Investigating the Compressibility of Sandy-Clay Soil in the Laboratory Soil Bin Caused by Agricultural Tire Traffic and Analyzed by the Adaptive Neuro–Fuzzy Inference System

Abstract

Agricultural soil compaction caused by tractors and heavy farm machines has a direct impact on farm productivity. Therefore, the effect of influencing parameters on soil compaction was studied and evaluated using a wheel tester device in the soil bin environment. Experiments were carried out at 3 levels of vertical load (170, 250, and 320 kg), 3 levels of tire inflation pressure (10, 15, and 20 psi), 3 levels of soil moisture content (2%, 7%, and 13% wet basis), and 2 levels of forward speed (0.386 and 0.879 km/h) in the form of a factorial design and a randomized complete block design in 3 replications. Next, soil compaction was predicted under the influence of investigated parameters using ANFIS. The results showed that the advance of the wheel at low speed and high soil moisture content significantly increases soil compaction. The present findings showed that the soil compaction increases linearly with the relative increase of the vertical load on the tire. Meanwhile, the relative increase of soil compaction in wet soil (7%–13% relative humidity, wb) was relatively 9.93 times higher than the soil compaction in low humidity (2%–7%). The results also show that reducing tire inflation pressure from 20 to 15 psi reduces soil compaction by 12.94%. The correlation coefficient between the measured and predicted data using ANFIS for soil compaction was equal to 1, which showed the high accuracy of ANFIS models in predicting the studied parameters. This approach provides criteria for a more appropriate selection of agricultural tires.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Today, due to the importance of limiting soil compaction and increasing traction efficiency (TE), the goal of agricultural engineers and farm managers is to increase the contact surface of the wheel with the soil as much as possible so that the load on the wheel is distributed in a wider area and as a result, the pressure on the soil is reduced. In this regard, the huge variety of wheels in terms of dimensions, construction, and manufacturer provides a wide range of choices for mobile agricultural equipment. In order to make this choice scientifically, testing and evaluating the performance of wheels are on the agenda of researchers and designers. For this purpose, various systems have been designed and used to perform wheel tests. Predicting soil compaction under the influence of repeated traffic from tractors and agricultural machines enables engineers to reduce soil damage by managing loads at the farm level [1]. Expanding knowledge about the dynamic characteristics of agricultural tires can lead to a decrease in rolling resistance, a decrease in fuel consumption, and an increase in TE [2].

Today, due to the importance of reducing soil compaction and on the other hand, the desire to increase the TE of farm tractors, the goal of agricultural engineers and farm managers is to increase the contact surface of the wheel with the soil as much as possible, so that the load on the wheel is spread over a wider area [3]. The pressure of the tractor wheel and heavy machinery may break the cohesive soil grains and leave negative effects on the soil structure. According to the field results obtained by Moinfar et al. [4], increasing tractor wheel slip has a significant effect on increasing soil compaction. Based on their results, the least slippage of the tractor wheel occurred using the 4WD system, in comparison to the rear wheel drive (RWD) system and forward wheel drive (FWD) system. Increasing tractor speed in the FWD system increased tractor wheel slippage and soil compaction. In addition, the increase in soil moisture led to an increase in soil compaction, which was more severe in fine soils such as clay loam [4].

On the other hand, it has been found that soil compaction beyond the permissible limit increases soil bulk density and mechanical resistance and has adverse effects on plant growth and prevents roots from penetrating the soil [5]. Wang et al. [6] investigated the effect of traffic-induced compaction on soil bulk density and key growth indices of maize in the North China Plain. Their experiments confirmed that soil compaction by tractors and other large machines can affect corn plant growth indicators including corn height, stem diameter, leaf area index, root growth, and crop yield per hectare. When the number of consecutive passes is less than 7, tractors with small axle loads produce more apparent soil density in the soil layer with a depth of 0–20 cm, and when the number of consecutive passes is more than 7, tractors with large axle loads cause more apparent density in the soil layer with a depth of 20–80 cm. Another research also indicated that the compaction of agricultural soils due to tire traffic leads to a decrease in plant rooting, and ultimately a decrease in crop yield [7]. Delmond et al. [8] studied the effect of different sugarcane harvesting operations on soil compaction. According to the results of this study, the use of the tractor and trailer set led to the fact that 60% of the traffic area of the tires showed a mechanical resistance against penetration of more than 2.5 MPa. This limitation caused the regrowth of sugarcane to face the problem of mechanical resistance for root development, and finally, this limitation caused a significant decrease in the yield of the product.

