Modeling of bentonite/sepiolite plastic concrete compressive strength using artificial neural network and support vector machine

Abstract

Plastic concrete is an engineering material, which is commonly used for construction of cut-off walls to prevent water seepage under the dam. This paper aims to explore two machine learning algorithms including artificial neural network (ANN) and support vector machine (SVM) to predict the compressive strength of bentonite/sepiolite plastic concretes. For this purpose, two unique sets of 72 data for compressive strength of bentonite and sepiolite plastic concrete samples (totally 144 data) were prepared by conducting an experimental study. The results confirm the ability of ANN and SVM models in prediction processes. Also, Sensitivity analysis of the best obtained model indicated that cement and silty clay have the maximum and minimum influences on the compressive strength, respectively. In addition, investigation of the effect of measurement error of input variables showed that change in the sand content (amount) and curing time will have the maximum and minimum effects on the output mean absolute percent error (MAPE) of model, respectively. Finally, the influence of different variables on the plastic concrete compressive strength values was evaluated by conducting parametric studies.

Keywords

bentonite/sepiolite plastic concrete / compressive strength / artificial neural network / support vector machine / parametric analysis

Introduction

Water tightness and seepage control are important considerations in the design and construction of dams. Various methods exist to prevent the seepage of water from dams. In this regard, the construction of cut-off walls is one of the most common ways to prevent water seepage under a dam. Based on the rigid diaphragm of cut-off walls in their simplest structural form, any deformation of earth embankment may lead to its rupture. The importance of rupture considerations greatly returns to decreasing flow efficiency of the cut-off walls and consequently compromising the safety of dams. On the other hand, deformations of earth embankments due to fluctuations in impounded reservoir level or seismic activity can cause to develop cracks in concrete cut-off wall [¹]. As a solution for this issue, engineers have used plastic concrete with similar deformation characteristics to dam embankment soils [²]. Plastic concrete must be strong and watertight and have stiffness comparable to the surrounding soil. Satisfying strain-compatibility between the wall and surrounding soil will moderate the likelihood of overstressing the wall and will allow the wall and soil to deform without separating [³]. This type of concrete shows great promise to satisfy the requirements of the strength, stiffness and permeability for remedial cut-off wall construction [⁴]. It has a higher formability, but lower strength and permeability that result from the usage of clay slurry in the concrete mix design [⁵]. Plastic concrete generally consists of aggregate, cement, water, and bentonite clay which mixed at a high water cement ratio to produce a ductile material than conventional structural concrete [⁵]. It is worth noting that bentonite has so far, been defined and used for sealing purposes in civil and hydraulic engineering for a long period of time [⁶–⁹].

The lack of pure bentonite, especially in south Asia and on the contrary, the abundance of minerals such as kaolinite caused the researchers to examine the possibility of using mixtures of bentonite and kaolinite instead of using pure bentonite in the construction of impermeable clay coatings. In this regard, the results of the studies by Karunaratne et al. (2001) indicated that the properties of consolidation capability and hydraulic conductivity value of the mixture of bentonite and kaolinite with a consolidation ratio of 50:50 is very close to the permeability of pure bentonite. They admitted that the bentonite-kaolinite mixture with the ratio of 50:50 could be an appropriate alternative for pure bentonite [¹⁰]. Stavridakis (2005) evaluated the impact of cement on soils composed of clay, bentonite and sand. The findings showed that adding cement to such soils can improve the durability and compressive strength of the soil [¹¹]. In another study, by comparing the effect of bentonite and kaolinite clay, Tahershamsi et al. (2009) concluded that by increasing of the assay of kaolinite clay, the samples' compressive strength has decreased about 16% and the variations have been the same for different ages of the concrete samples. Based on the findings of this research, it was specified that in the case of using the samples' compressive strength as a criterion for evaluating the influencing range of the clay type on the plastic concrete mechanical properties, the bentonite clay has more favorable outcomes as compared to kaolinite clay in the concrete [¹²]. This caused the researchers to seek for a better alternative for bentonite and kaolinite in their studies.

Sepiolite mineral is one of the most abundant minerals in the arid regions (precipitation<400 mm per year) of the world and the most frequent presence of this mineral is seen in the geographic latitudes of 30 to 40 degrees in the northern and southern hemispheres [¹³–¹⁵]. On this basis, by manufacturing bentonite/sepiolite concrete samples, Abbaslou et al. (2015) found that a 20% replacement of cement by sepiolite could provide a desirable strength range for plastic concrete. Although in this type of concrete, the amount of water penetration was not significantly changed in comparison with bentonite samples. However, regarding the special gridded structure of this clay, it resulted in the ability of absorbing more heavy metals [¹⁶].

