Two-Dimensional Cutting Theory of Soils

Abstract

The mechanical proprieties of the slip line fields proposed by many workers for two-dimensional cutting process were examined, considering not only the stress states but the deformation states. Then Kudo's slip line field for metal machining with long cutting blade, which was acceptable for an upper bound solution, was extended for frictional soils and, hence, cutting resistance based on this field was calculated (Fig, 8(a)-(e)). By this calculation, the following results were obtained.
1. For the fixed value of cutting angle r, the effects of the parameters φ′ (external friction angle between soil and blade), φ (internal friction angle of soil) and c′/c (ratio of adhesion to cohesion) on the specific cutting resistande r_c are larger than the others in order.
2. The larger φ′, the larger is the effect of φ on r_c.
3. The smaller r is, the larger the effect of φ on r_c is.
4. For the fixed values of r, φ′ and c′/c, the relation between φ and r_c is nearly exponential.
5. The larger c′/c is and the smaller r is, the larger the ratio of increment of upper limit of r_c to that of φ is.
Furthermore, comparing the above theoretically calculated values with the experimental values reported by the other workers, they have qualitatively the same trend (Fig. 9 and 10). In general, however, the theoretical values are larger than the experimental values. This may be due to the fact that slip line solutions, free body solutions and some other recent solutions are all based on Coulomb's law for perfectly plastic material. Hereafter more accurate theories which are free from the excess limit conditions such as Coulomb's law and take account of the effect of soil weight should be established.