1 Introduction
2 Experimental Map
2.1 Materials and Mixtures
2.1.1 Cement
Chemical properties | |||||||||
---|---|---|---|---|---|---|---|---|---|
Material | SiO2 | Al2O3 | Fe2O3 | CaO | MgO | SO3 | Na2O | K2O | Loss on ignition |
Cement | 21.89 | 5.3 | 3.34 | 53.27 | 6.45 | 3.67 | 0.18 | 0.98 | 3.21 |
RHA | 87.86 | 0.68 | 0.93 | 1.30 | 0.35 | – | 0.12 | 2.37 | – |
Physical properties | |||
---|---|---|---|
Material | Specific gravity (g/cm3) | Specific surface (BET) (m2/g) | Specific surface (Blain) (m2/kg) |
Cement | 1.7 | – | 314 |
RHA U series | – | 36.47 | – |
2.1.2 Rice Husk Ash
2.1.3 SiO2 Nanoparticles
Diameter (nm) | Surface volume ratio (m2/g) | Density (g/cm3) | Purity (%) |
---|---|---|---|
15 ± 3 | 160 ± 12 | <0.14 | >99.9 |
80 ± 5 | 560 ± 32 | <0.14 | >99.9 |
2.1.4 Aggregates
2.1.5 Mixture Proportioning
Sample number | Sample designations | Cement (kg/m3) | RHAa (kg/m3) | 15 nm nanoparticle (kg/m3) | 80 nm nano particle (kg/m3) |
---|---|---|---|---|---|
1,2 | C0a1,2 | 450 | 0 | 0 | 0 |
3,4 | Ub1 | 427.5 | 22.5 | 0 | 0 |
5,6 | U2 | 405 | 45 | 0 | 0 |
7,8 | U3 | 382.5 | 67.5 | 0 | 0 |
9,10 | U4 | 360 | 90 | 0 | 0 |
11,12 | FN1c | 447.75 | 0 | 2.25 | 0 |
13,14 | FN2 | 445.5 | 0 | 4.5 | 0 |
15,16 | FN3 | 443.25 | 0 | 6.75 | 0 |
17,18 | FN4 | 441 | 0 | 9 | 0 |
19,20 | CN1d | 447.75 | 0 | 0 | 2.25 |
21,22 | CN2 | 445.5 | 0 | 0 | 4.5 |
23,24 | CN3 | 443.25 | 0 | 0 | 6.75 |
25,26 | CN4 | 441 | 0 | 0 | 9 |
27 | FN1–RHAe5 | 425.25 | 22.5 | 2.25 | 0 |
28 | FN2–RHA5 | 423 | 22.5 | 4.5 | 0 |
29 | FN3–RHA5 | 420.75 | 22.5 | 6.75 | 0 |
30 | FN4–RHA5 | 418.5 | 22.5 | 9 | 0 |
31 | FN1–RHA10 | 402.75 | 45 | 2.25 | 0 |
32 | FN2–RHA10 | 400.5 | 45 | 4.5 | 0 |
33 | FN3–RHA10 | 398.25 | 45 | 6.75 | 0 |
34 | FN4–RHA10 | 396 | 45 | 9 | 0 |
35 | FN1–RHA15 | 380.25 | 67.5 | 2.25 | 0 |
36 | FN2–RHA15 | 378 | 67.5 | 4.5 | 0 |
37 | FN3–RHA15 | 375.75 | 67.5 | 6.75 | 0 |
38 | FN4–RHA15 | 373.5 | 67.5 | 9 | 0 |
39 | FN1–RHA20 | 357.75 | 90 | 2.25 | 0 |
40 | FN2–RHA20 | 355.5 | 90 | 4.5 | 0 |
41 | FN3–RHA20 | 353.25 | 90 | 6.75 | 0 |
42 | FN4–RHA20 | 351 | 90 | 9 | 0 |
43 | CN1–RHAf5 | 425.25 | 22.5 | 0 | 2.25 |
44 | CN2–RHA5 | 423 | 22.5 | 0 | 4.5 |
45 | CN3–RHA5 | 420.75 | 22.5 | 0 | 6.75 |
46 | CN4–RHA5 | 418.5 | 22.5 | 0 | 9 |
47 | CN1–RHA10 | 402.75 | 45 | 0 | 2.25 |
48 | CN2–RHA10 | 400.5 | 45 | 0 | 4.5 |
49 | CN3–RHA10 | 398.25 | 45 | 0 | 6.75 |
50 | CN4–RHA10 | 396 | 45 | 0 | 9 |
