# Relationship between the Shear Strength and Microscopic Pore Parameters of Saline Soil with Different Freeze-Thaw Cycles and Salinities

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Soil Properties and Sample Preparation

^{+}, HCO

_{3}

^{−}, and SO

_{4}

^{2−}. Table 2 lists the mineralogical composition, tested by X-ray diffraction, which indicates that the primary mineral was the main mineral in the soil. In addition, the maximum dry density and optimum water content of the tested saline soil, obtained by a compaction test, were 1.63 g/cm

^{3}and 21.3%, respectively. The soil was named as lean clay according to the Unified Soil Classification System (USCS) [32].

_{3}

^{−}and SO

_{4}

^{2−}content in the collected saline soil was approximately 1:1. Therefore, anhydrous NaHCO

_{3}and anhydrous Na

_{2}SO

_{4}were mixed at a ratio of 1:1 to prepare remolded soil samples with different salt contents. In addition, the water content of all remolded soil samples was set to the optimum water content. Before preparing the remolded soil samples, the collected saline soil was desalinized with distilled water first, and then dried in an oven. Next, the dried soil was crushed and sieved through a 2 mm sifter. After that, the calculated amount of salt powder and distilled water was added into the dried soil and mixed evenly. The soil samples were wrapped with airtight bags and sealed for 24 h to let the water and salt distribute uniformly. Then, the soil samples were compacted into three layers in a cylindrical mold at a 90% compaction degree, according to the maximum dry density. The target dry density of the compacted soil samples was 1.467 g/cm

^{3}. Finally, the remolded soil samples were sealed with fresh-keeping films and put them in a moisturizing container to spare.

#### 2.2. Freeze–Thaw Tests

#### 2.3. Triaxial Tests

^{−1}. GB/T50123-1999 [31] indicates that if there is a peak value existent in the stress–strain curve, the value is the failure strength of the soil sample; otherwise, the failure strength of the soil sample is considered as the principal stress difference corresponding to a 15% axial strain. Based on the triaxial test results, the cohesion and internal friction angle of the soil samples could be obtained by the Mohr–Coulomb criterion.

#### 2.4. SEM Tests

#### 2.5. Acquisition of Microscopic Parameters

- 1.
- Porosity

- 2.
- Average pore diameter

- 3.
- Average shape coefficient

- 4.
- Surface fluctuation fractal dimension

- 5.
- Orienting probability entropy

## 3. Results and Discussion

#### 3.1. Shear Strength Characteristic

#### 3.1.1. Failure Strength

#### 3.1.2. Shear Strength Parameters

#### 3.2. Microstructure Characteristics

#### 3.2.1. General Description of Microstructure of Soil Samples

#### 3.2.2. Porosity

#### 3.2.3. Average Pore Diameter

#### 3.2.4. Average Shape Coefficient of Pores

#### 3.2.5. Surface Fluctuation Fractal Dimension of Pores

#### 3.2.6. Orienting Probability Entropy of Pores

#### 3.3. Relationship between Failure Strength and Microscopic Pore Parameters

## 4. Conclusions

- The stress–strain characteristics of soil samples with different salinities and freeze–thaw cycles all belong to the strain–hardening type. The failure strength of the soil samples increased with increasing confining pressure under different experimental conditions. Compared with the salt content, the number of freeze–thaw cycles had a greater influence on the failure strength of the soil samples. As the number of freeze–thaw cycles increased, the failure strength of the soil samples showed a decreasing trend. The decreasing rate was the largest after the first 10 freeze–thaw cycles and tended to be slow in the range of 10–60 freeze–thaw cycles, while the decreasing rate increased again after 120 freeze–thaw cycles. When the number of freeze–thaw cycles was no larger than 60, the failure strength of the soil samples decreased first, then increased with the increasing salt content, but when the number of freeze–thaw cycles was 60–120, the failure strength decreased continuously with the increasing salt content.
- The cohesion of the soil samples decreased with the increase in freeze–thaw cycles, and the decreasing rate was the largest in the first 10 freeze–thaw cycles, which was similar to the variation trend of the failure strength, while the variation of the internal friction angle of the soil samples was relatively small with an increase in freeze–thaw cycles. When the number of freeze–thaw cycles was the same, the variation of the shear strength parameter of the soil samples with salt content was relatively small, the cohesion of the soil samples decreased with the increasing salt content, and the variation trend of the internal friction angle was similar to the failure strength.
- The SEM tests showed that the surface of the soil samples not experiencing freeze–thaw cycles was flat and dense, while after experiencing freeze–thaw cycles, the proportion of pores and fissures in the soil increased, the structure became loose, and the structural change of the soil samples was most obvious in the first 10 freeze–thaw cycles. When the number of freeze–thaw cycles was the same, the agglomeration degree of the soil particles increased as the salt content increased.
- The quantitative analysis results of the microstructure showed that, with the increase in salt content and freeze–thaw cycles, the failure strength of the soil samples was generally negatively correlated with the porosity and average pore diameter, and the orienting probability entropy of the pores showed a decreasing trend overall. The orientation of the pore arrangement became better. However, the variation of the average shape coefficient and surface fluctuation fractal dimension of the pores under different experimental conditions was relatively small.
- A reasonable regression model was established to express the relationship between the microscopic pore parameters and failure strengths of the soil samples based on principal component regression analysis. The results showed that the failure strength of the saline soil was mainly affected by the size and orientation of the pores in the soil, while it was affected little by the pore morphology. The failure strength of the soil was negatively correlated with the size of the pores and positively correlated with the orienting probability entropy of the pores.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Stress–strain curves of soil samples with different salt contents and freeze–thaw cycles at a confining pressure of 200 kPa, with (

