# Stability Analysis of Soil Embankment Slope Reinforced with Polypropylene Fiber under Freeze-Thaw Cycles

Authors: Yafeng Gong; Yulong He; Chunpeng Han; Yangfan Shen; Guojin Tan
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

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 freeze-thaw cycles. The orthogonal experiments of three factors (freeze-thaw 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 high-fill soil slope of freeway in northeast China was established whose basic material parameters were taken as the parameters of shear strength of different freeze-thaw 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 freeze-thaw cycles was realized. The results show that the addition of fibers improves the cohesion under the action of freeze-thaw 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 freeze-thaw cycle. The improvement is particularly noticeable in the case, and this improvement effect decreases as the number of freeze-thaw cycles increases.


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## Body

## 1. Introduction

It is ordinary in seasonal frozen regions such as northeast China that the instability of soil slope continues to emerge due to freeze-thaw (F-T) cycles [1]. Slope stability under F-T cycles has been demonstrated by laboratory experiments and numerical simulations in current research studies [2–7]. The main reason of slope instability is that shear strength parameters of soil vary considerably under F-T cycles [8–10]. Therefore, the preliminary study of slope instability in seasonal frozen area is necessary to investigate the shear strength variation of slope soil under F-T cycles.Generally, the performance of soil under F-T cycles can be effectively improved by reinforcement materials. The F-T behavior of reinforced soil with inorganic binders has been studied, and test results revealed that its F-T behavior presented the favorable improvement. Adding lime to soil is a proven technique for improving the strength and stabilization of soil [11–13]. In addition, there are other scholars who increased the strength of soil under F-T by adding fly ash to soil [14, 15]. However, these chemical additives usually lead to the high stiffness and less suitability for soil.As a new type of soil reinforcement technology, fiber-reinforced soil technology is widely used in embankment retaining wall, slope, soft soil foundation, and bridge abutment backfill engineering [16–18]. Because of the advantages of good dispersing ability, higher inertia, and uniform enhancement effect, a practical application prospect of fiber-reinforced soil has been attracting more attentions [19–23]. Random addition of dispersed palm fiber to clay can improve its consolidation and shear behavior [19]. Hay of wheat was added to swelling clay to improve and stabilize its mechanical and deformation properties [20]. The addition of sisal fiber into silty clay improves its strength, deformation, and shear failure characteristics [21]. It was concluded that the shear strength of clay can be significantly improved by random distribution of coir fibers through a series of consolidated undrained triaxial compression tests [22]. Akbulut et al. found that polypropylene fiber added into soil can effectively improve its compressive strength, and the optimum content is 0.2% according to the unconfined compression strength results [23]. A series of studies have shown that fiber can effectively improve the F-T resistance of soil, and the peak stress of unreinforced and reinforced soil usually decreases when F-T cycles increase. Soil samples reinforced with polypropylene fibers usually behave in a more ductile than unreinforced samples [24]. Roustaei et al. showed that soil reinforced with polypropylene fiber can reduce the influence of F-T cycle on cohesive force of soil [25]. Ghazavi and Roustaie found that the unconfined compressive strength of clay samples decreased by 20–25% with increasing F-T cycles. In addition, the unconfined compressive strength of clay can be improved by adding fiber to clay sample. Moreover, it can be concluded that adding 3% polypropylene fibers leads to the increase of unconfined compressive strength of soil before and after applying F-T cycles by 60% to 160% and decrease of frost heave by 70% [26]. The addition of geofiber and synthetic fluid can improve the California bearing ratio (CBR) performance of fine-grained soils under different freezing and thawing conditions [27].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 high-fill soil slope of freeway in northeast China was established, thus the stability analysis of soil embankment slope reinforced with polypropylene fiber under F-T 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 in-depth and systematic; (2) the object of numerical analysis is the typical high-fill 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.


## 2. Materials and Methods

### 2.1. Materials

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 E40-2007 [28]. Corresponding results are listed in Table 1. According to the screening experiment of soil, the particle-size distribution of the soil was obtained, and the particle-size distribution curves of the soil are shown in Figure 1.Table 1
Physical properties of soil samples.
Properties
Specific gravity
Maximum dry density (g/cm3)
Optimum water content (%)
Liquid limit (%)
Plastic limit (%)
Plasticity index (%)
Value
2.65
1.86
11.4
33.3
24.0
9.3Figure 1
Particle-size 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 fiber-shaped strip (shown in Figure2), which was obtained from the Hebei Hongxing company. The main physical and mechanical parameters of the polypropylene fiber are given in Table 2.Figure 2
Materials: (a) polypropylene fiber; (b) fiber soil.
(a)
(b)Table 2
Physical and mechanical parameters of polypropylene fiber.
Properties
Density (g/cm3)
Breaking tensile strength (MPa)
Modulus of elasticity (MPa)
Elongation (%)
Diameter (μm)
Melting point (°C)
Value
0.96
500
3850
10–28
18–48
165


