1 Introduction
“Concrete mix design” is a significant but mysterious topic that demands an in-depth comprehension of several specialized concerns. The structure can be used confidently if concrete with the right strength and other utility criteria is obtained. The strengthening and hydration of concrete are permanent procedures. As a result, any flaws in the design of the mixture of concrete are extremely expensive to the owner during construction and reduce the profitability of the edifice because of its diminished durability. To improve properties such as concrete strength, density, workability, or durability, concrete mixtures of cement, coarse and fine aggregate, and water are generally reinforced with additives and admixtures
Concrete is produced as the final product from a concrete mixture. The cement hydration process, and cement and water chemical thermal interaction initiates the concrete strengthening procedure. Cement hydration producers are gel, hydroxide, and a few secondary chemicals that aid in fine and coarse aggregate bonding. Throughout the hydration procedure, the by-products of hydration progressively settle on initial cement particles and cover the area vacated by water. When the water molecules retreat or there is no longer any unreacted cement, the procedure of hydration is complete. Concrete hardens furthermore and reaches full compressive strength during the 28 days [1,2,3]. Concrete mix design is about choosing the right quantities of cement, fine and coarse aggregate, and water to generate concrete with the desired qualities [4,5,6]. The design of concrete mixtures is progressing at a steady pace. The most common approach for measuring the number of primary ingredients required has been utilized for years and includes evaluating the bending strength of concrete mortar [7,8,9,10]. These systems have numerous drawbacks and are time-consuming to implement. We want to demonstrate a way to create concrete using a mathematical formula derived by a machine learning algorithm. The adopted neural network architecture is described in the accompanying paper, which will be fed by an extensive collection of concrete mixture dataset. We offer a mathematical equation as a conclusion, for calculating concrete compressive strength. The created method will use cement, water, and fine and coarse aggregates as its four input parameters to determine the compressive strength of concrete.
The proposed formula involves boundary conditions and does not precisely capture the behavior of concrete. However, it is a first step toward using machine learning techniques in the concrete mix design. It can be used to make a preliminary estimate of the concrete class in its current state. In future attempts, we plan to focus on concrete mixtures design in concern with the aspects of durability and estimation of service lifetime. The use of concrete admixtures such as superplasticizers, for example, would be essential.
2 Concrete mix designing based on deep learning techniques
2.1 Mathematical model
Determining the correct quantitative content and percentage of concrete mixture elements is the main purpose of water cement development. We must select a combination that permits us to get the most precise results. Concrete performance is defined by various characteristics, the most important of which are compressive strength and durability. In the concrete mix design, both strength and durability should be considered. In an aggressive setting, the question of durability is critical [11,12,13,14,15]. According to our research, there are a few popular techniques to build a mixture of concrete within European corporate engineering practice. Three of these methods are the Bukowski, Eyman and Klaus, and Paszkowski methods. Following results are found through the “Three Equations Method,” also known as the Bolomey method, a mixed experimental-analytical technique [16,17]. It implies that the experimental evidence should back up the mathematical technique. We use analytical techniques to calculate the volume of required components and destructive laboratory testing to confirm the results.
To determine the three required values, we utilize a fundamental endurance, consistency, and stiffness equation: the amount of water, cement, and aggregate represented in kg/m3. The first formula (equation (1)) is the compressive strength formula, also known as the Bolomey formula.
(1)
where f cm is the concrete’s medium compressive strength in N/mm2. A 1,2 denotes coefficients that vary based on cement grade and aggregate type, C is the amount of cement in one cubic meter of concrete in kg, W denotes the quantity of water in one cubic meter concrete in kg.
Equation (2), consistency equation, is incorporated into the watershed management formula to make a geopolymer concrete with the desired texture.
(2)
where W is the weight of water in one cubic meter of concrete in kg, C is the weight of cement in one cubic meter of concrete in kg, K is the aggregate water demand index in dm3/kg, w c is the cement-water demand index.
The simple volume formula includes equation (3).
