Analysis of Models to Predict Mechanical Properties of High-Performance and Ultra-High-Performance Concrete Using Machine Learning

Abstract

High-Performance Concrete (HPC) and Ultra-High-Performance Concrete (UHPC) have many applications in civil engineering industries. These two types of concrete have as many similarities as they have differences with each other, such as the mix design and additive powders like silica fume, metakaolin, and various fibers, however, the optimal percentages of the mixture design properties of each element of these concretes are completely different. This study investigated the differences and similarities between these two types of concrete to find better mechanical behavior through mixture design and parameters of each concrete. In addition, this paper studied the correlation matrix through the machine learning method to predict the mechanical properties and find the relationship between the concrete mix design elements and the mechanical properties. In this way, Linear, Ridge, Lasso, Random Forest, K-Nearest Neighbors (KNN), Decision tree, and Partial least squares (PLS) regressions have been chosen to find the best regression types. To find the accuracy, the coefficient of determination (R²), mean absolute error (MAE), and root-mean-square error (RMSE) were selected. Finally, PLS, Linear, and Lasso regressions had better results than other regressions, with R² greater than 93%, 92%, and 92%, respectively. In general, the present study shows that HPC and UHPC have different mix designs and mechanical properties. In addition, PLS, Linear, and Lasso regressions are the best regressions for predicting mechanical properties.

1. Introduction

The development of Ultra-High-Performance Concrete (UHPC) dates back to the 60th decade in France [1,2]. UHPC has many applications because of its high mechanical properties, such as infrastructure objects, bridge construction, 3D printing, and architectural applications [3,4,5,6]. The UHPC constitutes Portland cement as a binder, additives (fine silica sand, silica fumes, and quartz flour), high-range water reducers like superplasticizers, discontinuous internal combustion steel or organic fibers, and a water/cement ratio less than 0.25. According to the UHPC mechanical properties, compressive strength is more than 150 MPa and tensile strength is over 5 MPa. High-Performance Concrete (HPC) constitutes Portland cement, sand, gravel, different types of fibers such as basalt fiber, and water/cement ratio between 0.25 and 0.35 [7,8,9]. The HPC and UHPC are two different concrete types that have many advantages and similarities, as well as many disadvantages.

Meng et al. [10] understood that UHPC is a new type of cement matrix made by low water/binder ratio. The study shows that the water/binder ratio of UHPC is from 0.18 to 0.22. However, UHPC shows a tensile strength exceeding 5 MPa, and researchers have demonstrated its strain hardening behavior after cracking at 7–15 MPa [11]. According to the study’s results, the best water/binder ratio used was 0.25 to achieve high mechanical properties, high workability, and good durability. Moreover, the UHPC has better durability than conventional concrete due to the covering of the pore structure among cement matrix and fine aggregate [12,13]. Wetzel et al. [14] studied the effect of silica fume on the mechanical properties of UHPC. The research shows that high-strength cement paste can increase the mechanical properties, and metakaolin can improve the mechanical properties [15]. Swaminathan et al. [16] understood that metakaolin helps to increase the strength and durability of concrete. Hongjian Du [17] analyzed the effect of metakaolin on the HPC with cement replacement. Adanagouda et al. [18] studied the effect of metakaolin and hybrid fiber, and 10% of metakaolin has the best performance. Another study investigated the effect of 3D printing Polylactic acid (PLA) filament reinforced to improve the UHPC. Hematibahar et al. [5] found that 3D printing reinforcement can improve the ductility and failure behavior of UHPC, however, they found that the shape of the reinforcement is an essential parameter to improve the concrete mechanical properties [6]. In another example, Chiadighikaobi et al. [19] reinforced HPC with a 3D printing truss structure. They could increase the flexural strength by adding a 3D printing truss as reinforcement. They found that 3D printing trusses can improve the HPC flexural strength. The similarities between HPC and UHPC are the high and specific durability and high toughness of both types of concrete, while HPC compressive strength is commonly more than 50 MPa and UHPC compressive strength is almost more than 120 MPa [20,21,22]. Another similarity between HPC and UHPC is the addition of some materials such as fly ash and silica soot to reduce shrinkage, improve strength, and strain hardening. Another advantage of adding minerals is improving resistance to sulfate attack and the activity of alkaline aggregates [23,24,25,26]. Another similarity between HPC and UHPC is an increase in the compressive strength by adding different types of fibers. For example, when 80% of steel fibers and 20% of polypropylene fibers were added to UHPC the compressive strength improved to 180 MPa, moreover when HPC was reinforced by steel, glass, and carbon fibers the mechanical properties increased [27,28].

Several studies are based on the addition of fiber to concrete to improve its mechanical and chemical properties. For example, several fiber types, such as polypropylene and steel hybrid fiber, can improve the compressive and flexural strengths and decrease the tensile strength [29]. The concept of adding fibers to concrete is to prevent micro-cracks, increase tensile strength, and decrease the brittleness of concrete [30,31,32,33]. Another example shows that polypropylene fiber can improve the temperature resistance of HPC [34]. Steel fibers are used as the common fiber for commercial reasons, moreover, steel fiber increases the tensile strength because of an increase in the cement matrix [35]. Zinc-coated steel fiber is a solution for the corrosion of steel inside the concrete, also the low percentage of steel fiber can improve the ductility of UHPC [36,37]. The UHPC flexural strength was 50% improved by incorporating steel fiber [38].

Many studies have been investigated in the field of predicting the mechanical behavior of concrete [39,40,41]. Mechanical and chemical prediction of concrete can reduce the cost and time of investigation to find a reasonable mix design and mechanical and chemical behavior of concrete. Hematibahar et al. [42] studied the HPC concrete to find a predictive model for the compressive stress-strain curve. They found a new method based on soft programming through a logistic algorithm to predict the compressive stress-strain curve. Their verification results, based on the Coefficient of Determination (R²), were more than 0.96 which shows their results were accurate. In another example, Hasanzadeh et al. [43] used machine learning methods to predict the mechanical behavior of HPC. They used linear regression (LR), support vector regression (SVR), and polynomial regression (PR), and their results illustrated that PR had the best R² results with more than 0.99, 0.94, and 0.98 for compressive, flexural, and tensile strengths prediction, respectively. Liua et al. [44] used artificial neural networks (ANNs) to predict the concrete abrasion depth and optimization of the concrete mixture. According to their research, they used Random Forests (RF) and artificial neural networks (ANNs) to predict the abrasion depth throughout the concrete mixture proportions, curing age, and hydraulic properties. They used more than 5000 randomly generated mixture designs. Ma et al. [45] predicted the compressive strength of recycled concrete coarse aggregate in cold regions using a mathematical model simulation. According to their results, the maximum deviation was 24.5% and the minimum was 6.6%. Parhi and Panigrahi [46] predicted machine learning with Random Forest and XGBoost due to Alkali–silica reaction (ASR) expansion in concrete. They understand that the XGBoost method had better results (R² = 0.96) than the Random Forest method. Harith et al. [47] forecasted the compressive strength of high-performance concrete with machine learning method. They studied more than 528 experimental results, and they used hierarchical quadratic regression and multiple linear regression of machine learning methods to predict compressive strength. According to their results, hierarchical quadratic regression R² was 0.97, and linear regression was 0.91%. O. Bernardo et al. [48] predicted the torsional capacity of reinforced concrete (RC) beams via machine learning. They used Decision Tree (DT), Bagging Meta-Estimator (BME), Forests of Randomized Trees (FRT), AdaBoost (AB), and Gradient Tree Boosting (GTB). Their results showed that the best was for GTB with R² = 0.99, and next the BME with R² = 0.988. Mahmood et al. [49] studied the prediction compressive strength of Self-Compacting Concrete (SCC) with Ridge regression, Lasso regression, K-Nearest Neighbors (KNN), support vector machine (SVM), Decision Tree (DT), Random Forest (RF), and boosting methods such as gradient boost (GB), XG boost (XGB), and adaptive boosting (ADB) of machine learning method. They found that the best prediction results were for RF and DT with 0.998 and the next GB with R² = 0.997. Overall, the prediction of concrete is a way to decrease the time and cost of investigation and to find new ways to improve the mechanical and chemical properties of the concrete.

