Soil Deformation beneath a Wheel during Travel Repetition

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Research Paper EAEF () : 796, Soil Deformation beneath a Wheel during Travel Repetition Khwantri SAENGPRACHATANARUG *, Masami UENO *, Yasuaki KOMIYA * and Eizo TAIRA * Abstract To elucidate the

1 Research Paper EAEF () : 796, Soil Deformation beneath a Wheel during Travel Repetition Khwantri SAENGPRACHATANARUG *, Masami UENO *, Yasuaki KOMIYA * and Eizo TAIRA * Abstract To elucidate the phenomenon of the soil compaction observed during actual machine operation, a model wheel was traveled repeatedly and the subsequent soil deformation was analyzed. As repetitive travel progressed, soil particles drew similar trajectories with accompanying changes in the size and shape of the trajectories leading to the formation of spirallike patterns. The changes depended on traveling slip and depth of the soil layer. The void ratio increased in with repetitions in the shallow layers, but decreased in the deeper layers. The change in void ratio in high slip conditions was larger than those in low slip conditions, indicating that repetitions in high slip caused more deformation and compaction than did those in low slip. [Keywords] soil bin test, soil deformation, travel repetition, soil strain I Introduction In actual farm operations, agricultural machinery repeatedly travels along the same track line. That is, the mechanical load is repeatedly applied to the soil, leading to the soil compaction. For example, during sugarcane harvesting, a large scale harvester cuts the base of the cane stalks and chops the stalks into small billets, and then loads them into a truck while all the time running along the track line between the furrows. The harvester and the truck run side by side as shown in Fig.. One track line is passed over at least times by the front and rear wheels and, as a consequence, is subjected to a heavy mechanical load. Such travel causes a large amount of soil compaction that directly affects the growth of crops and reduces crop production. Many studies on soil compaction have been reported. Wong (967) described how soil particles were displaced, drawing an elliptic trajectory by the approach and passage of the wheel. Shikanai et al. () introduced a precise measurement of soil deformation under the wheels. Moreover, soil displacement at the ground contact surface was measured and analyzed in our previous study (Khwantri et al., 9) Although the characteristics of soil deformation were clarified by the abovementioned studies, those reports were limited to the effects of a single travel. Soil deformation or soil compaction by repetitive travel during actual farming operations cannot be accurately elucidated from those results. Therefore, the main purpose of this paper is to clarify the compaction process and soil deformation by the travel repetition of a test wheel. II Materials and methods Fig. Harvesting of sugarcane by a large scale harvester at Daito Island, Okinawa, Japan.. Traveling test apparatus A sophisticated wheel test apparatus (Nohse et al., 99) was employed. The apparatus consists of a soil bin, a set of sensors attached to a rigid wheel mounted on a carriage, and a data collection system. The soil layer was prepared at 7 mm in thickness and with a.6 void ratio by spraying airdried Toyoura standard sand into the soil bin. The weight of the wheel was 7 N and the peripheral speed was adjusted to. mm/s. Traveling was repeated * JSAM Member, Corresponding author, Faculty of Agriculture, University of the Ryukyus, Senbaru Nishihara Okinawa, 9, Japan ; khwantri@gmail.com * Faculty of Agriculture, University of the Ryukyus, Senbaru Nishihara Okinawa, 9, Japan

