# Prediction of the Subgrade Soil California Bearing Ratio Using Machine Learning and Neuro-Fuzzy Inference System Techniques: A Sustainable Approach in Urban Infrastructure Development

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## Abstract

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^{2}value of 0.81, surpassing both MLR and ANN. Sensitivity analysis revealed the PI as the most significant parameter affecting the CBR, carrying a relative importance of 46%. The findings underscore the potent potential of machine learning and neuro-fuzzy inference systems in the sustainable management of non-renewable urban resources and provide crucial insights for urban planning, construction materials selection, and infrastructure development. This study bridges the gap between computational techniques and geotechnical engineering, heralding a new era of intelligent urban resource management.

## 1. Introduction

^{2}). The ANFIS model, with its ability to handle complex relationships and non-linear data, is expected to outperform the traditional MLR models and potentially rival the predictive performance of ANN models. This study contributes to advancing sustainable urban resource management by utilizing machine learning techniques and theoretical simulations. The findings will improve our understanding of the factors influencing CBR values and provide valuable insights for decision-makers and engineers involved in urban infrastructure development. Applying these predictive models can optimize the design and construction of urban geotechnical infrastructure, leading to more sustainable and efficient urban development practices.

## 2. Soil Database and Laboratory Testing

## 3. Data Analysis

#### 3.1. MLR Analysis

_{i}= α

_{0}+ α

_{1}× x

_{i1}+ α

_{2}× x

_{i2}+ … + α

_{p}× x

_{ip}+ E

_{i}= The dependent variable

_{i}= Independent variables

_{0}= intercept on the y-axis

_{p}= coefficients of slopes of independent variables

#### 3.2. Artificial Neural Network

^{2}value and lower RMS error. One hidden layer with five neurons offered the optimum network structure for the inputs such as soil type, PI, MDD, and CBR as an output (3-5-1). Of the total data points, 70% were used to train the model, 15% were used to test the model, and the remaining 15% were validated using MATLAB r2022a software. The suggested ANN model architecture is shown in Figure 3.

#### 3.3. Adaptive Neuro-Fuzzy Inference System (ANFIS)

_{1,i}is the target output of the nth node of layer l. A square node represents the adaptive nodes.

_{1,n}= µ

_{An}(Soil Type) for n = 1, 2, 3

_{1,n}= µ

_{Bn−3}(PI) for n = 4, 5, 6

_{1,n}= µ

_{Cn−6}(MDD) for n = 7, 8, 9

_{An}, µ

_{Bn−3}, and µ

_{Cn−6}represent the trapezoidal membership functions.

_{n}).

_{2,n}= w

_{n}= μ

_{An}(Soil Type) × μ

_{Bn}(PI) × μ

_{Cn}(MDD) for n = 1, 2, 3.

_{n}, q

_{n}, r

_{n,}and s

_{n}) are adjustable parameters called consequent parameters.

#### 3.4. Performance Criteria

^{2}values. These criteria are defined by the equations below.

## 4. Results and Discussion

#### 4.1. MLRA Results

_{0}= CBR is not related to Soil Type, PI, and MDD,

_{1}= CBR is related to Soil Type, PI, and MDD.

#### 4.2. ANN Results

^{2}(coefficient of determination) and RMSE (root mean square error) values for the training, testing, and validation data sets. The data was split into three sets to validate the accuracy of the ANN model for predicting the CBR: training, testing, and validation. The model was trained on 70 percent of the data, and the R

^{2}value obtained for this training data set was 0.67, indicating that the model explains 67% of the variation in the CBR (Figure 8). The RMSE value was 2.63, indicating the average difference between the predicted and actual CBR values. Similarly, the R

^{2}and RMSE values were calculated for the testing and validation data sets. For the testing data set, the R

^{2}value was 0.65, and the RMSE value was 2.70. The R

^{2}and RMSE values for the validation data set were 0.66 and 2.64, respectively. The results of the ANN model were compared to those obtained from a Multiple Linear Regression Analysis (MLRA), which is a traditional statistical method used for predicting the CBR. The results showed that the ANN model outperformed the MLRA analysis in predicting the CBR value [25,28,31]. The success of the ANN model can be attributed to its ability to process complex networks and establish the connection between input and output parameters, resulting in more accurate results. The scatterplot in Figure 9 compares the predicted CBR values by the ANN model and the actual CBR values.

#### 4.3. ANFIS Results

^{2}value of 0.81 and an RMSE of 2.26 for the training data set, indicating that the model explains 81% of the variation in the CBR. Similarly, for the testing data set, the R

^{2}value was 0.82, and the RMSE value was 2.29. The R

^{2}and RMSE values for the validation data set were 0.82 and 2.23, respectively. These results suggest that the ANFIS model could predict soil CBR values with high accuracy, as evidenced by the high correlation coefficient and low mean square error.

^{2}values and low RMSE values obtained from the training, testing, and validation data sets indicate the model’s high degree of accuracy [30,31]. The use of ANFIS models in soil analysis can provide valuable insights into the behavior of soil properties, which can be useful in designing geotechnical structures and infrastructure projects.