The scientific problem of the research is the lack of systematized knowledge about the fundamental differences between high-performance concrete and ultra-high-performance concrete, as well as the optimal ways to predict their properties using artificial intelligence methods. The objective of this study is to eliminate these scientific deficiencies. This study closes a number of gaps in modern construction science and the science of artificial intelligence in construction. The knowledge about the differences between High-Performance Concrete and Ultra-High-Performance Concrete has been systematized. The main aspects and necessary features that influence decision-making on the construction of buildings and structures from such concrete have been identified. An important scientific task is being solved to bridge the gaps and connect the level of scientific knowledge between the sciences of artificial intelligence and the sciences of predicting the reliability of building structures. The scientific novelty of this study is the dependencies obtained based on an in-depth analysis of literature data and our results, showing the fundamental differences between High-Performance and Ultra-High-Performance Concrete. The relationships between the best-performing machine learning methods and the issues of predicting the properties of High-Performance Concrete and Ultra-High-Performance Concrete are shown.

This current study looks at High-Performance Concrete (HPC) and Ultra-High-Performance Concrete (UHPC) to find their similarities and differences. In this current article, the effect of the additive substances and different fibers on both types of concrete will be investigated as well as the mechanical and chemical properties of both types of concrete. Finally, machine learning is used to find the dependence of each type of concrete on each mix design parameter and to find predictions of mechanical properties.

2. Materials and Methods

This research was focused in two ways. First, the review of the Ultra-High-Performance Concrete (UHPC) and High-Performance Concrete (HPC). This part concentrated on the mechanical and chemical properties of the two types of concrete. The second part of this research focused on the prediction of the mechanical properties of UHPC and HPC. In this prediction, over 400 mix designs were used.

This study investigated the cause of the basic solution to the difference between HPC and UHPC according to mechanical properties, chemical properties, cement matrix chemical reaction, mixture design, and the effect of materials. Another part of this article shows the effect of the correlation between design materials and the prediction of mechanical and chemical properties.

Figure 1 illustrates the process of the current study. In this study, first HPC and UHPC are reviewed, and next data is collected as a dataset. Finally, machine learning with Linear, Ridge, Lasso, Random Forest, K-Nearest Neighbors (KNN), Decision Tree, and Partial least squares (PLS) regressions have been selected.

2.1. Prediction of Mechanical Properties

Machine learning is similar to a system that can automatically learn and improve operations from experience without reprogramming. Furthermore, machine learning can be classified into four types [50]:

Supervised Learning (SL). SL is used in this study because this type of algorithm is the most common type of machine learning. Also, the SL algorithm tries to create a model based on the relationship between the input and output data and then predicts the future data. In the SL method, the algorithm was a subset of classification and regression. Classification is processing data to data segmentation in different ways. Regression is used to predict values via dependent and independent variables.

Unsupervised Learning (USL). USL has a self-organized algorithm. In this program, input data is provided to the algorithm. This algorithm does not use the unlabeled method. The task of USL is to cluster, correlate, and reduce the dimensionality of the dataset.

Semi-Supervised Learning (SSL). SSL is between the SL and USL families. SSL uses tagged and untagged data for training.

Reinforcement Learning (RL). The trial-and-error search and delayed reward are the most relevant features of RL. RL allows the automatic determination of ideal behavior in a specific context to maximize optimal performance. RL is a loop that depends on agent, environment, situation, action, reward, and policy. The objective of RL is to optimize to find the final solution.

In this study, Python has been used as the programming software. To find the prediction and correlation of the mixture design, three types of regressions have been chosen. The Ridge regression (RR) was selected for this purpose, and the Spyder plugin was selected from the Anaconda navigator. It should be noted that most of the commands of the current study is extracted from “Sklearn”, a programming open-source library in Python software (v. 3.10.2).

2.2. Regression Types

The Linear regression is illustrated in Equation (1) [51]:

$$y=ax+b$$

(1)

where x and y are variables, and a and b are the slope and intercept coefficients, respectively.

Ridge regression is a regression type that can analyze multiple data with multicollinearity. Moreover, by adding a degree of bias to the regression estimates, Ridge regression illustrated in Equation (2) decreases errors and obtains more accuracy [52,53]:

$$v={\delta }_0+{\delta }_1{w}_1+{\delta }_2{w}_2+{\delta }_3{w}_3+{\delta }_4{w}_4+\epsilon +\lambda \sum ({\delta }_1^2+{\delta }_2^2+{\delta }_3^2+{\delta }_4^2)$$

(2)

where v is the dependent variable, w is the independent variable, δ₀ is the y-intercept, and δ₁ is the regression coefficient representing the change in v concerning the change in w, also called the slope, and λ is the Ridge regression penalty ratio, ε is the error term, ∑(${\delta }_i^2$) represents the sum of the squares of the coefficients.

Lasso regression means Least Absolute Shrinkage and Selection Operator (LASSO). Lasso regression is a usual regression for solving multicollinearity issues, while unlike Ridge regression, results in some coefficient predictions are equal to zero. Equation (3) shows the Lasso regression equation [53,54]:

$$v={\delta }_0+{\delta }_1{w}_1+{\delta }_2{w}_2+{\delta }_3{w}_3+{\delta }_4{w}_4+\epsilon +\lambda \sum \left|{\delta }_1\right|+\left|{\delta }_2\right|+\left|{\delta }_3\right|+\left|{\delta }_4\right|$$

(3)

where v is the dependent variable, w is the independent variable, δ₀ is the y-intercept and δ₁ is the regression coefficient representing the change in v concerning the change in w, also called the slope, moreover the λ is regularization parameter, ε is the error term, $\sum \left|{\delta }_i\right|$ is the sum of absolute values of coefficients.

Figure 2 shows the Random Forest regression method. Considering the Random Forest regression method, after collecting the data, the data set was transferred to the training data. In the first stage, n diversity of trees is predicted from the next training data set through Random Forest and finds the final prediction of the regression according to the average of all predictions [55,56].

K-Nearest Neighbors (KNN) is commonly used for classification, although the regression algorithm of KNN is also used as a prediction method. The KNN prediction algorithm is as follows:

Training example as $\left\{x_i, \left.y_i\right\}\right.$, where training example values are $x_i$ and $y_i$ are output character of actual values. The test point is known as x and the construction is known as the prediction [57].

