Strength index analysis of concrete with large size recycled aggregate based on back propagation neural network

Abstract

A back propagation (BP) neural network (NN) model was used to analyze the relationship between the cube compressive strength and various strength indicators of concrete with large-sized recycled aggregates (LSRA) (80 mm maximum size). Factors such as strength and replacement rate of recycled aggregates were used as input parameters to establish the neural network model. The BP-NN model was optimized by analyzing the influence and sensitivity of each parameter in the model. Then the mechanical properties of concrete with LSRA were predicted. Results showed that the strength of new concrete had a more significant impact on the strength of recycled concrete with LSRA, followed by the strength of old concrete. While considering all the factors, including the mechanical strength and the replacement ratio regarding the maximum utilization of RA, the 30% incorporation rate was suggested as an ideal incorporation rate.

Keywords

recycled aggregate concrete large size recycled aggregate strength index back propagation neural network prediction model

Introduction

In past years, various Artificial Neural Network (ANN) has been used to predict the performance of concrete with strong non-linear characteristics. Scientists Rumelhart and McClelland proposed the backpropagation neural network (BPNN) in 1986. It is a multi-layer feed-forward neural network trained according to the “error backpropagation algorithm,” and it is the most widely used neural network. Zhou et al. (2020) and Koneru et al. (2020) used BPNN to predict the ultimate bond strength of the FRP-concrete interface and concrete strength, and the prediction results were satisfactory. Yong (2020) and Naderpour et al. (2018) established a prediction model for concrete strength, predicting the compressive strength of normal water–cement ratio range and age of concrete. Tan (2018) studies four kinds of neural networks in prediction for the performance of 3D printed concrete and recommended RBF neural network to predict the performance of recycled concrete and provide a reference for choosing architectural 3D printing materials. Duan et al. (2018) analyzed each element or materials parameter as input by ANN and reduced the prediction error of ANN by adopting the 14-16-1 ANNs model. Xu et al. (2019a, 2019b) used multiple non-linear regression (MNR), ANN and hybrid genetic algorithm artificial neural network (GA-ANN) to simulate mechanical triaxial loads. The performance results of recycled aggregate concrete (RAC) with ANN showed that that the developed MNR equation and neural network model can satisfactorily predict the behavior of RAC under triaxial load. Kim et al. (2013) also used ANN-based genetic algorithms (ANN-GA) to optimize the mix ratio of RAC and reduce the waste of concrete in the construction process.

In terms of structural concrete members, the application of the ANN can be applied in various ways. Tran et al. (2020) adopted column length, steel tube diameter, steel tube thickness, steel tube yield strength, ultimate strength, and concrete compressive strength as input variables to establish an ANN model to predict the axial compression capacity of the column. The results were quite convincing. Oh et al. (2020) used the acceleration response time history to automatically extract the correlation between the features from the acceleration response through the convolution and merge operations in each CNN layer and the displacement response. Cai et al. (2019) established a BP-NN model to predict the shear strength of RAC beams with input layers as beam height, beam width, time, the cross-sectional area of the stirrup, stirrup spacing, concrete strength, and concrete cover thickness parameters. The study found that BP-NN can accurately predict the shear strength of RC beams after a fire.

There are many types of neural networks, and some scholars have compared the effects of different ANN models in engineering. Han et al. (2019) compared ANN models with three different learning algorithms, namely BP, particle swarm optimization (PSO), and the new hybrid PSO-BP algorithm in predicting the compressive strength of ground granulated blast furnace slag (GGBFS) concrete. The results show that the PSO-BP neural network model is superior to the simple ANN trained by a single algorithm and is suitable for predicting the compressive strength of GGBFS concrete. Hammoudi et al. (2019) applied the response surface method and ANN method to the 28-day and 56-day compressive strength of RAC. The results show that the ANN model shows better accuracy. Madani et al. (2020) compared the adaptive neural fuzzy inferance system (ANFIS), ANN technology, and linear and non-linear regression analysis to predict the accuracy of nano-modified mixtures. The results show that ANN and ANFIS are better tools of analysis than regression analysis. Xu et al. (2019a, 2019b) used MNR and ANN to simulate the mechanical properties of RAC using the critical parameters of the RAC mixture identified by gray system theory. The results show that the MNR and ANN methods can provide a more accurate prediction of the mechanical properties of RAC. Khademi et al. (2016) used ANN, ANFIS, and multiple linear regression (MLR) to predict the compressive strength of concrete at 28 days. The study concluded that ANN and ANFIS had better 28-day compressive strength assessment of RAC than MLR. Deshpande et al. (2014) used backpropagation ANN, model tree, and non-linear regression (NLR) to predict the compressive strength of RAC for 28 days. The results showed that ANN learned and mastered the basic domain rules for controlling parameters of concrete strength from literature and experimental values.

