Examining $k\text{-}E$ Relationship of Pavement Subgrade Based on Load-Deflection Consideration

Most rigid-pavement design methods in use today adopt the Westergaard’s approach that characterizes pavement foundation by $k$ , the modulus of subgrade reaction. $k$ is measured by a standard plate loading test conducted in the field. However, since this test is elaborate, expensive, and time consuming, the $k$ value of a subgrade soil is usually estimated from other soil properties. In this regard, the relationship between $k$ and the modulus of elasticity $E$ of the soil is of special interest. This is because $E$ is a fundamental engineering property and that there exists various test methods for determining $E$ either in the field or in the laboratory. This paper proposes a procedure to estimate $k$ from $E$ by establishing an equivalency between two theoretical pavement models, a model of pavement slab supported by an elastic solid foundation (termed the $E$ model) and a model of pavement slab supported by a dense liquid foundation (termed the $k$ model). Instead of matching the $k$ and $E$ models directly as is done in currently available $k\text{-}E$ relationship models, this study proposes to define an equivalent $k$ model and an equivalent $E$ model, separately, with respect to actual rigid pavements. The equivalency is established using back-calculation analysis based on load-deflection considerations. Using the deflection test data of the long-term pavement performance database, it is found that there exists a relationship between the radii of relative stiffness of the two theoretical systems, and this relationship can be used to estimate $k$ from a given $E$ value.