Compressive strength is an important parameter for quality control of concretes. Several factors can affect the compressive strength of plastic concretes including properties of concrete materials, mixing ratio and curing time. Usually at the site of dam construction and during production of plastic concrete, samples taken from various mixers should be tested by specialized equipments and expert personnel and this is of a great importance. But due to special circumstances in workplace such as construction problems, storage and curing process of a large number of concrete samples and the necessity of faster awareness of the sample's resistance in order to amend the used ratios make this process encounter with difficulties and clearly require more time and significant cost. Therefore, a relatively accurate and comprehensive estimate (in the desired confidence level) of compressive strength of concrete provides the needed tool for a correct decision. Therefore, by taking advantage of empirical regression models, researchers attempted to predict the compressive strength of bentonite plastic concrete with variables such as the contents of water, cement, bentonite, and sand or the curing time [¹²,¹⁷,¹⁸].

In recent decades, various methods of machine learning methods have attracted the attention of many researchers in different fields of engineering. At the beginning of the use of data mining, machine learning methods, such as neural network prediction models, were preferred. This preference can be attributed to no need of neural networks for a predetermined mathematical model for their computations and tolerating experimental noise (inaccuracies) far better than other predicting methods [¹⁹].

However, as time passed other methods such as Fuzzy Polynomial Neural Networks (FPNN) [²⁰], Probabilistic Neural Networks (PNN) [²¹], Adaptive Probabilistic Neural Network (APNN) [²²] and GMDH-type Neural Network [²³,²⁴] were developed to increase the accuracy, speed and improving the performance of neural networks, but until now the largest share of literatures are allocated to artificial neural network method [²⁵–³²]. In addition to ANN, some researchers have used other machine learning methods, such as support vector machine (SVM) and adaptive neuro-fuzzy inference system (ANFIS), in their researches and according to the comparative results, high potential of these methods in the process of prediction has been approved [³³–³⁸]. For example Sobhani et al. (2013) compared ANN method with an optimized SVM to predict the compressive strength of no-slump concrete. The results showed the superiority of SVM modeling in terms of optimization speed in comparison with ANN method [³⁵].

Besides several research works in the field of prediction of compressive strength of different types of concretes by using of machine learning methods, still lack of a research based on machine learning methods, in which the properties of plastic concrete specially with different clay type is assessed is observable. In the present study, after conducting laboratory studies and creating an experimental dataset for compressive strength of bentonite/sapiolite plastic concrete, ANN and SVM methods have been used to model the compressive strength and sensitivity analysis of the superior model.

Experimental framework

Material and mix design

In this study, fine-grained gravel (4.76 mm<particle diameter<19 mm) and sand (0.075 mm<particle diameter<4.76 mm), river bed material were used to make concrete samples. It should be noted that the physical properties of aggregates used in this research are consistent with ASTM C-33 specifications. The mixture of clay and silt passing #200 sieve (a sieve with a diameter of less than 0.075 mm) was also used as silty clay in half of the mixing designs. Also, type II cement of Kerman cement factory was used in all mixing designs. The chemical analysis of cement in Table 1 indicates its conformity with the ASTM C-150 criteria.

In addition, two types of clay soils including calcium bentonite of Sorkhoon mine of Hormozgan and sepiolite of Fariman mine of Khorasan Razavi have been used in this study (Fig. 1). The weight percentages of chemical compounds of bentonite as well as sepiolite clays based on XRF analysis and their engineering properties are given in Tables 2 and 3, respectively.

As can be seen in Fig. 2, for each set of bentonite and sepiolite, four different mixes were considered. In both sets of bentonite and sepiolite concretes, the aggregate amounts have been considered respectively equal to 1550 kg.m^-3 and 1750 kg.m^-3 for the mix designs without silty clay (Mix.1 and Mix.4) and equal to two identical values of kg.m^-3 for the mix designs containing silty clay (Mix.2 and Mix.3). Moreover, in the mix designs with kg.m^-3 aggregate (Mix.2 and Mix.3), the amounts of silty clay have been considered equal to two values of 205 kg.m^-3 and 225 kg.m^-3. The cement factor, indicating the total used cement and bentonite/sepiolite clays are also selected to be equal to two values of 180 kg.m^-3 and 200 kg.m^-3, and two identical values of 280 kg.m^-3 for the mixtures with and without silty clay, respectively. Cement and the bentonite and sepiolite clays were also considered as six different states; so that, the replacement value of bentonite/sepiolite was considered as a variable ranging between 10 to 60 percent of the cement factor. For producing the mixture of bentonite and sepiolite concrete, the colloidal materials including two types of clay were first soaked in some water (30 percent of the clay weight) for 48 hours and conserved inside closed containers (in order to prevent evaporation). The purpose was curing of the clay minerals in water environment and bringing them to chemical balance on the crystals’ surface [¹¹]. Finally, the obtained paste along with the remained water of the design were turned into mud and added to aggregates and cement. It is worth mentioning that the amount of the consumed water was obtained considering the slump value equal to 20 cm for all the mixture designs. Also, the electrical conductivity of used water was 1.2 dsm^-1.

