Study on novel steel slag foam concrete pore structure and bp neural network prediction model

In this paper, a new type of steel slag foamed concrete was prepared. Its pore structure was analyzed by MATLAB image processing technique, and the influence of steel slag on the compressive strength of foamed concrete was investigated. In addition, a BP neural network prediction model for the pore structure of foam concrete was established. The research results show that when the content of steel slag is 30%, the pore structure of steel slag foamed concrete is appropriate. The compressive strength of steel slag foamed concrete increases with the decrease of the density and the proportion of irregular pores. With the density remaining unchanged, the compressive strength of foamed concrete increases with the increase of the ratio of round and small pores. The prediction errors of the BP neural network model in the average pore diameter and average pore roundness factor were less than 8.5% and 5%, respectively.This research can provide a theoretical basis for the production of steel slag foam concrete.


Introduction
Foamed concrete, as a lightweight material with high strength and excellent thermal insulation performance, is widely used in modern energy-saving structures. Foamed concrete is characterized by a porous structure, which has a significant impact on its performance. The relationship between pore structure and foamed concrete performance has gained extensive research attention [1][2][3][4]. Ammer A et al [5] found that the internal pore structure affects the strength and durability of foamed concrete. For the evaluation of pore structure, not only porosity but also pore morphology, pore size, and pore size distribution should be considered. Kellsley et al [6] reported that the compressive strength of foamed concrete decreases with the increase in porosity. He et al [7] believe that pore size and pore size distribution greatly affect compressive strength and thermal conductivity. Dang et al [8] prepared foamed concrete by protein-assisted foaming. The diameter of the pores is 60-800 μm; with the increase of the density grade, the proportion of irregular holes decreases while the proportion of circular holes increases. Liu et al [9] found that the water-cement ratio affects the size, size distribution and connectivity of pores in foamed concrete; with the increase of the water-cement ratio, the compressive strength of foamed concrete shows an inverted V-shaped change. Ramamurthy et al [10] regarded pore size distribution as one of the most important microscopic properties affecting the strength of foamed concrete and concluded that foamed concrete with a narrower pore size distribution has higher strength. Wang et al [11] thought that foam concrete could be regarded as a three-phase solid-gas-liquid reactor polyethylene composite structure. The pore walls of foamed concrete are the main source of its strength. Various factors affect the composition of pore walls, and the type of pores affects the strength of the foamed concrete. When the pores are spherical or show similar morphology, and the pore diameter is small, the strength of the foamed concrete is high. Yu et al [12] analyzed the pore structure and microstructure of foamed concrete by scanning electron microscopy and optical Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. microscopy combined with digital image analysis; it was found that the uniform distribution of fine and dense pores in foam concrete is the main factor leading to high strength.
Fang et al [13] studied the properties and pore structure of foamed concrete prepared from cement, fly ash, steel slag, and foaming agent. The results show that the compressive strength of foamed concrete doped with cement is higher than that of foamed concrete with steel slag incorporation; with the increase in the porosity, the average size of the pores increases while the roundness factor decreases. Zhang Leilei [14] studied the influence of fly ash on pore structure and found that with the increase of fly ash content, the pores of foamed concrete are more uniform, and the pore diameter is slightly increased. Qi Wei [15] believed that with the increase in the proportion of pores with circularity values of 1.15-1.45 and the decrease in the proportion of those with circularity values >1.6, the compressive strength of foam concrete increases. Saleh Ali Khawaja et al [16] prepared bagasse ash foamed concrete and found that the adsorption of bagasse ash would cause the implosion of foam bubbles and changes in pore size distribution. K Dhasindrakrishna et al [17,18] studied the collapse mechanism of the pores and the influence of foam content. It was demonstrated that the yield stress is the key factor affecting the collapse, and the basic performance depends on the rheology, stability, density, porosity and pore morphology of the foamed concrete. The challenges in the mass production and practical application of GFC were also discussed.
According to the above literature, the pore structure of foamed concrete has an important influence on its compressive strength. In China, the utilization rate of steel slag as solid waste is less than 30%. In this paper, steel slag was used as aggregate to prepare foamed concrete, and its effect on the pore structure of foamed concrete was explored. The effect of pore structure on the compressive performance of foamed concrete was also investigated, and a BP neural network prediction model of foamed concrete was established. This study can provide a theoretical basis for the preparation and performance improvement of foamed concrete with steel slag as aggregate.

