Shear transfer strength estimation of concrete elements using generalized artificial neural network models

1 Introduction

“Neural networks” is a highly masculine term. It implies that robots resemble brains and may be burdened with the science fiction semantics of the Frankenstein mythos [1]. The origins of neural networks may be traced back to the early 1940s. It became more popular in the late 1980s. This was due to the discovery of new methodologies and breakthroughs, as well as general advancements in computer hardware technology. The human brain is believed to be made up of 1,011 (100 billion) nerve cells or neurons, with a highly stylized example illustrated in Figure 1. Cross-electrical signals, which are short-lived impulses or “mutations” in the voltage of the cell’s or membrane’s wall, allow neurons to communicate. Electrochemical crossings known as synapses, which are situated on cell branches known as dendrites, mediate interneuron interactions. Each neuron frequently receives hundreds of connections from nearby neurons, resulting in a constant barrage of incoming messages that finally reach the cell body. They are integrated in some way here, and if the resultant signal exceeds a certain threshold, the neuron will “fire” or generate a voltage impulse. This is then sent to nearby neurons through an axon, which is a branching fiber [2].

Figure 1

Essential components of a neuron shown in stylized form [2].

Zhang et al. in 2020 [3] adopted a comparison valuation offer of the suggested support vector regression-genetic algorithm (SVR-GA) model, which clearly demonstrates better competency in predicting the shearing strength capacity of simply supported deep beams. The SVR-GA model’s generated findings are remarkably similar to the actual results. In terms of qualitative findings, the coefficient of correlation of results “R ²” during the testing phase was 0.95, whereas other equivalent models obtained correlation values ranging from 0.884 to 0.941.

Bai et al. in 2003 [4] estimated that artificial neural networks (ANNs) model the workability of concrete with the replacement of cement materials. ANN has been approved to become more precise in forecasting the nominal strength of the shear of reinforced concrete (RC) specimens. Cladera and Marí in 2004 [5] modeled proposed equations for regular concrete strength and concrete with high-strength specimens based on the observed behavior. Abdalla et al. in 2007 [6] used ANN to forecast and estimate the shear strength of RC beams utilizing the normalized shear concrete strength, concrete compressive strength, secondary and longitudinal reinforcements, depth and breadth of the beam’s section, and the ratio of the shear span-to-depth (a/d) parameters. The effectively studied terms aid in limiting the parameter list and guiding further research. In addition, this research developed an ANN model based on backpropagation procedures with multiple functions of transfer and modeled nominal shear strength behavior on surfaces and curvatures. Though fast backpropagation engaging changed the descent, it is likely to become trapped in local optima and is hence unsuitable for projecting the best-performing model. Arslan composed 76 tested experimental outcomes founded in the previous literature to predict the torsional strength of reinforced concrete beams and created them using ANN proposed models on the concrete’s compressive strength, the cross-section area of members, the ratio of steel longitudinal reinforcements and secondary reinforcement (stirrups), the dimensions of the closed stirrup that are used, the magnitude of reinforcing yield strengths, stirrup spacing, and the cross-sectional area for one leg of the closed stirrups. This study showed that ANN models estimate the torsional concrete strength of beams more accurately than protocol equations that were formulated by Arslan [7]. Oreta in 2004 [8] designed a model using the ANN-designed models to assess the influence of magnitude on the ultimate capacity of shear for reinforced concrete beams with or without steel stirrups of reinforcement. This scholar created an effective ANN model using five-input variables and determined that the ANN model outperformed the current proposed equation. Naderpour and Nagai [9] adopted an ANN model with seven-input variables to estimate the shear strength of RC joints. The model created a simulation with the present suggested formulas and examined the relative influence of input results on shear resistance using a regression analysis. The findings demonstrated that the reinforcement ratio is the most relevant parameter for the tensile resistance of RC joints, which may help guide future research in terms of simulation analysis. Mansour et al. [10] investigated the use of ANN to forecast the shear strength of RC beams. They examined the influence of concrete strength, longitudinal and transverse steel content, shear-span-to-effective-depth ratio, and beam size on expected shear strength values as specified by the American Concrete Institute (ACI) and Canadian Standards Association specification codes. Cladera and Mari [11] used ANN models in stirrup-equipped beams for the shear design of regular and high-grade steel-reinforced concrete beams. Proposed computational neural network models have been shown to be a powerful tool for guessing the ultimate shear capacity of steel-reinforced concrete specimens (beam samples). Moreover, blind fitting to the data is avoided by means of a parametrical study. Armoosh et al. in 2015 [12] used a finite element model for simulating the shear of lean duplex steel beams. Kim and Kim in 2008 [13] used an ANN model to forecast the relative crest settling of concrete-faced rock-fill dams. Caglar et al. in 2008 [14] used a neural network to analyze the dynamic behavior of reinforced concrete structures. The results obtained by the ANN model were truly competent and showed good generalization. A careful study of the results leads to observations of excellent agreement between ANN predictions and finite element method outcomes. Amani and Moeini in 2012 [15] adopted an ANN model with a multilayer perceptron and a backpropagation procedure to estimate the shear strength of reinforced concrete beams. Erdem in 2010 [16] used ANN to predict the moment capacity of RC slabs under fire. Within the range of input parameters evaluated, the ANN model predicts the ultimate moment capacity of RC slabs in fire with a high degree of accuracy. The results of the ultimate moment capacity equation are consistent with the moment capacities predicted by ANN. Deifalla and Nermin in 2022 [17] suggested a model based on large neural networks that give a good accuracy and trustworthy depiction of the behavior. Effective depth has been the most important input parameter, followed by an fiber reinforced polymer reinforcement ratio and finally a strengthening scheme, with fiber orientation having the least influence on forecast output accuracy.

