Modeling wheel-induced rutting in soils: Rolling J.P. Hambleton, A. Drescher * Department of Civil Engineering, University of Minnesota, 500 Pillsbury Drive SE, Minneapolis, MN 55455, USA Received 17 June 2008; received in revised form 19 February 2009; accepted 25 February 2009 Available online 3 April 2009 Abstract Theoretical models for predicting penetration of non-driving (towed) rigid cylindrical wheels rolling on frictional/cohesive soils are presented. The models allow for investigating the influence of soil parameters and wheel geometry on the relationship between the inclined rolling force and wheel sinkage in the presence of permanently formed ruts. The rolling process is simulated numerically in three dimensions using the finite element code ABAQUS. The numerical simulations reveal that the advanced three-dimensional process of rutting can be regarded as steady, and an approximate analytic model for predicting sinkage under steady-state conditions, which accounts for three-dimensional effects, is also developed. The differences between wheel rolling and wheel indentation (considered in a separate paper) are discussed. Numerical and analytic results are compared with test results available in the literature and obtained from preliminary small-scale experiments, and general agreement is demonstrated. Ó 2009 ISTVS. Published by Elsevier Ltd. All rights reserved. 1. Introduction Models for predicting soil rutting induced by a rolling wheel can be used to determine the impact of off-road vehi- cles (ORVs) in sensitive natural areas (cf. [1]), assess mobil- ity of ORVs in adverse terrain, and facilitate methods for evaluating in situ soil properties premised on relating rut depth to material strength parameters [2]. Formation of permanent ruts by the rolling wheels of ORVs presents a particularly complex and challenging problem when ana- lyzed within the framework of mechanics. The primary rea- son is that rutting is a result of a process rather than a particular state of loading, with the latter often being suf- ficient in the study of geomechanics problems. When rut- ting occurs, the soil undergoes a loading–unloading sequence resulting from wheel contact that ultimately induces extremely large and inherently three-dimensional deformation. In a separate paper [3], the initial phase of rutting was modeled as an indentation process in which the wheel dis- places normally into the soil without rotation or horizontal (i.e., longitudinal) translation of the wheel. This paper is dedicated to modeling the formation of a rut in the process of a wheel rolling on soil and, in particular, the advanced phase when the process can be regarded as steady. In the steady configuration, stresses and the velocity field when measured with respect to the wheel do not change with time. Both papers have their origin in the exploratory work presented in [2,4] and complement numerous monographs and papers in the literature on the subject (e.g., [5–13]). All phases of rutting are considered here as quasi-static, which is acceptable for wheels traveling with slow or mod- erate velocities. The modeling is further limited to non- driving wheels, which do not transmit a torque. Non-driv- ing wheels include the front wheels of many vehicles and wheels of towed equipment. This assumption simplifies the analysis, whereas slip and erosion induced by driving wheels complicates the problem significantly. The most essential characteristic of wheel-induced rut- ting is the three-dimensionality of the deformation field, which involves only one plane of symmetry parallel to the midplane of the rolling wheel. The deformation field depends on the type of soil and its previous loading history, which affect possible soil distortional and volumetric 0022-4898/$36.00 Ó 2009 ISTVS. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jterra.2009.02.003 * Corresponding author. Tel.: +1 612 625 2374; fax: +1 612 626 7750. E-mail addresses: [email protected] (J.P. Hambleton), dresc001@ umn.edu (A. Drescher). www.elsevier.com/locate/jterra Available online at www.sciencedirect.com Journal of Terramechanics 46 (2009) 35–47 Journal of Terramechanics
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