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The shear strength of the soil refers to the ultimate strength of the soil against shear failure, which is one of the important indicators used to measure slope stability. This paper presents a simulation of direct shear tests on root-soil composites with different root embedding angles under different stress conditions. By comparing and analyzing the simulation results of ABAQUS software and the laboratory test results, the enhancement effect of plant roots on soil shear strength was explored. Conclusions can be drawn as follows: the excellent agreement between numerical models and laboratory shear tests suggested that the developed model can quickly and conveniently predict the shear strength of the root-soil composites. The shear strength was related to the rooting arrangement. For a single root system, when the inclination angle of the root was about 64° to the shear direction, the shear resistance of soil was much improved, while the root reinforcement had less effect when the inclination angle was greater than 90°. In the case of multiple roots, the hybrid rooting method can more effectively improve the shear resistance of the root-soil composite. Therefore, in the practical application of using the root to strengthen the soil, the angle of a single root and arrangement of multiple roots should be comprehensively considered.

Before the end of 2019, the total mileage of highways in China has exceeded 5.0125 million kilometers. However, Slopes are inevitably generated during mountain road constructions; these kinds of the slope are prone to landslides and other geological problems, such as soil erosion. All these problems seriously affect road traffic safety and the ecological environment [

The interaction between soil and plant roots mainly contributes to plant slope protection [

Most scholars have researched the shear performance of root-soil composites through experimental methods. The mechanism of shear behavior depends on the interaction of friction and constraint between root and soil. The shear characteristics of the root-soil composite are affected by many factors, such as the internal friction angle, cohesion force, and water content of the soil [

Various finite element numerical analysis software products have been used to analyze actual engineering problems [

In order to quickly and conveniently analyze the effect of root on soil reinforcement, we explore the best arrangement of the root system in soil and enrich the theory of root-soil consolidation and numerical simulation-related research. In this study, through ABAQUS finite element software, the direct shear friction test of the

The root embedded in the soil will be stretched and produce tension when the soil is sheared. The tension force can be decomposed into the horizontal direction and vertical direction, the horizontal force can be directly used to resist shear deformation, and the vertical force can be converted to positive stress to increase the friction force. When the root was inserted vertically into the soil, the incremental shear strength of the root-soil composite can be calculated by the following equation.

When the root system is orthogonal to the shear plane (Figure

Root deformation diagram: (a) the root is orthogonal to the shear plane; (b) the root intersects the shear plane obliquely.

When the root system is oblique to the shear plane (Figure _{S} is the cross-sectional area,

The shear strength of the soil and its increment of cohesion force can be calculated for different root angles. The results were further explored to determine the most appropriate root embedding angle, which would improve the shear resistance of soil and enhance the stability of the slope most. Based on the results of the field tests, Likitlersuang et al. [_{r} is the total area of the root system on the shear plane.

There have been few studies on the thickness of the shear zone

After understanding the reinforcement mechanism of the root system to the soil, further relevant experiments and numerical simulation studies were carried out, and the feasibility of the model was verified by comparing the errors between the simulated values and the experimental and theoretical values.

The study area is located in the Yueyang section of the Da-Yue highway (east longitude 112°10′3″ to 114°9′6″, north latitude 28°25′33″ to 29°48′47″), which has a humid continental monsoon climate. Its annual average temperature is between 16.5°C and 17.2°C, the highest temperature ranges from 39.3°C to 40.8°C, the lowest extreme temperature ranges from −11.4°C to −18.1°C, and the average annual precipitation is from 1289.8 to 1556.2 mm. There is more rainfall in the eastern part than the western part of the test section. The same area has more rainfall in spring and summer than autumn and winter. The studied slope is relatively high, with the highest point at 36.31 meters. Considering the effect and aesthetics of slope protection, we selected

Landscape of studied slope: (a) before slope protection; (b) after planting plants.

We used a ring knife to select soil on the test slope as the test soil. By referring to “Test Methods of Soils for Highway Engineering” in China, the soil water content was measured as 15.3%–21.4% by oven drying method. The natural density of the soil was tested as 1.65 g/cm^{3}–1.82 g/cm^{3} through the cutting ring method, and the particle composition of the soil was obtained through the sieving analysis test and is listed in Table

Results of sieving analysis test.

