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A Novel Method for Optimizing Parameters influencing the Bearing Capacity of Geosynthetic Reinforced Sand Using RSM, ANN, and Multi-objective Genetic Algorithm

Brahim Lafifi

Brahim Lafifi

Laboratory of Civil Engineering and Hydraulics, University 8 Mai 1945 GuelmaGuelma, Algeria
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Lafifi, Brahim
, 
Ammar Rouaiguia

Ammar Rouaiguia

Laboratory of Civil Engineering and Hydraulics, University 8 Mai 1945 GuelmaGuelma, Algeria
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Rouaiguia, Ammar
 y 
El Alia Soltani

El Alia Soltani

Laboratory of Civil Engineering and Hydraulics, University 8 Mai 1945 GuelmaGuelma, Algeria
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Soltani, El Alia
  
31 may 2023
A Novel Method for Optimizing Parameters influencing the Bearing Capacity of Geosynthetic Reinforced Sand Using RSM, ANN, and Multi-objective Genetic Algorithm's Cover Image
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Categoría del artículo: Original Study
Publicado en línea: 31 may 2023
Páginas: 174 - 196
Recibido: 21 may 2022
Aceptado: 03 abr 2023
DOI: https://doi.org/10.2478/sgem-2023-0006
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© 2023 Brahim Lafifi et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

View of the laboratory-scale model.
View of the laboratory-scale model.

Figure 2:

Geometric model and studied parameters of the problem.
Geometric model and studied parameters of the problem.

Figure 3:

Grain size curve of the testing material.
Grain size curve of the testing material.

Figure 4:

Geosynthetic reinforcements used in this study.
Geosynthetic reinforcements used in this study.

Figure 5:

Effect of length on q – s/B relationship (U=0.25B, N=1, X=0.5B).
Effect of length on q – s/B relationship (U=0.25B, N=1, X=0.5B).

Figure 6:

Effect of length on q–s/B relationship (U=0.5B, N=2, X=0.75B).
Effect of length on q–s/B relationship (U=0.5B, N=2, X=0.75B).

Figure 7:

Effect of reinforcement number on q–s/B relationship (U=0.25B, L=5.0B, X=0.5B).
Effect of reinforcement number on q–s/B relationship (U=0.25B, L=5.0B, X=0.5B).

Figure 8:

Effect of reinforcement number on q–s/B relationship (U=0.5B, L=7.0B, X=0.75B).
Effect of reinforcement number on q–s/B relationship (U=0.5B, L=7.0B, X=0.75B).

Figure 9:

Effect of the depth of the first layer on q–s/B relationship (L=5.0B, N=1, X=1.0B).
Effect of the depth of the first layer on q–s/B relationship (L=5.0B, N=1, X=1.0B).

Figure 10:

Effect of the depth of the first layer on q–s/B relationship (L=7.0B, N=2, X=0.75B).
Effect of the depth of the first layer on q–s/B relationship (L=7.0B, N=2, X=0.75B).

Figure 11:

Effect of the depth of the first layer on q–s/B relationship (L=9.0B, N=3, X=0.5B).
Effect of the depth of the first layer on q–s/B relationship (L=9.0B, N=3, X=0.5B).

Figure 12:

Effect of the spacing reinforcement on q–s/B relationship (U=0.5B, N=2, L=7.0B).
Effect of the spacing reinforcement on q–s/B relationship (U=0.5B, N=2, L=7.0B).

Figure 13:

Effect of geometric parameters on the bearing capacity for the three soils.
Effect of geometric parameters on the bearing capacity for the three soils.

Figure 14:

ANN architecture (4 -8 -1) for bearing capacity q.
ANN architecture (4 -8 -1) for bearing capacity q.

Figure 15:

Predicted versus experimental values for bearing capacity q.
Predicted versus experimental values for bearing capacity q.

Figure 16:

ANN architecture (4 -8 -1) for the bearing capacity q.
ANN architecture (4 -8 -1) for the bearing capacity q.

Figure 17:

Predicted versus experimental values for the bearing capacity q.
Predicted versus experimental values for the bearing capacity q.

Figure 18:

Results of sensitivity analysis using CAM.
Results of sensitivity analysis using CAM.

Figure 19:

Bar plot of PS values.
Bar plot of PS values.

Figure 20:

Comparison between predicted and experimental values for q with RSM and ANN models (a- geogrid reinforcement. b- geotextile reinforcement).
Comparison between predicted and experimental values for q with RSM and ANN models (a- geogrid reinforcement. b- geotextile reinforcement).

Figure 21:

Diagram of the genetic algorithm.
Diagram of the genetic algorithm.

Optimization results_

Reinforcement L (B) N U(B) X(B) q (kPa) Cost (B)
Geogrid 5.00 2 0.25 0.50 324.65 10.76
Geotextile 5.00 2 0.25 0.50 374.44 10.85

GA parameters_

Parameters Values
Number of variables 4
Size of population 100
Selection function Stochastic uniform
Crossover fraction 0.8
Mutation probability 0.2
Number of generations 100

Physical and mechanical properties of utilized reinforcement_

Description GeotextileAS30 Geogrid AFITEX RTE 35–35–40
- Total weight per unit area (g/m2) 300.0 135.0
- Thickness (mm) 1.60 -
- Mesh aperture size (mm) - 40×40
- Peak tensile strength (kN/m) 25.0 35.0
- Extension at maximum load (%) 75 10
- CBR punching strength (kN) 3.40 -

Levels of the input parameters used in the experimental design_

Input parameters Minimal value Mean value Maximal value
Length (L) 5B 7B 9B
Number (N) 1 2 3
Depth of the first layer (U) 0.25B 0.5B 0.75B
Spacing between layers (X) 0.5B 0.75B 1.0B

