An Anchoring Capacity Study Focused on a Wheel’s Curvature Geometry for an Autonomous Underwater Vehicle with a Traveling Function during Contact with Loose Ground Containing Water

: The current scallop fishery sector allows many scallops to remain in specified fishing zones, and this process leads to heavy losses in the sector. Scallop fishermen aim to harvest the remaining scallops to reduce their losses. To achieve this, a fisherman must understand the scallop ecology on the seafloor. In our previous study, we proposed a method for measuring scallops using wheeled robots. However, a wheeled robot must be able to resist disturbance from the sea to achieve high measurement accuracy. Strong anchoring of wheels against the seafloor is necessary to resist disturbance. To better understand anchoring performance, we confirmed the wheel anchoring capacity in water-containing sand in an experiment. In this experiment, we towed fixed wheels on water-containing sand and measured the resistance force acting between the wheel and the sand. Afterward, we considered the resistance force as the wheel anchoring capacity on the water-containing sand. The experimental results capture the tendency for the anchoring capacity of sand with/without water to increase with sinkage. The results also demonstrate that the anchoring capacity of water-containing sand is lower than that of non-water-containing sand. However, the results indicate that when the wheels possess lugs, their presence tends to increase the wheels’ anchoring capacity in water.


Introduction
Current scallop fishing activities involve the release of scallops into a fishing zone and their harvest after they have grown to a specific size.The use of this method helps scallop fishermen to catch around 5.5 million tons of scallops annually.However, the figure of 5.5 million tons represents only 40-60% of the total released scallops.The remaining scallops represent a loss of approximately CNY 50 billion.Scallop fishermen aim to harvest the remaining scallops to increase their catches.The causes of scallop loss include predation by starfish and mortality due to rough seas.However, the other causes of loss are not yet fully understood.To understand these causes, it is necessary to investigate the relationship between the scallops' physical condition and the environment on the seafloor.
The authors of previous studies have attempted to understand scallops' physical condition by visualizing them on the seafloor.This method involves a camera being lowered from a ship and the ship being steered so that photographs of the seabed can be taken [1].The seabed photographs that are taken will show the number and location of scallops over a wide area.Then, information from these photographs can be used to indicate the scallop distribution in the fishing zone.However, using their distribution alone prevents one from fully understanding scallops' physical condition.In light of this problem, fishermen require a new method to obtain more information other than simply the scallops' location and number to understand their physical condition.One way to increase the amount of measurement information gained is to directly measure the detailed physical quantities of scallops (mass, size, and detailed shell condition).This method requires the examination of the seafloor to avoid causing stress to the scallops and reducing their value.Therefore, our research team proposes a method to measure the physical quantity of scallops directly on the seafloor using an underwater robot as shown in Figure 1.The steps of the proposed method are described below:

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First, lower the robot with a robotic arm and camera from the ship.

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Second, use the robot's camera to recognize scallops.• Third, navigate the robot to the location of the scallop until the robot arm reaches the scallop.

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Fourth, instruct the robot to seize the scallop and measure its physical quantity.

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Fifth, instruct the robot to release the scallop and begin to recognize other scallops.
Geotechnics 2024, 4, FOR PEER REVIEW . Scallop physical quantity measurement method involving the use of robots.

Problems of Scallop Measurement with Wheeled Robots on the Seabed
When a wheeled robot is on the seafloor, the ocean current causes disturban robot.This disturbance makes it possible for the robot to move in an unintended d This movement then causes errors in the measurements taken and reduces measu accuracy.The robot's wheels must possess strong anchoring capacity on the soft where scallops live in order to resist this disturbance.The robot's wheel anchorin ity on the soft ground is the combined force of the passive earth pressure  (E (1)) and the shear resistance  (Equation ( 2)), as shown in Figure 2 [26,27]. occur when disturbance acts on the soil adjacent to a fixed wheel on the soft groun the external force pushes the fixed wheels on the soft ground, the wheels generate gular soil mass (Area A) on the wheels, as shown in Figure 2. The shear resistanc ated between Area A and the soil below Area A is  . is the combined passi pressure generated when Area A acts on Area B like a plate.Other forces are pred be small compared to  and  , and in this current study, we did not consid forces.

