Pozzolanic concrete has superior properties, such as high strength and workability. The precise proportioning and modeling of the concrete mixture are important when considering its applications. There have been many efforts to develop computeraided approaches for pozzolanic concrete mix design, such as artificial neural network (ANN) based approaches, but these approaches have proven to be somewhat difficult in practical engineering applications. This study develops a twostep computeraided approach for pozzolanic concrete mix design. The first step is establishing a dataset of pozzolanic concrete mixture proportioning which conforms to American Concrete Institute code, consisting of experimental data collected from the literature as well as numerical data generated by computer program. In this step, ANNs are employed to establish the prediction models of compressive strength and the slump of the concrete. Sensitivity analysis of the ANN is used to evaluate the effect of inputs on the output of the ANN. The two ANN models are tested using data of experimental specimens made in laboratory for twelve different mixtures. The second step is classifying the dataset of pozzolanic concrete mixture proportioning. A classification method is utilized to categorize the dataset into 360 classes based on compressive strength, pozzolanic admixture replacement rate, and material cost. Thus, one can easily obtain mix solutions based on these factors. The results show that the proposed computeraided approach is convenient for pozzolanic concrete mix design and practical for engineering applications.
Concrete plays an important role in the growing construction industry. Presently, various types of byproduct materials, such as fly ash, silica fume, rice husk ash, and others have been widely used as pozzolanic materials in concrete. Studies [
Several researchers have looked into the characteristic parameters that affect the compressive strength and slump of conventional and highstrength concrete [
Artificial neural networks (ANNs) were originally developed to simulate the function of the human brain or neural system. Subsequently, they have been widely applied to diverse fields, ranging from biology to many engineering fields. ANNs exhibit a number of desirable properties not found in conventional symbolic computation systems, including robust performance when dealing with noisy or incomplete input patterns, a high degree of fault tolerance, high parallel computation rates, the ability to generalize, and adaptive learning [
In light of the above developments, this study develops a twostep computeraided approach for pozzolanic concrete mix design. The first step is establishing the dataset of pozzolanic concrete mixture proportioning which conform to American Concrete Institute (ACI) code. The dataset consists of experimental data collected from the literature and numerical data generated by computer program. In this step, ANNs are employed to establish the prediction models of compressive strength and slump of concrete. Sensitivity analysis of the ANN is used to evaluate the effect of inputs on the output of the ANN. The two ANN models are tested using data of experimental specimens made in laboratory for twelve different mixtures. The second step is classifying the dataset of pozzolanic concrete mixture proportioning. A classification method is utilized to categorize the dataset into 360 classes based on compressive strength of concrete, pozzolanic admixture replacement rate, and cost of the concrete.
ANNs form a class of systems that are inspired by biological neural networks. The topology of an ANN model consists of a number of simple processing elements, called nodes, which are interconnected to each other. Interconnection weights that represent the information stored in the system are used to quantify the strength of the interconnections; these weights hold the key to the functioning of an ANN.
Among the many different types of ANN, by far the most commonly applied neural network learning model, due to its simplicity, is the feedforward, multilayered, supervised neural network with error backpropagation algorithm, the socalled backpropagation (BP) network [
The second stage is error backpropagation and adjustment of the network weights. The training process applies mean square error (
Hung and Lin [
Instead of forming the matrix
The search direction is given by
The step length,
The problem of selecting a learning ratio through trial and error in the BP algorithm is thus circumvented in the adaptive LBFGS learning algorithm.
The ANN models, compressive strength prediction neural network (CSPNN) and slump prediction neural network (SPNN), are used in this study for prediction of the 28day compressive strength (abbreviated below as compressive strength) and slump of pozzolanic concrete, respectively. The architectures of the CSPNN and SPNN are illustrated in Figure
The architectures of (a) CSPNN and (b) SPNN.
Range of input parameters of CSPNN and SPNN in dataset.
Input parameters  Range (kg/m^{3}) 

