# Microscopic Mechanism of the Macroscopic Mechanical Properties of Cement Modified Subgrade Silty Soil Subjected to Freeze-Thaw Cycles

^{1}

^{2}

^{*}

## Abstract

**:**

_{p}) and the average particle abundance (C), respectively. When the cement content was 2%, the cohesion was chiefly affected by the particle size fractal dimension (D

_{ps}), while the internal friction angle was mainly related to the average pore diameter (D

_{h}). The main principle of cement improvement was to decrease D

_{h}of soil under F-T cycles.

## 1. Introduction

^{6}km

^{2}, accounting for 53.5% of the country’s land area [1,2], widely distributed in the northeast and northwest. The freezing and thawing cause the strength of the subgrade soil to decrease during the spring-thaw period, resulting in the part or all of the bearing capacity being lost, thereby reducing the pavement quality. The silty soil as a widely distributed subgrade material in the northeast of China is exposed to at least one freeze-thaw (F-T) cycle each year. Because it has low natural moisture content, a small plasticity index, and weak shear strength, these make it sensitive to frost heave and water stabilities [3,4]. In general, the subgrade material in the seasonally frozen area filled with silty soil has the problems of large settlement deformation and difficult compaction, so it is necessary to modify it before using as the subgrade material [5,6,7,8,9].

## 2. Materials and Test Programs

#### 2.1. Materials

#### 2.2. Test Programs

#### 2.2.1. Static Triaxial Test

#### 2.2.2. SEM Test

## 3. Effects of F-T Cycles on the Mechanical Properties and Microscopic Parameters

#### 3.1. Effect of F-T Cycles on Shear Strength and Its Parameters

#### 3.2. Effect of F-T Cycles on Particle Morphological Characteristics

#### 3.2.1. Effect of F-T Cycles on Average Particle Diameter Percentage and Average Particle Diameter

_{p}) percentage in each section was calculated and is shown in Figure 4.

_{p}percentage of S0. This indicated that the largest proportion of particles was 20~50 μm, followed by 5~20 μm and >50 μm. The particles <5 μm were the least. With the increase of F-T cycles, the particles of 5~20 μm increased, while 20~50 μm and >50 μm showed a decreasing trend. The reason might be that the F-T cycles caused the large particles of the plain soil to be broken, the small particles to increase, and the particle agglomeration to lower.

_{p}percentage of S2 in each section was exactly contrary to that of S0. The reason was that, with the addition of cement, the small particles adhered to the surface of the skeleton structure dominated by large particles due to the F-T, leading to the rupture and reorganization of soil particles. Hence, the soils still had better agglomeration and high cohesion under F-T cycles.

_{p}, the D

_{p}of S0 and S2 after F-T cycles are listed in Table 3.

_{p}of S0 was the largest when unfrozen-thawed, it decreased sharply after the first F-T cycle and then decreased with the degree of 8.4%~25.87%. The first F-T cycle had a significant influence on unmodified soil. The D

_{p}of S2 increased in within the whole change range from 5.5% to 17.7% and was greater than that of S0, indicating that F-T cycles caused S0 particles to shatter and recombine; the particles appeared to be in a “fragmented” state. As for S2, the small particles were filled and adhered to the large particles to form larger particles, which was called the state of “agglomeration”. Therefore, the cohesion of S2 was higher than that of S0 after F-T cycles.

#### 3.2.2. Effect of F-T Cycles on Particle Size Fractal Dimension

_{ps}) is used to describe the degree of unevenness of the particle size (r), which is characterized by the distribution characteristic of the cumulative number $\mathrm{N}\left(\le \mathrm{r}\right)$ of particles smaller than a certain particle size and expressed by the morphological characteristics of the $\mathrm{r}-\mathrm{N}\left(\le \mathrm{r}\right)$. curve. It can be known from the mass distribution feature [38] that the two have a good power function correspondence.