𝐹
tan 45° where  is the density of the ground,  is the sinkage,  is the internal frictio  is the adhesion force,  is the vertical stress acting on the bottom of the soil ma the wheel,  is the shear displacement, and  is the shear displacement coeffic The vertical stress  in Equation ( 2) is similarly affected by wheel width, w dius, and wheel sinkage because Equation (3) (the combined vertical componen stress acting on the wheel from the ground W) depends on width, radius, and sin To perform the procedure above, the proposed robot requires a scallop recognition function, a scallop acquisition function, the ability to move near scallops, and a scallop measurement function.The authors of previous studies have examined the recognition of scallops on the seafloor through the use of cameras [2][3][4][5][6].Additionally, the authors of previous studies have also examined the use of an underwater robotic arm [7][8][9] and a specific gripper mechanism for catching scallops [10,11].Therefore, scallops could be recognized and acquired on the seafloor by adding robots to the methods used in previous studies.In addition, approaching scallops is possible with the use of existing underwater robots.Existing underwater robots can be broadly classified into floating and grounding types.The floating type swims underwater.An example of a floating-type underwater robot is a drone [12,13].The floating type is affected to a lesser extent by terrain as it travels without contact with the ground.Thus, floating robots have high mobility performance and can easily approach scallops.In contrast, a grounding-type underwater robot moves over the seafloor.Examples of the grounding type are crawled, legged, and wheeled robots [14][15][16][17][18][19][20][21][22].This type is easily affected by terrain when in contact with the seafloor.Therefore, the grounding type is inferior to the floating type in terms of mobility performance.However, the robot must maintain its posture to improve measurement accuracy.If the robot's posture is unstable, this results in decreased measurement accuracy.In addition, the robot must maintain its posture because an unstable posture can lead to errors in measurements.The floating type cannot achieve good performance and maintain its posture since this type of underwater robot is always floating and unable to maintain a fixed posture.Therefore, the grounding type is more suitable for the proposed method.
Among grounding robots, we focus on wheeled robots because of their simple structure and ease of control.However, there are concerns about wheeled robots with regard to maintaining their posture on the seabed.If a wheeled robot is placed on the seabed, ocean currents apply force to the robot and disturb the maintenance of the robot's position on the seabed.Robots must strongly anchor their wheels on the seafloor to resist ocean currents.
Thus, the robot's wheel design needs to take into consideration mobility performance and good anchorage to the ground.To achieve such a design, research on the relationship between fixed wheels and water-containing soft ground surfaces is necessary.Although there are studies in the literature related to compression and shear force measurement tests on water-containing ground surfaces, there is a lack of research on the forces exerted by fixed wheels on this type of ground [23][24][25].Therefore, in this study, we focused on the interaction between fixed wheels and the water-containing ground and carried out experiments to confirm the anchoring capacity of wheels acting on this type of ground to better understand this interaction.

