Abstract
Various developing countries are confronted with serious environmental difficulties due to excessive resource utilization and insufficient waste management system. In particular, construction and demolition waste poses a grave threat to the environment, contributing to escalating energy consumption, the depletion of landfill capacities, and the generation of harmful noise and dust pollution. Consequently, the research community is tasked with the daunting challenge of devising effective strategies to incorporate this waste material in producing concrete, without compromising the critical strength and durability characteristics. The investigation aims to attain the aforementioned objective by examining the effects of using recycled aggregates as a distinct partial replacement of 0%, 5%, 10%, 15%, and 20% on the compressive and split tensile strength traits, contingent upon 7 and 28 days of age of curing. Experimental test results show that the optimal concrete production is achieved when 10% of coarse aggregate is replaced with recycled aggregate, maintaining 98% of the materials compressive and split tensile strength. To further validate the obtained experimental data, model equations were derived through regression analysis and the framed model equation is further assessed for accuracy using error analysis. In this study, a MATLAB program was utilized for prediction of compressive and split tensile strength with five distinct network types and the Levenberg-Marquardt algorithm is used for optimization. A comparative analysis was conducted between the regression analysis values and the performance of the ANN modelling. The findings demonstrate that the Artificial Neural Network (ANN) serves as a highly effective model, offering significantly improved accuracy in predicting the optimal correlation between compressive strength and split tensile strength of concrete.
1 Introduction
In recent years, the surging demand for modern structures has resulted in a severe dearth of essential building materials like cement, fine and coarse aggregates. Stringent state regulations on natural resource extraction have only exacerbated this problem [1, 2]. Consequently, finding sustainable alternatives that satisfy both strength and durability criteria is crucial. Various binding materials have been investigated in previous studies [3–7] including metakaolin, ground granulated blast furnace slag, fly ash, silica fume, limestone powder, etc., in either partial or full replacement proportions. Additionally, researchers [8–11] have examined M-sand, recycled aggregates, modified plastics, crushed limestone, natural fibers, agro-waste, and E-waste for use in concrete production. Recycled aggregates, in particular, have garnered significant interest among researchers for their potential use in construction. However, the safety of buildings beyond their intended service life is a concern for both occupants and nearby structures, necessitating their demolition [12]. During this process, valuable materials such as bricks, aggregates, wooden doors and windows, and rebar can be salvaged for reuse [13, 14]. Nevertheless, according to the Building Material Promotion Council's statistical report, around 150 million tonnes of construction and demolition (C&D) waste are produced annually, with just 1% being recycled on a daily basis and the remainder being dumped in landfills [15].
Sharholy et al. and Nanda et al. [10, 16] have claimed that improper utilization of waste can lead to its dumping in land and water, causing significant environmental damage and posing life-threatening risks such as water and soil contamination, and increasing the risk of natural disasters and global warming. Therefore, it is essential to utilize sustainable materials, such as recycled aggregates, in examining the characteristics of concrete. In the present investigation, recycled aggregates were partially used to replace coarse aggregates in varying proportions of 0%, 5%, 10%, 15%, and 20%, and tested at curing periods of 7, 14, and 28 days. To validate the experimental findings, an analytical investigation was conducted and model equations were developed using regression analysis [17]. These equations were used to evaluate the compressive strength by integrating variables such as percentage of replacement and age of curing days. The relationship between the strength parameters was determined using error analysis, and it was then compared to earlier literature studies. The relationship equation framed by the past research studies include Carino et al., who explored the relationship between compressive strength and split tensile in normal weight concrete [18], while Arioglu et al. proposed a simple power function for calculating split tensile strength from cylinder compressive strength, finding that an increase in compressive strength leads to a reduction in split tensile strength and vice versa [19]. Raphael developed an equation to determine the flexural tensile strength of high strength concrete using compressive strength values [6], and Oluokun et al. derived an equation that established the relationship between splitting tensile strength and compressive strength at early ages [20]. The effectiveness of the correlation between the researchers' existing and earlier experimental results and the anticipated values acquired from the models is assessed using error analysis. However, the coefficients in these derived equations vary due to important factors such as aggregate properties, curing conditions, admixture type, specimen strength levels, concrete age, etc.