Decision Tree is used for both classification and regression algorithm [58,59], and the direct node includes root nodes, inner nodes, and leaf nodes as a simple algorithm. Commonly, nodes in the Direct Tree algorithm predict a data category or direct data [59]. Finally, the operation process multiplies judgments to predict values with different characteristics [60].

Figure 2. Random Forest scheme [61].

Figure 2. Random Forest scheme [61].

Partial least squares (PLS) is multiple linear regression modeling which is based on simulating predictors and observing and transferring data to new space [62].

2.3. Accuracy Finding

To find the prediction accuracy of each forecasting model, three indicators, including the coefficient of determination (R²), mean absolute error (MAE), and root-mean-square error (RMSE), have been selected. According to the results, every R² was closer to 1. The prediction is more accurate, moreover, when RMSE and MAE are closer to 0 the results are more validated. In this study, the result of R² is the reference index in the actual modeling. R² can find future prediction results, as shown in Equation (4) [63]:

$$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^N{\left(y_i-{\widehat{y}}_i\right)}^2}}{{\displaystyle \sum _{i=1}^N{\left(y_i-\overline{y}\right)}^2}}}$$

(4)

here y_i is the actual predicted and ${\widehat{y}}_i$ is the mean of the actual value. MAE is equal to the sum of the numerical differences of the values of community set divided by whole numbers (n). It calculates the average error, utilizing the absolute difference between the actual data and the predicted results (Equation (5)) [63]:

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left(y_i-\widehat{y}\right)}^2}}$$

(5)

RMSE measures the average deviation of each actual data point and the predicted results. It is obtained through Equation (6) [63]:

$$\mathrm{MAE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|y_i-\widehat{y}\right|}$$

(6)

Mean Absolute Percentage Error (MAPE) is an effective metric for analyze accuracy of regression models.

3. Results and Discussion

3.1. HPC Concrete

3.1.1. HPC Mixture Design

The most effective performance of HPC is due to the use of a homogeneous cement matrix in the design mixture, which increases the mechanical and chemical properties of HPC compared to conventional concrete [64,65,66]. According to Table 1, HPC concrete types use a high amount of cement content. For example, in this study, the cement content was from 450 to 954.1 (kg/m³) and the water/cement ratio was between 0.22 and 0.4. Cement, as a binding material, was the most important character in the concrete mix design. However, water has a relationship with cement in finding an accurate cement matrix. Equation (7) is presented for cement and water in (kg/m³) when w/c is between 0.3 and 0.4.

$$C=2.63\times W$$

(7)

where C is cement (kg/m³) and W is water (kg/m³).

Equation (4) provides the relationship between cement and water; it can show the influence of water on cement and find the suitable amount of water.

HPC usually uses silica fume or micro fume as mineral admixture, however, some studies used metakaolin. Silica fume is the most important nanoparticle and is a very effective pozzolan with high silica content. Due to the geopolymer gels of silica fume and high content of Si, the strength of the concrete increased and the porosity of the cement matrix decreased, therefore water absorption increased [67,68,69,70,71,72]. Silica fume can fill microspores and pores between aggregates, which prevents the creation of micro-cracks in the cement. According to the evidence, silica fume reacts to Ca(OH)₂ at a certain time. Fifty percent of silica fume in cement releases Ca(OH)₂ in 14 days and 20% in 90 days. In terms of petrochemicals, silica fume is an acidic technology. Silica fume is a pozzolan and the most reactive pozzolan. The hydration reaction described by the equation SiO₂ + Ca(OH)₂ → produces C-S-H gel. C-S-H (calcium silicate hydrate) on the part of silica fume not only improved the flexural strength of the concrete but also increased the compressive strength and bond strength [49,50,51,52,53,54,55].

Another material that is added to HPC is metakaolin. Metakaolin is a type of kaolin clay that is used as an important pozzolana material that improves the strength, chemical, and durability of concrete. However, the metakaolin reduces the hydration heating. Metakaolin can react with calcium hydroxide to create cement hydration and produce an additional cement matrix. Metakaolin reduced the effect of chloride ions and decreased the effect of corrosion in the steel rebar [73,74,75,76,77,78]. Metakaolin can react with the calcium hydroxide and make calcium silicate hydrate gel (C-S-H). Also, metakaolin decreases the workability of HPC. However, metakaolin can increase the compressive strength of concrete and decrease the flexural strength of concrete [79,80].

According to Ayub et al. [9], sizes of coarse aggregate ranging from 10 mm to 20 mm and river sand as fine aggregate were used. The fine aggregate was less than 10 mm. In Mohaghegh et al. [62], the fine aggregate size was between 4 mm and 8 mm, however, the coarse aggregate was 8 mm and 16 mm, and the filler size between 0 and 4 mm was used. Kharun et al. [32] and Alaraza et al. [63] used quartz sand as a fine aggregate with a size between 0.8 mm and 2 mm. They used crushed granite as a coarse aggregate with sizes between 5 mm and 20 mm.

The research shows that the fine aggregate size was between 0.8 mm and a maximum of 8 mm, while the coarse aggregate size was between 8 mm as a minimum and 20 mm as a maximum, however, Kharun et al. [32] and Alaraza et al. [63] added quartz flour as the concrete filler.

One of the most important characteristics of HPC is adding basalt fiber in the form of chopped (micro) basalt fiber and minibars (macro basalt fiber) to the concrete. Sometimes steel fiber was added to HPC. Basalt fiber is produced by heating a volcanic basalt rock at temperatures between 1450 °C and 1500 °C. Basalt fiber has good mechanical properties, chemical properties, high elastic properties, and high-temperature resistance. Basalt fiber was used in 1998 Highway Innovations Deserving Exploratory Analysis (IDEA) Project 45 for the first time in concrete technology [81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96]. According to studies, adding basalt fiber to concrete reduces the workability of the concrete. When a 12 mm length basalt fiber was added to the concrete, the slump of the concrete was reduced by 0.14% (150 mm), and when a 24 mm length basalt fiber was added to the concrete, the slump was reduced to (100 mm) [85,91]. Guo et al. [92] illustrated that adding basalt fiber to the cement matrix increases the number of voids. Additionally, Jiang et al. [93] understood that adding basalt fiber increases the void content of concrete. The mixture properties of HPC are shown in Figure 3.

Table 1. Mixture Design of different studies of HPCs.