51 | CN1–RHA15 | 380.25 | 67.5 | 0 | 2.25 |
52 | CN2–RHA15 | 378 | 67.5 | 0 | 4.5 |
53 | CN3–RHA15 | 375.75 | 67.5 | 0 | 6.75 |
54 | CN4–RHA15 | 373.5 | 67.5 | 0 | 9 |
55 | CN1–RHA20 | 357.75 | 90 | 0 | 2.25 |
56 | CN2–RHA20 | 355.5 | 90 | 0 | 4.5 |
57 | CN3–RHA20 | 353.25 | 90 | 0 | 6.75 |
58 | CN4–RHA20 | 351 | 90 | 0 | 9 |
2.2 Preparation of Test Specimens
2.3 Percentage of Water Absorption of Nano Silica–RHA Particles Blended Concrete
2.4 Velocity of Water Absorption of NS–RHA Particles Blended Concrete
2.5 Coefficient of Water Absorption
3 Experimental Results and Discussion
3.1 Percentage of Water Absorption
Sample number | Sample designations | Percentage of water absorption (%) | Velocity of water absorption (m/s1/2) | Coefficient of water absorption (m2/s) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
7 | 28 | 90 | 7 | 28 | 90 | 7 | 28 | 90 | ||
1 | C01a | 7.47 | 5.60 | 4.80 | 13.22 | 12.34 | 10.14 | 9.02 | 2.86 | 1.35 |
2 | C02 | 8.32 | 5.71 | 4.92 | 13.26 | 12.56 | 10.18 | 9.06 | 2.98 | 1.40 |
3 | U1b (W) | 6.90 | 5.22 | 3.98 | 12.64 | 11.38 | 6.89 | 8.56 | 2.47 | 1.03 |
4 | U1b (LW) | 6.94 | 5.54 | 3.84 | 12.65 | 11.41 | 6.85 | 8.61 | 2.49 | 1.02 |
5 | U2 (W) | 6.67 | 5.11 | 3.51 | 10.72 | 8.64 | 5.14 | 7.30 | 1.97 | 0.89 |
6 | U2 (LW) | 6.73 | 5.42 | 3.36 | 10.80 | 8.67 | 5.09 | 7.33 | 2.00 | 0.88 |
7 | U3 (W) | 6.94 | 5.28 | 4.01 | 12.60 | 11.70 | 8.32 | 8.67 | 2.55 | 1.12 |
8 | U3 (LW) | 6.54 | 5.33 | 3.14 | 10.78 | 8.66 | 5.05 | 7.29 | 1.97 | 0.85 |
9 | U4 (W) | 7.10 | 5.41 | 4.14 | 12.86 | 11.73 | 9.16 | 8.83 | 2.57 | 1.20 |
10 | U4 (LW) | 6.32 | 5.19 | 3.02 | 10.69 | 8.62 | 4.99 | 7.26 | 1.96 | 0.84 |
11 | FNc 1 (W) | 7.15 | 4.82 | 4.12 | 12.83 | 7.51 | 7.09 | 7.82 | 1.53 | 1.30 |
12 | FNc 1 (LW) | 7.20 | 4.71 | 4.00 | 12.85 | 7.53 | 7.00 | 7.85 | 1.52 | 1.28 |
13 | FN2 (W) | 7.23 | 4.73 | 4.01 | 12.95 | 7.25 | 6.78 | 7.96 | 1.48 | 1.18 |
14 | FN2 (LW) | 7.28 | 4.56 | 3.86 | 13.00 | 7.23 | 6.67 | 7.98 | 1.46 | 1.12 |
15 | FN3 (W) | 7.31 | 4.60 | 3.92 | 13.07 | 6.99 | 6.52 | 8.15 | 1.44 | 1.07 |
16 | FN3 (LW) | 7.42 | 4.39 | 3.71 | 13.10 | 6.95 | 6.48 | 8.20 | 1.40 | 1.04 |
17 | FN4 (W) | 7.42 | 4.41 | 3.78 | 13.18 | 6.73 | 6.35 | 8.32 | 1.39 | 0.95 |
18 | FN4 (LW) | 7.56 | 4.22 | 3.54 | 13.21 | 6.69 | 6.31 | 8.37 | 1.36 | 0.92 |
19 | CNd 1 (W) | 7.02 | 5.00 | 4.05 | 12.67 | 8.01 | 6.81 | 7.69 | 1.56 | 1.25 |