_{ps}whose meaning is equivalent to the uneven coefficient C

_{u}of the coarse-grained soil. The larger the D

_{ps}is, the worse the degree of homogenization of particles is. The scatter plot of the two is plotted under the double logarithmic coordinates where r is the abscissa and $\mathrm{N}\left(\le \mathrm{r}\right)$ is the ordinate. If the relationship between the particle size content and the particle size is linear, as well as the slope of the line is b, then D

_{ps}= 3 − b. The changes in the D

_{ps}of S0 and S2 under F-T cycles are drawn in Figure 5.

_{ps}of S0 increased as F-T cycles continue. The D

_{ps}of S2 was between 1.88 and 2.15. The D

_{ps}of S2 was obviously smaller than that of S0, and this demonstrated that the properties of particles were relatively stable under F-T after cement was mixed. The particles of S0 only recombined simply due to water migration after F-T, so the particles after recombination showed a non-uniform state. However, because of the existence of the skeleton structure in S2, more small particles attached to the surface of large particles through water migration to form larger particle structures, making the particles uniform, which was consistent with the result discussed above.

#### 3.2.3. Effect of F-T Cycles on Particle Abundance Percentage and Average Particle Abundance

#### 3.2.4. Effect of F-T Cycles on Average Particle Roundness

_{p}, D

_{ps}, and C after F-T. The small particles filled between the large particles due to the new skeleton structure formed by the hydration reaction of cement, which augmented the degree of particle homogenization. Therefore, the macro performance was that the cohesion of S2 was obviously greater than that of S0 after F-T cycles.

#### 3.2.5. Effect of F-T Cycles on Particle Surface Relief Fractal Dimension

_{i}, then the corresponding ruler number is N (ε

_{i}). A series of ruler lengths ε

_{1}, ε

_{2}, ..., ε

_{n}($\mathrm{n}\to \infty $) would correspond to a series of ruler numbers N(ε

_{1}), N(ε

_{2}), ..., N(ε

_{n}). The relationship between ε

_{i}and N(ε

_{i}) is reflected in the double logarithmic coordinates, and the connection curve of each point reflects the degree of particles fluctuating. The steeper the curve, the more significant change has happened in the length of the curve, indicating that the undulation degree of the particles is greater. Hence, the negative slope value of the linear portion about the lnε~lnN(ε) curve can be used to characterize the particle surface relief fractal dimension value (D

_{pr}) (the same as Equation (1)). The larger the D

_{pr}is, the higher the surface undulation will be. The effects of F-T cycles on D

_{pr}are displayed in Figure 9.

_{pr}of S0 fluctuated between 1.11 and 1.15 under F-T, while the D

_{pr}of S2 decreased with the increase of F-T cycles, which was smaller than that of S0, meaning that the skeleton structure of S2 not only reduced the surface undulation of particles, but also enhanced the ability of soils to resist deformation after F-T cycles.

#### 3.3. Effect of F-T Cycles on Particle Arrangement

#### 3.3.1. Effect of F-T Cycles on Particle Orientation Probability Entropy

_{m}) [40]. The formula is as follows:

_{m}is the probability entropy of the particle arrangement, n is the number of azimuth zones, and ${\mathrm{P}}_{\mathrm{i}}$ is the probability of the particle being in a certain azimuth zone.

_{m}denotes that the particles are arranged in the same direction or not when the value tends to zero or one, respectively. The diversifications of H

_{m}under F-T cycles are shown in Figure 10.

_{m}of S0 and S2 were both between 0.90 and 0.99, showing that the order of particles in each azimuth zone was poor. The H

_{m}of S0 and S2 was relatively large after the first F-T cycle, indicating that particle arrangement was the most chaotic and the soil state was the most unstable, while macro-performance was that cohesion and shear strength sharply decreased after the first F-T cycle.

#### 3.3.2. Nightingale Rose Diagram of the Particle Distribution under F-T cycles

#### 3.4. Quantitative Analysis of Pores under F-T Cycles

#### 3.4.1. Effect of F-T Cycles on Average Pore Diameter Percentage and Average Pore Diameter

_{p}, but also of the average pore diameter (D

_{h}) during F-T; the change of D

_{h}caused the changing appearance of the soil. Hence, D

_{h}was divided into three sections: small pores, medium pores, and large pores, whose diameters were <4 μm, 4~16 μm, and >16 μm, respectively. The D

_{h}percentage in each section is shown in Figure 13, and D

_{h}versus F-T cycles are listed in Table 5.