Mohsenimanesh and Ward [9] analyzed the soil compaction under agricultural tires in the Ansys software. In order to obtain the contact pressure distribution, the investigation was carried out at different levels of vertical load and tire pressure and compared with the experimental results. The results showed that the calculated maximum pressure between the tire and the soil in the numerical method was approximately 32%–53% lower than the experimental results in the same conditions.

The effect of tractor forward speed on the compaction caused by tractor wheels was investigated by Stafford et al. [10]. They came to the conclusion that with increasing forward speed, the amount of soil compaction decreases. They also studied the effect of soil moisture content on compaction and found that with increasing soil moisture and decreasing forward speed, soil compaction increases. According to this study, the effect of advancing speed on soil compaction was more intense at a depth of 5 cm. They mentioned that the reason for the increase in compression with decreasing speed is the effect of forward speed on the shear strain of the soil, because the shear strain at higher speeds is lower than at lower speeds. Therefore, an increase in forward speed can reduce the compaction by 50%. It is worth noting that a certain amount of soil compaction is necessary to feed the roots from nutrients in the soil and for better stability of the plant in the soil, but excessive compaction prevents the penetration and lateral expansion of the roots inside the soil and ultimately leads to reducing the yield of crop production. By increasing the soil density beyond the permissible limit, the percentage of voids in the soil is reduced, so the plant needs much more energy for the development of its roots instead of the growth of the aerial part [11]. According to the research of Hamza and Anderson [12], by increasing the mechanical resistance of the soil to 2.5 MPa, plant growth and the penetration of surface roots in the soil are stopped [12].

Taghavifar and Mardani [13] considered soil penetration resistance and tire tread as two important influential factors for estimating soil compaction. They investigated soil compaction at three levels of vertical load (1, 2, and 3 kN), three levels of forward speed (0.5, 0.75 and 1 m/s), and three stages of tire passage in loam-clay soil in a soil bin. Finally, they concluded that increasing wheel load and number of passes significantly increased soil compaction, while increasing forward speed had the opposite effect on soil compaction [13].

According to the research of Darvish Pasand et al. [14], soil compaction caused by the movement of machinery significantly reduces the hydraulic characteristics of the soil and as a result, the movement of water and solutes decreases and root growth is disturbed [14].

In recent years, there has been a continuous movement to semitheoretical approaches especially for problems for which there are no analytical solutions, or they cannot be solved easily, see e.g., Abu-Hamdeh and Reeder, [1] Moeeinfar et al. [15], and Shahgholi et al. [16]. Choosing an appropriate method and approach for modeling a system depends entirely on the complexity of that system, and complexity has an inverse relationship with our knowledge and understanding of that system. Humans have always tried to model the system with the highest possible accuracy, but if they do not have enough knowledge about it, they have to match the desired accuracy of the model with their knowledge of the system [17]. According to Golanbari et al. [18], the interaction of off-road vehicle tires with soil is one of the complex mechanical problem, which is very difficult to model and analyze in conventional and previous methods due to the involvement of multiple and variable parameters. According to these researchers, the prediction of various soil properties such as soil compaction, TE, energy consumption in tillage, soil deformation, and factors related to the interaction of agricultural equipment with farm soil will increase day by day using artificial intelligence [18]. Among the new modeling methods, fuzzy logic is considered as an effective tool in complex systems that are difficult to understand or issues that depend on human reasoning, decision-making, and inference [19]. Meanwhile, the fuzzy set theory provides a suitable method for analyzing complex systems and decision-making processes, especially when there is a pattern of uncertainty due to inherent variability or ambiguity beyond randomness. In this regard, the combination of fuzzy systems based on logical rules and the method of artificial neural networks (ANNs) enables researchers to simultaneously use human knowledge and experimental tests in building models. The method presented on this basis is called the adaptive neuro–fuzzy inference method, i.e., ANFIS [20].

