Abstract
The primary objective of this paper is to develop an appropriate predictive formula for the compressive strength of pervious concrete, which depends on its mixture. This will allow for the improvement of the proportioning procedure that considers both the target porosity and target compressive strength. To achieve this, an effective computational strategy is first constructed and investigated for the creation of simple and easily applicable symbolic regression functions within the Genetic Programming-based Symbolic Regression framework. Recent advancements in fast logical parallelism and model-based algorithms are also applied to perform calculations on a large quantity of examples, with the aim of finding the most suitable analytical solutions at a low computational cost. Next, to assess the effectiveness of this model in predicting the compressive strength of concrete in general, computations are carried out using the well-known Yeh's dataset on conventional concrete compressive strength. This dataset has been extensively studied using both "black-box" and "white-box" machine learning algorithms. The results reveal that more suitable formulas can be generated through this computational process, compared to several scenarios discussed in the literature. Furthermore, the model is extended to pervious concrete, based on the dataset of 164 samples of 28-day compressive strength collected from 14 different sources. The findings for pervious concrete exhibited high accuracy compared to the most effective black-box models and micromechanical/empirical models, with a coefficient of determination of approximately 0.9 for simple predictive equations, thereby supporting the effectiveness of the proposed approach.
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This research is funded by Ministry of Education and Training under Grand Number B2023-XDA-03.
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Appendix
Appendix
The data for pervious concrete is available and attached to the paper.
No. | Sand mass | Minimum coarse aggregate size | Water-to-cement ratio | aggregate-to cement ratio | Effective porosity | compressive strength | Reference |
|---|---|---|---|---|---|---|---|
Unit | kg/m3 | mm | – | – | % | MPa | |
Notation | MS | AS | WC | AC | EP | CS | |
1 | 340 | 4.75 | 0.3 | 3.35 | 20.44 | 14.1 | [43] |
2 | 340 | 4.75 | 0.3 | 3.63 | 21.42 | 15 | |
3 | 340 | 4.75 | 0.3 | 3.92 | 21.98 | 15 | |
4 | 340 | 4.75 | 0.3 | 4.06 | 22.23 | 16.3 | |
5 | 340 | 4.75 | 0.3 | 4.2 | 22.42 | 18.4 | |