In conventional concrete, the size of coarse aggregate is generally below 40 mm, so the size of conventional recycled aggregate is also less than 40 mm (Xiao 2018). However, in hydraulic engineering, the size can reach up to 100 mm, so waste concrete can be crushed to a larger size and used as large-sized recycled aggregates (LSRA) and form continuous gradation with conventional coarse aggregate. Since the LSRA is treated as coarse aggregates, rather than a new component being mixed with fresh concrete. To distinguish LSRA, they are not referred as recycled concrete lumps in this study. Recycled concrete has multiple interfaces, so the non-linear characteristics of mechanical properties are strong. The structure of concrete with LSRA is more complex. Due to the complex composition of concrete with LSRA, the mechanical properties are non-linear, and it is challenging to reveal its principles using conventional analytical methods. At the same time, it is difficult to test because of the larger aggregate size. Based on the research results from the literature, this article selects the BP-NN to establish the relationship between the strength indicators of concrete with LSRA and calculates its mechanical performance indicators before the experimental test.

Method for BP-NN prediction model

In order to analyze the influence of recycled aggregate (RA) incorporation rate, old concrete strength (original concrete cube compressive strength of RA), new concrete strength (design cube compressive strength without RA), and size of RA on the cube compressive strength, and to analyze the relationship between RAC strength indicators, two neural networks were established. One is the prediction model of the cube compressive strength of RAC, and another is the conversion model of the strength index of RAC. Using the BP-NN, the test results were analyzed. The learning process of the back error’s propagation algorithm was used to find out the influence of different factors on each strength index of RAC. These factors include the strength grade of new concrete, RA’s original concrete strength grade, and RA’s incorporation rate.

According to the operational mode of BP-NN, a network model with supervised learning is adopted. Because of the less amount of data obtained from the experiment, all data were used for training the network. After training is completed, a set of data is randomly selected for testing. If the error is less than the threshold, then only the model is used. The neural network toolbox of MATLAB was used to build a neural network with a hidden layer. The activation function of the hidden layer is the asymmetric sigmoid function. The transfer functions of the hidden and output layers are “tansig” (S-type tangent), “logsig” (S-type logarithmic), and “purelin” (pure linear) functions. Also, the linear normalization method is used to normalize the data using the “mapminmax” function of MATLAB. The data are converted to decimals within the interval [−1, 1] so that the output of the transfer function of the Sigmoid function can be prevented from entering a supersaturated state, and ‘trainr’ (the training function is updated in random order) function is used to train the data obtained.

The selection of the initial weight has a significant influence on whether the neural network can reach the local optimum, whether it converges or the learning rate. The weights were taken as random numbers in the form of (−1, 1). The learning rate of the neural network determines the modification range of the node weights after each training. A tremendous learning rate will produce more local minimum points and cause the network to be unstable. Therefore, a lower learning rate is usually selected, set to 10⁻², and the error is set to 10⁻⁴. Since the types of input data greatly influence ANN’s output and decrease the impact of the data, the input and output parameters are normalized by using the normalization method shown in equation (1).

{x^{'}}_{k} = \frac{x_{k} - \bar{x}}{δ}

(1)

\bar{x} = \frac{1}{n} \sum_{i = 1}^{n} x_{k}

(2)

δ = \sqrt{\frac{1}{n - 1} {\sum_{k = 1}^{n} (x_{k} - \bar{x})}^{2}}

(3)

where n is the number of data in a group.