According to the previous extensive studies, the effect of excessive compaction of agricultural soils due to the frequent traffic of tractors and farm machines on the reduction of crop yield has been clearly identified and investigated, but paying attention to the double interaction effects and even in higher steps, the triple interaction effects of factors affecting soil compaction have not been well studied. On the other hand, the rolling resistance of agricultural tires strongly depends on the amount of soil compaction and tire sinkage in the soil. Therefore, in the present study, the measurement and modeling of soil compaction due to the different variables including vertical load on the tire, tire inflation pressure, soil moisture content, tire movement speed, and number of traffic have been investigated in the controlled conditions of soil bin for singular effects and multiple interactions. In the continuation of the research, soil compaction modeling has been analyzed in ANFIS. The result of the present research is important for the management of soil compaction caused by the traffic of farm tires in terms of adjusting the tire pressure, the optimal forward speed, and the moisture content of the farm soil.

2. Materials and Methods

2.1. Theory of Sinkage

The structure of agricultural soils consists of three important parts of organic matter, mineral matter, and voids, all three of which play a role in determining the compaction caused by the traffic of agricultural wheels. The mineral part consists of hard solid materials such as sand, silica, and clay particles, which are not compressible, but depending on their composition and the percentage of organic matter in the soil, they are surrounded by open pores, and these open pores increase the degree of compressibility and soil compaction. In dry soil conditions, these pores are filled with air and the solid particles are in contact with each other, so the friction between the soil particles during compaction and against deformation is very high, and as a result, the amount of soil compaction is minimum. Accordingly, the amount of a tire sinking into the soil depends on the adhesion and friction characteristics of the soil structure ($k_c$ and $k_{\phi }$, respectively) by relying on Bekker’s model [2] given by the following equation:$$\begin{array}{}\text{(1)}& z={\frac{P}{k_c/b+k_{\phi }}}^{1/n},\end{array}$$where z is the amount of sinkage or vertical compression of the soil, P is the surface pressure caused by the vertical load on the soil from the wheel (P = W/A, where W and A are the vertical loads on the tire and the contact cross-section of the tire with the soil, respectively), $k_c$ is the sinkage parameter associated with the effects of adhesion between soil particles, and b is the tire width. The magnitude of $k_c$ depends on the type of mineral particles that make up the soil texture, the amount of organic matter in the soil texture, and the amount of soil moisture. With the increase of soil moisture, the pores between the solid particles are filled with a mixture of compressible air and water. Water acts as a lubricant and reduces the friction between soil particles. As a result, by applying a vertical load to the soil surface by the tire, the soil is easily compressed and deformed. In other words, the values of $k_c$ and $k_{\phi }$ for wet soil are lower than dry soil; therefore, the amount of sinkage in wet soil is higher than in dry soil. With a further increase in soil moisture content and saturated soils, the voids between solid particles are completely filled with water and the water itself has no compressibility, so the amount of sinkage in saturated soils decreases again. According to equation (1), with the increase of $k_{\phi }$, which is related to soil friction effects, the amount of soil compaction decreases.

Assuming a uniform distribution of the pressure caused by the tire to the soil surface, the compressive stress under the center line of the tire at the depth x for agricultural soils is modified as shown in equation (2), which is known as the Boussinesq equation (1885), see Figure 1.$$\begin{array}{}\text{(2)}& {\sigma }_x={\sigma }_{0}1-{\frac{x}{\sqrt{x^2+b^2}}}^{\alpha },\end{array}$$where ${\sigma }_0$ is the compressive stress on the soil surface, which is shown in equation (1) with the term P. By inserting the value of P from equation (1) in equation (2), one obtains the following:$$\begin{array}{}\text{(3)}& {\sigma }_x=\frac{k_c}{b}+k_{\phi }1-{\frac{x}{\sqrt{x^2+b^2}}}^{\alpha }{z}^n.\end{array}$$

[figure(s) omitted; refer to PDF]

The obtained relation (equation (3)) is important from the point of view that it establishes a relationship between the amount of tire sinkage (z) and the maximum compressive stress at the depth x. Since the soil engineering properties ($k_c$, $k_{\phi }$, n, and α) have been obtained in the test of sinkage plates (see Table 1), therefore the maximum soil stress at different depths can be calculated by using equation (3). Estimation of stress in the soil is important for predicting the possibility of causing problems for plant roots to spread inside the soil.

