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Review

A Review of Discrete Element Method Applications in Soil–Plant Interactions: Challenges and Opportunities

by
Yuyuan Tian
1,
Zhiwei Zeng
1,* and
Yuan Xing
2
1
Department of Agricultural Engineering Technology, University of Wisconsin-River Falls, River Falls, WI 54022, USA
2
Department of Engineering & Technology, University of Wisconsin-Stout, Stout, WI 54751, USA
*
Author to whom correspondence should be addressed.
Agriculture 2024, 14(9), 1486; https://doi.org/10.3390/agriculture14091486
Submission received: 15 July 2024 / Revised: 20 August 2024 / Accepted: 26 August 2024 / Published: 1 September 2024
(This article belongs to the Section Agricultural Technology)
Browse Figure
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Abstract

:
The discrete-element method (DEM) has become a pivotal tool for investigating soil–plant interactions in agricultural and environmental engineering. This review examines recent advancements in DEM applications, focusing on both the challenges and opportunities that shape future research in this field. This paper first explores the effectiveness of DEM in simulating soil and plant materials, including seeds, roots, and residues, highlighting its role in understanding interactions that affect agricultural practices. Challenges such as long computation times and the complexity of determining accurate contact parameters are discussed, alongside emerging methods like machine learning that offer potential solutions. Notable advancements include the integration of machine learning algorithms for contact parameter estimation, the use of expanded particle models for dynamic processes, and the development of new techniques for detailed post-processing of DEM simulations. The review also identifies key future research directions, including the incorporation of environmental factors such as air and water, and the exploration of residue management for carbon storage and erosion prevention. By addressing these challenges and seizing these opportunities, future research can enhance the accuracy and applicability of DEM models, advancing our understanding of soil–plant interactions and contributing to more sustainable agricultural and environmental practices.

1. Introduction

A plant begins its life as a seed buried in the soil, with roots gradually penetrating the earth as it matures. Throughout its lifecycle, a plant remains deeply intertwined with the soil, leaving behind residues that mark its presence. The physical interactions between soil and various parts of a plant—seeds, roots, stems, leaves, and residues—are foundational to fields such as crop lodging resistance, nutrient uptake, plant health, erosion control, slope stabilization, and phytoremediation.
Understanding soil–plant interactions is also critical for various agricultural and engineering applications. For instance, seed emergence is influenced by factors like seeding depth [1] and seed–soil contact [2], which are determined by planting equipment design. Insights into soil–seed dynamics are essential for optimizing sowing machinery [3], while knowledge of root–soil interactions aids in designing effective cultivation and harvesting equipment. Moreover, incorporating crop residues into the soil post-harvest plays a crucial role in enhancing soil health and sustainability.
Historically, empirical observations and experimental methods have been the primary approaches for studying soil–plant interactions. Simplified models and laboratory tests have provided foundational insights [4,5], but these methods are often time-consuming and costly. As technology advanced, simulation-based methods like the finite element method (FEM) emerged, offering more efficient tools for modeling these interactions. However, FEM often struggled with the discontinuous nature of granular materials like soil, leading to challenges in accuracy and convergence.
The discrete-element method (DEM), introduced by Cundall and Strack in 1979 [6], offers a significant advancement in studying soil–plant interactions. Unlike FEM, DEM models individual particles and their interactions, making it particularly effective for simulating granular materials. DEM has demonstrated consistent results in complex scenarios like root reinforcement [7] and has overcome many limitations of traditional methods.
A variety of contact models have been developed to expand DEM’s applicability, such as the Hertz–Mindlin with JKR model for varying soil moisture levels [8,9] and the parallel-bond model for simulating different materials [10,11]. Despite its potential, DEM’s application in soil–plant interactions, particularly in engineering contexts, remains underexplored. This review synthesizes existing knowledge, addresses current challenges, and identifies new research opportunities in this field.
In conclusion, researchers have applied DEM to study the interactions between soil and plant materials, including seeds [8], roots [12], and residues [13], as illustrated in Figure 1. These studies employ diverse contact models and calibration methods tailored to specific applications. In this review, we examine the literature on DEM’s application in understanding soil–plant interactions across disciplines ranging from plant physiology to soil science to biosystem engineering. The review is structured around different plant materials—seeds, roots, and residues—aiming to foster interdisciplinary synergy and bridge knowledge gaps. For each type of plant material, we synthesize the challenges of understanding its interactions with soil, summarize the current research status and trends, and review the use of DEM in these contexts, focusing on research objectives, methods, and contact models employed. Finally, we identify future directions and opportunities for research and development in this field. The terms “soil–plant” and “plant–soil” are used interchangeably throughout the review.

2. Seed–Soil Interaction

2.1. Challenges

A seed marks the beginning of a plant’s life cycle, whether directly sown into the soil to germinate or transplanted as a seedling, as seen with crops like rice and many vegetables. For this discussion, the term “seed” encompasses dry seeds, cotyledons, and seedlings. The interaction between seeds and soil is crucial from the moment of seeding, through germination, and during early growth, influencing plant establishment, crop yield, and economic outcomes.
During seeding, dry seeds are deposited on the soil surface or into furrows, marking the initial contact with the soil. These seeds are then covered by soil and, in some cases, compacted by a press wheel to create optimal conditions for germination. This process aims to establish a favorable environment that supports seed germination and seedling emergence. The seed absorbs water from the surrounding soil and pushes against soil resistance to break through to the surface. For transplanted seedlings, soil contact occurs after germination, but the interaction remains vital for continued growth.
Successful seed germination and emergence depend on several factors, including water availability, air, nutrients, and temperature—each of which is influenced by the quality of seed–soil contact. However, terms like “adequate” and “reasonable”, when used to describe seed–soil contact, are subjective and difficult to quantify experimentally [2,4]. Soil resistance, a key factor in this interaction, significantly affects emergence rates, as it reflects the level of soil compaction that seeds must overcome to emerge [14,15]. Soil compaction not only impacts the emergence path but also varies with different soil conditions, making it challenging to quantify and utilize in seed breeding and crop cultivation practices.
The effectiveness of the seeding process is further determined by seeding characteristics such as sowing depth, plant spacing, and row spacing. These factors not only influence seed germination and emergence but also have lasting impacts on field management and harvesting. The initial and final locations of seeds in the soil, determined by soil conditions, seed characteristics, and the configuration of seeding equipment, play a critical role in these outcomes [16,17]. The complexity of soil covering and compacting processes, which affect these locations, has hindered progress in experimental studies aimed at analyzing the factors influencing seeding equipment [9].

