# Prediction of the Mechanical Properties of Fibre-Reinforced Quarry Dust Concrete Using Response Surface and Artificial Neural Network Techniques

Authors: Jayaprakash Sridhar; Shanmugam Balaji; Dhanapal Jegatheeswaran; Paul Awoyera
Journal: Advances in Civil Engineering
 (2023)

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## Abstract

The focus of this study is to forecast the 28-day compressive strength and split tensile strength of concrete with various percentages of jute and coconut fibres mixed with quarry dust. The response surface methodology (RSM) and the artificial neural networks (ANN) methods were adopted for 3 variable process modelling (coconut fibres of 0% to 2.5%, jute fibres of 0% to 2.5%, and quarry dust of 0% to 25% by weight of cement). The RSM Box−Behnken design (BBD) method was adopted to design the experiments. Test results showed that compressive strength of 34.6 N/mm2 was obtained for concrete with 0% jute, 0% coir, and 12.5% quarry dust. Similarly, the maximum split tensile strength of 3.8 N/mm2 was obtained for concrete with 1.25% jute fibres, 1.25% coconut fibres, and 12.5% quarry dust. ANOVA and Pareto charts were used to assess regression models for response data. Each progression variable’s statistical significance was assessed, and the resulting models were expressed as second-order polynomial equations. Levenberg−Marquardt (LM) algorithm with feed-forward back propagation neural network was used for assessing the compressive strength and split tensile strength of concrete. The statistical data, root mean square error (RMSE), mean absolute error (MAE), mean absolute and percentage error (MAPE), and determination coefficient (R2) show that both techniques, ANN and RSM, are effective tools for predicting compressive strength and split tensile strength. Furthermore, RSM and ANN models have a high correlation with experimental data. However, the response surface methodology model is more accurate.


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## Body

## 1. Introduction

Over many decades, concrete has been the most often used building material in the world, and its use in the construction sector has steadily increased. This situation is possible due to its strength, toughness, and affordability. However, its use has been constrained because of its susceptibility to fragility under stiffness, a meager resistance to cracking, and low fracture strain capacity. To overcome this fragile behaviour of plain concrete and issues relating to the shortage of raw materials, fibre-reinforced concrete with quarry dust has considered an alternative. Concrete with a higher percentage of recycled aggregate decreases the compressive strength from 22.62% to 18.56%. The predicted results using ANN reveal that it is an effective tool [1]. Three variable process modelling may be utilised to forecast compressive strength utilising response surface methodology (RSM) and artificial neural networks (ANN) [2]. Related to other models, the RSM model’s prediction of compressive strength using nondestructive testing has high accuracy [3]. The use of RSM is simpler than any basic formula and offers an effective output for predicting the strength of concrete proportioning. Moreover, concrete strength properties can be estimated from established ANN [4]. RSM needs no calibration, which is a promising tool for strength prediction, while ANN needs calibration to get the best accuracy [5]. Mechanical properties of concrete decrease with a complex percentage substitution of quarry dust, while abrasion resistance and sorptivity properties increase with a 30% replacement of quarry dust and metakaolin [6, 7]. The fresh concrete properties increase with addition of 0.50% of jute fibres, and on the other hand, hardened properties increase with 0.25% of jute fibres [8]. Concrete with 25% of quarry dust has a 7.9% higher modulus of elasticity, while 100% of sand substitution with quarry dust has 8.6% less modulus of elasticity [9]. Compressive strength and split tensile strength of 26.4 Mpa and 26.1 Mpa, respectively, were achieved for concrete containing 1.5% bamboo and 2% jute fibres by weight of cement. SEM analysis exposes that the breaking of fibres is due to debonding of fibres from the concrete matrix [10]. Concrete with combined micro and macro fibres enhances the mechanical properties of concrete [11]. When glass powder is substituted for cement by 5% and plastic waste by 10%, the mechanical properties of the concrete rise [12]. The compressive strength of concrete increases by 50% for 20% replacement of quarry dust for sand and flexural strength, and split tensile strength decreases by 25% for 20% replacement when compared with conventional concrete [13]. The addition of chopped jute fibres in M25 concrete of 1.5% by weight of cement increases the compressive strength by 19.7%, and tensile strength increases by 30.8% at 28 days of curing. The workability of concrete reduces by 1.5% due to the hydrophilic nature of jute fibre [14]. The compressive strength of concrete is increased by 84.27% when paraffin-coated coconut fibre makes up 0.5% of the cement weight [15]. The addition of jute fibres has effectively filled the microcracks in the concrete thereby reducing the porosity of the concrete and preventing the propagation of cracks [16]. Steel and polymer fibres increase the flexural capacity of RC beams, whereas the glass fibres addition has less influence on concrete as it increases the strength only by 5% [17]. Ultimate load and ductility of concrete containing macro synthetic fibres [18] increase. Artificial fibres pose health and environmental risks in addition to being expensive. Natural fibres are small-diameter discrete and are dispersed randomly in concrete. They benefit the environment, economy, and conservation in terms of energy and resources [8, 19]. The combined effects of silica fume and steel fibres in concrete have significantly improved the mechanical characteristics though concurrently lowering the elastic modulus. Test findings show that silica fume and sisal fibres may be used to strengthen concrete, and they also show an improvement in the material’s mechanical qualities for M30 and M40 concrete [20, 21]. The typical range of optimum dose of Jute fibres varies from 1% to 2% depending on the length and diameter of jute fibres [22]. Coconut fibre enhanced the mechanical performance of concrete by preventing cracks, similar to synthetic fibres, but decreased the flowability of concrete [23]. RSM offers statistically proven prediction models that may be adjusted to obtain the best process configurations. RSM is often beneficial when many factors impact one or more performance attributes or reactions. It may also be used to optimise one or more responses to fulfill a set of requirements. More crucially, RSM allows for adequate experimental interpretation of the nonlinear response surfaces of experimental data [24, 25]. RSM has various benefits for optimization over the one component-at-a-time strategy, which is time-consuming and does not account for factor interaction [26]. Design of experiments (DOE), ideally known as response surface methodology, is used to explore the impact of self-governing factors on outcomes with minimum experiments. It is generally utilised in concrete technology because to its precision in generating precise results [2, 27–29]. Because of the construction of a model with strong performance, ANN is increasingly being used to handle a wide range of civil engineering and material science challenges. To circumvent the drawbacks of the empirical approach, an artificial neural network (ANN) has been employed in many engineering applications in modelling of nonlinear multivariate interrelationships of the behaviour of concrete strength and setting time. The ability of artificial neural networks to learn from the display of sample data sets (patterns), which expresses the system behaviour, is one of their most important qualities [30]. In this study, two models namely Box Behnken Design (BBD) of RSM and Levenberg−Marquardt (NN-LM) algorithm with feed-forward back propagation neural network was developed and compared to predict the compressive strength, split tensile strength of fibre reinforced concrete having of quarry dust, jute, and coconut fibres. The coefficient of determination (R2), root mean square error (RMSE), mean square error (MSE), mean absolute error (MSE), and mean absolute and percentage error (MAPE) of both models were compared to assess the efficiency of each method. To our knowledge, this is the first report comparing RSM and ANN in the prediction of the compressive strength and split tensile strength of concrete containing jute and coconut fibres.