Problems of Scallop Measurement with Wheeled Robots on the Seabed
When a wheeled robot is on the seafloor, the ocean current causes disturbance to the robot.This disturbance makes it possible for the robot to move in an unintended direction.This movement then causes errors in the measurements taken and reduces measurement accuracy.The robot's wheels must possess strong anchoring capacity on the soft ground where scallops live in order to resist this disturbance.The robot's wheel anchoring capacity on the soft ground is the combined force of the passive earth pressure F 1 (Equation ( 1)) and the shear resistance F 2 (Equation ( 2)), as shown in Figure 2 [26,27].F 1 and F 2 occur when disturbance acts on the soil adjacent to a fixed wheel on the soft ground.When the external force pushes the fixed wheels on the soft ground, the wheels generate a triangular soil mass (Area A) on the wheels, as shown in Figure 2. The shear resistance generated between Area A and the soil below Area A is F 2 .F 1 is the combined passive earth pressure generated when Area A acts on Area B like a plate.Other forces are predicted to be small compared to F 1 and F 2 , and in this current study, we did not consider such forces.
where γ is the density of the ground, z 0 is the sinkage, φ is the internal friction angle, c is the adhesion force, σ is the vertical stress acting on the bottom of the soil mass under the wheel, jx is the shear displacement, and kx is the shear displacement coefficient.
Geotechnics 2024, 4, FOR PEER REVIEW the lower the shear resistance is [23][24][25].This fact shows that the shear resistanc plied to a wheel on water-containing soft ground, such as the seabed, is smaller.T anchorage force on the water-containing sand surface is expected to be lower than non-water-containing sand.However, the combined earth pressure  in water is because the soil mass of Area A and the soil mass of Area B have different co compared to the soil mass of the non-water-containing sand surface due to the i of water.To clarify the anchoring capacity on water-containing sand, we need t stand how the pressure of Area B changes in water.Understanding this change is because the properties of the soil become very complex as a result of the inclusion Therefore, in this study, we conducted an experiment in which an external force is to a fixed wheel to generate  and  to investigate how  and  change de on the presence of water and to confirm the anchoring performance of the wheel o containing sand.Specifically, we first submerged the wheel in sand with water.In the next towed the wheel laterally to simulate the lateral force applied by ocean current ward, the shear direction force generated at this time was measured.We condu experiment in the presence and absence of water to understand the specific effec ter.The vertical stress σ in Equation ( 2) is similarly affected by wheel width, wheel radius, and wheel sinkage because Equation (3) (the combined vertical component of the stress acting on the wheel from the ground W) depends on width, radius, and sinkage, as shown in Figure 3 [26].
where p(θ) is the stress in the sand under the wheel, k c is the coefficient governed by the adhesive force of the sand, k φ is the coefficient governed by the internal friction angle in the sand, B is the wheel width, R is the wheel radius, n is the sinking index, θ is the wheel angle at an arbitrary point, and θ s is the wheel angle at the starting point of the wheel and ground contact [28].

Experimental Procedure
Equations ( 1)-( 3) show that the wheel anchorage force on soft ground increases with wheel sinkage, wheel width, and wheel radius.This fact suggests the possibility of obtaining high anchorage force even in water-containing sand by having wheels with a great degree of sinkage, a large wheel width, and a large wheel radius.However, the shear resistance of sand decreases with the increase in water content.Thus, the shear resistance of sand saturated with water is low.Additionally, low shear strength decreases the interlocking of the sand, and the ground particles are more likely to move, resulting in lower Equation (1) suggests that the anchoring capacity increases with the increase in sinkage.Moreover, Equation (2) and Figure 2 suggest that increasing the radius slightly increases the anchoring capacity.Additionally, Equation (3) suggests that the right-hand side depends on the radius and width.Equation (3) shows that the required sinkage decreases when the width and radius increase.
The equations above can be used to determine the anchoring capacity on non-watercontaining sand.However, these equations do not consider the effect of water on the sand.The authors of previous studies have found that the more water there is in the soft ground, the lower the shear resistance is [23][24][25].This fact shows that the shear resistance F 2 applied to a wheel on water-containing soft ground, such as the seabed, is smaller.Thus, the anchorage force on the water-containing sand surface is expected to be lower than that on non-water-containing sand.However, the combined earth pressure F 1 in water is unclear because the soil mass of Area A and the soil mass of Area B have different conditions compared to the soil mass of the non-water-containing sand surface due to the influence of water.To clarify the anchoring capacity on water-containing sand, we need to understand how the pressure of Area B changes in water.Understanding this change is difficult because the properties of the soil become very complex as a result of the inclusion of water.Therefore, in this study, we conducted an experiment in which an external force is applied to a fixed wheel to generate F 1 and F 2 to investigate how F 1 and F 2 change depending on the presence of water and to confirm the anchoring performance of the wheel on water-containing sand.
Specifically, we first submerged the wheel in sand with water.In the next step, we towed the wheel laterally to simulate the lateral force applied by ocean currents.Afterward, the shear direction force generated at this time was measured.We conducted this experiment in the presence and absence of water to understand the specific effects of water.

