The Tarim River is the largest inland river in Northwest China (34°55′-43°08′N, 73°10′-94°05′E). The area has serious soil erosion due to the lack of vegetation cover and infertile soil. The sampling site of this test is in the downstream of the Tarim River. According to the relevant information and the layering of the soil body at the site, the samples were taken in two layers, each with a thickness of 40-45 cm, and the samples were taken for indoor geotechnical tests to analyze the physical and mechanical properties. When the experimental data were combined, it was found that the lower layer was predominantly made up of fine-grained sandy soil, while the higher layer was mainly made up of sandy loam. The soil showed an internal friction angle between 30.7° and 33.9° and a cohesiveness between 3.1 and 13.5 kPa. Table 1 shows the soil's physical properties. Trees, shrubs, and herbaceous plants make up the majority of vegetation in the Tarim River, which covers an area of 25.88×10⁶ hm². Tree species include Populus euphratica Oliv. and Populus pruinosa Schrenk., while shrubs encompass Tamarix ramosissima Ledeb., Haloxylon ammodendron (C. A. Mey.) Bunge, Alhagi camelorum Fisch., Apocynum venetum L., and so on. Herbaceous plants primarily include Phragmites australis (Cav.) Trin. ex Steud.

Based on the influence of different root systems on growth effects, researchers have categorized plant root systems into supporting and absorbing roots. Usually found at the ends of the root system, researchers distinguished by a profusion of fine root hairs that increased the surface area of the roots for better uptake of nutrients and water (de Bauw et al., 2020). The primary function of the plant's support roots was to stabilize and uphold the plant's body. Typically, they were planted further down into the soil and secured there to improve the stability of the plant (Karizumi and Tsutsumi, 1958; Jin et al., 2013). Thus, this research primarily focused on the growth morphology and distribution of support roots in order to provide a more thorough understanding of the composition and operation of plant root systems.

Three varieties of shrub vegetation, each having a growth age of one year, were chosen to be studied (Perkons et al., 2014). We removed mulch around the root system with a brush as the soil was collected using dry excavation method. By identifying the main and lateral roots' growth paths and distribution patterns, this procedure established the comprehensive properties of intact plant root systems (Operstein and Frydman, 2000; Finér et al., 2011). The diameters of the main and lateral roots were measured, and they ranged from 1.5 to 2.0 mm.

The morphology of root systems comprises primary roots and lateral roots, with primary roots playing a dominant role in configuration and lateral roots enhancing water absorption by expanding the root-soil contact area (Zobel, 2008; Armengaud et al., 2009). The position of primary roots and the growth status of lateral roots fundamentally determine the overall structural form of the root systems. Studies indicated that various root measurement indices, including root length, root weight, and absorption area, could reflect root configuration to some extent. Scholars classified root system morphology including downward-rooted, outward-rooted, and horizontal-rooted types. Among them, downward-rooted types were further divided into shallow, intermediate, and deep-rooted types, while horizontal-rooted types were categorized as dispersed, intermediate, and concentrated types. When analyzing the impact of plant root systems on slope protection, research primarily focused on the root configuration of plant species (Saint et al., 2019). The ability of plants to absorb nutrients and water from the soil largely depended on the morphology of their root systems (Coppin and Richards, 1990). Therefore, understanding the root configurations of different plants was of significant scientific value for a deeper understanding of the roles played by plants in soil stabilization processes.

The generalized process of the root system model is depicted in Figure 1. Initially, we collected feature points of the main supporting roots based on the results obtained through dry excavation method. In order to restore the morphology of root systems as much as possible, we calculated the total root density of root systems in the area containing all the roots, and took the average value as V_m. If the ratio of V_i (root density in any area) to V_m within V_i unit area was greater than or equal to V_m (V_i≥V_m), the set was considered part of the same root system. If V_i was less than or equal to V_m (V_i≤V_m), it was treated as a distinct root system, continuing until the search for all root systems was completed.