The present study also proposes a data mining tool, ANN for predicting the compressive and split tensile strength of recycled aggregate concrete. In recent decades, numerous researchers have employed a variety of methodologies to forecast the characteristics of concrete formulated with different mix proportions. Among these approaches, ANN have gained significant popularity. This preference can be primarily attributed to the ease of utilization and remarkable accuracy in ANN modelling. However, ANN are currently utilized to predict the split tensile and compressive strengths of concrete. The efficacy of ANN in predicting the split tensile and compressive strength of recycled aggregate concrete with and without silica fume in concrete was investigated in a study by Z.H. Duan et al. and Topcu et al. [7, 21]. Similarly, Cahit Bilim et al., investigated the capability of ANN to anticipate the compressive strength of concrete with GGBS. The study utilized the results obtained from laboratory investigation that involved the concrete strength for 45 cubes in the ANN study [22] and the model demonstrated strong predictive power with a high correlation coefficient in estimating the compressive strength of concrete with and without blast furnace slag, for both short- and long-term predictions. Raghu Prasad et al. developed ANN model that is capable of predicting the compressive strength of 28-day cured normal, high-performance concrete (HPC) and high strength self-compacting concrete (SCC) specimens with high volume fly ash [23]. These findings demonstrate the effectiveness of the ANN model in predicting the compressive strength of conventional as well as high strength SCC and HPC with high volume fly ash content.
Palika Chopra et al. endeavoured to formulate models with two data mining approaches, ANN and Genetic Programming (GP) for estimating the compressive strength of concrete. The test data's used for developing the models was procured through laboratory experiments conducted under controlled standard conditions at three distinct curing periods: 28-, 56-, and 91-day [24]. An ANN model was used to forecast the compressive strength of environmental friendly concrete by Hosein Naderpour et al. The test data's utilized to develop the ANN model was obtained from 139 existing datasets from 14 published literature sources, which was split for training and testing sets [25]. Based on the aforementioned literature reviews and the use of artificial intelligence in the construction industry, ANNs are discovered to be a useful tool for the analysis of concrete strength parameter. This is a result of ANN's capability to manage intricate, data-intensive, non-linear interactions, as well as its adaptability to changing circumstances and ability to make precise predictions. In this investigation, an ANN model has been proposed to predict the best relationship value for the compressive and split tensile strength of concrete with eleven input parameters and an output parameter. It is then executed in a MATLAB programme with five different network types by dividing the data set to train, test, and validate the experimental data. Finally, the Levenberg-Marquardt algorithm is used for iterative trial and error procedures to achieve the best output parameter. The performance of the ANN modelling was compared to the results of the regression analysis in order to determine the most accurate prediction method.
2 Material and its properties
2.1 Cement
In this investigation, ordinary Portland cement, grade 53 was used, in accordance with the Indian standards outlined in IS: 12269-2013 [26]. Various fundamental properties of the cement, such as consistency, specific time, and specific gravity, were determined and tabulated in Table 1.
Physical characteristics of concrete components
| Characteristics | M-Sand | Coarse aggregate | Recycled aggregate | Cement |
| Specific gravity | 2.66 | 2.64 | 2.65 | 3.148 |
| Water absorption (%) | 3.09 | 0.21 | 2.3 | - |
| Fineness modulus | 3.10 | 4.29 | 5.8 | - |
| Aggregate impact value (%) | - | 11.43 | 16.92 | - |
| Bulk density (kg m−3) | 1733 | 1635 | 1676 | - |
| Consistency (%) | - | - | - | 34 |
| Initial setting time (min.) | - | - | - | 32 |
| Final setting time (min.) | - | - | - | 547 |
2.2 M-sand
Table 1 lists the characteristics of fine aggregate made from Manufacturing sand, which passes through a sieve of 4.75 mm and retained on a sieve of 150 μm, in accordance with Indian standards (IS-383-1970) [27], corresponding to Zone-II gradation.
2.3 Coarse aggregate
Table 1 lists the characteristics of 20 mm size coarse aggregates which are used in this investigation, and obtained from a nearby quarry. The aggregates were tested for sieve analysis and met the required specifications. Specific gravity, water absorption, fineness modulus, aggregate impact value, and bulk density were among the characteristics determined for the coarse aggregates [28].
2.4 Recycled aggregate
Recycled aggregates were produced by collecting crushed concrete samples from a nearby source and crushing them into different sizes. Sieve analysis testing was conducted during the initial screening process, which resulted in obtaining coarse aggregates with an average size ranging from 16 to 20 mm. Table 1 lists the basic characteristics of these recycled aggregates.
2.5 Admixture
In this study, Fosroc Conplast WL was utilized as an additive. This liquid, based on lingo sulphonates, is readily dispersible in water and has a dark brown color [29].
2.6 Water
Throughout the experimental study, potable water with a pH range of 6–7 is the preferred choice for both the mixing and curing processes.
3 Mix proportion and specimen details
For this experimental investigation, the M60 grade concrete mix was formulated in accordance with the Indian standards outlined in (IS 10262-2019) codal provisions [30]. The mix proportion for this study was 1 (C): 1.56 (FA): 2.89 (CA): 0.35 (W/c), which was carefully designed. For studying the effect of recycled aggregates on the concrete, the recycled aggregates at varying proportions of 0%, 5%, 10%, 15%, and 20% for different curing periods of 7, 14, and 28 days were taken into account. Table 2 lists the precise mix proportions (for 1 m3 of concrete) for each of the replacement level.