Preparation process
(1) Steel slag, NaSO 4 , lime, gypsum, cement and water-reducing agent was added in the mixer according to the test proportion, and dry mixed until uniform distribution.
(2) The tap water was heated to 55°C and then poured into two mixers (with the amount of water in the two mixers being the same). Water in one mixer was mixed with Na 2 O·2SiO 2 and NaOH, and that in the other mixer was mixed with aluminum powder and foam stabilizer to make 1%-3% suspension.
(3) The mixture of Na 2 O·2SiO 2 and NaOH was poured into a mixer and stirred for 1-3 min.
(4) The suspension was added to the slurry and stirred for 15-50 s.
(6) The foamed concrete was placed in a curing box (60°C, relative humidity of 90%) for 24-h pre-curing, then placed in a drying box (80°C) for 4 to 6 h, and then released the mold.

(7)
The foamed concrete was put into the curing box (60°C, relative humidity of 90%), and cured after demolding.
The benchmark ratios for steel slag foamed concrete are shown in table 2. Steel slag foamed concrete was prepared following the above procedure according to these ratios. Figure 1 shows the fabricated steel slag foamed concrete blocks.

Steel slag foamed concrete image acquisition and processing
A 13-megapixel digital camera was used in this experiment. The steps for acquiring and processing photos are as follows. To avoid the influence of section staining on the porosity, the stain on the section of the foamed concrete was removed first. We can assume that the pore structure of the foamed concrete section is the same as the overall pore structure since the density in the section is equal to the spatial volume density [19] according to the stereology principle. Grayscaling, denoising, sharpening, histogram equalization, and mean filter processing were performed after the images were captured. After these processes, the pore structure may be specifically defined. The processed images were binarized to make it easier to understand the pore structure of foamed concrete. The principle is as follows: determne a gray value S in a given technique as a threshold, and divide the images into two groups. The value of pixels larger than or equal to the threshold becomes 1, and the value of pixels less than the threshold becomes 0. The point was assigned a value of 0 (zero). Following the steps below,as shown in figure 2, the images were transformed into a binary matrix of 0 and 1.
The binary matrix was inverted. Specifically, the 0,1 matrix was inverted into a 1,0 matrix. Pixels with a value of 0 are presented in white, while those with a value of 1 are shown in black to make it easier to observe the final pore structure. The following is the final image: Figure 1. Steel slag foamed concrete block. In the formula, S represents the threshold; ( , indicates the processed image; 0 represents the pore of steel slag foamed concrete; 1 represents the pore wall of steel slag foamed concrete.
The inverted binary matrix was scanned by a self-editing program, and the porosity, pore size, pore morphology, and pore size distribution were statistically analyzed. The white part of the inverted binary matrix represents the pore, while the black part represents the pore wall. The steel slag foamed concrete block was sliced to better observe its pore structure. The picture processing procedure is shown as follows [20]: The camera used in this experiment has 13 million pixels, and the average side length of the specimen is 3602 pixels. The actual specimen size in the photo is known to be 100 mm * 100 mm, indicating that the camera can recognize pores with diameters as small as 100/3602 = 0.02776 mm [21].
The shape factor determines the morphology of the pore, and its calculation formula is: In the formula, S stands for the pore roundness factor, P is the pore perimeter, mm, and A represents the pore area, mm 2 . When the S value is 1, the pores are round, and a higher or smaller value indicates that pores are less circular. .

