A Theoretical Study of the Soil Cutting Resistance Based on the Upper and Lower Bound Theorems

摘要

Cutting resistances acting on flat soil cutting blades were calculated based on the plasticity theory. In this paper, a calculation scheme for estimating a rational cutting resistance by combining the slip line method (SLM) and the upper bound method (UBM) is presented. Geometrical configurations of stress characteristics described by SLM were assumed as the failure mechanism for calculation schemes in UBM. Since it can be considered that a solution obtained by SLM belongs to a lower bound solution, an exact solution must lie between each solution derived from UBM and SLM, respectively. Accordingly, if the difference between the results obtained for each solution is small, an exact solution of cutting resistance can be estimated rationally. As the result of the calculations, the proposed method is feasible when the angle of internal friction of soil, Φ is comparatively small, but as for Φ ≥ 30 deg, the upper bound value drastically increases and the range where the exact solution can take spreads greatly.