Screen hole diameter (mm) | Percentage (%) | Screen hole diameter (°) | Percentage (%) |
---|---|---|---|

40 | 0 | 1 | 11.8 |

20 | 5.0 | 0.5 | 15.3 |

10 | 14.2 | 0.25 | 5.7 |

5 | 17.8 | 0.075 | 1.5 |

2 | 28.3 | <0.075 | 0.3 |

The horizontal excavation method was used to collect the plant roots for experimental research. After excavating, the roots were wrapped in the soil sample and placed in a shear box and were watered for proper conservation. In this test, the diameter of

Morphological characteristics of different root systems: (a) root system with a length of about 20 mm; (b) root system with a length of about 28.8 mm.

The direct shear test was used in this paper because of its simple and easy operation. ZJ strain-controlled quadruple direct shear instrument produced by the Nanjing Soil Instrument Factory was chosen.

An iron wire was inserted to ensure the buried root position while preparing cylindrical specimens with a diameter of 61.8 mm and a height of 20 mm. The moisture content of the soil sample is consistent with that of the slope site soil, and its value is 18.62%, the iron wire was removed to insert the root, and the hole was compacted with soil. Then, the sample was covered with filter paper and pervious stone before being pushed into the shear box. During the test, vertical pressures of 100 kPa, 150 kPa, 200 kPa, and 250 kPa were applied to each group of specimens. The transmission was opened to shear at a speed of less than 0.02 mm/min until the shear damage occurred; during the process, the device automatically records the shear stress. In the shearing process, as the shear deformation of the root-soil composite increased, the shear strength of the root-soil composite was equal to shear stress when the shear failure occurred. The test process is shown in Figure

Shear test process of root-soil composites: (a) perforated cloth root of the direct shear specimen; (b) finished sample. (c) direct shear devices; (d) specimens after shear failure.

Multiple groups of laboratory direct shear tests were performed to record the corresponding shear strength under each vertical pressure. The direct shear test results were analyzed, and the relationship curve between the shear strength and normal stress of the root-soil composites was fitted in Table

Soil parameters in the numerical simulation.

Parameter | Value | Unit |
---|---|---|

Soil density | 1450 | kg/m^{3} |

Elastic modulus | 10 | MPa |

Poisson’s ratio | 0.3 | — |

Cohesion | 24.44 | kPa |

Friction angle | 29.44 | ° |

Coefficient of friction | 0.564 | — |

Moisture content | 18.62 | % |

Laboratory results of the direct shear test.

Plant species | Root angle with the horizontal direction | Curve fitting | ^{2} (%) | tan | ||
---|---|---|---|---|---|---|

No root | — | 99.43 | 4.435 | 0.564 | 29.449 | |

90° + 90° | 99.62 | 7.792 | 0.689 | 34.567 | ||

M. multiflora | 45° + 45° | 99.47 | 7.085 | 0.719 | 35.743 | |

45° + 90° | 99.53 | 8.292 | 0.753 | 36.987 |

The solid model with a diameter of 61.8 mm and a height of 20 mm was established to maintain the same size as the actual soil sample. It meshed with a three-dimensional first-order hexahedron element (C3D8), including a total of 564 nodes and 870 nodes. In the finite element simulation, the Mohr-Coulomb ideal plasticity model was applied. The specific values are shown in Table

Plant roots can be divided into three types according to their morphology: straight type, scattered type, and horizontal type [^{3}. The specific root distribution is shown in Figure

Top view and main view of three root insertion modes: (a) 90° + 90°; (b) 90° + 45°; (c) 45° + 45°.

The contact in the simulation of the direct shear test mainly includes the contact of the soil and the contact between the roots and the soil. The “Surface-to-Surface contact” was adopted between the soils, the upper and the down soil contact surfaces are selected as “Master surface” and “Slave surface,” respectively. The “Penalty formula” is used to calculate the friction force in the tangential behavior, and the contact type in the normal behavior is “hard” contact. The contact between the roots and soil was modeled by the embedded region constraints model in the ABAQUS constraint menu, and the roots were treated as embedded bodies.

The simulation did not take into account the shear rate, which simplified the test process appropriately, because the time of soil failure will not affect the results. Stress boundary conditions were used to simulate the vertical pressure, and displacement boundary conditions were used to play the role of the shear box. The numerical simulation was carried out following three steps: the initial step, load step, and shear step. The first step is to define the properties of the soil-soil and soil-root contact surfaces and fix the displacement of the specimen in the

Numerical simulation of the laboratory direct shear test.

Taking the model under 250 kPa vertical load as an example, the equivalent stress cloud diagram of the composite and root in the shear direction is shown in Figure

The stress cloud diagram of the composite and plant roots: (a) equivalent stress of bottom soil; (b) equivalent stress of plant roots.