Water  125 ≤ Water ≤ 240 
Cement  110 ≤ Cement ≤ 500 
GGBFS  0 ≤ GGBFS ≤ 300 
Fly ash  0 ≤ fly ash ≤ 300 
CA  CA ≥ 450 
FA  FA ≥ 450 
SP  SP < 2% (cement + pozzolanic admixtures) 
Cybenko [
If there is a network with
The firstorder partial derivative of the
This study develops a computeraided approach for pozzolanic concrete mix design. This approach is suitable for designing a mix of pozzolanic concrete with compressive strength,
Schematic diagram of the proposed approach for pozzolanic concrete mix design.
As shown in Figure
Collecting experimental data of pozzolanic concrete mixture proportioning from the literature [
Generating numerical data of pozzolanic concrete mixture proportioning since the collected experimental data may be insufficient. Before generating numerical data, the ranges of material contents (as listed in Table
Using a portion of collected experimental data of pozzolanic concrete mixture proportioning to train CSPNN and SPNN. The effect of input parameters on the output is evaluated by sensitivity analysis. The prediction accuracy of CSPNN and SPNN is tested using the remainder of the collected experimental data and data from experimental specimens made in our laboratory for twelve different mixtures.
Using trained CSPNN and SPNN to predict compressive strength and slump of experimental and numerical data, respectively. Data that satisfy the following conditions are kept in the dataset.
Cementitious materials requirements for concrete exposed to deicing chemicals “Table 2 is reproduced from Kosmatka et al. [
Cementitious materials  Maximum percent of total cementitious materials by mass 

Fly ash and natural pozzolans  25 
Slag  50 
Silica fume  10 
Total of fly ash, slag, silica fume, and natural pozzolans  50 
Total of natural pozzolans and silica fume  35 
Approximate mixing water and target air content requirements for different slumps and nominal maximum sizes of aggregate “Table 3 is reproduced from Kosmatka et al. [
Slump (mm) or air content  Water, kilograms per cubic meter of concrete, for indicated sizes of aggregate (kg/m^{3})  

9.5 mm  12.5 mm  19 mm  25 mm  37.5 mm  50 mm  75 mm  150 mm  
Nonairentrained concrete  
25 to 50  207  199  190  179  166  154  130  113 
75 to 100  228  216  205  193  181  169  145  124 
150 to 175  243  228  216  202  190  178  160  – 
Approximate amount of entrapped air in nonairentrained concrete (%)  3  2.5  2  1.5  1  0.5  0.3  0.2 


Airentrained concrete  
25 to 50  181  175  168  160  150  142  122  107 
75 to 100  202  193  184  175  165  157  133  119 
150 to 175  216  205  197  184  174  166  154  – 
Recommended average total air content, percent, for level of exposure:  
Mild exposure  4.5  4.0  3.5  3.0  2.5  2.0  1.5  1.0 
Moderate exposure  6.0  5.5  5.0  4.5  4.5  4.0  3.5  3.0 
Severe exposure  7.5  7.0  6.0  6.0  5.5  5.0  4.5  4.0 
Bulk volume of coarse aggregate per unit volume of concrete “Table 4 is reproduced from Kosmatka et al. [
Nominal maximum size of aggregate (mm)  Bulk volume of dryrodded coarse aggregate per unit volume of concrete for different fineness moduli of fine aggregate  

2.40  2.60  2.80  3.00  
9.5  0.50  0.48  0.46  0.44 
12.5  0.59  0.57  0.55  0.53 
19  0.66  0.64  0.62  0.60 
25  0.71  0.69  0.67  0.65 
37.5  0.75  0.73  0.71  0.69 
50  0.78  0.76  0.74  0.72 
75  0.82  0.80  0.78  0.76 
150  0.87  0.80  0.83  0.81 
Relationship between water to cementitious material ratio and compressive strength of concrete “Table 5 is reproduced from Kosmatka et al. [
Compressive strength at 28 days (MPa)  Watercementitious materials ratio (by mass)  

Nonairentrained concrete  Airentrained concrete  
45  0.38  0.30 
40  0.42  0.34 
35  0.47  0.39 
30  0.54  0.45 
25  0.61  0.52 
20  0.69  0.60 
15  0.79  0.70 
Maximum watercementitious material ratios and minimum design strengths for various exposure conditions “Table 6 is reproduced from Kosmatka et al. [
Exposure condition  Maximum watercementitious material ratio by mass for concrete  Minimum design compressive strength, 

Concrete protected from exposure to freezing and thawing, application of deicing chemicals, or aggressive substances  Select watercementitious material ratio on basis of strength, workability, and finishing needs  Select strength based on structural requirements 
Concrete intended to have low permeability when exposed to water  0.50  28 
Concrete exposed to freezing and thawing in a moist condition or deicers  0.45  31 
For corrosion protection for reinforced concrete exposed to chlorides from deicing salts, salt water, brackish water, sea water, or spray from these sources  0.40  35 
Recommended slumps for various types of construction “Table 7 is reproduced from Kosmatka et al. [
Concrete construction  Slump (mm)  

