# Research on the Prediction Model of Loess Collapsibility in Xinyuan County, Ili River Valley Area

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Sources

#### 2.2. Test Method

#### 2.3. Physical Properties

- Particle size composition analysis

- 2.
- Micro-structure analysis

- 3.
- Material composition analysis

_{2}, Na (ALSi

_{3}O

_{8}), Fe

_{2}O

_{3}, and others. Figure 5b was produced using a quantitative analysis of the XRD test data. As can be shown, the loess samples in the study area have a Na (ALSi

_{3}O

_{8}) content of 52.5%, a SiO

_{2}content of 41.8%, and a Fe

_{2}O

_{3}content of 5.7%.

## 3. Correlation Analysis between Soil Properties and Loess Collapsibility

#### 3.1. Correlation Analysis Data

- Between 0.800 and 0.857, or a substantial association, is shown by the Pearson correlation coefficient between the collapsibility coefficients δ
_{s}, density ρ, and saturation Sr. The density ρ, saturation Sr, and collapsibility coefficients δ_{s}all have an extremely strong negative connection. Figure 6a through Figure 6b display the scatter plots. The scatter plots of the sample points in the figures show that they are ordered in a systematic way, with a high correlation trend and great significance. - Between 0.628 and 0.768, or a strong association, is indicated by the Pearson correlation coefficient between the collapsibility coefficient δ
_{s}, porosity n, dry density ρ_{d}, void ratio e, and moisture content ω. The collapsibility coefficient δ_{s}and porosity n and void ratio e have a strong positive correlation, whereas the collapsibility coefficient δ_{s}and dry density ρd and moisture content ω have a strong negative correlation. Figure 6c through Figure 6f display the scatter plots. The scatter plots of the sample points in the figures can be seen to be organized and to have a high correlation trend and great significance.

#### 3.2. Correlation Analysis between Collapsibility Index and Single Physical Index

#### 3.3. Selection of Prediction Model Indicators

_{d}, void ratio e, degree of saturation S

_{r}, porosity n, and moisture content ω, of loess in the study area were extremely strong and strong. There was a computational relationship between density ρ and dry density ρ

_{d}, as well as between porosity n and the void ratio e, and their physical meaning was similar. In addition, in the prediction model, they lead to a strong collinearity relationship, affecting the significance and effectiveness of the prediction model. Therefore, this paper selected four parameters, density ρ, degree of saturation S

_{r}, porosity n, and moisture content ω, as the discriminative indicators of the prediction model.

## 4. Construction of the Prediction Model of Loess Collapsibility

#### 4.1. Multiple Linear Regression Model

^{2}= 0.816. The square of the modified correlation coefficient was R

^{2}= 0.812, and the error of the standard estimate was S = 0.02233. When 0.8 < R < 1, this indicates that the fitting degree of the prediction regression model is extremely high [28].

#### 4.2. Neural Network−Based Prediction Model

#### 4.3. Model Simulation Effect Evaluation Index

_{obs}represents the measured collapsibility coefficient; δ

_{sim}represents the collapsible coefficient δ

_{obs}simulated by the prediction model; ${\overline{\delta}}_{\mathit{obs}}$ and ${\overline{\delta}}_{\mathit{sim}}$ represent the average value of the measured collapsible coefficient and the collapsible coefficient simulated by the prediction model. Table 6 is the evaluation index of the model simulation effect.