20 | CNd 1 (LW) | 7.10 | 5.02 | 3.91 | 12.73 | 8.07 | 6.78 | 7.74 | 1.59 | 1.23 |
21 | CN2 (W) | 7.10 | 5.08 | 3.94 | 12.82 | 8.23 | 6.65 | 7.83 | 1.67 | 1.13 |
22 | CN2 (LW) | 7.16 | 5.12 | 3.80 | 12.87 | 8.27 | 6.63 | 7.85 | 1.69 | 1.09 |
23 | CN3 (W) | 7.21 | 5.17 | 3.87 | 12.91 | 8.42 | 6.42 | 7.99 | 1.79 | 1.01 |
24 | CN3 (LW) | 7.23 | 5.23 | 3.68 | 12.94 | 8.47 | 6.36 | 8.03 | 1.82 | 0.98 |
25 | CN4 (W) | 7.29 | 5.32 | 3.71 | 13.06 | 8.61 | 6.21 | 8.18 | 1.88 | 0.88 |
26 | CN4 (LW) | 7.34 | 5.35 | 3.51 | 13.09 | 8.65 | 6.18 | 8.21 | 1.89 | 0.85 |
27 | FN1–RHAe5 | 7.22 | 5.00 | 3.32 | 13.48 | 7.93 | 4.71 | 9.18 | 1.49 | 0.83 |
28 | FN2–RHA5 | 7.29 | 5.02 | 2.96 | 13.68 | 8.03 | 4.57 | 9.27 | 1.53 | 0.80 |
29 | FN3–RHA5 | 7.46 | 5.07 | 2.71 | 13.86 | 8.08 | 4.46 | 9.34 | 1.58 | 0.72 |
30 | FN4–RHA5 | 7.61 | 5.12 | 2.54 | 13.90 | 8.15 | 4.34 | 9.58 | 1.64 | 0.67 |
31 | FN1–RHA10 | 7.24 | 5.03 | 3.30 | 13.50 | 7.96 | 4.69 | 9.21 | 1.56 | 0.81 |
32 | FN2–RHA10 | 7.32 | 5.07 | 2.90 | 13.72 | 8.09 | 4.54 | 9.32 | 1.59 | 0.74 |
33 | FN3–RHA10 | 7.51 | 5.13 | 2.62 | 13.95 | 8.16 | 4.38 | 9.43 | 1.65 | 0.63 |
34 | FN4–RHA10 | 7.64 | 5.21 | 2.49 | 14.15 | 8.27 | 4.22 | 9.71 | 1.73 | 0.51 |
35 | FN1–RHA15 | 7.43 | 5.14 | 3.11 | 13.71 | 8.11 | 4.51 | 9.38 | 1.59 | 0.69 |
36 | FN2–RHA15 | 7.61 | 5.19 | 2.81 | 13.98 | 8.23 | 4.46 | 9.54 | 1.62 | 0.61 |
37 | FN3–RHA15 | 7.82 | 5.25 | 2.50 | 14.18 | 8.34 | 4.28 | 9.68 | 1.69 | 0.54 |
38 | FN4–RHA15 | 7.91 | 5.39 | 2.38 | 14.37 | 8.41 | 4.12 | 9.87 | 1.74 | 0.48 |
39 | FN1–RHA20 | 7.62 | 5.19 | 2.99 | 13.86 | 8.21 | 4.38 | 9.49 | 1.61 | 0.63 |
40 | FN2–RHA20 | 7.81 | 5.23 | 2.71 | 14.05 | 8.36 | 4.26 | 9.68 | 1.72 | 0.58 |
41 | FN3–RHA20 | 7.95 | 5.42 | 2.42 | 14.26 | 8.44 | 4.11 | 9.79 | 1.79 | 0.50 |
42 | FN4–RHA20 | 8.01 | 5.51 | 2.21 | 14.51 | 8.56 | 4.01 | 9.96 | 1.91 | 0.43 |
43 | CN1–RHAf5 | 7.07 | 5.03 | 3.12 | 12.88 | 8.26 | 4.26 | 8.83 | 1.69 | 0.77 |
44 | CN2–RHA5 | 7.16 | 5.08 | 2.80 | 12.92 | 8.31 | 4.01 | 8.92 | 1.72 | 0.71 |
45 | CN3–RHA5 | 7.20 | 5.19 | 2.57 | 13.04 | 8.42 | 3.89 | 8.99 | 1.78 | 0.69 |
46 | CN4–RHA5 | 7.28 | 5.23 | 2.46 | 13.21 | 8.58 | 3.72 | 9.11 | 1.84 | 0.60 |
47 | CN1–RHA10 | 7.10 | 5.05 | 3.00 | 12.91 | 8.32 | 4.12 | 8.91 | 1.73 | 0.70 |
48 | CN2–RHA10 | 7.19 | 5.14 | 2.61 | 13.08 | 8.45 | 3.89 | 9.05 | 1.82 | 0.65 |
49 | CN3–RHA10 | 7.29 | 5.26 | 2.42 | 13.24 | 8.59 | 3.76 | 9.17 | 1.91 | 0.61 |