2 8 Engineering in Agriculture, Environment and Food Vol., No. () Table Experiment conditions at the ground contact surface of the wheel (hereafter Wheel type Rigid wheel with rubber referred to as GCSW). The range of analysis for soil deformation was from a depth of mm to 6 mm under the Wheel size mm diameter mm width original soil surface, and a width of mm centered on Peripheral speed. mm/s the centerline of the wheel. This area was divided into a Dynamic load 7 N x mm grid. Soil displacement of the nodal points of the Traveling Slippage 5%, % grid could be measured using the Particle Image Soil Airdried Toyoura sand Velocimetry (PIV) software. Void ratio.6 Thickness of soil layer 7 mm. Strain and void ratio calculation Number of repetition times in same direction Soil strain in the area analyzed was calculated by taking the linear functions of the displacement of three nodal times in the same direction. Test conditions are shown in Table. points as a finite element analysis. In the calculation of soil strain at the GCSW,. Analysis of soil deformation displacement distribution along the soil surface was The soil bin and wheel were of almost the same width in order to maintain plane strain conditions, and the wheel velocity was quite low. Therefore, movement of the soil particles was limited to two dimensions; that is, in the vertical and horizontal planes. To detect and record soil deformation, a series of pictures was taken from the side through a transparent acrylic wall in the soil bin with a digital camera (Nikon Dx) with resolution of. mm per pixel. The new system for visualizing soil deformation developed in our former study (Khwantri et al., 9) was applied. The series of photographs taken during the travelling of the wheel was then analyzed using an image processing technique. Displacement of the ends of acrylic wires were analyzed using Particle Tracking Velocimetry (PTV) software.. The displacement of the wire ends was regarded equivalent to the displacement of the soil particles necessary. Displacement of the nodal points, including the soil surface, was denoted as U j i, where i represents the wheel rotation step and j denotes the depth layer, j = ~6, and j= is the soil surface. Relative horizontal distance, D i, between the initial position of the acrylic wire or that of the node and the vertical centerline of the wheel was measured for each wheel rotation step. The soil layer depth was denoted as z j. Figure shows the displacement collecting system. U j i,was then rearranged in the D i z i space to indicate the change in soil displacement distributions with wheel rotation. Triangular meshes were set in the area analyzed using the displacement distributions at the GCSW and soil particles as shown in Fig.. Soil strains for each element were calculated using the FEM technique. Volumetric strain after the wheel travel was used for void ratio calculations. Volumetric strain and void ratio are regarded as indices of soil compaction. Figure shows a t t Wheel surface t t+ t U i D i+ D i D i U i Initial position of observed wire Soil surface U i+ i U U i U i+ j U i j U i U j i+ observed area of soil i : index of rotation degree of wheel j : index of depth of observed layer Fig. Displacement distribution of acrylic wire and soil and its notation

3 SAENGPRACHATANARUG, UENO, KOMIYA, TAIRA : Soil Deformation beneath a Wheel during Travel Repetition 8 j U i Triangle element of soil j U i+ Void ratio, e, was given by the initial void ratio e and the current volumetric strain ε v as follows: e = ( + e ε + e (5) v ) i j 5 Relative horizontal distance, D (mm) Fig. Measured displacements and triangular mesh for strain calculation flowchart of the deformation analyses. The following definitions were employed to calculate the normal, shear and volumetric strains: u ε x = () x v ε y = () y u v γ xy = + () y x ε ε + ε v = () x y j+ U i+ D i where ε x, and ε y represent normal strain in the horizontal and vertical directions, respectively, γ xy is shear strain, ε v is volumetric strain, and u and v are the horizontal and vertical components of soil displacement, U j i, respectively. Run traveling test III Results and discussion. Trajectory of soil displacement Trajectories of the acrylic wires and soil particles for the first travel of the wheel at % slip are shown in Fig. 5. The initial points of the wires and soil particles at 9 mm and 8 mm in depth were adjusted to form the origins of the coordinate system. The wires moved forward and upward during the approach of the wheel, and then turned forward and downward after they came into contact with the wheel surface, drawing a circular arc. Further, the direction of the movement vector changed to backward and downward, and the particle reached its lowest position when the center of the wheel was located directly above the particle. After the wheel passed, the particle was displaced backward and upward before finally coming to rest. The trajectories of the soil particles at 9 mm and 8 mm in depth showed similar movements and both drew circular arcs, but the radius of those arcs decreased with increased depth. These tendencies are similar to those reported in previous papers by the authors group (Fukami et al., 6). The values for maximum width of horizontal displacement, X max, and vertical displacement, Y max, were collected to analyze the properties of the trajectory circles at different depths, slip ratios and numbers of travel. The ratio Y max /X max was used to represent the deviation from a circle. A value larger than for Y max /X max indicates a vertical ellipse, while a value smaller than indicates a horizontal ellipse. Collect Relative distance, D i Collect depth of observed layer, z j Every degree of rotational wheel ; i Collect displacement of acrylic wire, U i Plot U j i in D i z j space Soil displacement distribution under wheel Make triangle element for calculate volumetric strain distribution of soil Collect displacement of soil at nodal points under acrylic wire, U j i (j = ) Characteristic of displacement trajectories of soil particle after repetition Y max X max 5 Horizontal displacement, U x (mm) Acrylic wire 9 mm 8 mm Vertical displacement, Uy (mm) Calculation of void ratio after repetition Fig. Data analysis flow chart Fig. 5 Trajectories of soil particle