## 5. Discussion

#### 5.1. Comprehensive Comparative Analysis of the Models

#### 5.2. The Advantages and Limitations of RBF Neural Network Model

## 6. Conclusions

- The engineering geological conditions and the physical properties of the loess in the study area were analyzed. The single−layer soil of the Quaternary loess in the research area is mostly collapsible and self−weight collapsible, with poor engineering geological conditions. The loess particle structure in this area is mainly cylindrical, flat, and irregular. The main contact between particles is support contact, supplemented by inlay contact, forming many inter−particle pores and some large pores. The loess in the study area is mainly composed of quartz and albite, with less hematite.
- The correlation between the loess collapsibility coefficient and soil property indicators in the study area was analyzed. The correlation analysis results showed that the loess collapsibility coefficient δ
_{s}in the study area was extremely strongly correlated with the density ρ and the degree of saturation Sr; strongly correlated with the porosity n, dry density ρd, void ratio e, and moisture content ω; moderately correlated with the liquidity index I_{L}; weakly correlated with the sampling depth h and plasticity index Ip; extremely weakly correlated with the plastic limit ωp; and not correlated with the compression modulus Es, compression coefficient a, and liquid limit ω_{L}. Finally, four parameters, the density ρ, degree of saturation Sr, porosity n, and moisture content ω, were selected as determination indicators for the prediction model. - In the studied region, a prediction model for loess collapsibility was developed. According to the prediction model’s results, the likelihood that a given event will occur is predicted with a 76.70% accuracy for multiple linear regression and a 94.42% accuracy for RBF neural network prediction. Simultaneously, the RBF neural network prediction model’s evaluation index clearly outperforms the regression prediction model’s. As a result, the thorough comparison analysis demonstrates that the RBF neural network prediction model outperforms the regression prediction model in terms of accuracy and dependability.
- The collapsibility of loess is the primary subject of this investigation. Subsequent research can take into account the relationship between additional soil indicators, such as the relationship between soil physical parameters and the compression coefficient, and develop a prediction model. At the same time, how to further deal with the results of this study, so that one can carry out rapid evaluation in engineering construction, is a direction of future research.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**SEM results of collapsible loess in the study area. (

**a**) The 1000× SEM image; (

**b**) 50,000× SEM image; (

**c**) 20,000× SEM image; (

**d**) 50,000× SEM image.

**Figure 5.**XRD experimental analysis. (

**a**) XRD test analysis diagram; (

**b**) mineral composition pie chart.

**Figure 6.**Fitted graphs of the relationship between the loess collapsibility coefficient and the physical property indicators in the study area. (

**a**) Collapsibility coefficient and density; (

**b**) collapsibility coefficient and saturation; (

**c**) collapsibility coefficient and porosity; (

**d**) collapsibility coefficient and moisture content; (

**e**) collapsibility coefficient and dry density; (

**f**) collapsibility coefficient and porosity.

**Figure 7.**Comparison between the actual loess collapsibility coefficient and the predicted value of the regression model.

**Figure 8.**Comparison between the actual loess collapsibility coefficient and the predicted value of the RBF model in the study area.

Mean Value | Standard Deviation | Coefficient of Variation | Maximum Value | Minimum Value | |
---|---|---|---|---|---|

Sampling depth, h | 11.93 | 13.44 | 1.13 | 74.8 | 0.60 |

Moisture content, ω (%) | 12.73 | 5.32 | 0.42 | 26.97 | 3.39 |

Density, ρ (g/cm^{3}) | 1.58 | 0.23 | 0.14 | 2.13 | 1.232 |

Dry density, ρ_{d} (g/cm^{3}) | 1.4 | 0.17 | 0.12 | 1.90 | 1.06 |

Porosity ratio, e | 0.95 | 0.23 | 0.24 | 1.53 | 0.42 |

Saturation, Sr (%) | 39.96 | 23.33 | 0.58 | 110.05 | 8.31 |

Porosity, n (%) | 47.88 | 6.3 | 0.13 | 60.51 | 29.51 |

Liquid limit, ω_{L} (%) | 26.59 | 1.46 | 0.06 | 31.6 | 24.00 |

Plastic limit, ω_{p} (%) | 17.65 | 1.43 | 0.08 | 22.6 | 14.80 |

Plasticity index, I_{p} | 8.94 | 0.72 | 0.08 | 9.96 | 6.10 |

Liquidity index, I_{L} | −0.54 | 0.57 | −1.05 | 1.11 | −1.54 |

**Table 2.**Correlation analysis between the collapsibility coefficient and each soil property parameter in the study area.

Correlation Index | Regression Equation | Saliency Score | Correlation Coefficient | Correlation |
---|---|---|---|---|

δ_{s} − ρ | δ_{s} = −0.194ρ + 0.375 | 0.000 | −0.857 | extremely strong |

δ_{s} − S_{r} | δ_{s} = −0.002S_{r} + 0.138 | 0.000 | −0.800 | extremely strong |

