**1. Introduction**

Conventional concrete is one of the most widely used building materials in the world [1–3]. It is considered a complex substance, which is a mixture of fine and coarse aggregates coupled with a cementitious matrix that is suspended in the air [4–6]. However, fresh concrete without enough flowability makes casting, pumping, spreading, and molding around steel reinforcement extremely difficult [7–9]. The product's low strength and poor durability result from inadequate compaction [10–14]. Inadequate cohesion and surface finishing difficulties might also contribute to problems. Fresh concrete must be able to be carried, placed, poured into molds and around reinforcement, compacted, and finished without separating [12,15–19]. To make fresh concrete more fluid, just adding more water is ineffective since the water forms pores that weaken the hardened product [20,21]. Therefore, water-reducing admixtures are desirable and frequently utilized because they can maintain flow at a lower water content, resulting in a substantial boost in concrete's strength and durability [22–24]. For high-rise construction, considerable

**Citation:** Amin, M.N.; Ahmad, A.; Khan, K.; Ahmad, W.; Ehsan, S.; Alabdullah, A.A. Predicting the Rheological Properties of Super-Plasticized Concrete Using Modeling Techniques. *Materials* **2022**, *15*, 5208. https://doi.org/10.3390/ ma15155208

Academic Editor: Krzysztof Schabowicz

Received: 2 June 2022 Accepted: 12 July 2022 Published: 27 July 2022

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attention is paid to making concrete pumpable without segregation and bleeding [25,26]. To avoid cold joints, segregation, honeycombing during pumping, transportation, and placement, and compactions around the reinforcement, freshly mixed concrete must have acceptable flowability [27].

Plastic viscosity (PV) refers to the resistance a fluid presents to free flow [28]. This resistance is caused by friction between the deforming liquid and the particles and liquids in the drilling mud [29]. PV is a Bingham plastic model parameter that represents the slope of the shear stress/shear rate line above the yield point [30]. PV is a crucial rheological property that influences the parameters of drilling fluid [31]. However, experimentally and computationally, the yield stress is associated with common field-friendly measuring methods, such as the slump and slump flow test, for evaluating flowability [32].

Rheology is the study of the deformation and flowability of concrete [33–35]. It entails measuring yield stress and plastic viscosity at various shear rates and times [36–38]. Controlling fresh characteristics enables the production of concrete with the requisite green strength and viscosity [39]. Therefore, the evaluation of fresh characteristics in terms of rheology provides an effective tool for monitoring the requisite flowability in concrete 3-D printing [40–43]. Even though there have been papers written about constitutive equations that describe how fresh concrete behaves rheologically, only the Bingham model and the Herschel and Bulkley (H–B) model have been accepted [44]. For normal slump concrete, Bingham's material model has been demonstrated to suit experimental data fairly well and is defined as follows.

$$
\pi = \pi\_0 + \mu\_p \gamma. \tag{1}
$$

where *τ*, *μp*, and γ. indicates the stress (shear), PV, and shear rate, respectively. Modeling and describing the flow of fresh concrete is based on the assumption that it follows the Bingham model. The rheological properties of concrete have been measured using the same assumption, but the data points are different depending on the testing device [45]. Until a consistent test method for assessing the rheological characteristics of concrete is created, the characterization of concrete's fresh qualities will remain in a state of uncertainty.

The application of predictive modelling techniques to anticipate the various properties of the objects based on the input parameters is gaining popularity [46–52], especially supervised predictive machine learning (PML) algorithms, which can predict the required outcome more precisely. Asri et al. [53] also employed various PML techniques to predict the YS and PV of self-compacting concrete (SCC). They used the number of PML approaches on the data set and predicted the aforementioned result. The Ghanbari et al. [54] study was based on the anticipation of PV of self-compacting fiber reinforced concrete. The study reported better precision for the required outcome. AICHA et al. [55] incorporated the NN model and multi-variable regression to anticipate the rheological parameters of the SCC. A total of 59 data points were retrieved from the literature for running the selected models. Yousef et al. [56] employed the ANN model from PML algorithms to predict the YS and PV of the SCC. The experimental data set was developed for running the model for the predictive result. Mohammed et al. [57] study was based on the application of nonlinear regression (NLR) model and ANN model to investigate the predictive outcome for both the rheological properties and strength of cement paste. They reported that the NLR precision level was better as compared to the ANN model toward the prediction

The purpose of the present study is to introduce the soft computing techniques which can successfully predict the complex, time-consuming, and experimental effort-related properties of concrete in a limited time. These novel approaches can help to execute the project work fluently without waiting for the testing results from the laboratory. This research describes the predictive modeling applications of the rheological properties of super-plasticized concrete. In order to avoid bias and increase the robustness of the study, the artificial neural network (NN) machine learning (ML) approach has been selected from the individual ML approaches, while the random forest (R-F) technique has been selected from the ensemble ML approaches for predicting the outcomes. Ensemble ML algorithms normally use weak learners and split the model into 20-sub models for high accuracy. The plastic viscosity (PV) and yield stress (YS) have been investigated with NN and R-F approaches from predictive machine learning (PML). Statistical checks and validation approaches were also adopted to confirm the employed model's legitimacy. This research is novel in that it describes the effect of both ensemble (R-F) and individual (ANN) PML methods to anticipate the rheological properties of fresh concrete. This research will be beneficial for construction industries by saving time, experimental effort, and money.