Compressive strength test

144 concrete cube samples with dimensions of 10 × 10 × 10 cm³ were made to perform axial compressive strength tests (72 samples containing bentonite and 72 samples containing sepiolite). All samples were taken from the molds after 24 hours and stored in a protected and preset place in a water pond until the time of the experiment. Also, the curing condition was identical for all the samples. Compressive strength testing of concrete cubes was performed based on ASTM C109 standard for samples at age 7, 28 and 90. It must be stated that loading speed of mentioned test was 0.3 MPa.sec^-1.

General results of experimental work

The obtained results of compressive strength tests of bentonite and sepiolite plastic concrete samples are given in Table 4 and Table 5, respectively. The lowest strength was seen after 7 days curing as compared with 28 and 90 days curing, while 90 days curing specimens exhibited the highest strength. In addition, increasing the clay dosage decreased the compressive strength in all curing times. The results also demonstrate that the 28-day compressive strength of the Mix. 1 is on average 25.10% and 26.78% higher than 7-day compressive strength for bentonite and sepiolite plastic concretes, respectively. These values are 84.36% and 57.52% for Mix 2, 85.06% and 37.10% for Mix. 3, and 37.37% and 38.47% for Mix. 4, respectively. Also, it can be seen that the compressive strength of Mix. 1, after 28 days of curing, for bentonite and sepiolite plastic concretes reach to averagely 69.33% and 55.48% of 90-day compressive strength of the same sample, respectively. The mentioned values are equal to 71.35% and 70.77% for Mix.2, 72.32% and 61.73% for Mix. 3, and 61.84% and 72.58% for Mix. 4, respectively.

Based on the great attention given to plastic concrete cutoff wall technology in the 1980s, by the International Committee on Large Dams, it was pointed out that 28 days compressive strength should range from 1 to 5 MPa [⁵]. In this regard, samples with ideal values of 28 days compressive strength are shown as bold numbers in Table 4 and 5. But in general, Mix.3 in both types of bentonite and sepiolite concretes has the highest number of samples with acceptable range of compressive strength. On the other hand, in order to gain useful strength for plastic concrete; in the case of few clay resources, sample No. 43 of Mix.3, with a significantly lower percentage of clay substitution than other samples (10%) for both concrete types, can be considered as an optimum mixture. It is notable to say that in a situation of good mixture design, such as good quality and quantity of aggregates and cement, it would be possible to gain the required compressive strength with fewer sepiolite clay amounts rather than the bentonite clay amount [¹⁶].

Modeling using machine learning algorithms

Artificial neural network

The simulation of important features of the human nervous system is being used in a modeling tool that is known as Artificial Neural Network (ANN). In this method, the past experiences play substantial rule in solving the problems. Analogous to a human brain, an ANN uses many simple computational elements, named artificial neurons, connected by variable weights [³⁹]. An artificial neuron is shown in Fig. 3. By training the ANN, reaching to a specific target with a particular input is being possible. The comparison of the output and the target enables this method to be trained and this will continue until the ANN output matches the target. Several pairs of inputs and targets are needed to train an ANN efficiently.

One kind of ANN method that is helpful in solving special problems with requirements like recognition of complex patterns and performing nontrivial mapping function is the feed-forward back-propagation neural network architecture which is shown in Fig. 4 [³⁹,⁴⁰].

The training of aforementioned algorithm involves two steps [⁴¹,⁴²]:

• Forward Phase. During this phase, the free parameters of the network are being fixed. The propagation of input signal takes place through the network layer by layer. This phase ends up with the computation of an error signal.

(1)e_i=d_i-y_i.

where d_i is the desired response, and y_i is the actual output produced by the network in response to the input x_i.