Three main forms of root systems were found through the study and examination of the plants below the Tarim River, i.e., dispersed, horizontal, and vertical root types. There was one primary root and several lateral roots that made up the vertical root type. A main-lateral root system structure was formed, which stretched deep into the soil, as the main root expanded downward and the lateral roots grew to both sides. P. australis was the representative plant. The majority of the roots in the horizontal root type were dispersed throughout the top soil layer, with root systems that grew mainly horizontally. T. ramosissima was the representative plant. The dispersed root type was more widely distributed and featured well-developed branching roots in addition to less pronounced main roots. Alhagi sparsifolia Shap. was the representative plant. Figure 1d displays the conceptual diagram of these root systems.

Pullout test on individual root was carried out in the experiment using the helical tension test apparatus (NK-200, Shenzhen Liance Electronic Technology Co., Ltd., Shenzhen, China). Three distinct shrub species were subjected to pullout test. Each root sample was chosen from the same diameter class, and each type of root systems underwent at least 15 test repeats. The link between diameter tensile force and tensile strength was determined using pullout test data. The tensile strength of root systems was determined by the following equation:

where T is the tensile strength of root systems (MPa); F is the tensile force exerted on root systems when it fractures (N); and d is the diameter of root systems (mm).

As can be seen in Figure 2, the tensile strength of vegetative root systems increases as the diameter of root systems increases, and the expansion of cross-sectional area allows root systems as a whole to resist the tensile force more effectively, so the tensile strength gradually increases. There were notable variations in tensile stress between various vegetative root systems while the root diameter remained constant. This resulted from differences in material characteristics of various vegetative root systems, such as elastic modulus and tensile strength, which in turn affected the root systems' overall strength and tensile performance. Additionally, as the root diameter reached 1.5 mm, the variations became more noticeable, suggesting that prior to a particular growth stage, there were not many changes in the tensile force of various vegetative root systems.

Regression equations are tested using a combination of numerical analysis softwares (Origin and Matlab) and coefficient of determination (R²), significance, and regression coefficient significance tests (Table 2). Based on Table 2, it is evident that there is a power-law relationship between root diameter and tensile force. The regression equation was able to accurately describe the relationship between two variables during vegetation root growth period, as evidenced by R² values, which were all greater than 0.90.

The anisotropy of soil can be reflected by its directional contact fabric (Oda, 1972). After shearing, the directional contact fabric of the specimen undergoes certain displacements along the normal and tangential directions. The contact fabric in the normal direction, denoted as E(θ), and the normal contact force fabric F_n(θ), as well as the tangential contact force fabric F_t(θ), can be represented by Fourier series functions (Rothenburg and Bathurst, 1989):

where θ is the angle between the normal direction of particle-particle contacts (°); f₀ is the average normal contact force among all particle-particle contacts (N); θ_t, θ_n, and θ_a are the angles of the principal directions of anisotropic distributions for tangential contact force between particles, normal contact force, and normal direction, respectively (°); and a_t, a_n, and a are the Fourier fitting coefficients reflecting the degree of anisotropy in the distributions of tangential contact force between particles, normal contact force, and normal direction, respectively.

In this study, we initially generated a specific number of particles based on the porosity range of sand. These generated particles were then classified into soil particles using the ''group'' command. Subsequently, root particles with distinct shapes (vertical, horizontal, and claw) were created at specified coordinates using ''create position''. These root particles were grouped using the ''group'' to facilitate subsequent parameter calibration process, whereby model parameters were assigned to root and soil particles separately.

Figure 6a and b presents a relationship of shear stress and volumetric strain with displacement for four sets of specimens under normal stress of 100 kPa. The three RSCs showed initial shear stress characteristics that were comparable to remolded soil: shear stress steadily stabilized after reaching its maximum strength, and a notable strain hardening phenomenon was noted. In comparison with remolded soil, the shear strength of vertical, claw-type, and horizontal RSCs increased by 21.8%, 19.8%, and 9.7%, respectively.

As can be seen in Figure 6a, the initial shear stress of remolded soil increased rapidly as the shear displacement increased. However, after reaching the shear peak, the strain softened noticeably, causing a rapid decrease in shear strength. In the presence of identical normal stress conditions, the three RSCs showed longer times to reach the shear peak and higher peak shear stress, suggesting that the presence of roots strengthened the soil's shear strength by acting as a framework support.