Studies	Specimens	Cement (kg/m3)	Water (kg/m3)	Mineral Admixture (kg/m3)	Filler (kg/m3)	Superplasticizer	Fiber (%)	Fine Aggregate (kg/m3)	Coarse Aggregate (kg/m3)
Ayub et al. [9]	P-0	450	180	-	-	-	0 (Basalt Fiber)	670	1100
	PB-1	450	180	-	-	-	1 (Basalt Fiber)	670	1100
	PB-2	450	180	-	-	-	2 (Basalt Fiber)	670	1100
	PB-3	450	180	-	-	-	3 (Basalt Fiber)	670	1100
	S-0	450	180	45 (Silica Fume)	-	-	0 (Basalt Fiber)	670	1100
	SB-1	450	180	45 (Silica Fume)	-	-	1 (Basalt Fiber)	670	1100
	SB-2	450	180	45 (Silica Fume)	-	-	2 (Basalt Fiber)	670	1100
	SB-3	450	180	45 (Silica Fume)	-	-	3 (Basalt Fiber)	670	1100
	MB-1	450	180	45 (Metakaolin)	-	-	1 (Basalt Fiber)	670	1100
	MB-2	450	180	45 (Metakaolin)	-	-	2 (Basalt Fiber)	670	1100
	MB-3	450	180	45 (Metakaolin)	-	-	3 (Basalt Fiber)	670	1100
Mohaghegh et al. [83]	S-I-0	495.6	184.4	63.2 (Silica Fume)	161.1	12	0 (Basalt Fiber)	1066.6	419.3
	S-II-0	495.6	184.4	63.2 (Silica Fume)	161.1	12	0 (Basalt Fiber)	1066.6	419.3
	S-III-0.5	495.6	184.4	63.2 (Silica Fume)	159.7	12	0.5 (Basalt Fiber)	1057.7	415.8
	S-IV-1	495.6	184.4	63.2 (Silica Fume)	158.4	12	1 (Basalt Fiber)	1048.9	412.3
	S-V-1.33	501.0	184.2	63.9 (Silica Fume)	175.5	14	1.33 (Basalt Fiber)	1043	410
	S-VI-1.67	501.0	184.2	63.9 (Silica Fume)	156.6	14	1.67 (Basalt Fiber)	1037	407.7
	S-VII-2	501.0	184.2	63.9 (Silica Fume)	155.7	14	2 (Basalt Fiber)	1031.1	405.4
Nguyen et al. [94]	A	954.1	215.9	73.8 (Silica Fume)	-	-	0	1078.2	-
	B	954.1	215.9	73.8 (Silica Fume)	-	-	2 (Steel Fiber)	1058.1	-
	C	954.1	215.9	73.8 (Silica Fume)	-	-	4 (Steel Fiber)	1038.1	-
Kharun et al. [32]	HPC0	500	125	125 (Micro Silica)	100	12.5	0	585	1005
	HPC06	500	125	125 (Micro Silica)	100	12.5	0.6 (Chopped Basalt Fiber)	585	1005
	HPC09	500	125	125 (Micro Silica)	100	12.5	0.9 (Chopped Basalt Fiber)	585	1005
	HPC12	500	125	125 (Micro Silica)	100	12.5	1.2 (Chopped Basalt Fiber)	585	1005
	HPC15	500	125	125 (Micro Silica)	100	12.5	1.5 (Chopped Basalt Fiber)	585	1005
	HPC18	500	125	125 (Micro Silica)	100	12.5	1.8 (Chopped Basalt Fiber)	585	1005
Alaraza et al. [84]	HPC0	500	125	125 (Micro Silica)	100	12.5	0	585	1005
	HPC06	500	125	125 (Micro Silica)	100	12.5	0.6 (Minibar Basalt Fiber)	585	1005
	HPC09	500	125	125 (Micro Silica)	100	12.5	0.9 (Minibar Basalt Fiber)	585	1005
	HPC12	500	125	125 (Micro Silica)	100	12.5	1.2 (Minibar Basalt Fiber)	585	1005
	HPC15	500	125	125 (Micro Silica)	100	12.5	1.5 (Minibar Basalt Fiber)	585	1005
	HPC18	500	125	125 (Micro Silica)	100	12.5	1.8 (Minibar Basalt Fiber)	585	1005

Table 1. Mixture Design of different studies of HPCs.

Studies	Specimens	Cement (kg/m3)	Water (kg/m3)	Mineral Admixture (kg/m3)	Filler (kg/m3)	Superplasticizer	Fiber (%)	Fine Aggregate (kg/m3)	Coarse Aggregate (kg/m3)
Ayub et al. [9]	P-0	450	180	-	-	-	0 (Basalt Fiber)	670	1100
	PB-1	450	180	-	-	-	1 (Basalt Fiber)	670	1100
	PB-2	450	180	-	-	-	2 (Basalt Fiber)	670	1100
	PB-3	450	180	-	-	-	3 (Basalt Fiber)	670	1100
	S-0	450	180	45 (Silica Fume)	-	-	0 (Basalt Fiber)	670	1100
	SB-1	450	180	45 (Silica Fume)	-	-	1 (Basalt Fiber)	670	1100
	SB-2	450	180	45 (Silica Fume)	-	-	2 (Basalt Fiber)	670	1100
	SB-3	450	180	45 (Silica Fume)	-	-	3 (Basalt Fiber)	670	1100
	MB-1	450	180	45 (Metakaolin)	-	-	1 (Basalt Fiber)	670	1100
	MB-2	450	180	45 (Metakaolin)	-	-	2 (Basalt Fiber)	670	1100
	MB-3	450	180	45 (Metakaolin)	-	-	3 (Basalt Fiber)	670	1100
Mohaghegh et al. [83]	S-I-0	495.6	184.4	63.2 (Silica Fume)	161.1	12	0 (Basalt Fiber)	1066.6	419.3
	S-II-0	495.6	184.4	63.2 (Silica Fume)	161.1	12	0 (Basalt Fiber)	1066.6	419.3
	S-III-0.5	495.6	184.4	63.2 (Silica Fume)	159.7	12	0.5 (Basalt Fiber)	1057.7	415.8
	S-IV-1	495.6	184.4	63.2 (Silica Fume)	158.4	12	1 (Basalt Fiber)	1048.9	412.3
	S-V-1.33	501.0	184.2	63.9 (Silica Fume)	175.5	14	1.33 (Basalt Fiber)	1043	410
	S-VI-1.67	501.0	184.2	63.9 (Silica Fume)	156.6	14	1.67 (Basalt Fiber)	1037	407.7
	S-VII-2	501.0	184.2	63.9 (Silica Fume)	155.7	14	2 (Basalt Fiber)	1031.1	405.4
Nguyen et al. [94]	A	954.1	215.9	73.8 (Silica Fume)	-	-	0	1078.2	-
	B	954.1	215.9	73.8 (Silica Fume)	-	-	2 (Steel Fiber)	1058.1	-
	C	954.1	215.9	73.8 (Silica Fume)	-	-	4 (Steel Fiber)	1038.1	-
Kharun et al. [32]	HPC0	500	125	125 (Micro Silica)	100	12.5	0	585	1005
	HPC06	500	125	125 (Micro Silica)	100	12.5	0.6 (Chopped Basalt Fiber)	585	1005
	HPC09	500	125	125 (Micro Silica)	100	12.5	0.9 (Chopped Basalt Fiber)	585	1005
	HPC12	500	125	125 (Micro Silica)	100	12.5	1.2 (Chopped Basalt Fiber)	585	1005
	HPC15	500	125	125 (Micro Silica)	100	12.5	1.5 (Chopped Basalt Fiber)	585	1005
	HPC18	500	125	125 (Micro Silica)	100	12.5	1.8 (Chopped Basalt Fiber)	585	1005
Alaraza et al. [84]	HPC0	500	125	125 (Micro Silica)	100	12.5	0	585	1005
	HPC06	500	125	125 (Micro Silica)	100	12.5	0.6 (Minibar Basalt Fiber)	585	1005
	HPC09	500	125	125 (Micro Silica)	100	12.5	0.9 (Minibar Basalt Fiber)	585	1005
	HPC12	500	125	125 (Micro Silica)	100	12.5	1.2 (Minibar Basalt Fiber)	585	1005
	HPC15	500	125	125 (Micro Silica)	100	12.5	1.5 (Minibar Basalt Fiber)	585	1005
	HPC18	500	125	125 (Micro Silica)	100	12.5	1.8 (Minibar Basalt Fiber)	585	1005

3.1.2. HPC Mechanical Properties

One of the most important characteristics of the w/c ratio is the efficiency and performance of concrete. The compressive strength of concrete decreases with an increasing w/c ratio. The w/c ratio can change the tensile strength of concrete [70,71]. Rao and Sen [97] found that when the w/c ratio increases, the efficiency also increases; when the w/c ratio increases from 0.5 to 0.65, the efficiency increase is 0.05.