_{h}were in the range of 4~16 μm and >16 μm. The pores of S0 in 4~16 μm increased as F-T cycles continued, and the pores of >16 μm decreased, indicating that F-T cycles increased the medium pores. From Figure 13b, D

_{h}of S2 was similar to that of S0, manifesting that the soil was mainly composed of medium pores before and after being mixed with cement. With the number of F-T cycles, the variation of the D

_{h}percentage of S2 was completely contrary to that of S0.

_{h}of S0 increased with F-T cycles, and that of S2 showed a similar trend with that of S0, both of them having the maximum D

_{h}after the second F-T cycle, which meant the soil had minimum strength under the second F-T. The D

_{h}of both increased with the increasing F-T cycles, indicating that F-T reduced the joint force between particles and caused the increase of pores, so the cohesion and the shear strength of both decreased. However, the D

_{h}of S2 was smaller than that of S0, meaning that the addition of cement reduced the effect of F-T on the bonding force between particles. The D

_{h}was closely related to the “fragmentation” and “agglomeration” of particles under F-T cycles.

#### 3.4.2. Effect of F-T Cycles on Pore Size Fractal Dimension

_{hs}) is similar to D

_{ps}. The larger the D

_{hs}is, the larger the difference of the pores will be. Figure 14 shows the variation of D

_{hs}under different F-T cycles.

_{hs}of S0 increased with repeated F-T cycles, while that of S2 decreased. Meanwhile, the D

_{hs}of S0 was larger than that of S2, illustrating that the addition of cement made the particles maintain good agglomeration, so high cohesion and shear strength obtained after F-T and improved the frost heave resistance of the soil.

## 4. Correlation between the Microscopic Parameters and Shear Strength Parameters under F-T Cycles

#### 4.1. Principle of GRA

_{i}can be calculated by Equation (10).

#### 4.2. Analysis of GRA Results between Microscopic Parameters and Cohesion

_{p}and the cohesion of S0 was 0.785, indicating that the cohesion of S0 was most sensitive to D

_{p}. D

_{p}characterized the overall size and the accumulation of soil particles. The agglomeration of soil without cement was mainly contributed by the accumulation of particles. The other microscopic parameters related to cohesion were R, C, D

_{hs}, D

_{pr}and H

_{m}.

_{ps}and the cohesion of S2 was 0.687, which was the largest and meant that D

_{ps}had the greatest influence on the cohesion of S2. The reason was that, when the cement was mixed, the main acquisition mode of the soil particles agglomeration was changed from physical action to chemical action, which weakened the effect of F-T on D

_{ps}. The other microscopic parameters related to S2 cohesion were H

_{m}, D

_{hs}, and C.

#### 4.3. Analysis of GRA Results between Microscopic Parameters and Internal Friction Angle

_{hs}, D

_{pr}, H

_{m}, and D

_{h}were all higher than 0.70, representing their close relationship. C was the most essential factor affecting the internal friction angle of S0. The reason might be that the internal friction angle of S0 mainly depended on the friction between particles. C reflected the shape of soil particles as a whole, which pertained to the arrangement of the particles. Furthermore, R and D

_{p}were associated with the internal friction angle of S0.

_{h}, and it was perceived that the internal friction angle of S2 was most affected by D

_{h}. This was mainly because the structure of soil was relatively stable with the hydration reaction of the addition of cement. D

_{h}reflected the size of pores: the larger the pores, the smaller the internal friction angle.

_{hs}, and H

_{m}, and decreased as D

_{pr}and D

_{h}increased. The method of improving C, D

_{hs}, and H

_{m}and reducing D

_{pr}and D

_{h}could increase the internal friction angle of unmodified soil after F-T, and the frictional strength could be effectively enhanced, thereby achieving the aim of improving the shear strength and frost heave resistance of soil.