### 2.2. Test Scheme

The F-T cycles, fiber content, and fiber length are the three most important factors for the shear strength parameters (internal friction angle and cohesion) of fiber-reinforced soil. Taking these three factors as control factors, the orthogonal experiments of fiber-reinforced soil were designed with three factors and three levels, and nine groups of fiber-reinforced soil were determined, which are listed in Table3. The previous studies showed that the soil has reached a new balance after 6 F-T cycles, whose physical and mechanical properties changed little [29–31]. Therefore, the maximum F-T cycles in this test was set as 6 cycles. A series of direct shear tests of fiber-reinforced soil were carried out under the optimum water content condition by Welker and Josten, and the optimum fiber content was determined to be 0.2% through the maximum shear strength [32]. Therefore, the fiber content in this paper is taken as 0.1%, 0.2%, and 0.3%. The shear strength parameters of 9 groups of fiber-reinforced soil specimens were tested using direct shear test, and the optimum fiber content and fiber length can be determined by comprehensive analysis.Table 3
Experimental scheme based on orthogonal design.
Specimen number
F-T 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
0.2The optimum fiber content and fiber length were used for fiber-reinforced soil specimens, and the ordinary soil specimen was also made. The shear strength parameters of ordinary soil and fiber-reinforced soil under 0, 1, 3, and 6 F-T cycles were tested, respectively. The reinforcement mechanism of fiber on soil under F-T cycles was analyzed by comparing the variation of shear strength parameters with F-T cycles for fiber-reinforced soil and ordinary soil.


### 2.3. Test Methods

Based on compaction test, the optimum moisture content of soil can be obtained as 11.4% (Table1). Water was added to soil based on the optimum moisture content after drying and crushing, and then soil and fiber were mixed thoroughly and evenly following the designed experimental scheme. According to the provisions of the “Technical Specifications for Construction of Highway Subgrade” (JTG F10-2006) [33], the static pressure method was adopted to compact specimens in accordance with the compaction degree of 96%. The low-temperature test device (ADX-300-40) was used for F-T cycles, and the precision of F-T temperature can be controlled within 0.1°C. According to the temperature monitoring data of subgrade in cold regions, the freezing temperature was set as −15°C and the melting temperature was set as 15°C. One F-T cycle lasts for 24 hours (the freezing and melting need 12 hours, respectively). During F-T cycles, specimens were wrapped with multilayers of plastic wrap to prevent water loss.According to the provisions of the “Test Methods of Soils for Highway Engineering” [28], the SDJ-II type three-speed electric strain direct shear instrument, made by Nanjing Soil Instrument Company, was used for test scheme design of soil samples. The controlling loading rate was 0.8 mm/min for shearing, and the test was completed within 3–5 min. The precision of shear displacement measurement was controlled by 0.01 mm scale indicator. Four specimens were used for each shear group, which were cut to crush under the vertical pressure of 50 kPa, 100 kPa, 200 kPa, and 300 kPa, respectively.


## 2.1. Materials

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 E40-2007 [28]. Corresponding results are listed in Table 1. According to the screening experiment of soil, the particle-size distribution of the soil was obtained, and the particle-size distribution curves of the soil are shown in Figure 1.Table 1
Physical properties of soil samples.
Properties
Specific gravity
Maximum dry density (g/cm3)
Optimum water content (%)
Liquid limit (%)
Plastic limit (%)
Plasticity index (%)
Value
2.65
1.86
11.4
33.3
24.0
9.3Figure 1
Particle-size 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 fiber-shaped strip (shown in Figure2), which was obtained from the Hebei Hongxing company. The main physical and mechanical parameters of the polypropylene fiber are given in Table 2.Figure 2
Materials: (a) polypropylene fiber; (b) fiber soil.
(a)
(b)Table 2
Physical and mechanical parameters of polypropylene fiber.
Properties
Density (g/cm3)
Breaking tensile strength (MPa)
Modulus of elasticity (MPa)
Elongation (%)
Diameter (μm)
Melting point (°C)
Value
0.96
500
3850
10–28
18–48
165


