Variable Modulus of Subgrade Reaction - Settlement Profile Convergence Method

The modulus of subgrade reaction (Ks), is a commonly used parameter for a mat foundation analysis. But, it is not one of the basic soil properties and depends on many parameters including soil stiffness, foundation stiffness, foundation shape, size etc. Researchers and engineers agree that the general practice of using a constant modulus of subgrade reaction, is over simplified and may produce erroneous results. In fact, assumed contact pressure distribution may vary significantly from the actual one and shows a considerable spatial variation [8]. However, due to the non-availability of any standard method, engineers tend to avoid a proper distribution of the modulus of subgrade reaction. A proper distribution cannot be assumed or pre-calculated, rather it must be a result of a soil-structure interaction analysis.

This paper proposes an automated method to accurately distribute subgrade modulus. It is an iterative solution, and relies on the convergence of displacement profiles of two successive analysis. Any of the standard equations can be used to calculate soil stress and the corresponding settlement at any point of the mat. First iteration of Ks at a given point is then estimated as the ratio of soil stress to the settlement. The solution will then iterate and calculate new sets of Ks after each successful analysis by dividing the base pressure with the displacement. A few case studies have been presented to verify the effectiveness of the proposed method. As expected, resulting distribution of the subgrade modulus shows a spatial variation. Also, the vertical displacement diagram of a mat under uniformly distributed load, takes the shape of a bowl. Another case study is done to understand the effect of foundation stiffness. It shows changes in contact pressure due to the change in foundation thickness. A flow-chart has been provided to help create a computer program.