## 2. Materials

In this examination, OPC of grade 53, specified by IS 12269-2013 [31], was employed. Its initial setting time was 30 minutes, and its specific gravity was 3.2. Fine aggregate with specific gravity 2.69 conforming to zone III as per IS 10262 2019 [32] and 20 mm coarse aggregate with specific gravity 2.81 were used in the mixture. The quarry dust used for fractional replacement for sand was collected from a local area crusher with a specific gravity of 2.5. Naturally available untreated jute and coconut fibres having 0.2 mm diameter, as shown in Figure 1, are used to prepare the concrete.Figure 1
(a) Coconut fibres; (b) jute fibres.
(a)(b)


### 2.1. Mix Proportion

The mix proportion utilised in making concrete specimens is 1 : 1.61 : 3.04 at a continual W/C of 0.48. The replacement of sand by quarry dust was done from 0% to 25%. At the same time, the substitution of jute and coconut fibres content was made from 0% to 2.5%.


### 2.2. Test Methods

The concrete mix was cast in a cubical mould of size 150 × 150 × 150 mm for compressive test, and for splitting tensile strength, a cylindrical mould of diameter 150 mm and height 300 mm was used. Concrete was placed into the mould in 3 layers, and each layer was compacted manually with 25 blows of a tamping rod. The concrete samples were detached from moulds after drying for 24 hrs and kept at room temperature. A total of 45 concrete cube specimens and 45 cylinders were cast for testing experimentally, with 3 samples tested per mix at each curing age. The average of triplicate strength values was taken as the concrete strength. After twenty-eight days, the concrete specimens were removed and tested using a compression testing machine for compressive and split tensile tests.


## 2.1. Mix Proportion

The mix proportion utilised in making concrete specimens is 1 : 1.61 : 3.04 at a continual W/C of 0.48. The replacement of sand by quarry dust was done from 0% to 25%. At the same time, the substitution of jute and coconut fibres content was made from 0% to 2.5%.


## 2.2. Test Methods

The concrete mix was cast in a cubical mould of size 150 × 150 × 150 mm for compressive test, and for splitting tensile strength, a cylindrical mould of diameter 150 mm and height 300 mm was used. Concrete was placed into the mould in 3 layers, and each layer was compacted manually with 25 blows of a tamping rod. The concrete samples were detached from moulds after drying for 24 hrs and kept at room temperature. A total of 45 concrete cube specimens and 45 cylinders were cast for testing experimentally, with 3 samples tested per mix at each curing age. The average of triplicate strength values was taken as the concrete strength. After twenty-eight days, the concrete specimens were removed and tested using a compression testing machine for compressive and split tensile tests.


