Modeling of soil displacement and soil strain distribution under a traveling wheel Khwantri Saengprachatanarug a,⇑ , Masami Ueno b,⇑ , Eizo Taira b , Takashi Okayasu c a Department of Agricultural Engineering, Faculty of Engineering, Khon Kaen University, Muang, Khon Kaen 40002, Thailand b Faculty of Agriculture, University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213, Japan c Faculty of Agriculture, Kyushu University, Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan Available online 15 August 2012 Abstract The empirical Gaussian-based mathematical model of the soil displacement increment under a traveling wheel was extended to be applicable to any depth of soil layer under the ground contact surface of the wheel. The unknown coefficients were obtained by least mean-square fitting with the soil displacement curve measured through a sophisticated laboratory soil bin test. Those coefficients were then re-derived as a function of depth. The movement of soil particles at the ground contact surface was modeled by dividing movement into two kinds; first, the free movement of soil particles before contact with the wheel and the movement of the particles after they are separated from the wheel surface and, second, soil movement during attachment to the wheel surface. By combining the models for the ground contact surface of the wheel with that for all soil layers, an extended model that can describe soil displacement increment in both vertical and horizontal directions using one equation was established. The predicted results obtained using the extended model fitted quite well with the measured values. The predicted strain increment distributions also show the same trends as the measured distributions. Ó 2012 ISTVS. Published by Elsevier Ltd. All rights reserved. Keywords: Soil displacement; Mathematical model; Soil bin test; Soil strain 1. Introduction Studies on soil deformation and soil compaction can be generally classified into three groups; those based on numerical analysis, those based on field experiments, and those based on laboratory experiments. First, among those based on numerical analysis, there have been many attempts to simulate the traveling phe- nomena, including soil deformation, by Finite Element Method (FEM), Distinct Element Method (DEM), and combined FEM/DEM. Some of these methods have pro- gressed to high level analyses. However, soil deforms with strong non-linearity between stresses and strains, so that there is no satisfactory practical solution. Moreover, it is difficult to verify the solutions due to a lack of accurate experimental data for comparison. For those based on field experiments, the SST/DST method is the most widely used, such as in Horn’s [1] study on changes in the physical properties of soil due to heavy forestry vehicles. In this method the Soil Stress Transducer System (SST) is connected by a rigid tube to the displace- ment transducer system (DTS) and placed deep under the traction line of a traveling roller. In addition, the rut depth probe is connected in the same way for measuring soil deformation at the surface. The complete system is sup- ported on a suspending frame with fixed point of rotation with uniball bearings which allow free movement of the SST and sinkage probe on two axes; the horizontal and vertical. Thus, the vertical and horizontal displacement of 0022-4898/$36.00 Ó 2012 ISTVS. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jterra.2012.06.001 ⇑ Corresponding authors. Address: Khon Kaen University, Faculty of Engineering, 123 Nai Muang, Muang, Khon Kaen 40002, Thailand. Tel./ fax: +66 043 362 148 (K. Saengprachatanarug), Tel.: +81 098 895 8769; fax: +81 098 898 8770 (M. Ueno). E-mail addresses: khwantri@kku.ac.th, khwantri@gmail.com (K. Saengprachatanarug), ruenom@agri.u-ryukyus.ac.jp (M. Ueno). www.elsevier.com/locate/jterra Available online at www.sciencedirect.com Journal of Terramechanics 50 (2013) 5–16 Journal of Terramechanics