Abstract
The present research introduces the best architecture approach and model for predicting the unconfined compressive strength (UCS) of cohesive virgin soil by comparing the multivariable regression analysis (MRA), gaussian process regression (GPR), and gene expression programming (GEP) approaches. The present research reveals the effect of the quality & quantity of the training database and the impact of the multicollinearity on the performance and overfitting of the MRA, GPR, and GEP models. The performance of the soft computing models has been measured by root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), weighted mean absolute percentage error (WMAPE), coefficient of determination (R2), correlation coefficient (r), variance accounted for (VAF), Nash–Sutcliffe efficiency (NS), normalized mean bias error (NMBE), Legate McCabe's Index (LMI), root mean square error to observations’ standard deviation ratio (RSR), a20-index, index of agreement (IOA), and index of scatter (IOS) statistical tools. The performance comparison of MRA, GPR, and GEP shows that GPR model MD11 has predicted UCS of soil with high performance (R = 0.9959, VAF = 99.18, NS = 0.9909, LMI = 0.1026, RSR = 0.0952, a20-index = 100.00, IOA = 0.9487 & IOS = 0.0531) and the least prediction error (RMSE = 2.4482 N/cm2, MAE = 1.8840 N/cm2, MAPE = 5.0849 N/cm2, WMAPE = 0.0408 N/cm2, NMBE = 0.1299 N/cm2). In the validation, model MD11 has achieved RMSE = 3.4849 N/cm2, MAE = 3.1845 N/cm2, R = 0.9040, R2 = 0.8172, confidence interval of ± 5.0% by predicting UCS of lab-tested twelve soil samples, which is acceptable. This study shows that the GPR approach predicts better UCS in the presence of multicollinearity and using a small database. The sensitivity analysis illustrates that the UCS prediction of cohesive virgin soil is very highly influenced by fine content, dry unit weight, porosity, void ratio, degree of saturation, and specific gravity of soil.
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Data availability
The data would remain confidential and shared by the corresponding author at the request. Software support: MATLAB R2020a: for employing soft computing models, analysis, evaluation, prediction. Origin Lab 2022b: for graphical presentations and analysis.
Abbreviations
- \(C^{\prime}\) :
-
Cohesion (N/mm2)
- \(CBR_{10}\) :
-
CBR of soil compacted with 10 blows (%)
- \(CBR_{30}\) :
-
CBR of soil compacted with 30 blows (%)
- \(CBR_{65}\) :
-
CBR of soil compacted with 65 blows (%)
- \(C^{C}\) :
-
Cement condition
- \(C_{{\text{C}}}\) :
-
Coefficient of curvature
- \(C^{{\text{T}}}\) :
-
Curing period (days)
- \(C_{{\text{U}}}\) :
-
Coefficient of uniformity
- \(C^{{{\text{cc}}}}\) :
-
Curing condition
- \(L^{{\text{C}}}\) :
-
Lime content (%)
- \(L_{{\text{S}}}\) :
-
Linear shrinkage (%)
- \(M^{{\text{O}}}\) :
-
Molar concentration of alkali solution
- \(M^{{\text{S}}}\) :
-
Micro silica (%)
- \(V_{{\text{p}}}\) :
-
Primary ultrasonic wave velocity (m/s)
- \(\gamma_{{\text{w}}}\) :
-
Wet density (g/cc)
- A/B:
-
Amount of alkali to binder
- AI:
-
Artificial intelligence
- ANFIS:
-
Adaptive neuro-fuzzy inference system
- ANN:
-
Artificial neural networks
- ASTM:
-
American standard for testing and materials
- BFS:
-
Blast furnace slag (%)
- BUW:
-
Bulk unit weight (g/cc)
- C:
-
Clay content (%)
- CBR:
-
California bearing ratio (%)
- CC:
-
