Spatial distribution of Winkler spring stiffness for rectangular mat foundation analysis

Structural design of mat foundations of buildings is often done by performing static analysis of a slab resting on vertical uncoupled Winkler springs. It is already well established that the simplifying assumption of a uniform modulus of subgrade reaction throughout the mat foundation leads to inaccurate results that significantly underestimate the bending moments in the mat. This paper examines the spatial variation of the Winkler spring stiffness constants that is necessary for the mat-on-springs analysis to produce the same slab deflections and bending moment diagrams as finite element analysis that treats the soil as continuum. For this purpose, three-dimensional parametric analyses of slabs resting on elastic soil are performed using the finite element method for various values of soil elastic properties, slab geometrical characteristics and column load configurations. The finite element analysis results were used for back-calculating analytically the equivalent Winkler spring constants at each node of the mat. Based on the numerical results, equations describing the spatial distribution of spring stiffness are proposed. The performance of the proposed equations is compared against existing spring stiffness spatial distribution approaches used in practice.