6 | 340 | 4.75 | 0.3 | 4.48 | 22.51 | 18 | |
7 | 340 | 4.75 | 0.3 | 4.76 | 22.77 | 17.2 | |
8 | 0 | 4.75 | 0.33 | 4.99 | 34 | 3.9 | [44] |
9 | 0 | 4.75 | 0.33 | 4.99 | 31.5 | 4.5 | |
10 | 0 | 4.75 | 0.31 | 5.56 | 25.7 | 10.9 | [45] |
11 | 0 | 2.36 | 0.31 | 5.56 | 25.6 | 15.2 | |
12 | 0 | 2.36 | 0.31 | 5.56 | 24.7 | 16.5 | |
13 | 0 | 2.36 | 0.31 | 5.56 | 25.1 | 13.5 | |
14 | 0 | 4.75 | 0.31 | 5 | 25.1 | 13.9 | |
15 | 0 | 2.36 | 0.31 | 5 | 23.7 | 16.3 | |
16 | 0 | 2.36 | 0.31 | 5 | 23.1 | 17.9 | |
17 | 0 | 2.36 | 0.31 | 5 | 24.2 | 19.7 | |
18 | 0 | 4.75 | 0.31 | 4.55 | 23.9 | 19.1 | |
19 | 0 | 2.36 | 0.31 | 4.55 | 22.4 | 20.1 | |
20 | 0 | 2.36 | 0.31 | 4.55 | 23.1 | 21.6 | |
21 | 0 | 2.36 | 0.31 | 4.55 | 24.3 | 22.2 | |
22 | 0 | 4.75 | 0.31 | 4.17 | 22.5 | 18.1 | |
23 | 0 | 2.36 | 0.31 | 4.17 | 21.2 | 19.3 | |
24 | 0 | 2.36 | 0.31 | 4.17 | 20.5 | 21.5 | |
25 | 0 | 2.36 | 0.31 | 4.17 | 21.3 | 20.4 | |
26 | 0 | 4.75 | 0.31 | 3.85 | 20.3 | 14.7 | |
27 | 0 | 2.36 | 0.31 | 3.85 | 20.2 | 16.6 | |
28 | 0 | 2.36 | 0.31 | 3.85 | 19.9 | 19.5 | |
29 | 0 | 2.36 | 0.31 | 3.85 | 18.7 | 18.2 | |
30 | 0 | 2.36 | 0.31 | 4.55 | 23.3 | 22.2 | |
31 | 0 | 2.36 | 0.31 | 3.7 | 17.9 | 25.2 | [47] |
32 | 0 | 2.36 | 0.31 | 4 | 18.7 | 24.7 | |
33 | 0 | 2.36 | 0.31 | 4.35 | 21.1 | 19.4 | |
34 | 0 | 4.75 | 0.31 | 4.35 | 21.7 | 27.6 | |
35 | 0 | 4.75 | 0.31 | 4.76 | 24 | 24.1 | |
36 | 0 | 4.75 | 0.31 | 5.27 | 27.3 | 20.3 | |
37 | 0 | 4.8 | 0.35 | 3.7 | 18.64 | 19.73 | [46] |
38 | 0 | 4.8 | 0.35 | 2.88 | 9.2 | 24.72 | |
39 | 0 | 4.8 | 0.35 | 3.74 | 16.41 | 19.38 | |
40 | 0 | 4.8 | 0.35 | 2.91 | 8.45 | 26.73 | |
41 | 0 | 4.8 | 0.22 | 2.32 | 21.31 | 10.02 | |
42 | 0 | 6.3 | 0.35 | 3.31 | 14.8 | 17.3 | [42] |
43 | 0 | 8 | 0.35 | 3.3 | 15.6 | 15.3 | |
44 | 0 | 10 | 0.35 | 3.3 | 17.8 | 13.5 | |
45 | 0 | 12.5 | 0.35 | 3.3 | 19.5 | 11 | |
46 | 0 | 1.19 | 0.45 | 2.5 | 16.28 | 23.4 | [41] |
47 | 0 | 1.19 | 0.45 | 3 | 24.16 | 14.4 | |
48 | 0 | 1.19 | 0.45 | 3.5 | 28.37 | 10.6 | |
49 | 0 | 2.38 | 0.45 | 2.5 | 17.05 | 22.9 | |
50 | 0 | 2.38 | 0.45 | 3 | 24.56 | 12.9 | |
51 | 0 | 2.38 | 0.45 | 3.5 | 29.41 | 8.6 | |
52 | 0 | 4.75 | 0.45 | 2.5 | 20.4 | 18.1 | |
53 | 0 | 4.75 | 0.45 | 3 | 25.82 | 11.3 | |
54 | 0 | 4.75 | 0.45 | 3.5 | 29.57 | 9.1 | |
55 | 0 | 1.19 | 0.55 | 2.5 | 13.63 | 23.2 | |
56 | 0 | 1.19 | 0.55 | 3 | 23.88 | 12.4 | |
57 | 0 | 1.19 | 0.55 | 3.5 | 29.11 | 8.4 | |
58 | 0 | 2.38 | 0.55 | 2.5 | 18.75 | 17.6 | |
59 | 0 | 2.38 | 0.55 | 3 | 24.9 | 11.5 | |
60 | 0 | 2.38 | 0.55 | 3.5 | 29.59 | 7.5 | |
61 | 0 | 4.75 | 0.55 | 2.5 | 20.49 | 16 | |
62 | 0 | 4.75 | 0.55 | 3 | 25.89 | 10.5 | |