2.2. Applications and Case Studies

The DEM has been used to quantify the contact conditions and flow characteristics at the interface of soil and seeds under different situations including seeding, covering, compacting, and growing processes. For example, rolling friction between the seed and soil, the contact characteristics between soil and seed, and the seed–soil flow direction and volume have been heavily examined in the literature. The key information of these studies is summarized in Table 1 and further discussed below. One should note that the contact model listed in the table includes that for soil and seed particles.
In the realm of seeding research, most studies have dealt with the interaction between various seeding tools and seeds. The interaction between the seed and the soil, which directly determines the final position of the seed, is often overlooked. Lysych et al. [21] simulated the impact interaction of pelleted seeds with the soil using the DEM. In their study, the effect of soil cohesion and travel speed on the penetration depth of seeds was examined. Unfortunately, the contact model and associated parameters are not available in the paper. The authors indicated that the sole evaluation indicator, penetration depth, is rather limiting and recommended to include other indicators in future studies of the seeding process.
Compared to the seeding process, the covering and compacting have been explored more with the DEM modeling and simulations in the literature with a focus on soil flow characteristics. Yan et al. [18] tested and simulated the soybean seed throwing process, which includes throwing, covering, and compacting phases. The seed location at various points, such as before and after covering, and after compacting, was monitored to analyze the seed displacement in the whole process. The soil was compressible and sticky. Therefore, the Edinburgh Elasto-Plastic Adhesion model was used in the study, which was developed to simulate the cohesive solids subjected to different flow and stress regimes, such as sticky and soft soil, as well as wet sand [22].
Xu et al. [9] analyzed the change of seed displacement during the covering and compacting process under the influence of different working conditions, including travel speed, disc open angle, and compaction force. The soil is sandy loam, and most of the soil particles are non-spherical. Therefore, three different forms of particles were applied to reproduce the actual situation in the soil bin. The soil particle diameter was enlarged to enhance the computation efficiency. The Hertz–Mindlin with JKR model was used to represent the cohesion between soil particles. The pilling test was used to calibrate the surface energy, and the rest of the parameters were adopted from an earlier study [23].
Zhou et al. [2] carried out a study using bonded particles to investigate the contact characteristics of different types of soil and seed. In their model, different soil densities were applied to the bottom soil and the topsoil to represent the real soil environment. Meanwhile, the seed diameter varied from 2 to 14 mm, which simulated different types of seed. The simulation results abide by the previous experimental study [4], which indicates that the DEM provides an effective way to study the characteristics of seed–soil contact.
Using the DEM to simulate the seed growth process has received some attention in recent years. Gong et al. [8] studied the soybean seed germination and emergence process. Firstly, the seed model expands to transform into cotyledon, and then the cotyledon model moves up to soil surface. The DEM model was employed to monitor the pattern of seed-soil contact number and the soil resistance in both the seed expansion and cotyledon movement process. In this paper, the seed model was represented by six ellipsoidal particles, which allowed the change in dimensions to show the seed expansion process. The soil was silt clay with a moisture content of 15%, which was constructed with the Hertz–Mindlin with JKR. The contact parameters in this study were calibrated through the free-fall test.
Zeng et al. [19] applied DEM to predict the seed–soil dynamics, including resistance force, contact number, and kinetic energy, for different cotyledon sizes and orientations. The soil model was based on the parallel-bond model in PFC3D. The soybean seed was represented by a rigid particle. The soil particles were represented by spherical particles with a uniform diameter of 4 mm. In the beginning, the soil bin was partially filled with soil particles with the model cotyledon placed on the top. Then, the cotyledon was covered with 40 mm of soil particles. The results showed that the effect of cotyledon size was more dominant than the cotyledon orientation on the dynamic attributes. The seed size significantly increased the resistance as they move up through soil during the emergence process.
Soil compactness is another important factor affecting resistance in the seed emergence process. Gong et al. [15] investigated the canola seed emergence under different soil compaction levels. In this model, a special particle, namely “pore” particles, was introduced into the soil particles; it is assumed to have the properties of air. The soil container was filled with a random mixture of soil and pore particles to achieve different soil compaction levels. In this study, the soil resistance was treated as the main indicator. The Hertz–Mindlin with bond model was used to construct the soil, and the seed was considered as a single sphere. The soil penetration test was used to calibrate the stiffness of the soil bond, and the rest of the parameters were adopted from the literature [24,25].
Gong et al. [20] simulated the process of soybean seed growing in soil. In this research, the soil was represented by the bonded sphere particles. The contacts between the particles followed the linear parallel-bond contact law. The soybean seed was simplified as a cotyledon which was simulated by a clump of spherical particles. In this study, the soil penetration test was used as the calibration method. The emergence path and the forces of the soybean seed were monitored. Then, the same model was applied to the lunar soil. The main difference between Zeng et al. [19] and this paper is the emergence path of the cotyledon. In the former study, the path is straight, while the emergence path is based on the minimal force path in the latter study. The results showed that the emergence force was reduced by almost 20%, while the travel path increased by 12% as compared to the results in Zeng et al. [19]. On top of that, a different growth media, the lunar soil, was considered in the simulation.

