Analysis of Effect of Grouser Height on Tractive Performance of Tracked Vehicle under Different Moisture Contents in Paddy Soil

Abstract

Grouser height and soil moisture content have a significant effect on the tractive performance of tracked vehicles. Paddy soil has the mechanical properties of both clay soil and sandy soil and can have a wide range of water content values, and it has a considerable influence on the tractive performance of tracked agricultural machinery. To study the influence of grouser height on the tractive performance of a single-track shoe under different soil moisture contents, a three-dimensional shearing model of the single-track shoe and the contact soil was established based on the ground vehicle mechanics theory, and an experimental platform with a soil bin, sensors, and a control system was established. Six preset levels of moisture contents (7%, 12%, 17%, 22%, 27%, and 32%) of paddy soil were prepared for the research experiment. The mechanical properties of the soil with different moisture contents were obtained through the use of a direct shear test, penetration test, and compaction test. The obtained physical parameters of the soil have special characteristics that are different from typical soil. Combined with the three-dimensional model and the obtained soil parameters, the parameters of the tractive performance, such as thrust, running resistance, and traction with different moisture contents were analyzed and calculated. The test results revealed that the thrust at different grouser heights shows a regular waveform growth trend with an increase in soil moisture content. The minimum value and the maximum value of thrust were obtained at moisture contents of 7% and 12%, respectively. The curve of different grouser heights of the running resistance shows similar changes with different moisture contents. The two peak points and inflection points of the fluctuation curve are for moisture contents of 17% and 27%. The change curve of the traction is highly similar to the curve of thrust. The maximum value of the traction was found at a moisture content of 12%, and the minimum value at 22% or 27%. Under different moisture conditions, tracked vehicles with higher grousers have better tractive performances.

1. Introduction

Tracked vehicles have been popularized in many fields such as agriculture, forestry, mining, the military and planetary exploration [1]. A tracked vehicle uses a track system composed of track plates and grousers as its mobility system. While a track system has lower drive autonomy than a wheel system, it provides a large contact area and lowers ground contact pressure, enabling better traction [2]. Since they can provide better floatation and traction than wheeled ones, which makes them suitable for rough and relatively complex terrains, tracked vehicles have been extensively applied in the agricultural field and agricultural machinery. The tractive performance of tracked vehicles, including thrust and resistance, is very important for terrain trafficability and is influenced by both vehicles and terrains, besides the intrinsic characteristics of the vehicle [3].

It is essential to predict the tractive performance of tracked vehicles, which depends upon the proper evaluation of the mechanics of the track–terrain interaction, involving soil shear by track grousers and the slip–sinkage effect [4]. The fundamental essence of track traction mechanics is the development of thrust from the grouser system in the interaction between the track/grouser system and the supporting soil surface/substrate [5]. The tracked vehicle shears the contact soil under the action of the driving wheel, and the sheared soil produces a reaction force to prevent the track shoe from slipping on the ground. Track shoes and grousers are devices that are in direct contact with the ground. The soil–track interaction is usually characterized by two phenomena: forces arising at the soil–device interface (thrust, lateral force, and vertical force) and the displacement of soil particles (soil disturbance) [6]. Traction as the force derived from the interaction between track (grouser shoe) and soil could be influenced by two kinds of factors: the soil conditions and the dimensions of track shoe [7]. The soil conditions mainly include the physical and mechanical properties reflected in the shear strength and bearing capacity, such as soil type, moisture content, friction angle, cohesive modulus, etc. Soil properties are important for the generation of the tractive force of a track–soil system [1,2]. The dimensions of the track shoes and grousers mainly include structural parameters such as pitch, height, thickness, broadness, etc. To predict the performance of a traction device, the distribution of normal load and shear stress at the soil–tire/track interface and the geometry of the 3-D contact surface should be determined [8].

The interaction between the track shoe and the contact soil mainly results in the occurrence of pressure–sinkage and shear–displacement. The sinkage of soil occurs when a vertical load is applied to the contact surface of soil; the area sinks in the soil at a certain depth until the resistance of the soil is balanced with the applied force. Ground pressure, which is the stress distribution in the context of the soil–track interface, is an important parameter for mobility, tractive performance, and soil compaction. However, ground pressure is not uniform, especially in the case of a flexible track. The stress distribution at the soil–track interface has a significant impact on the stress pattern in the soil profile. The mean stress and change in volume produced by shearing greatly affect the shear strength and deformation characteristics of soil [9,10,11,12]. The soil strength is largely influenced by soil structure, soil–root interactions, and soil matric potential. Soils generally exhibit higher shear strength with increasing mean stress (applied pressure) due to interlocking effects [13,14]. The mean stress can be reduced by either reducing the load or by increasing the contact area of the track. Furthermore, soil stress can be reduced by achieving a close-to-uniform stress distribution at the track–soil interface [15,16].

The mechanical behavior of soils may be approximated using different models that depend on special soil characteristics and simplifying assumptions. In the past few decades, a variety of constitutive models and approaches, mainly empirical, semi-empirical, and computer-aided, have been developed to describe various aspects of soil behavior and predict the tractive performance of track–soil interaction [17]. Micklehwaite studied the thrust of the driving wheel of a tracked vehicle and proposed a calculation method, the Coulomb–Terzaghi shear strength equation, to estimate the maximum propulsion of the tracked mechanism [8]. Subsequently, other researchers conducted experiments and theoretical work promoting the rapid development of the interaction mechanics between the track and ground. Bekker proposed using soil penetration plates comparable in size to the contact patch of a tire (or track) and producing pressures and shear forces of comparable magnitudes to those produced by a vehicle and developed an empirical approach named the Bevameter technique for the evaluation of the traction of a tracked vehicle [2,18]. Another well-known empirical method for evaluating off-road vehicle performance is that developed by the US Army Corps of Engineers Waterways Experiment Station (WES), and a model known as the WES VCI model was proposed for the prediction of vehicle performance on fine- and coarse-grained inorganic soils by collecting data (CI, Vehicle Cone Index, Rating Cone Index, etc.). This empirical method is not suited for vehicle development, design, and operation purposes [19].