Table 1

The physical and mechanical characteristics of the examined soil.

Parameter	Symbol	Unit	Value
Soil bulk density	γ	gr/cm3	1.6
Soil adhesion	C	kPa (kN/m2)	20
Internal friction angle of the soil	φ	Degree (°)	35
Soil adhesion constant	$k_c$	kPa/mn−1	679.7
Frictional resistance constant of soil particles	$k_{\phi }$	kPa/mn	2577
Soil sinkage constant	$n$	—	1.34
Soil concentration factor	$\alpha$	—	3

2.2. Experimental Setup

The set of experimental equipment of the current research was obtained from the optimization and changes in the previously built soil bin, located in the machinery hangar of Biosystem Group. The length, width, and height of the soil bin were 6 m, 1.60, and 1.50 m, respectively. The distance between the metal plate of the soil bed and the bottom of the moving chassis was 90 cm. The depth of the soil inside the soil bin was 45 cm in the tests. After conducting the texture determination test by the hydrometric method, the desired soil had 47% sand, 39% silt, and 14% clay, which is included in the loamy soil group, based on the Soil Texture Calculator chart. The physical and mechanical characteristics of the soil under test are presented in Table 1.

To achieve more accurate results, several modifications were made to the location of the sensors and the way of applying force to the carrier. For this purpose, a new chassis was made from a can profile with a square cross-section of four 200 kg load cells (two for measuring horizontal force, one for measuring vertical force, and one for measuring lateral force), see Figure 2. Horizontal load cells were installed between the two arms connected to the wheel and the vertical load cell was placed between the wheel and the power adjustment screw and the side load cell was placed on the wheel dog. Before installing the load cells, the calibration of the load cells was performed. In order to prevent any lateral deviation of the guide and movement in the vertical direction, the adjustment screw was fixed with the vertical axis by four bearings in the form of a rail. The other end of the load cells was fixed to the opposite side of the profile with a number of screws (Figure 2).

[figure(s) omitted; refer to PDF]

A three-phase industrial electric motor with a power of 4 hp and a rotation speed of 1430 rpm was used to start the required power of the wheel carrier. A gearbox was also used to reduce the rotation speed of the system. To start and stop the moving chassis, the start and stop keys were used to command the contactor and the driving electric motor. Also, in the electrical circuit, two contactors were used to turn the motor left and right, and by commanding them, the motor provided the proper direction of the moving chassis.

A wheel tire with a width of 14 cm and a diameter of 52 cm was used to perform the experiments. The tests were performed in three stages of soil moisture changes: before moistening (dry soil), 5 h after moistening (wet soil), and one day after moistening (semi-moist soil). The tests related to the contact surface of the moving wheel with the soil and the depth of the wheel sinking into the soil were performed by choosing three appropriate levels of tire inflation pressure, three appropriate levels of vertical load, three levels of soil moisture content, and three levels of the amount of traffic. To reduce possible errors, each experiment was repeated three times and by averaging the repetitions, the available data were reduced to 162. In this test, 81 treatments were performed with a forward speed of 0.386 km/h; then, by changing the gearbox ratio, the forward speed increased to 0.879 km/h and 81 treatments were also performed at this forward speed (with three repetitions). The inflation pressure applied to the tire was considered at three levels of 10, 15, and 20 psi; measured by a pressure gauge; and adjusted. The vertical load on the wheel was considered at three levels of 170, 250, and 320 kg to model the load on the wheel of a light to medium tractor common in rice fields. A 500 kg Zemic load cell, made in China, was used for vertical load measurements (Figure 2). The vertical loads were applied through the pressure adjustment lever. By turning the lever to the left, the wheel axis moved down and pressure was placed on the load cell that was installed between the lever and the wheel. By connecting the load cell to the data logger, the desired applied load to the wheel was displayed and recorded. It is worth mentioning that at the beginning of the route and before starting the movement, the load on the wheel was adjusted, and after each test, the soil was stirred and the test was repeated. In the desired soil moisture content, after preparing the soil bed and loading the vertical force and adjusting the tire pressure, the soil compaction was measured by the penetrometer at three points along the wheel’s path, see Figure 3. For this purpose, the tip of the penetrometer was sunk into the soil at a constant speed of 3 cm/min, and then by reading the number on the penetrometer gauge and matching it with the relevant table, the amount of the applied force was obtained in kN (Figure 3). This test was performed at three different levels of soil moisture content (2%, 7%, and 13% wb). After performing each test at different levels, the soil was stirred to get a precise result.

