ML techniques have been effectively implemented in several industries, including medical and biomedical equipment, entertainment, finance, and engineering applications. The KNN method is a simple supervised ML technique that can be utilized in order to solve both classification and regression problems. Date:2/1/2023, Publication:Special Publication Mater. Song, H. et al. Constr. In addition, the studies based on ML techniques that have been done to predict the CS of SFRC are limited since it is difficult to collect inclusive experimental data to develop models regarding all contributing features (such as the properties of fibers, aggregates, and admixtures). On the other hand, K-nearest neighbor (KNN) algorithm with R2=0.881, RMSE=6.477, and MAE=4.648 results in the weakest performance. Recently, ML algorithms have been widely used to predict the CS of concrete. This is a result of the use of the linear relationship in equation 3.1 of BS EN 1996-1-1 and was taken into account in the UK calibration. Six groups of austenitic 022Cr19Ni10 stainless steel bending specimens with three types of cross-sectional forms were used to study the impact of V-stiffeners on the failure mode and flexural behavior of stainless steel lipped channel beams. However, this parameter decreases linearly to reach a minimum value of 0.75 for concrete strength of 103 MPa (15,000 psi) or above. consequently, the maxmin normalization method is adopted to reshape all datasets to a range from \(0\) to \(1\) using Eq. Further information on the elasticity of concrete is included in our Modulus of Elasticity of Concrete post. Sci Rep 13, 3646 (2023). Also, it was concluded that the W/C ratio and silica fume content had the most impact on the CS of SFRC. According to the results obtained from parametric analysis, among the developed models, SVR can accurately predict the impact of W/C ratio, SP, and fly-ash on the CS of SFRC, followed by CNN. Mater. Founded in 1904 and headquartered in Farmington Hills, Michigan, USA, the American Concrete Institute is a leading authority and resource worldwide for the development, dissemination, and adoption of its consensus-based standards, technical resources, educational programs, and proven expertise for individuals and organizations involved in concrete design, construction, and materials, who share a commitment to pursuing the best use of concrete. Sanjeev, J. All three proposed ML algorithms demonstrate superior performance in predicting the correlation between the amount of fly-ash and the predicted CS of SFRC. Li, Y. et al. Whereas, it decreased by increasing the W/C ratio (R=0.786) followed by FA (R=0.521). Flexural strength of concrete = 0.7 . Constr. This useful spreadsheet can be used to convert the results of the concrete cube test from compressive strength to . 1. The value of flexural strength is given by . One of the drawbacks of concrete as a fragile material is its low tensile strength and strain capacity. Zhu, H., Li, C., Gao, D., Yang, L. & Cheng, S. Study on mechanical properties and strength relation between cube and cylinder specimens of steel fiber reinforced concrete. The sensitivity analysis demonstrated that, among different input variables, W/C ratio, fly ash, and SP had the most contributing effect on the CS behavior of SFRC, followed by the amount of ISF. Google Scholar. Compressive strength, Flexural strength, Regression Equation I. The testing of flexural strength in concrete is generally undertaken using a third point flexural strength test on a beam of concrete. where fr = modulus of rupture (flexural strength) at 28 days in N/mm 2. fc = cube compressive strength at 28 days in N/mm 2, and f c = cylinder compressive strength at 28 days in N/mm 2. 2.9.1 Compressive strength of pervious concrete: Compressive strength of a concrete is a measure of its ability to resist static load, which tends to crush it. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Further information can be found in our Compressive Strength of Concrete post. Cloudflare is currently unable to resolve your requested domain. Date:7/1/2022, Publication:Special Publication A. However, regarding the Tstat, the outcomes show that CNN performance was approximately 58% lower than XGB. Moreover, among the three proposed ML models here, SVR demonstrates superior performance in estimating the influence of the W/C ratio on the predicted CS of SFRC with a correlation of R=0.999, followed by CNN with a correlation of R=0.96. Constr. J. Enterp. Constr. Build. A calculator tool is included in the CivilWeb Flexural Strength of Concrete suite of spreadsheets with this equation converted to metric units. Mater. Shade denotes change from the previous issue. In Artificial Intelligence and Statistics 192204. Among different ML algorithms, convolutional neural network (CNN) with R2=0.928, RMSE=5.043, and MAE=3.833 shows higher accuracy. PubMed Central The flexural strength is the strength of a material in bending where the top surface is tension and the bottom surface. Conversion factors of different specimens against cross sectional area of the same specimens were also plotted and regression analyses Chou, J.