The most widely known methods for the semi-empirical analysis of tracked vehicle performance are based on the developments of Bekker’s pressure–sinkage equations and its modifications. Various models for predicting the performance of tracked vehicles have been developed [20,21,22,23,24,25,26]. Janosi and Hanamoto studied the shear displacement relationship expression of plastic soil based on Bekker’s research, which has been widely used in soil shear models [27]. Later, Reece modified Bekker’s soil-bearing model that can predict the performance of a tracked vehicle, considering the width effect of the pressure plate test and Mohr–Coulomb failure criteria for shear failure [28]. Wong proposed other semi-empirical models and given a modified pressure-sinkage relationship, based on the design parameters of vehicles and an idealization of the track–terrain interface [29,30].

With the rapid advances in computer technology and computational techniques over recent decades, computer-aided methods have become feasible to simulate the interaction between the track shoe and soil. The finite element method (FEM) is frequently utilized to analyze the tractive performance of agricultural vehicles. It was found that the results of the FEM method are highly consistent with the experimental results. In addition, the discrete element method (DEM) has also been used to simulate the interaction between soil and a track. Moreover, the DEM-FEM coupling method and computational fluid dynamics (CFD), which are used in many fields of study, are also gradually being applied in this area [31,32,33,34,35,36,37,38]. Although these computer-aided methods are powerful and can obtain more information and results, their algorithms are complex and time-consuming, often requiring the support of large-scale professional software.

The tractive performance is also influenced largely by the dimensions of grousers, such as the grouser spacing, the grouser thickness, and the grouser height, as well as the angle at which the grouser penetrates the soil [5,39]. Hata reported that gross traction was the most effective for achieving a grouser pitch-to-height ratio (GPH) in the range of 3 to 4 [40]. Wang examined the influence of grouser thickness and grouser height on a model of a grouser shoe and revealed the relationship between the grouser height, grouser thickness, and gross traction. Moreover, their experimental results showed that the optimum grouser height depended on the moisture content of the soil [41,42,43]. Ge studied the effect of grouser height on tractive performance under soil with different moisture contents with a single-grouser shoe and concluded that the optimum grouser heights for generating the maximum traction were different [44,45]. Yang studied the calculation method of thrust for a track shoe with a splayed grouser under different moisture contents on soft ground [46]. Li studied the single-track shoe model and analyzed the relation between the gross traction and the grouser height, giving the slippage ratio of the tracked vehicle [47]. In addition, a set of studies on tractive performance affected by the dimensions and configurations of grousers have been carried out on ground with soft, sandy, planetary soil and snow in recent years [48,49,50,51]. Moreover, variation in soil water contents can significantly affect the mechanical properties of soil. Therefore, a series of studies on the tractive performance of tracked vehicles influenced by the dimensions of track shoes under different water contents have been reported [52,53,54,55,56].

However, a study of the interactions between grouser height, moisture contents, and soil mechanical properties and how they affect the traction performance of the single-track shoe is needed. As an ideal agricultural soil in southern China, paddy soil has some special characteristics and mechanical properties that are different from the typical soils used in previous studies. Its composition is mainly loam, containing clay, silt, and sand particles, and the particle size is between 0.02 mm and 0.2 mm. The soil texture is between clay and sand, hence having the advantages of both clay and sandy soils. Generally, the texture of the topsoil layer is mostly loam soil, and the viscosity increases with the deepening of the profile. The clay content in the topsoil layer is lower than that in the core layer, and the clay rate in the middle and lower layers of the soil is higher, which indicates that the clay in the soil obviously has a strong cohesive effect [57]. Some research results showed that the mechanical properties of paddy soil varied in a very wide area [56,57,58]. However, the soil viscosity is very strong, and the water distribution range is very large, giving it great resistance to the walking of tracked agricultural machinery and making it prone to slipping and subsidence.

The objectives of this study were to (1) develop a theoretical model of a single-track shoe with a grouser and analyze the interaction between the track shoe and contact soil; (2) obtain the mechanical properties of paddy soil through a direct shear test, penetration test, and consolidation compression test under different moisture contents and vertical loads; and (3) reveal the principles and effects of the grouser height on tractive performance under different moisture contents and vertical loads of paddy soil.

2. Materials and Methods

2.1. Theoretical Model of Interaction of Single-Grouser Track and Soil

When a tracked vehicle driven by a sprocket walks on a soil surface, a shearing motion occurs on the interaction surface between the soil and the track. The track shoe and the grouser squeeze and shear the contact soil, and the soil is sheared to produce shear stress which reacts to the track shoe and the grouser. Because the track is not retractable, the thin and soft bottom material will produce shear displacement under the pressure depression between the track shoe and the grouser, resulting in the sliding of the track relative to the soil reference plane. It is assumed that the slip rate of each point where the track prick contacts the soil is the same when driving in a straight line, and the slip rate i of the track slip displacement in the horizontal direction accumulates along the grounding length and reaches the maximum at the rear end of the grounding, as shown in Figure 1.

Therefore, the shear displacement of each point in the contact section of the tracked vehicle during linear steady-state walking is:

$$j(x)=\frac{V_t-V_m}{V_t}x=ix$$

(1)

where The origin of coordinate O is the front end of the first track shoe contacting the ground and generating shear; Δx1, Δx2, and Δx3 are, respectively, the shear displacement of three grousers connected in turn, x is the distance from the front end of the first track shoe (point O), j(x) is the slip rate function of the track with respect to x, V_m is the actual speed of the track, V_t is the theoretical speed of the driving wheel, i is the slip rate of the track relative to the ground. According to Equation (1), the shear displacement of the track on the ground increases linearly from the front end to the rear end of the ground.

