Evaluating Shear Strength of Light-Weight and Normal-Weight Concretes through Artificial Intelligence

Abstract

The strength of concrete elements under shear is a complex phenomenon, which is induced by several effective variables and governing mechanisms. Thus, each parameter’s importance depends on the values of the effective parameters and the governing mechanism. In addition, the new concrete types, including lightweight concrete and fibered concrete, add to the complexity, which is why machine learning (ML) techniques are ideal to simulate this behavior due to their ability to handle fuzzy, inaccurate, and even incomplete data. Thus, this study aims to predict the shear strength of both normal-weight and light-weight concrete beams using three well-known machine learning approaches, namely evolutionary polynomial regression (EPR), artificial neural network (ANN) and genetic programming (GP). The methodology started with collecting a dataset of about 1700 shear test results and dividing it into training and testing subsets. Then, the three considered (ML) approaches were trained using the training subset to develop three predictive models. The prediction accuracy of each developed model was evaluated using the testing subset. Finally, the accuracies of the developed models were compared with the current international design codes (ACI, EC2 & JSCE) to evaluate the success of this research in terms of enhancing the prediction accuracy. The results showed that the prediction accuracies of the developed models were 68%, 83% & 76.5% for GP, ANN & EPR, respectively, and 56%, 40% & 62% for ACI, EC2 & JSCE, in that order. Hence, the results indicated that the accuracy of the worst (ML) model is better than those of design codes, and the ANN model is the most accurate one.

1. Introduction

Moving towards sustainable structures is the goal of all civilizations worldwide, which is being investigated by many researchers. Thus, many research studies seek to improve the current construction materials and develop new sustainable ones, particularly lightweight concrete [1,2,3,4,5,6,7]. The failure of concrete elements in shear is brittle, which could result in a catastrophic disaster. The shear resistance of concrete elements is composed of several mechanisms, including but not limited to the direct shear mechanism, arch mechanism, crack slippage mechanism and dowel resistance mechanism [8,9]. The importance and effectiveness of each mechanism are variable in the values of parameters for each element [8,9,10,11]. A closed form solution based on the mechanisms is extremely complicated, especially when shear is combined with other straining actions including torsion or axial tension. Thus, investigating the one-way and two-way shear strengths of concrete elements has been the subject of several research studies.

Many reinforced concrete (RC) elements support loads by flexure, shear and axial stresses [12,13,14,15,16,17]. The flexure and axial behaviors of RC elements are well established, while the shear behavior of RC elements is still far from reasonably established. Two types of shear cracks are web shear cracks initiated by shear forces and flexure ones initiated by bending moments. In addition, the effect of a/d on the strength and behavior was observed by several researchers as follows: (1) For a/d > 6 (very slender elements), the elements fail in flexure rather than shear, and (2) For 2.5 < a/d < 6 (slender elements), some of the flexural cracks grow and may become flexure-shear cracks. Therefore, a shear-tension failure diagonal may occur. Moreover, the effect of size was observed by many researchers. It can be concluded that the shear resistance depends on many parameters, including but not limited to the cross-section dimensions, the span length and the loading configuration, as well as the flexure reinforcement ratio and arrangements. In conclusion, the shear behavior is governed by several types of shear cracks and many effective parameters; therefore, it has been and continues to be a major area of investigation in RC structures. Lightweight concrete’s popularity has been increasing all over the world, which is due to it having significantly lower weight, better insulation and more ductility compared to normal-weight concrete. It is being used in several applications, including but not limited to high-rise buildings, additional floors of existing buildings, the retrofitting and repair of buildings and bridges as well as road constructions, especially at high altitudes of roads with less traffic. Despite lightweight concrete’s popularity, very little is known about the behavior of its elements, especially under shear. Most of the current lightweight concrete shear design provisions were developed back in the 1960s. Back in the ’60s, lightweight concrete was found to have lower shear resistance, which is due to lightweight concrete’s lower splitting and crack resistance through aggregate interlock compared to normal-weight concrete. In addition, there was a major advancement in the field of concrete manufacturing technology; thus, the performance of lightweight concrete was improved significantly. Moreover, the popularity of lightweight concrete is increasing; thus, updated shear design provisions are in need. Recently, the shear behavior of lightweight concrete elements was revisited, and several modifications were proposed for the shear design provisions of the AASHTO LRFD, which was implemented in the new ACI-19. Lightweight concrete’s performance is somewhat like normal-weight concrete; however, the basic properties of lightweight concrete are different, including but not limited to the resistance of concrete in tension, the flexure, the shear and the bond, as well as the modulus of elasticity. Thus, many researchers have investigated the behavior of lightweight concrete elements under shear, punching shear, flexure, torsion and axial loads, where the goal is to provide reliable design provisions for lightweight concrete. Most of the existing ones are developed and validated for normal-weight concrete with minor modifications. Deifalla and co-workers are working on a long-term project that aims to investigate the one-way and two-way shear as well as torsion of special concrete types including not limited to lightweight concrete, fiber reinforced polymer (FRP) reinforced concrete and steel fiber reinforced concrete. Deifalla and Mukhtar’s investigation of the shear resistance of lightweight concrete elements was found to require further discussion.