• Backward Phase. The backward direction for propagation of the error signal e through the network during this phase is the reason of this algorithm’s name. During this phase, the error e is being minimized in a statistical by applying adjustments to the free parameters of the network.

Support vector machine

The support vector machine (SVM) technique was first presented by Vapnik [⁴³]. Due to reducing the upper bound generalization error in comparison with local training error, developments based on statistical machine learning development and structural risk minimization was applied to it. It is a common technique previously used in machine learning methodologies [⁴⁴].

The SVM method has several advantages compared to other soft computing learning algorithms which are as follows: (1) by applying a high dimensional spaced set of kernel equations, which discreetly include non-linear transformation, makes linearly separable data indispensable and no need to assumption of functional transformation; and (2) The convex nature of the optimal problem makes this technique unique.

Eq. (2) to (5), represent the SVM functions in accordance with Vapnik’s theory. R={\{x_i-d_i\}}_i^n is used to assume a set of data points, where x_i indicates the input space vector of the data sample and d_i is indicative of the target value and n is data size. The equations according to SVM estimates are as follow:

(2)f(x)=w\varphi (x)-b.

(3){\mathrm{R}}_{\mathrm{SVMs}}(\mathrm{C})={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\Vert w\Vert }^{\mathrm{2}}+C{\displaystyle \frac{\mathrm{1}}{n}}{\displaystyle \sum _{i=\mathrm{1}}^{n}L(x_i,}{d}_i).

where \varphi (x) indicates the high dimensional space characteristic that maps the input space vector x while w and b are a normal vector and scalar, respectively. In addition, C{\displaystyle \frac{\mathrm{1}}{n}}{\displaystyle \sum _{i=\mathrm{1}}^{n}L(x_i,d_i)} stands for the empirical error, risk. Factors b and w are measured by minimizing a regularized risk equation followed by the introduction of positive slack variables {\xi }_i and {\xi }_i^{*}that indicate the upper and lower excess deviation:

(4){\mathrm{Minimize}R}_{\mathrm{SVMs}}(w,{\xi }^{\mathrm{(*)}})={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\Vert w\Vert }^{\mathrm{2}}+C{\displaystyle \frac{\mathrm{1}}{n}}{\displaystyle \sum _{i=\mathrm{1}}^{n}L({\xi }_i,}{\xi }_i^{*}).

S\mathrm{ubject\; to}{\{\begin{array}{l}{d}_i=w\varphi (x_i)+b_i\le \epsilon +{\xi }_i\\ w\varphi (x_i)+b_i-d_i\le \epsilon +{\xi }_i^{*}\\ {\xi }_i,{\xi }_i^{*}\ge \mathrm{0},i=\mathrm{1,}\mathrm{...},l\end{array}}_{}

where {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\Vert w\Vert }^{\mathrm{2}} is the regularization term, C represents the error penalty feature utilized to control the trade-off between the empirical error (risk) and regularization term, ϵ represents the loss function associated with the approximation accuracy of the trained data point, and the number of factors in the training dataset is defined as l.

The following generic function is being used to obtain optimality constraints and the Lagrange multiplier that are the requirements of solving Eq. (5):

(5)f(x,a,a_i^{*})={\displaystyle \sum _{i=\mathrm{1}}^n(a_i-a_i^{*})K(x,}{x}_i)+b.

K(x,x_i)=\varphi (x_i)\varphi (xj)in Eq. (5), refers to the kernel function, which is dependent on the two inner vector x_i and x_j in the feature space \varphi (x_i)and \varphi (xj), respectively. In this study, Radial Bias Function (RBF), was considered as kernel function which is defined as follows:

(6)K(x_i,x_j)=\exp (-\gamma {\Vert x_i-x_j\Vert }^{\mathrm{2}}).

where x_i and x_j are vectors of features computed from training or test samples in the input space. It should be noted that the accuracy of support vector machine has highly dependent on the selection of its three factors, including C, g and ϵ.