63 | 0 | 4.75 | 0.55 | 3.5 | 28.27 | 8.8 | |
64 | 0 | 4.5 | 0.35 | 8 | 35 | 2.21 | [40] |
65 | 0 | 9.5 | 0.35 | 8 | 38 | 2.45 | |
66 | 0 | 12.5 | 0.35 | 8 | 38 | 3.22 | |
67 | 0 | 4.5 | 0.35 | 8 | 42 | 2.42 | |
68 | 0 | 4.5 | 0.35 | 8 | 35 | 3.53 | |
69 | 0 | 9.5 | 0.35 | 8 | 38 | 2.8 | |
70 | 0 | 9.5 | 0.35 | 8 | 39 | 1.79 | |
71 | 0 | 9.5 | 0.35 | 8 | 35 | 3.92 | |
72 | 0 | 12.5 | 0.35 | 8 | 39 | 2.43 | |
73 | 0 | 12.5 | 0.35 | 8 | 36 | 3.67 | |
74 | 0 | 9.5 | 0.35 | 8 | 39 | 1.91 | |
75 | 0 | 9.5 | 0.35 | 8 | 35 | 3.59 | |
76 | 0 | 9.5 | 0.35 | 12 | 40 | 1.16 | |
77 | 0 | 12.5 | 0.35 | 12 | 40 | 1.06 | |
78 | 0 | 9.5 | 0.35 | 12 | 38 | 1.83 | |
79 | 0 | 9.5 | 0.35 | 7.2 | 35 | 4.76 | |
80 | 0 | 12.5 | 0.35 | 7.2 | 37 | 3.07 | |
81 | 0 | 9.5 | 0.35 | 7.2 | 36 | 3.45 | |
82 | 0 | 9.5 | 0.35 | 10 | 38 | 1.71 | |
83 | 0 | 12.5 | 0.35 | 10 | 38 | 1.67 | |
84 | 0 | 9.5 | 0.35 | 10 | 38 | 1.71 | |
85 | 0 | 9.5 | 0.35 | 6 | 30 | 6.95 | |
86 | 0 | 12.5 | 0.35 | 6 | 32 | 5.14 | |
87 | 0 | 9.5 | 0.35 | 6 | 31 | 6.45 | |
88 | 180 | 2.36 | 0.23 | 4.37 | 23 | 13.7 | [39] |
89 | 170 | 2.36 | 0.24 | 4.38 | 27 | 13.1 | |
90 | 160 | 2.36 | 0.23 | 4.39 | 31 | 8.8 | |
91 | 0 | 2.36 | 0.32 | 2.28 | 18.3 | 19.89 | [38] |
92 | 0 | 2.36 | 0.33 | 2.58 | 21.1 | 14.65 | |
93 | 0 | 2.36 | 0.33 | 3.13 | 25.5 | 9.66 | |
94 | 0 | 4.75 | 0.32 | 2.24 | 16.9 | 20.6 | |
95 | 0 | 4.75 | 0.33 | 2.61 | 22.3 | 15.89 | |
96 | 0 | 4.75 | 0.33 | 3.09 | 25.6 | 9.3 | |
97 | 0 | 9.5 | 0.32 | 2.39 | 19.5 | 19.13 | |
98 | 0 | 9.5 | 0.33 | 2.67 | 23.8 | 15.66 | |
99 | 0 | 9.5 | 0.33 | 3.28 | 24.6 | 7.55 | |
100 | 0 | 2.36 | 0.32 | 4.98 | 20.2 | 12.51 | |
101 | 0 | 4.75 | 0.32 | 4.67 | 19.5 | 17.61 | |
102 | 0 | 4.75 | 0.32 | 5.5 | 24.2 | 13.2 | |
103 | 0 | 4.75 | 0.33 | 7.65 | 28.9 | 7.7 | |
104 | 0 | 9.5 | 0.32 | 4.85 | 17.8 | 17.01 | |
105 | 0 | 9.5 | 0.32 | 5.74 | 24.2 | 12.24 | |
106 | 0 | 9.5 | 0.33 | 8.17 | 26.4 | 6.9 | |
107 | 107 | 1.18 | 0.26 | 3.74 | 26 | 22 | [37] |
108 | 109 | 1.18 | 0.36 | 3.69 | 23 | 25 | |
109 | 109 | 1.18 | 0.26 | 3.69 | 18.5 | 30 | |
110 | 100 | 2.36 | 0.25 | 4.14 | 28 | 17 | |
111 | 0 | 6.7 | 0.36 | 4.55 | 21.442 | 12 | [36] |
112 | 0 | 6.7 | 0.36 | 4.55 | 26.1396 | 12 | |
113 | 0 | 6.7 | 0.36 | 4.55 | 24.7444 | 11.5 | |
114 | 0 | 4.75 | 0.36 | 4.55 | 19.0868 | 17.5 | |
115 | 0 | 4.75 | 0.36 | 4.55 | 22.9524 | 14.5 | |
116 | 0 | 4.75 | 0.36 | 4.55 | 21.0196 | 14.5 | |
117 | 0 | 6.7 | 0.36 | 4.55 | 17.154 | 15.5 | |
118 | 0 | 6.7 | 0.36 | 4.55 | 11.5476 | 19.5 | |
119 | 0 | 6.7 | 0.36 | 4.55 | 18.9332 | 11.5 | |