Experimental Procedure
Equations ( 1)- (3) show that the wheel anchorage force on soft ground increases with wheel sinkage, wheel width, and wheel radius.This fact suggests the possibility of obtaining high anchorage force even in water-containing sand by having wheels with a great degree of sinkage, a large wheel width, and a large wheel radius.However, the shear resistance of sand decreases with the increase in water content.Thus, the shear resistance of sand saturated with water is low.Additionally, low shear strength decreases the interlocking of the sand, and the ground particles are more likely to move, resulting in lower earth pressure.Low pressure can increase the difficulty of obtaining the anchoring force that can resist disturbances such as ocean currents, even if the wheel has a high degree of sinkage, a large width, and a large radius.Therefore, we experimented with water-containing sand to confirm the effects of water on wheel anchorage force in this type of sand and the relationship between the wheel sinkage, wheel width, wheel radius, and wheel anchorage force in the sand.
The procedure in the experiment used to confirm the effect of water on the wheel anchoring capacity acting on the ground is shown in Figure 4.As shown in Figure 4a, the test apparatus consists of two wheels in contact with the ground, a force sensor to measure the forces acting on the ground and the wheels, a linear actuator to tow the wheels, and water-containing sand with a mixture of water and sand.
Geotechnics 2024, 4, FOR PEER REVIEW 5 earth pressure.Low pressure can increase the difficulty of obtaining the anchoring force that can resist disturbances such as ocean currents, even if the wheel has a high degree of sinkage, a large width, and a large radius.Therefore, we experimented with water-containing sand to confirm the effects of water on wheel anchorage force in this type of sand and the relationship between the wheel sinkage, wheel width, wheel radius, and wheel anchorage force in the sand.
The procedure in the experiment used to confirm the effect of water on the wheel anchoring capacity acting on the ground is shown in Figure 4.As shown in Figure 4a, the test apparatus consists of two wheels in contact with the ground, a force sensor to measure the forces acting on the ground and the wheels, a linear actuator to tow the wheels, and water-containing sand with a mixture of water and sand.The experimental procedure is performed as follows: • First, carefully set the wheels on the water-containing sand (Figure 4a).The sinkage at this time must be set to 0 mm (static sinkage).When the wheels are on the soil, they sink into the soil due to their weight.This form of sinkage is defined as static sinkage.

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Third, measure the degree of sinkage.The measured sinkage degree is taken as the initial sinkage.

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Fourth, the linear actuator tows the wheel unit, and the force sensor measures the resistance force acting on the wheel (Figure 4d).
In the experiment, we used both the non-water-containing sand and water-containing sand to confirm the effect of water on the relationship between wheel anchorage force and the soft ground.Additionally, we used multiple experimental wheel conditions (sinkage, width, and radius) to confirm the relationship between the wheel conditions and the wheel anchorage force on water-containing sand.
Note that the water conditions (water pressure, water quality, and other conditions) used in the experiment vary greatly from those on the actual seafloor.This difference makes it difficult to completely clarify the wheel anchoring capacity on the seafloor.However, since this experiment focuses on confirming the relationship between wheel anchorage force and soft ground changes with water, we ignored the effects of water pressure, water quality, and other elements.

Experimental Conditions and Environment
The experimental machine (Figure 5) consists of two wheels, a force sensor, a linear actuator, and water-containing/non-water-containing sand placed in a plastic tank.Additionally, the wheel distance indicates the distance between both wheels.The wheels used in the experiment are all made of PLA.Their shapes are shown in Figure 6.Wheel A is the base wheel; wheel B has a smaller radius than wheel A; wheel C has the same radius and The experimental procedure is performed as follows:

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First, carefully set the wheels on the water-containing sand (Figure 4a).The sinkage at this time must be set to 0 mm (static sinkage).When the wheels are on the soil, they sink into the soil due to their weight.This form of sinkage is defined as static sinkage.

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Second, rotate the wheels (number of rotations: 0, 0.5, 1, 1.5, or 2) to increase the degree of sinkage (Figure 4b,c).• Third, measure the degree of sinkage.The measured sinkage degree is taken as the initial sinkage.

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Fourth, the linear actuator tows the wheel unit, and the force sensor measures the resistance force acting on the wheel (Figure 4d).
In the experiment, we used both the non-water-containing sand and water-containing sand to confirm the effect of water on the relationship between wheel anchorage force and the soft ground.Additionally, we used multiple experimental wheel conditions (sinkage, width, and radius) to confirm the relationship between the wheel conditions and the wheel anchorage force on water-containing sand.
Note that the water conditions (water pressure, water quality, and other conditions) used in the experiment vary greatly from those on the actual seafloor.This difference makes it difficult to completely clarify the wheel anchoring capacity on the seafloor.However, since this experiment focuses on confirming the relationship between wheel anchorage force and soft ground changes with water, we ignored the effects of water pressure, water quality, and other elements.

