fume. Other works used rubber and fly ash with Portland cement as construction materials. Mortar-rubber aggregates with fly ash could be the leading material in sustainable construction (Yilmaz and Degirmenci, 2009). Wang et al. (2005) demonstrated that the effect of rubber in mortars had an acceptable mechanical properties and frost resistance. During the previous years, the fuzzy logic method (adaptive neuro fuzzy inference systems (ANFIS)), as a sub-field of intelligent systems, has been widely used in different fields to solve several engineering problems with complex mechanisms like in construction projects. Research modelling studies of Topçu and Sandemir (2008) predicted the mechanical behaviour of one type of material such as mortar-rubber particles with the Fuzzy logic method. Other ANFIS research of Lin and Huang (2013) focused on different types of membership functions (triangular function, trapezoidal function, bell function, and Gaussian function) for their models. The results from the four developed prediction models were compared with the verification data to confirm the feasibility of this approach for one type of metal materials. Furthermore, a similar modelling research elaborated by Turki et al. (2012) investigated the effect of filler on the mechanical behaviour modelling of mortar-rubber by using the ANFIS method. Other modelling studies (Turki, Zarrad, Mollines, Rouis and Queneudec, 2009) on the mechanical behaviour modelling of mortarrubber aggregates composite took into account the influence of the rubber volume fraction on mortar phase. The constitutive equations of the model were used to analyse inelastic properties of structures made of mortar-rubber aggregates in a multi-directional framework. However, some models seem to be more complicated to predict the mechanical behaviour of composites containing rubber and other additives. Otherwise, the mispredictions of compressive strength as a main mechanical characteristic of cementitious materials contribute to the excessive deflections and cracking. Therefore, an accurate prediction method is needed using the MATLAB fuzzy toolbox. Using a given input/output data set, the toolbox function ANFIS constructs a fuzzy inference system (FIS) whose membership function parameters are adjusted using either a back propagation algorithm alone or in combination with a least squares type of method. This adjustment allows fuzzy systems to learn a suitable model from the data (Lin and Huang, 2013). In addition, all of the previous studies lack the correlation between different materials to elaborate the best ANFIS model.

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First, the Fuzzy logic method proposed herein led to a useful model with less complexity (the number of rules) regarding its advantages of simplicity, transparency and linguistic explanation in comparison with other models used in civil engineering. It could reveal the relationship between input parameters and output results and its ability to generate new data. ANFIS is based on training and testing phases to obtain comparable values from the experimental results for two types of cementitious materials: mortar-rubber with filler and RCC containing rubber aggregates. Second, the purpose of this paper was to assess the performance of the constructed fuzzy model by ANFIS method for mortar and RCC containing rubber aggregates and filler. The comparison between the elaborated models confirms the reliability of ANFIS method through the error and the accuracy calculations for the best cementitious materials mixtures.


2. Materials and methods Rubber aggregates were obtained by shredding worn tyres. Rubber particles were introduced in mortar and RCC mixtures by partial volume substitution of sand and crushed sand. The RCC and mortar-rubber-free materials were taken as reference materials. Several specimen of mixtures were prepared with percentages ranging from 0 to 50 per cent and 5 per cent of rubber and filler, respectively. The mortar and RCC mixture parameters have two different water-cement ratios that are about 0.5 and 0.56, respectively. Different samples consist of a mixture of cement, water, sand, crushed sand, aggregates, rubber and filler (Table I). The semi-empirical method of Talbot Fuller-Thompson identified the RCC materials mass composition with an optimal water cement ratio that is determined by a modified Proctor test. The dry rubber apparent density is about 1,200 kg/m3 for the sand, 2,650 kg/m3 for the crushed sand and 2,550 kg/m3 for the aggregates. The sand, the crushed sand and rubber have 0-2, 0-5 and 1-4/2-8 mm size grading, respectively. The hydraulic binder was a Portland cement CPA CEM I 42.5 with a specific density of 3,100 kg/m3. The tests were carried out on prismatic samples (4 × 4 × 16 cm3) for mortar and cubic specimens (10 × 10 × 10 cm3) for RCC specimens. All samples have been cured for 28 days at a constant temperature (20°C) and with 100 per cent relative humidity prior to testing. The compressive strength (R) was performed on several prismatic and cubic test samples. Each value of compressive strength was the average of three tests. The modelling was developed using ANFIS. It is a formulation method from a given input and output using fuzzy logic with MATLAB user’s guide. The hybrid method is the combination of the back-propagation algorithm and the least-squares method. This involves identifying the various downstream calculation parameters by the least-square algorithm. The local settings would be adjusted upstream by calculating the learning of back-propagation algorithm (Baklouti and Alimi, 2012). The proposed model is based on the localization of the stress on the phase’s level (rubber and cementitious mixtures). In the training set, the case study of ANFIS system adopt Gaussian function that has seven inputs as variables for RCC: cement (C), water (W), sand (S), crushed sand (CS), gravel (G), rubber (R) and curing period (CP). However, mortar considers five inputs which are as follows: cement, sand, water, filler (F) and curing period. The number of inputs depends not only on variability of RCC and mortar mixtures’ components but also on the curing conditions to predict the best value of compressive strength that is