## 2.2. Test Scheme

The F-T cycles, fiber content, and fiber length are the three most important factors for the shear strength parameters (internal friction angle and cohesion) of fiber-reinforced soil. Taking these three factors as control factors, the orthogonal experiments of fiber-reinforced soil were designed with three factors and three levels, and nine groups of fiber-reinforced soil were determined, which are listed in Table3. The previous studies showed that the soil has reached a new balance after 6 F-T cycles, whose physical and mechanical properties changed little [29–31]. Therefore, the maximum F-T cycles in this test was set as 6 cycles. A series of direct shear tests of fiber-reinforced soil were carried out under the optimum water content condition by Welker and Josten, and the optimum fiber content was determined to be 0.2% through the maximum shear strength [32]. Therefore, the fiber content in this paper is taken as 0.1%, 0.2%, and 0.3%. The shear strength parameters of 9 groups of fiber-reinforced soil specimens were tested using direct shear test, and the optimum fiber content and fiber length can be determined by comprehensive analysis.Table 3
Experimental scheme based on orthogonal design.
Specimen number
F-T 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
0.2The optimum fiber content and fiber length were used for fiber-reinforced soil specimens, and the ordinary soil specimen was also made. The shear strength parameters of ordinary soil and fiber-reinforced soil under 0, 1, 3, and 6 F-T cycles were tested, respectively. The reinforcement mechanism of fiber on soil under F-T cycles was analyzed by comparing the variation of shear strength parameters with F-T cycles for fiber-reinforced soil and ordinary soil.


## 2.3. Test Methods

Based on compaction test, the optimum moisture content of soil can be obtained as 11.4% (Table1). Water was added to soil based on the optimum moisture content after drying and crushing, and then soil and fiber were mixed thoroughly and evenly following the designed experimental scheme. According to the provisions of the “Technical Specifications for Construction of Highway Subgrade” (JTG F10-2006) [33], the static pressure method was adopted to compact specimens in accordance with the compaction degree of 96%. The low-temperature test device (ADX-300-40) was used for F-T cycles, and the precision of F-T temperature can be controlled within 0.1°C. According to the temperature monitoring data of subgrade in cold regions, the freezing temperature was set as −15°C and the melting temperature was set as 15°C. One F-T cycle lasts for 24 hours (the freezing and melting need 12 hours, respectively). During F-T cycles, specimens were wrapped with multilayers of plastic wrap to prevent water loss.According to the provisions of the “Test Methods of Soils for Highway Engineering” [28], the SDJ-II type three-speed electric strain direct shear instrument, made by Nanjing Soil Instrument Company, was used for test scheme design of soil samples. The controlling loading rate was 0.8 mm/min for shearing, and the test was completed within 3–5 min. The precision of shear displacement measurement was controlled by 0.01 mm scale indicator. Four specimens were used for each shear group, which were cut to crush under the vertical pressure of 50 kPa, 100 kPa, 200 kPa, and 300 kPa, respectively.


## 3. Results and Discussion

### 3.1. Determination of Optimum Fiber Content and Fiber Length

The direct shear tests were carried out on 9 groups of fiber-reinforced soil. The shear strength parameters of fiber-reinforced soil were calculated, and Table4 lists the results of shear strength parameters (friction angle and cohesion).Table 4
Shear strength parameters of fiber-reinforced 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
50.22From the test results in Table4, the shear strength parameters of polypropylene fiber soil with different mixing ratios under F-T cycles were obviously different. Therefore, variance analysis and range analysis were conducted to examine the influences of three factors on mechanical properties of fiber soil in order to determine the optimum combination of fiber-reinforced soil under F-T cycles.The basic principle of analysis of variance (ANOVA) is to calculate variance (MS) by squared sum (SS) and degree of freedom (DF) and then calculateF value. If F > Fα (DFf, DFe ), where DFf is degree of freedom caused by factors and DFe is degree of freedom caused by error, it indicates that the influencing factors are significant. In order to calculate the variance for the orthogonal experiment, the sum of squares of total deviations and total degree of freedom should be decomposed firstly, as listed below:(1)SST=SSf+SSe,where SST is the sum of squares of total deviations; SSf is the sum of squares of deviations caused by factors; and SSe is the sum of squares of deviations caused by error.(2)DFT=DFf+DFe,where DFT is the total degree of freedom.Based on the sum of squares of deviations and degree of freedom, the variance of factor column and error column can be calculated by(3)MSf=SSfDFf,MSe=SSeDFe,where MSf is variances caused by factors and MSe is variances caused by error.According to the variance values, theF statistic can be constructed and analyzed:(4)Ff=MSfMSe.ANOVA results are given in Table5. The variance sources are namely F-T cycles, fiber length, fiber content, and empty column, respectively.Table 5
Analysis of variance (ANOVA) results for mechanical index.
Assessment index
Source of variance
SS
DF
Error sources
F value
Critical value
Significance
Internal friction angle (°)
F-T cycles
72.57
2
4.35
F
0.01 (2, 6) = 10.90F0.05 (2, 6) = 5.14F0.10 (2, 6) = 3.46
∗
Fiber length
2.06
2
√
Fiber content
27.21
2
√
Empty column
50.02
2
√
Cohesion (kPa)
F-T cycles
258.84
2
21.24
F
0.01 (2, 4) = 18.00F0.05 (2, 4) = 6.94F0.10 (2, 4) = 4.32
∗
∗
∗
Fiber length
20.95
2
√
Fiber content
95.94
2
7.87
∗
∗
Empty column
24.37
2
√
Note. √, the item of error sources; ∗∗∗, most significant; ∗∗, more significant; ∗, significance.ANOVA results showed that the effect of each influencing factor on internal friction angle was not significant. However, F-T cycles presented a significant effect on the internal friction angle due toF0.05 (2, 6) > 4.35 > F0.10 (2, 6). The influences of fiber length and fiber content on internal friction angle were submerged by error. As a result of 21.24 > F0.01 (2, 6), F-T cycles had a great influence on the cohesion of soil, which was the main significant influencing factor. According to F0.01 (2, 6) > 7.87 > F0.05 (2, 6), the influence of fiber content on the cohesion of soil is remarkable while the influence of fiber length on the cohesion of soil is not significant.A range analysis of various factors was carried out, and the results are presented in Table6. The mean Kj and the extreme value of the three factors at each test level were calculated, and the variation tendency of shear strength parameters with the influence factors is shown in Figures 3 and 4.Table 6
Analysis of variance (ANOVA) results for mechanical index.
Assessment index
Range
I
II
III
IV
F-T cycles
Fiber length
Fiber content
Empty column
Cohesion (kPa)
K
1
64.326
56.101
53.192
56.747
K
2
56.600
59.538
57.845
57.216
K
3
51.262
56.549
61.151
58.225
R
13.064
3.437
7.959
1.478
Internal friction angle (°)
K
1
34.503
30.967
32.993
28.633
K
2
29.923
31.110
28.783
31.240
K
3
27.680
30.030
30.330
32.233
R
6.823
1.080
4.210
3.600Figure 3
Tendency of the cohesion with influencing factors: (a) freeze-thaw cycles; (b) fiber length; (c) fiber contents.
(a)
(b)
(c)Figure 4
Tendency of the angle of internal friction with influencing factors: (a) freeze-thaw cycles; (b) fiber length; (c) fiber contents.
(a)
(b)
(c)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. F-T cycles had the greatest influence on cohesion index, followed by fiber content and fiber length. The cohesion decreases with the increase of F-T cycles, and the downward trend was slow. The trend of cohesion of fiber soil was consistent with that of general soil under F-T 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 fiber-reinforcing effect is weakened based on principle of friction between reinforcement and soil [34], and the overall strength enhancement effect of the fiber soil is not obvious; when the fiber length is too long, although the fibers are meshed between the fibers, the effect of the isotropic distribution is reduced in the soil. Obviously, with the increase of fiber content, cohesive force of soil increases significantly.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 F-T 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%.