This study focused on the establishment of the model of track–soil interaction and the acquisition of the physical and mechanical properties of paddy soil under this interaction. Although the modern computer-aided analysis methods are very powerful for analysis and optimization in almost all areas of study, the semi-empirical method, initially developed by M.G. Bekker, is still the most economical and popular method applied and adopted in this area of study for predicting the tractive performance of tracked vehicles. Hereby, we took one of the track shoes to establish a three-dimensional single-grouser-track shoe model of shearing soil, as shown in Figure 2. Track shoe pitch is L and width is B. The grouser was fixed below the track plate, and its height is h. The ratio of the grouser thickness to the shoe pitch is λ.

Based on the proposed three-dimensional shearing model, the forces acting on the track shoe model are shown in Figure 3. Under the vertical/normal load of W, the sinkage of the track shoe is z, while the sinkage of the grouser is z + h. The vertical load was determined by the following equation:

$$W=q_1(1-\lambda )LB+q_2\lambda LB$$

(2)

where q₁ is the contact pressure of the spacing surface of the track plate and q₂ is the pressure at the tip surface of the track grouser.

According to Bekker’s pressure sinkage formula [3], the vertical stress applied to the bottom of the track shoe and the grouser tip can be calculated as follows:

$$q_1=(\frac{k_c}{B}+k_{\phi })z^n$$

(3)

$$q_2=(\frac{k_c}{B}+k_{\phi }){(z+h)}^n$$

(4)

where k_c is the cohesive deformation modulus and k_φ is the friction deformation modulus of the contact soil. Additionally, n is the deformation index. The three parameters can be obtained via pressure–sinkage tests using two plates of different widths. So, the load equation can be determined by the following relationship:

$$W=LB(\frac{k_c}{B}+k_{\phi })\left[z^n(1-\lambda )+{(z+h)}^n\lambda \right]$$

(5)

For a single-grouser-track shoe, the soil thrust is the utmost critical parameter of the traction. It is the result of three components: the shearing force on the bottom surface of soil beneath the spacing surface (F_t1), the shearing force on the tip surface of the grouser (F_t2), and the shearing force of the grouser shoe’s lateral sides (F_t3). The F_t1 and F_t2 were measured using the following Equations (6) and (7):

$$F_{t1}=(1-\lambda )LB(C_a+q_1\tan \delta )$$

(6)

$$F_{t2}=\lambda LB(C_a+q_1\tan \delta )$$

(7)

where Ca is the soil adhesion; δ is the soil external friction angle.

The shearing force of the grouser shoe’s lateral sides F_t3 consists of three parts: the shearing force of the grouser’s lateral side (F_sg) expressed as Equation (8); the shearing force of spacing’s lateral side (F_sp) expressed as Equation (9); the shearing force of the lateral side of the soil beneath the spacing surface (F_ss) expressed as Equation (10).

$$F_{sg}=\lambda hL\left[C_a+\tan \delta \tan (45-\frac{\phi }{2})\left\{\frac{({\gamma }_{t}z+h)}{2}\tan (45-\frac{\phi }{2})-2C\right\}\right]$$

(8)

where φ is the soil internal friction angle and γ_t is the soil bulk density; C_a is the soil adhesion; C is the soil cohesion.

When z ≤ t, then:

$$F_{sp}=zL\left[C_a+\tan \delta \tan (45-\frac{\phi }{2})\left\{\frac{({\gamma }_{t}z+h)}{2}\tan (45-\frac{\phi }{2})-2C\right\}\right]$$

(9)

When z ≥ t, then:

$$F_{sp}=tL\left[C_a+\tan \delta \tan (45-\frac{\phi }{2})\left\{\frac{({\gamma }_{t}z+h)}{2}\tan (45-\frac{\phi }{2})-2C\right\}\right]$$

(10)

where t is the thickness of the track shoe.

$$F_{ss}=(1-\lambda )hL\left[C+\left\{q_2+\frac{({\gamma }_{t}z+2z)}{2}\right\}{\tan }^2(45-\frac{\phi }{2})\tan \phi -2C\tan (45-\frac{\phi }{2})\tan \phi \right]$$

(11)

Then, considering two sides of the single-grouser-track shoe, the F_t3 can be obtained by the following relationship:

$$F_{t3}=2(F_{sg}+F_{sp}+F_{ss})$$

(12)

The total soil thrust is the sum of all thrusts including F_t1, F_t2, and F_t3 as follows:

$$F=F_{t1}+F_{t2}+F_{t3}$$

(13)

Meanwhile, the vertical load applied on the top of the track shoe results in sinkage, which is accountable for the increase in running resistance. The running resistance R is determined by the following equation:

$$R=\frac{k_c+B{k}_{\phi }}{n+1}\cdot \left[{(h+z)}^{(n+1)}\lambda +z^{(n+1)}(1-\lambda )\right]$$

(14)

Therefore, the gross traction T of the track shoe is the subtraction of running resistance from total soil thrust, which can be expressed as the following equation:

T = F − R

(15)

2.2. Experimental Arrangement

The main purpose of this research is to study the effect of the grouser height of the single-grouser-track shoe on the tractive performance under different moisture contents in paddy soil. For this purpose, the mechanical properties and physical parameters of different moisture contents in paddy soil needed to be obtained first. Based on the theoretical model section, the derived equations determined the tractive performance. The mechanical properties of the soil in this study could be measured using three classical tests: the direct shearing test, penetration test, and compaction test. The methods and parameters that needed to be obtained for the three tests are shown in

Table 1. Experiment arrangement of soil properties for tractive performance analysis.

	Experimental Method	Parameters to Be Obtained
1	Direct shear test	Cohesion (C)
		Adhesion (Ca)
		Internal friction angle (φ)
		External friction angle (δ)
2	Penetration test	Soil sinkage (z)
		Sinkage exponent (n)
		Soil cohesive modulus (kc)
		Soil friction modulus (kφ)
3	Compaction test	Bearing capacity
		Bulk density (γt)

.