2.3. Opportunities

The existing studies have shown the potential of the DEM in quantifying and exploring seed–soil interactions. However, knowledge gaps and research opportunities exist. In the application of DEM modeling in seed planting, no study can be found dealing with cotyledons and seedlings. In addition, the soil and field conditions are very limited. Current DEM studies face significant limitations in accurately representing saturated soil conditions, particularly in environments like paddy fields. Traditional DEM models are well-suited for dry or partially wet granular materials but struggle with fully saturated soils. The presence of water not only dramatically alters the mechanical properties of the soil, including cohesion, internal friction, and overall load-bearing capacity, but also leads to complex behaviors such as fluid–soil interactions and reduced effective stress due to pore water pressure. The DEM could be coupled with other methods to represent different soil conditions. For instance, Tang et al. [26] applied the CFD-DEM coupling method to model the paddy soil, aiming to capture the complex fluid–particle interactions that occur in such environments. Le et al. [27] proposed a multifield coupling discrete-element model. Sun et al. [21] introduced a new coupling method of DEM-SPH for soil–liquid flows involving free surface. Younes et al. [28] proposed a phase field-based Lattice Boltzmann Method (LBM) model coupled with DEM for simulating unsaturated granular media. These techniques can be used to explore different soil environments.
In the covering and compacting process, the distribution of seeds is affected by the soil flow, and different soils showed different patterns of soil flow. The DEM could be used to quantify the soil flow mechanism. At the same time, different seeds require various conditions to grow. The soil flow characteristics can be combined with the seeds’ features to obtain the physical and biological conditions for seed growth, which can be represented through the DEM.
In the seed expansion process during germination, the seed shape would change, which could affect the seed–soil contact form. Existing studies simplify the process by using a few ellipsoidal particles and changing the dimensions to represent the germination process, which is suboptimal. The process of the water absorption of seeds can be understood as the reverse process of seed drying. Karunasena et al. [29] applied a coupled SPH-DEM model to explore the structural deformations of plant cells during drying. Therefore, the SPH-DEM coupling method can be a potential technology to explore the germination process. Additionally, Gong et al. [20] explored the effect of soil resistance on the path of emergence. Additional factors, such as porosity and the inclusion of rocks, might be considered to provide a comprehensive understanding of the emergence process.

2.4. Summary

In this section, the challenges of seed–soil interaction are analyzed according to the features of seed and soil. The interactions between the soil and seed can be divided into the processes of seeding and growth. The main challenge in the seeding process is ensuring the seeding characteristics in different situations, such as different soil types and seeds, are being captured in the model. The seed–soil interactions provide “adequate” and “reasonable” conditions for seed growth. Quantifying these conditions has become the biggest challenge in the seed growing process. The existing seed–soil interaction studies using the DEM were reviewed, including their research objectives, features, contact models, and calibration methods. Considering the challenges and current research status, the author identified a series of research gaps that require further investigation. Some potential technologies have been identified to address these problems. For instance, the DEM can be coupled with SPH to explore the germination process.

3. Root–Soil Interaction

3.1. Challenges

The root is a crucial part of a plant, directly interacting with the soil and serving as its foundation. Some roots, such as potatoes, yams, onions, carrots, and certain Chinese medicinal plants, are consumed by humans and animals. The soil provides both physical and biological support to the plant through its root system. Root development is influenced by the biological, chemical, and physical properties of the soil environment [30]. For consumable roots, soil physical parameters also play a significant role in determining crop yield [31]. Additionally, roots can alter soil properties, such as shear strength, highlighting the bidirectional relationship between soil and roots.
Root development is particularly affected by the soil’s physical properties, especially its mechanical resistance to penetration. Soil macropores, which provide oxygen and a path of least resistance for root elongation, are a key factor influencing root development [32]. Conversely, soil compaction reduces root branching and increases the cortical proportions of roots, though the mechanisms underlying these effects require further investigation.
One well-documented effect of roots on soil is root reinforcement, where roots enhance soil stability. Vegetation is often used as a “live” protective measure against landslides, erosion, and debris flows [33]. Root reinforcement has been quantified through various methods, including numerical models [34], physical tests [35], and finite element model-based predictions [36]. However, a common limitation of these methods is their difficulty in application to different situations with varying soil properties.
During the harvesting process, root vegetables are excavated along with the soil and then separated from it. The soil that adheres to the crops acts as a cushioning material during harvesting and post-harvesting processes. Understanding the movement patterns of root vegetables and soil can optimize this process. Traditional methods rarely capture or measure the root vegetable–soil mixture during harvesting [37]. Furthermore, different soil types, especially those with varying moisture content, exhibit distinct separation characteristics [38], making it crucial to quantify these characteristics for effective harvester design.