### 3.2. Comparative Analysis of Shear Strength Parameters between Fiber-Reinforced Soil and Ordinary Soil

Table7 and Figure 5 presented the shear strength parameters of fiber-reinforced soil and ordinary soil under the optimum fiber content and fiber length.Table 7
Shear strength parameters of fiber-reinforced soil and ordinary soil under F-T cycles.
Soil type
Cycle times of F-T
Cohesion (kPa)
Internal friction angle (°)
Fiber-reinforced 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
33.88Figure 5
Shear strength index contrast of fiber soil and soil under the freezing and thawing: (a) internal friction angle; (b) cohesion.
(a)
(b)As observed from Figure5(a), the internal friction angle of plain soil increases gradually with the increase of F-T cycles, and the enhancement effect was the most remarkable between one F-T cycle and three F-T cycles. The internal friction angle of fiber soil in the first F-T cycle has been greatly enhanced. With the increasing of F-T cycles, the internal friction angle decreased. After three F-T cycles, the internal friction angle of fiber-reinforced soil was smaller than that of ordinary soil. Due to the presence of fibers, the water film is more likely to adhere to the surface of fiber. During the freezing process, the ice crystals along the fiber distribution made the structure more completely broken, the increase in the number of pores, the pore shape direction tend to be irregular, longitudinal cracks deep, and irregular shapes appear in the original complete place. Rearranging these will cause the soil particles to be in close contact with them and increases the point of contact between the soil particles which make the arrangement more rough. Therefore, it was conducive to play the friction between particles to increase friction and increase the internal friction angle, but the interwoven point between fibers increased after F-T, and the interweaving mechanism between fibers was more obvious which was conducive to the increase of cohesion; consequently, the internal friction angle will also decrease.It is obvious from Figure5(b) that the cohesion of ordinary soil and fiber-reinforced soil decreased gradually with the increase of F-T cycles, while the decrease tendency of cohesion decreased. At the first F-T cycle, the cohesion declined most significantly. The cohesion of the fiber-reinforced soil was greater than that of the ordinary soil under the same F-T cycles, and the cohesion of fiber-reinforced soil was stronger than that of clay with the increase of F-T cycles. With the increase of F-T cycles, the strengthening effect of fiber and soil on cohesive force of soil was increasing gradually. When the fiber was added, the fiber had a negative charge, which can collect the water film between the soil particles and the fiber. It can transfer the tension and strengthen the cohesive force of the whole soil mass.