According to the results of

Table 2. Mechanical Properties of HPC.

Studies	Specimens	Compressive Strength (MPa)	Tensile Strength (MPa)	Flexural Strength (MPa)
Ayub et al. [9]	P-0	88.73	5.16	5
	PB-1	84.71	5.16	6.42
	PB-2	89.66	5.40	7.46
	PB-3	89.36	6	5.99
	S-0	102.37	6.65	5.66
	SB-1	103.43	6.71	6.54
	SB-2	101.3	6.72	7.16
	SB-3	100.97	7.99	6.84
	MB-1	103.43	5.49	7.09
	MB-2	101.3	5.89	7.16
	MB-3	100.97	7.18	6.86
Mohaghegh et al. [83]	S-I-0	79.5	-	-
	S-II-0	81.2	-	-
	S-III-0.5	81.6	-	-
	S-IV-1	78.6	-	-
	S-V-1.33	79.8	-	-
	S-VI-1.67	78.6	-	-
	S-VII-2	77	-	-
Nguyen et al. [94]	A	97.8	8.2	-
	B	98.5	8.6	-
	C	99	12.1	-
Kharun et al. [32]	HPC0	101.43	5.53	14
	HPC06	92.78	5.3	15.6
	HPC09	92.68	5.29	17.4
	HPC12	102.3	5.56	18.9
	HPC15	97.6	5.41	18.1
	HPC18	95.68	5.37	18.3
Alaraza et al. [84]	HPC0	101.43	-	14.1
	HPC06	101.43	-	16.8
	HPC09	105.39	-	19.8
	HPC12	90.50	-	17.2
	HPC15	89.51	-	16.4
	HPC18	92.30	-	17.1

, w/c is an important factor in mechanical properties. Other characteristics, such as fine and coarse aggregates, mineral admixture, and types of aggregates, affect the mechanical properties. Table 2 shows that adding metakaolin and 1% chopped basalt fiber increased the compressive strength from 88.73 MPa to 103.43 MPa, and also adding 1% silica fume increased the compressive strength from 88.73 MPa to 103.43 MPa [9]. Alaraza et al. [84] used micro silica and added 0.9% of minibars (macro basalt fiber). The compressive strength increased from 101.43 MPa to 105.39 MPa. The results of the mechanical properties of HPC show that by adding a basalt minibar to concrete, its mechanical properties were higher than when chopped basalt fibers and steel fibers were added. It should be noted that when the basalt minibar was added to HPC, the flexural strength was higher than when chopped basalt fibers and steel fibers were added. Mohaghegh et al. [83] used more fine aggregates than coarse aggregates, however, in HPC there are more coarse aggregates than fine aggregates. Nguyen et al. [94] only added fine grains without coarse grains. Ayub et al. [9], Kharun et al. [32], and Alaraza et al. [84] added more coarse aggregate than fine aggregate. The results of compressive, tensile, and bending strengths show that Ayub et al. [9], Kharun et al. [32], and Alaraza et al. [84], due to the use of coarse aggregate, have better results than fine aggregate, but some studies that have investigated fine aggregate achieve better mechanical behavior [83,94]. Figure 4 illustrates the mechanical properties of HPC for compressive, tensile, and flexural strengths.

3.2. UHPC Concrete

3.2.1. UHPC Mixture Design

UHPC contains more fine aggregates than coarse aggregates, silica fume and metakaolin, fly ash or other powder additives, and a lower water/cement ratio. According to Table 3, the minimum w/c ratio was more than 0.18 and the maximum w/c was more than 0.4. However, the effect of the w/c ratio defined the mechanical and chemical properties of concrete.

The important aspect of UHPC is using admixture powder and pozzolan to fill the gaps and voids inside the concrete sample and improve the mechanical and chemical properties. Dolomite is a sedimentary rock which has similar properties as cement. In addition, dolomite reduces carbon emissions and has many ecological benefits [98,99]. Swaminathan et al. [16] understood that adding dolomite to concrete helps to increase its durability. Gusian et al. [82] analyzed that adding the dolomite powder to concrete reduces the water/cement ratio and improves workability. Another usage of dolomite is as filler and aggregate in concrete. The use of filler can increase the strength of concrete [98,100,101].

Another example is fly ash as a filler, which can fill voids between aggregates. Fly ash is derived from burning coal. The chemical composition of fly ash includes Silica Oxide (SiO₂), Alumina Oxide (Al₂O₃), Iron Oxide (Fe₂O₃), and Sulfur Trioxide (SO₃). Fly ash is a worldwide material that can protect the environment by reducing the amount of cement used in concrete and improving the durability and strength of concrete [102,103,104]. The usage of fly ash reduces water usage and increases the ultimate strength, and fly ash in concrete gives maximum workability [105].

Considering the size of fine and coarse aggregate, Saji and Unnikrishnan [81] utilized fine aggregate from crushed stone with a specific gravity of 2.65, where the coarse aggregate size was between 4.75 mm and 20 mm, and the specified gravity was 2.74. For Patel et al. [86], the fine aggregate specified gravity was 2.56 and the fineness modulus was 2.84, while the coarse aggregate specified gravity was more than 2.71 and the fineness modulus was 3.38. Ghazy et al. [106] examined the natural sand and quartz as fine aggregates with a maximum practical size of 2.63 mm. In Tahwia et al. [107] the coarse aggregate was crushed dolomite with a maximum size of 12 mm and a specific gravity of 2.56. In another example, Zhou et al. [108], the maximum coarse aggregate size was 1.18 mm and the minimum aggregate size was 0.315 mm, while the maximum size of the fine aggregate was 0.16 mm.

According to the fine and coarse aggregate size, the mechanical and chemical properties of concrete depend on many elements. The common mixture design properties of UHPC are illustrated in Figure 5.

Table 3. UHPC mixture design of different studies.

