Mathematical models for soil displacement under a rigid wheel

Soil–wheel interaction especially soil deformation caused by the wheel motion was investigated experimentally using a sophisticated soil bin test apparatus and an on-line measurement system for soil displacement. Based on these test results, characteristics of soil deformation were summarized focusing on the behavior and distribution of displacement increment vectors. Mathematical models were examined in order to describe the displacements of soil particles. Properties of the displacement loci are described. The magnitude of the displacement increment vector, its horizontal and vertical components are discussed, and characteristics of these distributions with respect to the relative horizontal distance from the vertical centerline of the wheel to the target point are clarified. Shapes of these distribution curves were closely similar to those of the derivatives of a Gaussian function. A distribution curve of the horizontal displacement increment had two peaks and that of the vertical one had three peaks. Based on the results, mathematical models for those displacement increments were proposed by employing a Gaussian function through multiplication of a linear function and a quadratic function. Predicted distributions and displacement loci of the models agreed with high accuracy to the measured values. The mathematical models were extended taking into consideration the wheel slip. The predicted distributions according to test conditions agreed very well to the measured results.