Determination of shear strength of steel fiber RC beams: application of data-intelligence models

Abstract

Accurate prediction of shear strength of structural engineering components can yield a magnificent information modeling and predesign process. This paper aims to determine the shear strength of steel fiber reinforced concrete beams using the application of data-intelligence models namely hybrid artificial neural network integrated with particle swarm optimization. For the considered data-intelligence models, the input matrix attribute is one of the central element in attaining accurate predictive model. Hence, various input attributes are constructed to model the shear strength “as a targeted variable”. The modeling is initiated using historical published researches steel fiber reinforced concrete beams information. Seven variables are used as input attribute combination including reinforcement ratio (\rho \mathrm{\%}), concrete compressive strength ({{\displaystyle f}}_c^{\text{'}}), fiber factor ({{\displaystyle F}}_{\mathrm{1}}), volume percentage of fiber ({{\displaystyle V}}_f), fiber length to diameter ratio ({\displaystyle {{\displaystyle l}}_f{{\displaystyle l}}_d}) effective depth (d), and shear span-to-strength ratio ({\displaystyle ad}), while the shear strength ({{\displaystyle S}}_s) is the output of the matrix. The best network structure obtained using the network having ten nodes and one hidden layer. The final results obtained indicated that the hybrid predictive model of ANN-PSO can be used efficiently in the prediction of the shear strength of fiber reinforced concrete beams. In more representable details, the hybrid model attained the values of root mean square error and correlation coefficient 0.567 and 0.82, respectively.

Keywords

hybrid intelligence model / shear strength / prediction / steel fiber reinforced concrete

Introduction

Fiber reinforced concrete (FRC) is concrete that is reinforced with fibers that are randomly distributed [¹]. Small fibers are dispersed in FRC and then randomly distributed in the concrete to improve its properties in every direction. Steel fibers help to convert concrete from its brittle characteristics to that of a ductile one. Fibers thus serve the role of resisting cracks from being formed in the concrete by providing pinching forces at the tips of the crack [²,³]. This makes the shear strength of fiber steel concrete to be increased to its maximum limit. The typical presentation of steel fiber reinforced concrete beam is explained in Fig. 1.

It is evident that the use of fibers in concrete alters the properties of the concrete. Some of the essential properties affected by the use of fibers in concrete include the shear strength, shrinkage, creep, tensile strength among others [⁴–⁶]. There are various methods, destructive and non-destructive, that can be used in the determination of the stated properties of concrete. This research paper focuses on the determination of the shear strength of steel fiber reinforced concrete without using stirrups. The advancement of technology has enable the use of artificial intelligence to determine the various properties of steel fiber reinforced concrete including the shear strength. Various novel artificial intelligence techniques have been invented for determining the shear strength of reinforced concrete.

The implementation of soft computing (SC) approaches in the fields of engineering and sciences had received much attention in the last two decades by the scholars [⁷–¹¹]. Within the scopes of structural and material engineering, there are several types of SC used in the determination various aspects [¹²–¹⁶]. Shear strength of steel fiber reinforced concrete is one of the essential component in structural engineering design that computed manually using multiple empirical formulation [¹⁷,¹⁸]. In this paper, the motivation is to use modern data-intelligence model to predict shear strength. A hybrid ANN-PSO is developed for this purpose. Artificial neural networks (ANNs) are systems of computation whose inspiration springs from the biological neural networks [¹⁹]. Such systems learn to perform activities through the consideration of examples based on artificial neurons collected together. Each of the collections can transmit signals between the neurons. The neuron at the recipient end then processes the signal and then it signals the connected neurons at its downstream [²⁰]. The organization of the neurons is normally in layers, so that signals can travel from the input layer to that of the output layer after passing through all the hidden layers. Particle swarm optimization (PSO) is an optimization approach is used to optimize a problem through improvement of its candidate solutions [²¹]. The application of the hybrid ANN-PSO model showed impressive predictability in various engineering problems [²²–²⁹]. The layers in ANN are the input layer, hidden layer and the outer layer. When data is presented to the neural network, it targets the input and the output layers. The weights are then regulated in the hidden layer to obtain a pattern for achieving the target values from the input data. The trend is known as training the network in order to predict the target values. When the number of data and input variables is less, the result is a better training for the network, thus leading to more reliable weights obtained and a more accurate prediction of the network.

The main objective of the current study is to apply relatively new model to scope of structural engineering to predict one of the essential element in the design concept which is shear strength. The paper structured as follow Section 2 explained the methodology and experimental data set. Section 3 identified the application and analysis of the modeling. Whereas, the final section presented the conclusion of the research.