The precise mix proportions
| Replacement (%) | Cement (kg m−3) | Water (kg m−3) | M-sand (kg m−3) | Coarse aggregate (kg m−3) | Recycled aggregate (kg m−3) | Admixture (kg m−3) |
| 0 | 421.47 | 147.516 | 661.103 | 1218.53 | 0 | 4.21 |
| 5 | 421.47 | 147.516 | 661.103 | 1157.604 | 60.926 | 4.21 |
| 10 | 421.47 | 147.516 | 661.103 | 1096.677 | 121.853 | 4.21 |
| 15 | 421.47 | 147.516 | 661.103 | 1035.751 | 182.779 | 4.21 |
| 20 | 421.47 | 147.516 | 661.103 | 974.824 | 243.706 | 4.21 |
Cube specimens of 150 mm (length) × 150 mm (width) × 150 mm (height) were casted for the compression test and cylinder specimens 150 mm (diameter) × 300 mm (height) for split tension test. Materials were selected for each replacement percentage as specified in mix proportion of Table 2. Initially, M-Sand, recycled aggregate, and coarse aggregates were thoroughly mixed with cement to ensure a dry mixture. After the dry mixture was thoroughly mixed, the calculated amount of water was progressively added with the admixture. While pouring the mixture into the cube or cylinder moulds, appropriate compaction was done in three levels around the perimeter of the specimens using steel rod. 9 cube specimens and 9 cylinder specimens were cast versus 7, 14, and 28 days for each of the replacement percentages (3 specimens for each of the curing days). For the compression and split tension tests, 45 numbers of cube specimens and 45 numbers of cylinder specimens were cast for the various replacement percentages as given in Table 3. Specimens were demoulded after 24 h of casting and then allowed for water curing for 7, 14 and 28 days.
Specimen details
| S. No | Replacement of recycled aggregates | Specimen casted for | |
| Compression test | Split tension test | ||
| 1 | 0% | 9 | 9 |
| 2 | 5% | 9 | 9 |
| 3 | 10% | 9 | 9 |
| 4 | 15% | 9 | 9 |
| 5 | 20% | 9 | 9 |
| Total specimens | 45 | 45 | |
4 Methodology
4.1 Experimental testing and determination of fresh and hardened concrete properties
The fresh and hardened characteristics of concrete were examined through a series of rigorous tests. Workability of the fresh concrete, made from recycled aggregates, was determined by conducting Slump cone and compaction factor tests. The compaction factor and slump cone equipment is cleaned, levelled, and attached firmly to the non-absorbent surface. The components required for the concrete are thoroughly mixed to achieve homogeneity according to the precise mix proportions listed in Table 2. Three equal layers of mixed concrete, each one-third of the cone's height thick, are poured into the slump cone. With a consistent number of tamping blows (usually 25 with a 16 mm diameter tamping rod for each layer), each layer is compacted. A trowel is used to remove extra concrete from the slump cone's top, and the cone is then raised vertically to allow the concrete to settle. The height of the cone is measured from the point at which the concrete slumps. Similarly, the components required for the concrete are thoroughly mixed according to the precise mix proportions listed in Table 2. The upper hopper is filled with the mixed concrete after making sure the trap door is shut. Now let the concrete entirely flow into the bottom hopper by opening the trap door. The compacted volume of the concrete in the lower hopper should be measured. The compacted volume to the original volume of the concrete sample is used to compute the compaction factor. Using a Compression Testing Machine (CTM) with a 100 T capacity, the specimens' compressive strength was evaluated by applying constant stress at a rate of 14 Nmm−2 min till failure. It is calculated by dividing the load at failure with the corresponding cross-sectional area. Additionally, split tensile strength tests were also be performed CTM, by keeping the specimen horizontal and centered while applying a continuous load at a notional rate of 2.4 Nmm−2 min. By dividing the load at failure by the required geometric variables, such as the diameter and length of the cylinder specimen, the split tensile strength was calculated.
4.2 Prediction tool for hardened concrete properties
In this study, the obtained experimental data results were analyzed by using two different predictive tools: regression analysis and artificial neural network modeling.