With the help of equation (1), the normalized data were input in the ANN and then inversely change the output data to obtain the result to avoid the impact of the difference in the number of data.

The attempt determines the number of neurons in the network’s hidden layer, and the established neural network is tested by two methods, the perfect matching criterion and the optimal similarity criterion. The exact matching standard requires that the error of any data value in each set of output data is less than the threshold. At the same time, the optimal matching method requires that the angle between the vector consisting of each set of output data and the data vector consisting of the target data is less than the threshold. The model for predicting the cube compressive strength is tested using exact matching labels. The RAC strength index conversion model is tested using both the perfect matching label and the optimal similarity standard. To decrease the influence of the variation in the number of output data components on the network output accuracy computation while utilizing the optimum similarity standard for the network accuracy test, the output components are split by the corresponding target components, and the relative error of each output component is then calculated.

Building a prediction model of BP-NN

Establishment of prediction model of cube compressive strength

The influences of the strength of new concrete, old concrete, and incorporation rate of RA on the cube compressive strength of the specimens were analyzed, and the established neural network is shown in Figure 1. The left and right nodes are the input and output nodes, and the middle node is the hidden node. The data used for training are listed in Table 1 and come from the experiment of Li et al. (2016). In Table 1, the natural coarse aggregate size adopted is from 5 to 25 mm whereas, the recycled coarse aggregate size adopted is 25 mm. There are four neurons in the input layer of the network corresponding to the influencing factors: the size of aggregate, the strength of old concrete, the strength of the new concrete and the incorporation rate of RA. The number of hidden layers was selected to train the network 105 times and check the exact matching criteria for each training result. The training results obtained are shown in Figure 2. It can be seen from the figure that the number of hidden layer neurons needs to be higher than 10. Otherwise, the accuracy of ANN is below 0.7, showing the characteristics of “underfitting.”

Figure 1.

Back propagation neural network for cube compressive strength prediction.

Table 1.

Training data of the cube compressive strength prediction model.

Maximum size of recycled aggregate (mm)	Strength grade of old concrete (MPa)	Strength grade of new concrete (MPa)	Recycled aggregate incorporation rate (%)	Cubic compressive strength (MPa)
50	30	30	0	33.44
50	30	30	10	35.49
50	30	30	20	37.88
50	30	30	30	34.81
50	30	30	40	32.91
50	30	30	49	33.73
63	30	30	0	37.42
63	30	30	10	35.72
63	30	30	20	30.16
63	30	30	30	26.88
63	30	30	40	28.30
63	30	30	50	31.37
63	30	40	0	38.80
63	30	40	10	41.35
63	30	40	20	40.36
63	30	40	30	33.81
63	30	40	40	36.64
63	30	40	50	39.40
80	30	30	0	25.76
80	30	30	20	26.43
80	30	30	30	26.87
80	30	30	30	24.47
80	40	40	0	33.25
80	40	40	20	34.83
80	40	40	30	33.37
80	40	40	40	28.51

Figure 2.

The effect of the number of nodes in different hidden layers on the neural network.

As the number of neurons reaches 50 the accuracy of the model reaches 0.9 and with further increase in the number of neurons the accuracy is not improved leading to a condition of “overfitting.” So, the number of network nodes is kept at 50, and after the network training is completed, the mean value of the absolute value of the ownership value coefficient ${| ω_{i j} |}_{m} = 0.27$ and the mean square deviation ${| ω_{i j} |}_{cr} = 0.11$ , both shows a smaller value indicating that the number of neurons in the hidden layer of the network is appropriately selected.

To consider the influence of deviation weight on the BP-NN for predicting the compressive cube compressive strength the change in the output accuracy of the network is tested, the uniform weighted random disturbance is added to the determined weight. It can be seen from Figure 3 that the network accuracy is more sensitive to weight changes. It is assumed that the data fluctuations follow the normal distribution with the training data having the mean and the variance as $d$ , and the input data is superimposed with the mean value of 0, and the variance is $d$ . This data with random noise was used to test the changes in the output accuracy of the neural network. Figure 4 shows the change of the network output accuracy after adjusting the data variance. From Figure 4, it can be seen that the data change has a more significant impact on network accuracy. When the $d$ is 0.1, the network accuracy is lower than 0.9, and when the $d$ value is 0.5, the network accuracy is lower than 0.2. The actual mixed concrete will have strength fluctuations during the test.