It was noted from Figure 6b that all four sets of specimens first underwent shear contraction and subsequently shear dilation as the shear displacement increased. Shear dilation was the primary characteristic of weak shear contraction in remolded soil. There were different degrees of enhanced shear contraction once the reinforcement was added. Soil dilatation was reduced and shear contraction was heightened by the addition of roots. The following ranking of the soil's shear dilation behavior would suggest a favorable link between the addition of RSCs and the reduction of shear dilation: remolded soil>horizontal type>claw type>vertical type. Roots' ability to establish adequate contact between root systems and soil particles created a network anchor structure that, in part, trapped more soil particle aggregates. These particle aggregates filled in the spaces left by the larger soil particles' force chains and improved the inter-particle bonding. Out of the three varieties of roots, the specimen of vertical type showed the least amount of shear dilation and the least noticeable softening effect.

Correlations of shear stress and volumetric strain with displacement are established by applying various normal stresses, as shown in Figure 6c and d. Figure 6c and d showed that the shear stress peak for the remolded soil sample and the vertical RSCs sample progressively rose during the shearing operation. Furthermore, the volumetric strain-displacement curves for both groups of samples showed a progressive drop in their initial slope, which suggested a rise in shear contraction. The samples' internal soil particle connections tightened as the normal stress rose, increasing the samples' overall cohesiveness. This result implied that there was a positive relationship between shear contraction and shear stress peak values. Additionally, the degree of softening rose as normal stress increased for both sets of samples; however, the vertical RSCs sample showed less strain softening than the remolded soil sample. Additionally, strain softening started in the remolded soil samples at 100 kPa, whereas it started in the vertical RSCs at 200 kPa. To some degree, strain softening may be reduced in the presence of vertical roots.

Typically, the tangential and normal forces between particles form force chain networks. The patterns of stress transmission and particle movement in the sample could be examined by looking at the force chain network that forms during shearing. The distribution of force chains' length and number revealed details on the structural properties of particle packing as well as the interaction between particles.

A comparative diagram of force chain networks under shearing conditions for four sets of samples at a normal stress of 100 kPa is shown in Figure 7. The remolded soil sample displayed homogenous material, as seen in Figure 7a, meaning that shear forces were dispersed equally throughout the samples during shearing. Strong force chains, with a maximum force chain strength of only 11.2 kN, were comparatively evenly distributed throughout the interior at later stages of shearing, but their overall strength was lower, suggesting a reduced resistance to shear failure.

The reinforcement offered by plant roots clearly increased the force chain network's overall strength, as seen in Figure 7b-d. For the vertical, claw-like, and horizontal RSCs, the highest force chain strengths under the normal stress of 100 kPa were 34.8, 31.7, and 16.7 kN, respectively. As the particles packed tightly after reaching the shear peak, the strong force chains progressively condensed inside the roots' distribution region. These chains were primarily dispersed in an approximate diagonal pattern on the left side of the higher shear box and the right side of the lower shear box. During the later stages of shearing, the three reinforced soil samples' weak force chains gradually shrank while the strong force chains rearranged and interacted with the weaker force chains around them to form a more distinct force chain distribution in the diagonal region. Among these, the vertical root sample created an internal force chain network that was both comprehensive and interconnected, suggesting a well-organized particle arrangement as well as strong cohesion and shear strength. Strong force chain areas were arranged as follows: vertical type>horizontal type>claws type.

In order to better understand how particles interact with one another and investigate how they deform and fail during test, it may be possible to determine the force conditions of particles based on their speed and direction of motion. With four sets of samples and a normal stress of 100 kPa, Figure 8 shows the fluctuation in velocity fields during shearing process. As shown in Figure 8, kinetic energy was first transmitted from the inner walls of specimen to adjacent particles during the early stages of shearing. The specimens 'top walls' velocity vectors on each side converged toward the shear box's center, creating vortices inside the lower shear box. The velocity field within the specimen exhibited a hierarchical difference at reaching the peak shear stress, and thereafter, as the shearing progressed, the velocity fell progressively.

Upon introducing roots into the soil, a continuous transition zone developed within the specimen upon reaching the peak shear stress, as demonstrated in Figure 8b-d. Particles inside the soil traveled more slowly than those outside the roots, and the velocity of particles was lower near the roots than elsewhere. The early chaos in particle motion gave way to a more consistent direction. The presence of roots primarily contributed to the early stage of shearing until the shear stress reached its peak, unifying the direction of particle motion within the specimen. In the later stage of shearing, there was little difference in the velocity field between samples with and without roots. Soil particles in the remolded soil samples' lower shear box remained disorganized throughout the shearing operation, as shown in Figure 8. This result provided additional evidence that roots could impede soil particle migration during shear, minimizing the amount of soil damage and deformation.