3.2. Applications and Case Studies

The DEM has been used to investigate the interaction between roots and soil. The discrete-element particles with different contact models were used to represent different soil features. The root was constructed by different methods to simulate the root–soil interactions. A relatively small number of studies focus on the bidirectional relationship between soil and roots, i.e., the effect of soil on roots and the effect of roots on soil. The majority of the recent literature deals with the interaction between soil and roots in the harvesting and handling process of root crops. The key information of these studies is summarized in Table 2 and further discussed below.
Soil significantly impacts root system development, influencing various growth processes. Nakashima et al. [39] proposed a DEM model to simulate root growth, focusing on elongation and shape formation. In their model, soil particles of three different diameters were generated to recover the soil environment. After that, the soil particles self-consolidated their own weight. The study assumed that root shape results from dynamic interactions with the surrounding soil, with root elongation driven by internal energy. Root growth was modeled as the expansion of a compressed element, which continuously replaced the previous root cap. The simulation results were compared to real roots cultivated in a soil box, marking the first study to model root growth using DEM.
Roots also play a crucial role in soil reinforcement, enhancing stability. Bourrier et al. [40] simulated granular soil reinforcement by roots, modeling the soil as interacting spheres and roots as deformable cylinders. In this model, DEM in its simplest form consists in modeling the soil as an assembly of rigid locally deformable spheres that can interact by contact forces. The roots are modeled as deformable cylinders in the soil matrix. The model allows users to account for the root tensile loading until breakage. The root slippage is associated with a frictional resistance at the root–soil surface. Due to the small diameter of roots, a scaling process was implemented to ensure the forces and torques in the model matched those of actual roots. Their results showed that root reinforcement effects significantly depend on shear strain, regardless of soil type.
Bai et al. [41] explored the mechanical properties of root-reinforced soil and developed a DEM model using PFC2D. Roots were modeled as chains of bonded discs to simulate tensile behavior, while the soil was represented by granular particles. The soil model was constructed through the following steps. Firstly, a specified number of particles with artificially smaller radii are placed at random coordinates within the soil bin. Then, the particles are expanded to achieve the desired porosity of the soil sample. The study focused on calibrating DEM parameters through a series of laboratory tests, including pull-out tests to determine the interfacial interactions between roots and soil particles. The findings indicated that root reinforcement is significant only when shear strain exceeds a critical value, which varies with different conditions. Root inclination and the number of roots also significantly influence the shear strength of rooted soil.
As for the harvesting, Li et al. [37] proposed a DEM model to optimize the harvesting process for white asparagus. The model included soil, end-effectors, and the asparagus itself. The soil particles were 1 mm with 0.8–1.2-times random distribution, which made the particles consistent with the soil and simultaneously accounted for the computation performance. Soil sub-models were obtained by establishing a particle factory to drop particles into the soil bin. The study monitored soil disturbance and compressive stress on the asparagus, providing a quantitative method to evaluate interactions between the soil, asparagus, and harvesting tools. However, the calibration process was not fully discussed.
Liu et al. [12] applied DEM to study the taro harvesting process, which involves complex interactions between particle mechanics and multi-body dynamics. The study used Hertz–Mindlin with bonding to construct the flexible tiller petiole and leaf, connected to the taro corm model. The soil, characterized as sandy loam, was modeled with Hertz–Mindlin with JKR, while adhesion between soil and taro corm used Hertz–Mindlin with bonding. In this model, the material moisture is assumed to be uniformly distributed, wrapped around the particle to form a uniform water film. The soil trough simulated the actual growth situation. The study provided insights for optimizing the taro-harvesting design.
For spinach, which grows in shallow soil, the low tensile strength of the petiole and leaf requires cutting the root during harvesting. Yuan et al. [47] used DEM to model the spinach root–soil complex, representing the root with Hertz–Mindlin with bonding, while the soil was modeled with Hertz–Mindlin with no slip. The contact parameters were determined through repeat tests. The soil particles drop from the particle factory randomly. This study introduced a novel approach to analyzing vegetable harvesting, though it lacked discussion on contact parameter calibration.
Li et al. [42] calibrated the contact parameters of sandy soil with different water content using EDEM. The calibration can improve the accuracy of the discrete-element simulation in the potato–soil mixtures separating process. Different contact models were applied to satisfy the different soil conditions. The slabby soil agglomerates were considered as the less hard rocks. Therefore, the Hertz–Mindlin with bonding was applied for it. Most of other soil types were presented by the Hertz–Mindlin with JKR model combined with different contact parameters. In this study, the potato was constructed by the multi-sphere, which means that the potato surface damage cannot be detected. A series of experiments were carried out and compared with the simulation test to verify the reality of the contact parameters. Moreover, the author used the Plackett–Burman test to explore the significant parameters affecting the model.
Yam harvesting is complicated by the strong bonding between soil and yam tubers, leading to high damage rates. Hao et al. [43] developed a DEM model for the yam–soil complex, calibrating critical parameters. The study modeled yam tubers as homogenous and isotropic using a bimodal approach, significantly reducing the number of parameters needed to represent yam tuber mechanics. The yam grows in the sandy loam soil. Therefore, the soil was represented by Hertz–Mindlin with JKR, and a series of experiments were conducted to calibrate the model parameters.
Liu et al. [44] focused on simulating the yam–soil complex with DEM, particularly examining shear strength during harvesting. The soil sample was collected from different depth layers to determine the properties of the soil accurately. The same simulation process as the real shear test was created to obtain the key parameters of the soil simulation model. In a further step, significant factors were analyzed through the Plackett–Burman test. The study found that the total surface area of roots significantly influences the shear strength of the yam–soil complex. However, the model was largely based on laboratory experiments, limiting its application to field conditions.
Finally, Wei et al. [45] applied DEM to simulate the potato separation process, aiming to understand the damage and bruising mechanisms caused by impact and collision. The model considered the features of the potato, soil, and separation equipment. Potatoes were modeled as rigid multi-particles, and the soil as bonded particles based on Hertz–Mindlin with bonding, which would break under impact, allowing soil particles to act as a buffer layer to protect the potatoes.

3.3. Opportunities

The literature shows that the DEM provides a new direction to explore root–soil interaction. At the same time, the DEM can achieve consistent results and avoid convergence problems as compared to other numerical simulation methods [6]. However, the application of DEM in root–soil interaction studies is not very common. There are many opportunities to further explore the root–soil interaction using the DEM.
It is obvious that soil properties have significant influences on the root system via its growth process. However, only one paper applied the DEM to study the process [39]. The study used the DEM to simulate the roots growing in the soil with different densities. The technology can be combined with the root-growing features to investigate the law of root cultivation. For instance, different planting strategies can be used to relieve soil compaction [46], which can be quantified in detail using the DEM. Moreover, root reinforcement can be enhanced by cultivating roots according to the principles of root development. The existing root–soil models are simplified due to various factors. Most of them use 2D models and often ignore important aspects of root morphology, such as root diameters. Therefore, the relevant model calibration methods and the model construction warrant more attention in future research.
The harvesting process has been studied more than the growing process of the root vegetable, including the digging and the separation. The majority of the existing studies used the multi-sphere to construct the root vegetable, mainly because of the gain in computational efficiency as compared to the single-sphere approach. However, the damage mechanism of the root vegetable cannot be fully analyzed with multi-sphere models. In addition, some root vegetables have anisotropic and inhomogeneous characteristics growing in complicated environments, such as the lotus root in saturated soil. Further studies are needed to improve the robustness and fidelity of the DEM models used in simulating root vegetable–soil interactions.