## 3. Mathematical Models

### 3.1. Response Surface Methodology

Response surface methodology (RSM) discovers the association between several illustrative variables and one or more output variables by analysing the design of experiments. The DoE aims to select the most suitable points where the response should be well examined. Response surface optimization aids in adjusting the experimental circumstances that yield the best response [33]. Response surface methodology (RSM) efficiently optimises trials by taking into account both statistical and mathematical approaches for analysis to compute the total number of experimental data for better performance [34, 35]. In circumstances where there are multiple variables, RSM can be used to investigate the impact of each variable and their interactions on answers (properties), as well as the relevance of each variable in the replies or models [36]. Under experimental designs of BBD, Box−Behnken of 3-factor design was adopted. BBD was adopted to study the effects of mix factors, including quarry dust, coconut fibres, and jute fibre on the mechanical characteristics of concrete. The independent variables were jute fibre X1, coconut fibre X2, and quarry dust X3, and the designed responses were the compressive strength fcs28 and split tensile strength fSTS28. The obtained response is expressed as shown in equation (1).(1)y=fX1,X2,X3.A second-order model was developed, as arrayed in equation (2), to elucidate the numerous mechanical properties of concrete and to comprehend the link between the response function and the combined factors as shown as follows:(2)y=k0+∑kixi+∑kixi2+∑∑kijxixj,where y = required response variable; k0, ki, kj, kij = regression coefficients. The coefficient of determination R2 helps determine the accuracy of the arrived equation. Factors and levels of variables required are given in Table 1, which is for the two responses in DOE of RSM autonomous variables. The three-factor BBD approach was applied to 15 mixes to ascertain the effects of jute fibres, coconut fibres, and quarry dust on the strength qualities of concrete, as shown in Table 2.Table 1
Levels of variables.
Variables (%)Minimum (%)Maximum (%)Jute fibre02.5Coconut fibre02.5Quarry dust025Table 2
Combinations obtained from RSM model.
Mix designationJute fibres (%)X1Coconut fibres (%)X2Quarry dust (%)X3Fibre length (mm)Coarse aggregate (kg/m3)Fine aggregate (kg/m3)Cement (kg/m3)JCQD0101.250501214.268642.576359.210JCQD021.251.2512.5501214.268642.576399.125JCQD031.252.50501214.268642.576399.125JCQD041.251.2512.5501214.268642.576399.125JCQD052.52.512.5501214.268642.576379.170JCQD062.51.2525501214.268642.576379.170JCQD070012.5501214.268642.576379.170JCQD0802.512.5501214.268642.576399.125JCQD091.2500501214.268642.576359.210JCQD101.251.2512.5501214.268642.576379.170JCQD1101.2525501214.268642.576379.170JCQD121.25025501214.268642.576359.210JCQD131.252.525501214.268642.576379.170JCQD142.51.250501214.268642.576379.170JCQD152.5012.5501214.268642.576359.210A regression equation (having factors such as linear, interactive, and quadratic coefficients) was used to find the optimum response. To perform this investigation, 15 trials were obtained from RSM and their mix composition is shown in Table2.


### 3.2. Artificial Neural Network

ANN is a computational framework comprising input layers, hidden layers, and output layers. This prediction method is proven to be quite useful for the correct forecasting of output variables in modelling. The primary advantage of the ANN tool is its ability to provide precise modelling for nonlinear models with numerous inputs. Furthermore, ANN tools are widely used because of their ability to deal with inconsistent and unreliable data, as well as their fault tolerance and sturdiness [37, 38]. They comprise a large number of basic handling units which are wired together in a complex communication network. These layers have many dense interconnected units called neurons. The communication between neurons is made with interconnected relations between neurons. To obtain a single output through equation (3), the neurons are multiplied with corresponding weights, added together, and applied to an activation function.(3)Z=f∑i=0−nwixi+dwhere “Z” is the yield from the neuron, “xi” is the contribution value, “wi” is the linking weights, “d” is the bias value, and “f” is the initiation function.In this study, feed-forward propagation of passing the information from contribution nodes is adopted among feed forward and backward propagations. The neural network used for this study is shown in Figure2.Figure 2
Neural network diagram.


### 3.3. Comparison Parameters

Using various statistical studies like the coefficient of correlation (R), coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error, the implications of RSM and ANN models were evaluated (MAPE) [39]. The error calculations can be performed using equations (4)–(6).(4)RMSE=∑1ny−x2n,(5)MAE=1n∑1ny−x,(6)MAPE=∑1ny−x∗100.Here,x is the real data, y is forecast data, and n is the number of samples.


## 3.1. Response Surface Methodology

Response surface methodology (RSM) discovers the association between several illustrative variables and one or more output variables by analysing the design of experiments. The DoE aims to select the most suitable points where the response should be well examined. Response surface optimization aids in adjusting the experimental circumstances that yield the best response [33]. Response surface methodology (RSM) efficiently optimises trials by taking into account both statistical and mathematical approaches for analysis to compute the total number of experimental data for better performance [34, 35]. In circumstances where there are multiple variables, RSM can be used to investigate the impact of each variable and their interactions on answers (properties), as well as the relevance of each variable in the replies or models [36]. Under experimental designs of BBD, Box−Behnken of 3-factor design was adopted. BBD was adopted to study the effects of mix factors, including quarry dust, coconut fibres, and jute fibre on the mechanical characteristics of concrete. The independent variables were jute fibre X1, coconut fibre X2, and quarry dust X3, and the designed responses were the compressive strength fcs28 and split tensile strength fSTS28. The obtained response is expressed as shown in equation (1).(1)y=fX1,X2,X3.A second-order model was developed, as arrayed in equation (2), to elucidate the numerous mechanical properties of concrete and to comprehend the link between the response function and the combined factors as shown as follows:(2)y=k0+∑kixi+∑kixi2+∑∑kijxixj,where y = required response variable; k0, ki, kj, kij = regression coefficients. The coefficient of determination R2 helps determine the accuracy of the arrived equation. Factors and levels of variables required are given in Table 1, which is for the two responses in DOE of RSM autonomous variables. The three-factor BBD approach was applied to 15 mixes to ascertain the effects of jute fibres, coconut fibres, and quarry dust on the strength qualities of concrete, as shown in Table 2.Table 1
Levels of variables.
Variables (%)Minimum (%)Maximum (%)Jute fibre02.5Coconut fibre02.5Quarry dust025Table 2
Combinations obtained from RSM model.
Mix designationJute fibres (%)X1Coconut fibres (%)X2Quarry dust (%)X3Fibre length (mm)Coarse aggregate (kg/m3)Fine aggregate (kg/m3)Cement (kg/m3)JCQD0101.250501214.268642.576359.210JCQD021.251.2512.5501214.268642.576399.125JCQD031.252.50501214.268642.576399.125JCQD041.251.2512.5501214.268642.576399.125JCQD052.52.512.5501214.268642.576379.170JCQD062.51.2525501214.268642.576379.170JCQD070012.5501214.268642.576379.170JCQD0802.512.5501214.268642.576399.125JCQD091.2500501214.268642.576359.210JCQD101.251.2512.5501214.268642.576379.170JCQD1101.2525501214.268642.576379.170JCQD121.25025501214.268642.576359.210JCQD131.252.525501214.268642.576379.170JCQD142.51.250501214.268642.576379.170JCQD152.5012.5501214.268642.576359.210A regression equation (having factors such as linear, interactive, and quadratic coefficients) was used to find the optimum response. To perform this investigation, 15 trials were obtained from RSM and their mix composition is shown in Table2.