-S., Tsai, C.-F., Pham, A.-D. & Lu, Y.-H. Machine learning in concrete strength simulations: Multi-nation data analytics. Phone: +971.4.516.3208 & 3209, ACI Resource Center Intersect. CAS 27, 102278 (2021). CAS Linear and non-linear SVM prediction for fresh properties and compressive strength of high volume fly ash self-compacting concrete. The presented paper aims to use machine learning (ML) and deep learning (DL) algorithms to predict the CS of steel fiber reinforced concrete (SFRC) incorporating hooked ISF based on the data collected from the open literature. The findings show that up to a certain point, adding both HS and SF increases the compressive, tensile, and flexural strength of concrete at all curing ages. Setti, F., Ezziane, K. & Setti, B. In terms of comparing ML algorithms with regard to IQR index, CNN modelling showed an error dispersion about 31% lower than SVR technique. Mahesh et al.19 noted that after tuning the model (number of hidden layers=20, activation function=Tansin Purelin), ANN showed superior performance in predicting the CS of SFRC (R2=0.95). Google Scholar. Finally, the model is created by assigning the new data points to the category with the most neighbors. To develop this composite, sugarcane bagasse ash (SA), glass . Constr. Moreover, in a study conducted by Awolusi et al.20 only 3 features (L/DISF as the fiber properties) were considered, and ANN and the genetic algorithm models were implemented to predict the CS of SFRC. Constr. Since the specified strength is flexural strength, a conversion factor must be used to obtain an approximate compressive strength in order to use the water-cement ratio vs. compressive strength table. Despite the enhancement of CS of normal strength concrete incorporating ISF, no significant change of CS is obtained for high-performance concrete mixes by increasing VISF14,15. Hence, the presented study aims to compare various ML algorithms for CS prediction of SFRC based on all the influential parameters. Development of deep neural network model to predict the compressive strength of rubber concrete. J. Comput. The flexural strengths of all the laminates tested are significantly higher than their tensile strengths, and are also higher than or similar to their compressive strengths. Civ. Flexural strength may range from 10% to 15% of the compressive strength depending on the concrete mix. Mater. Moreover, the regression function is \(y = \left\langle {\alpha ,x} \right\rangle + \beta\) and the aim of SVR is to flat the function as more as possible18. 12. ADS Explain mathematic . Among these techniques, AdaBoost is the most straightforward boosting algorithm that is based on the idea that a very accurate prediction rule can be made by combining a lot of less accurate regulations43. While this relationship will vary from mix to mix, there have been a number of attempts to derive a flexural strength to compressive strength converter equation. Adv. The feature importance of the ML algorithms was compared in Fig. Date:10/1/2022, Publication:Special Publication The flexural strength of concrete was found to be 8 to 11% of the compressive strength of concrete of higher strength concrete of the order of 25 MPa (250 kg/cm2) and 9 to 12.8% for concrete of strength less than 25 MPa (250 kg/cm2) see Table 13.1: What factors affect the concrete strength? Build. Adv. 2 illustrates the correlation between input parameters and the CS of SFRC. Nguyen-Sy, T. et al. The SFRC mixes containing hooked ISF and their 28-day CS (tested by 150mm cubic samples) were collected from the literature11,13,21,22,23,24,25,26,27,28,29,30,31,32,33. B Eng. Moreover, according to the results reported by Kang et al.18, it was shown that using MLR led to a significant difference between actual and predicted values for prediction of SFRCs CS (RMSE=12.4273, MAE=11.3765). 27, 15591568 (2020). Date:9/1/2022, Search all Articles on flexural strength and compressive strength », Publication:Concrete International 4) has also been used to predict the CS of concrete41,42. Dao, D. V., Ly, H.-B., Vu, H.-L.T., Le, T.-T. & Pham, B. T. Investigation and optimization of the C-ANN structure in predicting the compressive strength of foamed concrete. The correlation of all parameters with each other (pairwise correlation) can be seen in Fig. For example compressive strength of M20concrete is 20MPa. The air content was found to be the most significant fresh field property and has a negative correlation with both the compressive and flexural strengths. 