Analysis of compressive strength of sustainable fibre reinforced foamed concrete using machine learning techniques

This study emphasizes the usage of Silica Fume (SF) and Marble Sludge Powder (MSP) as a partial replacement for fly ash in Fibre Reinforced Foamed Concrete (FRFC). The compressive strength for various samples was analyzed using Artificial Neural Network (ANN) methods. In this research work, the utilization of silica fume, fly ash, marble sludge powder, polypropylene fiber, and foaming agent in fiber-reinforced foamed concrete is presented and a sincere attempt has been made to use silica fume and marble sludge powder for the replacement of fly ash with various percentages. In addition to that polypropylene fiber (PPF) was used in various proportions of 0%, 0.1%, 0.2%, 0.3%, 0.4%, and 0.5%. The Feed Forward Propagation (FFP) network of the machine learning method with one hidden layer was taken as the ANN structure of FRFC. In this ANN work, cement, silica fume, fly ash, marble sludge powder, foaming agent, water, and polypropylene fiber were used as input parameters and compressive strength is the output parameter. The correlation coefficient with the ANN methods was found as 0.940 for compressive strength. In machine learning techniques, the ANN method was found to be accurate in estimating and analyzing strength prediction responses with effective parameters.


Introduction
Concrete is vital to the expansion of the construction industry.Various by-product materials like fly ash, silica fume, rice husk ash, quartz powder, marble powder, etc, are extensively used as a replacement for pozzolanic materials in foamed concrete [1,2].Various investigations demonstrated that the usage of pozzolanic materials not only enhances concrete properties such as strength, durability, and thermal properties but also contributes to environmental preservation [3].The rise in concrete consumption will increase the demand for cement.In India, the annual production of cement is approximately 410 Mt, produced by approximately 142 major and 396 minor facilities.It is anticipated to reach 580 Mt by 2024.The industrial productions of CO 2 from the cement industry, accounting for up to 50% are the result of chemical processing, 40% is the result of fuel combustion and the remaining 10% is the result of gas emissions [4,5].Cement production contributes to the emission of greenhouse gases both directly through the thermal decomposition of calcium carbonate, which releases CO 2 , lime, and indirectly through the use of energy, particularly the combustion of fossil fuels.To maximize the utilization of natural resources in developing countries, it is necessary to investigate the recycling and reuse of refuse materials [6,7].Modernly, foamed concrete is regarded as an attractive building material due to its flexible production technology, exceptional target properties, and economic advantages [8,9].
During cement hydration, the heat generated by foamed concrete differs significantly from that of normalweight concrete [10,11].Foamed lightweight concrete is a cellular cementitious material produced by incorporating preformed foam into the cement matrix [12].By combining these two components, air voids are created within the underlying microstructures of the material, resulting in several advantageous properties, which include, first and foremost, low self-weight, especially when the density is low [13].This is extremely beneficial for reconstruction operations or reducing the load on structures of a building to minimize loading, and secondly, thermal insulating properties and acoustic absorption, both of which are advantageous for facilitating partite construction operations [14].Low-to-medium density foam concrete components are utilized for non-structural elements and partitions in buildings, substrates in road construction, and industrial concrete floors, whilst greater densities may be used for structural purposes [15].Therefore, a compelling area of research is the exploration of solutions aimed at attaining acceptable strength levels without necessitating an increase in density.The phenomenon of core temperature increases in foamed concrete when it is placed in a well-insulated mold with a regular shape has been observed [16,17].Despite the existence of various publications discussing the thermal effect in foamed concrete, there remains an absence of information regarding the interdependencies between foamed concrete parameters and their impact on the increase in temperature [18,19].The conversion of raw materials, whether they are utilized or waste materials, offers substantial energy savings through the reduction of industrial processes involved in material production [20][21][22][23].The use of fibers in foam concrete has been shown to enhance its flexural strength and effectively mitigate the drying shrinkage phenomenon [24][25][26][27].In the framework of lightweight concrete, the exploration of reinforcing systems including composite grids and fiber-reinforced meshes was also undertaken [28].The present study effort has been prompted by the potential effectiveness of employing strategies that involve the simultaneous presence of embedded short fibers of polypropylene fiber in the cementitious matrix used to increase the mechanical strength of fiber-reinforced foamed concrete.
The usage of the analysis model is demonstrated, whereby the compressive strengths of several mix designs may be estimated using ANN methods.This allows for the selection of mix designs that meet the necessary strength requirements, hence facilitating subsequent physical testing [29,30].Moreover, it is possible to ascertain the most cost-effective option from the set of choices that need compressive strength for economic evaluation [31].Numerous endeavors have been made to devise computer-assisted methodologies for foam concrete mix design, including those based on artificial neural networks [32].However, the implementation of these techniques in real engineering applications has encountered some challenges [33].In recent years, there has been a growing trend towards the widespread adoption of machine learning techniques for the prediction of certain compressive strength characteristics [34,35].The analysis considers the mechanical, environmental, and economic performance of concrete [36,37].Additionally, machine learning methods are employed to investigate the effects of these materials both in combination and individually.The present research work utilized experimental data from 27 combinations to investigate the influence of different factors on the compressive behavior of fiber-reinforced foam concrete, employing machine learning technology for enhanced understanding.