120 | 0 | 4.75 | 0.36 | 4.55 | 18.3188 | 15.5 | |
121 | 0 | 4.75 | 0.36 | 4.55 | 20.1876 | 13 | |
122 | 0 | 4.75 | 0.36 | 4.55 | 21.122 | 13.5 | |
123 | 0 | 4.75 | 0.36 | 4.55 | 17.922 | 17 | |
124 | 0 | 4.75 | 0.36 | 4.55 | 17.922 | 16.5 | |
125 | 0 | 4.75 | 0.36 | 4.55 | 19.8164 | 13 | |
126 | 0 | 6.7 | 0.36 | 4.55 | 21.57 | 15 | |
127 | 0 | 6.7 | 0.36 | 4.55 | 20.0468 | 17 | |
128 | 0 | 6.7 | 0.36 | 4.55 | 20.7636 | 15.5 | |
129 | 0 | 4.75 | 0.36 | 4.55 | 18.8692 | 17 | |
130 | 0 | 4.75 | 0.36 | 4.55 | 16.0276 | 22.5 | |
131 | 0 | 4.75 | 0.36 | 4.55 | 18.8692 | 17.5 | |
132 | 242.41 | 4.75 | 0.38 | 4 | 11.2788 | 30.5 | |
133 | 240.07 | 4.75 | 0.38 | 4 | 12.226 | 31.5 | |
134 | 237.74 | 4.75 | 0.38 | 4 | 13.1732 | 28 | |
135 | 247.87 | 4.75 | 0.36 | 4 | 9.3716 | 34.5 | |
136 | 247.87 | 4.75 | 0.36 | 4 | 9.3716 | 32 | |
137 | 250.21 | 4.75 | 0.36 | 4 | 8.4244 | 33 | |
138 | 262.75 | 4.75 | 0.34 | 4 | 3.6756 | 49 | |
139 | 262.75 | 4.75 | 0.34 | 4 | 3.6756 | 46.5 | |
140 | 262.75 | 4.75 | 0.34 | 4 | 3.6756 | 43 | |
141 | 254.20 | 4.75 | 0.32 | 4 | 7.4644 | 39.5 | |
142 | 258.90 | 4.75 | 0.32 | 4 | 5.57 | 42 | |
143 | 251.84 | 4.75 | 0.32 | 4 | 8.4116 | 40 | |
144 | 257.39 | 4.75 | 0.3 | 4 | 6.5172 | 41 | |
145 | 257.39 | 4.75 | 0.3 | 4 | 6.5172 | 41 | |
146 | 252.67 | 4.75 | 0.3 | 4 | 8.4116 | 39 | |
147 | 252.67 | 4.75 | 0.3 | 4 | 8.4116 | 42 | |
148 | 252.67 | 4.75 | 0.3 | 4 | 8.4116 | 44 | |
149 | 259.75 | 4.75 | 0.3 | 4 | 5.57 | 43 | |
150 | 232.18 | 4.75 | 0.28 | 4 | 16.9492 | 23 | |
151 | 232.18 | 4.75 | 0.28 | 4 | 16.9492 | 26.5 | |
152 | 227.44 | 4.75 | 0.28 | 4 | 18.8436 | 23.5 | |
153 | 0 | 4.75 | 0.27 | 4.67 | 25.3 | 17.3 | [35] |
154 | 104 | 4.75 | 0.27 | 4.37 | 18.3 | 25.2 | |
155 | 0 | 4.75 | 0.27 | 4.5 | 25.3 | 17.3 | [34] |
156 | 0 | 9 | 0.27 | 4.5 | 33.6 | 11.9 | |
157 | 100 | 9 | 0.22 | 4.81 | 20.2 | 20.2 | |
158 | 100 | 4.75 | 0.27 | 4.38 | 18.3 | 25.2 | |
159 | 100 | 4.75 | 0.22 | 4.81 | 19 | 23.1 | |
160 | 100 | 4.75 | 0.21 | 4.61 | 26 | 9 | |
161 | 100 | 4.75 | 0.24 | 5.15 | 14.1 | 18.9 | |
162 | 0 | 4.75 | 0.27 | 4.5 | 18.9 | 21.4 | |
163 | 0 | 4.75 | 0.27 | 4.5 | 22.1 | 21.4 | |
164 | 100 | 4.75 | 0.27 | 4.38 | 19 | 26.5 |
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Le, BA., Tran, BV., Vu, TS. et al. Predicting the Compressive Strength of Pervious Cement Concrete based on Fast Genetic Programming Method. Arab J Sci Eng 49, 5487–5504 (2024). https://doi.org/10.1007/s13369-023-08396-2
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DOI: https://doi.org/10.1007/s13369-023-08396-2