To calculate all the forces acting on the track shoe and simulate the tractive performance, the details of the dimension of the single-grouser-track shoe model used for this study are shown in

Table 2. Dimension details of the single-grouser-track shoe model.

Parameters/Unit	Symbol	Value
Pitch of track shoe/(mm)	L	100
Width of track shoe/(mm)	B	150
Height of grouser/(mm)	h	50–400
Thickness of shoe plate/(mm)	t	40
Ratio of grouser thickness to pitch	λ	0.1

.

2.3. Soil Sample Preparation

Paddy soil in this study was collected from a paddy field in the Yunyuan Experimental Base of Hunan Agricultural University, Hunan Province, China (112°59′2″ E 28°06′44″ N). The soil cores at depths of 0–400 mm were sampled using a customized soil sampler. The physical properties of in situ paddy soil basically accord with the description in the literature [56,57,58]. In order to obtain the average physical properties, the soils from different sampling points and depths were mixed together as the initial soil samples of this experiment. After being sun-dried, the soil sample was crushed into powder using a hammer and sieved with a 20-mesh sieve and then put into a container.

The experimental soil samples with different moisture contents were configured by adding water to the original dry soil. According to the specific moisture content preset in the experiment, the calculated water was added into the initial soil sample, measuring the mass of water with the balance scale. The moisture content of the initial dry soil was measured via oven drying. In the preliminary preparation test, it was found that when the moisture content of the soil sample was lower than 5%, the physical characteristics were close to the original soil, while when the moisture content was higher than 35%, the soil became very thin and soft, and so it was more likely that overflow or leakage would occur in the experiment, which affected the evaluation of the results. Moreover, referring to the treatments of similar studies [44,45,55], the initial level of moisture content in this study was 7%, and the change gradient was 5%. Therefore, only six different moisture contents, 7%, 12%, 17%, 22%, 27%, and 32%, were applied for the soil sample preparation. In the direct shear test and compaction test, the configured soil samples were put into different containers, labeled with their moisture content, and sealed with agriculture films in case of evaporation. Then, they were kept at room temperature for more than 24 h in the laboratory to promote full moisture permeation. In the penetration test, the experimental soil sample was configured in the soil bin of the test platform. By slowly being laid layer by layer in a container and being evenly sprayed with appropriate amounts of water, the soil sample was gradually put into the soil bin until the depth reached more than 350 mm. The soil samples were placed in the soil bin according to the increase in moisture contents. The same method was used for the direct shear test and compaction test. When recording data in the tests, the specific average moisture content was measured randomly in 3 different places in the container and soil bin. The final moisture content of the tested soil was measured using a temperature and humidity sensor, and it was ensured that the deviation between the measured and the configured samples was less than 1%.

2.4. Direct Shear Test

A direct shear test was performed in a laboratory. This is one of the simpler forms of shear test. In this test, shear force was applied with a constant rate of strain until shearing force failure occurred. The soil samples under consideration were placed in a metal shear box with a round shape and spliced at the mid height. The soil strength in this study was tested with a strain-controlled direct shear test apparatus, shown in Figure 4 (ZJ-1B type, Cangzhou Xingye Experimental Instrument Factory Co., Ltd., Cangzhou, China). The tester mainly consists of five parts: a shear box, stress measuring device, power mechanism, vertical load mechanism, and digital display control unit. The shear box is composed of an upper box and a lower box in pairs, forming a cylindrical cavity with a diameter of 62 mm and depth of 40 mm. Before the test started, the soil sample was placed into the shear box, isolated separately with a permeable stone on the upper and lower surfaces. Applying a vertical load from the weight lever to the cover of the upper shear box and a constant horizontal force on one half of the shear box with a DC servo motor, shear displacement occurred and was measured by the strain ring and dial gauge. The shear speed could be set (six selectable preset speeds) and displayed by the digital display and control unit, and the vertical load could be switched (selectable: 400, 300, 200, 100, and 50 kPa) by the different counterweights through the weight lever. The real-time shear stress value of the soil sample with different parameters used could be obtained. In this study, 2 shear speeds (slow: speed I, 0.8 mm/min; fast: speed II, 2.4 mm/min), and all 5 vertical loads were selected for the testing. The read of the dial gauge for every 1 mm of shear displacement was recorded until the it exceeded 6 mm, which indicated the end of the experiment. Each test was repeated 3 times, and the average result was used.

Furthermore, the shear strength (τ), internal friction angle (φ), and cohesion (C) of the soil sample were determined by Coulomb’s law (Equations (16) and (17)).

τ = C + σtanφ

(16)

F = AC_a + Wtanδ

(17)

where F is shearing force, N; A is the contact shearing area, m².

2.5. Penetration Test

As a power function, the parameters of Bekker’s pressure–sinkage model, including the soil cohesion modulus (K_c), soil friction modulus (K_φ), and sinkage exponent (n), can be obtained through the penetration test of two plates with different specifications. In this study, two steel plates, A and B (length × width × thickness are 76 × 50 × 10 mm and 57 × 45 × 10 mm, respectively), were used in the penetration test. In this experiment, 3 speeds, slow, medium, and fast, were used to apply a vertical load to the steel plate. Referring to the universal tensile and pressure tester, the 3 speeds were set as speed I (10 mm/min), speed II (20 mm/min), and speed III (30 mm/min), respectively. In the process of testing a steel plate penetrating the soil with a set uniform speed, the sinkage of the steel plate and the pressure force (reaction force of the soil) were obtained and recorded in the computer. Each test was repeated 3 times, and the average result was used.

