Predicting wheel forces using bearing capacity theory for general planar loads

Abstract

This paper assesses the applicability of bearing capacity theory for evaluating the forces generated on wheels operating on clay under steady rolling conditions. Considering recent advances in bearing capacity theory, namely with respect to the interaction diagrams developed for general loading, a theoretical model for computing the horizontal force or torque from fundamental input parameters such as the vertical force (weight), wheel diameter, and undrained shear strength of the soil is presented. The predictions are compared with existing analytical solutions and data from laboratory testing, and reasonable agreement is demonstrated. The foremost conclusion is that bearing capacity theory can be used to obtain reasonable predictions of wheel forces analytically under any operating condition (driven, braked, or towed), provided the contact length and so-called contact angle, which defines the position of the contact interface, can be estimated. Aside from providing a rigorous and highly convenient framework for evaluating wheel forces under arbitrary loading, the analysis enables a natural physical interpretation of the mobility problem.