In this study, an ANN model is employed in intelligent data analysis to estimate the shear strength resistance of RC direct tests using a variety of relevant literatures. An experimental database was constructed in this work, and the impacts of numerous factors were explored. Furthermore, factors such as steel reinforcement ratio, fiber content and aspect ratios, and concrete compression strength were used to create neural network models. Furthermore, many models were developed, and their strengths were compared to those of the experimental database findings and the current design models. Finally, the significance of the various factors on strength was discovered and addressed. This research might help in the creation of design code.

2 Shear strength in concrete element

Reinforced concrete members with shorter span lengths, such as corbels, brackets, and ledger beams, may fail due to direct shear. Brittle failure may occur in high-strength concrete. Steel fibers prevent cracking, improve ductility, absorb energy, and increase tensile strength. Steel fibers were added to concrete to increase its tensile strength and fracture qualities. This modification resulted in the addition of ductility to an otherwise brittle material. The addition enhanced the strain capacity and conferred an improvement in ductility, commonly known as pseudo-ductility. For all aspect ratios, the ductility factor improved up to a steel fiber volume fraction of 0.5 percent [2]. As a result, steel fibers can be used as shear reinforcement to enhance ductility, minimize deformation, and raise the ultimate capacity of connections.

3 Modeling by ANN procedure

Even with its well-organized detail skills, neural networks with multilayers of feed-forward models are always the widely used systems. Figure 2 depicts a multilayer neural network using feed-forward modeling [18].

Figure 2

Flow-chart of the multilayered ANN model system studied [18].

This neural network system comprises feedback input data, hidden layer(s), and output results layer(s). These layers, known as nodes or neurons, are solely interconnected by arrows and contain a variety of processing units. Weights are input parameters that reflect neural strength parameters. Each neuron has a functionality that is proportionate to the amount of impact input received from other neurons through connected neurons. There are an optimal number of layers and neurons in each hidden layer. A trial-and-error approach should be employed to select an appropriate number of nodes in the concealed layer of neurons in each hidden layer, as used by [2,18].

Backpropagation is the most efficient method, and it is applied in this study. The output is produced by the buried neurons and is sent to the findings. In the initial hidden layer, each neuron is attached to the network, and each network output is linked to each neuron. The entire connection will be referred to as ANN in this situation. The original weight values were assigned to the stochastic process, as were the existing network input parameters. Eq. (1) is used to compute the neuron’s output [19]:

where F denotes the incentive function of the neurons (the function that takes any real value as input and outputs values in the range 0–1), W ij denotes the neuron weight of the model process, O i illustrates the neuron output, I j denotes the input of neurons networks, and b i denotes the estimated neuron's bias; the standard incentive role function of the hidden layer was hyperbolic tangential form.

The networking mistake is then transmitted to the input layer, where the output layer’s link parameters are changed. This method is used until the error is reduced to the appropriate level [19]. The efficiency error is determined using Eq. (2) and is represented as a mean squared error (MSE) as follows [19]:

where y _ij denotes the estimation progression of the output rate and t _ij is the target value.

4 Modeling using ANN of shear tests

The parameters gathered in the proposed ANN model and outcome results parameter for the output layer from (174) experimentally tested samples using the direct shear testing technique are shown in Table 1. The input parameters are illustrated in Table A1, which were collected from many related references [20–32]. Because high precision in these parameters is not required in this engineering problem, only one hidden layer was used [33,34,35], as shown in Figure 3. In variables, the standard has been chosen. About 30% of the partition has been designated for testing and 70% for training. In the incentive function, the hyperbolic identity procedure used the results of the hidden layer and the output layer with a modified standardized correction value of 0.05. Batches had been designated for the mode of training and are now available as an option.

Figure 3

The skeleton of the recent ANN model (from SPSSV.19 software).