Making physical sense of the behavior of lightweight concrete elements under shear requires further digging due to its complexity at many levels. After the first onset of cracking, stress distribution becomes complex while being affected by a combination of several parameters and mechanisms. In the late ’90s, the ASCE-ACI Committee 445 reported significant shear transfer mechanisms as follows: (1) shear in the uncracked compression zone of the element; (2) shear in the cracking interface due to aggregate interlock as well as the surface roughness along inclined cracks; (3) dowel action of the longitudinal reinforcement; (4) residual tensile stresses across inclined cracks; and (5) arch mechanism.

Each of the shear mechanisms is different and influenced by many parameters. The compression zone mechanism occurs after the first onset of cracking. The compression zone contributes to shear resistance, which is significantly dependent on the depth of the zone. Thus, this mechanism’s contribution is relatively small for elements subjected to a relatively low ratio of bending moments to shear or those with relatively large depth. In addition, the interface shear across cracks mechanism, which occurs at the roughness along the cracking surfaces, provides resistance against slippage and thus contributes to the shear resistance, while the significance of the contribution is dependent on the crack width, aggregate size and aggregate type. Thus, in an element with a larger crack width, smaller aggregate size and weaker aggregate, this contribution is small because lightweight concrete undergoes relatively smooth crack plane compared to normal-weight concrete. Moreover, the dowel action mechanism, which occurs once cracks pass through concrete cover and reaches the flexure reinforcements, is significantly dependent on the concrete cover thickness and the shear reinforcement ratio. The contribution of this mechanism is significantly reduced for elements without shear reinforcements. Last but not least, regarding the residual tensile stresses mechanism, for crack widths of less than 0.06–0.16 mm, small concrete pieces bridging the concrete cracks contribute to shear resistance by the residual tensile stresses. Thus, for small crack widths (i.e., less than 0.06 mm), the contribution of this mechanism is significant. Finally, the arch action mechanism occurs when the arch action is a dominant shear transfer mechanism in the case of deep elements (i.e., a/d < 2.5), where the shear forces are transmitted directly to the supports via an inclined strut. Reliability and uncertainty analysis may be implemented in further research to improve the accuracy of the prediction [17].

Since the current methods for lightweight concrete elements under shear lack the consistency and accuracy needed for a reasonable design, many researchers have been directed toward machine learning models. Machine learning and artificial intelligence methods have been focused on the research of concrete element strength because of its capability to predict the actual behavioral trends in a sophisticated way [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. Thus, in this study, three artificial intelligence models were developed and validated for the shear strength of normal-weight and lightweight concrete elements. The importance of the considered parameters was investigated, the models were compared with the existing design codes and guidelines, and the concluded remarks were outlined.

2. Experimental Dataset

A total of 1710 elements (Appendix A) tested under vertical loading were collected and failed in shear. The dataset was a combination of several previous datasets [9,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65], where information was taken from the collected database or the original research study, depending on availability. For each element, the following parameters were considered:

• Specific gravity of concrete mix (G_s = γ_c/γ_w),
• Beam width (b) in meters,
• Beam depth (d) in meters,
• Concrete cylinder compressive strength at 28 days (fc’) in MPa,
• Shear span (a/d),
• Longitudinal reinforcement ratio of steel (ρ),
• Maximum nominal size of aggregates (da) in m,
• Ultimate shear capacity (V_u) kN.

The gathered elements were split into two sets of data. The first is the training set (1350 elements), and the second is the validation set (360 elements).

Table 1. Statistical measures of the dataset.