## 3.2. Artificial Neural Network

ANN is a computational framework comprising input layers, hidden layers, and output layers. This prediction method is proven to be quite useful for the correct forecasting of output variables in modelling. The primary advantage of the ANN tool is its ability to provide precise modelling for nonlinear models with numerous inputs. Furthermore, ANN tools are widely used because of their ability to deal with inconsistent and unreliable data, as well as their fault tolerance and sturdiness [37, 38]. They comprise a large number of basic handling units which are wired together in a complex communication network. These layers have many dense interconnected units called neurons. The communication between neurons is made with interconnected relations between neurons. To obtain a single output through equation (3), the neurons are multiplied with corresponding weights, added together, and applied to an activation function.(3)Z=f∑i=0−nwixi+dwhere “Z” is the yield from the neuron, “xi” is the contribution value, “wi” is the linking weights, “d” is the bias value, and “f” is the initiation function.In this study, feed-forward propagation of passing the information from contribution nodes is adopted among feed forward and backward propagations. The neural network used for this study is shown in Figure2.Figure 2
Neural network diagram.


## 3.3. Comparison Parameters

Using various statistical studies like the coefficient of correlation (R), coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error, the implications of RSM and ANN models were evaluated (MAPE) [39]. The error calculations can be performed using equations (4)–(6).(4)RMSE=∑1ny−x2n,(5)MAE=1n∑1ny−x,(6)MAPE=∑1ny−x∗100.Here,x is the real data, y is forecast data, and n is the number of samples.


## 4. Results and Discussion

### 4.1. Compressive Strength and Split Tensile Strength

The influence of jute fibres, coconut fibres, and quarry dust under compression at 28 days was studied which are arrayed in Figures3 and 4. The highest strength under compression of 31.9 N/mm2 was obtained for JCQD11, having 1.25% jute fibres, 1.25% coconut fibres, and 12.5% quarry dust. Similarly, it is obvious that JCQD07 having 0% jute fibres, 0% coconut fibres, and 12.5% quarry dust has compressive strength of 34.9 N/mm2. It is evident that adding jute and coconut fibres has a marginal increment in compressive strength. Higher percentage addition of jute and coconut fibres decreases the compressive strength [40]. Due to the JFRCC’s high porosity and low specific gravity in comparison to reference concrete, a declining trend in compressive strength was seen when jute fibres were added. Similarly, an extreme split tensile strength of 3.8 N/mm2 was obtained for JCQD11. The findings demonstrate that the jute and coconut fibres help to increase split tensile strength. Additionally, split tensile strength decreased for concrete specimens containing more than 0.5% by weight of jute and coconut fibres due to the uneven distribution of fibre in the concrete [40].Figure 3
Concrete compressive strength with jute fibres, coconut fibres, and quarry dust.Figure 4
Concrete split tensile strength with jute fibres, coconut fibres, and quarry dust.


### 4.2. RSM Model

Conferring to the BBD, the study was performed to study the influence of the variables jute, coconut fibres, quarry dust to forecast the compressive strengthfcs28 and split tensile strength fSTS28 of concrete mixes at 28 days. As arrayed in Table 3, experiments were conducted for compressive strength and split tensile strength and the responses that were found were articulated in the equations (7) and (8), and the results are arrayed in Table 3.(7)fcs28=33.82−4.24X1−4.66X2+0.110X3+0.651X12+0.175X22−0.00491X32–0.238X1∗X2−0.1973X1∗X3+0.0846X2∗X3,(8)fSTS28=1.388+1.940X1+1.630X2+0.0850X3−0.680X12−0.568X22−0.00472X32–0.352X1∗X2−0.000X1∗X3+0.0080X2∗X3,where X1, X2,X3 are jute, coconut fibre, and quarry dust, respectively.Table 3
Predicted strengths.
Mix designationJute fibres (%)X1Coconut fibres (%)X2Quarry dust (%)X3fcs28 (N/mm2)fSTS28 (N/mm2)JCQD0101.25028.252.8JCQD021.251.2512.522.73.7JCQD031.252.5019.71.9JCQD041.251.2512.522.53.8JCQD052.52.512.512.171.3JCQD062.51.252511.021.2JCQD070012.534.61.3JCQD0802.512.525.062.5JCQD091.250029.392.9JCQD101.251.2512.531.93.8JCQD1101.252522.52.1JCQD121.2502521.62.2JCQD131.252.52517.21.7JCQD142.51.25019.71.9JCQD152.5012.523.22.3


