土質材料におけるせん断帯の形態

抄録

The velocity gradient is discontinuous on the necking plane that forms a boundary between the shear band and its outside. On the other hand, a characteristic plane is the plane beyond which solutions cannot be extended without additional information, because some of the derivatives normal to the plane cannot be determined by their governing equations alone. Therefore, on the characteristic plane some derivatives of stress rates become indefinite and such property must be also required for the necking plane where some of the velocity gradients are discontinuous. We examine the mode of the characteristic plane in the well known Cam-clay model, which has only two modes under plane strain rate, that is, modes P and O. Mode N that the characteristic plane is a principal plane cannot be realized in non-cohesive soil. The angle between the shear band and the maximum compressive principal direction is predicted to be 45 degrees under plane strain compression when the hardening modulus h vanishes, though it is smaller than 45 degree at the dilatant state. On the assumption that plastic instability occurs when h=0, the predicted angle does not agree with the experimental result of about 30 degrees.