_{h}and D

_{pr}and increased as R, D

_{ps}, and D

_{p}increased. Comparing with Figure 15 and according to the results of 3.2.5 and 3.4.1, we could conclude that the principle of cement improvement was mainly to decrease the D

_{pr}and D

_{h}of the unmodified soil under F-T cycles; F-T cycles weakened the soil strength mainly by increasing D

_{h}. Hence, the use of modifiers to reduce D

_{h}could most effectively increase the shear strength after F-T cycles, reducing maintenance costs and prolonging the service life of the subgrade material.

## 5. Conclusions

- (1)
- The shear strength and its parameters of CMSS after F-T cycles were obtained through the static triaxial test. The results showed that the cohesion and shear strength of S0 and S2 decreased as F-T cycles continued, the internal friction angle not being obvious. The shear strength of both increased with the increasing confining pressure. The increase of the cohesion, the internal friction angle, and the shear strength of S2 doubled compared to that of S0.
- (2)
- The microscopic parameters D
_{p}, D_{ps}, C, R, D_{pr}, H_{m}, D_{h}, and D_{hs}of S0 and S2 at optimum moisture content after F-T cycles were studied and analyzed by SEM and IPP. With the increase of F-T cycles, the D_{ps}, D_{h}, and D_{hs}of S0 increased, the D_{p}and R decreased, while the C, D_{pr}, and H_{m}had no obvious variations. As F-T cycles continued, the D_{p}, R, and D_{h}of S2 increased and the D_{pr}and D_{hs}decreased. The D_{ps}, C, and H_{m}fluctuated in a certain range. - (3)
- The correlations between microscopic parameters and macroscopic parameters were calculated on the basis of GRA. The results manifested that the most important factor affecting the cohesion of S0 was D
_{p}, while the cohesion of S2 was more sensitive to D_{ps}. Concerning the internal friction angle, C was the most important for that of S0, and D_{h}was primarily related to that of S2. The use of modifiers to reduce D_{h}could most effectively increase the shear strength of soil after F-T cycles. - (4)
- The samples under different moisture contents should be analyzed by SEM to study the effect of moisture content on the microstructure parameters of CMSS under F-T cycles. Meanwhile, more research should be carried out on the fractal dimension of soil.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Chen, X.; Liu, J.; Liu, H.; Wang, Y. Freezing Action of Soil and Foundation; Science Press: Beijing, China, 2011; pp. 10–15. [Google Scholar]
- Xu, X.; Wang, J.; Zhang, L. Physics of Frozen Soil, 2nd ed.; Science Press: Beijing, China, 2010; pp. 75–82. [Google Scholar]
- Mohseni, S.; Payan, M.; Chenari, R.J. Soil–structure interaction analysis in natural heterogeneous deposits using random field theory. Innov. Infrastruct. Solut.
**2018**, 3, 62. [Google Scholar] [CrossRef] - Wang, F.; Cheng, P.; Wang, L.; Wang, X. Study on engineering properties of silt sand and construction technology of subgrade. J. Chin. Foreign Highw.
**2010**, 30, 42–45. [Google Scholar] - Hossain, K.M.A.; Lachemi, M.; Easa, S. Stabilized soils for construction applications incorporating natural resources of Papua New Guinea. Conserv. Recy.
**2007**, 51, 711–731. [Google Scholar] [CrossRef] - Hossain, K.M.A.; Mol, L. Some engineering properties of stabilized clayey soils incorporating natural pozzolans and industrial wastes. Constr. Build. Mater.
**2011**, 25, 3495–3501. [Google Scholar] [CrossRef] - Anupam, A.; Kumar, P. Use of various agricultural and industrial waste materials in road construction. Procedia Soc. Behav. Sci.
**2013**, 104, 264–273. [Google Scholar] [CrossRef] [Green Version] - Cai, Y.; Zheng, Y.; Liu, Z.; Wang, C. Study of dynamic response of silty sand subgrade loaded by airplane. Rock Soil Mech.
**2012**, 33, 193–198. [Google Scholar] - Cheng, P.; Yu, D.; Fan, Y. Monitoring and analysis of moisture and temperature of silty soil subgrade in seasonally frozen region. Highway
**2011**, 10, 192–197. [Google Scholar] - Chen, Y. Experimental Study on Road Performance of Reinforced Soil with Bessel Curing Agent; Jilin University: Changchun, China, 2007. [Google Scholar]
- Wang, T.; Liu, J.; Tian, Y. Static properties of cement- and lime-modified soil subjected to freeze-thaw cycles. Rock Soil Mech.