Table I. Mass composition of mortar and RCC mixtures (Kg/m3)

Material

Cement

Water

Sand

Crushed sand

Aggregates

RCC Mortar

250 450

140.59 225

244.27 1,350

843.58 –

967.03 –


considered as a single output. The architecture of ANFIS used in this research is shown in Figure 1. After training, tests were performed to obtain comparable values to the experimental results. 3. Results and discussion 3.1 Structure of ANFIS Several systems are not amenable to conventional modelling approaches due to the lack of precise, formal knowledge about the system, strongly nonlinear behaviour, high degree of uncertainty, or time varying characteristics. Fuzzy modelling has been recognized as a powerful tool which can facilitate the effective development of models by combining information from different sources, such as empirical models, heuristics and data (Babuska, 2002). ANFIS system predicts a complex nonlinear mapping by utilizing fuzzy inference methodologies with the input-output relationship of models ( Jang, 1993). Because it is a more compact and computationally efficient representation than a Mamdani system, the Sugeno system lends itself to the use of adaptive techniques for constructing fuzzy models. These adaptive techniques can be used to customize the membership functions so that the fuzzy system best models the data. It should be noted that the advantage of using such system is that it gives out realistic values, not a fuzzy value that needs a defuzzification phase (Zadeh, 1999). The FIS has basically four components: fuzzyfication, fuzzy rule base, fuzzy output engine, defuzzyfication and application of fuzzy steps (AND, OR and NOT) in the rule’s antecedent (Zadeh, 1965). For the conception of ANFIS system, the zero-order Sugeno type was selected as an inference system (Mamdani, 1974). ANFIS structure was completed by the selection of a learning hybrid algorithm. Then, it constructs an FIS whose membership functions are adjusted using either the back-propagation algorithm alone or by using the hybrid method (Topçu and Sandemir, 2008). For a Sugeno fuzzy model, a typical rule set with 162 fuzzy rules of mortar and 1,458 fuzzy rules of RCC can be expressed as follows:


Rule n : IfðC is Ai Þ and ðW is Bi Þ and ðS is C i Þ and ðCS is Di Þ and ðA is E i Þ and ðF is F i Þ and ðR is Gi Þ and ðCP is H i Þ then f i ¼ pi C þqi W þr i S þsi CSþt i Aþui F þvi R þwi CPþZ i

(1)

where i represents a membership function and fi the output variable.

Inputs

Fuzzy Inference System

Output

Cement (C) Water (W) Sand (S)/Filler (F) Crushed Sand (CS) Rubber (R) Aggregate (A) Curing Period (CP)

Sugeno type: Fuzzyfication – Defuzzyfication processes

Compressive strength (R) Figure 1. Structure of adaptive neuro fuzzy inference system (ANFIS)