## 3.1. Determination of Optimum Fiber Content and Fiber Length

The direct shear tests were carried out on 9 groups of fiber-reinforced soil. The shear strength parameters of fiber-reinforced soil were calculated, and Table4 lists the results of shear strength parameters (friction angle and cohesion).Table 4
Shear strength parameters of fiber-reinforced 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
50.22From the test results in Table4, the shear strength parameters of polypropylene fiber soil with different mixing ratios under F-T cycles were obviously different. Therefore, variance analysis and range analysis were conducted to examine the influences of three factors on mechanical properties of fiber soil in order to determine the optimum combination of fiber-reinforced soil under F-T cycles.The basic principle of analysis of variance (ANOVA) is to calculate variance (MS) by squared sum (SS) and degree of freedom (DF) and then calculateF value. If F > Fα (DFf, DFe ), where DFf is degree of freedom caused by factors and DFe is degree of freedom caused by error, it indicates that the influencing factors are significant. In order to calculate the variance for the orthogonal experiment, the sum of squares of total deviations and total degree of freedom should be decomposed firstly, as listed below:(1)SST=SSf+SSe,where SST is the sum of squares of total deviations; SSf is the sum of squares of deviations caused by factors; and SSe is the sum of squares of deviations caused by error.(2)DFT=DFf+DFe,where DFT is the total degree of freedom.Based on the sum of squares of deviations and degree of freedom, the variance of factor column and error column can be calculated by(3)MSf=SSfDFf,MSe=SSeDFe,where MSf is variances caused by factors and MSe is variances caused by error.According to the variance values, theF statistic can be constructed and analyzed:(4)Ff=MSfMSe.ANOVA results are given in Table5. The variance sources are namely F-T cycles, fiber length, fiber content, and empty column, respectively.Table 5
Analysis of variance (ANOVA) results for mechanical index.
Assessment index
Source of variance
SS
DF
Error sources
F value
Critical value
Significance
Internal friction angle (°)
F-T cycles
72.57
2
4.35
F
0.01 (2, 6) = 10.90F0.05 (2, 6) = 5.14F0.10 (2, 6) = 3.46
∗
Fiber length
2.06
2
√
Fiber content
27.21
2
√
Empty column
50.02
2
√
Cohesion (kPa)
F-T cycles
258.84
2
21.24
F
0.01 (2, 4) = 18.00F0.05 (2, 4) = 6.94F0.10 (2, 4) = 4.32
∗
∗
∗
Fiber length
20.95
2
√
Fiber content
95.94
2
7.87
∗
∗
Empty column
24.37
2
√
Note. √, the item of error sources; ∗∗∗, most significant; ∗∗, more significant; ∗, significance.ANOVA results showed that the effect of each influencing factor on internal friction angle was not significant. However, F-T cycles presented a significant effect on the internal friction angle due toF0.05 (2, 6) > 4.35 > F0.10 (2, 6). The influences of fiber length and fiber content on internal friction angle were submerged by error. As a result of 21.24 > F0.01 (2, 6), F-T cycles had a great influence on the cohesion of soil, which was the main significant influencing factor. According to F0.01 (2, 6) > 7.87 > F0.05 (2, 6), the influence of fiber content on the cohesion of soil is remarkable while the influence of fiber length on the cohesion of soil is not significant.A range analysis of various factors was carried out, and the results are presented in Table6. The mean Kj and the extreme value of the three factors at each test level were calculated, and the variation tendency of shear strength parameters with the influence factors is shown in Figures 3 and 4.Table 6
Analysis of variance (ANOVA) results for mechanical index.
Assessment index
Range
I
II
III
IV
F-T cycles
Fiber length
Fiber content
Empty column
Cohesion (kPa)
K
1
64.326
56.101
53.192
56.747
K
2
56.600
59.538
57.845
57.216
K
3
51.262
56.549
61.151
58.225
R
13.064
3.437
7.959
1.478
Internal friction angle (°)
K
1
34.503
30.967
32.993
28.633
K
2
29.923
31.110
28.783
31.240
K
3
27.680
30.030
30.330
32.233
R
6.823
1.080
4.210
3.600Figure 3
Tendency of the cohesion with influencing factors: (a) freeze-thaw cycles; (b) fiber length; (c) fiber contents.
(a)
(b)
(c)Figure 4
Tendency of the angle of internal friction with influencing factors: (a) freeze-thaw cycles; (b) fiber length; (c) fiber contents.
(a)
(b)
(c)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. F-T cycles had the greatest influence on cohesion index, followed by fiber content and fiber length. The cohesion decreases with the increase of F-T cycles, and the downward trend was slow. The trend of cohesion of fiber soil was consistent with that of general soil under F-T 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 fiber-reinforcing effect is weakened based on principle of friction between reinforcement and soil [34], and the overall strength enhancement effect of the fiber soil is not obvious; when the fiber length is too long, although the fibers are meshed between the fibers, the effect of the isotropic distribution is reduced in the soil. Obviously, with the increase of fiber content, cohesive force of soil increases significantly.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 F-T 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%.