Figure 3.

The effect of weight disturbance on the accuracy of the neural network.

Figure 4.

Effect of data variance on network accuracy.

The generalized analysis of the neural network was carried out using the data when the strength of new concrete and old concrete strength is C30 and C20, respectively, along with RA incorporation rate from 0 to 40% with RA of size 50 mm. The selected test data are shown in Table 2 and the minimum size of recycled aggregates (RA) is 25 mm, and the natural coarse aggregates is of size 5–25 mm. Compared with the actual strength, the predicted cube compressive strength of the BP-NN model is shown in Figure 5. It can be seen from Figure 5 that the generalization ability of the neural network is good, and the prediction accuracy of the strength of the RAC with a strength of less than 30 MPa is above 0.8.

Table 2.

Cube compressive strength data for “extrapolation” test (adopted from Li et al. (2016)).

Maximum size of recycled aggregate (mm)	Strength grade of old concrete (MPa)	Strength grade of new concrete (MPa)	Recycled aggregate incorporation rate (%)	Cubic compressive strength (MPa)
50	20	30	0	30.91
50	20	30	10	30.86
50	20	30	20	30.46
50	20	30	30	28.81
50	20	30	40	29.72

Figure 5.

Extrapolation error of predicted data

Establishment of a conversion model for strength index of RAC

The multi-factor analysis was carried out on the cube compressive strength, axial compressive strength and splitting tensile strength of specimens with maximum aggregate size of 50 mm, 63 mm, and 80 mm. The number of hidden layer nodes of different neural networks was selected and establish the neural network, as shown in Figure 6, and the training data are presented in Table 3.

Figure 6.

Conversion of strength index of recycled aggregate concrete back propagation neural network.

Table 3.

Training data of strength index conversion prediction model.

Recycled aggregate incorporation rate (%)	Recycled aggregate size (mm)	Cubic compressive strength (MPa)	Axial compressive strength (MPa)	Splitting tensile strength (MPa)
0	50	33.44	23.32	2.30
30	50	34.81	17.73	1.74
0	30	25.76	19.66	1.99
30	30	26.87	15.87	1.75

After 105 training iterations, each training result is verified using the complete matching method and the optimal matching method. The obtained training results are shown in Figure 7. It can be seen from the figure that when the number of nodes of the hidden layer is below 60, the prediction accuracy of the network is below 0.9, and there is a significant fluctuation, which decreases slightly afterward and drops to 0.8 at 100 nodes. At the same time, it can be seen that the prediction accuracy of the network using the optimal matching method is relatively high, reaching more than 0.9, and the prediction accuracy of the network gradually increases with the increase of the number of hidden layer nodes. Based on the above two evaluation results, it is more appropriate to choose 60 hidden layer nodes.

Figure 7.

The influence of the number of hidden layer nodes on the network accuracy. (a) Exact matching method. (b) Optimal matching method.

After the network training is completed, the mean value is ${| ω_{i j} |}_{m} = - 0.73$ , and the mean square error is ${| ω_{i j} |}_{cr} = 0.48$ , both are small, indicating that the number of hidden neurons in the network is selected appropriately. By adding the uniform random disturbance within the weight $[- d, d]$ , the output accuracy of the network is tested. The change in network output accuracy after the disturbance is applied, shown in Figure 7. It can be seen from the figure that under the full matching method, due to the increase in the weight change, the network’s predictive ability declines linearly, but the decline is not very prominent. When the range of weight change is [−1,1], the prediction accuracy of the network drops to 0.7, but at this time, the output data dispersion increases significantly.

The random error with the mean value of zero and favorable distribution is superimposed on the input data, and the output error of the BP-NN with different variances was studied. The effect of superimposed random error on network prediction accuracy is shown in Figure 8. It can be seen from the figure that the prediction accuracy of the network does not change much after adding random errors. The output error was studied using the perfect matching method. When the variance is 0.4, the prediction accuracy decreases significantly, reaching 0.7, and the curve changes more smoothly. Using the optimal matching method, the network output accuracy is always kept above 0.95 when the variance is not significant.