Experimental Conditions and Environment
The experimental machine (Figure 5) consists of two wheels, a force sensor, a linear actuator, and water-containing/non-water-containing sand placed in a plastic tank.Additionally, the wheel distance indicates the distance between both wheels.The wheels used in the experiment are all made of PLA.Their shapes are shown in Figure 6.Wheel A is the base wheel; wheel B has a smaller radius than wheel A; wheel C has the same radius and width as wheel A, albeit with the addition of lugs; and wheel D has a smaller wheel width than wheel A. Table 1 summarizes the specifications of the experimental machine.
Geotechnics 2024, 4, FOR PEER REVIEW width as wheel A, albeit with the addition of lugs; and wheel D has a smaller whe than wheel A. Table 1 summarizes the specifications of the experimental machin   width as wheel A, albeit with the addition of lugs; and wheel D has a smaller wheel width than wheel A. Table 1 summarizes the specifications of the experimental machine.Table 1.Specifications of the experimental device.

Experimental Results and Considerations
Figure 7 shows images of the experimental procedure above (Figure 5).The experimental results are shown in Figures 8-10 and Table 2. Figure 8 shows the relationship between the number of wheel rotations and the initial sinkage on each type of sand in Figure 7b.Figures 9 and 10 show the relationship between initial sinkage, towing time, and anchoring capacity when the wheel shown in Figure 7c is towed.Figures 9 and 10 show the anchoring capacity under different sand conditions.Table 2 summarizes the relationship between the number of rotations, the initial sinkage shown in Figure 8, and the maximum anchoring capacity shown in Figures 9 and 10.A description of the charts above and consideration of the experimental results are included below.
degree of sinkage, a large width, a small radius, and the presence of lugs.Under the same degree of sinkage, the effects of width and sinkage on anchoring capacity are consistent with the trends expressed in Equations ( 1) and (2).However, the effect of the radius, as explained in Equation ( 2), is possibly only small.In addition, these effects are not necessarily valid.Equation (3) shows that wheels with a larger width and radius are less likely to sink.This means that a larger wheel width and radius increase the number of revolutions required for the wheel to sink.This increase makes wheel sinkage inefficient.Moreover, increasing the width and the radius of the wheel increases its buoyancy due to the increased volume and makes sinking difficult.In addition, the use of lugs is suitable if they are appropriately sized.However, the use of lugs that are too large increases the risk of breakage.Excessively large lugs also result in too much sand being removed from under the wheels and prevent the robot from moving.Therefore, for a wheeled robot to maintain high posture performance and mobility efficiency, its wheels must possess the appropriate width, radius, and number of lugs.degree of sinkage, a large width, a small radius, and the presence of lugs.Under the same degree of sinkage, the effects of width and sinkage on anchoring capacity are consistent with the trends expressed in Equations ( 1) and ( 2).However, the effect of the radius, as explained in Equation ( 2), is possibly only small.In addition, these effects are not necessarily valid.Equation (3) shows that wheels with a larger width and radius are less likely to sink.This means that a larger wheel width and radius increase the number of revolutions required for the wheel to sink.This increase makes wheel sinkage inefficient.Moreover, increasing the width and the radius of the wheel increases its buoyancy due to the increased volume and makes sinking difficult.In addition, the use of lugs is suitable if they are appropriately sized.However, the use of lugs that are too large increases the risk of breakage.Excessively large lugs also result in too much sand being removed from under the wheels and prevent the robot from moving.Therefore, for a wheeled robot to maintain high posture performance and mobility efficiency, its wheels must possess the appropriate width, radius, and number of lugs.First, the relationship between the number of wheel rotations and the initial sinkage (Figure 8) shows a trend of increasing sinkage with more rotation on both types of sand.Additionally, as the wheel rotates on water-containing sand, the degree of sinkage is greater than on non-water-containing sand.In particular, wheel C, including lugs, is susceptible to sinkage as the lugs tend to concentrate stress.Wheels B and D, with a small radius and width, are susceptible to sinkage for the same reason.