The shear stress and the shear displacement are recorded in Figure

Shear stress-displacement curves of root-soil composites with different root arrangement: (a) ordinary soil; (b) 90° + 90°; (c) 90° + 45°; (d) 45° + 45°.

According to the results of the direct shear test in the laboratory and numerical simulation, their shear strength had no significant difference, as shown in Figure

Relationship curve between shear strength and vertical load.

To make the experimental results more apparent and the data laws more straightforward, the root diameter was appropriately increased, the incremental cohesion force of “

Incremental cohesion values at various angles.

Angle (°) | Increase in cohesion (kPa) |
---|---|

10 | 7.13 |

20 | 7.37 |

30 | 7.51 |

40 | 7.59 |

50 | 7.63 |

60 | 7.65 |

70 | 7.65 |

80 | 7.65 |

90 | 7.64 |

Finite element simulations were based on theoretical studies to analyze the effect of plant embedding angle on the shear strength of the root-soil composite and were also further combined with theory to verify the accuracy of the model. The roots were embedded in the soil model at different angles, the shear strength of the soil without roots was compared with that of the composite material, the effect of roots on the cohesion increment of the soil was analyzed, and the correlation curve between the root angle and the cohesion increment is plotted in Figure

Relationship curve between root embedding angle and cohesion incremental.

It can be seen that the simulation results and the theoretical analysis results showed the same pattern. The cohesion increment was the greatest when the root system was embedded at an angle of about 64°. The curve of formula (

The above study combines theoretical analysis with finite element simulations to explore the effect of a single embedding angle on cohesion increment. It was determined that the angle of root entry had an effect on the viscous cohesion increment of the composites. In the actual project, the number of roots planted on the slope is relatively large, and there are various combinations between roots and roots; for example, the same single inclination arrangement can be used, or mixed roots can be used, and the development of suitable rooting method to effectively expand the root reinforcement effect on the soil is crucial. The study of single and mixed rooting methods was carried out using both laboratory tests and numerical simulations. Due to the limitation of the size of the straight shear test block, only two better inclination angles of 45° and 90° have been used for this combination. The plotting of the rooting method and shear strength correlation curve is as follows (Figure

The relation curve between cloth root and shear strength.

This study conducted a finite element simulation of the direct shear test of the root-soil composite material. The simulation results were compared with the laboratory results to verify the feasibility of the model. At the same time, some application prospects of the model were proposed here; that is, the effect of root embedding angle on cohesive force increment was analyzed through numerical simulation, and the effect of root arrangement in soil on shear strength was explored. For some cases that are not easy to realize by experimental methods, numerical simulation can show its unique advantages. The following conclusions can be drawn:

The root system of

The shear strength is not only affected by factors such as the root diameter and root cross-section ratio but is also related to the manner of root distribution and the angle between the root and shear surface. Through theory, experiment, and simulation results, it can be seen that the root was inserted into the soil at different angles, and there is a difference in the improvement of the root-soil composite shear strength. When the inclination angle of the root is around 64°, the shearing strength of the soil was much improved, and when the inclination angle of the root was greater than 90°, the effect of roots on the soil was not pronounced. Besides, in the case of multiple root distributions, the shear strength of the 45° + 90° distribution was the largest; that is, the shear strength of the mixed root distribution manner is larger than that of the single root distribution manner

This paper explored the above problems by means of numerical simulation, and the conclusions obtained are consistent with the theoretical analysis and experimental results, the average value of the relative error of shear strength obtained from the multiple sets of tests was 2.9%, and the maximum relative error was 5.2%. After multiple verifications, it is feasible to study the shear strength of the root-soil composite by numerical simulation. The research results and research methods of this article have a good guiding significance for the development of related research on root growth regulation and slope protection

All data used to support the findings of this study are included within the article.

The authors declare no conflicts of interest.

Conceptualization was done by ZiFan Sui and Wen Yi; methodology was prepared by ZiFan Sui; resources and software were provided by ZiFan Sui; validation was conducted by ZiFan Sui, Wen Yi, and YunGang Lu; formal analysis was done by ZiFan Sui; investigation was performed by ZiFan Sui; data curation was done by Liang Deng; the original draft was written by ZiFan Sui; reviewing and editing were done by ZiFan Sui; visualization, supervision, and project administration were carried out by ZiFan Sui; funding acquisition was contributed by Wen Yi. All authors have read and agreed to the published version of the manuscript.

This research was funded by the Introduction of Key Technologies for Landscape Restoration of Deep Cut Slopes, under grant number 2015-4-38, and Research on Key Technology of Ecological Landscape Restoration of Highway Slope Road in Ecological Fragile Area, under grant number 201803.