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ANFIS does not provide a specific equation in comparison with other types of models (Neil and Senouci, 1994; Shafieyzadeh, 2013; Turki et al., 2012). The model was developed by Turki, Zarrad, Mollines, Rouis and Queneudec (2009) and Turki, Ben Naceur, Makni, Rouis and Sai (2009) in the thermodynamic frame of non-associated plasticity with the Continuum Damage Mechanics theory. This framework allowed considering observations and experimental results and avoiding behaviour incompatibilities. Shafieyzadeh (2013) proposed a mathematical model that focusses on the relationship between compressive strength and time of curing in water with a logarithmic equation by Popovics (1998). Neil and Senouci (1994) developed a model in order to predict the strength of rubberized concrete. Two neural network models were developed to predict the reduction in the compressive and tensile strength as a result of replacing the mineral aggregate with a rubber aggregate. A maximum difference of 9.2 per cent between test results and model prediction was detected during the testing of the neural network. The fuzzy-logic-based algorithm model is obtained with the help of coding in MATLAB software. Since grid partitioning was selected, fuzzy rules are established for the inference system. Variables and laws are associated to use the technique of decomposition max-min with logical AND operator. ANFIS embedded MATLAB is used primarily for fuzzy systems of Sugeno type to a single output by introducing parameters as examples, representing the input variables and desired outputs associated with these variables . The parameters associated with the membership functions will be changed throughout the learning process, because the calculation of these parameters or adjustment is facilitated by the gradient vector. It provides a measure giving information about how Fuzzy system models the input/ output for a given database of examples and reduces measurement errors (Inan et al., 2007). The training phase can determine the characteristic of parameters that are the centres of membership functions. Furthermore, the membership function plots of RCC input variables in the R training are shown in Figure 2. 3.2 Prediction performance of compressive strength by the ANFIS model Experimental compressive strength (R). Rubber particles significantly affect the mechanical properties of mortar and RCC specimens especially the compressive strength. It decreases from 48, 63 and 81 per cent to 10, 20 and 30 per cent of mortar-rubber substitution, respectively (Table II). As a result, some fine particles were added, as fillers, to remedy the R decrease. The addition of filler slightly improves the compressive strength of mortar-rubber samples. The R revealed 17, 41 and 65 per cent decreases for 10, 20 and 30 per cent of rubber substitution, respectively. However, RCC compressive strength seems constant until 20 per cent of rubber substitution and the decrease is observed to be quite weak upto 30 per cent (Table II). Predicted compressive strength. The predicted values obtained using ANFIS for the compressive strength have been plotted against their respective experimentally obtained values as shown in Table III. The R prediction of RCC and mortar filler with rubber were illustrated by the ANFIS model (Figure 1). The case study system has considered seven inputs for RCC that are illustrated in Table I as a mass composition of different mixtures (cement, sand, crushed sand, gravel, rubber and water) with the curing period in days. Moreover, mortar mixtures depend only on five inputs which consist of the dosage components (cement, sand, water and filler) with the curing period in days, too. However, it has a single output “R” which is the compressive strength measured experimentally (Table II). To achieve an optimal fuzzy model, different clustering radii were introduced to subtract clustering algorithm and the performance of the consequent fuzzy model was investigated. Subtractive clustering was generated by a design parameter, called clustering radii (Zargar et al., 2014). Each cluster may contain a variety of mass composition of cementitious materials.

(a)

Membership function plots plot points:

in2mf1 1

in2mf2

181

(b)

in2mf3

in1mf1 1


in1mf2

0.5

0.5

150

160

170

180

190

200

210

220

230

240

14

250

16

18

Input variable “cement”

(c)

20

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26

28

Input variable “days”


in4mf1 1


0

0


181

(d)

181


in4mf3 in5mf1 1

in4mf2

181

in5mf2

in5mf3

0.5

0.5

0

0 550

600

650

700

750

800

850

970

975

980

Input variable “crushed-sand”

(e)


(f)

181

in6mf2

in6mf1 1

985

990

995

1,000 1,005 1,010

Input variable “qravel”

in6mf3

0.5


in3mf1 1

181

in3mf2

in3mf3

0.5

0

0 0

50

100

150

244 245 246 247

Input variable “rubber”

248

249

250

251

252

253

254

255

Input variable “sand”

