Dynamic Soil Reaction to Axially Loaded Piles

The dynamic soil‐reaction characteristics of axially loaded single piles are studied numerically to find simple and rational numerical models for beam‐on‐Winkler foundation‐type analyses of axially loaded single piles. The proposed dynamic $t‐z$ and $Q‐z$ models are shown to yield reliable pile responses for a variety of soil‐pile and loading conditions. One of the convenient features of the models is that they can be easily incorporated into both frequency‐ and time‐domain analyses. Therefore, the proposed models can be extended to problems with nonlinear soil‐pile interaction effects, even though the models are based purely on linearly elastic soil‐pile conditions. The proposed models may be utilized in a variety of problems. For static applications, the models can be used to improve the reliability of existing static $t‐z$ and $Q‐z$ relations at small pile settlements. For dynamic problems, the models can be used to predict the axial responses of dynamically loaded pile foundations.