4.2.1 Regression analysis
- i.Based on the experimentally determined compressive and split tensile strength values for different curing ages, three different linear regression model equations and a power function equation are framed to assess the strength and significance of the correlation between factors using parameters like the coefficient of determination (R-squared), which denotes the percentage of variation in the variable that is dependent explained by the variables that are independent. Typically, the power function equation and constructed linear regression model will take the form of equations 1 and 2:
- ii.To assess the correlation between the laboratory's obtained experimental data results and the regression data results, the developed model equation is utilized by substituting the values of compressive strength, split tensile strength, and the number of curing days from the experimental data into the equation. This comparison helps evaluate the relationship and agreement between the two sets of data.
- iii.To examine the correlation for the developed power function equation, the experimental compressive strength values was utilized. Additionally, the obtained experimental values were substituted into the equations from previous research conducted by researchers [1, 6, 18-20, 31] to assess their effectiveness.
- iv.In addition, error analysis was conducted by employing statistical parameters, which includes mean square error (MSE), root mean square error (RMSE), integral absolute error (IAE), normal efficiency error (NEE), mean absolute percentage error (MAPE), and mean absolute deviation (MAD). The obtained error values were then compared with those reported in previous research. This error analysis provides a quantitative assessment of the discrepancies between paired observations.
4.2.2 ANN model
ANN models are computational models that are developed by the structure and functioning of the human brain. ANNs are used to process information, recognize patterns, and make decisions based on the input data [32]. A huge number of interconnected processing nodes called neurons which may collaborate to carry out particular tasks. The neurons are arranged in layers, where each layer processes the input data and transmits the outcomes to the following layer, and so on, until the output is produced [33].
When developing an ANN model, various factors must be considered [34]. First and foremost, it is necessary to choose the proper ANN model architecture. The number of layers and the units in each layer must also be established, along with the activation function. A suitable model often has numerous layers and assumes complete interconnections between all of its components. Depending on the model used, these connections may be unidirectional or bidirectional. During the learning phase, The ANN is capable of organising or representing the information it receives in a way that is uniquely its own [35].
The objective of this model is to predict the best relationship value for the compressive strength and split tensile strength of concrete using ANN. Ninety data samples from experimental research are used in the dataset for ANN training in order to achieve this. The proposed model entails various trails by changing the hidden layers with neurons. This study proposes an ANN model with 11 input parameters and one output parameter, namely, cement, M-sand, coarse aggregate, recycled aggregate, water, replacement percentage, admixture, slump, compaction factor, mix ratio, and age of curing under the MATLAB program. The structure of ANN modelling in mat lab program is shown in Fig. 1. Using a random division method, the data set is split into training, validation, and testing sets. To be more precise, 70–75% of the data set is set aside for training, 20–30% for validation, and 11–15% for testing, allowing for an in-depth assessment of the model. The ANN model in this study is trained using the Levenberg-Marquardt (LM) technique. This widely used algorithm is used in ANNs to reduce the difference between the expected and real output. It works by incrementally lowering the sum of squared errors between the output that is anticipated and the output that actually occurs, which then modifies the inter-neuronal connection weights within the ANN. The LM algorithm is an effective optimization technique for enhancing the accuracy of ANNs [36].
Schematic diagram of ANN proposed model in MAT LAB program
Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00734
4.2.2.1 Performance evaluation
The study utilized five distinct types of networks to analyse the various training sets, they are feed forward back propagation, cascade forward propagation, probabilistic, radial basis, and layer recurrent. For supervised learning tasks like classification or regression, feed forward back propagation is a common learning method used in ANNs. The algorithm is based on the back propagation of errors through the network, allowing it to adjust its weights and biases to reduce the difference level between the output and the desired target [37]. Cascade forward propagation is a method used in ANN modelling for training and updating the network's weights and biases. It involves the sequential flow of information through the network, starting from the input layer and progressing towards the output layer [38]. By iteratively performing cascade forward propagation, the ANN model gradually learns the underlying patterns and relationships in the training data, allowing it to make predictions on new, unseen data. This process of forward and backward pass, coupled with weight and bias updates, helps the network converge towards an optimal solution.
In ANN modelling, probabilistic approaches refer to methods that incorporate probabilistic concepts or techniques to enhance the modelling and prediction capabilities of the network. These approaches aim to provide a measure of uncertainty or probability associated with the network's predictions. By incorporating probabilistic approaches in ANN modelling, we can obtain more informative predictions. Instead of relying solely on point estimates, these methods provide a probabilistic framework that can quantify uncertainty and enable more robust decision-making [39]. The radial basis function (RBF) is a type of activation function commonly used in certain layers of the network. The RBF activation function is named after the shape of its response curve, which resembles a radial basis or a bell-shaped curve. The radial basis function plays a vital role in ANN modelling by providing a localized and flexible activation function that allows the network to learn and represent complex relationships in the data. A layer recurrent structure refers to a specific architecture where recurrent connections are introduced within a layer of neurons. This architecture allows the network to retain and utilize information from previous time steps or iterations. By incorporating layer recurrent structures, ANN models gain the ability to capture and exploit temporal patterns, making them well-suited for tasks involving sequential data. The recurrent connections enable the network to learn and adapt to complex temporal relationships, leading to improved performance in tasks such as sequence prediction, sequence generation, and temporal pattern recognition [40].