The experiment was performed at the Key Laboratory of Intelligent Agricultural Machinery and Equipment, College of Mechanical and Electrical Engineering, Hunan Agricultural University, China. A 3000 mm-long, 700 mm-wide, and 550 mm-deep soil bin experimental platform was established to measure the mechanical properties of paddy soil. The platform mainly consisted of a soil bin, a testing device, many sensors, and a set of control units. It could make a real-time measurement of soil moisture, penetration force, traction force of the track shoe, and driving torque of the tracked vehicle at different positions. The parameters obtained by the sensors were transmitted to the terminal control interface in the computer through an RS485 signal. Therefore, the parameter values varied based on the time they were recorded onto the computer files. The experimental platform is shown in Figure 5 and Figure 6.

2.6. Compaction Test

Consolidation compression characteristics, obtained through the compaction test, also reflect the bearing capacity of the soil. A universal testing machine (CMT5105 type, Shenzhen Xinsansi Material Testing Co., Ltd., Shenzhen, China) was used to test the mechanical properties of consolidation compression, loading the soil sample with a cylindrical metal container (diameter 60 mm and height 40 mm), and compressing with a metal piston. The real-time data of the pressure and displacement were obtained and stored by the machine and plotted with the form of a coordinate curve at the same time. The soil sample at each moisture content was compressed at 3 speeds (slow, medium, and fast). Like the penetration test, the test was performed at 3 speeds: speed I (10 mm/min), speed II (20 mm/min), and speed III (30 mm/min). Each test was repeated 3 times, and the average result was adopted. The testing process is shown in Figure 7.

3. Results and Discussion

3.1. Direct Shear Test

Although there was a slight deviation in the actual moisture content measurement of the soil samples, the primary configured six groups of moisture contents were still used to mark the results and statistics. The shear stress changes under different moisture contents and shear speed under different vertical loads were recorded. Considering the esthetics of the isometric change in the abscissa, only four vertical loads (A:100 kPa, B:200 kPa, C:300 kPa, and D:400 kPa) were selected for statistics. The results are shown in Figure 8.

It can be seen from the above figures that the change in vertical load has a significant impact on the shear stress of soil, while the change in shear speed has little effect on the change in soil shear stress. The shear stress shows a significant linear growth trend with the uniform increase in vertical load, and this linear correlation is more obvious with the increase in vertical load. Under the same moisture content and vertical load, the shear stress of speed I is slightly higher than that of speed II; that is, the shear strength under the slow shear speed is slightly higher than that under the fast shear speed. The statistics of the shear stresses when the shear displacement is 4 mm under different vertical loads and different shear speeds are shown in Figure 9.

Under the same vertical load and shear speed, the shear stress of soil gradually decreases with the increase in soil moisture content and gradually stabilizes, as shown in Figure 9. In the experiment with slow shear (speed I), when vertical load A or B is applied, the shear stress rises firstly and then gradually decreases with the increase in soil moisture content, in which the rising area is between 12% and 17%, and the decreasing area is from 22% to 27%. Meanwhile, the shear stress reaches the maximum value when the moisture content is 17%, while the stress tends to be stable when the moisture content exceeds 27%. When vertical load C is applied, the shear stress decreases monotonously and steadily with the increase in soil moisture content. When vertical load D is applied, the shear stress gradually decreases with the increase in soil moisture content until it reaches 27%, reaching the minimum value at this turning point, and then gradually increases. In the fast shear experiment (speed II), when vertical load A or B is applied, the changing trend of shear stress is similar to that of slow shear (speed I), rising firstly and then decreasing gradually, in which the rising area is between 12% and 17%, while the decreasing area is from 17% to 27%. Meanwhile, the shear stress reaches the maximum value when the moisture content is 12% and tends to be stable when it exceeds 27%. When the vertical load C is applied, the shear force decreases monotonously and steadily with the increase in soil moisture content. When the vertical load D is applied, the shear stress gradually increases with the increase in soil moisture content, reaches the maximum value at 17%, and then decreases from 17% to 27%, stabilizing or rising slightly when it exceeds 27%.

To sum up, the shear strength of soil is at its best when the moisture content is between 12% and 17%. Therefore, for the track shoe, the bearing capacity of the soil with moisture content in this range is also the largest correspondingly. When the soil moisture content reaches 37% or more, overflow or leak from the shear box is liable to occur due to its high fluidity. At the same time, the water seepage rate of the soil increases significantly with the increase in vertical load, leading shear stress to appear uncertain or leading to a rapid decrease.

To show the changing trend of shear stress with the increase in vertical load, the shear stress of the soil when shear displacement reaches 4 mm under two shear speeds was plotted, as shown in Figure 10.

It can be seen from the figure that the shear stress of soil is directly related to the vertical load, showing a significant linear increase trend with the increase in vertical load, and the linear growth rate increases slightly with the increase in soil moisture content. At the same time, the shear stress curves are very close, with minor fluctuations with a moisture content from 7% to 17%. Overall, the growth rate of shear stress under different moisture contents gradually increases with the increase in vertical load.

The cohesion and internal friction angle of soil can be obtained by processing the results of the direct shear test. Considering that the two shear speeds have little effect on the shear stress, the average linear trend line can be obtained by linear regression fitting the combined data of the two sets. The linear fitting results of shear stress vary with the increase in vertical load under different moisture contents, as shown in Figure 11.

It can be seen from the figure that the shear stress has a significant linear relationship with the vertical load when the soil moisture content is between 7% and 32%. When the moisture content reaches 37% or more, the shear stress changes irregularly because of overflow or leakage from the shear box under a big vertical load. Additionally, the shear speed influences the changing trend of shear stress. When the linear regression model is performed using the above method of making no distinction between the two sets of results, the fitting trend line can be obtained, but the R² coefficient is about 0.56. When the soil moisture content reaches 37%, the changing trends of shear stress under the two shear speeds still show a very strong linear correlation in the linear regression model fitting, and the R² coefficients are 0.948 and 0.898, respectively.

The experimental results of soil cohesion and soil adhesion at different moisture contents are shown in Figure 12. The statistics of the internal friction angle and external friction angle at different moisture contents are shown in Figure 13.

