A Simple Closed-Form Solution for Backcalculating Dynamic Foundation Coefficients

A number of dynamic rigid pavement models rely on a damped Winkler-type foundation for characterizing the soil support. While the static subgrade modulus can be determined from existing backcalculation procedures, researchers have typically picked an arbitrary value for the damping ratio. This approach cannot be used for a realistic characterization of a specific subgrade soil condition in a particular site. In fact, for certain site conditions, it may lead to a completely erroneous characterization of foundation support. This paper presents a simple and rational method for backcalculating the dynamic subgrade stiffness and damping coefficients from Falling Weight Deflectometer (FWD) deflection basins. The method can also be used to detect a stiff layer underneath the pavement system. The method consists in first decomposing the transient deflection signal of each sensor into a series of harmonic motions using Fast Fourier Transform (FFT) algorithm. Then, for each frequency of interest, the real and imaginary components of the displaced volume underneath the slab are calculated from the complex deflection basin. The dynamic force- displacement relationship is decomposed into real and imaginary parts, leading to a simple system of equations that can be easily solved for k and c. The method was verified for different soil profiles using both analytical and experimental results. The analytical verification used results from 3-D finite element analysis. The experimental verification used results from deflection measurements on airfield and highway pavements obtained with the WES vibrator and MDOT Falling Weight Deflectometer, respectively. The results showed very good agreement.