Modeling of Beams on Reinforced Granular Beds

The paper describes a mechanical model for estimating the flexural response of a strip footing, supporting a column (imposing a concentrated load), resting on a compacted granular bed overlying a reinforcement layer for example, geogrids, geomats etc. below which lies a loose soil deposit. The footing is idealized as a beam and the reinforcing element is assumed to have finite bending stiffness and negligible frictional resistance. The upper and lower soil layers are idealized by a series of linear and discrete springs (Winkler springs) of different stiffness values. To find the response of such a model the governing differential equations have been derived and expressed in a nondimensional form. A closed form analytical solution of the same has been obtained subjected to appropriate boundary conditions. Using the present approach the resulting solution for a degenerated case of a long beam is found to be identical to the same of Hetenyi (1946, Beams on elastic foundations, University of Michigan press, Ann Arbor, MI). Parametric studies reveal that the ratio of flexural rigidity of upper and lower beam and the ratio of stiffness of the upper and lower soil layers affect significantly the response of the foundation.