Experiment on the performance of steel slag foam concrete
The experiment on compressive strength and dry density of steel slag foam concrete was conducted in accordance with 'JG/T266-2011 Foam Concrete' [22].

Results and discussion
3.1. Analysis of compressive strength and pore structure at different steel slag ratios 3.1.1. Compressive strength analysis at different steel slag ratios On the basis of the benchmark ratio and fabrication procedure, the mass ratio of steel slag and slag is 65%, with the steel slag ratio increasing from 20% to 60% and the slag ratio decreasing from 60% to 20%. Five groups of foamed concrete with a density of 800 kg m −3 were prepared. The change in intensity is depicted in figure 3. The strength test was conducted according to 'JG/T266-2011 Foam Concrete'. The sample size was 100 * 100 * 100 mm, and the curing time was 28 d.    The compressive strength of foamed concrete decreases with the increase of steel slag content, as shown in figure 3. This anomaly is mainly attributed to the slow hydration of steel slag and low early activity, which can be well verified by SEM tests (as shown in figure 4), and the dissolution of alumino-silicate mineral produce featureless microstructure [23]. The steel slag does not produce many crystals during the hydration, so the enhancement effect is not clearly reflected. When the content of steel slag increases from 20% to 60%, the compressive strength of foamed concrete decreases from 1.98 MPa to 0.59 MPa, with a decrease rate of 70%. When the content of steel slag is 30%, the compressive strength is only reduced by 6%. When the content of steel slag exceeds 30%, the strength of foamed concrete decreases significantly. The root cause is that the hydration of steel slag slows down with the increase in slag content.
3.1.2. Pore structure analysis at various steel slag ratios It can be seen from figure 5 that when the content of steel slag gradually increases from 20% to 60%, the roundness factor of the pores is 0-1.6, and the proportion of pores with a roundness factor in this range first increases and then decreases. When the content of steel slag is 30%, the pores with a roundness factor of 0-3.6 constitute the largest group, accounting for 92.3%, and the pores with a roundness factor greater than 3.6 account for 7.7%.
As shown in figure 6, the average pore size of steel slag foam concrete is mainly 0-400 μm, regardless of the steel slag content. Pores with a diameter of 400-800 μm constitute the second largest group. When steel slag content is 20%, the pores with a diameter of 0-400 μm account for at least 67.21%, and when steel slag content is 30%, the pores with a diameter of 0-400um account for 74.95%.
As can be seen from figures 5 and 6, the steel slag content has a great impact on the roundness factor and the mean pore diameter. The roundness factor shows a trend of decreasing first and then increasing. The fundamental reason is that steel slag and slag promote reciprocal hydration, which improves the pore structure. The density of steel slag is higher than that of other materials, and more aluminum powder is required to attain the same density level, resulting in more bubbles, a larger probability of mutual fusion between bubbles, and a higher proportion of macropores. It can be concluded that the ideal steel slag content is 30% to satisfy the  strength and pore structure requirements of foamed concrete. The current widely-accepted steel slag ratio is 20%-25% [24], indicating that the steel slag has a high utilization rate.

Compressive strength and pore structure at various density levels 3.2.1. Compressive strength analysis at various density levels
In this paper, the steel slag content was determined as 30% for compressive strength analysis at various density levels. Four groups of specimens with a density of 600 kg m −3 to 900 kg m −3 were fabricated according to the benchmark ratio and preparation procedure. The results are shown in figure 7. The compressive strength of steel slag foamed concrete gradually increases when the density class increases, as shown in figure 7.

