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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
, 
Ammar Rouaiguia
Ammar Rouaiguia
 e 
El Alia Soltani
El Alia Soltani
   | 31 mag 2023
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Article Category: Original Study
Pubblicato online: 31 mag 2023
Pagine: 174 - 196
Ricevuto: 21 mag 2022
Accettato: 03 apr 2023
DOI: https://doi.org/10.2478/sgem-2023-0006
Parole chiave
© 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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