**a**) freeze–thaw cycles (FTC) = 10 and (

**b**) salt content (s) = 2%.

**Figure 2.**Failure strength of soil samples with different salt contents and freeze–thaw cycles at a confining pressure of (

**a**) 100 kPa; (

**b**) 200 kPa; and (

**c**) 300 kPa.

**Figure 3.**Reduction rate of the failure strength of soil samples with freeze–thaw cycles at a confining pressure of (

**a**) 100 kPa; (

**b**) 200 kPa; and (

**c**) 300 kPa.

**Figure 4.**Shear strength parameters of soil samples with different salt contents and freeze–thaw cycles for (

**a**) cohesion and (

**b**) the internal friction angle.

**Figure 7.**Average pore diameter ($\overline{D}$) of soil samples with different (

**a**) freeze-thaw cycles and (

**b**) salt contents.

**Figure 8.**Average shape coefficient of pores ($K$) of soil samples with different (

**a**) freeze-thaw cycles and (

**b**) salt contents.

**Figure 9.**Surface fluctuation fractal dimension of pores ($F$) of soil samples with different (

**a**) freeze-thaw cycles and (

**b**) salt contents.

**Figure 10.**Orienting probability entropy of pores (${H}_{m}$) of soil samples with different (

**a**) freeze-thaw cycles and (

**b**) salt contents.

Property | Value | Testing Method |
---|---|---|

Natural water content (%) | 26.6 | Oven-drying method |

Natural density (g/cm^{3}) | 1.92 | Cutting ring method |

Dry density (g/cm^{3}) | 1.517 | |

Particle size distribution (%) | Combined densimeter and sieve method | |

Sand (2–0.075 mm) | 2.20 | |

Silt (0.075–0.005 mm) | 79.55 | |

Clay (<0.005 mm) | 18.25 | |

Liquid limit (%) | 43.0 | Liquid-plastic limit joint determination method |

Plastic limit (%) | 22.0 | |

Soluble salt content | ||

Total (%) | 1.42 | Water-bath evaporation |

Na^{+} (mmol/100 g) | 3.48 | Flame photometer |

HCO_{3}^{−} (mmol/100 g) | 1.87 | Neutralization titration |

SO_{4}^{2−} (mmol/100 g) | 1.72 | EDTA complexometry titration |

Mineral | Quartz | Alkali Feldspar | Plagioclase | Calcite | Illite | Kaolinite |
---|---|---|---|---|---|---|

Content (%) | 43 | 12 | 29 | 4 | 7 | 5 |

**Table 3.**Correlation coefficient between the failure strength and microscopic pore parameters of soil samples.

$\overline{\mathit{D}}$ | $\mathit{K}$ | $\mathit{F}$ | ${\mathit{H}}_{\mathit{m}}$ | $\mathit{N}$ | |
---|---|---|---|---|---|

100 kPa | −0.843 | −0.169 | 0.430 | 0.901 | −0.976 |

200 kPa | −0.870 | −0.184 | 0.423 | 0.885 | −0.955 |

300 kPa | −0.899 | −0.178 | 0.401 | 0.891 | −0.939 |

$\overline{\mathit{D}}$ | ${\mathit{H}}_{\mathit{m}}$ | $\mathit{N}$ | |
---|---|---|---|

$\overline{D}$ | 1.000 | −0.856 | 0.827 |

${H}_{m}$ | −0.856 | 1.000 | −0.902 |

$N$ | 0.827 | −0.902 | 1.000 |

Confining Pressure | Principal Component Regression Equation | $\mathbf{Adjusted}\text{}{\mathit{R}}^{2}$ |
---|---|---|

100 kPa | $\tau =$−144.10$\overline{D}$ + 2612.03${H}_{m}$ − 276.76$N$ − 2049.38 | 0.901 |

200 kPa | $\tau =$ −126.40$\overline{D}$ + 2893.71${H}_{m}$ − 306.61$N$ − 2232.60 | 0.894 |

300 kPa | $\tau =$ −131.64$\overline{D}$ + 3013.52${H}_{m}$ − 317.64$N$ − 2272.78 | 0.906 |

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**MDPI and ACS Style**

Wang, J.; Wang, Q.; Lin, S.; Han, Y.; Cheng, S.; Wang, N.
Relationship between the Shear Strength and Microscopic Pore Parameters of Saline Soil with Different Freeze-Thaw Cycles and Salinities. *Symmetry* **2020**, *12*, 1709.
https://doi.org/10.3390/sym12101709

**AMA Style**

Wang J, Wang Q, Lin S, Han Y, Cheng S, Wang N.
Relationship between the Shear Strength and Microscopic Pore Parameters of Saline Soil with Different Freeze-Thaw Cycles and Salinities. *Symmetry*. 2020; 12(10):1709.
https://doi.org/10.3390/sym12101709

**Chicago/Turabian Style**

Wang, Jiaqi, Qing Wang, Sen Lin, Yan Han, Shukai Cheng, and Ning Wang.
2020. "Relationship between the Shear Strength and Microscopic Pore Parameters of Saline Soil with Different Freeze-Thaw Cycles and Salinities" *Symmetry* 12, no. 10: 1709.
https://doi.org/10.3390/sym12101709