Figure 8.

Influence of weight disturbance on network accuracy.

The generalized analysis of the neural network was carried out using the data that the strength of new concrete is C20, old concrete strength is C30, and RA incorporation rate is 0–40%, and the size of RA is 50 mm. The selected data are shown in Table 4 and the minimum size of all RA in Table 4 is 25 mm, and the natural coarse aggregates are of size 5–25 mm. Due to the lack of corresponding splitting tensile strength, only the network accuracy analysis of the complete matching method is selected. The calculated axial compressive strength at incorporation rate of 0% and 30% of old concrete using the data in Table 4 is 22.01 MPa and 16.97 MPa, which are about 0.6 and 0.7 lower than the target value, indicating that the network is not suitable for “extrapolation” due to the lack of training data and weak generalization ability. However, due to the excellent accuracy near the training data points, it can be used to analyze the existing test data.

Table 4.

Coagulation strength data for “extrapolation” test (adopted from Guo (2011)).

Recycled aggregate incorporation rate (%)	Maximum size of recycled aggregate (mm)	Cubic compressive strength (MPa)	Axial compressive strength (MPa)	Splitting tensile strength (MPa)
0	50	30.91	33.84	—
30	50	28.81	29.57	—

Results and discussion

Multi-factor analysis of cube compressive strength

The previous model tests show that the BP-NN model established for cube compressive strength prediction can reflect the influence factors such as the new concrete strength, old concrete strength, and RA incorporation rate to the cube compressive strength index of concrete specimens. After increasing the axial compressive strength and splitting tensile strength, the conversion model for the strength index of RAC can reflect the relationship between the strength indicators. Create a grid by dividing the strength of new concrete and strength of the old concrete equally in the interval [30, 40], and the incorporation rate of the RA in the interval [0, 0.4], and the size of aggregate in the interval [40, 80]. The neural network is used to find the predicted value of the cube compressive strength at each node in the space, and the generated hypersurface is used to analyze the in the cube compressive strength under the influence of multiple factors. By using the same method to establish the hypersurface of each mechanical index and then using it to analyze the relationship between the mechanical indexes, the established cube compressive strength hypersurface in two-dimensional and three-dimensional space is shown in Figure 9.

Figure 9.

Cube compressive strengths under different recycled aggregate concrete back incorporation and old concrete strength. (a) 50 mm aggregate contour. (b) 63 mm aggregate contour. (c) 80 mm aggregate contour. (d) 80 mm aggregate surface.

As shown in Figure 9(a), when the size of aggregate is 50 mm, and the strength of the new concrete is C30, the use of RAs with a strength higher than C30 can increase the cube compressive strength of the RAC. The degree of strength improvement is evident when the RA mixing rate is low, and the strength of new concrete is between 35 MPa and 38 MPa. As concrete comprises coarse aggregate, mortar, and various interfacial transition zones, the strength is determined by the weak points between each phase. Due to the rough surface, hydration activity, RA can be well bonded with the mortar in the new concrete. When the strength of the RA is not much different from the mortar matrix, the strength of the two determines the formation and development of cracks in the concrete. When the strength of RA is higher than that of the mortar matrix, RA will no longer become a weak link in RAC, and while increasing the strength of RA does not significantly increase the strength of RAC. This reduction exists even if the original concrete strength of recycled aggregate is relatively higher. Since the strength of the mortar in the recycled aggregate is always lower than that of the natural aggregate in the experiment. The RAC with higher strength is more likely to form a stress concentration at the edge of the coarse aggregate, and the stress distribution in the concrete is uneven. Also, due to the damage in RA, the strength of RAC will be reduced to a certain extent when the RA strength is high. The reason that the increase of the mixing ratio of RA leads to a decrease of the strength of RAC can be attributed to the more interface transition zones because of the higher incorporation ratio of RA, which amplifies the effect of the strength difference between the RA and new concrete on the strength of the RAC.