	Gs	B	d	fc’	a/d	ρ	da	Vu
	–	(m)	(m)	(MPa)	–	–	(m)	(kN)
The First Set for Training
Minimum	1.40	0.05	0.06	6.00	0.52	0.00	0.00	7.23
Maximum	2.40	1.00	1.89	194.00	9.05	0.07	0.05	299.12
Average	2.30	0.19	0.30	38.16	3.48	0.02	0.02	76.93
Standard Deviation	0.26	0.10	0.21	20.50	1.05	0.01	0.01	58.58
Coefficient of Variation	11%	53%	69%	54%	30%	53%	32%	76%
The Second Set for Validation
Minimum	1.40	0.05	0.06	12.90	1.00	0.00	0.00	7.79
Maximum	2.40	0.61	1.92	116.00	8.10	0.07	0.04	289.84
Average	2.28	0.18	0.31	38.58	3.53	0.02	0.02	78.11
Standard Deviation	0.28	0.08	0.22	16.85	1.14	0.01	0.00	59.24
Coefficient of Variation	12%	44%	73%	44%	32%	56%	29%	76%

and

Table 2. Matrix for Pearson Coefficient of Correlation.

	Gs	b	d	fc’	a/d	ρ	Da	Vu
Gs	1.00
B	0.12	1.00
D	0.16	0.35	1.00
fc’	0.09	0.09	0.00	1.00
a/d	0.15	−0.03	−0.04	−0.11	1.00
ρ	0.09	−0.18	−0.19	0.11	0.20	1.00
da	0.48	0.05	0.12	−0.09	0.15	0.02	1.00
Vu	0.17	0.71	0.71	0.21	−0.15	0.01	0.09	1.00

summarize their statistical measures and the Pearson correlation matrix between the variables and the strength. Figure 1 shows the histograms for the variables’ distribution.

3. Models’ Development

Artificial intelligence (AI) is a wide research title that includes many approaches and serves many applications. AI approaches could be classified into knowledge & logic approached, mathematical & statistical approaches and approaches based on mimicking biological systems/creatures. On the other hand, AI applications could be classified into optimization applications, regression applications, classification applications and decision-making applications. Figure 2 summarizes both AI approaches and applications and illustrates the most famous suitable techniques for each application. For regression applications (in the case of this research), GP, ANN and EPR are the most suitable techniques.

Genetic algorithm (GA) is a mathematical technique that simulates the evolution process of biological creatures. It depends on one simple rule: “The most fitting creature will survive”. To apply this principle to optimization, there must be a pool of solutions for the considered problem, a fitting criterion and a procedure to generate new solutions by mixing the existing ones. Biological creatures transfer their data to the next generation as an arranged series of genes called “chromosomes”, and similarly, GA presents the solution (chromosomes) as an arranged list of steps (genes). This allows GA to apply genetic operations (such as crossover & mutation) to the solutions. Crossover is a mixing procedure used to generate two new solutions from two existing ones by swapping the heads and tails of the two existing solutions. Mutation represents a random change in genetic data due to radiation, chemicals and copying errors. It is applied by randomly changing a step of the considered solution. The algorithm cycle begins with generating a set of random solutions for the considered problem (population), evaluating the fitness of each solution using the fitting criteria, selecting the best fitting solutions and deleting the rest and finally restoring the original population size by mixing the survival solutions (using crossover and mutation procedures) to generate new ones, and the cycle starts again. Cycle after cycle, the fitting of the solutions increases until the accepted level is reached [66].

Genetic programming (GP) is an application of the previously mentioned GA technique. It depends on using GA as a “multi-variable and structure free regression technique”, where the populations are a set of randomly generated mathematical formulas, and the fitting criteria is the “sum of squared errors (SSR)” between the predicted values and the correct values of the training dataset. In order to apply genetic operations, each solution (formula) must be presented in genetic form (as chromosomes) instead of the steps list of GA. The chromosome consists of two parts; the first is a list of mathematical operators (=, +, −, ×, /…), and the second one is a list of variables. Crossover and mutation procedures are applied on both formulas’ operators and variables separately to generate new formulas (solutions). Cycle after cycle, the SSE decreases, and the accuracy of the solutions (formulas) increases. Finally, the accuracy of the developed formula is tested using a new (validation) dataset [66].