Evaluation of models performance

In this research, the following statistical indicators have been used to represent the performance of models:

1. Root mean squared error (RMSE):

(7)\mathrm{RMSE}=\sqrt{{\displaystyle \frac{\mathrm{1}}{M}}{\displaystyle \sum _{i=\mathrm{1}}^M(h_i-}{t}_i{)}^{\mathrm{2}}}

2. Coefficient of determination (R²):

(8)R^{\mathrm{2}}={\left[{\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^M(h_i-{\bar{h}}_i)(t_i-{\bar{t}}_i)}}{\sqrt{{\displaystyle \sum _{i=\mathrm{1}}^M{(h_i-{\bar{h}}_i)}^{\mathrm{2}}}{\displaystyle \sum _{i=\mathrm{1}}^M{(t_i-{\bar{t}}_i)}^{\mathrm{2}}}}}}\right]}^{\mathrm{2}}

3. Mean absolute deviation (MAD):

(9)\mathrm{MAD}={\displaystyle \frac{{\displaystyle {\sum }_{i=\mathrm{1}}^M\left|h_i-t_i\right|}}{M}}

4. Mean absolute percent error (MAPE):

(10)\mathrm{MAPE}={\displaystyle \frac{{\displaystyle {\sum }_{i=\mathrm{1}}^M\left|h_i-t_i\right|}}{{\displaystyle {\sum }_{i=\mathrm{1}}^M{h}_i}}}\times \mathrm{100}

where M denotes the total number of data, the h_i and t_i are the actual and predicted output values for the ith outputs, respectively. {\bar{h}}_i and {\bar{t}}_i are, respectively, the average of the actual and predicted outputs. It should be noted that, the lower values of RMSE, MAD and MAPE indicate the better performance of the prediction model. In fact, for an accurate prediction model (without any error) the expected value of R² is equal to 1 while the expected ones for RMSE, MAD, and MAPE is 0.

Prepared dataset

Two unique sets of 72 data, obtained from an experimental study, were used to develop models for predicting the compressive strength of bentonite and sepiolite plastic concrete samples. In both sets of data, the amounts of gravel, sand, clay, cement, bentonite or sepiolite (all in kg/m³), water (lit/m³), and curing time (day) were considered as independent variables variables on the compressive strength (MPa) of plastic concrete was assumed as dependent variable. The statistical characteristic of the dataset is presented in Tables 6 and 7. The minimum and maximum values of variables indicate dispersion, while the values of standard deviation indicate their optimal uniformity. In addition, comparing the mentioned tables shows that, under the same conditions, bentonite samples with a mean compressive strength of 5.98 MPa were more resistant to sepiolite samples with an average compressive strength of 3.92 MPa.

In order to create a comprehensive model that provides the possibility of predicting the compressive strength of plastic concrete considering the clay type used in its mixture design, the two sets of 72 data presented in Tables 4 and 5 were merged together (total of 144 data). For this purpose, a new independent variable entitled clay type was added to the dataset, to which the values of 0 or 1 could be assigned in the cases of using bentonite or sepiolite clays, respectively. Then, with the aim of controlling of the training process and testing models, the dataset was divided into 3 subsets including training by assigning 60 percent of the entire data (87 data), testing by assigning 30 percent of the entire data (43 data), and validating by assigning 10 percent of the entire data (14 data). Statistical parameters of training, testing and validating sets are shown in Table 8.

Results and discussion

ANN Model

In this study, the ANN toolbox of MATLAB was employed to assess ANN method. The main feature of this toolbox can be attributed to allocation of initial weights and biases randomly in each run. With the aim of preventing the negative effects of random allocation of initial weights and biases on the performance of the trained ANN, a code was developed in MATLAB. This code actually handles the trial and error process automatically to determine the optimum architecture of ANN. Control parameters for training of ANN including "max_fail", "epoch", "min_grad", "goal" and "mu", were considered as 3, 2000, 1e-10, 1e-7 and 1e+10, respectively. Finally, considering the type of clay as an independent parameter, three predictive models with the same hidden layer and various architectures including ANN-B, for the compressive strength of bentonite plastics concrete, ANN-S for compressive strength of sepiolite plastic concrete and ANN-B/S for compressive strength of bentonite/sepiolite plastic concrete were created.

In order to having a proper prediction accuracy, 7-43-1 architecture for ANN-B, 7-14-1 architecture for ANN-S and 8-15-1 architecture for ANN-B/S model was chosen. In these three architectures, 43, 14 and 15 are the number of neurons in hidden layer. The transfer function in hidden layer and output layer was assumed as the hyperbolic tangent sigmoid (tansig) and linear transfer function (Purelin), respectively. Also the Levenberg-Marquardt algorithm was used to train the neural network [⁴⁵,⁴⁶].