**2011**, 31, 2863–2868. [Google Scholar] - Wang, F.; Cheng, P. Application of compactness detector in compaction test of silty sand subgrade. J. Chin. Foreign Highw.
**2015**, 35, 18–22. [Google Scholar] - Ma, W.; Xu, X.; Zhang, L. Influence of frost and thaw cycles on shear strength of lime silt. Chin. J. Geotech. Eng.
**1999**, 21, 158–160. [Google Scholar] - Wang, H.; Yin, Z.; Yu, X. CBR test study of silt embankment filler. Subgrade Eng.
**2006**, 1, 56–58. [Google Scholar] - Osula, D.A. Lime stabilization of clay minerals and soils. Eng. Geol.
**1996**, 42, 71–80. [Google Scholar] [CrossRef] - Wang, J.; Peng, L.; Zhang, Z.; Abdulali, A. Experimental study on road performance of Libyan silty soil. J. Chin. Foreign Highw.
**2015**, 35, 314–317. [Google Scholar] - Song, A.; Zhang, Y. Strength characteristics of cement soil and fly ash cement soil under freeze-thaw cycles. J. Chin. Foreign Highw.
**2017**, 37, 221–223. [Google Scholar] - Yan, C.; Tang, H.; Sun, Y. Study on the soil of slipping zone in landslides and its significance by scanning electron microscope and X-ray diffractometer. Geol. Sci. Technol. Inform.
**2001**, 20, 89–92. [Google Scholar] - Zhang, X.; Shi, B. SEM analysis of micro-structure of the particle clusters in lime-treated expansive soils. J. Eng. Geol.
**2007**, 15, 654–660. [Google Scholar] - Wang, B.; Zhang, M.; Shi, B. Quantitative analysis of orientation distribution of soil grains based on slop-aspect theory. Chin. J. Rock Mech. Eng.
**2010**, 29, 2951–2957. [Google Scholar] - Cuisinier, O.; Aurio, J.C.; Borgne, T.L.; Deneele, D. Microstructure and hydraulic conductivity of a compacted lime-treated soil. Eng. Geo.
**2011**, 123, 187–193. [Google Scholar] [CrossRef] - Chen, F.H. Foundations on Expansive Soils, 2nd revised ed.; Elsevier Science Ltd.: Amsterdam, The Netherlands, 2015; pp. 9–58. [Google Scholar]
- Otálvaro, I.F.; Neto, M.P.C.; Caicedo, B. Compressibility and microstructure of compacted laterites. Transp. Geotech.
**2015**, 5, 20–34. [Google Scholar] [CrossRef] - Choobbasti, A.J.; Kutanaei, S.S. Microstructure characteristics of cement-stabilized sandy soil using nanosilica. J. Rock Mech. Geotech. Eng.
**2017**, 9, 981–988. [Google Scholar] [CrossRef] - Cordão Neto, M.P.; Hernández, O.; Reinaldo, R.L.; Borges, C.; Caicedo, B. Study of the relationship between the hydromechanical soil behavior and microstructure of a structured soil. Earth Sci. Res. J.
**2018**, 22, 91–101. [Google Scholar] [CrossRef] - Zhang, Q.; Wang, J.; Liu, B.; Zeng, Y. Quantitative research on microstructure of modified soil with cement. Hydrogeol. Eng. Geo.
**2015**, 42, 92–96. [Google Scholar] - Liao, Y.; Zhang, Z.; Xiao, S.; Liu, K.; Yang, X. Microstructure research on cement stabilized clays. Chin. J. Rock Mech. Eng.
**2016**, 35, 4318–4327. [Google Scholar] - Wang, J.; Zhou, L.; Zhong, C.; Zhang, Y. Study on the influence of microstructure change of silty sand on macroscopic mechanical parameters under freeze-thaw cycles. Highway
**2017**, 10, 22–29. [Google Scholar] - Xiao, S.; Liao, Y.; Zhang, Z.; Liu, K.; Yang, X. Microstructure research on cement stabilized sandy soils. Chin. J. Undergr. Space Eng.
**2018**, 14, 43–50. [Google Scholar] - Sun, S. Study on Mechanical Properties of Subgrade Cement Modified Silty Soil in Seasonally Frozen Area; Jilin Jianzhu University: Changchun, China, 2019. [Google Scholar]
- (JTG E40-2007). Test Methods of Soils for Highway Engineering; Renmin Communication Press: Beijing, China, 2010. [Google Scholar]
- (JTG E51-2009). Test Methods of Materials Stabilized with Inorganic Binders for Highway Engineering; Renmin Communication Press: Beijing, China, 2010. [Google Scholar]
- Bing, W. Freezing Damage and Prevention; Harbin Institute of Technology Press: Harbin, China, 1991. [Google Scholar]
- He, Y. Dynamic and Static Mechanical Properties Study on Polypropylene Fiber Improving Fly Ash Soil; Jilin University: Changchun, China, 2010. [Google Scholar]
- Zaman, M.M.; Naji, K.N. Effect of freeze-thaw cycles on class C fly ash stabilized aggregate base. In Proceedings of the 82nd Annual Meeting: Transportation Research Board, Washington, DC, USA, 12–16 January 2003. [Google Scholar]
- Yu, L.; Xu, X.; Qiu, M.; Li, P.; Yan, Z. Influence of freeze-thaw on shear strength properties of saturated silty clay. Rock Soil Mech.
**2010**, 31, 2448–2452. [Google Scholar] - Chang, D.; Liu, J.; Li, X.; Yu, Q. Experiment study of effects of freezing-thawing cycles on mechanical properties of Qinghat-Tibet silty sand. Chin. J. Rock Mech. Eng.
**2014**, 33, 1496–1502. [Google Scholar] - Liu, S.; Fang, L.; Chen, H. Argument on the fractal structure of special soil particle size distribution. Chin. J. Geotech. Eng.
**1993**, 15, 23–30. [Google Scholar] - Li, X.; Hu, R.; Zhang, L. Microstructural changes in soft soil consolidation. Earth Geosci. Front.
**2000**, 7, 147–152. [Google Scholar] - Shi, B. Quantitative evaluation of microstructure during compaction of cohesive soil. Chin. J. Geotech. Eng.
**1996**, 18, 60–65. [Google Scholar] - Liu, S.; Cai, H.; Yang, Y. Research progress on grey relational analysis model. Sys. Eng. Theory Pract.
**2013**, 33, 2041–2046. [Google Scholar] - Lin, W. Correlation analysis of physical and mechanical properties of geotechnical materials. Chin. Rural Water Hydropower.
**2007**, 27–32. [Google Scholar]