4 8 Engineering in Agriculture, Environment and Food Vol., No. (). Displacement trajectories in repetition travel. At 5% slip Displacement trajectories for repetitions at 5% slip are shown in Fig. 6(a). The initial position for each of the acrylic wires during the first travel of the wheel was at the origin of the coordinate system. Those of the soil particles in soil layers at, 8,, 6, and mm in depth are shown at their respective depths in the figure. The final position of soil particles after the each travel was taken as the initial position for the subsequent travel. In the following travels, the trajectories drew similar circles thus forming a spiral pattern. In the first travel of the wheel, the deeper soil layers were compacted, and the size of the displacement trajectories decreased with increased depth. In the following travels, the size of the displacement trajectories decreased markedly compared with those for the first travel, especially in the deeper layers. In order to grasp the changes in trajectories, representative values for X max and Y max were plotted against the number of repetitions as shown in Fig. 6(b) and Fig. 6(c). Both X max and Y max in the deeper layers decreased exponentially with increased repetitions, whereas those in the shallower layers decreased only slightly. At the GCSW, X max and Y max were almost same regardless of repetition, and the X max /Y max ration increased within a narrow range, as shown in Fig. 6(d). The trajectory varied from a circle to a horizontal ellipse after the first travel. The values of X max and Y max at mm in depth decreased in a similar manner so that the value of X max /Y max increased slightly, but remained at around, thus maintaining a circular shape. Because the soil was strongly compacted down to the deep layers by the first travel, soil particles in the deep layers moved little in the subsequent travels. Therefore, the trajectories of the particles in the shallower layers became (a) st travel nd travel (b) Xmax rd travel th travel 8 Vertical displacement, Uy (mm Vertical displacement, Uy (mm) Displacement (mm) (c) Ymax Number wire of repetition mm mm (d) Xmax/Ymax Number of repetition Number of repetition Horizontal displacement, U x (mm) Fig.6 Displacement trajectories in the repetition at 5 % slip

5 SAENGPRACHATANARUG, UENO, KOMIYA, TAIRA : Soil Deformation beneath a Wheel during Travel Repetition 8 horizontal ellipses. Thus, at a small slip ratio, the effect of the first travel was relatively large, and that of each following travel was small.. At % slip The displacement trajectories at % slip are shown in Fig. 7(a). Large horizontal displacement occurred in the shallower layers, including the GCSW, with little vertical displacement. Thus, the spiral trajectories lengthened horizontally. The final positions of the soil particles in the shallow zone were slightly higher after each travel. These results show that the shallow soil layers were loosened by travel repetitions, which is contrary to that observed at 5% slip. On the other hand, the size of the trajectories was considerably decreased with increased depth and the final positions of the particles tended to be lower. The values of X max and Y max at the GCSW tended to increase with repetitions as shown in Fig. 7(b) and 7(c). The X max at mm in depth varied slightly, whereas Y max remained constant. On the other hand, the trajectories of the soil particles at mm in depth remained almost constant during the repetitions. The X max /Y max value in Fig. 7(d) remained high, which indicates a horizontal ellipse, with little change observed during the repetitions. Since, the changes in the size and shape of the soil displacement trajectories by repetitions were small, it could be concluded that the wheel caused a similar amount of compaction for each repetition at a high slip ratio.. Profile of the area of the displacement trajectory Since the size of the soil displacement trajectory was affected by several factors, particularly, depth of the soil (a) Vertical displacement, Uy (mm) st travel st pass nd travel nd pass rd travel pass th travel pass 8 Horizontal displacement, U x Ux (mm) (mm) Number Xmax wire Number wireof repetition mm of repetition mm mm Ymax p (b) 6 (c) Number of repetition Fig. 7 Displacement trajectories in the repetition at % slip Xmax/Ymax Number of repetition (d).5 6

