Polypropylene fiber is a common soil reinforcement material which is used to reinforce a common clay in northeast China. Numerical analysis method was performed to investigate the effect of polypropylene fibers on stability of embankment slope subjected to freezethaw cycles. The orthogonal experiments of three factors (freezethaw cycle, fiber content, and fiber length) and three levels were carried out, and the corresponding nine groups of specimens were made, whose shear strength parameters (internal friction angle and bond force) were measured by direct shear test. Then, the experimental results were analyzed by analysis of variance and range analysis so that the optimum fiber content and fiber length can be determined. The finite element model of typical highfill soil slope of freeway in northeast China was established whose basic material parameters were taken as the parameters of shear strength of different freezethaw cycles under the optimum fiber content and fiber length. The concept of shear strength reduction was introduced into the finite element model, and the convergence of the finite element model was taken as the judging criterion of slope stability. Thus, stability analysis of soil embankment slope reinforced with polypropylene fiber under freezethaw cycles was realized. The results show that the addition of fibers improves the cohesion under the action of freezethaw cycles, and the internal friction angle is improved in the case of freezing and thawing. This phenomenon leads to the improvement of the stability of the embankment slope in a freezethaw cycle. The improvement is particularly noticeable in the case, and this improvement effect decreases as the number of freezethaw cycles increases.
It is ordinary in seasonal frozen regions such as northeast China that the instability of soil slope continues to emerge due to freezethaw (FT) cycles [
Generally, the performance of soil under FT cycles can be effectively improved by reinforcement materials. The FT behavior of reinforced soil with inorganic binders has been studied, and test results revealed that its FT behavior presented the favorable improvement. Adding lime to soil is a proven technique for improving the strength and stabilization of soil [
As a new type of soil reinforcement technology, fiberreinforced soil technology is widely used in embankment retaining wall, slope, soft soil foundation, and bridge abutment backfill engineering [
In this study, polypropylene fiber was adopted to strengthen a common clay in northeast China, and the optimum fiber length and content were also obtained by the orthogonal test. A finite element model of typical highfill soil slope of freeway in northeast China was established, thus the stability analysis of soil embankment slope reinforced with polypropylene fiber under FT cycles has been realized. The innovations of this paper are mainly reflected in the following aspects: (1) the research thinking is extended from the layer of material mechanical properties to the level of structural stability, which is more indepth and systematic; (2) the object of numerical analysis is the typical highfill soil slope, which is very close to the engineering practice so that the research results are easy to be popularized and applied in engineering practice.
The soil material in this study is a typical soil in northeast China, which was from a construction site in Harbin, China. The sampling depth was 1.2–1.5 m, and the sample color was yellow brown. The proportion, liquid plastic limit, and heavy compaction tests of soil samples were carried out to determine the main physical properties of soil samples according to JTG E402007 [
Physical properties of soil samples.
Properties  Specific gravity  Maximum dry density (g/cm^{3})  Optimum water content (%)  Liquid limit (%)  Plastic limit (%)  Plasticity index (%) 

Value  2.65  1.86  11.4  33.3  24.0  9.3 
Particlesize distribution curves of soil.
Polypropylene fiber is a kind of synthetic fiber obtained by isotactic polypropylene as raw materials which has good tensile strength, excellent manufacturing stable performance, good corrosion resistance, and antiability after some processes. Thus, it is one of the most common engineering reinforcement materials and widely applied to engineering projects. The polypropylene fiber used in this study is white, soft, and smooth textured monofilament fibershaped strip (shown in Figure
Materials: (a) polypropylene fiber; (b) fiber soil.
Physical and mechanical parameters of polypropylene fiber.
Properties  Density (g/cm^{3})  Breaking tensile strength (MPa)  Modulus of elasticity (MPa)  Elongation (%)  Diameter ( 
Melting point (°C) 

Value  0.96  500  3850  10–28  18–48  165 
The FT cycles, fiber content, and fiber length are the three most important factors for the shear strength parameters (internal friction angle and cohesion) of fiberreinforced soil. Taking these three factors as control factors, the orthogonal experiments of fiberreinforced soil were designed with three factors and three levels, and nine groups of fiberreinforced soil were determined, which are listed in Table
Experimental scheme based on orthogonal design.
Specimen number  FT cycle (time)  Fiber length (mm)  Fiber content (%) 