^{2}values ranging from 0.80 to 0.93 for MLRA, 0.78 to 0.97 for ANN, and 0.98 for ANFIS, respectively, for the CBR prediction with smaller datasets comprising 124 to 264 samples [25,26,28,29,30,31]. In contrast, our investigation employed a more extensive dataset consisting of 2191 samples, encompassing diverse soil types. Consequently, the variability in R

^{2}values might be attributed to the larger dataset. Nonetheless, our study aligns with the observed trend of higher prediction efficacy achieved by the ANFIS model, followed by the ANN and MLRA models. Table 7 compares the predicted CBR values from the developed model with the actual laboratory data.

#### 4.4. Sensitivity Analysis

## 5. Conclusions

^{2}value of 0.45, prompted the exploration of advanced methods. The artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) models were developed and compared, with promising results. The ANN model improved predictive ability, achieving R

^{2}values of 0.67, 0.65, and 0.66 for training, testing, and validation, respectively. The ANFIS model, outperforming the MLR model, yielded higher predictive accuracy with R

^{2}values of 0.81, 0.82, and 0.82 for training, testing, and validation data, respectively. While the use of a larger dataset (2191 data points with a variety of soil types) resulted in lower R

^{2}values compared to the previous literature, which utilized smaller data samples. However, the trend of prediction efficiency remained consistent, showing the ANFIS model outperforming both the ANN and MLRA models in estimating the CBR, which aligns with previous studies. The results confirm the efficacy of soft computing techniques, particularly the ANFIS model, in predicting the CBR based on soil type, PI, and MDD values, providing more accurate and efficient CBR estimation. These models offer a viable alternative to traditional statistical analysis methods and contribute to the sustainable management of urban resources. Accurate CBR prediction is crucial for optimizing the design and construction of urban infrastructure, promoting efficient resource utilization, and ensuring the long-term sustainability of cities. The combination of machine learning techniques and theoretical simulations demonstrated by the ANN and ANFIS models offers a powerful approach to CBR prediction. The developed models provide valuable insights into the factors influencing the CBR and can assist engineers and decision-makers in making informed choices for urban infrastructure development. Further research can explore incorporating additional soil parameters and examining the applicability of these models in different geotechnical contexts.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**Measured versus predicted CBR values obtained from the ANN model for (

**a**) training data, (

**b**) testing data, and (

**c**) validation data.

**Figure 10.**Measured versus predicted CBR values obtained from the ANFIS model for (

**a**) training data, (

**b**) testing data, and (

**c**) validation.

**Figure 11.**Variation of the CBR with changes in (

**a**) soil type and PI, (

**b**) soil type and MDD, and (

**c**) PI and MDD.

Methodology Used | Input Parameters Considered | No. of Samples | R^{2} | Ref. |
---|---|---|---|---|

GP | OMC, MDD, S, G, LL, and PI | 151 | 0.92 | [24] |

MLRAANN | Sieve analysis, Atterberg limits, MDD, and OMC. | 124 | 0.88 0.95 | [25] |

ANN | OMC, MDD, L, and LS | 51 | 0.84 | [26] |

GMDH | Gravel content (GC), Sand content (SC), Fine content (FC), LL, PI, OMC, and MDD | 158 | 0.96 | [27] |

MLRAANN | D60 and MDD | 207 | 0.93 0.97 | [28] |

ANN | Gradation, OMC, MDD, LL, PI, and percentages of SO3, Soluble salt, Gypsum, and Organic materials. | 358 | 0.78 | [29] |

ERFANFIS | Hydrated lime-activated rice husk ash, LL, PL, PI, OMC, MDD, and Clay activity. | 121 | 1.00 0.99 | [30] |

MLRAANNANFIS | LL, PL, PI, S, G, C/Si, MDD, and OMC | 264 | 0.80 0.90 0.98 | [31] |

ELM-CSO | Gravel %, Sand %, Fines %, LL, PL, OMC, and MDD. | 149 | 0.90 | [32] |

Particulars | Test Codes | Mean | Standard Deviation | Sample Variance | Kurtosis | Skewness | Minimum | Maximum |
---|---|---|---|---|---|---|---|---|

PI | ASTM D4318-00 | 10.80 | 9.37 | 87.82 | −0.68 | 0.44 | 0 | 39 |

MDD | ASTM D698 | 1.91 | 0.16 | 0.02 | −0.16 | −0.30 | 1.5 | 2.31 |

CBR | ASTM D1883-16 | 11.48 | 5.77 | 33.33 | −0.68 | 0.44 | 2.11 | 27.4 |

Sample No | Soil Type | Soil Description | Encoded to | PI (%) | MDD (g/cc) | CBR (%) |
---|---|---|---|---|---|---|

