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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 FEmethod and BDWF solution. It employs the soil-displacement-influence coefficients Is to consider the pile-soil interaction (resembling the spring constant kx in the BDWF) and provides conservative estimations of maximumkinematic bendingmoments 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-displacementinfluence coefficients Is for such cases with Vb [ABSTRACT FROM AUTHOR]

Based on the hypothesis that the penetration of a single pile can be simulated by a series of spherical cavity expansions, this paper presents an analytical solution of cavity expansion near the sloping ground. Compared with the cavity expansion in the half-space, the sloping free boundary has been taken into account as well as the horizontal free boundary. The sloping and horizontal free surfaces are considered by the introduction of a virtual image technique, the harmonic function, and the Boussinesq solution. The results showthat the sloping free boundary and the variation of the inclination angle have pronounced influences on the distribution of the stress and displacement induced by the spherical cavity expansion. The present solution provides a simplified and realistic theoreticalmethod to predict the soil behaviors around the spherical cavity near the sloping ground. The approach can also be used for the determination of the inclination angle of the slope according to the maximum permissible displacement. [ABSTRACT FROM AUTHOR]