#### 4.2.1. Lack of Fit (p Value) and Pareto Analysis

The importance of progression factors is aided by thep value. The likelihood value of the F test, which should be at a minimum, is the p value of the model. If the progression variable’s p values are <0.005 and <0.00, respectively, it can be calculated as being considerable. The progression variable is deemed to be insignificant if the p value is greater than 0.005. According to ANOVA Table 4, X1 has a lower p value than X2andX3, indicating that jute fibres are an important factor in determining the strength of concrete under compression. The Pareto chart in Figure 5 demonstrates that jute fibre is more significant than coconut fibre and quarry dust for compressive strength at 28 days of curing because its value was greater when compared to the linear (A) and (B&C). Similarly, considering the tensile strength at 28 days from ANOVA Table 4, the quadratic interaction of X1 and X2 contributes to tensile strength, of which jute fibres were more substantial and the p value is less than 0.005. Similar observations can be seen from the Pareto chart shown in Figure 6. The effect of jute fibre was higher than coconut fibre which is higher than the standard value of 2.57. Because of the bridging action between the concrete and the fibres, the tensile strength of the concrete was increased. From the responses observed, it is concluded that the addition of jute fibres improves both compressive and tensile strength compared to coconut fibres.Table 4
Analysis of variance of RSM model.
SourceCompressive strengthfcs28Split tensile strengthfSTS28DFF valuep valueDFF valuep valueModel927.120.00198.230.016Linear374.190.00033.210.121X11148.620.00013.510.120X2161.870.00111.480.278X3112.090.01814.640.084Square30.920.494318.520.004X1211.580.265129.250.003X2210.110.750120.410.006X3210.900.388114.090.013Two way interaction32.980.03832.980.135X1∗X218.490.65318.490.033X1∗X310.000.01110.001.000X2∗X310.440.15010.440.537Figure 5
Pareto chart for compressive strength.Figure 6
Pareto chart for split tensile strength.


#### 4.2.2. Surface Plot Analysis and Optimization of Progression Variables

Figures7 and 8 show the 3D surface plots to show the impact of jute fibres, coconut fibres, and quarry dust on the responses of compressive strength and split tensile strength. From the figure, it is learned that extreme compressive strength was obtained for 0.5% of jute and coconut fibres from 0.5% with 12.5% of quarry dust at 28 days of curing, and above 1.25% jute and coconut fibres, the strength decreased. Although adding jute fibres and coconut fibres somewhat improved the compressive strength of concrete, jute fibres had a far more significant impact than quarry dust and coconut fibres after 28 days of curing. Additionally, the compressive strength has decreased when the weight fraction of jute and coconut fibres exceeds 1.25% due to the larger volume of fibre content. The results showed that a suitable accumulation of jute fibre could efficiently fill the microcracks in concrete, reduce the permeability of the concrete structure, and increase the tensile strength and delay the spread of cracks. The optimized strength under compression and split tensile strength is shown in Figure 9. From Figure 9, it can be seen that to attain the highest compressive strength and split tensile strength at 28 days, the optimal value of jute fibres, coconut fibres, and quarry dust were 0.6547%, 0.8081%, and 9.0909%, respectively.Figure 7
Surface plots for compressive strength as a function of (a) jute fibre and coconut fibre; (b) jute fibre and quarry dust; (c) coconut fibre and quarry dust.Figure 8
Surface plots for split tensile strength as a function of (a) jute fibre and coconut fibre; (b) jute fibre and quarry dust; (c) coconut fibre and quarry dust.Figure 9
Response optimization for compressive and split tensile strengths.


### 4.3. ANN Model

Compressive strength and split tensile strength were forecast using ANN feed-forward back propagation neural network at 28 days of curing. The model contains 75% of samples deployed for training, and the rest 25% is used for validation and testing set. Jute fibre, coconut fibres, and quarry dust are taken as contribution parameters, compressive strength and split tensile strength are considered as output layers, and two hidden layers with 10 neurons were selected to make sound ANN models. The outcomes of training and cross-validation are presented in Figure10, and it reveals a very robust association with R2 = 0.88336 for the training and R2 = 0.9994 for the authentication, where R is the linear correlation coefficient. This shows that the trained neural network is good and accurate.Figure 10
Coefficient of determination for training and cross-validation of ANN.The competence of the ANN models was determined using the coefficient of determination value by comparing actual data with predicted data.The anticipated and actual values for compressive strength and split tensile strength, respectively, were equal, demonstrating well-fitted data. A positive correlation between the actual and expected values is shown by the compressive strength and split tensile strengthR values, which are both more than 0.9. Additionally, the ANN models that are trained using real data have successfully predicted the outcomes. The predicted strength using RSM and ANN are arrayed in Table 5.Table 5
Predicted strength values of concrete using RSM &ANN.
Sample noJute fibres (%)X1Coconut fibres (%)X2Quarry dust (%)X3Compressive strength (N/mm2)Split tensile strength (N/mm2)ExpRSMANNExpRSMANNJCQD0101.25028.2528.2728.432.82.542.62JCQD021.251.2512.522.719.8220.233.73.802.04JCQD031.252.5019.718.2419.121.92.181.98JCQD041.251.2512.522.519.8220.223.83.802.03JCQD052.52.512.512.177.048.131.30.890.88JCQD062.51.252511.025.706.781.21.460.72JCQD070012.534.634.4333.441.31.723.42JCQD0802.512.525.0621.2320.232.52.492.08JCQD091.250029.3929.5429.452.92.762.88JCQD101.251.2512.522.519.8218.983.83.801.88JCQD1101.252531.925.3126.712.11.972.70JCQD121.2502521.623.0524.122.21.932.34JCQD131.252.52517.26.478.121.71.860.80JCQD142.51.25019.720.9919.191.92.041.91JCQD152.5012.523.221.7320.782.32.312.07