Cement
Ordinary Portland Cement (OPC) of 53 Grade was used as per as per IS 12269-2013 specification is suitable [38].Due to its uniform particle size distribution and better crystalline structure, 53 Grade OPC increases concrete strength and durability.Table 1 lists the cement's physical properties whereas, table 2 lists the properties of its chemical composition.

Silica fume
Amorphous silicon dioxide (SiO 2 ) makes up between 85 and 98 percent of silica fume and this component is the major component of silica fume.Carbon, silicon carbide, and the oxides of alkaline (earth) metals are the most common types of impurities.Silica fume, also known as micro silica, is a by-product of the production of silicon and ferrosilicon alloys.

Flyash
The burning of coal produces Fly ash is a by-product.The fly ash of Class F as a supplemental cementitious material was utilized, which was provided by Integrity Filter Material.A shade of grey best describes the color of the fly ash.It implies that the grey colors that are lighter represent a greater quality of fly ash.In this study, fly ash Conforming to IS 3812-2003 (Part 1) [42] was used.The fly ash was replaced by marble sludge powder and silica fume at 0%, to 100% of 5% variation respectively.Table 3 lists the properties of the chemical composition.The specific gravity of flyash is 2.7.

Marble sludge powder (MSP)
MSP is extracted wet from the Marble plant deposits.Wet MSP must be disinfected earlier to sample processing.MSP comprises many different types of marble and marble stones.Consequently, the remaining marble sludge was sieved using 1mm sieve.The high calcium oxide concentration verified the provenance of the marble and limestone.Additionally, the sludge was examined for the presence of organic matter to ensure its suitability for use in concrete compositions., table 3 lists the properties of chemical composition.The specific gravity of MSP is 2.6.

Foaming agent
The foaming agent was mixed with water at a ratio of 1:20 to produce foam, which means that produces foam one part of the foaming agent and 20 parts of water were taken.Sodium Lauryl Sulphate, commonly referred to as SLS, was the particular foaming agent that was put to use in this investigation.It is a kind of foaming agent that is based on synthetic materials.The ratio of water to cement has been estimated as 0.5, and the ratio of cement to fly ash was found to be 1:2.Within the scope of this investigation, the density of foamed concrete was held constant at 1600 kg m −3 .Table 4 outlines the characteristics of the foaming agent's details.