6 8 Engineering in Agriculture, Environment and Food Vol., No. () Ellipse area of trajectory A (mm ) 8 6 (a) 5% slip (b) % slip st travel nd travel rd travel th travel Fig. 8 Ellipse area of soil displacement trajectory related with depth of soil layer layer, slip ratio and number of repetitions, the following equation for ellipse area A was used to represent the trajectory's size for describing the relation between the size of trajectory and those factors:: A πx Y max max = (6) Figures 8(a) and 8(b) show changes in the profiles of the area A according to depth, with an increase in depth producing an exponential decrease in the area A. In the first travel at 5% slip, the trajectory s area decreased rapidly from 7. mm at the GCSW to. mm at a depth of mm. After that, area A gradually decreased until it reached a minimum value at a depth of mm. There was a clear difference between the first travel and subsequent travels at 5% slip. After the second travel the area A became very small in middle and deeper layers; therefore, the changes in profiles showed a different trend to that of the first travel, as shown in Fig. 8(a). On the other hand, at % slip, the profiles were almost the same shape for all travels. The area A was increased by repetitions in the shallow layers. These results show that soil deformation due to repetition was relatively small compared to that for the first travel at 5% slip. Moreover, in order to grasp the influence of all the abovementioned factors on the soil deformation profile, the observed trajectory area was divided by the reference trajectory area to give the specific area, a n z.that is; n A a = (7) z where n z A n A is the area of trajectory at z mm depth for the z n th travel of the wheel, and A is that of the trajectory at the GCSW for the first travel. The values of a n z were arranged according to the number of repetitions, depth of the soil layer and slip ratio, as shown in Table. The value of a n was markedly increased with increases in repetition at % slip, whereas it was decreased at 5% slip. The increase in the specific area near the GCSW is caused by the disturbance of the soil structure and increased void ratio. 5. Changes in volumetric strain with travel repetition Distributions of volumetric strains for each travel at 5% and % slip are shown in Fig. 9(a) and 9(b), respectively The strains for each travel in the figure were calculated by subtraction from the last state in each travel except the n Table the specific area a z Traveling slip 5% % Repetition st nd rd th st nd rd th Shallow layer (The GCSW) Middle layer (8 mm depth) Deeper layer ( mm depth)