Studies	Sample		Cement (kg/m3)	Water (kg/m3)	Coarse Aggregate (kg/m3)	Fine Aggregate (kg/m3)	Metacaoline (kg/m3)	Dolomite (kg/m3)	Super-Plasticizer (%)	Silica Fume (kg/m3)	Quartz Fluor (kg/m3)	Fly Ash (kg/m3)
Saji and Unnikrishnan [81]	MC	0.26	523	141	1252	604	-	-	2.61	-	-	-
	MK10	0.3	470.7	141	1252	604	52	-	2.61	-	-	-
	MK20	0.3	418	141	1252	604	104	-	2.61	-	-	-
	MK30	0.38	366	141	1252	604	156	-	2.61	-	-	-
	MK10D5	0.315	447	141	1252	604	52	23	2.61	-	-	-
	MK10D7.5	0.32	435	141	1252	604	52	35	2.61	-	-	-
	MK10D10		423	141	1252	604	52	47	2.61	-	-	-
	MK10D12.5		414	141	1252	604	52	56	2.61	-	-	-
Patel et al. [106]	C0	0.99	450	141	1134	731	-	-	2.61	-	-	-
	C1		450	141	1134	731	18.5	-	2.61	-	-	-
	C2		450	141	1134	731	23	-	2.61	-	-	-
	C3		450	141	1134	731	35	-	2.61	-	-	-
	C4		450	141	1134	731	-	-	2.61	18.5	-	-
	C5		450	141	1134	731	-	-	2.61	23	-	-
	C7		450	141	1134	731	-	-	2.61	28	-	-
Ghazy et al. [109]	UHPC	0.17	950	170	-	750	-	-	3	200	450	-
	UHPC 1-C		950	170	-	725	-	-	3	200	400	-
	UHPC 1-HE		950	170	-	725	-	-	3	200	400	-
	UHPC 2-C		950	170	-	700	-	-	3	200	350	-
	UHPC 2-HE		950	170	-	700	-	-	3	200	350	-
	UHPC 3-C		950	170	-	650	-	-	3	200	750	-
	UHPC 3-HE		950	170	-	650	-	-	3	200	300	-
Tahwia et al. [107]	Co	0.27	450	125	1110	740	-	-	12.5	50	-	-
	CO-SF		450	125	1110	740	0.75	-	12.5	50	-	-
	CO-MF		450	125	1110	740	-	-	12.5	50	-	-
	M1		450	125	1110	740	0.75	-	12.5	50	-	-
	M2		450	125	1110	740	1	-	12.5	50	-	-
	M3		450	125	1110	740	0.75	-	12.5	50	-	-
	M4		450	125	1110	740	0.53	-	12.5	50	-	-
	M5		450	125	1110	740	0.92	-	12.5	50	-	-
	M6		450	125	1110	740	0.75	-	12.5	50	-	-
	M7		450	125	1110	740	0.57	-	12.5	50	-	-
	M8		450	125	1110	740	0.97	-	12.5	50	-	-
	M9		450	125	1110	740	0.75	-	12.5	50	-	-
	M10		450	125	1110	740	0.75	-	12.5	50	-	-
	M11		450	125	1110	740	0.75	-	12.5	50	-	-
	M12		450	125	1110	740	0.5	-	12.5	50	-	-
	M13		450	125	1110	740	0.75	-	12.5	50	-	-
Han and Zhou [110]	A		470	165	1000	500	-	-	4.8	-	-	-
	B	0.402	410	165	1000	500	-	-	4.8	-	-	25
	C	0.54	350	165	1000	500	-	-	4.8	-	-	50
	D		260	165	1000	500	-	-	4.8	-	-	90
	E		180	165	1000	500	-	-	4.8	-	-	120
Zhou et al. [108]	PC-80	0.212	856	182	-	1177	-	-	4	214	-	-
	PC-55	0.31	577	178	-	1154	-	-	4	210	-	-
	PC-35		364	177	-	1145	-	-	4	208	-	-
	PC-35-NS		359	177	-	1145	-	-	4	205	-	-
	PC-35-NA		359	177	-	1145	-	-	4	205	-	-
	PC-35-AA		369	177	155	1145	-	-	4	207	-	311
Liu et al. [111]	A 0.24	0.23	1054.6	242.6	210.9	1054.5	-	-	3	316.4	-	-
Fan et al. [112]	ST-0		700	180	-	1104	-	-	2	125	-	175
	ST-0.5		700	190	-	1104	-	-	2	125	-	175
	ST-2		700	200	-	1104	-	-	2	125	-	175

Table 3. UHPC mixture design of different studies.

Studies	Sample		Cement (kg/m3)	Water (kg/m3)	Coarse Aggregate (kg/m3)	Fine Aggregate (kg/m3)	Metacaoline (kg/m3)	Dolomite (kg/m3)	Super-Plasticizer (%)	Silica Fume (kg/m3)	Quartz Fluor (kg/m3)	Fly Ash (kg/m3)
Saji and Unnikrishnan [81]	MC	0.26	523	141	1252	604	-	-	2.61	-	-	-
	MK10	0.3	470.7	141	1252	604	52	-	2.61	-	-	-
	MK20	0.3	418	141	1252	604	104	-	2.61	-	-	-
	MK30	0.38	366	141	1252	604	156	-	2.61	-	-	-
	MK10D5	0.315	447	141	1252	604	52	23	2.61	-	-	-
	MK10D7.5	0.32	435	141	1252	604	52	35	2.61	-	-	-
	MK10D10		423	141	1252	604	52	47	2.61	-	-	-
	MK10D12.5		414	141	1252	604	52	56	2.61	-	-	-
Patel et al. [106]	C0	0.99	450	141	1134	731	-	-	2.61	-	-	-
	C1		450	141	1134	731	18.5	-	2.61	-	-	-
	C2		450	141	1134	731	23	-	2.61	-	-	-
	C3		450	141	1134	731	35	-	2.61	-	-	-
	C4		450	141	1134	731	-	-	2.61	18.5	-	-
	C5		450	141	1134	731	-	-	2.61	23	-	-
	C7		450	141	1134	731	-	-	2.61	28	-	-
Ghazy et al. [109]	UHPC	0.17	950	170	-	750	-	-	3	200	450	-
	UHPC 1-C		950	170	-	725	-	-	3	200	400	-
	UHPC 1-HE		950	170	-	725	-	-	3	200	400	-
	UHPC 2-C		950	170	-	700	-	-	3	200	350	-
	UHPC 2-HE		950	170	-	700	-	-	3	200	350	-
	UHPC 3-C		950	170	-	650	-	-	3	200	750	-
	UHPC 3-HE		950	170	-	650	-	-	3	200	300	-
Tahwia et al. [107]	Co	0.27	450	125	1110	740	-	-	12.5	50	-	-
	CO-SF		450	125	1110	740	0.75	-	12.5	50	-	-
	CO-MF		450	125	1110	740	-	-	12.5	50	-	-
	M1		450	125	1110	740	0.75	-	12.5	50	-	-
	M2		450	125	1110	740	1	-	12.5	50	-	-
	M3		450	125	1110	740	0.75	-	12.5	50	-	-
	M4		450	125	1110	740	0.53	-	12.5	50	-	-
	M5		450	125	1110	740	0.92	-	12.5	50	-	-
	M6		450	125	1110	740	0.75	-	12.5	50	-	-
	M7		450	125	1110	740	0.57	-	12.5	50	-	-
	M8		450	125	1110	740	0.97	-	12.5	50	-	-
	M9		450	125	1110	740	0.75	-	12.5	50	-	-
	M10		450	125	1110	740	0.75	-	12.5	50	-	-
	M11		450	125	1110	740	0.75	-	12.5	50	-	-
	M12		450	125	1110	740	0.5	-	12.5	50	-	-
	M13		450	125	1110	740	0.75	-	12.5	50	-	-
Han and Zhou [110]	A		470	165	1000	500	-	-	4.8	-	-	-
	B	0.402	410	165	1000	500	-	-	4.8	-	-	25
	C	0.54	350	165	1000	500	-	-	4.8	-	-	50
	D		260	165	1000	500	-	-	4.8	-	-	90
	E		180	165	1000	500	-	-	4.8	-	-	120
Zhou et al. [108]	PC-80	0.212	856	182	-	1177	-	-	4	214	-	-
	PC-55	0.31	577	178	-	1154	-	-	4	210	-	-
	PC-35		364	177	-	1145	-	-	4	208	-	-
	PC-35-NS		359	177	-	1145	-	-	4	205	-	-
	PC-35-NA		359	177	-	1145	-	-	4	205	-	-
	PC-35-AA		369	177	155	1145	-	-	4	207	-	311
Liu et al. [111]	A 0.24	0.23	1054.6	242.6	210.9	1054.5	-	-	3	316.4	-	-
Fan et al. [112]	ST-0		700	180	-	1104	-	-	2	125	-	175
	ST-0.5		700	190	-	1104	-	-	2	125	-	175
	ST-2		700	200	-	1104	-	-	2	125	-	175