The range of shear band during shearing process was closely associated with particle displacement, which could be categorized into three degrees: highly mobile particles, fixed particles, and relatively mobile particles. Both highly mobile and fixed particles could be considered non-load-bearing entities during shearing process. Consequently, the shear zone was consisted of those particles that moved towards each other.

Four sets of samples were exposed to the same horizontal thrust at a normal stress of 100 kPa. The deformation results of the shear bands are shown in Figure 9. During the initial phase of shearing, the particles in each of the three groups of RSCs were dispersed evenly and exhibited minimal displacement or deformation. During the intermediate shearing stage, there was a discernible displacement and deformation of particles surrounding the walls and root systems due to an increase in shear stress, which eventually resulted in the formation of entire and continuous shear bands. The continuous shear bands that had developed during the late stage of shearing eventually thinned out at both ends of root systems as the shear tension stabilized and they stretched from transverse to longitudinal development.

Each of the four sample groups showed clearly different shear band ranges, with the soil samples having the shortest range and the particles showing more noticeable stretching and dislocation within it. The friction and cohesiveness of the soil increased as a result of the formation of root systems because root expanded the contact area between soil particles. Tensile strength of RSCs increased and deformation decreased as the shear bands broadened because more soil particles distributed the initially concentrated stress. Vertical RSCs had the greatest longitudinal depth for shear bands, as seen in Figure 9. This phenomenon resulted in the greatest increase in friction and cohesion between soil particles and the least amount of deformation within the shear band area. The width of shear bands followed the order of vertical type>horizontal type>claw type>remolded soil.

Figure 10 shows the composition of contact number of four groups of specimens during loading at a vertical stress of 100 kPa. As shown in Figure 10a, the inner walls of the two shear boxes restricted the soil on both sides as the sample compressed in the shear direction during shear process, increasing tension at the ends of top shear box. In relation to shear motion, the direction of acute angles caused an increase in the contact number inside the samples. Reduced contact numbers resulted from the energy loss that occurred during soil particle movement, which loosened soil particle structures in normal direction. The isotropy of particles was usually assessed by the degree of homogeneity in the composition diagram of normal contact numbers.

Homogeneity of contact number distributions varied significantly among four groups of samples, as shown in Figure 10b. Undisturbed soil samples had the highest aspect ratio, reflecting the sample's strongest anisotropy. A vertical-type sample exhibited good isotropy in various directions and had strong vertical limitations on soil particles due to the uniform and symmetrical distribution of roots in the soil. As a result, there was a nearly circular composition diagram of contact numbers due to the relatively uniform distribution of contact numbers between particles. Although there were fewer lateral roots in claw type roots than in vertical type roots, the distribution pattern of roots in the soil was still similar to that of vertical type roots, suggesting less restriction on soil particles. With horizontal type roots, there were more contact numbers along the direction of shear motion because the roots were concentrated horizontally in the soil. The four groups of samples had varying degrees of isotropy. This result implies that adding roots to the soil improves the strength of RSCs and makes them more resilient to external stresses coming from different directions.

Past studies primarily focused on the diameter and density of root systems. However, little was known about the coordination between different types of root systems (Lu et al., 2023). Based on the field investigation results, Zong et al. (2018) found that the root diameter of dominant vegetation along the Tarim River was positively correlated with tensile strength. The mechanical response of RSCs with various root types under shear stress was investigated through numerical simulation. The numerical simulation offered a multifaceted examination of efficient resistance of root systems to outside influences. In this paper, the shear stress-displacement and deformation of RSCs in 100-400 kPa were compared. With increasing depth of soil layers, the shear stress of RSCs decreased slightly after reaching its peak, whereas the shear stress of remolded soil showed a significant decrease after reaching its peak. This phenomenon was also observed by Wang et al. (2010) in direct shear tests. The shear stress peak is positively correlated with shear ability (Sadek et al., 2011; Yang and Li, 2019), which is the effect of mechanism of root systems (Gray and Ohashi, 1983). With changes in root types, there were noticeable differences in the shear compressibility of RSCs, with the highest shear compressibility observed in the vertical root-soil composite, and the most pronounced dilatation in remolded soil. When root types were consistent, the shear shrinkage properties of RSCs were primarily influenced by normal force applied during shearing, with greater normal forces resulting in increased shrinkage properties and reduced shear dilatation properties of RSCs (Wang et al., 2021).