(g)


in7mf1 1

181

in7mf3

in7mf2

Figure 2. Membership functions of RCC input variables for compressive strength (output)

0.5

0 120

125

130

135

140

145

150

155

Input variable “water”

Rubber substitution RCC Mortar Mortar with fillers

0%

10%

20%

30%

40%

50%

25.50 44.70 44.70

25.50 21.87 37.49

25 16.56 26.50

17 8.43 15.51

12.25 7.25 11.34

7.25 6.87 7.12

In this research, 88 experimental testing were performed on prismatic and cubic specimens of mortar and RCC. In fact, the number of experimental tests was variable in similar research studies using ANFIS method for modelling. For instance, Lin and Huang (2013) used data from 66 experimental tests, 48 were dedicated for training set and 18 for testing set.

Table II. Evolution of Rc (MPa) for mortar and RCC containing rubber and fillers

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Topçu and Sandemir (2008) investigated 52 different mixes with 180 specimens which were gathered from the literature. The data used in the artificial neural networks and fuzzy logic models were arranged in a format of nine input parameters. In our case study, 30 of the mixes were employed for training to assess the fuzzy base rules, whereas 22 were exploited for testing to validate the mortar model results. Nevertheless, 36 experimental results were investigated, 27 for training to assess the fuzzy base rules and 9 for testing to validate the RCC model results. The membership function plots of input variables were used in the R training. Training phase can determine the characteristic parameters of membership functions, standard deviations. The training principle is to minimize the sum of squared errors. Moreover, fuzzy rules are established for the inference system to determine output based on input. The variability effect of input parameters using the fuzzy logic method ensures the reliability of output with a minimum root mean square error (RMSE). The compressive strength output obtained from training, testing of ANFIS model and experiments is illustrated in term of minimum, maximum and average (Table III). The training and testing values are compared to the experimental results to predict the compressive strength of mortar-RCCrubber mixtures with the suitable percentage of substitution. Fuzzy model performance. The assessment of ANFIS model performance took into consideration the experimental results as a database and conducted to separate each of them into training and testing sets by selecting data randomly (Baldwin and Dong, 2005). In all, 72 per cent of whole data were used in training set (32 training data for mortar and 27 data for RCC from 88 experimental data, the rest of data is focused in testing sets). Moreover, the training continued for over 1,000 iterations (Epoch) until error stabilization. Figures 2 and 3 show a cross-plot of the predicted RCC and mortar-filler with rubber vs the measured values. The model precision was evaluated by the RMSE which is defined by the sum of the difference in square of the output calculated by ANFIS and the target output: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðt i oi Þ RM SE ¼ n

(2)

In addition, the precision assessment was measured by the percentage of the mean absolute error (MAPE), which is illustrated by the relationship below: M APE ¼

n 1X t i oi 100 n i¼1 t i

(3)

where n is the number of samples; i ∈ [1, n]; ti the desired output value determined experimentally; and oi the output value determined by the model.

Table III. Statistics of experimental, training and testing data for RCC and mortar with fillers (ANFIS method)

Rc RCC Mortar with fillers

Experimental data used for training Training and testing data obtained by and testing ANFS model Training Testing Average Training Testing Average Min. Max. Min. Max. Training Testing Min. Max. Min. Max. Training Testing 4.25 25.5

2.5

12.25 12.9510

7.33 32.57 7.12 49.15 10.565

6.3330 4.25

25.5

3.76

12.56

12.9518

7.018

16.0148 7.109 32.560 4.5721 34.5517 16.3694 16.8552

Predicted compressive strength (MPa)


Compressive strength of cementitious materials

30

25

291

20 Line y=x 15

Figure 3. Cross-plot showing correlation between predicted and experimental compressive strength results of mortar (ANFIS training and testing sets)

Training results

10

Testing results 5 5

10

15

20

25

30

Experimental compressive strength R (MPa)

Then, using the same training and testing sets to get the accuracy each time, the accuracy for training and testing sets was calculated for modelling prediction problems according to this formula (Baldwin and Dong, 2005): Accuracy ¼ T predicted – T experimental =T average