The optimal architecture of the ANN-B/S model is shown schematically in Fig. 5 in which the parameters such as N1, N2, . . . , N14 and N15 represent the neurons in the hidden layer. This optimal performance of the ANN-B/S model is also understandable for the training, testing and validating dataset according to R² values of 0.9968, 0.9886 and 0.9989 (Fig. 6). According to Fig. 6, the ANN-B/S model is capable of predicting the compressive strength of sepiolite and bentonite plastic concretes within the error range of less than 10% from equality line. Also, the predicted compressive strength values of ANN-B/S model and the experimental compressive strength of training and testing datasets are shown in Fig. 7. As can be seen, the fitting of the predicted values on the laboratory values indicates the high accuracy of this model.

SVM model

In order to create prediction models by using SVM method, a code was developed by the help of MATLAB software, which was capable of obtaining three parameters of C, g and ϵ using trial and error approach. For providing the possibility of comparing the results from the models created using SVM method with those created using ANN method, it was used from identical training, testing and validating datasets with ANN method of modeling. The number of allowed failures in validation checks, like the ANN method, was limited to 3 consecutive epochs. Finally, the optimized values of parameters C, g and ϵ were determined respectively equal to 39.9964, 0.0001 and 0.0001 for the SVM-B model, 16.4245, 0.00001 and 0.00001 for the SVM-S model, and 29.6282, 1.9013 and 0.0062 for the SVM-B/S model. Figure 8 shows the R² values of 0.9885, 0.9648 and 0.9885, for the training, test and validation datasets, respectively according to SVM-B/S model. In addition, regarding the performance of model SVM-B/S presented in Fig. 8, it can be realized the weakness of predicting compressive strength values for testing dataset with an R² difference equal to 0.0237 relative to the training dataset. It is worth noting that this difference was equal to 0.0082 for ANN-B/S model. The predicted compressive strength values by the SVM-B/S method and the experimental compressive strength for the two training and testing datasets are shown in Fig. 9. As can be seen, in the spite of the good adaptation of the predicted values on the experimental ones in the training dataset, more weakness is observed in the testing dataset in comparison with ANN-B/S model.

ANN and SVM comparison

Considering the calculated values for the statistical parameters, presented in section 3-3, it can be concluded that in spite of the higher speed of SVM modeling , due to requiring less parameters for modeling [³⁵], the built models of ANN method have better accuracy and performance and can be useful for parametric studies. According to Table 9, the difference between R² values for training and testing datasets in ANN models is lower than SVM ones. Similarly, the values of the RMSE, MAD, and MAPE parameters are less in ANN models. In addition, by comparing the performance of three different models made by the ANN method, it can be seen that, despite the superiority of the R² value in the testing dataset for the ANN-B model (R² = 0.9906), the ANN-B/S model, considering its more comprehensiveness compared to ANN-B model, will be more reliable and more practical.

It is worth noting that the developed ANN and SVM models are capable to predict compressive strength of plastic concrete for data in range of the data used to build these models.

Models comparison with empirical equations from literature

Despite the wide range of experimental studies conducted about compressive strength of plastic concrete, as it was mentioned in the literature, only a few of them have dealt with presenting empirical regression relations. Since all of the relations existing in the literature are only related to bentonite plastic concrete, the values of four parameters of R², RMSE, MAD and MAPE were calculated by using the input variables of the dataset presented in Table 6 and by predicting the compressive strength using the empirical equations presented in the literature and the models developed in the present study. As can be seen in Table 10, the models of current study were significantly more accurate than the empirical ones. So that the R² value for the ANN-B/S model (R² = 0.9960) in comparison with the best experimental model presented in literature, (first model of Bahrami et al. (2014) with R² = 0.7502 [¹⁸]), has a difference of 0.2458. The difference is equal to 3.6109 for RMSE values, 2.7336 for MAD values and 45.7355 for MAPE ones.

Sensitivity analysis

A method for determining the importance degree of each input parameter on the output parameter is cosine amplitude method (CAM), which could be used in order to investigate the effect of each input parameter on the output parameter [⁴⁷]. In this method, the sensitivity degree of the input parameter is defined by determining correlation degree between input and output pairs of data and by using the following relation:

(11)R_i={\displaystyle \frac{{\displaystyle \sum _{k=\mathrm{1}}^m{x}_{ik}{y}_k}}{\sqrt{{\displaystyle \sum _{k=\mathrm{1}}^m{x}_{ik}^{\mathrm{2}}}{\displaystyle \sum _{k=\mathrm{1}}^m{y}_k^{\mathrm{2}}}}}}

where x_ik is the value of ith independent variable for kth data and y_k is the value of dependent variable for kth data (like x_ik) and m is total number of data. Fig. 10 illustrates the importance of each parameter on the compressive strength of plastic concrete. This sensitivity analysis is done based on two sets of 72 experimental data. According to Fig. 10, it can be seen that within the range of evaluated data in this paper and for both types of concrete, cement and sand have the most impact on compressive strength, respectively while the parameter of silty clay has the least one.