Maximum  Minimum  
Reinforced foundation walls and footings  75  25 
Plain footings, caissons, and substructure walls  75  25 
Beams and reinforced walls  100  25 
Building columns  100  25 
Pavements and slabs  75  25 
Mass concrete  75  25 
Requirements for concrete exposed to sulfates in soil or water “Table 8 is reproduced from Kosmatka et al. [
Sulfate exposure  Watersoluble sulfate (SO_{4}) in soil, percent by mass  Sulfate (SO_{4}) in water, ppm  Cement type  Maximum watercementitious material ratio, by mass  Minimum design compressive strength, 

Negligible  Less than 0.10  Less than 150  No special type required  –  – 
Moderate  0.10 to 0.20  150 to 1500  II, MS, IP(MS), IS(MS), P(MS), I(PM) (MS), I(SM) (MS)  0.50  28 
Severe  0.20 to 2.00  1500 to 10,000  V, HS  0.45  31 
Very severe  Over 2.00  Over 10,000  V, HS  0.40  35 
The flow chart of ACI mix design method.
To produce a dataset of pozzolanic concrete mixture proportioning which is more feasible and convenient for engineering applications, it is classified further.
In classification, a sampling unit (subject or object) whose class membership is unknown is assigned to a class on the basis of the vector,
The proposed classification of the dataset of pozzolanic concrete mixture proportioning is according to compressive strength, pozzolanic admixture replacement rate, and cost. As shown in Figure
The second stage is the classification of dataset according to pozzolanic admixtures replacement rate. Pozzolanic admixtures may be used as a partial replacement of cement in concrete. The pozzolanic admixtures used in this study are fly ash and ground granulated blast furnace slag. Pozzolanic admixture replacement rate,
The third stage is the classification of dataset according to the cost of pozzolanic concrete. Each class in the second stage is divided into six smaller classes. The class intervals of the cost of pozzolanic concrete are 0 (NTD/m^{3})–≤2000 (NTD/m^{3}), >2000 (NTD/m^{3})–≤2250 (NTD/m^{3}), >2250 (NTD/m^{3})–≤2500 (NTD/m^{3}), >2500 (NTD/m^{3})–≤2750 (NTD/m^{3}), >2750 (NTD/m^{3})–≤3000 (NTD/m^{3}), and >3000 (NTD/m^{3}). There are 360 classes overall in the dataset of pozzolanic concrete mixture proportioning.
All 482 samples collected were used to train and test the CSPNN. Among the 482 samples, 462 and 20 samples were used to train and test CSPNN, respectively. Here, the CSPNN is constructed with seven, fourteen, and one nodes in input layer, hidden layer, and output layer, respectively, and denoted as CSPNN(7141). The complete offline training process took 47 cycles. The
Comparison of exact compressive strength with CSPNNpredicted compressive strength for the 20 testing samples.
No. of sample  Exact compressive strength ( 
Predicted compressive strength ( 


1  57.67  54.93  2.74 
2  67.06  58.74  8.32 
3  54.90  51.92  2.98 
4  41.67  41.12  0.54 
5  57.45  58.72  −1.27 
6  51.08  52.51  −1.43 
7  60.70  62.97  −2.27 
8  44.70  38.17  6.53 
9  24.20  16.85  7.35 
10  46.14  54.93  −8.79 
11  44.62  40.39  4.23 
12  40.80  44.19  −3.39 
13  25.00  30.28  −5.28 
14  57.00  59.32  −2.32 
15  77.00  70.62  6.38 
16  69.00  65.30  3.70 
17  64.00  57.01  6.99 
18  84.30  85.01  −0.71 
19  78.10  75.91  2.19 
20  59.00  59.52  −0.52 
Performance of the 20 testing compressive strength samples.
Figure
Distribution of compressive strength and water for the training samples of the CSPNN.
Distribution of water and the firstorder partial derivative of compressive strength with respect to water for the training samples of the CSPNN.
Figure
Distribution of compressive strength and cement for the training samples of the CSPNN.
Distribution of cement and the firstorder partial derivative of compressive strength with respect to cement for the training samples of the CSPNN.
Figure
Distribution of compressive strength and SP for the training samples of the CSPNN.
Distribution of SP and the firstorder partial derivative of compressive strength with respect to SP for the training samples of the CSPNN.
As mentioned, only 295 samples have slump data among the total of 482 collected samples. Therefore, 295 samples were used to train and test the SPNN. Among the 295 samples, 285 and 10 samples were used to train and test SPNN, respectively. Here, the SPNN is constructed with seven, six, and one nodes in the input layer, hidden layer, and output layer, respectively, and is denoted as SPNN(761). The complete offline training process took 31 cycles. The
Comparison of exact slump with SPNNpredicted slump for the 10 testing samples.
No. of sample  Exact slump ( 
Predicted slump ( 


