The Effect of the Variation of the Modulus of Subgrade Reaction on the Design of Large Shallow Foundations

Abstract

The design of mat foundations is a common application of soil-structure interaction. In a typical mat foundation design, the structure element (mat) is modeled as either rigid or flexible plate overlying an elastic subgrade. The founding terrain is generally modeled by a coefficient of subgrade reaction (ks) introduced by Winkler in 1867. The coefficient of subgrade reaction is highly influenced by the deformation parameters of the founding terrain, the load magnitude and the load geometry/characteristics. Difficulties in estimating these parameters raise the uncertainty in the values of the modulus of subgrade reaction which lead most designers to consider a uniform coefficient of subgrade reaction under shallow foundations, irrespective of their size or geometry. However, this assumption has negative consequences on the accuracy of the results which are assessed in detail in this study. In 1995, the American Concrete Institute (ACI) published a State-of-the-Art Review on Design and Performance of Mat Foundations (Special Publication SP-152) in which various aspects of foundation modeling are addressed, including the coefficient of subgrade reaction. An iterative procedure, known as the Discrete Area Method, was recommended to promote the consideration of variable ks values along the mat foundation. The effect of the variability of ks along the same raft on steel reinforcements is investigated while taking into consideration other aspects such as mat rigidity and soil/rock modulus values. With the use of variable coefficient across the mat foundation, a significant decrease in the steel reinforcement is witnessed and an optimized/ more adapted steel distribution is observed.