Methods and materials

The hybrid ANN-PSO model

In this research, the hybrid ANN-PSO is proposed to predict the shear strength of SFRC beam. Seven inputs attributes combinations including the physical characteristics and the concrete properties are used to construct the predictive model. The neural network consists of middle layer as its hidden layer was considered. There were ten neurons located in this hidden layer. Figure 2 illustrated the graphical presentation of the data-intelligence model developed for this current application. In order to achieve transfer function, purelin and tangent sigmoid are used for the output layer and the hidden layer, respectively. Before the model was trained, normalization of the database was performed using Eq. (1):

(1){{\displaystyle x}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}=\mathrm{2}*{\displaystyle \frac{{{\displaystyle x}}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}}-{{\displaystyle x}}_{\min }}{{{\displaystyle x}}_{\max }-{{\displaystyle x}}_{\min }}}-\mathrm{1}

In Eq. (1), {{\displaystyle x}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}} represents the normalized value of the parameter in question, while {{\displaystyle x}}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}} represent the experimental value. The minimum and the maximum values are represented by {{\displaystyle x}}_{\min } and {{\displaystyle x}}_{\max } respectively for this parameter. After studying the existing researches and their relations with the regulations which are certified, the determined input parameters were selected to be effective in conducting analysis on steel fiber reinforced concrete beam. Figure 3 shows the PSO graph obtained for this network during training.

The graph in Fig. 3 starts with high values as it decreases to lower values. This indicates that there was a success in the learning process of the ANN. The beginning of the learning process shows a large learning error, but as the learning continued and the weights used where changed, the amount of error reached 0.005, 0.1, and 0.09 in the 31^st step for training, test and validation, respectively. The reduction of the gradient is presented in Fig. 4. This figure shows the network procedure of learning. This gradient reduction continues until the values of PSO reached the minimum. At this minimum point, the values of the gradient become constant, thus learning stops. The proposed hybrid predictive model had a very small error. The PSO algorithm was used as the optimized algorithm for modeling and successfully implemented.

Experimental data

In order to train the neural network, a historical experimental information was gather from the published researches [³⁰–⁴²]. The total experimental records are 85, 80% of the total records used to train the predictive neural network model while the remaining 20% using to conduct the testing phase of this data. The creation of ANN was based on seven inputs such as reinforcement ratio (\rho \%), concrete compressive strength ({{\displaystyle f}}_c^{\text{'}}), fiber factor ({{\displaystyle F}}_{\mathrm{1}}), volume percentage of fiber ({{\displaystyle V}}_f), fiber length to diameter ratio ({\displaystyle \frac{{{\displaystyle l}}_f}{{{\displaystyle l}}_d}}) effective depth (d), and shear span-to-strength ratio ({\displaystyle \frac{a}{d}}). The shear strength {{\displaystyle S}}_s was considered as the output in this study.

Application, analysis and discussion

The motivation of the current research is to investigate new hybrid data-intelligence model for shear strength of steel fiber reinforced concrete beam. As a primary inspection of the partiality between each input attribute and the targeted shear strength, the visualization of the relationship between all predictors and predictand are plotted in Fig. 5. Based on the presented information, it is observed that the reinforcement ratio, concrete compressive strength, fiber factor, and fiber length to diameter ratio had a highly distributed and random influence on the magnitude of the {{\displaystyle S}}_s. On the other hand, the other three attributes demonstrated at similar value of each input combination remarkable variance. Based on this graphical exhibition, the investigated problem is highly stochastic, random and non-linear regression problem that emphasis the potential of soft computing to be undertaken.

The modeling accuracy between the applied hybrid data-intelligence model and the experimental records analyzed using the relative error (RE%) distribution metric (see Fig. 6). This metric is magnificent in examining the error percentage at each particular experimental record. It can be observed that in general the RE% is limited between negative and positive 20% for more than 70% of the total validated data records. However, there are a couple record exceeded the positive 35% (over predicted). This is can be identified by the nonlinearity of these records is highly complicated in which the network could not achieve high level of learning. Over all, the figure showed good attained results in term of modeling using the applied hybrid model.

Another representable demonstration for machine learning models’ evaluation is the scatter plot variation between the actual and predicted values. The comparison carried out between the network results and the experimental results of the literature. Figure 7 showed these experimental results against the ANN-PSO model. The curve in the figure indicates proper prediction of the model corresponding to the 45-degree fit-line. Most of the network prediction points fall within the neighborhood of 45-degree line indicating the accuracy of the network with correlation coefficient magnitude 0.82. Finally, Figure 8 illustrated the testing phase of the conducted hybrid model as a time series of actual experiment and predicted values. The figure explained a very acceptable match between these two time series.