With the increase in soil moisture content, the soil cohesion increases at first and then decreases, followed by another increase and decrease. The change curve is similar to the hump curve. The two rising areas are for moisture contents of 7–17% and 22–27%, while the two declining areas are for moisture contents of 17–22% and 27–32%. Therefore, the cohesion reaches the peak value (37.72 kPa and 37.09 kPa) when the moisture content is 17% or 27% and reaches the lowest value (23.88 kPa and 29.59 kPa) when the moisture content is 7% or 22%.

As for soil adhesion, although the fluctuation amplitude is small, the characteristic of fluctuation is significant. With the increase in soil moisture content, its changing curve decreases continuously when the moisture content is 7–27% and then increases when the moisture content is 27–32%. The maximum value (0.16 kPa) and the minimum value (0.10 kPa) of the adhesion are obtained when the moisture content is 7% and 27%, respectively. Overall, the change in the moisture influences the variation of the adhesion, but not by much.

As to the external friction angle, its changing curve is same to that of the soil adhesion, and the fluctuation amplitude is small. With the increase in the moisture content, its changing curve decreases continuously when the moisture content is 7–27% and then increases when the moisture content is 27–32%. The maximum value (10.21°) and the minimum value (6.48°) of the external friction angle are obtained when the moisture content is 7% and 27%, respectively. Overall, the change in the moisture content influences the external angle slightly.

As to the internal friction angle, its changing curve is the opposite to that of the soil cohesion. The internal friction angle decreases at first and then increases slightly, followed by another decrease and increase. The two declining areas are for moisture contents of 7–17% and 22–27%, while the two increasing areas are for moisture contents of 17–22% and 27–32%. Therefore, the internal friction angle reaches the peak value (24.57° and 16.73°) when the moisture content is 12% and 27% and reaches the valley value (24.55° and 15.69°) when the moisture content is 17% and 32%. The maximum value (27.92°) and the minimum value (15.69°) are obtained when the moisture content is 7% and 27%, respectively.

The above results are quite different from the results of similar previous research [44,45,55].

3.2. Soil Penetration and Sinkage

Like the direct shear test, the theoretical moisture contents are still used to mark the results and data statistics. However, moisture content exceeding 32% was not included because of its little stress or no stress due to large fluidity. The forces and sinkage of soil samples under different moisture contents are obtained, as shown in Figure 14.

As can be seen from the figure, the pressure increases gradually with the increase in sinkage on the whole.

Different penetration speeds have some impact on the change in pressure, as well as a relatively large impact on plate A and a relatively small one on plate B. For plate A, when the moisture content is 7–17%, there is a significant difference between speed I and speed II as well as speed III, while there is no obvious difference between speed II and speed III. When the moisture content is 22–27%, the penetration speed has little impact on the pressure. When the moisture content is 32%, the influence increases slightly. Therefore, with the increase in the soil moisture content, the effect of different penetration speeds on the pressure gradually decreases. For plate B, with the increase in moisture content, the effect of penetration speed on the pressure is relatively slight. This means that when the moisture content is 17–22%, the penetration speed has a significant effect on the bearing capacity of soil. When the moisture content changes from 7% to 17%, the increase in pressure gradually accelerates with the increase in sinkage, close to the power function (exponent > 1) growth relationship. The soil behaves as hard and brittle soil, and the mechanical property is similar to that of sandy soil. When the moisture content changes from 22% to 32%, the increase in pressure gradually slows down with the increase in sinkage, which is close to the power function (exponent < 1) growth relationship. The soil behaves as soft plastic soil, with certain features of clay soil.

The soil sinkage increases with the increase in pressure, which conforms to the general law of soil pressure–sinkage. At the same time, the pressure gradually decreases with the increase in moisture content. When it exceeds 32%, the pressure does not change significantly with the sinkage due to the soil being in a viscous rheological state.

Compared the result of the penetration tests, when penetrating to the same depth with the same speed, the pressure of plate A with a large length–width ratio is significantly greater than that of plate B with a small length–width ratio. Obviously, the biggest difference exists in the condition in which the soil moisture content is 7%, the penetration speed is speed III, and the sinkage is 50 mm. The maximum pressure of plate A reaches 1105 kPa, while the maximum pressure of plate B is only 533 kPa. The corresponding reaction forces are 4200 N and 1370 N, respectively. Therefore, with the increase in moisture content from 7% to 22%, the difference gradually becomes smaller and smaller. When the soil moisture content is 22–32%, the difference in pressure between the two plates is very small.

To obtain the influence rule of penetration speed on the change in pressure with the moisture content, the difference in pressure between plate A and plate B (i.e., the pressure of plate A minus the pressure of plate B) under different penetration speeds was obtained. The result changes with the increase in the soil moisture content, as shown in Figure 15.

It can be seen from the figure that the influence of speeds II and III on pressure is very close, especially when the moisture content is 17% or more, for which there is almost no difference between them. The effect of speed I on pressure is obviously different from the other two speeds. When the moisture content is 7–17%, the difference reaches the maximum value. When the moisture content reaches 17% or above, the three speeds have little effect or no effect on the pressure change with the increase in the moisture content. Furthermore, with the slow penetration speed (speed I), the pressure increases up to the vertical load applied and the area of contact soil. With the increase in the penetration speed (such as medium and fast speeds), the effect of the length–width ratio on the pressure becomes more and more significant.

The parameters of Bekker’s pressure sinkage model, including the soil friction modulus K_φ, soil cohesion modulus K_c, and sinkage exponent n, were obtained through the penetration tests, and the results are shown in Figure 16.

It can be seen from the figure that the parameters of Bekker’s model fluctuate regularly with the change in soil moisture content, appearing in obvious peaks and troughs. The soil friction modulus K_φ rises linearly at first and then declines straightly, followed by another rise-and-decline with the increase in soil moisture content. The first peak appears at the moisture content of 17%, and the second peak appears at the moisture content of 27%. The middle valley value appears at the water content of 22%. The highest value is the first peak value, and the lowest value is the value with moisture content of 7%. The curve features are very similar to the soil cohesion coefficient.