**Figure 11.**Nightingale rose chart of S0 after (

**a**) 0, (

**b**) 1, (

**c**) 2, (

**d**) 3, (

**e**) 4, (

**f**) 5, (

**g**) 6, and (

**h**) 8 F-T cycles.

**Figure 12.**Nightingale rose chart of S2 after (

**a**) 0, (

**b**) 1, (

**c**) 2, (

**d**) 3, (

**e**) 4, (

**f**) 5, (

**g**) 6, and (

**h**) 8 F-T cycles.

**Figure 15.**The curve of the internal friction angle of S0 versus the five most relevant microscopic parameters after F-T cycles: (

**a**) C, (

**b**) D

_{hs}, (

**c**) D

_{pr}, (

**d**) H

_{m}, and (

**e**) D

_{h.}

**Figure 16.**The curve of the internal friction angle of S2 versus the five most relevant microscopic parameters after F-T cycles: (

**a**) D

_{h}, (

**b**) R, (

**c**) D

_{ps}, (

**d**) D

_{p}, and (

**e**) D

_{pr.}

Particle Diameter (mm) | 5.0 | 2.0 | 1.0 | 0.5 | 0.25 | 0.075 | 0.01 | 0.005 | 0.002 | 0.001 |
---|---|---|---|---|---|---|---|---|---|---|