By conducting an analysis of five different network types using ANN modelling, the objective was to determine the best network type in terms of R-squared coefficient of determination. This analysis aimed to determine the best fit for the developed model equation.
Finally, to identify the most efficient method for examining the developed model equation, results from ANN modelling and regression analysis are compared.
5 Result and discussion
5.1 Experimental results
According to Indian Standards (IS: 1199-1959), the slump cone and compaction factor test are used for assessing the fresh characteristics of concrete [41], with various replacements of coarse aggregates by recycled aggregates. The slump cone test revealed a moderate degree of workability, with slump values ranging from 79 to 82 mm, and a compaction factor of around 0.95 was obtained. Table 4 shows the experimental test results. The nature of workability achieved through the fresh concrete test suggests that the recycled concrete prepared falls within the plastic to flowing workability category.
Workability factors
| Replacement percentage of coarse aggregate with recycled aggregate (%) | Slump (mm) | Compaction factor |
| 0 | 81 | 0.959 |
| 5 | 80 | 0.959 |
| 10 | 82 | 0.957 |
| 15 | 79 | 0.958 |
| 20 | 80 | 0.958 |
Following a standard protocol (IS 516:1959) [42], the specimens of 7, 14, and 28 days of curing were performed to test against compression and split tension strength tests. Table 5 provides a summary of the results obtained. The control specimens exhibited an average compressive strength of 45.31 N mm−2 after 7 days, but this value slightly reduced to 44.57 N mm−2 with a 5% replacement of recycled aggregates. As the proportion of recycled aggregates increased to 10%, 15%, and 20%, the average compressive strength continued to decrease, measuring 44.03, 42.22, and 40.35N/mm2, respectively. These results indicate a continuous decline in strength with increase in percentage of replacement of recycled aggregates, demonstrating the significant impact of replacement on the strength of the concrete. Similar trends were observed after 14 and 28 days of curing, as illustrated in Fig. 2, where the average compressive strength reduced by 0.46%, 2.29%, 3.31%, and 5.18% with a 5%, 10%, 15%, and 20% replacement of recycled aggregates, respectively. Inadequate bonding between the new and recycled aggregates may be accountable for the reduction in strength. According to the test results, the average compressive strength of the concrete decreases as the percentage of recycled aggregates increases.
Specimen details
| Replacement of recycled aggregates (%) | Average compressive strength (Days) | Average split tensile strength (Days) | ||||
| 7 | 14 | 28 | 7 | 14 | 28 | |
| 0 | 45.31 | 61.93 | 73.21 | 3.53 | 4.11 | 5.75 |
| 5 | 44.57 | 60.75 | 72.87 | 3.53 | 4.11 | 5.73 |
| 10 | 44.03 | 59.36 | 71.53 | 3.52 | 4.06 | 5.63 |
| 15 | 42.22 | 57.98 | 70.79 | 3.17 | 3.95 | 5.48 |
| 20 | 40.35 | 56.67 | 69.42 | 3.05 | 3.86 | 5.30 |
Replacement of Recycled aggregates Vs Average compressive strength
Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00734
Figure 2 exhibits that the mean compressive strength escalates proportionally with the duration of the curing process. Specifically, the mean compressive strength of the unaltered sample, devoid of recycled aggregates (0% replacement), demonstrated a notable rise of 26.84% and 38.21% upon being subjected to 14 and 28 days of curing, respectively, relative to 7 days of curing. Notably, the mean compressive strength of the sample infused with 20% replacement of recycled aggregates also exhibited a discernible surge, reaching a peak of 28.29% and 41.82% respectively at 14 and 28 days after curing. The increase in strength is the result of calcium silicate hydrate (CSH) gel developing in the pores of the concrete.
The mean split tensile strength exhibits a comparable trend with the mean compressive strength, albeit with some reduction observed in Fig. 3 as the ratio of replacement by recycled aggregates increased. It was found that after 7 days of curing, neither the mean split tensile strength of the control sample nor a 5% replacement of recycled aggregates changed. However, a declining trend was noted in the range of 6.08%–9.68% for replacement percentages of recycled aggregates ranging from 10% to 20% for all curing durations. In contrast, the mean split tensile strength increased from 38.61% to 42.45% for 28 days of curing and replacement levels ranging from 0% to 20%, relative to 7 days of curing.
