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Prediction of UCS of fine-grained soil based on machine learning part 1: multivariable regression analysis, gaussian process regression, and gene expression programming

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Multiscale and Multidisciplinary Modeling, Experiments and Design Aims and scope Submit manuscript

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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Funding

No funding was received in assisting the preparation of this manuscript.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Rajasthan Technical University, Kota, Rajasthan, India

    Jitendra Khatti & Kamaldeep Singh Grover

Authors
  1. Jitendra Khatti
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  2. Kamaldeep Singh Grover
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Contributions

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.

Corresponding author

Correspondence to Jitendra Khatti.

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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

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