Correlation coefficient
- CI:
-
Compressibility index
- COD:
-
Coefficient of determination
- CSO:
-
Cuckoo search optimization
- D:
-
Sampling depth
- DCPI:
-
Dynamic cone penetration index
- DE:
-
Differential equation
- DS:
-
Degree of saturation (%)
- DT:
-
Decision tree
- DUW:
-
Dry unit weight (gm/cc)
- EPR:
-
Evolutionary polynomial regression
- FA:
-
Fly ash (%)
- FC:
-
Fine content (%)
- GA:
-
Genetic algorithm
- GB:
-
Gradient boosting
- GGBS:
-
Ground granulated blast-furnace slag
- GMDH:
-
Group method of data handling
- K :
-
Permeability (m/s)
- LI:
-
Liquidity index
- LL:
-
Liquid limit (%)
- MC:
-
Moisture content (%)
- MDD:
-
Maximum dry density (gm/cc)
- MRA:
-
Multiple regression Analysis
- MVR:
-
Multi-variable regression
- Na/Al:
-
Atomic proportion of Na to Al
- NF:
-
Neuro fuzzy
- NMC:
-
Natural moisture content (%)
- NWC:
-
Natural water content (%)
- OMC:
-
Optimum moisture content (%)
- ɸ :
-
Diameter (m)
- P :
-
Porosity (%)
- PA:
-
Pond ash (%)
- pH:
-
Potential of hydrogen
- PL:
-
Plastic limit (%)
- PSO:
-
Particle swarm optimization
- RA:
-
Regression analysis
- RBF:
-
Radial bias function
- RF:
-
Random forest
- RHA:
-
Rice husk ask (%)
- RVM:
-
Relevance vector machine
- S :
-
Sand content
- SG:
-
Specific gravity
- Si/Al:
-
Atomic proportion of Si to Al
- SLR:
-
Simple linear regression
- SUW:
-
Saturated unit weight (gm/cc)
- SVM:
-
Support vector machine
- UCS:
-
Unconfined compressive strength (N/cm2)
- Vp:
-
Primary ultrasonic wave velocity
- VR:
-
Void ratio
- W/c ratio:
-
Water/cement ratio
- γ :
-
Density (gm/cc)
- ϕ :
-
Internal friction angle (degree)
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JK: Main author, conceptualization, literature review, manuscript preparation, application of AI models, methodological development, statistical analysis, detailing, and overall analysis; KSG: Conceptualization, overall analysis, manuscript finalization, detailed review, and editing.
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Appendix
Appendix
Sample ID | FC (%) | DUW (gm/cc) | P (%) | VR | DS (%) | SG | Actual UCS | MD11 |
---|---|---|---|---|---|---|---|---|
1 | 93.64 | 1.72 | 20.11 | 3.57 | 103.16 | 2.53 | 33.85 | 29.91 |
2 | 87.00 | 1.77 | 13.74 | 3.17 | 94.09 | 2.41 | 42.11 | 38.38 |
3 | 85.33 | 1.75 | 18.99 | 3.43 | 103.31 | 2.55 | 36.77 | 32.10 |
4 | 76.00 | 1.64 | 17.62 | 3.83 | 108.99 | 2.44 | 40.55 | 37.60 |
5 | 80.64 | 1.69 | 14.76 | 3.43 | 101.26 | 2.37 | 30.97 | 26.22 |
6 | 78.94 | 1.71 | 13.30 | 3.27 | 93.65 | 2.33 | 37.20 | 40.78 |
7 | 73.20 | 1.77 | 14.08 | 3.18 | 96.69 | 2.41 | 32.32 | 37.22 |
8 | 80.23 | 1.77 | 13.30 | 3.11 | 97.93 | 2.40 | 17.97 | 17.30 |
9 | 81.41 | 1.85 | 16.29 | 2.96 | 83.30 | 2.51 | 40.93 | 36.92 |
10 | 75.08 | 1.80 | 7.41 | 2.86 | 100.21 | 2.28 | 20.03 | 22.58 |
11 | 80.08 | 1.76 | 23.68 | 3.57 | 98.50 | 2.70 | 36.43 | 34.83 |
12 | 86.87 | 1.65 | 23.17 | 4.01 | 103.43 | 2.59 | 27.46 | 26.60 |
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Khatti, J., Grover, K.S. Prediction of UCS of fine-grained soil based on machine learning part 1: multivariable regression analysis, gaussian process regression, and gene expression programming. Multiscale and Multidiscip. Model. Exp. and Des. 6, 199–222 (2023). https://doi.org/10.1007/s41939-022-00137-6
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DOI: https://doi.org/10.1007/s41939-022-00137-6