Effect of error in measuring of input variables on the compressive strength of plastic concrete

The influence of measurement error of input parameters on the predicted compressive strength of bentonite and sepiolite plastic concretes by using ANN-B/S model is showed in Fig. 11. For this purpose, the compressive strength of samples was predicted using ANN-B/S model by considering the amount of measurement error of input parameters at a range of –10 to+10 percent and keeping constant the other parameters. Then, regarding the measured and predicted values, the MAPE of the data was calculated. As evidence, both bentonite and sepiolite concretes are severely showing reaction to the variations of sand measurement error and result in much more MAPE increase relative to the other parameters. For instance, +10% error in sand content measurement in the laboratory creates errors of about 38.2266% (MAPE\approx38%) and 83.9769% (MAPE\approx84%) for the bentonite and sepiolite concretes, respectively. This implies on the high importance of precision in measuring this parameter in experimental studies. In addition, as it could be seen in both figures, the least error has been occurred at the range of the considered errors related to curing time, which for example, by applying 10% error in measuring this parameter, it would be associated with errors of about 5.7705% (MAPE\approx6%) and 8.7230% (MAPE\approx9%) for bentonite and sepiolite concretes, respectively.

Parametric study of ANN-B/S model

Time limitations and the lack of adequate facilities are usually considered as the main obstacles of experimental studies. In most cases, it is required to manufacture more samples and consuming longer times in order to investigate each of the variables influencing on the experimental results over a wide range of variations. One of the main advantages of developing predicting models is the possibility of using them with the aim of performing parametric studies and investigating of how each of the input variables influences the model output. On this basis, by considering gour affecting parameters including silty clay, bentonite or sepiolite, water content, and curing time, the compressive strength behavior of bentonite and sepiolite plastic concretes was studied for the changes of these variables. For this purpose, each of the parameters was changed within a range of the minimum and maximum values presented in Tables 4 and 5. When it was required to keep constant one of the variables, it was used from the mean value calculated for that variable. Of course, in this case, curing time was considered equal to 28 days and the water content was set to 325 l/m³ (due to having different mean values for bentonite and sepiolite concretes).

Effect of silty clay addition

Typically, during the production of plastic concrete, there are used of additives such as hydrated lime or silty clay as filler in order to compensate the lack of required mechanical properties of plastic concretes. Recent researches have shown that the addition of these materials to a mixture of plastic concrete has generally been accompanied by a reduction in compressive strength [⁴⁸]. This decreasing trend is also observable in the diagrams of Fig. 12 and 13 by increasing of silty clay content. On the other hand, increasing of gravel to sand ratio in both types of concrete has resulted in strength increase, which Pishe and Hosseini (2012) had investigated its influence on strength reduction in their experimental research entitled Coarse aggregate/Fine aggregate ratio [⁴⁹]. However, what can be found from Fig. 12 and 13 is that increase in the compressive strength of sepiolite concrete relative to bentonite concrete is done slower for increasing of gravel and reducing of sand contents. For instance, for a silty clay content equal to 225 and changing of the amounts of gravel and sand respectively from 300 and 1300 to 500 and 1100 kg·m^-3, the strengths of bentonite and sepiolite plastic concretes have increased 6.35 and 3.61 MPa, respectively.

Effect of Bentonite/ Sepiolite dosage

The increase in volume of clay minerals adjacent to water, due to their high water absorbability, will lead to a decreasing trend in strength of plastic concrete, which is known as plasticity effect. Besides, the more the content of clay, the more the number of clay particles in unit binding mortar. Actually, the addition of adverse impurities in cement paste is the main reason for decreasing the strength of hardened binding mortar. The plastic concrete failure is more probable to occur on aggregate interface or inside the binding mortar [⁵⁰]. As a result, the strength of plastic concrete will decrease with the increase of clay dosage [⁵¹]. Of course, it is obvious that the compressive strength of sepiolite concretes tends to be zero in fewer amounts of clay as compared to bentonite concretes, which seems logical regarding the high plasticity of sepiolite relative to bentonite. As can be seen in Fig. 14 and 15, the increment in amounts of clay will cause a decreasing trend in compressive strength of both bentonite and sepiolite plastic concretes while increasing the amount of cement will lead to an adverse effect on compressive strength of both types.