### 4.4. Validation and Comparison of ANN and RSM Models

The performance of developed RSM and ANN models was estimated byR2, RMSE, MAE, and MAPE, as shown in Table 6.Table 6
Validation and comparison of RSM and ANN models.
ParametersRSM (CMP)RSM (STS)ANN (CMP)ANN (STS)R20.97230.93680.999940.88336RMSE0.197350.27680.125050.49061MAE0.1628450.241250.1060.38MAPE2.2%8.5%1.6%9.4%When compared to ANN, RSM showed good accuracy for estimatedR2 for compressive strength and split tensile strength. In all cases, R2 values are almost 0.9. This suggests that models established by RSM were more operative and forecast the outcomes more exactly. According to the statistical analysis, RSM and ANN models have high-quality simulations due to their capacity for prediction and their ability to match data effectively. The RSM yet shows strong excellence when compared to ANN, as R2, RMSE, MAE, and MAPE in overall had shown lower values.The obtainedR2 values of compressive strength and split tensile strength in RSM are 0.9723 and 0.9368, respectively. Whereas the R2 values obtained for compressive strength and split tensile strength in ANN are 0.99994 and 0.88336, respectively. The RMSE values obtained for compressive strength and split tensile strength in RSM and ANN are 0.19735, 0.2768, 0.12505, and 0.49061, respectively. The MAE values obtained for compressive strength and split tensile strength in RSM are ANN are 0.162845, 0.24125, 0.106, and 0.38, respectively. The MAPE values obtained for compressive strength and split tensile strength are 2.2%, 8.5%, 1.6%, and 9.4%, respectively.


## 4.1. Compressive Strength and Split Tensile Strength

The influence of jute fibres, coconut fibres, and quarry dust under compression at 28 days was studied which are arrayed in Figures3 and 4. The highest strength under compression of 31.9 N/mm2 was obtained for JCQD11, having 1.25% jute fibres, 1.25% coconut fibres, and 12.5% quarry dust. Similarly, it is obvious that JCQD07 having 0% jute fibres, 0% coconut fibres, and 12.5% quarry dust has compressive strength of 34.9 N/mm2. It is evident that adding jute and coconut fibres has a marginal increment in compressive strength. Higher percentage addition of jute and coconut fibres decreases the compressive strength [40]. Due to the JFRCC’s high porosity and low specific gravity in comparison to reference concrete, a declining trend in compressive strength was seen when jute fibres were added. Similarly, an extreme split tensile strength of 3.8 N/mm2 was obtained for JCQD11. The findings demonstrate that the jute and coconut fibres help to increase split tensile strength. Additionally, split tensile strength decreased for concrete specimens containing more than 0.5% by weight of jute and coconut fibres due to the uneven distribution of fibre in the concrete [40].Figure 3
Concrete compressive strength with jute fibres, coconut fibres, and quarry dust.Figure 4
Concrete split tensile strength with jute fibres, coconut fibres, and quarry dust.


## 4.2. RSM Model

Conferring to the BBD, the study was performed to study the influence of the variables jute, coconut fibres, quarry dust to forecast the compressive strengthfcs28 and split tensile strength fSTS28 of concrete mixes at 28 days. As arrayed in Table 3, experiments were conducted for compressive strength and split tensile strength and the responses that were found were articulated in the equations (7) and (8), and the results are arrayed in Table 3.(7)fcs28=33.82−4.24X1−4.66X2+0.110X3+0.651X12+0.175X22−0.00491X32–0.238X1∗X2−0.1973X1∗X3+0.0846X2∗X3,(8)fSTS28=1.388+1.940X1+1.630X2+0.0850X3−0.680X12−0.568X22−0.00472X32–0.352X1∗X2−0.000X1∗X3+0.0080X2∗X3,where X1, X2,X3 are jute, coconut fibre, and quarry dust, respectively.Table 3
Predicted strengths.
Mix designationJute fibres (%)X1Coconut fibres (%)X2Quarry dust (%)X3fcs28 (N/mm2)fSTS28 (N/mm2)JCQD0101.25028.252.8JCQD021.251.2512.522.73.7JCQD031.252.5019.71.9JCQD041.251.2512.522.53.8JCQD052.52.512.512.171.3JCQD062.51.252511.021.2JCQD070012.534.61.3JCQD0802.512.525.062.5JCQD091.250029.392.9JCQD101.251.2512.531.93.8JCQD1101.252522.52.1JCQD121.2502521.62.2JCQD131.252.52517.21.7JCQD142.51.25019.71.9JCQD152.5012.523.22.3


### 4.2.1. Lack of Fit (p Value) and Pareto Analysis

The importance of progression factors is aided by thep value. The likelihood value of the F test, which should be at a minimum, is the p value of the model. If the progression variable’s p values are <0.005 and <0.00, respectively, it can be calculated as being considerable. The progression variable is deemed to be insignificant if the p value is greater than 0.005. According to ANOVA Table 4, X1 has a lower p value than X2andX3, indicating that jute fibres are an important factor in determining the strength of concrete under compression. The Pareto chart in Figure 5 demonstrates that jute fibre is more significant than coconut fibre and quarry dust for compressive strength at 28 days of curing because its value was greater when compared to the linear (A) and (B&C). Similarly, considering the tensile strength at 28 days from ANOVA Table 4, the quadratic interaction of X1 and X2 contributes to tensile strength, of which jute fibres were more substantial and the p value is less than 0.005. Similar observations can be seen from the Pareto chart shown in Figure 6. The effect of jute fibre was higher than coconut fibre which is higher than the standard value of 2.57. Because of the bridging action between the concrete and the fibres, the tensile strength of the concrete was increased. From the responses observed, it is concluded that the addition of jute fibres improves both compressive and tensile strength compared to coconut fibres.Table 4
Analysis of variance of RSM model.
SourceCompressive strengthfcs28Split tensile strengthfSTS28DFF valuep valueDFF valuep valueModel927.120.00198.230.016Linear374.190.00033.210.121X11148.620.00013.510.120X2161.870.00111.480.278X3112.090.01814.640.084Square30.920.494318.520.004X1211.580.265129.250.003X2210.110.750120.410.006X3210.900.388114.090.013Two way interaction32.980.03832.980.135X1∗X218.490.65318.490.033X1∗X310.000.01110.001.000X2∗X310.440.15010.440.537Figure 5
Pareto chart for compressive strength.Figure 6
Pareto chart for split tensile strength.