12), C, DMAX, L/DISF, and CA have relatively little effect on the CS. From the open literature, a dataset was collected that included 176 different concrete compressive test sets. In terms MBE, XGB achieved the minimum value of MBE, followed by ANN, SVR, and CNN. In fact, SVR tries to determine the best fit line. This is much more difficult and less accurate than the equivalent concrete cube test, which is why it is common to test the compressive strength and then convert to flexural strength when checking the concrete's compliance with the specification. Table 3 shows the results of using a grid and a random search to tune the other hyperparameters. Buildings 11(4), 158 (2021). Constr. 308, 125021 (2021). : New insights from statistical analysis and machine learning methods. The use of an ANN algorithm (Fig. As with any general correlations this should be used with caution. The stress block parameter 1 proposed by Mertol et al. Build. A comparative investigation using machine learning methods for concrete compressive strength estimation. 38800 Country Club Dr. Finally, it is observed that ANN performs weaker than SVR and XGB in terms of R2 in the validation set due to the non-convexity of the multilayer perceptron's loss surface. The compressive strength and flexural strength were linearly fitted by SPSS, six regression models were obtained by linear fitting of compressive strength and flexural strength. Where an accurate elasticity value is required this should be determined from testing. Materials 15(12), 4209 (2022). & LeCun, Y. Kang et al.18 collected a datasets containing 7 features (VISF and L/DISF as the properties of fibers) and developed 11 various ML techniques and observed that the tree-based models had the best performance in predicting the CS of SFRC. Eur. STANDARDS, PRACTICES and MANUALS ON FLEXURAL STRENGTH AND COMPRESSIVE STRENGTH ACI CODE-350-20: Code Requirements for Environmental Engineering Concrete Structures (ACI 350-20) and Commentary (ACI 350R-20) ACI PRC-441.1-18: Report on Equivalent Rectangular Concrete Stress Block and Transverse Reinforcement for High-Strength Concrete Columns The implemented procedure was repeated for other parameters as well, considering the three best-performed algorithms, which are SVR, XGB, and ANN. Mater. To generate fiber-reinforced concrete (FRC), used fibers are typically short, discontinuous, and randomly dispersed throughout the concrete matrix8. Question: How is the required strength selected, measured, and obtained? The correlation coefficient (\(R\)) is a statistical measure that shows the strength of the linear relationship between two sets of data. In other words, in CS prediction of SFRC, all the mixes components must be presented (such as the developed ML algorithms in the current study). Hameed et al.52 developed an MLR model to predict the CS of high-performance concrete (HPC) and noted that MLR had a poor correlation between the actual and predicted CS of HPC (R=0.789, RMSE=8.288). Mater. MLR predicts the value of the dependent variable (\(y\)) based on the value of the independent variable (\(x\)) by establishing the linear relationship between inputs (independent parameters) and output (dependent parameter) based on Eq. The simplest and most commonly applied method of quality control for concrete pavements is to test compressive strength and then use this as an indirect measure of the flexural strength. The presented work uses Python programming language and the TensorFlow platform, as well as the Scikit-learn package. The flexural strength of UD, CP, and AP laminates was increased by 39-53%, 51-57%, and 25-37% with the addition of 0.1-0.2% MWCNTs. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. TStat and SI are the non-dimensional measures that capture uncertainty levels in the step of prediction. This can be due to the difference in the number of input parameters. Karahan et al.58 implemented ANN with the LevenbergMarquardt variant as the backpropagation learning algorithm and reported that ANN predicted the CS of SFRC accurately (R2=0.96). As can be seen in Fig. Golafshani, E. M., Behnood, A. Invalid Email Address. For instance, numerous studies1,2,3,7,16,17 have been conducted for predicting the mechanical properties of normal concrete (NC). Comparison of various machine learning algorithms used for compressive strength prediction of steel fiber-reinforced concrete, $$R_{XY} = \frac{{COV_{XY} }}{{\sigma_{X} \sigma_{Y} }}$$, $$x_{norm} = \frac{{x - x_{\min } }}{{x_{\max } - x_{\min } }}$$, $$\hat{y} = \alpha_{0} + \alpha_{1} x_{1} + \alpha_{2} x_{2} + \cdots + \alpha_{n} x_{n}$$, \(y = \left\langle {\alpha ,x} \right\rangle + \beta\), $$net_{j} = \sum\limits_{i = 1}^{n} {w_{ij} } x_{i} + b$$, https://doi.org/10.1038/s41598-023-30606-y. Flexural strength is however much more dependant on the type and shape of the aggregates used. Ly, H.-B., Nguyen, T.-A. It means that all ML models have been able to predict the effect of the fly-ash on the CS of SFRC. Gler, K., zbeyaz, A., Gymen, S. & Gnaydn, O. Compressive Strength to Flexural Strength Conversion, Grading of Aggregates in Concrete Analysis, Compressive Strength of Concrete Calculator, Modulus of Elasticity of Concrete Formula Calculator, Rigid Pavement Design xls Suite - Full Suite of Concrete Pavement Design Spreadsheets. Build. 