Polypropylene fiber
The abbreviated form of PPF refers to polypropylene fiber, a linear polymer synthetic fiber that is produced by the polymerization of propylene.Additionally, it exhibits corrosion resistance and possesses a low weight, a high level of strength, a high degree of toughness, and a favorable strength-to-weight ratio.Table 2 outlines the various characteristics of PP fiber.In the implementation of this research, addition of PP fiber with 0.1% to 0.5% variation by the weight of cement was used.

Chemical properties of binder materials
The chemical properties of materials in the concrete mix play a crucial role in the performance, durability, and behavior of fiber-reinforced foamed concrete.The main chemical components involved in FRFC are cement, silica fume, fly ash and marble sludge powder, polypropylene fiber, foaming agent, and water.Here are the key chemical properties of binder materials in foamed concrete are given in table 3.

Mix proportions and methodology
In this experimental investigation, attention has been focused on various proportions of cement, silica fume, fly ash, marble sludge powder, foaming agent, polypropylene fiber, and water.The trial mixes were made by changing the cement-flyash ratio is 1:2 and the water-cement ratio is 0.5 and the mix with a design density of 1600 kg m −3 was used in the research work.In preliminary sensitivity studies, the foaming agent and water were mixed in a ratio of 1:20 to determine the correct foam content necessary to obtain the targeted densities of FRFC.Table 5 gives the mixed proportions of the fiber-reinforced foamed concrete.The usage of all material quantities is taken by proportion on a weight basis.

Compressive strength
The compressive strength test was conducted on cube specimens of fiber-reinforced foamed concrete of 70.6 mm × 70.6 mm × 70.6 mm was used as per IS:10080-1982 [43].The compressive strength of concrete is a crucial mechanical property that measures its ability to withstand compressive forces before it fails or undergoes permanent deformation.It is an essential parameter in the design and construction of structures like buildings, bridges, dams, and other infrastructure.Compressive strength is typically expressed in terms of MPa.To determine the compressive strength, the concrete is subjected to a compressive force until failure.The concrete mix proportions, curing conditions, and the quality of materials used influence the compressive strength of fiber-reinforced foamed concrete.The foamed concrete's compressive strength increases with its age, reaching its full potential after 28 days of curing.

Artificial neural network
The artificial neural network (ANN) can be characterized as a mathematical framework for logical inference.It draws inspiration from the biological structure and functioning of the human brain, which serves as the foundation for the feed-forward neural network, commonly referred to as a multilayer perceptron.This network consists of an input layer, a hidden layer, and an output layer.The learning rules of an artificial neural network (ANN) are often determined through the utilization of the gradient descent training method, which is frequently referred to as the backpropagation approach.This technique involves adjusting the weights and biases of the network to minimize the error between the actual outputs and the desired target outputs.In this particular approach, individual nodes are subjected to weighted inputs originating from other nodes, and afterward transmit their outputs to other nodes through the use of an activation function.In the process of learning, the nodes inside each layer establish connections with the nodes in the subsequent layer through a cyclic link.The connection connections, which are responsible for providing the weights, are often created to minimize the error in a training process.Ultimately, the desired outcomes of this training method provide the resultant values of the projected model.In this, a total of 27 data sets were evaluated, in that 80% was used for training and the remaining 20% was used for testing.
The study employed the Feed Forward Propagation (FFP) artificial neural network, which was first introduced as a double-hidden layer network.The Feedforward Propagation (FFP) technique was employed to conduct the training procedure for the Artificial Neural Network (ANN) model within the MATLAB program.Based on the available data from the concrete mix proportioning database, the input layer of the neural network consists of seven neurons, whereas the output layer comprises just one neuron.A feedforward neural network with one hidden layer was employed.The structure of the FFP-ANN employed in this work is shown in figure 1.