It can be seen from Figure 9(b) that when the size of aggregate is 63 mm, and the strength of the new concrete is C30, the cube compressive strength of the RAC gradually decreases with the increase of RA incorporation rate and the strength of the old concrete. As the size of aggregate increases, the restraining effect of the two ends of the specimen decreases, and there are more microcracks in the RA, which accelerates the development of microcracks. Therefore, compared with the small-size aggregate, the influence of the RA incorporation rate of the large-sized aggregate on the cube compressive strength of the RAC is more prominent. When the strength of the old concrete is lower than 36 MPa, the strength of the RAC decreases with the increase of the strength of the old concrete because the strength difference between the RA and the mortar matrix causes stress concentration, which is more noticeable when the restraining effect of the platen is weakened. When the strength of old concrete is significant, the hindered effect of RAs on the development of cracks in RAC becomes more apparent. The cracks stop at the aggregates or bypass the aggregates and develop in a more tortuous direction, therefore reducing RAC cracking.

As seen from Figure 9(c), when the size of aggregate is 80 mm, and the strength of the new concrete is C30, the incorporation rate of RAs has a more significant effect on the compressive strength of RAC than the specimen with an aggregate of 80 mm. When the mixing ratio of RAs reaches 40%, the strength of RAC is significantly reduced. As the size of aggregate increases, the restraining effect of the press platen decreases, and at the same time, the stress concentration phenomenon is more prominent. These factors cause the cracks to expand quickly as soon as they are formed, resulting in the loss of strength of the RAC. The effect of the strength of old concrete is not as significant if the size of aggregate is small because of the crack arresting effect of RA on crack development due to substantial differences is weakened, and the RA of larger size contains more micro -cracks which is Easy to crack and fail under load. For an aggregate size of 80 mm, it can be seen from Figure 9(c) that when the RA incorporation rate is below 30%, the strength of RAC decreases slowly, but after the incorporation rate exceeds 30%, the strength of RAC decreases sharply. Considering the production cost of RA and the maximum use of waste concrete, it is appropriate to select a 30% RA incorporation rate.

Figure 10 shows a contour diagram of the strength of RAC with a 30% RA mixing ratio, different RA strength, and new concrete strength. It can be seen from the figure that the impact of the strength of new concrete on the strength of RAC is significantly higher than the strength of old concrete on the cube compressive strength of RAC.

Figure 10.

Axial compressive strength under influencing factors. (a) 50 mm aggregate contour. (b) 63 mm aggregate contour. (c) 80 mm aggregate contour. (d) 80 mm aggregate surface.

As shown in Figure 10(a), for the 50 mm aggregate specimen, when the strength of new concrete is about 34 MPa, and the old concrete strength is near 30 MPa, the cube compressive strength of RAC is found to be lowest. At the same time, the strength of RAC is the highest when the strength of new concrete and old concrete is 40 MPa. When the strength of new concrete is low, about 33 MPa, the strength of old concrete increases, and the strength of RAC show a slight decrease. When the strength of the new concrete is greater than 33 MPa, the strength of RAC shows a trend of decreasing first and then increasing with the increase in the strength of old concrete. The difference in strength between new concrete and old concrete is also shown in the elastic modulus. The difference in elastic modulus between the new concrete and old concrete, resulting in stress concentration at the interface transition zone, reduces the RAC’s strength. Therefore, when RA and new concrete strength are similar, the RAC shows a higher strength.

Figure 10(b) shows the strength contour diagram when the aggregate size is 65 mm. At a mixing ratio of 30% RA, different new concrete strength and RA strength on the cube compressive strength. It can be seen from the figure that when the new concrete is still around 34 MPa, the strength of the old concrete is around 30 MPa, and the strength of the RAC is the lowest. The highest strength of RAC still occurs when the strength of new concrete and RA are both 40 MPa. Compared with the 50 mm aggregate specimen, the strength reduction of RAC caused by the difference in strength between new concrete and old concrete is more prominent. This is because the size of the RA is more significant, so the stress concentration is more prominent.