Replacement of Recycled aggregates Vs Average split tensile strength
Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00734
5.2 Regression analysis: development of model equation
- (i)Strength Vs Days and Replacement %
D – Age of curing days
RCA – Replacement level of coarse aggregate with RA, %.
RCA – Replacement level of coarse aggregate with RA, %
It was observed that model equations 3 to 5 had a good correlation with the obtained experimental test results, with an error percentage of 0.002 or 0.0006 percent.
- (ii)Relationship of compressive and split tensile strength
Relationship between strength parameters
Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00734
In order to test the correlation, the experimental compressive strength values were substituted in the developed model equation (6). Furthermore, the obtained experimental values were substituted in the previous research equations from the researchers [1, 6, 18–20, 31] to check its effectiveness, and the comparison is shown in Table 6.
Comparison with past researches
| Description on past research | Equation | Replacement of RA | ||||
| 0% | 5% | 10% | 15% | 20% | ||
| Experimental split tensile test results | - | 5.73 | 5.75 | 5.63 | 5.48 | 5.3 |
| Developed Model equation 6 | ft = 0.0078 fck1.546 | 5.757 | 5.716 | 5.555 | 5.467 | 5.305 |
| Equation based on (ACI318. 2014) | ft = 0.56√fck | 4.792 | 4.780 | 4.736 | 4.712 | 4.666 |
| Equation based on (Ahmad et al. 1985) | ft = 0.462fck0.55 | 4.900 | 4.887 | 4.837 | 4.810 | 4.758 |
| Equation based on (Ariogluet al. 2006) | ft = 0.321fck0.661 | 5.483 | 5.466 | 5.399 | 5.362 | 5.293 |
| Equation based on (Carino et al. 1982) | ft = 0.272fck0.71 | 5.733 | 5.715 | 5.640 | 5.598 | 5.521 |
| Equation based on (Oluokun et al. 1994) | ft = 0.294fck0.69 | 5.687 | 5.669 | 5.597 | 5.557 | 5.482 |
| Equation based on (Raphael 1984) | ft = 0.313fck0.667 | 5.485 | 5.468 | 5.401 | 5.364 | 5.294 |
Where ft and fck-split tensile strength and compressive strength respectively.
Table 6 indicates that the formulated model equation 6 exhibits a remarkable conformity with the acquired experimental values and prior researcher's investigations, exhibiting least possible errors.
Where, Ei experimental values (actual) and Oi obtained model equation values (forecast).
Error analysis was also performed using statistical parameters such as mean square error (MSE), root mean square error (RMSE), integral absolute error (IAE), normal efficiency error (NEE), mean absolute percentage error (MAPE), and mean absolute deviation (MAD) and compared with previous research. The error analysis expresses a measure of the number of errors that occur between the paired observations. Table 7 displays the various parameter formulas used to calculate the concern values. The average square of the errors between experimental values and the values anticipated by the model equations is known as MSE.
Statistical parameters formula
| S. No | Formula |
| 1 | MSE = |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 |
According to Table 8, the developed model equation 6 has the lowest MSE of all (value 0.0015), indicating a higher accuracy of prediction among the experimental and predicted values. The square root of mean square error is referred to as RMSE. It assesses the estimation of the accuracy of predicted values. In general, RMSE is most useful when outsized errors are highly disagreeable. The RMSE value obtained for the developed model equation 6 was 0.0394, and the lower of this value indicates that there was an intimate relationship between the experimental and predicted values, which is incomparable with previous research. MAD is the average of the total differences between each data value that deviates from the mean. The low variability (value 0.0183) described in Table 8 appears to indicate that the data is clustered together. MAPE communicates precision as a percentage of error. Because the MAPE is a percentage, it is easier to understand than other statics methods. As shown in Table 8, the MAPE of a developed model equation 6 is 0.5466, and the error percentage for forecasting is in the excellent range (Since the value of error is less than 10 percent). IAE is the value of the difference between the model equation values and the experimental values, expressed as a percentage of the obtained experimental values. IAE is found to be 0.5536 for the developed model equation 5, indicating that the penalty term (key difference) is very small and falls into the 'better' category. A NEE is a value that denotes the percentage of the obtained model equation's efficiency level in terms of forecasting outputs versus experimental values. In terms of prediction, the efficiency obtained is 99.45 percent, which appears to be very high. As a result of the error analysis, it was discovered that the developed model equation 6 is superiorly correlated with the experimental test values.