3.4. Summary

The interactions between the root and soil are a two-way process. The development of the root system is affected by soil conditions. The soil provides support for the root system, including both physical and biological aspects. On the other hand, soil properties can be influenced by root systems. The root systems can be considered an effective means of enhancing slope stabilization. This two-way process demonstrates the complexity of root–soil interactions, increasing the difficulty of related research. The DEM is considered an effective method for quantifying root–soil interactions. This section reviewed the research on using DEM to study the interaction between plant roots and soil, summarizing the research objectives, contact models, and calibration methods. The author found that there are a limited number of studies using DEM to explore the development process of the root system. In addition, the complexity of the DEM can be increased to obtain better simulation results.

4. Residue–Soil Interaction

4.1. Challenges

After harvesting, crop residues, including plant stems left on the soil surface and roots remaining beneath the topsoil, stay in the field. Crop residue management primarily involves surface retention, incorporation into the soil, and removal [48]. In recent years, conservation tillage has been widely adopted in many countries. Crop residues are considered the most readily available biomass in the field and contribute to an increase in soil organic matter. However, conservation tillage has also led to several issues. For instance, a yield loss of up to 13% has been reported in no-till corn fields [49]. This is due to the residue–soil interaction, which alters the chemical, biological, and physical properties of the soil. Understanding these interactions can help determine suitable residue management strategies based on different soil conditions and operational demands.
Different residue management methods result in varying roles of residues in residue–soil interactions. Residues can enhance soil aggregation, thereby changing the soil’s mechanical properties. For example, residues can increase soil shear resistance, directly affecting the performance of tillage tools. Additionally, higher soil hardness due to residues can influence seed germination. Natural factors, such as wind and raindrops, also affect residue–soil interactions. For instance, crop residues can protect soil from compaction caused by raindrops and help maintain soil moisture [48]. Clear and effective quantitative research is essential for developing appropriate residue management strategies. However, research on residue surface retention and incorporation is influenced by various factors, such as time period, soil type, and climate [50], posing challenges in exploring residue–soil interactions.
Furthermore, residues influence the soil’s biological and chemical properties through physical parameters, such as soil moisture and temperature. Residues remain in the field until the next production season, providing necessary conditions for organisms like bacteria and insects. Soil is a critical component of the global carbon cycle, but the mechanisms of carbon storage and emission are not yet fully understood. Factors such as soil particle diameter and temperature require further exploration in future research.

4.2. Applications and Case Studies

The DEM has been applied to investigate the relationships between the residue and soil. The key information of these studies is summarized in Table 3 and further discussed below.
Residue incorporation is a common method for handling crop residue in conservation agriculture. Zeng et al. [51] developed a DEM model to explore chisel ploughing tools, which are typically used in residue management. In this study, the soil model was constructed using bonded particles with a parallel-bond contact model. Soil particles were randomly generated and settled to reach an equilibrium state in a virtual soil bin. Corn residue pieces were represented by rigid blocks with dimensions and mass matching those used in real experiments. The model results were validated by comparing them with measured test data. During both the test and simulation processes, marked residue pieces and soil particles were used to investigate the performance of the tools, which can further help determine the effects of working parameters on their dynamic attributes. This model provides a foundation for understanding the soil–tool–residue interaction mechanism, which is crucial for determining optimal design and working parameters for better residue management.
The presence of crop residues in fields affects soil properties, impacting the performance of agricultural equipment. Adajar et al. [52] conducted an experiment to determine the mechanical properties of crop residues and explore their interaction with soil. A series of tests were conducted to obtain the macro and microscopic shear properties of five common crop residues and their interaction with soil. To focus on this research, spheres with a uniform particle size of 2 mm diameter were used to model both crop residue and soil particles. Two different contact models were employed to describe the contact between different particles: the soil particles were bonded using the parallel-bond model, and the built-in linear contact model was applied to soil–residue and residue–residue interactions. The particles were positioned inside the material vessels using the gravity deposition method, where they were left to fall inside with the effect of gravitational acceleration. Particles were allowed to settle until the system stabilized to reach a state of equilibrium. In this study, both crop residue and soil geometry were ignored, which could be further explored in the future. For example, clumped particles and irregularly shaped blocks may be more accurately represented using distinct contact models.
Gao et al. [53] calibrated a DEM model of the wheat straw–soil mixture to investigate the interaction between soil-engaging components and the wheat straw–soil mixture. The Hertz–Mindlin with JKR contact model was selected to represent the wheat straw–soil mixture. The model results were combined with physical tests to calibrate the contact parameters. Additionally, these contact parameters were ranked using the Plackett–Burman screening method and the steepest climbing method to determine the optimal combination range of contact parameters. The results showed that the buildup angle of the wheat straw–soil mixture mainly depends on the soil–straw static friction coefficient, soil–straw dynamic friction coefficient, and soil–soil dynamic friction coefficient. In this model, wheat straw was represented as rigid particles, impervious to deformation by external forces, a problem that can be addressed in future research.
The presence of crop roots in farmland affects seedbed preparation and planting operations in conservation tillage. Zhang et al. [54] developed a DEM model to simulate the maize root–soil complex, providing a valuable reference for conservation tillage. The maize root was represented as a cylindrical multi-sphere, which does not involve material bending and fracture. The contact between the root particles was described through the Hertz–Mindlin (no slip) contact model, while the Hertz–Mindlin with JKR was employed to calculate soil particle interactions and root–soil interactions. Combining physical and simulation experiments, critical parameters of the maize root and its interaction with soil were measured and verified by the angle of repose test.
The stubble–soil complex affects tillage operations after crop harvesting because the performance of soil-engagement tools depends on soil properties. Zhang et al. [13] utilized DEM to study the properties of the stubble–soil complex, comprising soil, maize stems, branching roots, and capillary roots. Due to soil’s higher adhesion and agglomeration characteristics, the Hertz–Mindlin with JKR contact model was used to simulate the soil, calibrated through the angle of repose test. After the soil particle size test, the model size of soil particle was enlarged to a range from 3 to 7 mm during simulated tests to reduce the number of particles and improve the efficiency of DEM simulation. Deformation and fracture occur during the tillage process, so maize stubble was constructed using the Hertz–Mindlin with bonding. This study incorporated specific root features into the model, dividing the root into four layers (R1, R2, R3, and R4) based on their growing depth. The results showed that maize stubble increased soil shear strength.
Pasthy and Tamas [55] applied a method coupling the discrete-element and mass-spring methods to explore soil–tool–root interaction. In this study, the plant root was represented by the mass-spring method, and soil particles were illustrated by the discrete-element method. The contact model between the particles and the mass-spring was the Hertz–Mindlin, used to calculate the contact force. When the root constructed by the mass-spring method exceeds a specific force, it breaks, allowing for the simulation of deformable and tearable bodies. This study primarily proposed a new direction for exploring soil–root–tool interaction, so some details were not extensively discussed.