For the soil friction module K_c, its change trend is exactly opposite to that of the soil friction module K_φ. With the increase in soil moisture content, it declines at first and then rises, followed by another decline-and-rise. The first valley value appears with the moisture content of 17%, and the second valley value appears with the moisture content of 27%. The middle peak value appears with the moisture content of 22%. The lowest value is the second valley value, and the highest value is the value with the moisture content of 7%.

Overall, with the increase in soil moisture content, the curve change of the sinkage exponent shows a downward trend, with slight fluctuations within it. Moreover, the fluctuation law is similar to the distribution curve of soil friction modulus. The curve of the sinkage exponent rises at first, reaches the highest value with the moisture content of 12%, and then continues to decline until it reaches the lowest value with the moisture content of 32%. Among them, there is a slight fluctuation at the moisture content of 22%.

3.3. Soil Consolidation Compression Test

The soil samples with eight different moisture contents (5–40%) were subjected to compaction tests with three speeds (slow speed I: 10 mm/min; medium speed II: 20 mm/min; fast speed III: 30 mm/min). Similarly, the theoretical moisture content value is used to mark the corresponding test. The results of the consolidation compression forces changing with the growth of compress displacement are shown in Figure 17.

The force change with the displacement is mainly divided into two stages. In the initial compression stage, the soil reaction force has no obvious change, rising very slowly, and the compression displacement is relatively large. In the consolidation compression stage, the soil reaction force increases significantly, and the rising speed gradually increases until it reaches the maximum value (the expected maximum displacement).

The moisture content has a significant effect on the change in compression force. Generally, the higher the water content, the easier the compaction. The lower the moisture content, the shorter the initial compression stage, the slower the rise in compression force in the consolidation compression stage, and the greater the maximum value that can be reached. On the contrary, the higher the moisture content, the longer the initial compression stage, the faster the increase in soil reaction force in the consolidation compression stage, and the smaller the maximum value that can be reached. At the same time, the compression speed also has a significant effect on the change of compression force. With the same moisture content, the faster the compression speed is, the shorter the initial compression stage, the faster the pressure rises in the consolidation compression stage, and the greater the maximum value obtained is. On the contrary, the slower the compression speed, the longer the initial compression stage, the slower the pressure rise in the consolidation compression stage, and the smaller the maximum value obtained is.

When the soil moisture content is 5–15%, the compression force shows a very regular exponential growth trend with the increase in compression displacement. When the soil moisture content is 20–25%, the compression force increases slightly at the beginning of the period of compression displacement and then rises rapidly to close to the maximum value in a short time. When the soil moisture content is 30–40%, the growth curve of the compression force is irregular, which is mainly due to the influence of the compression container. When the moisture content is large, the soil fluidity is also strong, which is prone to causing leakage or seepage of the soil. Especially when the moisture content exceeded 40%, the compression force performs very irregularly for the serious soil leaks.

Generally, the mechanical property of the soil is closer to solid or sandy soil when the moisture content is small. Due to the existing pores and space between the soil particles, the compression force increases gradually with the increase in compression displacement. With the increase in moisture content, the spaces between soil particles gradually shrink and generate adsorption force and adhesion force due to the close contact with each other. Therefore, once the soil is compacted tightly, the compression force increases rapidly.

The soil bulk density influences the shearing force of the grouser’s lateral side and spacing lateral side, according to Equations (8)–(10). We tested the soil bulk density of different moisture contents (soil sample of direct shear test) with a cylindrical sampler (diameter: 60 mm; height: 20 mm) and obtained the processed results, as shown in Figure 18.

It can be seen from the figure that the curve of soil bulk density changing with the increase in moisture content can be fitted with the linear regression model on the whole. The influence of moisture content on the bulk density is significant (R² of the fitting line is 0.9565). The bulk density increases steadily with the increase in moisture content, with which a major change occurs at 27–32%. This is likely because the water gradually adheres to the surface of soil particles until it slowly fills all the spaces between the soil particles, achieving the status of full permeation. The results and changing features are in line with the previous studies, except the rapid increase appears at a moisture content of 27% [44,45,55].

3.4. The Prediction Results of Tractive Performance

Based on the obtained soil parameters and the equations introduced in Section 2, the tractive performance of the single-grouser-track shoe with different grouser heights under different moistures could be determined. In this study, considering the depth range of the soil sample and the possible tillage depth for the agricultural machinery, the variation range of the grouser height was defined as 5–40 cm in the process of calculation and tractive performance prediction simulation. The results of the thrust change with the increase in moisture content are shown in Figure 19.

The thrust is the result of the shearing force on the interaction between the track shoe with the grouser and the soil, influenced by the mechanical properties of the soil. When the soil moisture content increases, the change trend of the thrust with different grouser heights shows a similar growth trend with a regular waveform, which rises at first and then falls, followed by another rise. The first rising stage is for the moisture content of 7–12%, the declining stage is for the moisture content of 12–22%, and the second rising stage is for the moisture content of 22–32%. The minimum value of thrust occurs at the lowest moisture content of 7%, and the maximum value of thrust occurs at the moisture content of 12%. Under the conditions of the same moisture content, with the same increase in the grouser height, the thrust increases gradually. This means that the higher the grouser height, the greater the thrust. When the moisture content is 27–32%, the thrust with changing grouser height increases steadily; the higher the grouser, the faster the thrust increases.

Similarly, the running resistances of the single-grouser-track shoe with different grouser heights were calculated. The results are shown in Figure 20.

