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

Lafifi, Brahim; Rouaiguia, Ammar; Soltani, El Alia

doi:10.2478/sgem-2023-0006

Figures & Tables

Geometric model and studied parameters of the problem.

Grain size curve of the testing material.

Geosynthetic reinforcements used in this study.

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=0.5B, N=2, X=0.75B).

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=0.5B, L=7.0B, X=0.75B).

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=7.0B, N=2, X=0.75B).

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

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

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

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

Predicted versus experimental values for bearing capacity q.

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

Predicted versus experimental values for the bearing capacity q.

Results of sensitivity analysis using CAM.

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

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
q (kPa)	Geotextile	Maximization	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 1q_Geogrid (kPa)	Response 2q_Geotextile(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

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

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Optimization results_

GA parameters_

Physical and mechanical properties of utilized reinforcement_

Levels of the input parameters used in the experimental design_

Optimization conditions_

Experimental results for the two types of reinforcement_

ANOVA results of the bearing capacity for geotextile reinforcement_

Comparison between RSM and ANN models_

Experimental central composite design L25 of the current study_

ANOVA results of the bearing capacity for geogrid reinforcement_

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