12, the W/C ratio is the parameter that intensively affects the predicted CS. American Concrete Pavement Association, its Officers, Board of Directors and Staff are absolved of any responsibility for any decisions made as a result of your use. Li et al.54 noted that the CS of SFRC increased with increasing amounts of C and silica fume, and decreased with increasing amounts of water and SP. Today Proc. Build. Gupta, S. Support vector machines based modelling of concrete strength. Build. Accordingly, 176 sets of data are collected from different journals and conference papers. The primary rationale for using an SVR is that the problem may not be separable linearly. Adding hooked industrial steel fibers (ISF) to concrete boosts its tensile and flexural strength. In contrast, KNN shows the worst performance among developed ML models in predicting the CS of SFRC. [1] ; Compressive Strength - UHPC's advanced compressive strength is particularly significant when . Then, nine well received ML algorithms are developed on the data and different metrics were used to evaluate the performance of these algorithms. Ray ID: 7a2c96f4c9852428 (2) as follows: In some studies34,35,36,37, several metrics were used to sufficiently evaluate the performed models and compare their robustness. 12. This is particularly common in the design and specification of concrete pavements where flexural strengths are critical while compressive strengths are often specified. Cite this article. Constr. The current 4th edition of TR 34 includes the same method of correlation as BS EN 1992. Struct. & Farasatpour, M. Steel fiber reinforced concrete: A review (2011). Answer (1 of 5): For design of the beams we need flexuralstrength which is obtained from the characteristic strength by the formula Fcr=0.7FckFcr=0.7Fck Fck - is the characteristic strength Characteristic strength is found by applying compressive stress on concrete cubes after 28 days of cur. However, it is worth noting that their performance in predicting the CS of SFRC was superior to that of KNN and MLR. Equation(1) is the covariance between two variables (\(COV_{XY}\)) divided by their standard deviations (\(\sigma_{X}\), \(\sigma_{Y}\)). More specifically, numerous studies have been conducted to predict the properties of concrete1,2,3,4,5,6,7. RF consists of many parallel decision trees and calculates the average of fitted models on different subsets of the dataset to enhance the prediction accuracy6. The performance of the XGB algorithm is also reasonable by resulting in a value of R=0.867 for correlation. A., Hassan, R. F. & Hussein, H. H. Effects of coarse aggregate maximum size on synthetic/steel fiber reinforced concrete performance with different fiber parameters. 183, 283299 (2018). Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Materials 13(5), 1072 (2020). The CivilWeb Compressive Strength to Flexural Conversion worksheet is included in the CivilWeb Flexural Strength spreadsheet suite. Dubai, UAE Phys. Whereas, Koya et al.39 and Li et al.54 reported that SVR showed a high difference between experimental and anticipated values in predicting the CS of NC. Int. Caution should always be exercised when using general correlations such as these for design work. Adv. Constr. and JavaScript. If there is a lower fluctuation in the residual error and the residual errors fluctuate around zero, the model will perform better. Eng. Build. The main focus of this study is the development of a sustainable geomaterial composite with higher strength capabilities (compressive and flexural). Compos. Khademi et al.51 used MLR to predict the CS of NC and found that it cannot be considered an accurate model (with R2=0.518). Therefore, these results may have deficiencies. Build. The authors declare no competing interests. Effects of steel fiber content and type on static mechanical properties of UHPCC. 2, it is obvious that the CS increased with increasing the SP (R=0.792) followed by fly ash (R=0.688) and C (R=0.501). Olivito, R. & Zuccarello, F. An experimental study on the tensile strength of steel fiber reinforced concrete. World Acad. fck = Characteristic Concrete Compressive Strength (Cylinder). As there is a correlation between the compressive and flexural strength of concrete and a correlation between compressive strength and the modulus of elasticity of the concrete, there must also be a reasonably accurate correlation between flexural strength and elasticity. Limit the search results from the specified source. Your IP: 103.74.122.237, Requested URL: www.concreteconstruction.net/how-to/correlating-compressive-and-flexural-strength_o, User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.0.0 Safari/537.36. Importance of flexural strength of . Intell. Eventually, among all developed ML algorithms, CNN (with R2=0.928, RMSE=5.043, MAE=3.833) demonstrated superior performance in predicting the CS of SFRC. Eng. For materials that deform significantly but do not break, the load at yield, typically measured at 5% deformation/strain of the outer surface, is reported as the flexural strength or flexural yield strength. 