δ_{s} − n | δ_{s} = 0.006n − 0.233 | 0.000 | 0.768 | strong |

δ_{s} − ρ_{d} | δ_{s} = −0.233ρ_{d} + 0.395 | 0.000 | −0.768 | strong |

δ_{s} − e | δ_{s} = 0.172e − 0.095 | 0.000 | 0.757 | strong |

δ_{s} − ω | δ_{s} = −0.006ω + 0.145 | 0.000 | −0.628 | strong |

δ_{s} − I_{L} | δ_{s} = −0.054I_{L} + 0.039 | 0.000 | −0.595 | medium |

δ_{s} − h | δ_{s} = −0.001h + 0.086 | 0.000 | −0.385 | weak |

δ_{s} − I_{P} | δ_{s} = 0.015I_{p} − 0.066 | 0.003 | 0.211 | weak |

δ_{s} − ω_{P} | δ_{s} = −0.005ω_{p} + 0.161 | 0.039 | −0.147 | extremely weak |

δ_{s} − Es | δ_{s} = 8.134E − 4Es + 0.059 | 0.197 | 0.092 | no |

δ_{s} − a | δ_{s} = 0.017a + 0.063 | 0.305 | 0.073 | no |

δ_{s} − ω_{L} | δ_{s} = −0.001ω_{L} + 0.106 | 0.571 | −0.041 | no |

_{s}is the collapsibility coefficients, ρ is the density, Sr is the saturation, n is the porosity, ρ

_{d}is the dry density, e is the porosity ratio, ω is the moisture content, I

_{L}is the liquidity index, h is the sampling depth, I

_{P}is the plasticity index, ω

_{P}is the Plastic limit, E

_{s}is the compression modulus, a is the compressibility coefficient, ω

_{L}is the liquid limit.

Model | R | R^{2} | $\overline{{\mathit{R}}^{\mathbf{2}}}$ | The Error of the Standard Estimate (S) |
---|---|---|---|---|

1 | 0.903 | 0.816 | 0.812 | 0.02233 |

Model | Parameter | Non−Normalized Coefficients | Normal Coefficient | t | Sig | |
---|---|---|---|---|---|---|

B | Standard Error | |||||

1 | (Constant) | −0.672 | 0.904 | −0.743 | 0.458 | |

Moisture content, ω (%) | −0.013 | 0.003 | −1.379 | 4.330 | 0.00 | |

Density, ρ (g/cm^{3}) | 0.116 | 0.334 | 0.513 | 0.349 | 0.728 | |

Degree of saturation, S_{r} (%) | 0.002 | 0.001 | 1.063 | 3.217 | 0.002 | |

Porosity, n (%) | 0.013 | 0.009 | 1.614 | 1.444 | 0.150 |

Data Message | Number of Samples N (Group) | Percentage |
---|---|---|

Train | 124 | 62.9% |

Test | 52 | 26.4% |

Reservation | 21 | 10.7% |

Valid | 197 | 100% |

Excluded | 0 | |

Grand total | 197 |

Name | Definition | Value Ranges | Optimal Value |
---|---|---|---|

Root Mean Squared Error (RMSE) | Measure the deviation between the predicted value and the true value | [0, +∞] | 0 |

Correlation Coefficient (CC) | Evaluate the simulated value and the measured value | [−1, 1] | 1 or −1 |

Nash–Sutcliffe Efficiency Coefficient (NSE) | The prediction accuracy of the quantitative simulation model | [0, 1] | 1 |

Percent Bias (PBIAS) | Evaluate the simulated value and the measured value | [−∞, +∞] | 0 |

Forecasting Model | Evaluating Indicator | |||
---|---|---|---|---|

RMSE | CC | NSE | PBIAS (%) | |

Regression model | 0.022 | 0.903 | 0.773 | −0.007 |

RBF neural network model | 0.014 | 0.962 | 0.919 | −1.494 |

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## Share and Cite

**MDPI and ACS Style**

Chen, L.; Chen, K.; He, G.; Liu, Z.
Research on the Prediction Model of Loess Collapsibility in Xinyuan County, Ili River Valley Area. *Water* **2023**, *15*, 3786.
https://doi.org/10.3390/w15213786

**AMA Style**

Chen L, Chen K, He G, Liu Z.
Research on the Prediction Model of Loess Collapsibility in Xinyuan County, Ili River Valley Area. *Water*. 2023; 15(21):3786.
https://doi.org/10.3390/w15213786

**Chicago/Turabian Style**

Chen, Lifeng, Kai Chen, Genyi He, and Zhiqi Liu.
2023. "Research on the Prediction Model of Loess Collapsibility in Xinyuan County, Ili River Valley Area" *Water* 15, no. 21: 3786.
https://doi.org/10.3390/w15213786