Numerically, the developed predictive model evaluated using several statistical indicators including scatter index (SI), mean absolute percentage error (MAPE), root mean square error (RMSE), mean absolute errors (MAE), and correlation coefficient (R²) (Table 1). The modeling performed its minimum magnitude of absolute error values and maximum correlation values in acceptable range.

Over all, the current study exhibited a convincing attempt of modeling structural engineering problem using the hybrid soft computing model. Indeed, it is a milestone new era of research trend that fulfilled into side step the conventional manual determination of engineering design.

Conclusions and remarks

In this research, hybrid artificial neural network integrated with particle swarm optimization (ANN-PSO) had been developed for predicting shear strength of steel fiber reinforced concrete beam without stirrups. There are seven inputs in the proposed model and one hidden layer having ten neurons. The biases values and the network on the experimental data together with the final network that has been proposed were tested. Using the technical data existing, the results of the 85 reinforced concrete shear strength beams for steel fiber is given. After training the neuron and validating the network outputs, the existing data were then simulated, thus resulting in high accurate outputs, thereby proving the ability of the trained neural network used in estimating the shear strength for steel fiber reinforced concrete beams. The maximum correlation obtained between the network output data and the experimental results was 0.82. On the other hand, the minimum value of RMSE was achieved 0.567. The hybrid ANN-PSO provide an excellent implementation at its best accuracy in shear strength predictions. As further step for future research, an investigation to approximate the input attributes of the modeling is still to be endeavored. Also, investigating other evolutionary optimization method to tune the SC predictive model is extensively enthused the scholars to explore.

References

[1] Zollo R F. Fiber-reinforced concrete: an overview after 30 years of development. Cement and Concrete Composites, 1997, 19(2): 107–122

[2] Park K, Paulino G H, Roesler J. Cohesive fracture model for functionally graded fiber reinforced concrete. Cement and Concrete Research, 2010, 40(6): 956–965

[3] Park S H, Kim D J, Ryu G S, Koh K T. Tensile behavior of ultra high performance hybrid fiber reinforced concrete. Cement and Concrete Composites, 2012, 34(2): 172–184

[4] Graybeal B A. Compressive behavior of ultra-high-performance fiber-reinforced concrete. ACI Materials Journal, 2007, 104(2): 146–152

[5] Pantelides C P, Garfield T T, Richins W D, Larson T K, Blakeley J E. Reinforced concrete and fiber reinforced concrete panels subjected to blast detonations and post-blast static tests. Engineering Structures, 2014, 76: 24–33

[6] Wang H, Belarbi A. Ductility characteristics of fiber-reinforced-concrete beams reinforced with FRP rebars. Construction & Building Materials, 2011, 25(5): 2391–2401

[7] Brewka G. Artificial intelligence—a modern approach by Stuart Russell and Peter Norvig, Prentice Hall. Series in Artificial Intelligence, Englewood Cliffs, NJ. Knowledge Engineering Review, 1996, 11(1): 78

[8] Lu P, Chen S, Zheng Y. Artificial intelligence in civil engineering. Mathematical Problems in Engineering, 2012, 2012: 1–22

[9] Rzevski G. Artificial intelligence in engineering: past, present and future. Artificial Intelligence in Engineering, 1995, X(July): 1–14

[10] Brunette E S, Flemmer R C, Flemmer C L. A review of artificial intelligence. ICARA 2009- Proceedings of the 4th International Conference on Autonomous Robots and Agents, 2009, 385–392

[11] Pao Y H. Engineering artificial intelligence. Engineering Applications of Artificial Intelligence, 1988, 1(1): 5–10

[12] El-Sayed A, El-Salakawy E, Benmokrane B. Shear strength of one-way concrete slabs reinforced with fiber-reinforced polymer composite bars. Journal of Composites for Construction, 2005, 9(2): 147–157

[13] Ince R. Prediction of fracture parameters of concrete by artificial neural networks. Engineering Fracture Mechanics, 2004, 71(15): 2143–2159

[14] Oreta A W C, Kawashima K. Neural network modeling of confined compressive strength and strain of circular concrete columns. Journal of Structural Engineering, 2003, 129(4): 554–561

[15] Khademi F, Akbari M, Jamal S M, Nikoo M. Multiple linear regression, artificial neural network, and fuzzy logic prediction of 28 days compressive strength of concrete. Frontiers of Structural and Civil Engineering, 2017, 11(1): 90–99