4.3. Opportunities

In recent years, conservation tillage has gained popularity, drawing researchers’ attention to the residue–soil interaction. Crop residues can directly and indirectly affect soil properties, including physical, chemical, and biological aspects. DEM has shown potential for investigating these interactions.
The interaction between residues and soil directly affects the physical properties, which are crucial for the performance of soil-engaging tools. Some researchers have utilized DEM to model residue–soil mixtures, primarily focusing on calibrating contact parameters. However, many of these studies overlooked both crop residue and soil geometry, treating crop residues as rigid bodies. While such approaches can increase simulation efficiency, they may reduce model accuracy. With the continual advancement of computer technology, future models can be constructed with a detailed contact model to capture the complex interactions that occur between irregularly shaped and deformable particles. These limitations suggest the need for more advanced modeling techniques, such as incorporating clumped particles, irregularly shaped blocks, and more complex contact models to better represent the physical characteristics and interactions in residue–soil systems.
Current DEM models largely focus on the physical interactions between residues and soil, with limited consideration of chemical and biological factors. There is a research gap in understanding how residues decompose and interact with soil microbiota, and how these processes influence soil fertility, nutrient cycling, and overall soil health. Incorporating these chemical and biological aspects into DEM models could provide a more comprehensive understanding of residue–soil interactions. Furthermore, DEM offers a pathway to explore the impact of physical alterations in soil–residue mixtures on chemical and biological properties. For instance, researchers have particularly emphasized soil carbon management. Additionally, crop residues are considered readily accessible biomass in the field, making DEM a valuable tool for exploring the effects of residue–soil interactions on carbon storage mechanisms.

4.4. Summary

Crop residues, including plant stems and roots, are left in the field after harvesting. These residues affect soil properties in many ways, including mechanical, biological, and chemical aspects. For example, the soil’s mechanical properties directly influence the performance of tillage tools. Quantifying residue–soil interactions can help optimize the design and operational parameters of these tools. Additionally, residues impact soil’s biological and chemical properties through physical parameters such as soil moisture and temperature. Upon reviewing current research, the author found that previous studies often utilized relatively simple models with limited applications. Furthermore, research exploring the relationships between soil’s physical, biological, and chemical properties is lacking. Based on this review, several research opportunities were proposed to address these gaps.

5. Opportunities and Challenges

5.1. Emerging Fields

Over the past few decades, DEM, based on various contact models, has been used to simulate different materials, including soil and plant materials. DEM has shown an excellent performance in studying plant–soil interactions. However, there are some drawbacks to this method, such as long computation times and difficulties in determining contact parameters, thus hindering more detailed research. For instance, critical plant features are often ignored to achieve satisfactory computational efficiency. In recent years, emerging methods have been integrated with the DEM, advancing its application to a higher stage. By combining DEM with these emerging methods, these drawbacks might be addressed in future research. The following paragraphs introduce these emerging methods.
Machine learning is a powerful and useful tool that has been applied in many fields, including numerical simulation. The combination of DEM and machine learning encompasses pre-simulation calculations and real-time simulation computations. The pre-simulation calculations include contact parameter estimation and contact model development. Yuan et al. [56] trained a machine learning model to predict the actual mechanical properties of a DEM model using the XGBoost algorithm, achieving prediction errors of less than 4% for mechanical parameters. This method shows potential for determining the contact parameters of a plant–soil model, a difficult part of DEM model development [8], which machine learning might solve in the future. Additionally, machine learning has been applied to develop contact models, which are fundamental to DEM. An efficient and effective contact model can significantly expand the application scope of DEM. Cui et al. [57] developed a contact model for simulating low-saturation wet granular systems using the Catboost algorithm. The model excels in predicting capillary forces between particles and between particles and walls. The computation process can also incorporate machine learning to accelerate calculation speed. Lu et al. [58] employed a convolutional neural network to replace the direction calculation of particle–particle and particle–boundary collisions, achieving a 78-fold speedup compared to traditional calculations with minimal loss of accuracy. However, if the geometry and granulation of particles change, the model must be re-trained and re-tested. Other attempts to combine DEM and machine learning have also been made. For instance, Liao et al. [59] developed a machine learning model to predict particle flow patterns, addressing the time consumption issue of DEM [6].
In addition to machine learning, several interesting methods have been coupled with or applied in DEM-related research. Firstly, various methods have been used to determine DEM model contact parameters, which is one of the challenges of DEM application. Recently, data analysis software has been used for contact parameter estimation. For instance, the Plackett–Burman test, based on the Design Expert software (V8.0.6.1), has been used to identify significant parameters affecting the model [38,45]. These applications effectively speed up the contact parameter analysis process.
Another trend involves using different methods to mimic dynamic processes, useful for representing plant growth. Gong et al. [8] used expanded particles to represent seed germination. Nakashima et al. [39] constructed a model to represent the root growth process by considering root growth as the expansion of a compress element, which continuously replaced the previous root cap element. This model was developed through a cone penetration program created by their research team.
Several researchers have applied different open-source software tools to simulate soil structure dynamics. Younes et al. [28] introduced a phase field-based Lattice Boltzmann Method (LBM) model coupled with DEM to simulate unsaturated granular media, including soil, air, and water. This model, developed using YADE, an open-source software, can simulate soil structures under varying moisture levels, offering a way to explore soil behavior during wetting and drying cycles. The results qualitatively reproduce the soil water characteristic curve and have been compared to a theoretical model. Le et al. [27] proposed a multifield coupling DEM-based scheme to study the mechanism of desiccation cracking under multifield coupling effects. Their model simulates the uneven distribution and transfer of moisture and also couples the moisture field with the stress field. These methods demonstrate the potential to simulate different soil structures, including unsaturated and saturated conditions such as those found in paddy fields, making them significant for plant development. Both models, being based on open-source software, offer greater flexibility for model development tailored to specific applications.
Various modeling methods for non-spherical particles, a commonplace in soil–plant systems, and efficient contact detection have been proposed in the literature. Xu et al. [9] used three different forms of soil particles to show the soil feature, which is based on the multi-sphere method. The mechanical behavior of a granular system is strongly influenced by particle shape, which is known as the primary characteristic of granular materials [60]. At the same time, the rapid development of computer technology allows researchers to construct the model with more details to explore the soil movement.
Lastly, an interesting study by Poppa et al. [61] developed a particle segmentation algorithm in DEM for contact localization during post-processing to predict potato damage. This algorithm used the API tool of EDEM to analyze simulation results with more accurate details, providing a new direction for exploring plant–soil interactions further.