Pore structure analysis at various density levels
In this paper, the steel slag foam concrete density was adjusted from 600 to 900 kg m −3 by changing the aluminum powder ratio. The pore diameter and pore roundness factor distribution of steel slag foamed concrete at various density levels are shown in figure 8 and figure 9.
The proportion of pores with a diameter exceeding 1200 μm at the density level of 600 kg m −3 can reach 7.81%, as shown in figure 8. The foam concrete with a density of 900 kg m −3 had the lowest proportion (4.33%)  of pores with a diameter above 1200 μm. With the increase in the density level, the proportion of pores with a diameter larger than 1200 μm drops; the proportion of pores with a diameter below 400 μm increases. Due to the low cementitious material content and high porosity of low-density foam concrete, the pore walls are thinner; the pores are easily broken during the stirring, pouring, and hardening processes, and small pores will combine to form bigger pores. As a result, the fraction of pores exceeding 1200 μm in low-density foamed concrete specimens is much higher than that in high-density specimens.
As shown in figure 9, when the density grade is 600 kg m −3 , the proportion of irregular pores is 7.75%; when the density grade is 900 kg m −3 , the proportion decreases to 2.39%. It can be concluded that the proportion of irregular pores decreases with the increase in density level. This is because the number of pores in low-density samples is much higher. The gas pressure in the pore, according to the Laplace formula, is [25]: where P a denotes ambient pressure, s denotes slurry viscosity, and r denotes pore radius. A larger pore radius indicates a smaller gas pressure in the pore and a higher density of the steel slag. The gravity of steel slag and slag is larger than the gas pressure in the pore during the gas generation process, which leads to the squeeze of the pore and makes it irregular-shaped rather than ball-shaped.   It can be seen that the stirring time has a certain influence on the strength of the sample. The root cause is that the stirring time affects the internal pore structure of the steel slag foam concrete, such as the pore size distribution and pore morphology. If the stirring time is too short, the slurry may not be evenly mixed; many pores will accumulate in the lower section of the slurry and will be crushed by the steel slag. The flat structure of the pores causes stress concentration during the compressive strength test, resulting in a low measurement value.   As shown in figure 11, the proportion of pores with a roundness factor of 0.8-1.2 is not more than 36%, whereas the pores with irregular morphologies account for as high as 64%. This is because the gravitational pull of the steel slag is greater than the gas pressure in the pores during the gas generation process, causing the squeeze of the pores and making them flat. The proportion of pores with a roundness factor of 0.8-1.2 is up to 35.33% after 35-s stirring, with an increase of 8.77% compared to that after 15-s stirring. The proportion of pores with a roundness factor of 0.8-1.2 after 45-s stirring is 4.43% lower than that after 35-s stirring. If the mixing period is too short, the slurry cannot be evenly stirred; more pores are dispersed in the lower section of the slurry and will be compressed by the steel slag. In this case, the stress is concentrated, which will lead to a low measurement value of the compressive strength. With the extension of stirring time, this problem can be gradually relieved. However, when the stirring time is increased from 35 s to 45 s, the compressive strength steadily falls. The reason is that in the situation where the stirring time is too long, the damage rate increases owing to the direct extrusion, the fraction of circular pores is excessively small, and the possibility of stress concentration increases. These results suggest that an appropriate stirring duration should be determined in the experiment, which can improve pore morphology. A larger fraction of pores with a roundness factor of 0.8-1.2 indicates higher circularity of the pores and larger compressive strength.
As shown in figure 12, the pore diameter of steel slag foam concrete is largely 0-400 μm, and the stirring time has a minimal effect on it. The strength is the lowest and highest when the stirring time is 15 s and 35 s, respectively. The pores with a diameter of 0-400 μm account for 68.76% when the stirring duration is 15 s, and account for 78.42% when the stirring time is 35 s. The compressive strength increases as the pore diameter decreases. It can be summarized that the pore structure is optimal when the stirring time is 35 s.

Prediction model of pore structure of steel slag foam concrete based on BP neural network
The pore structure of foamed concrete has a significant impact on its frost resistance [26][27][28], permeability [29][30][31], and thermal stability [32][33][34]. Pore structure prediction can provide a reference for the application of foamed concrete. However, the prediction is difficult because the pore structure is affected by many variables, such as the steel slag ratio, density, manufacturing technique, and curing period. A universally-recognized prediction formula should be constructed based on the BP neural network. In theory, the pore structure can be anticipated as long as the structure and parameters of the neural network are appropriate and a certain degree of network training is possible. In spite of the theoretical feasibility, the pore structure of foamed concrete has rarely been predicted based on BP neural network. In this paper, a prediction model based on the BP neural network is established to predict steel slag foamed concrete pore structure.