3.2.2. UHPC Mechanical Properties

Ghazy et al. [109] used a w/c ratio of 0.18 and also added quartz four and silica fume. Fine aggregate with a maximum size of 2.63 mm was used. The mechanical properties obtained are shown in

Table 4. UHPC mechanical properties such as compressive, tensile, and flexural strengths.

Studies	Sample	Compressive Strength (MPa)	Tensile Strength (MPa)	Flexural Strength (MPa)
Saji and Unnikrishnan [81]	MC	71.11	5.94	7.6
	MK10	72.88	6.22	8.4
	MK20	71.15	5.62	8
	MK30	69.77	5.37	7.2
	MK10D5	73.77	6.08	8.8
	MK10D7.5	74.66	6.29	8.4
	MK10D10	72.44	5.98	7.2
	MK10D12.5	70.22	5.85	6.4
Patel et al. [106]	C0	62.73	-	-
	C1	64.3	-	-
	C2	70.66	-	-
	C3	66.85	-	-
	C4	62.33	-	-
	C5	65.5	-	-
	C7	63.66	-	-
Ghazy et al. [109]	UHPC	120	9	18.66
	UHPC 1-C	130	10.5	22.65
	UHPC 1-HE	127	9.85	21.66
	UHPC 2-C	138	11.75	28.66
	UHPC 2-HE	132	11	26.02
	UHPC 3-C	150	12.55	30
	UHPC 3-HE	139	11.55	28
Tahwia et al. [107]	Co	67.2	-	10.5
	CO-SF	67.6	-	10.8
	CO-MF	68	-	11
	M1	72	-	13
	M2	73	-	13.6
	M3	72	-	13
	M4	74	-	13.9
	M5	76	-	14.5
	M6	76.8	-	14.9
	M7	70	-	12
	M8	71	-	12.4
	M9	72	-	13
	M10	69	-	12.2
	M11	72	-	13
	M12	72	-	12.5
	M13	72	-	13
Han and Zhou [110]	A	46	-	6.1
	B	46	-	5.8
	C	43	-	5.2
	D	41	-	4.8
	E	39	-	4.6
Zhou et al. [108]	PC-80	-	7.3	-
	PC-55	-	4.7	-
	PC-35	-	4.2	-
	PC-35-NS	-	4.7	-
	PC-35-NA	-	7	-
	PC-35-AA	-	6.7	-
Liu et al. [111]	A	84.9	6.9	-
Fan et al. [112]	ST-0	145	-	-
	ST-0.5	157	-	-
	ST-2	132	-	-

. According to the results from Ghazy et al. [109], UHPC 3-C had the maximum mechanical properties with maximum compressive, tensile, and flexural strengths of 150 MPa, 12.55 MPa, and 30 MPa. Fan et al. [112] had the maximum mechanical properties, such as the compressive strength of ST-0.5, 157 MPa. Fan et al. [113] used silica fume and fly ash class-c, river sand, with a w/c was 0.27.

The results show that when the w/c was less than 0.3, the mechanical properties increased and, when only fine aggregates were used, the mechanical strength increased. The compressive, tensile, and flexural strengths of concrete are related to admixture powder, w/c ratio, and the weight of fine aggregate. Figure 6 shows the compressive, tensile, and flexural strengths of different UHPC mixtures based on previous studies.

3.3. Differences between HPC and UHPC

The HPC and UHPC are two different concretes with similarities and differences. These two types of concrete are as similar as they are different in terms of mix design and mechanical properties. For the UHPC, the water/cement ratio is between 0.2 and 0.3, however, the best water/cement ratio is 0.25 [114,115]. When the water/cement ratio for HPC is between 0.2 and 0.4, the best water/cement ratio is 0.25. The UHPC uses more fine aggregate than the HPC. According to the results, it shows that the design of the UHPC mixture can withstand microcracks [114,115]. The UHPC mostly constitutes admixture powder, for example, Duan et al. [69] used quartz and silica fume, Teng et al. [116] added fly ash class-c, silica fume, and welan gun powder to cement. In another example, Azmee et al. [113] added silica fume, fly ash, and sand to cement with steel fiber.

Usually, the HPC has coarse aggregate and fine aggregate together. In HPC, the coarse aggregate weight is more than the fine aggregate. The UHPC is made of more admixture powder and fine aggregates. According to the experiments, the researchers added steel fibers. However, the HPC used basalt fiber [113,117,118].

The mechanical properties of UHPC such as compressive, tensile, and flexural strength are higher than in the HPC; while the HPC is used as constructional concrete, the UHPC is used for covering a place, restoration of the concrete, thin slab concrete, etc.

In the UHPC, adding metakaolin between 0% to 20% increases the compressive strength by over 15% [119]. It is important to note that as the curing time increases, the concentration of silica fume particles used for the pozzolanic reaction gradually decreases. As a result, the pressure improvement effect in the next stage of concrete modified with silica fume decreases [120]. The compressive strength increased with the addition of 10–20% silica fume to concrete, while no change was observed with the addition of 20–30% silica fume [121]. However, metakaolin produces more C-S-H in the cement matrix and increases the flexural strength [122]. According to the result findings, the ultra-fine fly ash with a practical size of 4.48 microns can increase the compressive strength by more than 153 MPa [123].

In general, HPC uses heavier aggregates and coarse aggregates, while UHPC uses fine aggregates. However, both concretes are mostly similar in terms of w/c ratio, though this ratio for UHPC is usually less than HPC.

3.4. Machine Learning Results

The mechanical properties prediction helps to find the coloration between the parameters of mixture designs and reduces time and cost to find the reasonable mechanical properties of concrete [57,124,125,126,127]. The current study used Python (v. 3.10.2) and Spyder (v. 5.5.5) software. In this program, the Numpy, Seaborn, Pandas, and Skylearn moduli have been used.

