Analytical solution for ductile and FRC plates on elastic ground loaded on a small circular area

The problem of an infinite FRC slab resting on a Winkler-type elastic foundation and subject to a transversal load distributed over a small circular area is investigated in the present work. The mechanical behavior is described by the Kirchhoff theory of elastic-perfectly plastic plates obeying Johansen\u2019s yield condition and associative flow rule. The governing equations within both the inner elastic-plastic circular region near to the loaded area and the outer elastic region are found in terms of the transversal displacement and solved in closed form. After the formation of radial positive yield lines, namely cracks at the bottom side of the slab, the onset of a circumferential crack at the top of the slab defines its load-carrying capacity. Two possible configurations are envisaged, depending on whether the circumferential crack occurs within the inner elastic-plastic region, where radial cracks take place on the bottom side, or the outer uncracked elastic region. The ratio between the subgrade modulus and flexural rigidity of the plate allows introducing a characteristic length. The influence of both material and geometrical parameters on the ultimate load is then investigated. Based on the analytical results, a simplified method for the calculation of the load-carrying capacity of FRC slabs on grade is also proposed and compared with previously developed models