Figure 10(c) shows the strength contour diagram when the aggregate size is 80 mm. At a 30% RA incorporation rate, new concrete strength and RAC strength on the cube compressive strength are different. It can be seen from the figure that the strength of RAC is the lowest when the strength of new concrete is 30 MPa, and the strength of old concrete is 40 MPa, while the strength of RAC is the highest when the strength of new concrete is 40 MPa, and the strength of RA is 40 MPa. The overall trend shown in the figure is that the strength of RAC increases with the increase in the strength of new concrete. As the strength of old concrete increases, the strength of RAC shows a downward trend before the strength of new concrete is 34 MPa. When the strength of the new concrete is greater than 34 MPa, as the strength of the old concrete increases, the strength of the RAC first decreases and then rises. Compared with the 50 mm aggregate specimen, the Cube compressive strength of the 80 mm aggregate specimen decreases more as the strength of the RA increases because the 80 mm aggregate specimen contains a larger size of the RA, the stress concentration caused by the difference in elastic modulus is more prominent.

In summary, the limited test data are extended to a full area through the neural network to study the change of the strength of cube compressive strength under the condition of different RA size. Through analysis, it is found that the strength of new concrete has a more significant impact on the strength of RAC, followed by the impact of RA incorporation rate, than the strength of old concrete. The possible reason is that the RAC cracks and damage. Most of the cracks are developed in the mortar matrix of new concrete. The strength of the mortar matrix of new concrete has a more significant influence on the propagation of cracks. The mixing ratio of RAs amplifies the effect of the difference between new concrete and RAs on the strength of RAC. The strength of old concrete on the strength of RAC is mainly reflected in the stress concentration caused by the difference in the rigidity of new concrete and RA and the hindrance to crack development. When the strength of old concrete and the strength of new concrete is not much different, the effect of RA strength is not very obvious. When the size of the RA is larger, considering the maximum utilization of RA, the 30% RA incorporation rate is ideal in the mixing ratio.

Multi-factor analysis among various strength indicators

Figure 11 shows the strong relationship among various strength indicators and different aggregate sizes, the strength of the old concrete and the new concrete, C30 and 30% RA. For comparison, simultaneously, the steady relationship curve of conventional concrete specimens without reclaimed aggregate.

Figure 11.

Correlation of specimen strength of recycled aggregate concrete back with different recycled aggregate sizes. (a) $f_{cu}$ and $f_{c}$ relationship. (b) $f_{cu}$ and $f_{t}$ relationship. (c) $f_{c}$ and $f_{t}$ relationship. (d) $f_{cu}$ , $f_{c}$ and $f_{t}$ relationship.

It can be seen from Figure 11(a) that the ratio of the axial compressive strength $f_{c}$ to the cube compressive strength $f_{cu}$ of RAC is less than the ratio of the conventional concrete. When the aggregate size is 50 mm, the average value of $f_{c} / f_{cu}$ conventional concrete is 0.70, and the maximum reaches 0.86. When $f_{cu}$ is 20–28 MPa, $f_{c} / f_{cu}$ first increases rapidly, then decreases slowly, $f_{cu}$ reaching a maximum value at 34 MPa. Correspondingly, the average value of ratio $f_{c} / f_{cu}$ of the RAC specimen with a 30% RA incorporation rate is 0.59, and the maximum value is 0.82, which is 16% and 5% lower than the corresponding conventional RAC specimen. The RAC curve has two peaks, corresponding to $f_{cu}$ = 26 MPa and =34 MPa. When the size of the aggregate reaches 80 mm, the changes in the $f_{c} / f_{cu}$ is not significant. The $f_{c} / f_{cu}$ average value of conventional concrete is 0.67, and the maximum value is 0.84. The average value $f_{c} / f_{cu}$ of the RAC is 0.57, and the maximum value is 0.83, which is 15% and 1% lower than the corresponding conventional concrete. The curve of conventional concrete is relatively gentle. The curve of RAC is almost unchanged before the cube compressive strength is 36 MPa, and then it increases rapidly. Due to the friction force of the press plate against the upper and lower surfaces of the concrete, it restricts the cracking of the concrete, thereby improving the cube compressive strength, and the axis of the prism specimen is less compressed between the upper and lower pressure plates. The effect of friction leads to $f_{c} / f_{cu}$ is less than 1. As the strength of the concrete increases, the frictional force between the press plate and the specimen weakens the cube compressive strength and the $f_{c} / f_{cu}$ increases accordingly. For RAC, since the incorporated RA has more internal damage, the frictional force increases the cube compressive strength more significantly, so the $f_{c} / f_{cu}$ RAC is lower than conventional concrete. The random distribution of the initial damage inside the RA is also a reason for the large fluctuations $f_{c} / f_{cu}$ as the cube compressive strength increases.