[figure(s) omitted; refer to PDF]

2.3. Data Analysis

The statistical analysis was conducted by factorial design and a randomized complete block design in 3 replications. All statistical analyses were performed in SAS and GenStat Release 14.1 software [21]. Excel software was also used to draw graphs.

For simulation, ANFIS was used with the help of MATLAB software. In this analysis, 162 datasets were used for independent variables in the input (vertical load, tire inflation pressure, moisture level, and forward speed) and for two variables in the output (soil compaction and the amount of wheel sinkage in the soil). According to the research conducted by Askari et al. [22], the data were divided into two groups of 130 for network training (80%) and 32 for testing the output model. In this study, several ANFIS models with different membership functions (dsigmf, trimf, pimf, etc.) were examined in order to find the best ANFIS model for predicting outputs (soil compaction and wheel sinkage). The membership functions were changed during the training process of the infinite network and their matching was performed by a gradient vector. The gradient vector is a scale to evaluate the performance of the ANFIS model. For this purpose, the hybrid method which is a combination of the least squares method and the backpropagation method was used in the training of the ANFIS structure. The error tolerance, which is used to create a criterion for stopping the training, was set to zero. Epochs (the number of network training steps) were limited to a maximum of 30 repetitions in the present analysis.

Finally, the models were compared with the experimental data and evaluated using the mean squared error (MSE) and coefficient of determination ($R^2$) presented in the following equations: $$\begin{array}{}\text{(4)}& \text{MSE}=\frac{1}{N}{\displaystyle \sum }_{i=1}^N{X_i-X_p}^2,\text{(5)}& R^2=\frac{{{\displaystyle \sum }}_{i=1}^N{X_i-X_{\text{mean}}}^2-{{\displaystyle \sum }}_{i=1}^N{X_i-X_p}^2}{{{\displaystyle \sum }}_{i=1}^N{X_i-X_{\text{mean}}}^2}.\end{array}$$

3. Results and Discussion

Variance analysis of the effect of input variables including tire inflation pressure, tire vertical load, forward speed, and soil moisture content on soil compaction is presented in Table 2. As can be seen in this Table 2, the effect of individual variables on soil compaction, including tire inflation pressure, vertical force, moisture content and forward speed, and dual effect (vertical load × moisture content), is significant, and the rest of the double and triple effects are not significant. However, unlike the results of the present research, in the research of Shahgholi et al. [7], the interaction effect (moisture content× forward speed) was also significant. Of course, the forward speed and the amount of soil moisture content in their research were both higher than the values of the present study. In addition, their test was conducted in the field with more uneven soil than the laboratory soil bin tests. Therefore, this difference in the significance of interactions in two different studies may be normal [7].

Table 2

Variance analysis of the effect of variables on soil compaction.

Source of variation	Degree of freedom (df)	Mean square soil compaction (Cn)
Vertical load (VL)	2	0.03579${}^{\mathrm{\ast }\mathrm{\ast }}$
Tire inflation pressure (TP)	2	0.03418${}^{\mathrm{\ast }\mathrm{\ast }}$
Soil moisture content (MC)	2	0.18511${}^{\mathrm{\ast }\mathrm{\ast }}$
Forward speed (FS)	1	0.02594${}^{\mathrm{\ast }\mathrm{\ast }}$
VL × TP	4	0.00024ns
MC × VL	4	0.00222${}^{\mathrm{\ast }\mathrm{\ast }}$
FS × VL	2	0.00083ns
TP × MC	4	0.00058ns
TP × FS	2	0.00048ns
MC × FS	2	0.00008ns
VL × TP × MC	8	0.00009ns
VL × TP × FS	4	0.00011ns
TP × MC × FS	4	0.00035ns
VL × TP × MC × FS	12	0.00027ns
Error	108	0.0004
Total	161	—
Coefficient of variation	—	10.8

Abbreviation: ns, not significant.