Error analysis
| S. No | Description on past research | MSE | RMSE | MAD | MAPE | IAE | NEE |
| 1 | Developed Model equation 6 | 0.0015 | 0.0394 | 0.0183 | 0.5466 | 0.5536 | 99.4534 |
| 2 | Equation based on ACI318 (2014) | 0.722 | 0.850 | 0.841 | 15.021 | 15.075 | 84.979 |
| 3 | Equation based on Ahmad et al. (1985) | 0.561 | 0.749 | 0.740 | 13.206 | 13.259 | 86.794 |
| 4 | Equation based on Arioglu et al. (2006) | 0.042 | 0.205 | 0.177 | 3.128 | 3.181 | 96.872 |
| 5 | Equation based on Carino et al. (1982) | 0.013 | 0.113 | 0.063 | 1.435 | 1.391 | 98.565 |
| 6 | Equation based on Oluokun et al. (1994) | 0.010 | 0.099 | 0.020 | 1.518 | 1.492 | 98.482 |
| 7 | Equation based on Raphael et al. (1984) | 0.041 | 0.202 | 0.175 | 3.091 | 3.143 | 96.909 |
5.3 Prediction of R2 value using ANN modelling
The study utilized five distinct types of networks to analyse various training sets, with the most promising outcomes in terms of R2-values being tabulated. The network types employed encompassed feed forward propagation, cascade forward propagation, probabilistic, radial basis, and layer recurrent. Diverse training trial sets were undertaken across different network types through repeated experimentation that involved alterations to the amount of neurons, transfer functions, training functions, and adaptive learning functions. This led to an increase in the number of perceptible R2 values. For instance, within the feed forward back propagation technique, consistent neuron quantities were maintained while altering transfer, training, and adaptive functions, leading to the attainment of distinct R2 values. Employing a trial and error approach, an optimal R2 value of 0.987 was obtained for the feed forward back propagation network type. This same methodology was applied to all other network types, yielding optimal R2 values of 0.962 for cascade forward propagation, 0.951 for probabilistic networks, 0.907 for radial basis networks, and 0.921 for layer recurrent networks.
The study employed regression values (R2-values) to evaluate the connection between the ANN networks' objectives and their outcomes. A value of unity in R2 indicates a robust relationship. The study relied on both MSE and R-values as evaluation criteria to appraise the performance of the generated networks. Based on these findings, it can be inferred that the feed forward propagation network type delivered the most accurate results.
A summary of the Feed forward back propagation training outcomes is presented in Figs 5–7. The result from Table 9, illustrate that the most competent performance networks are Feed forward back propagation, Cascade forward propagation and Probabilistic. Figure 5 shows the function fit for output element 1. The pictorial representation of function fit element represents that during the training process, the “fit” function performs a forward pass through the neural network to generate a prediction for each input in the training data which has been represented as testing, training and validation target in Fig. 5. Then, a loss function, such as mean squared error, is used to calculate the error between the targets and the outputs. This procedure is repeated until the error has been reduced to an acceptable level or for a predetermined number of epochs. The solid line depicts the ideal linear fit between the compressive and split tensile strength target values and output values. Once the training process is complete, the “fit” function returns the trained model, which can be used to make predictions on new data. In terms of R2-values, feed-forward-back propagation shows promising results and has the lowest MSE of all the networks examined.
The function fit for output element 1
Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00734
The performance of feed forward back propagation network
Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00734
Training state of feed forward back propagation network
Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00734
Optimum coefficient of determination R2 value results for five network types
| Network type | Case | Neurons/layers | Transfer function | Training function | Adaptive learning function | R2 value |
| Feed forward back propagation | 1 | 10 | logsig | traingdm | learngdm | 0.987 |
| Cascade forward propagation | 2 | 15 | purelin | traingda | learngd | 0.962 |
| Probabilistic | 3 | 20 | tansig | trainlm | learngdm | 0.951 |
| Radial basis | 4 | 16 | logsig | trainscg | learngd | 0.907 |
| Layer recurrent | 5 | 15 | purelin | trainr | learngdm | 0.921 |
The study under consideration employed MSE as the criterion to halt the training of ANN which is shown in Fig. 6. A lower value of MSE is indicative of an enhanced network performance. The decreasing pattern of the network's MSE, as evidenced by Fig. 6, is a positive indicator of a well-trained ANN. The graphic has three lines because the target and input vectors were randomly split into three different sets. The ANN is iteratively trained using the prescribed training vectors until the error of the network converges when evaluated against the validation vectors. The training is halted once it has been accomplished on the training set, at the cost of poorer generalization, to prevent over-fitting.
Figure 8 demonstrates the regression R2 value for the three stages of training, validation, and testing using a feed forward back propagation network. It can be shown that the R2 coefficient of determination values for the training set, testing set, and validation set were 0.99455, 0.97125, and 0.95104, respectively. The training set had a better fit than the testing set, according to the results. The entire effectiveness of the ANN's training, testing, and validation sets when compared to the desired results yields an R2 coefficient of determination of 0.98707. It has been proven that the built-in ANN model can accurately predict the optimal relationship value between the compressive strength and split tensile strength of concrete. According to Fig. 5, the effectiveness of the proposed neural network's training, testing, and validation sets when compared to the desired values shows that it is capable of learning a link between the various input parameters and the output parameter. Additionally, it was able to simulate the relationship between the compressive and split tensile strengths of concrete developed with recycled aggregate.