Evolutionary polynomial regression (EPR) is another application of GA, and it depends on optimizing the number of terms of the “traditional polynomial regression (TPR)”. TPR is a well-known mathematical regression technique that uses the “least squared error” principle to find the optimum coefficient values of a certain polynomial function to fit a certain dataset. The considered polynomial may be a single or multi variables depending on the considered problem configuration (dataset). The chosen polynomial degree (its highest power) depends on the complexity of the considered problem. A first degree polynomial (linear) may be used for simple problems, but for more complicated ones, second degree (quadratic), third degree (cubic) or polynomials of higher degrees may be required. The number of polynomial terms dramatically increases with the variable numbers and polynomial degree; for example, a two-variable second degree polynomial has only six terms (X² + Y² + XY + X + Y + C), while a three-variable third degree polynomial has 20 terms, a four-variable fourth degree polynomial has 70 terms and so on. As the number of polynomial terms increases, it becomes more difficult to apply and less practical. Hence, the EPR technique aims to optimize the TPR by eliminating the less important terms and keeping only the most effective ones using GA technique. So, the population (solutions) consists of a set of polynomials, the fitting criteria is the “Sum of Squared Errors (SSE)”, the chromosome consists of a list of polynomial terms and the length of the chromosome is the chosen number of terms. Cycle after cycle, the most important terms accumulate in the survival chromosomes, and the less important ones are deleted [66].

Artificial neural network (ANN) is an umbrella term for a wide range of AI techniques that depend on mimicking the behavior of biological neurons. They all consist of nodes (cells or neurons) and links to connect the nodes, but they have different neuron arrangements and connection patterns. “multi-layer perceptron (MLP)” is one of the earliest ANN types. It is the most commonly used type for regression problems. It consists of several nodes arranged in layers. The first layer is called the “input layer”, and it is used to receive the input values, while the last layer is called the “output layer” and is used to deliver output values. Between the input and the output layers, there are several intermediate layers called “hidden layers”, which are responsible for predicting the outputs from the inputs. MLP must have at least one hidden layer. Each node in a certain layer is connected to all the nodes in the previous and the next layers by links, but the nodes of each layer are not connected to each other. Each link has an importance factor called “weight”, and each node has a triggering formula called “activation function”; this could be any nonlinear function, but the most popular ones are the sigmoid, the hyper-tan and the ramp functions, which are responsible of the nonlinear capability of the ANN. Due to the variation in ranges of input values, all inputs must be scaled to a unified range. This process is called “standardization” if the input variance is divided by its standard deviation (SD) and called “normalization” if the inputs are scaled between 0 and 1 and called “hyper normalization” if the inputs are scaled between −1 and 1. The scaled inputs propagate from the input layer to the output layer through the hidden layers. The output of a certain node is the result of applying its activation function on the summation the node inputs multiplied by the corresponding links’ weights. After the output layer, the outputs must be de-scaled to their original renege. Any ANN model must be trained using a given dataset; during the training process, the weight values of the model’s links are adjusted to predict the correct outputs from the inputs. There are many training techniques that could be used to find the optimum values for the links’ weights, such as “back propagation (BP)”, “gradually reduced gradient (GRG)” and “genetic algorithm (GA)”.

Three models were proposed based on three different artificial intelligence (AI) techniques. Models were trained and validated using the datasets presented in Table 1. The proposed model was used to predict the strength of the gathered database. These techniques are evolutionary polynomial regression (EPR), artificial neural network (ANN) and genetic programming (GP). In the development of the proposed models, the following parameters were considered: the specific gravity of concrete (Gs), beam width (b) m, beam depth (d) m, concrete compressive strength (fc’) MPa, shear span (a/d), longitudinal reinforcement ratio of steel (ρ) and maximum nominal size of aggregates (da) m. The sum of squared errors (SSE) was used to evaluate the accuracy of each of the proposed models, as shown in

Table 3. Accuracies of developed models versus current design codes.

Technique	SSE	Avg. Error %	R2
GP-model	1,050,431	32.1	0.80
ANN-model	295,776	17.0	0.95
EPR-model	562,609	23.5	0.90
ACI	1,997,503	44.3	0.83
EC2	3,652,703	59.9	0.84
JSCE	1,477,730	38.1	0.85

.

3.1. ANN Model

An ANN model was developed with one hidden the layer using the nonlinear activation function (hyper tan) and back propagation. Figure 3 shows the used networks’ layouts, and their connation weights are illustrated in

Table 4. ANN model developed weights matrix.