(4)

where Tpredicted is the predicted target value; Texperimental the experimental target value in the database; and Taverage the range between the different values obtained from the experimental or predicted results (Table III). The statistical parameter values of RMSE and MAPE errors of different specimens, calculated from RCC- and mortar-filler models, are illustrated in Table IV. The probability error distribution of the Fuzzy logic predictions of RMSE are equal to 4.30 × 10−3, 2.193 and 4.586, 5.4157 MPa for RCC and mortar filler during training and testing sets, respectively. Whereas, MAPE values remain 0.01, 31.24 and 19.92, 27.18 per cent for RCC and mortar filler during training and testing sets, too. As a comparative study, the RMSE value of RCC materials during the training set is correlated with the results performed on metal materials (Lin and Huang, 2013) which are adopted from the same membership function (Gaussian function). The performance of ANFIS model for the metal material is less well the RCC case study then regarding the RMSE value is about 0.0311 and 4.30 × 10−3, respectively. Despite the research of Lin and Huang (2013) used more experimental data in the training set were used (48 experimental data). The RCC reveals a better accuracy of RMSE value using only 27 compressive strength data. Moreover, a correlative research of Chaojie Liu et al. (2017) was used as a neural network system to predict the accuracy of different methods based on PSO algorithm. Statistical parameters of fuzzy RMSE for training RMSE for testing logic model (MPa) (MPa) RCC Mortar with fillers

−3

4.30 × 10 4.586

2.193 5.4157

MAPE for training (%)

MAPE for testing (%)

0.01 19.92

31.24 27.18

Table IV. Statistical parameters of training and testing sets

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In this work, the GD-BP neural network could not obtain the expected error target (6.98 × 10−3) even after the maximum number of iterations has been reached (3,000). Comparing this result with the current work, the fuzzy model of RCC revealed a better RMSE in training set (4.30 × 10−3) even after a less number of iterations (only 1,000). Table IV shows that RMSE and MAPE of RCC values (except for testing) are more certain than those of the mortar mixtures. Similarly, the accuracy was calculated to be considered as a further indicator of the fuzzy model accomplishment for the prediction of compressive strength. Thus, comparing the ANFIS models of the two different cementitious materials (mortar and RCC) reveal a more reasonable accuracy of RCC than that of mortar mixtures (Table V ). The amounts of RCC accuracy are about 0.99922, 0.99922 and 0.96515, 0.96855 for the training set and the testing set, respectively. However, the amount of mortar accuracy calculated from training and testing data are equal to 0.91198, 0.94318 and 0.92428, 0.92805, respectively. In general, RMSE, MAPE and the accuracy values were seen closer in RCC mixtures than in mortar. They seem to be dependent on the number of input variables. RCC consists of seven inputs whereas mortar considers only five inputs as data. The variability of input parameters number in the ANFIS model using the fuzzy logic method, as an effective indicator, ensures the reliability of outputs (Behnia et al., 2013). Otherwise, the results are more accurate in the prediction of non-linear behaviours (Inan et al., 2007). Therefore, the favoured predicting results demonstrate a better performance with the lowest mean square error and a good accuracy. Optimizing the different components of cementitious mixtures with the presence of rubber or other fine additives would be the best criteria to get the desired mechanical properties. In addition, the variation of the experimental data, in terms of maximum and minimum values used in the training and testing sets, is more certain in RCC than in mortar mixtures. The maximum and minimum values of mortar are about 32.577, 7.331 MPa for the training and 49.147, 7.5 MPa for the testing, respectively. However, the experimental values in RCC training range from a maximum of about 25.5 MPa to a minimum of 4.25 MPa. During the testing set, the RCC variability of maximum and minimum data are 12.25 and 2.5 MPa, too. Therefore, the proposed models are valid in the case of minimum error and maximum accuracy. The fuzzy model has an excellent interpolation capability when the results performed by MATLAB software program estimated the compressive strength of RCC specimens with 20 per cent of rubber. Figure 4 shows the predicted R value of 22.918 MPa. This predicted result should be compared with the experimental data with 20 per cent of rubber aggregates substitution which is illustrated in Table II. It revealed that RCC and mortar-filler compressive strengths results (25 and 26.50 MPa, respectively) are quite close to those of the fuzzy model result. However, the mortar-rubber mixtures without filler revealed dispersed experimental values with the Fuzzy result (Rc is about 16.56 MPa). Consequently, the compressive strength values of mortar-filler or RCC containing different percentages of rubber aggregates could be predicted by the ANFIS method in a short period of time, i.e.