The first step to performing regression through Python is to prepare the data to identify the boundaries of the values and the characteristics of the data set, and then to determine the correlations. According to

Table 5. Data description.

	UHPC Cement	UHPC Water	UHPC Aggregates	HPC Cement	HPC Water	HPC Aggregates	UHPC Compressive Strength	HPC Compressive Strength
Mean	548.4	213.08	1007.1	550.5	235.4	1460.4	116.74	116.72
Std.	30.1	18.7	61.03	28.99	9.0	23.7	2.87	2.96
Min	436	180	900	500	220	1420	110	109
25%	523	200	956	526.25	228	1420	115	115
50%	552	213	1009	552	236	1461	117	117
75%	574.75	225	1056.75	573	243	1482.75	119	119
Max	608	264	1110	600	250	1500	125	125

, the description of the data is shown (Std is the standard deviation, Min is the minimum, and Max is the maximum).

According to Table 5, the minimum standard deviation is UHPC and HPC compressive strengths, with 2.87 and 2.96. The UHPC and HPC compressive strengths’ maximum and minimum values are 125 MPa, 125 MPa and 110 MPa, 109 MPa, respectively.

Figure 7 illustrates a histogram graph of each element and density. UHPC cement density is between 525 and 575. UHPC water histogram shows that the high density is on the 270, moreover, the UHPC aggregated, HPC cement, HPC aggregates, and HPC water density are distributed into all. UHPC compressive strength and HPC compressive strength density are focused on 118 MPa. Moreover, Figure 8 illustrates the test, train, and prediction dataset for all regressions.

The feature coefficient with Linear regression is more than 3.38, and the Lasso regression feature coefficient is more than 2.5. The Ridge regression feature coefficient had different values with different elements. For example, the Ridge regression feature coefficient for UHPC compressive strength is more than 2.9, for HPC water −0.8, and UHPC water is less than −0.2 (Figure 9).

This study has investigated more than 400 mixture designs. Figure 10 shows the heat map correlation between all elements of UHPC and HPC concrete types. Positive and negative effects are shown in red and blue, as well as minus and plus. Figure 11 illustrates HPC compressive strength and UHPC compressive strength correlation is more than 96%. The HPC compressive strength has a positive effect of 5.4% and a negative effect of 2.5% and 3.2%. UHPC compressive strength has more than 1.7% and 7.4% negative effects with UHPC and UHPC water, respectively, and a positive effect with 2.5% UHPC Aggregates.

Figure 11 illustrates a Pair Plot graph for feature correlation information.

This graph shows different dimensions, and according to these dimensions we can choose which dimension to ignore and which are more prone to error [128]. According to Figure 7:

• HPC Cement element lacks correlation with all characters except UHPC. This positive correlation was due to the near closeness of cement values of both mixture types.
• UHPC and HPC water did not correlate with characters. It noted that the UHPC and HPC water had no positive or negative effect on other elements.
• UHPC aggregates had a little positive effect on UHPC compressive strength. UHPC and HPC compressive strengths had a strong positive effect together.

Figure 12 and

Table 6. The regression results of UHPC and HPC.

Regression Types	RMSE	MAE	R2
Linear Regression	0.89	0.68	0.92
Lasso Regression	1.42	1.17	0.79
Ridge Regression	0.85	0.68	0.92
Random forest Regression	0.94	0.75	0.91
K Neighbors Regression	1.46	0.75	0.77
Decision tree Regression	1.16	1.16	0.86
PLS Regression	0.81	0.66	0.93

illustrate the regressions prediction results. Linear, Ridge, and Random Forest regressions had almost similar R² with 0.92, 0.92, and 0.91, respectively. While the best R² result was for PLS regression with 0.93, KNN, Lasso, and Decision Tree regressions had weaker R² with 0.77, 0.79, and 0.86, respectively. Considering MAE results, PLS, Ridge, and Linear regressions had the best results with 0.66, 0.68, and 0.68, respectively. Moreover, The RSME results show the same results. Conclusion results of RSME, MAE, and R² illustrated that the PLS, Linear, and Lasso regressions had the best results.

The work carried out is important for construction materials science. It shows the distinguishing features of Ultra-High-Performance Concrete [1,2,3,4,5,6,7,8,10,11,12,13,14,24,40,41,42,47,86,87] compared to High-Performance Concrete [9,16,17,18,19,31,32,42,43,81,84,87,94,107,129,130,131].

Differences between all regressions for R², MAE, and RMSE have been illustrated in Figure 13. Considering Figure 13, PLS regression, Linear regression, and Random Forest regression have the best results in R². In addition, PLS regression and Linear regression had the best MAE results, and RSME was the best results for PLS regression and Linear regression.

The main vectors for the development of the science of artificial intelligence in relation to concrete in various types of structures, namely High-Performance Concrete and Ultra-High-Performance Concrete, have been identified. The importance of predicting the properties of concrete based on verified data about their composition and structure is shown.

4. Conclusions

This study focused on two types of concrete, High-Performance Concrete and Ultra-High-Performance Concrete, and their differences and similarities. This paper examines the properties of HPC and UHPC mixture design, mechanical properties, and all additive materials. In addition, the present study examined the correlation matrix of HPC and UHPC to find the effect of each concrete parameter on the mechanical behavior and to predict the mechanical behavior of concrete. This study used Linear, Ridge, Lasso, Random Forest, K-Nearest Neighbors, Decision Tree, and Partial least squares regressions to predict the mechanical properties.

(1) The study first considered the differences between HPC and UHPC in the mix design. The UHPC mix design usually uses sand with a small size and binder such as silica fume and other powder, however, the HPC mixture design usually consists of gravel and sand together of different sizes, and silica fume and other types of chemical powder. The second difference is the water/cement ratio, where the HPC water/cement is 0.25 while for UHPC the water/cement ratio is between 0.2 and 0.3. The maximum compressive, tensile, and flexural strength of HPC was 105.39 MPa, 12.1 MPa, and 19.8 MPa, while the UHPC maximum compressive, tensile, and flexural strength was 157 MPa, 12.55 MPa, and 30 MPa, respectively.

(2) The study shows that the use the chemical powders such as silica fume and metakaolin has a positive effect on the mechanical properties of UHPC and HPC. Also, using different types of fiber has different effects on the HPC and UHPC. For example, basalt fiber minibar had the maximum mechanical properties of chopped basalt fiber and steel fiber when added to concrete.

(3) This article shows that the UHPC had a higher water/cement ratio than HPC and that UHPC had better mechanical properties than HPC. Due to the cementation nature of UHPC, designers should be careful in finding the w/c ratio of UHPC and paying attention to w/b for this type of concrete.

(4) The chemical powder and pozzolan improve the mechanical properties of HPC and UHPC. So, the compressive strength of HPC can be increased by adding metakaolin, and by adding metakaolin to UHPC, the compressive strength of concrete can be increased by more than 20%.

(5) The results of the correlation matrix show that the effect of cement and silica fume content on the compressive, flexural, and tensile strengths was great, and the effect of water on the flexural strength was negative. The R² results show high accuracy for PLS, Linear, and Lasso regression with 0.93, 0.92, and 0.92, respectively.