Samples for training and testing
The average pore diameter and average roundness factor were calculated to characterize the pore structure of steel slag foam concrete, and they were used as output parameters of the neural network. The calculation formulas are as follows.
The density level in this experiment is 600 kg m −3 -900 kg m −3 in order to ensure thorough alterations in the pore structure. Twelve sets of experimental data were obtained, as shown in table 3. Two sets were randomly selected as control samples, and the remaining ten sets were used as training samples. The density level and steel slag content were regarded as input parameters to ensure that the distribution of the pore structure could be clearly observed.
As shown in table 4, as the density level increases, the average pore diameter of steel slag foamed concrete drops, and the pores tend to be round. The average pore diameter and average pore roundness factor are the smallest when the steel slag content is 30%.

Design of BP neural network
The number of hidden layer nodes in a BP neural network has a significant impact on the model's prediction performance. In this study, the hidden layer was chosen based on the formula below [35].
The number of nodes in the input layer is n, the number of nodes in the output layer is m, and the constant a is between 0 and 10. A BP neural network prediction model of steel slag foamed concrete pore structure with two input nodes, 12 hidden layers, and two output nodes was developed by experimental simulation. The topological structure of the BP neural network model is shown in figure 13.
In order to avoid the large differences in the order of magnitude of the input values, the normalization function was introduced. Through normalization, the data can respond to its characteristics more effectively after the activation function is added. In this paper, the normalization function mapminmax in MATLAB was used for data processing. Its formula is shown below. where y min and y max represent the minimum and maximum output values, respectively; x min and x max indicate the minimum and maximum input values, respectively. By the normalization function, the minimum and maximum input and output values were normalized to [−1,1]. Only the prediction results obtained after normalization processing can be counternormalized to obtain the actual predicted thermal conductivity of foam concrete.

Neural network model training
Traingdm was used for network training [36], and the hyperbolic tangent sigmoid activation function was applied for the hidden layer node. Purelin was used for the output layer. The training parameters are as follows: error target Goal is 0.001; maximum training error number Epochs is 100000; learning rate Ir is 0.01, and other training parameters are default values in MATLAB neural network toolbox. The error curves of the training process are shown in figure 14. As shown in figure 14, when the number of training steps is 13,705, the minimum training error is 11.468%. Figure 15 shows the network regression analysis of the standard gradient descent algorithm. The comprehensive regression coefficient is R = 0.88944. A value closer to 1 mean indicates better regression and higher prediction accuracy.

Analysis of prediction results
The error parameters provided by the neural network can be satisfied by network training when the number of training steps is 13,705. Using the constructed and trained BP neural network model, the predicted average pore size and average roundness factor were obtained based on the two input parameters, namely, steel slag content and density. The predicted data were compared with the actual values. The prediction results and errors are as follows.
As shown in table 5, the prediction error of the BP neural network is small; the error in the average pore diameter is less than 8.5%, and the error in the average roundness factor is less than 5%. It can be summarized that the prediction of the average roundness factor by the BP neural network is more accurate than the prediction of the average pore diameter. It can be further concluded that the relationship of the pore roundness factor with density grade and steel slag content is closer than the relationship of average pore diameter with the two input parameters. The reason for the larger prediction error in average pore diameter may be that the training samples in the model are limited.
The small prediction errors suggest that it is feasible to predict the average pore diameter and average pore roundness of the steel slag foam concrete based on the steel slag content and density level by the BP neural network. The mesostructure of concrete and the intricate internal rules of macro components, however, cannot be described due to the limited training samples. Even though network learning is powerful, prediction errors cannot be avoided.