Additionally, the relationship between initial sinkage and anchoring capacity (Figures 9 and 10) shows a trend of increasing anchoring capacity with greater initial sinkage on both types of sand.This trend corresponds to Equation (1) and indicates that increasing sinkage is also effective in water-containing conditions.The information displayed in Table 2 also indicates that the anchoring capacity on the water-containing sand tends to be lower than the anchoring capacity on the non-water-containing sand when comparing the maximum anchoring capacity of all wheels.For example, the decreasing trend can be seen in the fact that the anchoring capacity of wheel A (where the sinkage is 20 mm and the anchoring capacity is 27.5 N) on water-containing sand is smaller than that of wheel A (where the sinkage is 16 mm and the anchoring capacity is 36.6N) on non-water-containing sand.This decreasing trend indicates that water exerts an effect of reducing the anchoring capacity on the soft ground.Note: When the wheel makes contact with the soil, the wheel sinks into the soil due to its weight.This form of sinkage is defined as static sinkage.
Additionally, Equation (2) and Figure 2 indicate that the larger the wheel width and radius for the same degree of sinkage, the higher the anchoring capacity.Equation (3) also suggests that the larger the width and radius, the higher the ground reaction force and the smaller the required sinkage.To confirm the increased trend in water, we compared the maximum anchoring capacity of each wheel when the sinkage was around the same as the value shown in Table 2. Table 2 shows that the anchoring capacity of wheel D (where the sinkage is 21 mm and the anchoring capacity is 23.2 N on water-containing sand) is smaller than that of wheel A (where the sinkage is 20 mm and the anchoring capacity is 27.5 N on water-containing sand).These results indicate that there is a tendency for an increase in anchoring capacity due to the increase in width, even in water.Therefore, the derstanding of wheel anchoring capacity, we conducted experiments with towing wheels on water-containing sand.From the results of our towing experiments, we came to the following conclusions: • The anchoring capacity of the same wheel at the same sinkage level tends to be lower on water-containing sand.This fact suggests that water weakens the ground strength, and the wheeled robot's ability to maintain its posture on water-containing sand decreases.• An increase in the sinkage level is effective at increasing the anchoring capacity of the wheel even underwater.The greater the degree of initial sinkage, the greater the anchoring capacity, even on water-containing sand.• The wheel shape affects the wheel's anchoring capacity in water.Wheeled robots require appropriate wheel shapes for high posture maintenance performance and mobility efficiency.
The results of our experiments show that water weakens the ground strength and reduces the anchoring capacity of wheels in water.The results also show that the relationship between the degree of sinkage, the wheel shape, and the wheel anchoring capacity does not change significantly in water.This finding suggests that the wheel can obtain a high anchoring capacity by adjusting its degree of sinkage and shape.To adjust these parameters, it is necessary to understand the sand properties (cohesion, shear strength, and so forth) that are changed in the presence of water.Therefore, we plan to construct an equation and model for the anchoring capacity in water by quantitatively observing how the sand properties change in the presence of water.In addition, the experimental conditions must more closely reflect the operating conditions of a wheeled robot on the seafloor to confirm the effectiveness of the robot in actual conditions.Therefore, we plan to create a site simulating the seabed (in consideration of water, water current, sand properties, sand gradient, etc.) and a testbed.We then plan to use them to conduct experiments.

Figure 1 .
Figure 1.Scallop physical quantity measurement method involving the use of robots.

Figure 2 .
Figure 2. Stress in sand applied to wheels.

Figure 2 .
Figure 2. Stress in sand applied to wheels.

Figure 2 .
Figure 2. Stress in sand applied to wheels.

Figure 3 .
Figure 3. Relationship between sinkage and the wheel on loose soil.

Figure 3 .
Figure 3. Relationship between sinkage and the wheel on loose soil.

Figure 8 .Figure 9 .Figure 9 . 9 Figure 8 .Figure 9 .Figure 10 .
Figure 8.The relationship between the number of rotations and initial sinkage.The vertical axis represents the initial sinkage, and the horizontal axis represents the number of wheel spins.The legend shows the wheel shape.(a) Non-water-containing sand and (b) water-containing sand.

Table 1 .
Specifications of the experimental device.

Table 1 .
Specifications of the experimental device.

Table 2 .
Relationship between the number of rotations, the initial sinkage, and the maximum anchoring capacity.