Effect of water content

The increment in water to fine material ratio is greatly dependent on different factors including the addition of bentonite and sepiolite to plastic concrete or increasing the clay content [¹⁶]. Generally, the increment in water to fine ratio will lead to a decreasing trend, as a result of higher (capillary) porosity. In fact, the lower content of water may reduce the ability of cement for sufficient hydration by decreasing the bond strength. However, such small amount of water is hardly used [⁵²–⁵⁴]. On the other hand, excessive fluid consistency may segregate the mixture, which its consequent problems in strength values are inevitable. In this regard, obtaining certain consistency by adding too much plasticizer can also slow down the progression of strength by means of increasing the hydration time. In this regard, as shown in Fig. 16 and 17, by increasing the amount of water from 200 to 480 l·m^-3, a drop can be seen in compressive strength. It should be noted that the slope of this descending trend will be increased, gradually. In addition, increase in the clay to cement ratio is associated with reducing of strength. However, the decreasing trend of sepiolite concretes is slower than the bentonite ones.

Effect of curing time

In general, researches have shown that the process of curing in plastic concretes will be completed much later than conventional ones. This can be related to the reduced hydration rate of concrete due to the presence of clay [⁵⁵]. This issue is understandable in Fig. 18 and 19 with respect to the steady slope of compressive strength by increasing the curing time. Actually, after 28 days, conventional concretes will usually experience strength increase with less slope that can be considered as the reason of aforementioned behavior.

Moreover, due to increasing of clay to cement ratio, compressive strength reduction will be done faster for clay contents more than 80 kg·m^-3 and cement contents less than 120 kg·m^-3. For instance, when bentonite and cement contents are respectively considered equal to 120 kg·m^-3 and 80 kg·m^-3, we will observe the curing process for bentonite concrete after 22 days, while it starts after 28 days for sepiolite ones. In addition, as can be seen in Fig. 18 and 19, the curing process of bentonite concretes will start much earlier than the sepiolite ones.

Conclusion

The results of current research are briefly summarized as following:

1. In order to having a proper prediction accuracy, 7-43-1 architecture for ANN-B, 7-14-1 architecture for ANN-S and 8-15-1 architecture for ANN-B/S model was chosen. In these three architectures, 43, 14 and 15 are the number of neurons in hidden layer. Also, the optimized values of parameters C, g and ϵ were determined respectively equal to 39.9964, 0.0001 and 0.0001 for the SVM-B model, 16.4245, 0.00001 and 0.00001 for the SVM-S model, and 29.6282, 1.9013 and 0.0062 for the SVM-B/S model.

2. The obtained results showed the superiority of ANN-B/S model to the other models with the values of R² and RMSE equal to 0.9968 and 0.2757 for training dataset and 0.9886 and 0.3805 for the testing dataset.

3. Sensitivity analysis of model also indicated that cement and silty clay have the maximum and minimum influences on the compressive strength, respectively.

4. Investigation of the effect of measurement error for each of the model input variables showed that change in the sand content (amount) and curing time will have the maximum and minimum effects on the MAPE output of model, respectively

5. By increasing the amount of gravel and decreasing the amount of sand, the incremental trend in compressive strength of sepiolite concrete becomes slower than the bentonite one.

6. The increment in amounts of clay will cause a decreasing trend in compressive strength of both bentonite and sepiolite plastics concretes while increasing the amount of cement will lead to an adverse effect on compressive strength of both types

7. By increasing the amount of water from 200 to 480 l·m³, a drop can be seen in compressive strength. It should be noted that the slope of this descending trend will be increased, gradually. In addition, increase in the clay to cement ratio is associated with reducing of strength. However, the decreasing trend of sepiolite concretes is slower than the bentonite ones.

8. The process of curing in plastic concretes will be completed much later than conventional ones. This can be related to the steady slope of compressive strength by increasing the curing time. Actually, after 28 days, conventional concretes will usually experience strength increase with less slope that can be considered as the reason of aforementioned behavior. In addition, the curing process of bentonite concretes will start much earlier than the sepiolite ones.

9. Due to increasing of clay to cement ratio, compressive strength reduction will be done faster for clay contents more than 80 kg.m^-3 and cement contents less than 120 kg·m^-3.

Lastly, it is suggested to conduct the sensitivity analysis (SA) using more recently methods such as global context or screening method to extend this work and provide additional insight on future studies. Implementation of these methods is widely referred in several published references [⁵⁶–⁶¹].

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