Model of rut formation on a linear strengthening soil under a periodic load

The aim of the study is to develop a mathematical model of rut formation on a forest soil, taking into account its partial elastic recovery with a decrease and removal of a periodic load, as well as its’ limited plastic deformations. The rheological model of the Bingham body was used as a theoretical basis for the development of the model. The numerical values of the model parameters are taken on the basis of the results of experiments to determine the mechanical properties of forest soils, carried out previously. To assess the limiting value of the model deformation, the results of previous studies were used to determine the rut depth basing on the methods of terramechanics and the theory of off-the-road locomotion. The proposed model was implemented in the Maple 2017 program; the solutions were obtained numerically by the Runge-Kutta method. The calculations show that the use of a variable plasticity limit, which increases in proportion to the deformation, makes it possible to take into account the limitation of the plastic deformations of forest soil, which qualitatively corresponds with the known experimental data. This distinguishes the proposed model from common elastic-viscous and elastic-visco-plastic models. In the future, the results obtained are planned to be integrated into mathematical models that reveal the dynamic effect of forestry machines on soils linked with vibrations during their movement, obstacles encountering, and trees processing. A separate area of further research consists in modeling the behavior of nonlinearly strengthening soil under the influence of forest machines.

1. Ageikin Ya.S. Passability of vehicles. M.: Mashinostroenie, 1981. 232 p. (In Russ.)

2. Khakhina A.M. Methods for forecasting and increasing the patency of wheeled forest machines : diss. ... Dr. Tech. Sciences: 05.21.01. SPb., 2018. 318 p. (In Russ.)

3. Khitrov E.G. Analysis of the components of the depth of the track formed under the influence of the propeller of the forest machine on the soil. Resources and Technology, 2019, vol. 16, no. 4, pp. 76–93. (In Russ.)

4. Khitrov E.G., Andronov A.V., Khakhina A.M., Grigorev G.V. Comprehensive assessment of the indicators of the interaction of machine propellers with forest soils based on the methods of the theory of traffic in off-road conditions. Resources and Technology, 2021, vol. 18, no. 1, pp. 1–52. (In Russ.)

5. Khitrov E.G., Kotenev E.V., Andronov A.V., Chzhan S.A., Nikiforova V.A. Environmental studies and certification issues of forest machine propellers. Sistemy. Metody. Tekhnologii, 2020a, no. 2 (46), pp. 100–105. (In Russ.)

6. Khitrov E.G., Andronov A.V., Khakhina A.M., Grigorev G.V. Mathematical models of the interaction of machine propellers with soils. Resources and Technology, 2020b, vol. 17, no. 4, pp. 15–64. (In Russ.)

7. Khitrov E.G., Andronov A.V., Martynov B.G., Spiridonov S.V. Interrelations of various soil types mechanical properties. Journal of Physics: Conference Series, 2019, pp. 012032.

8. Lukhminskii V.A. Improvement of models and methods for predicting the patency of caterpillar forest machines : diss. ... Cand. tech. Sciences: 05.21.01. SPb., 2018. 179 p. (In Russ.)

9. Peskov V.B. Improvement of models for assessing rutting and soil compaction under the influence of propellers of wheeled forest machines : diss. ... Cand. tech. Sciences: 05.21.01. SPb., 2018. 190 p. (In Russ.)