Input								Hidden	Output.
(Bias)	Gs	b	d	fc’	a/d	ρ	da		Vu
−0.48	−0.09	−0.01	−0.34	0.05	0.06	0.24	−0.02	H(1:1)	−2.22
−1.09	−0.13	1.13	−0.12	0.43	−0.86	−1.01	−0.06	H(1:2)	0.55
−0.92	1.46	−0.69	0.22	−0.87	−2.76	−0.13	−0.18	H(1:3)	1.29
−0.12	−0.84	−0.11	0.90	−0.79	0.53	−0.51	−0.21	H(1:4)	0.32
−0.45	2.44	0.40	0.34	0.79	2.74	0.07	0.13	H(1:5)	2.14
2.39	0.18	−0.53	−0.61	−0.38	1.03	−0.32	−0.21	H(1:6)	−0.59
0.83	−1.51	0.65	−0.31	0.76	3.08	0.02	0.45	H(1:7)	1.12
0.27	−0.06	0.17	−0.43	−0.24	0.08	−0.21	0.23	H(1:8)	0.90
−0.23	−0.10	0.02	−0.08	−0.01	0.13	0.36	−0.31	H(1:9)	2.04
0.25	−0.08	0.25	0.24	0.21	−0.19	0.22	0.14	H(1:10)	1.84
−3.64	−2.17	0.63	0.49	−0.06	−0.17	−0.54	0.74	H(1:11)	−0.55
−0.15	1.61	0.35	0.41	0.70	2.73	0.04	0.30	H(1:12)	−2.01
1.11	−1.37	−0.35	−0.76	0.79	0.06	−0.21	0.07	H(1:13)	0.38
−0.13	2.04	0.16	−0.27	0.48	−0.49	−1.35	1.46	H(1:14)	0.27
−0.96	0.34	0.74	−0.24	0.19	−0.36	−0.64	−0.15	H(1:15)	−0.93
								(Bias)	−2.00

. The average error % of the total dataset was 17.0%, and the R2 value was 0.95. The relative importance values for each input parameter are illustrated in Figure 4, which indicated that beam dimensions (b & d) are the most important factors, followed by the shear span (a/d), while other factors have a much lower effect.

3.2. GP Model

The GP model was developed using five levels of complexity. The number of populations, number of survivor and number of generations were 100,000, 25,000 and 200, respectively. The shear strength using the GP model is such that:

$$Vu=\sqrt{{fc}^{\prime }}+{\left[500 b \left(d+\sqrt{\rho }+0.164\right)\right]}^{{10}^{\rho }}$$

(1)

3.3. EPR Model

The EPR model was developed using a quadrilateral level for 7 inputs, and the expected terms totaled 330 (i.e., 210 + 84 + 28 + 7 + 1) as follows:

$${\displaystyle \sum }_{i=1}^{i=7}{\displaystyle \sum }_{j=1}^{j=7}{\displaystyle \sum }_{k=1}^{k=7}{\displaystyle \sum }_{l=1}^{l=7}{X}_i.X_j.X_k.X_l+{\displaystyle \sum }_{i=1}^{i=7}{\displaystyle \sum }_{j=1}^{j=7}{\displaystyle \sum }_{k=1}^{k=7}{X}_i.X_j.X_k+{\displaystyle \sum }_{i=1}^{i=7}{\displaystyle \sum }_{j=1}^{j=7}{X}_i.X_j+{\displaystyle \sum }_{i=1}^{i=7}{X}_i+C$$

(2)

Using the GA technique to optimize these 330 terms, only 24 of the most fitting terms were selected; thus, the shear strength for the EPR-model is such that:

$$\begin{array}{l}\mathrm{Vu}=\frac{\mathrm{d}\left(64 \mathsf{\rho }-24\mathrm{d}+6.8\right)-a\left(234\mathrm{b}.\mathsf{\rho }+1\right)-0.11}{\mathrm{b}.\mathrm{d}}+\frac{154 \mathrm{a}-1080 \mathrm{d}+66.5}{\mathrm{d}.{\mathrm{fc}}^{\prime }}\\ +\frac{\mathrm{d}\left(694 \mathrm{d}+370 \mathrm{b}-1317 \mathsf{\rho }\right)-11}{\mathrm{a}}+\frac{\mathrm{a}}{1.75{ \mathrm{d}}^2}-\frac{\mathrm{b}}{2.75 \mathsf{\rho }}-\frac{{\mathrm{fc}}^{\prime }{}^2}{580}-22.5\\ +19\mathsf{\rho } \left(360 \mathrm{b}+150 \mathrm{d}+{\mathrm{fc}}^{\prime }-950 \mathsf{\rho }\right)+128{ \mathrm{b}}^2-78.5{ \mathrm{d}}^2+31.9 \mathrm{a}\end{array}$$