### 4.2.2. Surface Plot Analysis and Optimization of Progression Variables

Figures7 and 8 show the 3D surface plots to show the impact of jute fibres, coconut fibres, and quarry dust on the responses of compressive strength and split tensile strength. From the figure, it is learned that extreme compressive strength was obtained for 0.5% of jute and coconut fibres from 0.5% with 12.5% of quarry dust at 28 days of curing, and above 1.25% jute and coconut fibres, the strength decreased. Although adding jute fibres and coconut fibres somewhat improved the compressive strength of concrete, jute fibres had a far more significant impact than quarry dust and coconut fibres after 28 days of curing. Additionally, the compressive strength has decreased when the weight fraction of jute and coconut fibres exceeds 1.25% due to the larger volume of fibre content. The results showed that a suitable accumulation of jute fibre could efficiently fill the microcracks in concrete, reduce the permeability of the concrete structure, and increase the tensile strength and delay the spread of cracks. The optimized strength under compression and split tensile strength is shown in Figure 9. From Figure 9, it can be seen that to attain the highest compressive strength and split tensile strength at 28 days, the optimal value of jute fibres, coconut fibres, and quarry dust were 0.6547%, 0.8081%, and 9.0909%, respectively.Figure 7
Surface plots for compressive strength as a function of (a) jute fibre and coconut fibre; (b) jute fibre and quarry dust; (c) coconut fibre and quarry dust.Figure 8
Surface plots for split tensile strength as a function of (a) jute fibre and coconut fibre; (b) jute fibre and quarry dust; (c) coconut fibre and quarry dust.Figure 9
Response optimization for compressive and split tensile strengths.


## 4.2.1. Lack of Fit (p Value) and Pareto Analysis

The importance of progression factors is aided by thep value. The likelihood value of the F test, which should be at a minimum, is the p value of the model. If the progression variable’s p values are <0.005 and <0.00, respectively, it can be calculated as being considerable. The progression variable is deemed to be insignificant if the p value is greater than 0.005. According to ANOVA Table 4, X1 has a lower p value than X2andX3, indicating that jute fibres are an important factor in determining the strength of concrete under compression. The Pareto chart in Figure 5 demonstrates that jute fibre is more significant than coconut fibre and quarry dust for compressive strength at 28 days of curing because its value was greater when compared to the linear (A) and (B&C). Similarly, considering the tensile strength at 28 days from ANOVA Table 4, the quadratic interaction of X1 and X2 contributes to tensile strength, of which jute fibres were more substantial and the p value is less than 0.005. Similar observations can be seen from the Pareto chart shown in Figure 6. The effect of jute fibre was higher than coconut fibre which is higher than the standard value of 2.57. Because of the bridging action between the concrete and the fibres, the tensile strength of the concrete was increased. From the responses observed, it is concluded that the addition of jute fibres improves both compressive and tensile strength compared to coconut fibres.Table 4
Analysis of variance of RSM model.
SourceCompressive strengthfcs28Split tensile strengthfSTS28DFF valuep valueDFF valuep valueModel927.120.00198.230.016Linear374.190.00033.210.121X11148.620.00013.510.120X2161.870.00111.480.278X3112.090.01814.640.084Square30.920.494318.520.004X1211.580.265129.250.003X2210.110.750120.410.006X3210.900.388114.090.013Two way interaction32.980.03832.980.135X1∗X218.490.65318.490.033X1∗X310.000.01110.001.000X2∗X310.440.15010.440.537Figure 5
Pareto chart for compressive strength.Figure 6
Pareto chart for split tensile strength.


## 4.2.2. Surface Plot Analysis and Optimization of Progression Variables

Figures7 and 8 show the 3D surface plots to show the impact of jute fibres, coconut fibres, and quarry dust on the responses of compressive strength and split tensile strength. From the figure, it is learned that extreme compressive strength was obtained for 0.5% of jute and coconut fibres from 0.5% with 12.5% of quarry dust at 28 days of curing, and above 1.25% jute and coconut fibres, the strength decreased. Although adding jute fibres and coconut fibres somewhat improved the compressive strength of concrete, jute fibres had a far more significant impact than quarry dust and coconut fibres after 28 days of curing. Additionally, the compressive strength has decreased when the weight fraction of jute and coconut fibres exceeds 1.25% due to the larger volume of fibre content. The results showed that a suitable accumulation of jute fibre could efficiently fill the microcracks in concrete, reduce the permeability of the concrete structure, and increase the tensile strength and delay the spread of cracks. The optimized strength under compression and split tensile strength is shown in Figure 9. From Figure 9, it can be seen that to attain the highest compressive strength and split tensile strength at 28 days, the optimal value of jute fibres, coconut fibres, and quarry dust were 0.6547%, 0.8081%, and 9.0909%, respectively.Figure 7
Surface plots for compressive strength as a function of (a) jute fibre and coconut fibre; (b) jute fibre and quarry dust; (c) coconut fibre and quarry dust.Figure 8
Surface plots for split tensile strength as a function of (a) jute fibre and coconut fibre; (b) jute fibre and quarry dust; (c) coconut fibre and quarry dust.Figure 9
Response optimization for compressive and split tensile strengths.