${}^{\mathrm{\ast }\mathrm{\ast }}$Significant at 1% probability level.

3.1. Investigating the Effect of Input Variables on Soil Compaction

According to the analysis of variance shown in Table 2, the interaction effect of most of the variables in soil compaction was not significant, so in the following, only the effects of single significant parameters are presented.

Based on the results shown in Figure 4, with the increase of vertical load on the wheel, soil compaction linearly increases. So, with the increase of the vertical load from 170 to 250 N (47% relative increase), the soil compaction increased by 16%. In the same way, by increasing the vertical load from 250 to 320 N (28% relative increase), an increase in soil compaction equal to 13% was obtained. The present finding shows that the relative increase in vertical load will result in a linear increase in soil compaction, at least at the examined relatively low vertical loads. The reason is that in small loads, soil settlement is in the elastic phase and according to Hooke’s law, the relationship between vertical stress and strain is linear. Interestingly, according to the model proposed by Soehne (1953) for stress distribution in an elastic material, which is common for modeling soil compaction, the vertical stress under an agricultural tire is linearly proportional to the vertical load. The theory of Boussinesq (1885) also indicates a linear relation between the vertical stresses at a certain depth with wheel load [23]. With a further increase in vertical load, the soil compaction gradually enters the plastic phase and according to the sigmoid shape of the soil stress–strain diagram, it is predicted that the amount of vertical strain starts to decrease.

[figure(s) omitted; refer to PDF]

The results related to the effect of tire inflation pressure on soil compaction are presented in Figure 5. According to the results shown in Figure 5, with the increase in tire inflation pressure, soil compaction increases. The highest compression value was obtained for the maximum examined tire inflation pressure, i.e., 20 psi. The results show that reducing tire pressure from 20 to 15 psi (25% reduction) reduces soil compaction by 12.94%. This result is consistent with the findings of Taghavifar and Mardani [23]. Alkhalifa et al. [24] investigated the simultaneous effect of vertical load up to 8 kN and tire inflation pressure at three levels of 179, 241, and 283 kP on the amount of tire deflection. According to their results, at low vertical loads (up to 3 kP), there was no significant difference between different inflation pressures in the amount of tire deflection. However, in vertical loads higher than 3 kN, with the decrease in tire pressure at a given vertical load, the amount of tire deformation increased. This finding shows that in low to medium vertical loads, there is no interaction effect between vertical load and tire pressure and they do not strengthen or weaken each other’s effect. However, in high vertical loads, there is an interaction between the vertical load on the tire and the tire inflation pressure. It is noteworthy that in the present study, where the maximum vertical load on the wheel was 3.2 kN (320 kg_f), the interaction effects between vertical load and tire pressure were not significant (see Table 2). Therefore, the results of both research studies are in line with each other and confirm each other’s findings.

[figure(s) omitted; refer to PDF]

In relation to the effect of tire air pressure on the increase of soil density, we can refer to the results of Damme et al.’s research [25]. According to the results obtained by these researchers, tire inflation pressure and wheel load are the key known factors of soil compaction. However, the effects of traction and repeated tire traffic are not yet fully understood and different results may be reported. In this regard, these researchers showed that a heavy tractor with high drawbar pull causes an increase in the density of soil as much as 6 times the repeated traffic of a passive agricultural tire.

In the following, the effect of soil moisture content on the soil compaction is shown in Figure 6. According to the obtained results, soil compaction increased significantly with the increase of the moisture content. The highest value of soil compaction was observed in 13% moisture content (wb) and the lowest value was observed in 2% MC (dry soil). According to the results shown in Figure 6, with the increase in moisture content from 2% to 7% (relative increase of 250%), the amount of soil compaction increased by 15.2%. The relative increase of soil compaction in changing moisture content from 7% to 13% (85.7% relative increase) was obtained equal to 51.75%, which was relatively 9.93 times the soil compaction in low moisture content (7%–2%). In the same direction and considering equation (1), the values of $k_c$ and $k_{\phi }$ for wet soil are lower than dry soil; therefore, for each vertical constant load, the amount of sinkage in wet soils is higher than in dry soil. Relevant experimental research conducted by Woldeyohannis et al. [26] also shows the positive effect of moisture content on soil compaction. They proved that soil compaction is easier in high soil moisture contents, which is completely consistent with the results shown in Figure 6 of this research.