## 3.2. Comparative Analysis of Shear Strength Parameters between Fiber-Reinforced Soil and Ordinary Soil

Table7 and Figure 5 presented the shear strength parameters of fiber-reinforced soil and ordinary soil under the optimum fiber content and fiber length.Table 7
Shear strength parameters of fiber-reinforced soil and ordinary soil under F-T cycles.
Soil type
Cycle times of F-T
Cohesion (kPa)
Internal friction angle (°)
Fiber-reinforced 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
33.88Figure 5
Shear strength index contrast of fiber soil and soil under the freezing and thawing: (a) internal friction angle; (b) cohesion.
(a)
(b)As observed from Figure5(a), the internal friction angle of plain soil increases gradually with the increase of F-T cycles, and the enhancement effect was the most remarkable between one F-T cycle and three F-T cycles. The internal friction angle of fiber soil in the first F-T cycle has been greatly enhanced. With the increasing of F-T cycles, the internal friction angle decreased. After three F-T cycles, the internal friction angle of fiber-reinforced soil was smaller than that of ordinary soil. Due to the presence of fibers, the water film is more likely to adhere to the surface of fiber. During the freezing process, the ice crystals along the fiber distribution made the structure more completely broken, the increase in the number of pores, the pore shape direction tend to be irregular, longitudinal cracks deep, and irregular shapes appear in the original complete place. Rearranging these will cause the soil particles to be in close contact with them and increases the point of contact between the soil particles which make the arrangement more rough. Therefore, it was conducive to play the friction between particles to increase friction and increase the internal friction angle, but the interwoven point between fibers increased after F-T, and the interweaving mechanism between fibers was more obvious which was conducive to the increase of cohesion; consequently, the internal friction angle will also decrease.It is obvious from Figure5(b) that the cohesion of ordinary soil and fiber-reinforced soil decreased gradually with the increase of F-T cycles, while the decrease tendency of cohesion decreased. At the first F-T cycle, the cohesion declined most significantly. The cohesion of the fiber-reinforced soil was greater than that of the ordinary soil under the same F-T cycles, and the cohesion of fiber-reinforced soil was stronger than that of clay with the increase of F-T cycles. With the increase of F-T cycles, the strengthening effect of fiber and soil on cohesive force of soil was increasing gradually. When the fiber was added, the fiber had a negative charge, which can collect the water film between the soil particles and the fiber. It can transfer the tension and strengthen the cohesive force of the whole soil mass.


## 4. Stability Analysis of Embankment Slope

### 4.1. Computational Model

The analysis process on stability of the fiber-reinforced soil slope was expounded by using the typical high-fill soil slope in northeast China which can be seen in Figure6. The finite element model of the high-fill soil slope was established based on the finite element analysis software ANSYS, and considering that the size of the road in the length direction was much larger than that on its cross section, the road slope could be simplified as a plane problem. Because of the symmetry of road to its centerline, only half of the cross section of the finite element model was established, and symmetric constraint was applied to the symmetry line to improve the computational efficiency. The finite element model of road slope was established by using the plane element PLANE82 provided in Figure 7, which had 8 nodes, and each node had two degrees of freedom with high accuracy and adaptability to irregular grid strong.Figure 6
Size of embankment slope (unit: m).Figure 7
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 D-P (Drucker-Prager) model, Cambridge model, and Duncan-Zhang model, among which the most commonly used is D-P model, so the D-P model was also chosen in this paper. In the D-P model, the equivalent stress σe can be obtained by equation (5) and Von Mises yield formula can be expressed as equations (6) and (7):(5)σe=3βσm+sTMs21/2,(6)F=3βσm+sTMs21/2−σy=0,(7)σy=6Ccosϕ33−sinϕ,where σm is the hydrostatic pressure, ß is the material parameter determined by internal friction angle φ; {s} is the deviation stress matrix; C is the cohesive force; and φ is the soil expansion angle. Therefore, when using the D-P model to set the material properties, two basic mechanical parameters of material need to be set: cohesive force C and internal friction angle φ. The finite element model using the measured shear strength parameters is listed in Table 7. The other material parameters are as follows: Es = 100 MPa, Poisson's ratio µ = 0.32, and soil density based on the maximum dry density ρdmax = 1.87 g/cm3.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 [35]. It was proposed that the number of iterations is 1000 and the relative difference of node displacement is less than 0. 001 which can be both regarded as convergence criterion [36]. In this paper, the convergence of finite element model was used as the criterion of slope instability, which means that if the finite element model converges, the slope is stable; otherwise, the slope is considered unstable. The convergence criterion of Reference [36] was used to determine whether the finite element model converges in this study.The strength reduction method was selected to realize the quantitative expression of slope stability. The formulas for calculating the shear strength parameters CohesionC′ and the internal friction angle φ′ after reduction are as follows:(8)C′=CF,tanϕ′=tanϕF.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′,φ′ by equation (8); (2) the shear strength parameters were input into the finite element model, and the model was solved. If the model converges, the slope is considered to be stable; (3) increase the F value gradually (take a small increment, such as 0.01) and repeate the steps (1) and (2) until the finite element model does not converge; the obtained F value was the slope stability coefficient.