After taking the weights from the program, as illustrated in Table 1, they have been multiplied by the input parameters, each with its own weight. The output parameter represented by x is evaluated as shown in Eq. (3) [19]:

where W _i is the weight of a hidden layer value and V _i is the value of the studied factors.

In addition, the parameters that were calculated in the proposed model are aspect ratio (L/D), fiber factor (F), volume fraction of fibers (V _f, %), bond factor (B _f) that accounts for the bond characteristics of the fibers, compressive concrete strength ( f ′ c , MPa), area of reinforced perpendicular to the shear plane (P _y F _y), and shear strength (Vu, kN).

The value of x is used to extract the output parameter (shear strength, Vu), as shown in Eq. (4):

where y represents the outcome magnitude (shear strength), θ ₂ illustrates the bias value of the outcome layer, w y is the coefficient of (H1:1) of the result parameter (i.e., mean of the shear strength), and the value of x represents the issued results from Eq. (3).

5 Results of the ANN model

The value of x in this research may be represented as in Eq. (5), it was employed as references [18,19]. To collect the independent parameters in term (X), Eq. (5) is predicated according to the nominal weights which are get from Table 1. Eq. (5) depends on six studied parameters.

Table 2 shows that the most important parameter in this study is the compressive strength, and the aspect ratio is of less effect. Figure 4 shows the normalized importance of the studied factors that are used in a recent ANN model. Furthermore, Figure 5 illustrates experimental and predicted simulated data from a recent ANN model for the testing inputs.

Table 2

Importance indictors of variables

	Importance percent	Normalized Importance (%)	Importance index
f c ′	0.356	100.0
P y F y	0.308	86.5
F	0.159	44.7
V f	0.102	28.7
B f	0.046	12.9
L/D	0.029	8.3

Figure 4

Normalized importance of recent ANN Model (from SPSSV.19 software).

Figure 5

Residuals of simulated data of recent ANN model (from SPSSV.19 software).

All of the simulated algorithms demonstrated a high degree of accuracy in their estimation. This study demonstrated the viability of using ANN models to estimate combined shear strength. The model’s skeleton is depicted in Figure 3. Eq. (6) expresses the outcome of the ANN design equation as follows:

where

for any above terms may be corrected by the following with maximum and minimum magnitudes that are shown in Table 4:

where β represents the value of limit, β min is the minimum limit from Table 4, and β max is the minimum limit from Table 4.

Therefore, the magnitude of ultimate shear strength can be predicted from Eqs. (6) and (7) using Eq. (9):

where y represents the predicted shear strength by the ANN model.

6 Results and discussions

Many parameters are adopted in this study. However, it is seen that the first important parameter is concrete compressive strength. Also, the, ρ _y f _y parameter has been a significant effect on the results of this model. While the lowered parameter is the aspect ratio of steel fibers on the prediction of shear transfer strength of concrete specimens.

The values of the mean absolute percentage of errors (MAPE) and the percentage of average accuracy (AA%) can be predicted by Eqs. (10) and (11), respectively, as follows:

where tor actual represents the accurate target (experimental) value and tor estimate is the estimated value of outcome shear strengths.

Table 3 shows the results of the regression analysis adopted using SPSS V.19 software. The results are illustrated by the coefficient of determination (R ²) and correlation coefficient (R). In addition, Table 4 shows the upper limit, lower limit, and ranges of values of the study’s input parameters. The correlation factor (R ²) is 83.12, indicating that there was a good connection within the input parameters; because the max differences of the results have been less than 20%. So, it can be represented as an acceptable value.

This relationship means that the model of ANN anticipated output may be obtained from experimental previous data having a reasonable degree of precision, as shown in Figure 6.

Figure 6

Comparison of shear force strength between experimental and predicted data.

7 Conclusions

This article shows how ANN can be used to estimate the shear capacity of reinforced concrete members using shear transfer direct tests. For this purpose, a database with 117 experimental results was compiled. Many outcomes can be summarized from this study:

1. The first important parameter is concrete’s compressive strength. Also, the overall tensile force magnitude, (ρ _y f _y ) parameter has been a significant effect on the results of this model. While the lowered parameter is the aspect ratio of steel fibers on the estimation of shear transfer strength of concrete members.

2. The correlation factor R ² is estimated to be about 83%, which means that it had a good correlation within the input parameters, and also, MAPE was 2.06.

3. Compared to conventional digital computing techniques Neural networks are advantageous because they can learn from examples and generalize solutions to new renderings of a problem, process information rapidly, and adapt to fine changes in the nature of the shear transfer strength of concrete.

4. Several empirical formulas were employed in concrete codes to compute the shear strength of RC beams. The models were used to forecast the shear resistance strength of RC beams. The most impacted characteristic in concrete shear strength may be described using a comprehensive design equation.

5. The comparative study conducted between the predicted values for the RC blocks concerning the ultimate response shows the results from the ANN are conservative and more accurate as compared to those obtained from the ACI Code.