Footing Vibration with Nonlinear Subgrade Support

Most theoretical procedures now available for design and analysis involve only linearly elastic subgrade resistance; in many structures such a representation is quite satisfactory, and the most rational theoretical approach at present is the elastic half-space representation. To study the effect of nonlinear subgrade resistance on the motions of a foundation undergoing harmonic vibration, a single-degree-of-freedom model was developed which in the elastic domain exhibited the same type of motion as the elastic half-space approach. Two types of nonlinear sub-grade resistance were studied. Since the analysis of the nonlinear vibration system is not a straightforward procedure, the results have been presented in a dimensionless form to make them of practical use. Comparisons with field data are presented, and the response was more closely represented in terms of shift of resonant frequency and shape of the response curves through use of the nonlinear hyperbolic tangent resistance than by a linearly elastic resistance. Use of the model for practical situations involving linear or nonlinear subgrade resistance, and for scaling between different size footings is presented.