1  23.0  19.9  3.1 
2  20.0  17.6  2.4 
3  23.5  24.6  −1.1 
4  27.0  27.2  −0.2 
5  13.5  16.1  −2.6 
6  11.5  11.5  0.0 
7  22.0  22.4  −0.4 
8  26.5  25.9  0.6 
9  26.0  22.8  3.2 
10  19.0  21.1  −2.1 
Performance of the 10 testing slump samples.
Figure
Distribution of slump and SP for the training samples of the SPNN.
Distribution of SP and the firstorder partial derivative of slump with respect to SP for the training samples of the SPNN.
Experimental specimens were also made in the laboratory to study the prediction accuracy of the CSPNN and SPNN in terms of pozzolanic concrete conforming to the ACI concrete mixture code. Twelve concrete mixtures (listed in Table
Twelve experimental concrete mixtures and their exact and predicted compressive strength and slump.
No. of concrete mix  Water (kg/m^{3})  Cement (kg/m^{3})  Fly ash (kg/m^{3})  GGBFS (kg/m^{3})  CA (kg/m^{3})  FA (kg/m^{3})  SP (kg/m^{3})  Exact compressive strength ( 
Predicted compressive strength ( 

Exact slump ( 
Predicted slump ( 


1  194  223  72  76  1040  669  0.74  44.10  34.32  9.77  19.0  19.0  0.0 
2  184  244  19  105  1104  649  0.79  47.99  32.26  15.73  20.0  18.5  1.5 
3  187  194  22  171  1072  650  0.81  49.75  34.85  14.90  20.0  19.0  1.0 
4  189  272  14  121  1040  670  0.70  52.87  35.60  17.27  20.0  19.2  0.8 
5  191  346  41  38  1136  549  0.73  46.70  45.96  0.74  20.0  16.9  3.1 
6  189  261  57  93  1072  619  0.88  47.06  39.04  8.02  20.0  18.7  1.3 
7  204  331  54  99  1136  457  0.77  54.52  54.55  0.03  18.0  14.1  3.9 
8  191  280  46  121  1104  555  0.68  47.61  50.16  2.55  19.5  17.2  2.3 
9  210  300  51  131  1040  535  0.54  46.06  52.05  5.99  20.5  16.7  3.8 
10  207  430  61  20  960  604  0.76  54.30  40.08  14.22  21.0  19.1  1.9 
11  190  329  52  112  1104  516  0.87  54.98  55.07  0.09  19.0  17.2  1.8 
12  208  351  121  52  960  554  0.72  55.13  40.91  14.22  21.5  14.1  7.4 
Figure
Comparison of exact compressive strength with CSPNNpredicted compressive strength for the 12 experimental concrete mixtures.
Figure
Comparison of exact slump with SPNNpredicted slump for the 12 experimental concrete mixtures.
The trained and tested CSPNN and SPNN represent accurate models for compressive strength and slump, respectively, and they were used to predict compressive strength and slump of experimental and numerical data. Among 1500 experimental and numerical data, 278 data satisfy Equation (
After establishing the dataset of pozzolanic concrete mixture proportioning, it was classified further according to compressive strength, pozzolanic admixture replacement rate, and cost of concrete. Tables
Concrete mixture proportioning samples for compressive strength = 210 kg/cm^{2} and cost ≤2000 NTD/m^{3}.
Waterbinder ratio  Water (kg/m^{3})  Cement (kg/m^{3})  Fly ash (kg/m^{3})  GGBFS (kg/m^{3})  CA (kg/m^{3})  FA (kg/m^{3})  SP (kg/m^{3}) 


Cost (NTD/m^{3}) 