Optimization conditions_

Parameters Objective Lower limit Upper limit
L (B) Is in range 5.0 9.0
N Is in range 1 3
U (B) Is in range 0.25 0.75
X(B) Is in range 0.5 1.0
q (kPa) Geogrid Maximization 140.0 395.0
Geotextile 160.0 525.0
Cost (B) Minimization 5.25 29.75

Experimental results for the two types of reinforcement_

Run Factor 1L (*B) Factor 2N Factor 3U (*B) Factor 4X (*B) Response 1qGeogrid (kPa) Response 2qGeotextile(kPa)
1 9 1 0.75 1 170.0 175.0
2 7 2 0.5 0.75 240.0 270.0
3 5 1 0.25 1 220 240
4 9 2 0.5 0.75 275 280
5 9 1 0.25 0.5 260 275
6 7 2 0.25 0.75 280 350
7 9 1 0.75 0.5 170 210
8 9 1 0.25 1 230 275
9 7 2 0.5 0.5 270 300
10 5 3 0.75 1 160 210
11 7 2 0.75 0.75 165 190
12 7 1 0.5 0.75 180 200
13 9 3 0.25 0.5 360 450
14 5 3 0.25 1 350 485
15 5 1 0.75 1 140 165
16 9 3 0.75 0.5 165 180
17 5 3 0.75 0.5 170 165
18 9 3 0.25 1 300 420
19 5 1 0.75 0.5 140 160
20 5 1 0.25 0.5 220 240
21 5 2 0.5 0.75 245 260
22 7 2 0.5 1 200 240
23 9 3 0.75 1 180 185
24 7 3 0.5 0.75 280 370
25 5 3 0.25 0.5 395 525

ANOVA results of the bearing capacity for geotextile reinforcement_

Source Sum of squares Df Mean square F value P-value Prob> F Cont (%) Remark
Model 2.601E+005 11 23,641.60 28.90 < 0.0001 Significant
L (length of layers) 1.39 1 1.39 1.698E-003 0.9678 0.001 Insignificant
N (number of layers) 61,250.00 1 61,250.00 74.86 < 0.0001 23.439 Significant
U (depth of the first layer) 1.458E+005 1 1.458E+005 178.20 < 0.0001 55.795 Significant
X (spacing between layers) 1422.22 1 1422.22 1.74 0.2101 0.544 Insignificant
L*N 4900.00 1 4900.00 5.99 0.0294 1.875 Significant
L*U 900.00 1 900.00 1.10 0.3134 0.344 Insignificant
N*U 42,025.00 1 42,025.00 51.36 < 0.0001 16.082 Significant
U*X 506.25 1 506.25 0.62 0.4456 0.194 Insignificant
L2 881.50 1 881.50 1.08 0.3182 0.337 Insignificant
U2 1144.99 1 1144.99 1.40 0.2580 0.438 Insignificant
X2 1666.27 1 1666.27 2.04 0.1771 0.638 Insignificant
Residual 10,636.42 13 818.19 0.313 Insignificant
Cor total 2.707E+005 24

Comparison between RSM and ANN models_

Type of reinforcement RSM ANN
R2 RMSE MPE (%) R2 RMSE MPE (%)
Geogrid 0.972 0.3595 0.7215 0.9991 0.057 0.0414
Geotextile 0.961 0.6366 1.027 0.9998 0.0286 0.021

Experimental central composite design L25 of the current study_

Run Factor 1L (*B) Factor 2N Factor 3U (*B) Factor 4X (*B)
1 9 1 0.75 1
2 7 2 0.5 0.75
3 5 1 0.25 1
4 9 2 0,5 0.75
5 9 1 0.25 0.5
6 7 2 0.25 0.75
7 9 1 0.75 0.5
8 9 1 0.25 1
9 7 2 0.5 0.5
10 5 3 0.75 1
11 7 2 0.75 0.75
12 7 1 0.5 0.75
13 9 3 0.25 0.5
14 5 3 0.25 1
15 5 1 0.75 1
16 9 3 0.75 0.5
17 5 3 0.75 0.5
18 9 3 0.25 1
19 5 1 0.75 0.5
20 5 1 0.25 0.5
21 5 2 0.5 0.75
22 7 2 0.5 1
23 9 3 0.75 1
24 7 3 0.5 0.75
25 5 3 0.25 0.5

ANOVA results of the bearing capacity for geogrid reinforcement_

Source Sum of squares Df Mean square F value P-value Prob> F Cont (%) Remark
Model 1.156E+005 11 10,512.06 40.30 < 0.0001 Significant
L (length of layers) 272.22 1 272.22 1.04 0.3256 0.234 Insignificant
N (number of layers) 22,050.00 1 22,050.00 84.52 < 0.0001 18.970 Significant
U (depth of the first layer) 74,112.50 1 74,112.50 284.10 < 0.0001 63.762 Significant
X (spacing between layers) 1605.56 1 1605.56 6.15 0.0276 1.381 Significant
L*N 2025.00 1 2025.00 7.76 0.0154 1.742 Significant
L*U 756.25 1 756.25 2.90 0.1124 0.651 Insignificant
N*U 11,025.00 1 11,025.00 42.26 < 0.0001 9.485 Significant
U*X 1225.00 1 1225.00 4.70 0.0494 1.054 Significant
L2 1303.60 1 1303.60 5.00 0.0436 1.122 Significant
U2 681.69 1 681.69 2.61 0.1300 0.586 Insignificant
X2 915.48 1 915.48 3.51 0.0837 0.788 Insignificant
Residual 3391.33 13 260.87 0.224 Insignificant
Cor total 1.190E+005 24
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