49, 554563 (2013). 1.1 This test method provides guidelines for testing the flexural strength of cured geosynthetic cementitious composite mat (GCCM) products in a three (3)-point bend apparatus. Compressive strength prediction of recycled concrete based on deep learning. (3): where \(\hat{y}\), \(x_{n}\), and \(\alpha\) are the dependent parameter, independent parameter, and bias, respectively18. Various orders of marked and unmarked errors in predictions are demonstrated by MSE, RMSE, MAE, and MBE6. In comparison to the other discussed methods, CNN was able to accurately predict the CS of SFRC with a significantly reduced dispersion degree in the figures displaying the relationship between actual and expected CS of SFRC. It's hard to think of a single factor that adds to the strength of concrete. These cross-sectional forms included V-stiffeners in the web compression zone at 1/3 height near the compressed flange and no V-stiffeners on the flange . SI is a standard error measurement, whose smaller values indicate superior model performance. 7). These equations are shown below. Build. Where as, Flexural strength is the behaviour of a structure in direct bending (like in beams, slabs, etc.) Distributions of errors in MPa (Actual CSPredicted CS) for several methods. New Approaches Civ. ACI members have itthey are engaged, informed, and stay up to date by taking advantage of benefits that ACI membership provides them. (b) Lay the specimen on its side as a beam with the faces of the units uppermost, and support the beam symmetrically on two straight steel bars placed so as to provide bearing under the centre of . Therefore, based on MLR performance in the prediction CS of SFRC and consistency with previous studies (in using the MLR to predict the CS of NC, HPC, and SFRC), it was suggested that, due to the complexity of the correlation between the CS and concrete mix properties, linear models (such as MLR) could not explain the complicated relationship among independent variables. Flexural strength is measured by using concrete beams. In contrast, the splitting tensile strength was decreased by only 26%, as illustrated in Figure 3C. Mech. 45(4), 609622 (2012). You do not have access to www.concreteconstruction.net. The raw data is also available from the corresponding author on reasonable request. This algorithm first calculates K neighbors euclidean distance. Among these tree-based models, AdaBoost (with R2=0.888, RMSE=6.29, MAE=4.433) and XGB (with R2=0.901, RMSE=5.929, MAE=4.288) were the weakest and strongest models in predicting the CS of SFRC, respectively. fck = Characteristic Concrete Compressive Strength (Cylinder) h = Depth of Slab October 18, 2022. In this regard, developing the data-driven models to predict the CS of SFRC is a comparatively novel approach. Mater. Concr. https://doi.org/10.1038/s41598-023-30606-y, DOI: https://doi.org/10.1038/s41598-023-30606-y. Flexural test evaluates the tensile strength of concrete indirectly. All these results are consistent with the outcomes from sensitivity analysis, which is presented in Fig. de Montaignac, R., Massicotte, B., Charron, J.-P. & Nour, A. Investigation of mechanical characteristics and specimen size effect of steel fibers reinforced concrete. Mahesh et al.19 used ML algorithms on a 140-raw dataset considering 8 different features (LISF, VISF, and L/DISF as the fiber properties) and concluded that the artificial neural network (ANN) had the best performance in predicting the CS of SFRC with a regression coefficient of 0.97. The primary sensitivity analysis is conducted to determine the most important features. (4). J. 12, the SP has a medium impact on the predicted CS of SFRC. Schapire, R. E. Explaining adaboost. PubMed Central Sci. Some of the mixes were eliminated due to comprising recycled steel fibers or the other types of ISFs (such as smooth and wavy). Constr. J Civ Eng 5(2), 1623 (2015). To avoid overfitting, the dataset was split into train and test sets, with 80% of the data used for training the model and 20% for testing. Step 1: Estimate the "s" using s = 9 percent of the flexural strength; or, call several ready mix operators to determine the value. Compressive strength estimation of steel-fiber-reinforced concrete and raw material interactions using advanced algorithms. Therefore, based on tree-based technique outcomes in predicting the CS of SFRC and compatibility with previous studies in using tree-based models for predicting the CS of various concrete types (SFRC and NC), it was concluded that tree-based models (especially XGB) showed good performance. Moreover, the ReLU was used as the activation function for each convolutional layer and the Adam function was employed as an optimizer. Zhu et al.13 noticed a linearly increase of CS by increasing VISF from 0 to 2.0%.

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