In general, with the increase in soil moisture content, the running resistance increases gradually. Except for grouser heights of 5 cm and 10 cm, the running resistance with different moisture contents has similar change trends, in which there are two fluctuation characteristics. When the grouser height is 10 cm or less, the resistance increases linearly with the increase in moisture content. When the grouser height is bigger than 10 cm, the curve of resistance has two stationary points at 17% and 27%. The curve can be divided into two stages. The first rise-and-fall stage occurs when the moisture content is 7–22%, and the second occurs when it is 22–32%. The first rising area is for a moisture content of 7–17%, and the running resistance reaches the first peak value at 17%. The second rising area is for a moisture content of 22-27%, and the running resistance reaches the second peak value at a moisture content of 27%. However, when the grouser height is 20 cm or less, the running resistance at this stage is still on the rise, and the maximum value is obtained at 32%. The moisture contents of 17% and 27% represent the two peak value points and inflection points of the fluctuation curve. For the same grouser height, the second peak value is bigger than the first peak value, and the minimum running resistance exists at the lowest moisture content. The reason for this phenomenon is that the soil is very dry and hard in this state, resulting in almost no sinkage of the grouser. With the increase in moisture content, the sinkage of the track shoe becomes larger and larger. Due to the mechanical properties influenced by moisture content, appropriate moisture content is conducive to slipping for the track shoe and the contact soil, resulting in a decline in running resistance. Moreover, the higher the grouser, the bigger of the influence. Under the same moisture contents, with the equal increase in the grouser height, the running resistance incrementally increases. This means that the higher the grouser height, the greater the running resistance.

Traction is the difference between the thrust and the running resistance. Therefore, the traction of the single-grouser-track shoe with different grouser heights can be determined. The results are shown in Figure 21.

From the figure above, the change curve of the traction is highly similar to the curve of thrust. When the soil moisture content increases, the change trend of the traction at different grouser heights shows a similar growth trend with fluctuation, which rises at first and then falls, followed by another rise (or fall when grouser height is 10 cm or less). The curve of the traction fluctuates regularly with a peak and a trough among it. The change curve can be divided into three stages: the first stage is the first rising stage of traction, the second stage is the falling stage of traction, and the third stage is the second rising stage of traction. In the first stage, with a moisture content of 7–12%, the traction with different grouser heights changes with the same trend, and the peak value can be obtained at 12%.

The range of moisture contents in the second and third stages varies with the change in the grouser height. When the grouser height is 5–30 cm, in the second stage, the moisture content is 12–22%, while the third stage has a moisture content of 22–32%, and the valley value of traction force is 22%. When the grouser height is 30–40 cm, the second stage has a moisture content of 12–27%, while the third stage’s is 27–32%, and the valley value of traction force can be obtained at 27%. When the grouser height is 5–10 cm, the third stage of traction force change is different from the others, falling instead of rising when the moisture content is 27–32%. In addition, the rising speed of traction in the third stage also increases with the increase in grouser height.

With the same soil moisture content, the traction also increases with the increase in the grouser height and incrementally increases with the equal increase in the grouser height. The higher the grouser, the greater the traction increase.

From the above, the traction with different grouser heights shows excellent performance when soil moisture content is 12%. In other words, the moisture content of 12–17% is ideal for the tractive performance of the tracked vehicle. Under different moisture conditions, tracked vehicles with higher grouser heights exhibit better traction performances.

4. Conclusions

Different from typical sandy soil and clay soil, paddy soil in this study has the physical properties of both sandy soil and cohesive soil. Six preset levels of moisture content were applied to this soil by varying the amount of water added. The mechanical properties of the soil with different moisture contents were obtained through the use of a direct shear test, penetration test, and compaction test. The obtained physical parameters of the soil have special characteristics that are different from typical soil.

The shear strength of soil is at its best when the moisture content is between 12% and 17%. Therefore, for the track shoe, the bearing capacity of soil with a moisture content in this range is also the largest correspondingly. The shear stress has a significant linear relationship with the vertical load when the soil moisture content is between 7% and 32%.

The change curve of the soil cohesion is similar to the hump curve. The two rising areas correspond to moisture contents of 7–17% and 22–27%, while the two declining areas are for moisture contents of 17–22% and 27–32%. Therefore, the cohesion reaches the peak value (37.72 kPa and 37.09 kPa) when the moisture content is 17% and 27% and reaches the lowest value (23.88 kPa and 29.59 kPa) when the moisture content is 7% and 22%. The changing curve of soil adhesion decreases continuously when the moisture content is 7–27% and then increases when the moisture content is 27–32%. The maximum value (0.16 kPa) and the minimum value (0.10 kPa) of the adhesion are obtained when the moisture contents are 7% and 27%, respectively. The changing curve of the external friction angle is the same as that of the soil adhesion. The maximum value (10.21°) and the minimum value (6.48°) of the external friction angle are obtained when the moisture content is 7% and 27%, respectively. The changing curve of the internal friction angle is opposite to that of the soil cohesion. The maximum value (27.92°) and the minimum value (15.69°) are obtained when the moisture contents are 7% and 27%, respectively.

Based on these parameters and soil mechanics theory, the three-dimensional shearing model of the single-grouser shoe was established. The tractive performance components such as thrust, running resistance, and traction were analyzed and calculated. The effect of grouser height on tractive performance with different moisture contents of paddy soil was simulated and predicted. The test results revealed that the thrust of different grouser heights shows a regular waveform growth trend with the increase in soil moisture content. The minimum value and the maximum value of thrust were obtained at moisture contents of 7% and 12%, respectively. The curve of different grouser heights of the running resistance has similar change trends with different moisture contents. The moisture contents of 17% and 27% correspond to the two peak points and inflection points of the fluctuation curve. The change curve of the traction is highly similar to the curve of thrust. The maximum value of the traction was obtained at a moisture content of 12%, and the minimum value was obtained at 22% or 27%. When paddy soil has a moisture content of 12–17%, it has strong bearing capacity, which an ideal condition for the tractive performance of a tracked vehicle. Under different moisture conditions, tracked vehicles with higher grouser heights exhibit better tractive performances.

Based on this study, the optimal traction performance for tracked agricultural machinery could be obtained by determining the appropriate grouser height according to the variation range of the paddy soil’s moisture content.