Feed forward back propagation network simulates regression of training, validation, and test
Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2023.00734
5.4 Comparing ANN modelling and regression analysis
In terms of prediction performance, the ANN approach outperforms the regression analysis technique, according to the evaluation of the ANN model and regression analysis carried out in this study. The higher R2 values of the ANN model show that it is more accurate at predicting the relationship between the compressive strength and split tensile strength values. A key parameter for judging the reliability of prediction models is the determination coefficient (R2), and prediction accuracy rises as R2 values get closer to 1. The ANN modelling approach used in this study produces R2 values higher than 0.98%, demonstrating that the developed model can account for at least 0.98% of the experimental/target data. These facts strengthen the usefulness of using ANN even more.
In contrast, the regression analysis model yielded an R2 value of 96% when predicting model equation 6. These findings suggest that both methods' models can be deemed reliable for accurate predictions, given their substantial explanatory capabilities. Nevertheless, it is noteworthy that the ANN model exhibited significantly superior predictive outcomes compared to the regression analysis model. Furthermore, the study convincingly demonstrates that a well-trained ANN model can effectively forecast Compressive and split tensile strength, obviating the need for extensive and time-consuming experimental studies entailing high costs.
6 Conclusion
Due to the hydration process, the average compressive strength of concrete tends to rise proportionally with the duration of curing. When cured for 14 or 28 days instead of just 7 days, the control sample's compressive strength increases by 26.84% and 38.21%, respectively.
However, the mean compressive strength value indicates a continuous downward trend as the fraction of recycled aggregates increases, suggesting that the amount of recycled aggregates has a negative effect on the strength of concrete. Nevertheless, it was established that a replacement of up to 10% of recycled aggregates would be optimal in attaining 98% compressive and split tensile strength.
Model equations were created to estimate the compressive and split tensile strength, considering the influencing factors of replacement percentage of recycled aggregates and age of curing days.
Moreover, a comparison with prior studies was conducted, and it was revealed that the model equation exhibited the slightest possible errors. To evaluate the accuracy level among the split tensile and compressive strength, an error analysis was performed, employing statistical parameters like MSE, RMSE, MAD, MAPE, IAE, and NEE. The model equation produced least possible errors, such as 0.0015, 0.0394, 0.0183, 0.5466, and 0.5536, with efficiency levels ranging from 84% to 96%.
The developed model equation demonstrated 99% efficiency when compared to previous research, indicating that it is well-correlated and can be employed to determine split tensile strength from compressive strength values.
This study involved in the development of ANN model to analyse the developed model equation with 11 input parameters and an output parameter. Regression coefficients were found to be 0.987, 0.962, 0.951, 0.907, and 0.921 for the network's training, validation, and testing phases, respectively.
The most optimal validation performance was attained during the eighth epoch with the Feed Forward Back Propagation network.
The created model equation with compressive and split tensile strength showed the least MSE value, demonstrating that the ANN technique has the capability of generating extremely accurate predictions.
Through regression analysis, the model equation yields a regression R2 value of 0.9696. Conversely, employing the feed-forward back propagation network in the ANN predictive tool results in an R2 value of 0.987 for the identical model equation. This comparison demonstrates that, in contrast to regression analysis, ANN modelling serves as an exceedingly effective predictive tool for accurately determining the optimal relationship between split tensile strength and compressive strength.
In foreseeable future, it would be worth exploring the durability aspects of recycled aggregate concrete fortified with other eco-friendly binders like GGBS, fly ash, silica fume, granite, and marble powder. A well-trained ANN and regression model tool can be used to predict concrete characteristics with accuracy, eliminating the need for lengthy and expensive experimental trials.
Funding
This work has not received any funds, grants, or other support.
Competing interests
There is no relevant financial or non-financial interest to disclose.
Author contributions
The research work was done by all of the authors. Karthiga Murugan: collected the materials, conducted the experiments, analysed the data, and wrote the manuscript. Meyyappan Palaniappan: Guidance and suggestions for tools and methods to complete the entire study, as well as contributions to the drafting of the entire manuscript. Balakrishnan Baranitharan: Conceptualization and guidance about ANN modelling.
Ethics approval and consent to participate
Not applicable.
Consent to publish
Not applicable.
Availability of data and materials
Not applicable.
Acknowledgement
Not applicable.
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