Regression analysis in concrete
The ideal conditions for casting, testing, and curing are maintained, the trends for strength ratios ought to remain consistent irrespective of the kind of specimen under examination.Even with the same concrete, it can be difficult to keep testing and sample creation conditions consistent.This is among the explanations for why extraordinary things do happen in the real world.This resulted in the realization that different concrete samples had to have their strengths compared independently and that these differences were not always present.A generic formula for the regression analysis of compressive strength for fiber-reinforced foamed concrete containing marble sludge powder, silica fume, and polypropylene fiber may be derived from the ratios of the strengths involved.The connection may be determined using strength ratios regardless of the type of specimen employed.In this analysis, figure 2 denotes, X1-Cement, X2-Silica Fume, X3-Flyash, X4-MSP, X5-Polypropylene Fiber, X6-Water, X7-Foaming Agent, and Y gives the output of Compressive strength of foamed concrete.

Compressive strength of FRFC
This section provides an analysis of the compressive strength of fiber-reinforced foam concrete.This section presents a discussion on the impact of compressive strength of 7, 14, and 28-day curing of fiber-reinforced foamed concrete as prepared in the present investigation.This section provides an analysis of the compressive strength of fiber-reinforced foam concrete.This section presents a discussion on the impact of compressive strength of 7, 14, and 28-day curing of fiber-reinforced foamed concrete as prepared in the present investigation.
Figure 3 illustrates the mean compressive strength achieved after a curing period of 7, 28, and 56 days.All mixes including SF and MSP, either alone or in combination, exhibited increased compressive strength.
For instance, the FRFC17 mixture, consisting of 100% cement, 65% fly ash, 20% silica fume, and 15% marble sludge powder, had a compressive strength of 7.4, 9.36, and 11.04 MPa for 7, 28, and 56 days respectively.The addition of 0.3% PP fibers to the controlled specimen of foamed concrete results in optimal compressive strength.The experimental results indicate that the FRFC24 combination exhibits superior compressive strength in comparison to other fiber-reinforced foamed concrete compositions, particularly when using 0.3% polypropylene fiber of 10.2, 12.97, 15.3 MPa for 7, 28, and 56 days respectively.When it comes to evaluating the properties of FRFC, compressive strength is regarded as being the single most important aspect that needs to be looked at.The reactivity of silica fume can lead to its reaction with calcium hydroxide, which is produced during cement hydration, hence leading to the generation of further C-S-H gel.The addition of silica fume has environmental considerations to sustainability goals.Its use may lead to a reduction in overall carbon dioxide emissions associated with concrete production and improved durability can result in a more environmentally friendly construction solution [44].The use of silica fume has the potential to greatly improve the compressive strength of foamed concrete.The addition of silica fume to the concrete matrix leads to a reduction in pore size, hence enhancing the density and impermeability of the resulting structure [18].The enhancement of the microstructure of concrete resulting from this reaction leads to an improvement in both its strength and durability.This effect is caused by the reduction in the size of the pores.In the same way, as silica fume possesses pozzolanic characteristics, marble sludge powder does as well.In the presence of water, it undergoes a reaction with calcium hydroxide that results in the formation of extra C-S-H gel, which contributes to the FRFC's strength and longevity [45].In terms of its workability, MSP, when used in acceptable proportions, may improve the workability of new concrete, making it simpler to handle and insert in the concrete mold.It has been demonstrated that amorphous spherical particles, such as silica fume and marble sludge powder, can improve the rheological features of fiber-reinforced foam concrete.As a result of their relatively tiny average particle size, silica fume, and MSP have a good infill effect and may be injected between cement particles in fiber-reinforced foamed concrete to increase the material's strength property.This improvement in strength can be attributed to the presence of PP fibers, which are the elements that are in charge of filling the voids that are produced by the foaming agent.However, it should also be noted that the compressive strength does not improve with an increase in the quantity of PP fiber content that is more than the optimal dose of 0.3% that has been identified.After 0.3% of PP fiber has been added to the fiber-reinforced foamed concrete, the compressive strength of the material will drop as a direct result of this.This is the findings of the research work.