50 | CN4–RHA10 | 7.47 | 5.38 | 2.24 | 13.45 | 8.73 | 3.52 | 9.26 | 2.01 | 0.54 |
51 | CN1–RHA15 | 7.22 | 5.22 | 2.82 | 13.14 | 8.46 | 4.00 | 9.01 | 1.84 | 0.61 |
52 | CN2–RHA15 | 7.31 | 5.34 | 2.61 | 13.29 | 8.61 | 3.72 | 9.15 | 1.96 | 0.53 |
53 | CN3–RHA15 | 7.39 | 5.47 | 2.40 | 13.38 | 8.75 | 3.61 | 9.32 | 2.09 | 0.48 |
54 | CN4–RHA15 | 7.51 | 5.58 | 2.22 | 13.54 | 8.91 | 3.41 | 9.44 | 2.21 | 0.42 |
55 | CN1–RHA20 | 7.34 | 5.31 | 2.68 | 13.27 | 8.58 | 3.82 | 9.13 | 1.96 | 0.54 |
56 | CN2–RHA20 | 7.45 | 5.49 | 2.50 | 13.42 | 8.73 | 3.61 | 9.32 | 2.11 | 0.46 |
57 | CN3–RHA20 | 7.52 | 5.59 | 2.29 | 13.59 | 8.88 | 3.45 | 9.48 | 2.23 | 0.39 |
58 | CN4–RHA20 | 7.61 | 5.80 | 2.08 | 13.71 | 9.04 | 3.29 | 9.66 | 2.35 | 0.31 |
3.2 Velocity of Water Absorption
3.3 Coefficient of Water Absorption
4 Neural Network Modeling
4.1 Model Description
4.2 Input Factors
4.3 Target Vector
4.4 Training Steps
4.5 Design Algorithm
Name | No. of PEs in HLb | Training set | Validation set | Testing set | All | Epochs | |||
---|---|---|---|---|---|---|---|---|---|
MSE | R | MSE | R | MSE | R | R | |||
NNM1 | 1 | 3.5103 | 0.95412 | 2.53146 | 0.95263 | 2.47188 | 0.97263 | 0.95979 | 224 |
Output = 0.94 × target + 0.38 | Output = 0.87 × target + 0.43 | Output = 0.97 × target + 0.31 | Output = 0.93 × target + 0.37 | ||||||
NNM2 | 6 | 1.60119 | 0.98889 | 1.46301 | 0.98451 | 1.38133 | 0.97156 | 0.98165 | 16 |
Output = 0.99 × target + 0.052 | Output = 0.94 × target + 0.18 | Output = 1 × target +0.071 | Output = 0.99 × target + 0.05 | ||||||
NNM3 | 11 | 1.08359 | 0.98449 | 1.15492 | 0.97645 | 1.25615 | 0.98985 | 0.98359 | 16 |
Output = 0.98 × target + 0.096 | Output = 0.99 × target + 0.21 | Output = 0.98 × target + 0.11 | Output = 0.98 × target + 0.12 | ||||||
NNM4 | 16 | 0.80060 | 0.98219 | 0.96029 | 0.99049 | 0.66266 | 0.97940 | 0.98402 | 15 |
Output = 0.99 × target + 0.07 | Output = 0.99 × target + 0.185 | Output = 1 × target +0.08 | Output = 1 × target + 0.049 | ||||||
NNM5 | 20 | 0.47303 | 0.9998 | 0.50148 | 0.99040 | 0.40688 | 0.99448 | 0.99303 | 14 |
Output = 1 × target + 0.001 | Output = 1 × target + 0.32 | Output = 0.94 × target + 0.32 | Output = 1 × target + 0.04 | ||||||
NNM6 | 24 | 0.97703 | 0.97889 | 1.00621 | 0.96456 | 0.70978 | 0.97889 | 0.97411 | 10 |
Output = 97 × target +0.21 | Output = 0.97 × target + 0.21 | Output = 0.98 × target + 0.11 | Output = 0.98 × target + 0.21 |