0.55  199  337  20  6  704  991  0.74  23.80  20.4  1952  7.16 
0.55  192  244  65  41  1024  703  2.26  23.45  23.0  1858  30.29 
0.48  177  221  39  106  1136  629  3.58  21.55  22.9  1971  39.62 
0.52  186  195  72  92  1056  671  2.67  23.87  23.3  1826  45.68 
Concrete mixture proportioning samples for compressive strength = 700 kg/cm^{2} and 2000 NTD/m^{3} < cost ≤ 2250 NTD/m^{3}.
Waterbinder ratio  Water (kg/m^{3})  Cement (kg/m^{3})  Fly ash (kg/m^{3})  GGBFS (kg/m^{3})  CA (kg/m^{3})  FA (kg/m^{3})  SP (kg/m^{3}) 


Cost (NTD/m^{3}) 


0.34  134  292  3  103  1104  763  2.43  71.16  22.2  2137  26.63 
0.30  145  281  97  101  1056  673  0.90  71.17  22.5  2013  41.34 
0.33  144  232  36  173  736  1009  3.56  68.25  23.4  2127  47.39 
0.32  157  253  3  239  1056  648  0.73  65.67  21.5  2065  48.89 
0.28  175  322  131  183  944  542  1.46  69.62  18.0  2213  49.37 
This study develops a twostep computeraided approach for pozzolanic concrete mix design. The first step is to establish a dataset of pozzolanic concrete mixture proportioning that conforms to ACI code. In this step, ANNs are employed to establish the prediction models of compressive strength and slump of concrete. The second step is to classify the dataset of pozzolanic concrete mixture proportioning. A classification method is utilized to categorize the dataset into 360 classes based on compressive strength of concrete, pozzolanic admixture replacement rate, and material cost. The following important conclusions are drawn from the results:
The CSPNN and SPNN were trained using a portion of collected experimental data. After training, the CSPNN and SPNN were tested using the rest of collected experimental data and data of experimental specimens made in our laboratory for twelve different mixtures. Results prove that CSPNN and SPNN can satisfactorily predict compressive strength and slump, respectively, from respective amounts of water, cement, ground granulated blast furnace slag, fly ash, coarse aggregate, fine aggregate, and superplasticizer.
Sensitivity analysis of the ANN can be used to explore the cause and effect relationship between network input and output. Therefore, sensitivity analysis of the CSPNN and SPNN, respectively, can be used to evaluate the effect of various concrete mix constituents (water, cement, ground granulated blast furnace slag, fly ash, coarse aggregate, fine aggregate, and superplasticizer) on the compressive strength and slump of concrete.
The distribution of slump and SP for the training samples of the SPNN shows that slump increases with an increase in the amount of SP in the concrete mixture. Slump is proportional to SP, and the slope of the fitted simple regression line is a positive value (0.6246). However, the mean of the firstorder partial derivative of slump with respect to SP for the training samples of the SPNN is a negative value (−0.146). The negative mean value of the firstorder partial derivative of slump with respect to SP indicates negative correlation between slump and SP, which is inconsistent with the positive slope value of the fitted simple regression line. The reason for this may be that SP is a material with larger variance and the properties of different brands of SP are different.
To construct a dataset of pozzolanic concrete mixture proportioning which is practical and convenient for engineering applications, it is classified further. Engineers can utilize the classified dataset to easily predict mix proportioning from required compressive strength of concrete, pozzolanic admixture replacement rate, and the necessary cost of concrete.
Artificial neural network
American Concrete Institute
Broyden–Fletcher–Goldfarb–Shanno method
Backpropagation network
Coarse aggregate
The class the
Compressive strength prediction neural network
Search direction
The firstorder partial derivative of the
The mean of
The desired output of the
The Euclidean distance between two vectors (points)
The Euclidean distance between the vector associate to the
Mean square error
The activation function
Fine aggregate
Compressive strength
Compressive strength predicted by CSPNN
Mean (designed) compressive strength of the
Compressive strength of the
Ground granulated blast furnace slag
The inverse Hessian matrix
The output of the
Limited memory Broyden–Fletcher–Goldfarb–Shanno
The output of
The calculated output of the
The number of instances in the training set
Pozzolanic admixtures
The absolute fraction of variance
Admixture replacement rate
Slump
The mean (designed) slump of the
The slump of the
Slump predicted by SPNN
Superplasticizer
Slump prediction neural network
Sum of the squares error
The weight associated with the
The weight associated with the
The weight associated with the
The weight associated with the
The threshold value of node
The threshold value of the
Learning ratio
Step length.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.