On the diagram of reaction pressures under the base of a rigid foundation

Abstract

The diagram is approximately determined, of the reaction pressure on the base of a rigid shallow foundation (loaded by a centered load and the boundary between the elastic and plastic zones in a compact sand bed), and the plane problem is examined. The conditions and assumptions under which the problem is solved are: a centered load acts on a rigid shallow foundation; the foundation base is rough; along the line of contact and the sand bed and the foundation u=const and v=o, where u and v are the vertical and horizontal displacements respectively under the foundation base; the plastic zones of the bed the displacement trajectories of the soil particles coincide with the slip lines; directly under the entire foundation base under any load there is an elastic stressed state in the bed; the boundary between the elastic and plastic zone of the bed under the edge of the foundation has two sections (section OA and the section ODC-illustrated); along both sides of the boundary in section OA all three components are mutually equal, whereas along both sides of the boundary in section ODC the normal and tangent to the boundary of the stress components are mutually equal; the slip lines of one of the families in the plastic zone of the base are directed vertically upon approaching the section of the boundary OA. Details are given of the determination of the loads on the bed, the stress components at any point of the elastic zone, the boundary between the elastic zone and the plastic zone, the values of the components of the plastic stresses at this boundary, and of the load coefficients.