### 4.2. Stability Analysis

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 Figure8, the maximum plastic strain of the slope can be seen in Figures 9 and 10 presents the maximum horizontal displacement of the slope.Figure 8
Slope stability coefficient.Figure 9
Plastic strain. P-0: plain soil of 0 F-T cycles; F-0: fiber soil of 0 F-T cycles; P-1: plain soil of 1 F-T cycle; F-1: fiber soil of 1 F-T cycle; P-3: plain soil of 3 F-T cycles; F-3: fiber soil of 3 F-T cycles; P-6: plain soil of 6 F-T cycles; F-6: fiber soil of 6 F-T cycles.Figure 10
Horizontal displacement: (a) displacement calculation result; (b) cloud picture of displacement of ordinary soil under the action of 1 time F-T cycle atF = 2.0; (c) cloud picture of displacement of fiber-reinforced soil under the action of 1 time F-T cycle at F = 2.0.
(a)
(b)
(c)As observed in Figure8, the slope stability coefficients of subgrade slope for each group showed that the stability coefficients of the ordinary soil slope and fiber-reinforced soil slope were the same before F-T cycle. Under the condition of one F-T cycle, the stability of the fiber-reinforced soil subgrade slope was improved, and the slope stability coefficient was increased by 42.86%, but the reinforcement effect of fiber soil was gradually weakened with the increase of F-T cycles. After three F-T cycles, the effect of fiber-reinforced soil on subgrade stability gradually stabilized.It is obvious from Figure9 that the plastic strain of both fiber-reinforced soil and ordinary soil is very small when the stability coefficient is less than a certain value. The plastic strain increases with the increase of stability coefficient, but the growth rate is slow. When the stability coefficient increases by a certain value (near the slope instability), the plastic strain increases rapidly and the plastic zone of subgrade slope will develop into a penetrating zone; the slope is in the unstable stage at this time. It can also be obtained from Figure 10 that when the stability coefficient of both fiber-reinforced soil and ordinary soil is less than a certain value, the horizontal displacement is very small. The horizontal displacement increases with the increase of stability coefficient, but the growth rate is slow. When the stability coefficient increases by a certain value (near the slope instability), the horizontal displacement increases rapidly, and the slope has the possibility of sliding at this moment. The calculation results of plastic strain in Figure 8 and horizontal displacements in Figure 10 are in good agreement with the calculated slope stability coefficient results, which is also a good verification of the slope stability analysis method. Moreover, a meaningful phenomenon can be found from Figures 9 and 10 that the plastic strain and horizontal displacement change obviously when the slope is near instability but not yet unstable, which may provide ideas for monitoring and early warning of fiber-reinforced soil slopes and ordinary soil slopes.


## 4.1. Computational Model

The analysis process on stability of the fiber-reinforced soil slope was expounded by using the typical high-fill soil slope in northeast China which can be seen in Figure6. The finite element model of the high-fill soil slope was established based on the finite element analysis software ANSYS, and considering that the size of the road in the length direction was much larger than that on its cross section, the road slope could be simplified as a plane problem. Because of the symmetry of road to its centerline, only half of the cross section of the finite element model was established, and symmetric constraint was applied to the symmetry line to improve the computational efficiency. The finite element model of road slope was established by using the plane element PLANE82 provided in Figure 7, which had 8 nodes, and each node had two degrees of freedom with high accuracy and adaptability to irregular grid strong.Figure 6
Size of embankment slope (unit: m).Figure 7
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 D-P (Drucker-Prager) model, Cambridge model, and Duncan-Zhang model, among which the most commonly used is D-P model, so the D-P model was also chosen in this paper. In the D-P model, the equivalent stress σe can be obtained by equation (5) and Von Mises yield formula can be expressed as equations (6) and (7):(5)σe=3βσm+sTMs21/2,(6)F=3βσm+sTMs21/2−σy=0,(7)σy=6Ccosϕ33−sinϕ,where σm is the hydrostatic pressure, ß is the material parameter determined by internal friction angle φ; {s} is the deviation stress matrix; C is the cohesive force; and φ is the soil expansion angle. Therefore, when using the D-P model to set the material properties, two basic mechanical parameters of material need to be set: cohesive force C and internal friction angle φ. The finite element model using the measured shear strength parameters is listed in Table 7. The other material parameters are as follows: Es = 100 MPa, Poisson's ratio µ = 0.32, and soil density based on the maximum dry density ρdmax = 1.87 g/cm3.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 [35]. It was proposed that the number of iterations is 1000 and the relative difference of node displacement is less than 0. 001 which can be both regarded as convergence criterion [36]. In this paper, the convergence of finite element model was used as the criterion of slope instability, which means that if the finite element model converges, the slope is stable; otherwise, the slope is considered unstable. The convergence criterion of Reference [36] was used to determine whether the finite element model converges in this study.The strength reduction method was selected to realize the quantitative expression of slope stability. The formulas for calculating the shear strength parameters CohesionC′ and the internal friction angle φ′ after reduction are as follows:(8)C′=CF,tanϕ′=tanϕF.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′,φ′ by equation (8); (2) the shear strength parameters were input into the finite element model, and the model was solved. If the model converges, the slope is considered to be stable; (3) increase the F value gradually (take a small increment, such as 0.01) and repeate the steps (1) and (2) until the finite element model does not converge; the obtained F value was the slope stability coefficient.