7 SAENGPRACHATANARUG, UENO, KOMIYA, TAIRA : Soil Deformation beneath a Wheel during Travel Repetition 85 first travel. Therefore, the strain represents the "strain increment" for each travel, not total strain, except for the first travel. Series colored red indicate a negative strain increment, which means the volume is decreasing, whereas those colored blue indicate a positive strain increment and, thus, that the is volume increasing. The isobars ranged from % to % at.% increments. The wheel expressed in the figure was at the final location of each travel, which was slightly raised on the soil surface. The red zone covered the shallow layers, whereas the blue, slightly increased region covered a wide area down to the deep layers for the first travel at 5% slip. The tangential stress given by the wheel rotation caused a change in volume known as dilatancy. The positive region gradually moved upwards with repetitions and was concentrated in shallow layers. In the deep layers, the volumetric strain turned from positive to negative with subsequent repetitions. This result shows that soil in the deeper layers was gradually compacted after the first travel. The compacted zone is spread far in front of the wheel, especially at mm to 5 mm length from the wheel axis. A similar tendency was observed in the rear of the wheel, except in the shallow layers. Large increases in volumetric strain occurred under the wheel at % slip. The area of this increase is clearly discernable in comparison with that for 5% slip, and it became shallower with travel repetitions. The surface layer near the GCSW was strongly compacted, whereas the soil was lifted upward in the shallow layers. The soil layer around mm in depth was again compacted. 6. Change in void ratio profile with repetition travel Void ratio profiles along the vertical centerline of the wheel at 5% and % slip are shown in Fig.. The increment of void ratio induced by each repetition was calculated using Eq. (5) from the volumetric strain increment. Figures (a) and (b) show the profiles at 5% slip and % slip, respectively. The change in void ratio at % slip was larger than that at 5% slip. At 5% slip, the value of the void ratio reached a maximum at mm in depth, and the minimum value occurred at a depth of mm. A similar tendency appeared even when the number of repetitions was increased. A small second peak was observed at mm in depth after the third travel. On the other hand, at % slip, the void ratio reached a minimum at mm in depth, and then increased to a maximum at a depth of 5 mm. Subsequently, st travel st travel. nd travel nd travel.... rd travel rd travel th travel th travel 6 6 Relative horizontal distance, D (mm) (a) 5% slip (b) % slip Fig. 9 Volumetric strain distribution of soil for each pass

8 86 Engineering in Agriculture, Environment and Food Vol., No. () void ratio, v void ratio, v st travel nd travel rd travel th travel 5 5 st travel nd travel rd travel th travel 5 5 (a) 5% slip (b) % slip Fig. Void ratio distribution of soil after wheel passed it decreased with depth until mm. The increase in the volume strain gradually moved downward until it reached the 5mm layer. The soil was compacted around a depth of mm. A similar trend was also observed after repetitions. The span of the void ratio observed at % slip was wider than that at 5% slip, and the void ratio at around mm in depth increased with repetitions. On the other hand, the negative peak at around mm in depth gradually increased with repetitions. It can be concluded that the repetitions at a high traveling slip ratio caused more deformation and compaction than those at a low slip ratio. IV Conclusions In order to clarify the progress of soil compaction due to the travel repetition of a wheel, the displacement trajectory of soil particles was analyzed, and the following results were obtained. ) The shape of the trajectories remained elliptical with subsequent repetitions, but their sizes varied according to the number of repetitions, depth and slip ratio. ) Soil particles drew a spiral trajectory with travel repetitions. ) At 5% slip, there was a clear difference in the compaction effect in the deep layers between the first and subsequent travels. On the other hand, at % slip, a similar trend in the profiles was observed throughout the repetitions. ) Soil near the GCSW was markedly raised at % slip, which indicates positive dilatancy. 5) The void ratio was increased in the shallow zone, particularly at % slip, but was decreased in the deeper zone. This tendency became more clearly defined with repetition. 6) It can be concluded that the repetitions at a high traveling slip ratio caused more deformation and compaction than those at a low slip ratio in deeper layer of soil. References Fukami, K., M. Ueno, K. Hashiguchi and T. Okayasu. 6. Mathematical models for soil displacement under a rigid wheel. Journal of Terramechanics :87. Khwantri, S., M. Ueno, Y. Komiya and E. Taira. 9. Measurement of soil deformation at the ground contact surface of a traveling wheel. Journal of Engineering in Agriculture, Environment and Food, Asian Agricultural and biological Engineering Association ():. Nohse, Y., K. Hashiguchi, M. Ueno, T. Shikanai, H. Izumi and F. Koyama. 99. A measurement of basic mechanical quantities of offtheroad traveling performance. Journal of Terramechanics 8():597. Shikanai, T., K. Hashiguchi, Y. Nohse, M. Ueno and T. Okayasu.. Precise measurement of soil deformation and fluctuation in drawbar pull for steel and rubber coated rigid wheels, Journal of Terramechanics 7():9. Wong, J. Y Behavior of soil beneath rigid wheels. Agr. Eng. Res. ():579. (Received:. January., Accepted: 6. April. )

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