## 4.3. ANN Model

Compressive strength and split tensile strength were forecast using ANN feed-forward back propagation neural network at 28 days of curing. The model contains 75% of samples deployed for training, and the rest 25% is used for validation and testing set. Jute fibre, coconut fibres, and quarry dust are taken as contribution parameters, compressive strength and split tensile strength are considered as output layers, and two hidden layers with 10 neurons were selected to make sound ANN models. The outcomes of training and cross-validation are presented in Figure10, and it reveals a very robust association with R2 = 0.88336 for the training and R2 = 0.9994 for the authentication, where R is the linear correlation coefficient. This shows that the trained neural network is good and accurate.Figure 10
Coefficient of determination for training and cross-validation of ANN.The competence of the ANN models was determined using the coefficient of determination value by comparing actual data with predicted data.The anticipated and actual values for compressive strength and split tensile strength, respectively, were equal, demonstrating well-fitted data. A positive correlation between the actual and expected values is shown by the compressive strength and split tensile strengthR values, which are both more than 0.9. Additionally, the ANN models that are trained using real data have successfully predicted the outcomes. The predicted strength using RSM and ANN are arrayed in Table 5.Table 5
Predicted strength values of concrete using RSM &ANN.
Sample noJute fibres (%)X1Coconut fibres (%)X2Quarry dust (%)X3Compressive strength (N/mm2)Split tensile strength (N/mm2)ExpRSMANNExpRSMANNJCQD0101.25028.2528.2728.432.82.542.62JCQD021.251.2512.522.719.8220.233.73.802.04JCQD031.252.5019.718.2419.121.92.181.98JCQD041.251.2512.522.519.8220.223.83.802.03JCQD052.52.512.512.177.048.131.30.890.88JCQD062.51.252511.025.706.781.21.460.72JCQD070012.534.634.4333.441.31.723.42JCQD0802.512.525.0621.2320.232.52.492.08JCQD091.250029.3929.5429.452.92.762.88JCQD101.251.2512.522.519.8218.983.83.801.88JCQD1101.252531.925.3126.712.11.972.70JCQD121.2502521.623.0524.122.21.932.34JCQD131.252.52517.26.478.121.71.860.80JCQD142.51.25019.720.9919.191.92.041.91JCQD152.5012.523.221.7320.782.32.312.07


## 4.4. Validation and Comparison of ANN and RSM Models

The performance of developed RSM and ANN models was estimated byR2, RMSE, MAE, and MAPE, as shown in Table 6.Table 6
Validation and comparison of RSM and ANN models.
ParametersRSM (CMP)RSM (STS)ANN (CMP)ANN (STS)R20.97230.93680.999940.88336RMSE0.197350.27680.125050.49061MAE0.1628450.241250.1060.38MAPE2.2%8.5%1.6%9.4%When compared to ANN, RSM showed good accuracy for estimatedR2 for compressive strength and split tensile strength. In all cases, R2 values are almost 0.9. This suggests that models established by RSM were more operative and forecast the outcomes more exactly. According to the statistical analysis, RSM and ANN models have high-quality simulations due to their capacity for prediction and their ability to match data effectively. The RSM yet shows strong excellence when compared to ANN, as R2, RMSE, MAE, and MAPE in overall had shown lower values.The obtainedR2 values of compressive strength and split tensile strength in RSM are 0.9723 and 0.9368, respectively. Whereas the R2 values obtained for compressive strength and split tensile strength in ANN are 0.99994 and 0.88336, respectively. The RMSE values obtained for compressive strength and split tensile strength in RSM and ANN are 0.19735, 0.2768, 0.12505, and 0.49061, respectively. The MAE values obtained for compressive strength and split tensile strength in RSM are ANN are 0.162845, 0.24125, 0.106, and 0.38, respectively. The MAPE values obtained for compressive strength and split tensile strength are 2.2%, 8.5%, 1.6%, and 9.4%, respectively.


## 5. Conclusion

RSM and ANN were used in this work to analyse the impact of adding natural fibres and quarry dust on the compressive strength and splitting tensile strengths of concrete. The following conclusions were drawn from the study:(i)
Fibre content up to 1.25% by weight of cement increases the split tensile strength due to its binding nature with the concrete. A higher percentage of fibre content decreases the compressive strength as it requires more cement content for proper mixing, leading to a decrease in strength.(ii)
Quarry dust can be used by itself to enhance compressive strength by up to 25%; however, it is not suited to enhance split tensile strength. The natural fibre addition greatly increases the split tensile strength by reducing the cracks at failure.(iii)
The RSM and ANN models’ outputs, which were developed using real data, demonstrate that the models are capable of providing accurate predictions of concrete properties. Results from comparing the two approaches revealed that RSM models outperform ANN in terms of prediction, with a determination coefficient of almost 1.(iv)
TheR2 values obtained for compressive strength and split tensile strength in RSM are 0.9723 and 0.9368, respectively. At the same time, the R2 values obtained for compressive strength and split tensile strength in ANN are 0.99994 and 0.88336, respectively. The comparison findings demonstrate that the RSM model outperforms the ANN model, with an excellent correlation coefficient (R2) close to 1.



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*Source: 8267639-2023-01-13.xml*