## 4.2. Stability Analysis

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 Figure8, the maximum plastic strain of the slope can be seen in Figures 9 and 10 presents the maximum horizontal displacement of the slope.Figure 8
Slope stability coefficient.Figure 9
Plastic strain. P-0: plain soil of 0 F-T cycles; F-0: fiber soil of 0 F-T cycles; P-1: plain soil of 1 F-T cycle; F-1: fiber soil of 1 F-T cycle; P-3: plain soil of 3 F-T cycles; F-3: fiber soil of 3 F-T cycles; P-6: plain soil of 6 F-T cycles; F-6: fiber soil of 6 F-T cycles.Figure 10
Horizontal displacement: (a) displacement calculation result; (b) cloud picture of displacement of ordinary soil under the action of 1 time F-T cycle atF = 2.0; (c) cloud picture of displacement of fiber-reinforced soil under the action of 1 time F-T cycle at F = 2.0.
(a)
(b)
(c)As observed in Figure8, the slope stability coefficients of subgrade slope for each group showed that the stability coefficients of the ordinary soil slope and fiber-reinforced soil slope were the same before F-T cycle. Under the condition of one F-T cycle, the stability of the fiber-reinforced soil subgrade slope was improved, and the slope stability coefficient was increased by 42.86%, but the reinforcement effect of fiber soil was gradually weakened with the increase of F-T cycles. After three F-T cycles, the effect of fiber-reinforced soil on subgrade stability gradually stabilized.It is obvious from Figure9 that the plastic strain of both fiber-reinforced soil and ordinary soil is very small when the stability coefficient is less than a certain value. The plastic strain increases with the increase of stability coefficient, but the growth rate is slow. When the stability coefficient increases by a certain value (near the slope instability), the plastic strain increases rapidly and the plastic zone of subgrade slope will develop into a penetrating zone; the slope is in the unstable stage at this time. It can also be obtained from Figure 10 that when the stability coefficient of both fiber-reinforced soil and ordinary soil is less than a certain value, the horizontal displacement is very small. The horizontal displacement increases with the increase of stability coefficient, but the growth rate is slow. When the stability coefficient increases by a certain value (near the slope instability), the horizontal displacement increases rapidly, and the slope has the possibility of sliding at this moment. The calculation results of plastic strain in Figure 8 and horizontal displacements in Figure 10 are in good agreement with the calculated slope stability coefficient results, which is also a good verification of the slope stability analysis method. Moreover, a meaningful phenomenon can be found from Figures 9 and 10 that the plastic strain and horizontal displacement change obviously when the slope is near instability but not yet unstable, which may provide ideas for monitoring and early warning of fiber-reinforced soil slopes and ordinary soil slopes.


## 5. Conclusions

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 F-T cycle. Then, the shear strength parameters of fiber-reinforced 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 high-fill 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:(i)
With the increase of F-T cycles, the cohesion difference between polypropylene fiber and soil increased gradually, and the reinforcement effect of internal friction angle was remarkable under one F-T cycle.(ii)
According to direct shear test, the optimum combination scheme can be obtained. The fiber-reinforced soil has the best enhancement effect when the fiber content is 0.3% and the fiber length is 9 mm.(iii)
The stability analysis method of soil slope combining finite element method and strength reduction method could be used to analyze the stability of polypropylene fiber-reinforced soil slope and ordinary soil slope, results of which were accurate and reliable.(iv)
The slope stability of fiber-reinforced soil embankment slope was better than that of ordinary soil embankment slope. With the increase of F-T cycles, the stability of polypropylene fiber-reinforced soil embankment slope with the optimal combination scheme was weakened, but the stability of fiber soil slope was significantly improved under one F-T cycle.(v)
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 fiber-reinforced soil slope and ordinary soil slope.



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*Source: 5725708-2019-01-21.xml*