Experimental data used for training

Training and testing data obtained by

and testing ANFIS model Table V. Training Testing Average Training Testing Average Accuracy of Min. Max. Min. Max. Training Testing Min. Max. Min. max. Training Testing experimental, training Rc and testing data for 0.997 0.999 0.911 0.981 0.99922 0.96515 0.997 0.999 0.941 0.982 0.99922 0.96855 RCC and mortar with RCC fillers (ANFIS method) Mortar with filler 0.874 0.971 0.964 0.975 0.91198 0.92428 0.870 0.971 0.734 0.964 0.94318 0.92805

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23

18 Training results

13

Testing results

8

Line x=y 3 2

7

12

17

22

293 Figure 4. Cross-plot showing correlation between predicted and experimental compressive strength results of RCC (ANFIS training and testing sets)

Experimental compressive strength R (MPa)

it does not need to experiment specimens after a 28-day curing period. Otherwise, without performing any experiments, the fuzzy model predicts the compressive strength results with a reasonable accuracy and a tolerable error. Otherwise, ANFIS has performed quite well in predicting the compressive strength and the accuracy of ANFIS is better than that of the other models (Figure 5).

Figure 5. Example of model application elaborated by ANFIS

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4. Conclusion Based on the results obtained in the present research, the following main summary remarks can be illustrated: (1) The characterization of cementitious materials containing rubber aggregates and filler at a hardened state exhibits the effect of rubber on the mechanical properties of RCC and mortar mixtures with filler. The compressive strength prediction was elaborated by the fuzzy logic method. The fuzzy approach (ANFIS) seems to be quite flexible to build a comprehensible model performance assessment of cementitious mixtures design that ensures the desired compressive strength and well adapted to the real values. (2) ANFIS method optimizes the different mass composition of cementitious mixtures with the presence of rubber and other fine additives like the filler. The variation of RMSE, MAPE errors and the accuracy of different RCC specimens, calculated from the model, are closer than those of the mortar mixtures. Therefore, the favoured predicting results demonstrate a better performance with the lowest RMSE and a good accuracy. Such a model depends on the number of the input variables (RCC uses seven inputs but mortar considers only five inputs). As a result, the variability of the input data ensures a reliability of outputs like the compressive strength. In addition, the variation of experimental data, in terms of maximum and minimum values used in the training and testing sets, are more accurate in RCC than in mortar mixtures. The model with the lowest mean square error and the good prediction accuracy is chosen as an optimal model. It was revealed that using this type of fuzzy approach could evaluate mixture design of cementitious materials containing rubber and filler. ANFIS illustrates a realistic representation and solution for mass composition optimized so as to get the desired mechanical behaviour mainly the compressive strength. Meanwhile, there are some areas that have relatively large errors. (3) Thus, the constructed fuzzy model needs further improvements such as the identification of other types of additives as inputs and further mechanical properties that characterize the outputs, as well as the quantification of accuracy for training and testing sets using other calculation methods.

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About the authors Dr Mohamed Turki is an Assistant Professor at Gabés University. His research interests are about the valorization of solid wastes in construction and building materials, environmental performance and green constructions. Dr Mohamed Turki is the corresponding author and can be contacted at: [email protected] Ines Zarrad is a PhD in Chimie Industrielle II Laboratory at Sfax University in Tunisia. His research interests are in cementitious composites, biomaterials and modelling. Michéle Quéneudec is a Professor at Picardie University of France and a member at Eproad laboratory. His research interests are in processing engineering mainly cementitious materials, biomaterials and polymers. Jamel Bouaziz is a Professor at National School of Engineers of Sfax and a Member of Chimie Industrielle II Laboratory at Sfax University in Tunisia. His research interests are in cementitious composites, biomaterials and ceramics.

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