[figure(s) omitted; refer to PDF]

According to the results shown in Figure 7, increasing the forward speed has an inverse effect on the amount of soil compaction. Therefore, with increasing forward speed, the amount of soil compaction decreases. The highest compression was obtained at the lower speed of 0.386 km/h and the lowest value was obtained at the higher speed of 0.879 km/h. This finding is consistent with the experimental results obtained by Stafford et al. [10]. In the same direction, Taghavifar and Mardani [13], concluded that increasing forward speed has the opposite effect on soil compaction, while increasing the wheel load and the number of passes significantly increases soil compaction [13].

[figure(s) omitted; refer to PDF]

3.2. The Effect of Soil Surface Compaction on Stress Distribution Inside the Soil

Figure 8 shows the effect of the tire sinkage on the amount of stress under the center line of the tire inside the soil based on the derived relationship, given by equation (5). According to the results shown in Figure 8, by increasing the tire sinkage from 2 to 5 cm, the amount of stress under the tire has increased 4 times. This increase in tension is kept constant up to a depth of 5 cm inside the soil and then decreases. However, this large difference in the amount of stress inside the soil is maintained up to a depth of 20 cm, and then the difference in stress decreases. This result shows at least qualitatively the effect of tire sinkage on soil compaction at the working depths of primary tillage operations, i.e., 0–20 cm. In the same direction, Moinfar et al. [4] found that at a depth of 40 cm, the apparent soil density is almost the same at all tire inflation pressures, while at a depth of 10 cm, there is a significant difference in soil compaction between different tire loads. The ability of soil to transfer stress to the subsoil depends on the soil structure, soil moisture content, and the amount of organic matter in the soil. Arvidsson et al. [27] reported that the difference between the stresses applied to the soil at a depth of 40 cm is almost negligible as a result of single-wheel traffic, two-wheel tractors, and tracks. The effect of these parameters such as soil structure, humidity, and organic matter in the soil in the transfer of surface compressive stresses to a certain depth is shown in the relation of Froelich (1934) by the parameter υ, called concentration factor in the form of ${\sigma }_x={\sum }_{i=0}^n\nu P_i/2\pi x_i^2{\cos }^{\nu +2}{\theta }_i$, [28]. For the values of υ = 3 in this relationship, it confirms the theory presented by Boussinseq (1885), but in any case, this parameter is different for different soils and must be determined experimentally.

[figure(s) omitted; refer to PDF]

3.3. The Results of ANFIS on Soil Compaction

In the next step, for the prediction of changes in soil compaction under the influence of the vertical load, tire dynamic parameters and soil moisture content were performed using the ANFIS software. The input parameters were vertical load on the tire in 3 levels, tire air inflation pressure in 3 levels, soil moisture content in 3 levels, and forward speed in 2 levels. The results presented in Table 3 show that in the desired output for the depth of the tire sinking into the soil, the dsigmf membership function in the input yields the best output result with the lowest squared error (MSE = 0.0422) and the highest correlation coefficient ($R^2$ = 1). The maximum repetition of network training steps was 30, see Table 3.

Table 3

The effect of different membership functions of ANFIS in predicting the compressibility of soil.

Implemented model	Membership function type		Number of membership function		Mean squared error (MSE)	Correlation factor ($R^2$)
	Input	Output	Input	Repetitions
1	Linear	Trimf	3, 3, 3, 2, 3	30	0.0531	0.9682
2	Hybrid	Gaussmf	3, 3, 3, 2, 3	30	0.0486	0.9588
3	Linear	Pimf	3, 3, 3, 2, 3	30	0.0645	0.9786
4	Hybrid	dsigmf	3, 3, 3, 2, 3	30	0.0422	1
5	Linear	Trimf	3, 3, 3, 2, 3	30	0.0501	0.9433

The results of the ANFIS optimal model for predicting changes in soil compaction under the influence of vertical force on the tire, tire inflation pressure, soil moisture content, and forward speed are shown in Figure 9. According to the results shown in Figure 9, the highest compression value is related to the maximum vertical load of 320 N and maximum inflation pressure of 20 psi. Similarly, as predicted by ANFIS, increasing soil moisture from 2% to 7% has no significant effect on soil compaction, but soil compaction increases significantly with increasing MC% from 7% to 13%.