The percentage of soil particles smaller than the particle size to the total mass of the soil (%) | 100 | 99.69 | 99.36 | 98.79 | 98.49 | 97.06 | 35.38 | 18.17 | 5.90 | 2.95 |

Sample | Cement Content (%) | Natural Moisture Content w (%) | Liquid Limit w_{L} (%) | Plastic Limit w_{P} (%) | Plasticity Index I_{P} | Optimum Moisture Content w_{opt} (%) | Maximum Dry Density ρ_{d}(g/cm^{3}) |
---|---|---|---|---|---|---|---|

S0 | 0 | 5.47 | 22.4 | 14.1 | 8.3 | 8.53 | 2.030 |

S2 | 2 | 5.47 | 26.6 | 17.6 | 8.9 | 9.69 | 2.042 |

Sample | F-T Cycles | |||||||
---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | |

S0 | 35.59 | 28.88 | 32.60 | 32.48 | 26.38 | 30.91 | 27.07 | 32.61 |

S2 | 38.61 | 36.49 | 41.36 | 45.20 | 38.64 | 41.64 | 45.46 | 39.15 |

Sample | F-T cycles | |||||||
---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | |

S0 | 0.486 | 0.451 | 0.477 | 0.479 | 0.444 | 0.490 | 0.452 | 0.475 |

S2 | 0.511 | 0.498 | 0.502 | 0.515 | 0.516 | 0.478 | 0.514 | 0.516 |

Sample | F-T cycles | |||||||
---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | |

S0 | 16.11 | 17.56 | 20.36 | 19.83 | 19.44 | 18.57 | 18.28 | 18.84 |

S2 | 16.01 | 17.43 | 19.77 | 17.43 | 16.25 | 17.16 | 16.11 | 16.34 |

Sample | Microscopic Parameters | |||||||
---|---|---|---|---|---|---|---|---|

D_{p} | D_{ps} | C | R | D_{pr} | H_{m} | D_{h} | D_{hs} | |

S0 | 0.785 | 0.510 | 0.710 | 0.716 | 0.671 | 0.671 | 0.575 | 0.673 |

S2 | 0.551 | 0.687 | 0.602 | 0.565 | 0.582 | 0.606 | 0.545 | 0.606 |

Sample | Microscopic Parameters | |||||||
---|---|---|---|---|---|---|---|---|

D_{p} | D_{ps} | C | R | D_{pr} | H_{m} | D_{h} | D_{hs} | |

S0 | 0.614 | 0.560 | 0.774 | 0.673 | 0.765 | 0.756 | 0.746 | 0.773 |

S2 | 0.679 | 0.683 | 0.648 | 0.686 | 0.667 | 0.664 | 0.687 | 0.658 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, H.; Sun, S.; Wang, L.; Zhang, Y.; Wang, J.; Luo, G.; Han, L.
Microscopic Mechanism of the Macroscopic Mechanical Properties of Cement Modified Subgrade Silty Soil Subjected to Freeze-Thaw Cycles. *Appl. Sci.* **2020**, *10*, 2182.
https://doi.org/10.3390/app10062182

**AMA Style**

Liu H, Sun S, Wang L, Zhang Y, Wang J, Luo G, Han L.
Microscopic Mechanism of the Macroscopic Mechanical Properties of Cement Modified Subgrade Silty Soil Subjected to Freeze-Thaw Cycles. *Applied Sciences*. 2020; 10(6):2182.
https://doi.org/10.3390/app10062182

**Chicago/Turabian Style**

Liu, Hanbing, Shuang Sun, Lixia Wang, Yunlong Zhang, Jing Wang, Guobao Luo, and Leilei Han.
2020. "Microscopic Mechanism of the Macroscopic Mechanical Properties of Cement Modified Subgrade Silty Soil Subjected to Freeze-Thaw Cycles" *Applied Sciences* 10, no. 6: 2182.
https://doi.org/10.3390/app10062182