1  1  12  0.3 
2  1  6  0.1 
3  1  9  0.2 
4  3  12  0.1 
5  3  9  0.3 
6  3  6  0.2 
7  6  6  0.3 
8  6  9  0.1 
9  6  12  0.2 
The optimum fiber content and fiber length were used for fiberreinforced soil specimens, and the ordinary soil specimen was also made. The shear strength parameters of ordinary soil and fiberreinforced soil under 0, 1, 3, and 6 FT cycles were tested, respectively. The reinforcement mechanism of fiber on soil under FT cycles was analyzed by comparing the variation of shear strength parameters with FT cycles for fiberreinforced soil and ordinary soil.
Based on compaction test, the optimum moisture content of soil can be obtained as 11.4% (Table
According to the provisions of the “Test Methods of Soils for Highway Engineering” [
The direct shear tests were carried out on 9 groups of fiberreinforced soil. The shear strength parameters of fiberreinforced soil were calculated, and Table
Shear strength parameters of fiberreinforced soil specimens.
Group serial number  Internal friction angle (°)  Cohesion (kPa) 

1  34.99  68.06 
2  34.99  58.18 
3  33.53  66.74 
4  32.08  51.37 
5  27.89  61.85 
6  29.80  56.58 
7  28.11  53.54 
8  31.91  50.03 
9  23.02  50.22 
From the test results in Table
The basic principle of analysis of variance (ANOVA) is to calculate variance (MS) by squared sum (SS) and degree of freedom (DF) and then calculate
Based on the sum of squares of deviations and degree of freedom, the variance of factor column and error column can be calculated by
According to the variance values, the
ANOVA results are given in Table
Analysis of variance (ANOVA) results for mechanical index.
Assessment index  Source of variance  SS  DF  Error sources 

Critical value  Significance 

Internal friction angle (°)  FT cycles  72.57  2  4.35 

 
Fiber length  2.06  2  √  
Fiber content  27.21  2  √  
Empty column  50.02  2  √  


Cohesion (kPa)  FT cycles  258.84  2  21.24 

 
Fiber length  20.95  2  √  
Fiber content  95.94  2  7.87 
 
Empty column  24.37  2  √ 
ANOVA results showed that the effect of each influencing factor on internal friction angle was not significant. However, FT cycles presented a significant effect on the internal friction angle due to
A range analysis of various factors was carried out, and the results are presented in Table
Analysis of variance (ANOVA) results for mechanical index.
Assessment index  Range  I  II  III  IV 

FT cycles  Fiber length  Fiber content  Empty column  
Cohesion (kPa) 

64.326  56.101  53.192  56.747 

56.600  59.538  57.845  57.216  

51.262  56.549  61.151  58.225  

13.064  3.437  7.959  1.478  


Internal friction angle (°) 

34.503  30.967  32.993  28.633 

29.923  31.110  28.783  31.240  

27.680  30.030  30.330  32.233  

6.823  1.080  4.210  3.600 
Tendency of the cohesion with influencing factors: (a) freezethaw cycles; (b) fiber length; (c) fiber contents.
Tendency of the angle of internal friction with influencing factors: (a) freezethaw cycles; (b) fiber length; (c) fiber contents.
In the light of the range analysis results, the influencing order of main factors was I > III > II (13.064 > 7.959 > 3.437) for cohesion of fiber soil. FT cycles had the greatest influence on cohesion index, followed by fiber content and fiber length. The cohesion decreases with the increase of FT cycles, and the downward trend was slow. The trend of cohesion of fiber soil was consistent with that of general soil under FT cycles. With the increase of fiber length, cohesion showed the trend of increasing first and then becoming smaller which had the maximum value when the fiber length is 9 mm. Since the fiber is an isotropic material in soil, when the fiber length is too short, the fiberreinforcing effect is weakened based on principle of friction between reinforcement and soil [
For the internal friction angle of soil, the ordering of factors was consistent with previous ordering of cohesion, but its range value was smaller than that of cohesive force. The effects of fiber and FT cycles on internal friction angle were smaller than cohesion.
The optimum combination scheme should be determined on the basis of the orthogonal experiment results. The basic principle of determining the optimum level combination under various factors was to determine the main assessment indexes firstly, and then the best combination scheme was determined based on the principle that main indicators, significant indicators, and large fluctuations in the indicators were given priority. In the evaluation index of this test, cohesive force made a great deal of difference on the shear strength of soil, and the numerical fluctuation of each level was also obvious, which was the main influence index. Therefore, the optimum combination scheme was a combination scheme with a fiber length of 9 mm and the fiber content of 0.3%.
Table
Shear strength parameters of fiberreinforced soil and ordinary soil under FT cycles.
Soil type  Cycle times of FT  Cohesion (kPa)  Internal friction angle (°) 

Fiberreinforced soil  0  96.82  19.18 
1  71.36  37.88  
3  61.85  27.89  
6  57.85  27.22  