#### **2. Materials and Data Description**

The application of Python coding played a vital role in the required models. The Spyder (4.1.4) of anaconda navigator software was used to introduce the relevant coding of Python for running the employed model [58]. The software adopted the six input parameters, including the sand, cement, water, small gravel, medium gravel, and superplasticizers, while each model ran two times for two different outcomes (PV and YS). The set of data, consisting of 139 data points, used for modelling was retrieved from the literature. Moreover, the coding was set in the software which automatically split the data set into training (80%), and testing (20%) purposes. The relation between the experimental result for both outputs and the predictive result from the modelling were compared. The statistical checks in the form of evaluating the various errors using same software were also applied along with the k-fold cross validation approach to satisfy the accuracy level of the models. In contrast, an additional analysis was carried out (sensitivity analysis) to figure out how much each input parameter affects the prediction of the rheological properties of fresh concrete. The descriptive statistical information of the input variables is listed in tabulated form as shown in Table 1. The histogram in Figure 1 gives the information on the relative frequency distribution of each variable used for running the models. However, the detailed adopted research methodology in the form of the flow chart is presented in Figure 2.

**Table 1.** Statistical description of the concrete's parameters data set.


**Figure 1.** Graphical representation of relative frequency distribution for input parameters.

**Figure 2.** Schematic representation of research's adopted methodology.

## *2.1. Predictive Modelling Approaches*

### 2.1.1. Artificial Neural Network (NN)

Neural networks (NN) are generally simple and small in size; yet, they feature strong knowledge-and-information-processing capabilities because of their similarities to the human brain [59]. In civil engineering, NNs have been used to find internal damage, identify structural systems, model the behavior of materials, optimize and control structures, monitor underground water, predict how much a shallow foundation will sink, and figure out how much of each ingredient to put in a concrete mix. Input neurons provide the raw content. Weights and biases create connections among input and hidden neurons. Output neurons provide the indication through connections among the hidden and output neurons. Neural networks are used a lot in engineering because they can recognize patterns, learn on their own, organize themselves, and work in real-time. In contrast to many other soft computing techniques, NNs instantly learn from the specified training patterns and builds the relationship between input and output parameters. In addition, NNs impose no constraints on the input parameters for distributions without defined relationships.

#### 2.1.2. Random Forest (R-F)

Leo Breiman proposed R-Fs12 in 2001 as an intelligent combination of classification algorithms based on statistical learning theory [60]. In R-F, the original data are resampled to obtain additional samples mostly via the bootstrap method. After constructing classification trees for each bootstrap sample, the final results are determined by voting on the combined predictions of the classification trees (Figure 1). R-F can be used for both classification and regression applications. It is employed as a regression tool in the current investigation. When utilizing R-F to solve regression problems, the output variables are fitted with values of the input parameters. For each input factor, the data set is divided into many points, and the Sum of Square Error (SSE) is computed at each point for the actual and projected values. The minimum SSE value for this node is then determined. It can also be investigated how important a variable is by switching around all the values of the input variables and measuring how much their accuracy rate changes in the out-of-bag samples (a number of observations that are not used in training and are referred to as the "out-of-bag" data set: OOB data set) [61].

#### **3. K-Fold Cross Validation (C-V)**

The estimation of prediction accuracy is crucial if our objective is to predict. The training error is a straightforward approximation of the prediction error; however, it is biased downwards. C-V, on the other hand, has an upward bias. The upward bias may be minor in leave-one-out cross validation, but it cannot always be ignored in the computationally preferred 5-fold or 10-fold cross validation. Since the training error has a downward bias and C-V has an upward bias, a family that connects the two estimates will contain an appropriate estimate. Generally, the performance of classification algorithms is tested using C-V. First, a data set is randomly partitioned into k distinct folds with roughly the same number of instances. Then, each fold assumes responsibility for evaluating the model suggested by the other k-1 folds. Throughout this procedure, the training data set is partitioned into multiple 'k' smaller pieces. Consequently, the term 'k'-fold was coined. On the basis of a random data set, k-fold is utilized for testing and k-1 for training. The prediction model's efficacy is evaluated using a stratified 10-fold cross-validation method. This approach divides the data set into ten folds at random. Consequently, each fold is utilized just once as a validation set. Finally, the error or accuracy measure for each fold can be compared; if they are comparable, the model is likely to generalize well.

#### **4. Results and Discussion**
