Using Finite Element to Modify Winkler Model for Raft Foundation Supported on Dry Granular Soils

Winkler foundation is a traditional model that is usually adopted in structural engineering to simulate the stiffness of underneath soil as decoupled springs with spring constant determined based on plate load test or based on a correlation with soil bearing capacity. This model leads to a fourth order differential equation. Analytical methods are usually adopted to solve the differential equation for regular loads and ideal boundary conditions while numerical methods, finite difference or finite element, are used to solve it for general loads and/or complex boundary conditions. The main drawback of Winkler model is neglecting or at best implicitly including, when spring constant is determined from correlation with soil bearing capacity, the interaction between adjacent soil prisms. This is in contrast with soil models adopted in geotechnical engineering which recognize soil shear strength and shear interaction between adjacent soil prisms. An abrupt change in soil subgrade reaction is usually seen under concentrated loads when using Winkler foundation and this change may be greater than the allowable soil capacity. With this situation, it is hard to compare the global behavior simulated by soil bearing capacity with the local behavior in the neighborhood of point loads. In this paper, raft foundations with regular columns arrangement, and supported by different underneath cohesionless dry soil profiles have been simulated using traditional Winkler foundation model and 3D finite element models. Linear regression models have been adopted to modify the results of Winkler model to take into account the aforementioned parameters. With these modifications, designers can preserve the benefits of Winkler foundation model, usually available in commercial software, while overcoming its drawbacks. Linear regression analyses applied on the results obtained from the two models show that two soil simulations are significantly correlated with correlation factors in the range of 0.9. The explanatory parameters adopted in regression analysis were raft dimensions, raft thickness, and material properties for both soil and concrete.