[figure(s) omitted; refer to PDF]

In the same way, the soil compaction caused by tire traffic has an inverse relationship with the increase in forward speed, so with the increase in forward speed, the amount of soil compaction decreases.

By comparing the soil compaction obtained from laboratory soil bin tests and the data predicted by ANFIS (Figure 10), it is concluded that the ANFIS model is able to predict the amount of soil compaction with high accuracy. The advantage of the analysis obtained in ANFIS is the possibility of predicting the output of the model for a specific input that has not been examined.

[figure(s) omitted; refer to PDF]

According to the results obtained by Moinfar et al. [4], the ANFIS has a higher potential for predicting the effect of multiple input variables on soil compaction ($R^2$ = 0.99) compared to ANNs and stepwise regression (SR). According to their result, depth in the soil, type of driving system, number of passes, moisture content, soil texture, travel speed, and tire inflation pressure were the factors significantly influencing soil bulk density, i.e., soil compaction [4].

4. Conclusions

In this research, the effect of various parameters related to the operation of an agricultural tire was experimentally investigated inside the laboratory soil bin, filled with loamy agricultural soil. Furthermore, the prediction of the compressibility of the examined soil was investigated and analyzed using the ANFIS. The results obtained in the present study indicate that increasing the load on the tires in the elastic range of the soil causes a linear increase of the soil compaction, but with a large increase in the load on the wheel, the behavior of the soil may go beyond the elastic limit against the compressive stresses and cause the soil to over-compact. Therefore, attention should be paid to choosing the right tractor for working in the field, and heavy tractors should not be used for simpler tasks such as weeding or spraying. Another very important issue is to pay attention to soil moisture before the tractors and equipment enter the field. The results showed that in high soil moisture contents, the amount of soil compaction caused by tire traffic is very significant. The next important point is to pay attention to reducing the tire inflation pressure within the permitted range recommended by the tire manufacturers. For example, reducing tire pressure from 20 psi to 15 psi reduces soil compaction by nearly 13%. Therefore, it is very important to produce agricultural tires with the ability to work at low pressures with a wider width to increase the contact surface of the tire with the soil in order to reduce soil compaction and increase traction at the same time. Certainly, with the advancement of science in the field of tire production, it is possible and recommended to produce more resistant tires for the ability to work at lower inflation pressures. This approach provides criteria for more appropriate selection of agricultural tires. However, considering that the present study was investigated in a controlled environment inside the soil bin and only for loamy soil, so its application in other types of soil should be investigated in future. The output of the ANFIS model can be used for a specific nonmeasured input, which is one of the advantages of modeling in this software.

Funding

This research received funding as a research project with grant number “02-1397-12” from Sari Agricultural Sciences and Natural Resources University (SANRU), Iran.

Acknowledgments

The present research work has been performed in the form of a research project with the financial support of Sari Agricultural Sciences and Natural Resources University (SANRU), which deserves appreciation and gratitude.

Glossary

Nomenclature

γSoil bulk density (gr/cm³)

CSoil adhesion (kPa (kN/m²))

φInternal friction angle of the soil (degree (°))

$k_c$Soil adhesion constant (kPa/mⁿ⁻¹)

$k_{\phi }$Frictional resistance constant of soil particles (kPa/mⁿ)

$n$Soil sinkage constant

$\alpha$Soil concentration factor

zSinkage or vertical compression of the soil (mm)

PSurface pressure caused by the vertical load on the soil from the wheel (N/m²)

bTire width (mm)

${\sigma }_x$Compressive stress at the depth x (N/m²)

${\sigma }_0$Compressive stress on the soil surface (N/m²)

ANFISAdaptive neuro–fuzzy inference system

wbWet basis

TETraction efficiency

FWDForward wheel drive

RWDRear wheel drive

SASStatistical analysis system

MCMoisture content

MSEMean squared error

TPTire inflation pressure

VLVertical load

FSForward speed

ANNArtificial neural network

SRStepwise regression

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