(3)

4. Comparison with Existing Models

4.1. Overall

Figure 5, Figure 6 and Figure 7 show the relationship between the predicted and calculated strength as well as the best fit line and the ideal 45-degree line. For the GP model, the average error % of total dataset is 32.1%, and the R2 value is 0.80. For the ANN model, the average error % of total dataset is 17%, and the R2 value is 0.95. For the EPR model, the average error % is 23.5%, and R2 values were 0.90 for the total datasets. Thus, the performance of the three proposed models exceeded that of the existing model in terms of accuracy and consistency. In addition,

Table 5. Comparison between proposed models and existing guidelines.

Measure	ANN	GP	EPR	ACI	EC2	JSCE
Minimum	0.41	0.21	0.36	0.34	0.54	0.36
Mean	1.01	0.96	1.03	1.56	2.07	1.45
Maximum	3.12	4.27	17.28	9.93	12.67	9.55
Cofficient of Variation	23%	40%	57%	45%	51%	52%
95% Lower Limit	1.00	0.94	1.00	1.53	2.02	1.41

shows the statistical measures for the ratio between the measured and calculated strength using all methods. The design codes are overly conservative, with mean values ranging between 1.45 and 2.07, while the proposed methods were much more accurate, with mean values ranging between 0.96 and 1.03. For consistency, the ANN model’s performance was consistent compared to all other models, where its coefficient of variation had a value of 23% compared to the other methods, which have a coefficient of variation valued between 40% and 57%. It is worth noting that the proposed models offer reasonably safe designs with a 95% lower limit value ranging between 0.94 and 1.00. Finally, the proposed models had a narrow range where the minimum and the maximum ratios are much closer compared to the existing design codes.

4.2. Concrete Strength

It is widely believed that shear is directly proportional with the concrete; however, it is undecided whether this increase is related to concrete compressive strength or tensile strength. Most design codes relate the shear resistance for the EC2, the JSCE and the ACI, respectively. Thus, it could be concluded that the concrete tensile resistance is the governing parameter.

Figure 8 shows the SR (ratio between measured and calculated strength) versus concrete compressive strength as well as the best fit trendline. The slope of the best fit line is 0.0001, −0.0048, 0.0041 and 0.0025 for ANN, ACI, EC2 and JSCE. For the safety calculated using selected design codes, there is significant inconsistency with respect to concrete strength, while for the ANN model, there is significant consistency with respect to concrete strength.

4.3. Effect of Size

The effect of size on the shear resistance of normal-weight concrete and lightweight concrete elements and slabs without shear reinforcements is a phenomenon where strength decreases with the increase in the element depth. In the late ‘50s collapse of the US Air Force warehouse, this phenomenon was one of the main reasons for element collapse while subjected to one half of the design load. For elements without stirrups under shear, the effect of size was found to be significant. Thus, the influence of element size is taken into account in the ACI. Many of the shear provisions of the design codes account for the effect of size in shear. A size factor is used as follows for both ACI and EC2 and for the JSCE. Figure 9 shows the SR (ratio between measured and calculated strength) versus size as well as the best fit trendline. The slope of the best fit line is −0.0016, −0.04053, −0.9436 and −0.5866 for ANN, ACI, EC2 and JSCE. For the safety calculated using selected design codes, there is significant inconsistency with respect to concrete strength, while for the ANN model, there is significant consistency with respect to size.

4.4. Flexure Reinforcement Ratio

The increase in the flexure reinforcement ratio decreases the crack width and thus increases the shear resistance and the dowel action. Moreover, a significant increase in the shear resistance for elements with flexure reinforcements distributed over the full depth was observed by several researchers. Most shear design provisions consider the influence of the flexure reinforcement ratio either in a direct or indirect manner. The increase in the flexure reinforcement ratio reduces the concrete crack width, consequently reducing the interface shear transfer, dowel action and thus the shear resistance.

Figure 10 shows the SR (ratio between measured and calculated strength) versus the flexure reinforcement ratio as well as the best fit trendline. The slope of the best fit line is −1.237, −3.4108, −2.4587 and −0.5215 for ANN, ACI, EC2 and JSCE. For the safety calculated using selected design codes, there is significant inconsistency with respect to concrete strength, while for the ANN model, there is significant consistency with respect to the flexure reinforcement ratio.

