A simple approach is formulated to predict the elastic, kinematic pile bending during harmonic or transient excitation for a circular pile (rather than a simplified thin strip). The kinematic response of a pile embedded in two-layer soil is resolved in the frequency domain caused by the upward propagation of shear waves from the underlying bedrock. The simplified approach is generally valid to nonhomogeneous soil profiles, in light of the good comparison with the dynamic FE method and BDWF solution. It employs the soil-displacement-influence coefficients to consider the pile-soil interaction (resembling the spring constant in the BDWF) and provides conservative estimations of maximum kinematic bending moments at the soil-layer interface (with a sharper stiffness contrast). The accuracy of the approach may be improved by incorporating the interaction of soil into the soil-displacement-influence coefficients for such cases with .
"Simplified Boundary Element Method for Kinematic Response of Single Piles in Two-Layer Soil." J. Appl. Math. 2013 (SI13) 1 - 12, 2013. https://doi.org/10.1155/2013/241482