It can be seen from Figure 11(b) that the ratio of the axial tensile strength $f_{t}$ to the cube compressive strength $f_{cu}$ of RAC is smaller than the ratio of the conventional concrete. The changing trend of the curve is the same as the curve $f_{c} / f_{cu}$ of conventional concrete, and the reasons are similar $f_{c} / f_{cu}$ . When the aggregate size is changed to 50 mm, the average value $f_{t} / f_{cu}$ of the RAC specimen is 0.072, and the maximum value is 0.086. The average $f_{t} / f_{cu}$ of the RAC specimen is 0.059, and the maximum value is 0.084, which is 18% and 3% lower than that of the conventional concrete specimen, respectively. The $f_{t} / f_{cu}$ of conventional concrete reaches its maximum value when $f_{cu}$ is 34 MPa and the maximum value of $f_{t} / f_{cu}$ of RAC at 26 MPa $(f_{cu})$ is smaller than the maximum value at 34 MPa $(f_{cu})$ . When the size of the aggregate reaches 80 mm, the change $f_{t} / f_{cu}$ is not significant. The average $f_{t} / f_{cu}$ of typical concrete specimens is 0.068, and the maximum value is 0.085. The average $f_{t} / f_{cu}$ of the RAC specimen is 0.059, and the maximum value is 0.085, which is 13% and 0 lower than that of the conventional concrete specimen, respectively. $f_{t} / f_{cu}$ of conventional concrete reaches its maximum value at 34 MPa. RAC has two maximum values, $f_{cu}$ = 26 MPa and $f_{cu}$ = 34 MPa, respectively.

It can be seen from Figure 11(c) that the ratio of the tensile strength $f_{t}$ the axial compressive strength $f_{c}$ of RAC is not much different from the ratio of the conventional concrete specimen because both are not affected by the friction force generated by the pressure plate on the surface of the specimen.

In summary, since the RAs mixed with RAC introduce a large number of micro-cracks, the friction force generated by the pressure plate on the upper and lower surfaces of the RAC cube specimen has a significant influence on its compressive strength. Therefore, for RAC, the axial compressive strength and tensile strength are not affected by this, $f_{c} / f_{cu}$ and $f_{t} / f_{cu}$ are lower than those of conventional concrete compared with the cube compressive strength.

Conclusion

In this article, a BP-NN prediction model for the cube compressive strength and multiple strength indicators relationship of concrete with different RA was established. The parameters in the model are optimized and used to analyze the effects of various factors on RAC. The following conclusions are obtained:

The BP-NN prediction model of cube compressive strength and relationship between strength indicators based on the size of the aggregate, the strength of the old concrete corresponding to the RA, the strength of the new concrete, and the replacement rate of the RA was established, and the prediction ability of the established model was tested. The prediction accuracy of the strength of the RAC with a strength of less than 30 MPa is above 0.8.

The BP-NN prediction model of the cube compressive strength shows that the strength of new concrete has a more significant impact on the strength of RAC, followed by the impact of RA incorporation rate than the strength of old concrete. When the size of the RA is larger, considering the maximum utilization of RA, the 30% RA incorporation rate is ideal in the mixing ratio.

The neural network model of the strength index relationship shows that for RAC, the axial compressive strength and tensile strength are lower than those of conventional concrete compared with the cube compressive strength.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the financial support from the National Natural Science Foundation (NSFC) of PR China (Nos. 51778463, 52078370, 51438007).

ORCID iD

Jianzhuang Xiao

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