1 | CI | Intermediate-Plasticity Clay | 1 | 19.00 | 1.83 | 6.40 |

2 | CL | Low-Plasticity Clay | 2 | 10.60 | 1.68 | 6.50 |

3 | GM | Silty Gravel | 3 | 9.00 | 1.88 | 10.89 |

4 | GP | Poorly Graded Gravel | 4 | 10.00 | 1.95 | 7.11 |

5 | SC | Clayey Sand | 5 | 14.00 | 1.77 | 4.05 |

6 | SM | Silty Sand | 6 | 26.00 | 1.98 | 11.60 |

7 | SP | Poorly Graded Sand | 7 | 0 | 2.11 | 17.60 |

8 | SW | Well-Graded Sand | 8 | 0 | 1.94 | 10.58 |

Regression Statistics | |
---|---|

Multiple R | 0.67 |

R Square | 0.45 |

Adjusted R Square | 0.45 |

RMSE | 4.270 |

Observations | 2191 |

Coefficients | Standard Error | T Stat | p-Value | |
---|---|---|---|---|

Intercept | 2.13 | 1.14 | 1.86 | <0.05 |

Soil Type | 1.24 | 0.05 | 26.16 | <0.05 |

PI | −0.25 | 0.01 | −25.39 | <0.05 |

MDD | 2.67 | 0.63 | 4.24 | <0.05 |

Analysis Performed | R^{2} Value | Root Mean Square Error (RMSE) | ||||
---|---|---|---|---|---|---|

Training | Testing | Validation | Training | Testing | Validation | |

MLRA | 0.45 | 4.6 | ||||

ANN | 0.67 | 0.65 | 0.66 | 2.63 | 2.70 | 2.64 |

ANFIS | 0.81 | 0.82 | 0.82 | 2.26 | 2.29 | 2.23 |

Soil Type | Encoded To | PI, % | MDD, g/cc | Actual CBR, % | Predicted CBR, % | ||
---|---|---|---|---|---|---|---|

MLRA Output | ANN Output | ANFIS Output | |||||

SP | 7.00 | 0.00 | 2.11 | 17.60 | 15.96 | 16.52 | 16.45 |

SC | 5.00 | 11.70 | 1.47 | 10.43 | 11.40 | 8.59 | 9.75 |

SM | 6.00 | 30.00 | 1.99 | 9.04 | 7.84 | 10.75 | 8.97 |

CL | 2.00 | 10.60 | 1.68 | 6.50 | 7.15 | 6.04 | 5.67 |

GP | 4.00 | 0.00 | 2.09 | 14.80 | 11.79 | 17.48 | 16.95 |

GM | 3.00 | 28.00 | 2.11 | 7.09 | 3.92 | 7.93 | 6.51 |

SW | 8.00 | 23.00 | 1.77 | 10.51 | 12.56 | 11.39 | 11.30 |

CI | 1.00 | 19.00 | 1.83 | 6.40 | 3.60 | 2.47 | 5.99 |

SC | 5.00 | 15.00 | 1.88 | 7.11 | 10.05 | 8.22 | 6.91 |

CI | 1.00 | 16.00 | 1.75 | 4.13 | 4.41 | 3.56 | 5.17 |

SW | 8.00 | 22.60 | 2.00 | 9.50 | 12.32 | 11.31 | 10.64 |

SW | 8.00 | 12.15 | 1.93 | 11.40 | 14.83 | 11.31 | 12.85 |

CL | 2.00 | 17.00 | 1.65 | 2.71 | 5.72 | 2.62 | 3.93 |

GP | 4.00 | 0.00 | 1.96 | 15.50 | 11.98 | 17.77 | 16.95 |

SM | 6.00 | 15.67 | 2.14 | 12.50 | 10.91 | 9.60 | 11.25 |

SM | 6.00 | 19.22 | 2.02 | 10.48 | 10.27 | 9.89 | 10.50 |

GP | 4.00 | 0.00 | 1.84 | 18.40 | 12.15 | 18.02 | 18.10 |

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## Share and Cite

**MDPI and ACS Style**

Gowda, S.; Kunjar, V.; Gupta, A.; Kavitha, G.; Shukla, B.K.; Sihag, P.
Prediction of the Subgrade Soil California Bearing Ratio Using Machine Learning and Neuro-Fuzzy Inference System Techniques: A Sustainable Approach in Urban Infrastructure Development. *Urban Sci.* **2024**, *8*, 4.
https://doi.org/10.3390/urbansci8010004

**AMA Style**

Gowda S, Kunjar V, Gupta A, Kavitha G, Shukla BK, Sihag P.
Prediction of the Subgrade Soil California Bearing Ratio Using Machine Learning and Neuro-Fuzzy Inference System Techniques: A Sustainable Approach in Urban Infrastructure Development. *Urban Science*. 2024; 8(1):4.
https://doi.org/10.3390/urbansci8010004

**Chicago/Turabian Style**

Gowda, Sachin, Vaishakh Kunjar, Aakash Gupta, Govindaswamy Kavitha, Bishnu Kant Shukla, and Parveen Sihag.
2024. "Prediction of the Subgrade Soil California Bearing Ratio Using Machine Learning and Neuro-Fuzzy Inference System Techniques: A Sustainable Approach in Urban Infrastructure Development" *Urban Science* 8, no. 1: 4.
https://doi.org/10.3390/urbansci8010004