Regression analysis model using ANN
Estimating the compressive strength of fiber-reinforced foamed concrete materials is one of the goals of this study.In this investigation, the ANN algorithm, which is a lifting-based machine learning approach, is utilized.Herewith random data division, Levenberg-Marquardt training, and Mean square error performance with MEX Calculations were done.MATLAB was used to generate figure 6. Figure depicts the ANN structure used in this study, which is a feed-forward network with a hidden layer.Using the same approach for feature selection, a total of seven features, including cement, silica fume, fly ash, marble sludge powder, polypropylene fiber, water, and foaming agent, were used as the raw data to find out the accurate findings for the experimental dataset.In this investigation the experimental data set was given in table 6.These features were used to find out the raw data.Technical parameters for ANNs are detailed in table 7. compressive strength performance indicators are depicted in figures 4-7.The obtained minimum Gradient of 0.73667 at epoch 11 for the compressive strength of FRFC.
Figure 4 depicts the training state of compressive strength parameters.In this training, validation, testing, and best parameters were studied to determine the best validation performance ranges.The behavior of compressive strength obtained MSME in the range of 10°−10 2 and the best validation is achieved at epoch 16 of 1.4968.
Figure 5 depicts the error histogram analysis of concrete compressive strength.It is the difference in error between targeted and projected values after training a feedforward neural network with machine learning methods.A total of 27 datasets were evaluated.From the analysis error values of compressive strength indicate that the error of 0.002522 for 4 instances of training was obtained.Figure 6 illustrates the correlation between experimental results and the sets used for training, validation, and testing in the context of compressive fiber-reinforced foamed concrete with marble sludge powder and silica fume.The present study provides evidence of a strong connection between the complete set of empirical observations and the data generated by the neural network model.The compressive strength of fiber-reinforced    foamed concrete is evaluated using an artificial neural network (ANN) model, which utilizes an experimental database to display its effectiveness.
Figure 7, shows that the relationship between the predicted and observed 28 days of compressive strength for fiber-reinforced famed concrete and the high correlation between all data sets are very clear.The coefficient of correlation for the 28 days of compressive strength prediction of 98% was achieved.

Conclusion
From the above investigation the following conclusions are drawn: • In this study, the compressive strength of FRFC24 was increased to a higher value of 10.2, 12.97, and 15.3 MPa for 7, 28, and 56 days respectively by adding 0.3% polypropylene fiber, 15% marble sludge powder, 20% silica fume, 65% fly ash, with constant proportion of cement.
• Polypropylene fibers are often used as reinforcement in concrete to improve its mechanical properties and overall performance.The addition of 0.3% of polypropylene fibers enhanced the tensile and flexural strength of fiber-reinforced foamed concrete.The fibers provide additional reinforcement that helps to distribute stress evenly and prevent cracking under load.
• The obtained R-value, which is very close to 1, shows that there is a strong correlation between the predicted and observed values with quality control was achieved.
• This lightweight concrete act as a fill material for floor and roof screeds.It provides thermal insulation and reduces the overall dead load on the structure and also it can be used in building foundations, especially in areas with poor soil conditions.Foamed concrete can be cast into various precast elements such as blocks, panels, and pipes.Because of its significance in engineering practices, predicting the compressive strength of concrete in a timely and precise manner has emerged as a topic of interest for a growing number of academics in the future.

Figure 3 .
Figure 3. Test results on compressive strength of FRFC.

Figure 4 .
Figure 4. Training state of compressive strength.

Figure 6 .
Figure 6.The regression of compressive strength.

Figure 7 .
Figure 7. ANN Model fitting of compressive strength.

Table 1 .
Table 3 lists the properties of the chemical composition.Silica Fume used in this investigation was Confirmed to IS 15388 [41].The specific gravity of silica fume is 2.2.Cement physical property.

Table 2 .
Property of PP fiber.

Table 3 .
Chemical properties of materials.

Table 4 .
Property of foaming agent.

Table 5 .
Mix proportion of fibre-reinforced foamed concrete.

Table 6 .
Experimental dataset for regression analysis.