(3)
where W denotes the water quantity in one cubic meter of concrete in kg, C denotes the quantity of cement in one cubic meter of concrete in kg. K denotes the quantity of aggregate in one cubic meter of concrete in kg, µ c denotes density of cement in kg/dm3, and µ k: denotes the aggregate density per dm3 in kg.
2.2 CNN modeling
Deep learning has been a rapidly increasing field of expertise in recent years. This technology is a branch of artificial intelligence science that includes subjects like statistics, computer science, and robotics [18,19,20,21]. In practice, machine learning tries to combine numerous revolutionary computer science breakthroughs to develop a system which can learn from datasets and, as a result, search themes and connections between variables and sets of variables that would be difficult to discover using conventional methods. In this scenario, learning can be thought of as implementing a complex algorithm. Convolution neural networks (CNNs) are one of the most common machine learning algorithms. Beginning with the initial input data, each composing module in CNN turns what is represented at a particular level into a higher and more complex level, similar to how a regular deep learning neural network works. Natural properties or complex functions could be learned by composing enough of these modifications [22,23,24]. CNN training is a comprehensive learning method [25,26,27,28] that may implicitly learn characteristics from data. As a result, manually extracting data features is unnecessary, as is initial processing or rebuilding the initial information [29]. The essential components of the first few units of CNN design are extremely similar. They use a serial convolution layer and a pooling layer to arrange data features layer-by-layer, and CNN was called after this architecture. The final unit comprises a few completely interconnected layers and a classic classification model. In many practical applications, recollecting data or rebuilding models is expensive, if not impossible, using most classic machine learning approaches [30]. Current CNN models (shown in Figure 1) demand a lot of processing power and have complicated computational requirements. Transfer learning is an excellent choice since they are exposed to local optimization difficulties or overfitting [30,31,32,33]. Another benefit of transfer learning is that it does not necessitate a huge amount of data records; however, it can achieve improved accuracy with a smaller dataset.
Figure 1
Convolution neural networks.
3 Simulation setup and results
Deep learning technique is one of the most used concrete mix designing algorithms. One of the most artificial expert system that is proposed is a CNN (shown in Figure 2) that can estimate the compressive strength of a concrete mix based on a huge number of tested concrete mix mixtures.
Figure 2
Exact CNNs structure.
The CNN calculates the concrete’s strength according to the proportions of the four essential ingredients in a concrete mix: cement, fine and coarse aggregate, and water. We converted the built CNN accordingly and reduced it to a single equation, defining concrete’s 28 days strength as a function of the four factors. The equation can calculate concrete compressive strength and validate the concrete mix recipe (Figure 3).
Figure 3
Illustrated diagram for cement mixing system [15].
Setting a border constraint for this procedure seems fair. However, because the CNN was trained on a few samples, predicting how it will react to material concentrations outside of the specified limits may be difficult. The water-cement ratio must be properly controlled since the right balance is required for full hydration of the cement. The impact of plasticizers has not been investigated. All algorithmic steps for classification and predication are shown in Figure 4.
Figure 4
The grading curves.
Many aspects, such as the curing procedure, indirectly affect the produced concrete strength and were not considered in the analysis. We anticipated that strict quality control would provide full-strength concrete. The most adopted database generation are listed in Table 1.
Table 1
Database adopted generation
| Compressive strength after 28days | Cement | Water | Sand 0–2 mm |
|---|---|---|---|
| cs_28target | Cement input | Water input | Fine_aggregate input |
| The compressive strength of concrete at 28 days after hydration Is considered as full strength | The weight of cement added to the mixture | The weight of water added to the mixture | The weight of sand added to the mixture |
Table 2 shows each input variable’s minimum, maximum, and average values.
Table 2
Input features range
| Input features | Minimum (kg/m3) | Maximum (kg/m3) | Average (kg/m3) |
|---|---|---|---|
| Cement | 86.00 | 540.00 | 278.00 |
| Water | 121.80 | 247.00 | 182.42 |
| Fine aggregate (sand 0–2 mm | 372.00 | 1329.00 | 768.55 |
| Coarse aggregate (aggregate above 2 mm | 597.00 | 1490.00 | 969.408 |
The parameters in Table 2 were separated into inputs and targets, that describe variables for input and output, respectively. Concrete strength gradually increases to full strength after starting the cement hydration process. During our deliberations, we assumed that concrete would achieve its intended compressive strength after 28 days. The concrete has some strength before the 28 days but cannot be deemed as full strength.
In our investigation, we thought the concrete attained full strength because the mixture was designed for it. The examined mixtures are presented in Table 1. The grading and aligning curves for the designed mixtures are shown in Figure 4.
The main algorithmic steps for implementation of the proposed system is shown in Figure 5, where the CNN is trained first with the training samples.
Figure 5
Flowchart for the proposed system.
Figure 6 shows the machine learning accuracy in the classification and prediction of the cement ratio system, whereas Figure 7 shows the comparison of the overfitting cases.
Figure 6
Accuracy of classification and prediction of cement ratio system.
Figure 7
Comparison of the overfitting cases.
Table 3 demonstrates how the CNN accuracy is affected by the input and hidden layer structures with three phases training, validation, and testing phase.
Table 3
Models’ metric performance
| Average | Total duration | Accuracy% | loss | |
|---|---|---|---|---|
| Training | Total | 1,028 | 89.72 | 0.23 |
| Transfer learning | 792 | 93.12 | 0.18 | |
| Random initialization | 1,264 | 86.32 | 0.31 | |
| Validation | Total | — | 84.16 | 0.35 |
| Transfer learning | — | 88.61 | 0.27 | |
| Random initialization | — | 79.72 | 0.47 | |
| Test | Total | 6.87 | 87.42 | 0.37 |
| Transfer learning | 6.59 | 89.52 | 0.21 | |
| Random initialization | 7.14 | 85.34 | 0.52 | |
Figure 3. Schematic diagram of the cement mixing system.
The statistics shown above suggest that for datasets with a small number of pictures, simple networks with few parameters and shallow depth can achieve excellent accuracy and efficiency. On the contrary, the use of complicated networks is prone to overfitting due to a lack of data, which would impair the training impact. Table 4 depicts CNN's performance, and it can be observed that it is nearly optimal for training data. Almost all of the datapoints are inside the 10% error limit. The CNN metamodel is shown to be more accurate for higher CS values than for CS values less than 50 MPa. The CNN on training and testing is seen to be 99 and 97%, respectively.
Table 4
Comparison results with literature research
| No. 1 | reference | Methods (accuracy 100%) | MSE | Max. error |
|---|---|---|---|---|
| 1 | [14] | AdaBoost regression 78% | 96.84 | 20.44 |
| 2 | [15] | Multi-layer perceptron 90% | 46.82 | 20.84 |
| 3 | [17] | Decision tree regression 94 | 26.09 | 21.20 |
| 4 | Our proposed system | CNN 98.6% | 10.06 | 10.7 |
4 Conclusion
The CNN formula showed low resilience for high strength concrete mixes (50 MPa and more). This could be owing to the limited amount of mixes used to train the CNN for these ranges. CNN’s behavior could indicate underfitting. We must emphasize that the method provided here is simply an introduction to the machine learning large application in concrete mix creation and does not cover the entire subject. It ignores certain critical concerns, such as the technological process and durability. Our research focuses on using machine learning in concrete mix ration and developing a practical tool for use in engineering practice. We created the best CNN architecture for the study and gave it a huge database of concrete mix formulas. A destructive laboratory test is associated with each concrete mix recipe record. The purpose of producing concrete with specific compressive strength is achieved by predicting optimal mixture of concrete materials using a neural network. More specifically, what materials ratio should be chosen to generate concrete with a suitable compressive value. Our database has 941 records.
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Funding information: The manuscript was done depending on the personal effort of the author, and there is no funding effort from any side or organization.
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Conflict of interest: There is no conflict of interest with anyone related to the subject of the manuscript or any competing interest.
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Data availability statement: Most datasets generated and analyzed in this study are in this submitted manuscript. The other datasets are available on reasonable request from the corresponding author with the attached information.
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