Ordinary soil  0  95.45  21.04 
1  63.50  21.74  
3  51.37  32.88  
6  45.09  33.88 
Shear strength index contrast of fiber soil and soil under the freezing and thawing: (a) internal friction angle; (b) cohesion.
As observed from Figure
It is obvious from Figure
The analysis process on stability of the fiberreinforced soil slope was expounded by using the typical highfill soil slope in northeast China which can be seen in Figure
Size of embankment slope (unit: m).
The finite element model of road slope.
The constitutive model of soil was a significant factor in the stability analysis of soil slope. The constitutive model of soil mainly includes DP (DruckerPrager) model, Cambridge model, and DuncanZhang model, among which the most commonly used is DP model, so the DP model was also chosen in this paper. In the DP model, the equivalent stress σ_{e} can be obtained by equation (5) and Von Mises yield formula can be expressed as equations (
When using the finite element method to analyze slope stability, there are two key problems to be solved which are the judgment criteria of slope instability and the quantitative expression of slope stability. Zienkiewic put forward that the convergence of calculation model can be used to judge whether the slope is unstable or not when using finite element method to calculate slope stability [
The strength reduction method was selected to realize the quantitative expression of slope stability. The formulas for calculating the shear strength parameters Cohesion
In accordance with the definition of strength reduction coefficient, the coefficient can objectively reflect the magnitude of slope stability, that is, it can realize the quantitative expression of slope stability, which was called slope stability coefficient in this paper. The calculation process of the slope stability coefficient is as follows: (1) let F take a small value and calculate the reduced shear strength parameters C′,
In the slope stability analysis, two kinds of loadings were applied to finite element model; one was the dead weight of soil slope which was applied to the whole slope, and the other was the uniformly distributed loading which was applied to the top of the finite element model for 98 kPa/m to simulate the vehicle load. Under the optimal fiber content and fiber length, the stability coefficients of fiber reinforced soil and ordinary slope under 0, 1, 3, and 6 F‐T cycles were obtained. The maximum plastic strain and maximum horizontal displacement of the slope were calculated by using the proposed slope stability analysis method, respectively. The stability coefficient results are shown in Figure
Slope stability coefficient.
Plastic strain. P0: plain soil of 0 FT cycles; F0: fiber soil of 0 FT cycles; P1: plain soil of 1 FT cycle; F1: fiber soil of 1 FT cycle; P3: plain soil of 3 FT cycles; F3: fiber soil of 3 FT cycles; P6: plain soil of 6 FT cycles; F6: fiber soil of 6 FT cycles.
Horizontal displacement: (a) displacement calculation result; (b) cloud picture of displacement of ordinary soil under the action of 1 time FT cycle at
As observed in Figure
It is obvious from Figure
In this study, polypropylene fiber was used to strengthen a common clay in northeast China, and the optimum fiber content and fiber length were determined by direct shear test considering the effect of FT cycle. Then, the shear strength parameters of fiberreinforced soil with the optimum fiber content and fiber length were tested. The stability analysis method of soil slope was put forward, and the stability of typical highfill soil slope in northeast China was calculated based on the finite element method and strength reduction method. On the basis of the research work of this paper, the following conclusions could be drawn:
With the increase of FT cycles, the cohesion difference between polypropylene fiber and soil increased gradually, and the reinforcement effect of internal friction angle was remarkable under one FT cycle.
According to direct shear test, the optimum combination scheme can be obtained. The fiberreinforced soil has the best enhancement effect when the fiber content is 0.3% and the fiber length is 9 mm.
The stability analysis method of soil slope combining finite element method and strength reduction method could be used to analyze the stability of polypropylene fiberreinforced soil slope and ordinary soil slope, results of which were accurate and reliable.
The slope stability of fiberreinforced soil embankment slope was better than that of ordinary soil embankment slope. With the increase of FT cycles, the stability of polypropylene fiberreinforced soil embankment slope with the optimal combination scheme was weakened, but the stability of fiber soil slope was significantly improved under one FT cycle.
It should be pointed that the plastic strain and horizontal displacement had obvious changes when the slope was near instability but not yet unstable, which may provide some ideas for the monitoring and early warning of fiberreinforced soil slope and ordinary soil slope.
The data used to support the findings of this study are included within the article. The data are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the National Natural Science Fund of China (Grant no. 51408258), Transportation Technology Program of Jilin Province of China (Grant nos. 2018ZDGC16, 201318, and 201819), Training Program for Outstanding Young Teachers of Jilin University, and Science and Technology Project of the 13th FiveYear Plan of Department of Education Jilin Province of China (Grant nos. JJKH20190015KJ and JJKH20190150KJ). We would like to acknowledge the following people from Northeast Forestry University for technical support in testing procedure and data processing: Sun Hao, Wang Zhongzhi, and Fang Liqun.