[16] Vu-Bac N, Duong T X, Lahmer T, Zhuang X, Sauer R A, Park H S, Rabczuk T. A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures. Computer Methods in Applied Mechanics and Engineering, 2018, 331: 427–455

[17] González-Fonteboa B, Martínez-Abella F. Shear strength of recycled concrete beams. Construction & Building Materials, 2007, 21(4): 887–893

[18] Kahn L F, Mitchell A D. Shear friction tests with high-strength concrete. ACI Structural Journal, 2002, 99(1): 98–103

[19] Yaseen Z M, El-Shafie A, Afan H A, Hameed M, Mohtar W H M W, Hussain A. RBFNN versus FFNN for daily river flow forecasting at Johor River, Malaysia. Neural Computing & Applications, 2015, doi: 10.1007/s00521-015-1952-6

[20] Lee J, Almond D, Harris B. The use of neural networks for the prediction of fatigue lives of composite materials. Composites. Part A, Applied Science and Manufacturing, 1999, 30(10): 1159–1169

[21] Premalatha K, Natarajan A M. Hybrid PSO and GA for global maximization. Int J Open Problems Compt Math, 2009, 2(4): 597–608

[22] Hoballah A, Erlich I. PSO-ANN approach for transient stability constrained economic power generation. 2009 IEEE Bucharest PowerTech: Innovative Ideas Toward the Electrical Grid of the Future, 2009

[23] Zhao H S, Jin L, Huang X Y. A prediction of the monthly precipitation model based on PSO-ANN and its applications. 3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice, 2010, 476–479

[24] Yi D, Ge X. An improved PSO-based ANN with simulated annealing technique. Neurocomputing, 2005, 63: 527–533

[25] Abdullah A G, Suranegara G M, Hakim D L. Hybrid PSO-ANN application for improved accuracy of short term Load Forecasting. WSEAS Transactions on Power Systems, 2014, 9: 446–451

[26] Hasanipanah M, Noorian-Bidgoli M, Jahed Armaghani D, Khamesi H. Feasibility of PSO-ANN model for predicting surface settlement caused by tunneling. Engineering with Computers, 2016, 32(4): 705–715

[27] Rukhaiyar S, Alam M N, Samadhiya N K. A PSO-ANN hybrid model for predicting factor of safety of slope. International Journal of Geotechnical Engineering, 2017, doi: 10.1080/19386362.2017.1305652

[28] Li J, Wang J. Research of steel plate temperature prediction based on the improved PSO-ANN algorithm for roller hearth normalizing furnace. Proceedings of the World Congress on Intelligent Control and Automation (WCICA), 2010, 2464–2469

[29] Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31

[30] Li V C, Ward R, Hamza A M. Steel and synthetic fibers as shear reinforcement. ACI Materials Journal, 1992, 89(5): 499–508

[31] Mansur M A, Ong K C G, Paramasivam P. Shear strength of fibrous concrete beams without stirrups. Journal of Structural Engineering, 1986, 112(9): 2066–2079

[32] Tan K H, Murugappan K, Paramasivam P. Shear behavior of steel fiber reinforced concrete beams. ACI Structural Journal, 1993, 90(1): 155–160

[33] Narayanan R, Darwish I Y S. Use of steel fibers as shear reinforcement. ACI Structural Journal, 1987, 84(3): 216–227

[34] Ashour S A, Hasanain G S, Wafa F F. Shear behavior of high-strength fiber reinforced concrete beams. ACI Structural Journal, 1992, 89(2): 176–184

[35] Swamy R N, Jones R, Chiam A T P. Influence of steel fibers on the shear resistance of lightweight concrete I- beams. ACI Structural Journal, 1993, 90(1): 103–114

[36] Narayanan R, Darwish I Y S. Fiber concrete deep beams in shear. ACI Structural Journal, 1988, 85(2): 141–149

[37] Sanad A, Saka M P. Prediction of ultimate shear strength of reinforced concrete deep beams using neuronal networks. Journal of Structural Engineering, 2001, 127(7): 818–828

[38] Adebar P, Mindess S, St.-Pierre D, Olund B. Shear tests of fiber concrete beams without stirrups. ACI Structural Journal, 1997, 94(1): 68–76

[39] Vu-Bac N, Lahmer T, Keitel H, Zhao J, Zhuang X, Rabczuk T. Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations. Mechanics of Materials, 2014a, 68: 70–84

[40] Vu-Bac N, Lahmer T, Zhang Y, Zhuang X, Rabczuk T. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites Part B: Engineering, 2014b, 59: 80–95

[41] Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015a, 96: 520–535

[42] Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015b, 68: 446–464

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature