Incipient plane-strain failure of a rectangular block under gravity

We consider the problem of the incipient plastic failure of a two-dimensional rectangular block of yield stress material under plane strain conditions and gravitational loading. The block is assumed to behave as a perfectly rigid-plastic material obeying the Tresca yield condition. There is no traction on the vertical sides and horizontal top, and the traction at the base is determined via a modifed Coulomb-type friction. We use slip-line field theory to calculate the stress field. Our analysis establishes the dimensions of the block which give incipient failure and also suggests a way of determining the yield stress. Furthermore, we show that the precise value of the coefficient of friction on the base can be unimportant in certain situations.