4.5. Shear Span to Depth Ratio

The decrease of the shear span to depth ratio (a/d) increases the shear resistance. The nominal shear resistance of tested elements with an a/d ratio of 2.5 are clearly higher than those with an a/d ratio around 3.0, which is because of the arch action mechanism. Many shear design provisions include a variable related to the a/d ratio in their predictions of shear capacity. It is more practical to use the moment to shear ratio in shear design provisions instead of the a/d ratio because the a/d ratio is not well defined for elements under distributed load.

Figure 11 shows the SR (ratio between measured and calculated strength) versus the shear span to depth ratio as well as the best fit trendline. The slope of the best fit line is 0.0077, −0.2444, −0.3813 and −0.2651 for ANN, ACI, EC2 and JSCE. For the safety calculated using selected design codes, there is significant inconsistency with respect to concrete strength, while for the ANN model, there is significant consistency with respect to the shear span to depth ratio.

4.6. Lightweight Concrete

Lightweight concrete elements were found to have relatively wider cracks and lower strength compared to NC strength. Thus, various design codes account for lightweight concrete in different manners, including: (1) a constant reduction for the strength such as the JSCE and (2) a reduction in the strength proportion to the concrete dry density, such as the EC2 and the ACI.

The effect of the concrete type in terms of aggregate size on the safety of design is investigated. Figure 12 shows the SR (ratio between measured and calculated strength) versus the aggregate size as well as the best fit trendline. The slope of the best fit line is −1.9192, −16.548, −35.603, −23.996 for ANN, ACI, EC2 and JSCE. For the safety calculated using selected design codes, there is significant inconsistency with respect to concrete strength, while for the ANN model, there is significant consistency with respect to the aggregate size.

The effect of the concrete type in terms of concrete dry density on the safety of design is investigated. Figure 13 shows the SR (ratio between measured and calculated strength) versus the concrete dry density as well as the best fit trendline. The slope of the best fit line is −0.095, −0.995, −1.621, −1.1299 for ANN, ACI, EC2 and JSCE. For the safety calculated using selected design codes, there is significant inconsistency with respect to concrete strength, while for the ANN model, there is significant consistency with respect to the concrete dry density.

5. Conclusions

This research presents three models using three artificial intelligence (AI) techniques: genetic programming (GP), artificial neural network (ANN) and evolutionary polynomial regression (EPR) to predict the shear capacity of concrete beams (Vu) using specific gravity of concrete (Gs), beam width (b), beam depth (d), cylinder compressive strength of concrete (fc’), shear span (a/d), longitudinal reinforcement ratio of steel (ρ) and maximum nominal size of aggregates (da). Three current international design codes (American Concrete Institute (ACI), Euro code 2 (EC2) and Japan Society of Civil Engineers (JSCE)) were used as benchmarks to evaluate the enhancement of shear capacity prediction.

The results of comparing the accuracies of the developed models with each other and with current design codes could be concluded in the following points:

• ANN is the most accurate and most complicated developed predictive model with an average prediction accuracy of 83.0%, the EPR model comes in the second with an average accuracy of 76.5% and finally, GP is the last with an average accuracy of 67.9%. On the other hand, the current design codes showed more conservative predictions with accuracies of 55.7%, 40.1% & 61.9% for ACI, EC2 & JSCE, respectively.
• Although ANN is more accurate than EPR, the output of EPR is closed form equations unlike the ANN matrix of weights; hence, it is recommended to implement the ANN model in computerized calculations and use the EPR for rough manual checks.
• The relative importance shown in Figure 3 indicates that beam dimensions (b & d) had major influence on the shear capacity, followed by shear span (a/d), while other parameters have minor effects. This conclusion matches the correlation factors shown in Table 2.
• The insignificant effect of (Gs) could be due to its limited variation, as indicated in the histogram in Figure 1.
• The GA technique successfully reduced the 330 terms of the conventional polynomial regression quadrilateral formula to only 24 terms without significant impact on its accuracy.
• Although all AI predictive models did not present a physical model or explanation for the shear failure mechanisms, they offered empirical alternatives based on actual test results.
• Like any other regression technique, the generated formulas are valid within the considered range of parameter values; beyond this range, the prediction accuracy should be verified.