5.2. Future Challenges

The interaction between plants and soil is a two-way process. Plant growth depends on soil properties, such as density and water content. Conversely, plants can alter soil properties. Understanding plant–soil interactions is crucial in fields like agriculture and biosystems engineering. As observed from the literature, the DEM is a popular and widely accepted method for investigating plant–soil interactions. However, some vital areas have been neglected in previous research, indicating opportunities for further study using DEM.
Future research should expand the scope to include different environmental factors, such as air and water, which are crucial for soil properties and plant growth. As an example, penetration resistance is not the only limitation in the root growing process. Previous studies have shown that plant roots can navigate through or along holes in the soil [62]. Therefore, incorporating additional factors into DEM models could provide a more comprehensive understanding of soil–plant interactions. For instance, the microscopic deformation and energy consumption characteristics of soil during fragmentation are influenced by soil moisture content. These properties are directly related to seed germination and root development. Liu et al. [63] investigated the microscopic deformation and fragmentation instability of soils with varying moisture levels under vertical axial loads. Their findings offer valuable insights for research on plant growth processes with varying environmental conditions.
Further steps could involve using DEM-based information to cultivate plant roots and root vegetables as needed. DEM applications can significantly reduce the time required for cultivation verification processes. Additionally, temperature should be considered in studies on seed germination and residue–soil interactions. To the best of the authors’ knowledge, related research on this aspect has been limited. Moreover, combining the mechanisms of residue–soil interaction with specific tillage practices to enhance carbon storage or prevent soil erosion might become a significant research focus in the future.
DEM parameter calibration is a crucial research objective, encompassing both material and contact parameters. Soil and plants, being natural materials, exhibit anisotropic and inhomogeneous characteristics that are often simplified in models. Even when parameter values are directly and precisely measured, this does not guarantee that the simulation will achieve the same level of accuracy at the bulk level [38]. Therefore, improving methods for parameter determination is essential to advancing DEM applications in plant–soil interaction studies. Common calibration methods include the angle of repose, direct shear, and triaxial tests, along with corresponding in situ soil measurements [64]. These methods can accurately determine contact parameters between soil particles, tools, or machines. However, most of these methods are not suitable for soil–plant interactions due to the unique properties of plant materials. Calibration methods need further development to account for these specific application characteristics. For example, Bai et al. [41] conducted a pull-out test to calibrate the friction parameters between soil and roots, demonstrating how tailored methods can effectively address the challenges posed by soil–plant interactions.

6. Conclusions

This paper reviews the role of DEM in studying plant–soil interactions within agriculture and biosystem engineering. DEM has emerged as a valuable tool, offering greater precision compared to traditional methods. However, challenges such as long computation times and difficulties in determining contact parameters have limited its application. Recent advancements in integrating machine learning with DEM have shown promise in overcoming these challenges. Techniques like the XGBoost algorithm and convolutional neural networks can enhance parameter estimation and simulation speed. Additionally, dynamic modeling methods and improved contact parameter estimation tools, such as the Plackett–Burman test, have refined DEM’s capability. Future research should focus on incorporating environmental factors like air, water, and temperature into DEM models to better understand soil–plant interactions. Enhanced parameter calibration methods and exploration of residue–soil interactions for conservation practices will also be crucial. By integrating DEM with emerging technologies, researchers can address current limitations and advance the study of plant–soil interactions, leading to more effective agricultural and engineering solutions.

Author Contributions

Conceptualization, Y.T. and Z.Z.; methodology, Z.Z.; software, Y.T.; validation, Y.T. and Z.Z.; formal analysis, Y.T.; investigation, Y.T.; resources, Y.T. and Y.X.; data curation, Y.T.; writing—original draft preparation, Y.T.; writing—review and editing, Z.Z. and Y.X.; visualization, Y.T. and Y.X.; supervision, Z.Z. and Y.X.; project administration, Z.Z.; funding acquisition, Z.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Dairy Innovation Hub.

Institutional Review Board Statement

Not applicable.

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Acknowledgments

The authors thank the editor and anonymous reviewers for providing helpful suggestions for improving the quality of this manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