The microscopic analysis focuses on the interaction between particles, such as force chain network formed by contact of multiple particles, the velocity field resulting from particle displacement under external forces, the number of contacts in different directions, and grid shear bands (Dai et al., 2015). Through further understanding of the role of roots in slope protection engineering, the influence of different root levels on soil stability can be further studied, solving a series of geological problems such as soil erosion and slope instability.

When subjected to external forces in the same direction, the internal particles of RSCs formed a continuous force chain network due to their own inertia and the cohesive action of roots. Vertical RSCs have a higher density of force chain networks and require higher shear damage forces. The reason for this is the greater range of action of root systems and the fact that, due to its structural peculiarities, an anchoring structure is formed all around shear surface (Ruff et al., 1987; Allmaras and Logsdon, 2019). The simulation results showed that the three types of root systems within the distribution of shear zone underwent different degrees of deformation, and the more uniform the distribution of root systems in all directions, the larger the area of shear zone and the smaller the degree of deformation (Liang and Chao, 2017). The reason for this is that the tensile force generated by root systems along the direction of deformation is decomposed into components perpendicular to the shear surface and parallel to the shear surface to jointly resist the deformation of the soil (van Beek et al., 2005a, b).

Combined with the results of field study, it was found that when the main root was surrounded by a large number of lateral roots, root systems came into full contact with the soil particles to form a web-anchored structure when the specimen was subjected to shear, which to a certain extent retained a larger number of small soil particles, thus filling in the gaps in the force chain formed by larger soil particles and enhancing the bonding effect between soil particles (Scippa et al., 2006; Wang et al., 2018). The root tensile force and surface friction are different due to the differences in fiber content and distribution range of different root systems. When the root tensile force is higher in the specimen, it can provide a greater resistance to shear damage in the soil, which leads to a higher peak shear stress (Wen et al., 2016). Thus, the soil particles inside RSCs show different degrees of cohesion. When the root tensile force in the sample is high, it can provide the soil with greater resistance to resist shear damage, so that the soil reaches a high peak shear stress.

The study assumed uniform tensile strength across different root segments during root system simulation, despite conducting microscopic analysis and physical trials (Zhang et al., 2023). It did not take into consideration differences in tensile strength across root segments that differed in diameter or location. In this study, the tensile strength of different root segments was assumed to be uniform, but did not consider differences in tensile strength of root segments with different diameters or different locations. The results of the study are limited to a two-dimensional plane, and two-dimensional simulations may not adequately capture the possibility of more complex particle arrangements, particle aggregation, and more extensive force chain networks in three-dimensional systems. This means that this study may not have taken into account all of the complex three-dimensional scenarios in real-world engineering or natural systems (Bourrier et al., 2013; Huang et al., 2023). Soil consolidation effect of vertical, horizontal, and claw type roots was compared and analyzed in this study. In addition to the three types of roots mentioned in this study, some scholars have summarized other root distribution types (Li et al., 2016), but due to the limitations of the study area and experimental apparatus, the other root types are not fully investigated and discussed in this study. Meanwhile, fine root whiskers were ignored when simulating root systems, leading to a larger error in the simulation accuracy (Li et al., 2016; Li et al., 2020). Nowadays, various computer capture techniques have been fully developed, and this topic can be combined with image scanning technology (Chen et al., 2011, 2018) and programming software such as OpenGL (Song and Lu, 2020) to improve simulation accuracy in future research. In practical engineering settings, despite microscopic analysis and physical tests, a more accurate assessment of stability is needed to take into account the three-dimensional soil structure and stress fluctuations in different root segments. To sum up, in future studies, attention should be paid to the macroscopic influence of size effect on slope protection by vegetation, stress fluctuation of different root segments, and soil consolidation effect of root types for a more accurate assessment.