Kinematic Winkler modulus for laterally-loaded piles

Beam-on-dynamic-Winkler-foundation models are widely used to study kinematic soil-pile interaction. Winkler models consider the pile as a flexural beam and simulate the restraining and dissipative action of soil through independent springs and dashpots along its axis. Their performance is related to the proper selection of the spring stiffness and dashpot coefficient which depends on parameters such as pile geometry, pile-soil stiffness ratio and boundary conditions. Expressions for static and dynamic Winkler moduli from literature were implemented in a Winkler model to assess its ability to predict the curvature ratio and kinematic response factors for various pile boundary conditions. Based on an existing static expression, a frequency-dependent, logarithmic-based Winkler modulus is proposed. This modulus offers an attractive and versatile alternative to existing mathematically complex formulations as it is capable of capturing resonant effects and can be used for both inertial and kinematic analyses, while all other frequency-independent expressions from literature are limited by their unique application to kinematic problems. A comprehensive graphical comparison is given between the results from the Winkler model, using existing and proposed moduli, and the more accurate FE solution to guide the user in selecting the most appropriate modulus for the problem to be analyzed.