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Agriculture 14 01486 g001
Figure 1. Common soil–plant interaction systems simulated by discrete-element method (DEM).
Figure 1. Common soil–plant interaction systems simulated by discrete-element method (DEM).
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Table 1. DEM research of seed–soil interaction overview.
Table 1. DEM research of seed–soil interaction overview.
ReferenceSoftwareSoil FeatureContact ModelSeed TypeSeed Model FeatureFigure
Yan et al., 2022 [18]EDEM (2018)Compressible and sticky soilThe Edinburgh Elasto-Plastic Adhesion ModelSoybean seed13-sphere modelAgriculture 14 01486 i001
Xu et al., 2022 [9]EDEM (2018)Sandy loamHertz–Mindlin with JKRSoybean seed5-sphere modelAgriculture 14 01486 i002
Zhou et al., 2014 [2]PFC3D (4.0)Different soil density between bottom and upper soilStiffness model; slip model; contact bond modelOilseed rape; wheat; soybean; pea; chickpea; maize; Canavalia ensiform;Single sphereAgriculture 14 01486 i003
Gong et al., 2019 [8]EDEM (2018)Silt clay with moisture content of 15%Hertz–Mindlin with JKRSoybean seed transform to cotyledonSix ellipsoidal particlesAgriculture 14 01486 i004
Zeng et al., 2020 [19]PFC3D (6.0)Sand:70%
Silt: 16%
Clay: 14%
Water: 26%		Linear parallel-bond modelSoybean seed (cotyledon)Irregular shapeAgriculture 14 01486 i005
Gong et al., 2022 [15]EDEM (2021)Sand: 70%
Silt: 16%
Clay: 14%
Water: 15.96%		Hertz–Mindlin with bondCanola seed (seedling)Single sphereAgriculture 14 01486 i006
Gong et al., 2023 [20]PFC3D (6.0)Earth and lunar soilLinear parallel-bond modelCotyledon (soybean seed)A clump of spherical particlesAgriculture 14 01486 i007
Table 2. DEM research of root–soil interaction overview.
Table 2. DEM research of root–soil interaction overview.
ReferenceSoftwareSoil FeatureContact Model of SoilRoot FeatureContact Model of RootResearch ObjectiveFigure
Nakashima et al., 2008 [39]--The Voigt modelRoot elongates using internally accumulated energyCompressed virtual springSimulate the root-growing processAgriculture 14 01486 i008
Bourrier et al., 2013 [40]Yade-DEM
(1st ed.)		--Roots with the same diameterLaw2 ScGeom6D CohFrictPhys CohesionMoment and ScGeom6DThe reinforcement mechanism of root on soilAgriculture 14 01486 i009
Bai et al., 2021 [41]PFC2D (-)--Single straight rootThe parallel bondThe root can enhance the soil shear strengthAgriculture 14 01486 i010
Li et al., 2020 [37]EDEM (-)-The Hertz–Mindlin (no slip)-The Hertz–Mindlin with bondingSelect the best harvesting scheme and the suitable range of driving forcesAgriculture 14 01486 i011
Liu et al., 2022 [12]EDEM (-)Sandy loamHertz–Mindlin with JKR-The Hertz–Mindlin with bondingInvestigate the taro harvesting processAgriculture 14 01486 i012
Yuan et al., 2020 [42]EDEM (-)Granular soil;The Hertz–Mindlin (no slip)-The Hertz–Mindlin with bondingInvestigate the spinach harvesting using a cutting shovelAgriculture 14 01486 i013
Li et al., 2022 [43]EDEM (2020)Slabby soil agglomerates; granular soil;The Hertz–Mindlin with bonding
The Hertz–Mindlin with JKR		Rigid body-Simulate the potato separation processAgriculture 14 01486 i014
Hao et al., 2019 [44]EDEM (-)Sandy loam soilThe Hertz–Mindlin with JKRHomogenous and isotropicThe Hertz–Mindlin with bondingCalibrate the contact parameters of the mixture modelAgriculture 14 01486 i015
Liu et al., 2022 [45]EDEM (-)Sand: 62%
Silt: 24%
Clay: 14%
Moisture: 22%		The Hertz–Mindlin with bonding-The Hertz–Mindlin with bondingConstruct a yam–soil complex model for future researchAgriculture 14 01486 i016
Wei et al., 2020 [46]EDEM (-)lumpy soilThe Hertz–Mindlin with bondingRigid body-Simulate the potato separation processAgriculture 14 01486 i017
Table 3. DEM research of residue–soil interaction overview.
Table 3. DEM research of residue–soil interaction overview.
ReferenceSoftwareSoil FeatureContact Model of SoilResidue FeatureContact Model of ResidueResearch ObjectiveFigure
Zeng et al., 2020 [51]PFC3D (6.0)Sandy loamThe parallel bondRigid bodyThe multi-particleInvestigate the working performance of different toolsAgriculture 14 01486 i018
Adajar et al., 2021 [52]PFC3D (6.0)Sandy loamThe parallel bondDifferent crop residuesThe built-in linear contact model (single sphere)To determine the simulation parametersAgriculture 14 01486 i019
Gao et al., 2022 [53]EDEM (-)High moisture contentThe Hertz–Mindlin with JKRRigid bodyThe multi-particleCalibrate the model of the wheat straw–soil mixtureAgriculture 14 01486 i020
Zhang et al., 2022 [54]EDEM (2020)-The Hertz–Mindlin with JKRRigid bodyThe Hertz–Mindlin (no slip)Calibrate the model of the maize root–soil mixtureAgriculture 14 01486 i021
Zhang et al., 2023 [13]EDEM (2020)Loamy soilThe Hertz–Mindlin with JKRDividing the root into four layersThe Hertz–Mindlin with bondingThe mechanical properties of maize residue–soil complexAgriculture 14 01486 i022
Pasthy and Tamas, 2023 [55]PFC3D (-)-The Hertz–Mindlin-The mass-spring methodExplore the soil–residue–tool interactionAgriculture 14 01486 i023
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Tian, Y.; Zeng, Z.; Xing, Y. A Review of Discrete Element Method Applications in Soil–Plant Interactions: Challenges and Opportunities. Agriculture 2024, 14, 1486. https://doi.org/10.3390/agriculture14091486

AMA Style

Tian Y, Zeng Z, Xing Y. A Review of Discrete Element Method Applications in Soil–Plant Interactions: Challenges and Opportunities. Agriculture. 2024; 14(9):1486. https://doi.org/10.3390/agriculture14091486

Chicago/Turabian Style

Tian, Yuyuan, Zhiwei Zeng, and Yuan Xing. 2024. "A Review of Discrete Element Method Applications in Soil–Plant Interactions: Challenges and Opportunities" Agriculture 14, no. 9: 1486. https://doi.org/10.3390/agriculture14091486

APA Style

Tian, Y., Zeng, Z., & Xing, Y. (2024). A Review of Discrete Element Method Applications in Soil–Plant Interactions: Challenges and Opportunities. Agriculture, 14(9), 1486. https://doi.org/10.3390/agriculture14091486

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