The resistance of a soil layer to steady horizontal vibration of an elastic pile is theoretically investigated. The pile is assumed to be vertical and of circular cross-section. The soil is modelled as a linear viscoelastic layer with hysteretic material damping. A closed form solution is obtained for the resistance of the soil layer to the motion. This resistance depends on shear modulus of soil, frequency, pile slenderness, material damping and Poisson's ratio. A parametric study of the effect of these parameters is included. The soil layer resistance is expressed in a form which can be used directly in the solution of the soil-pile interaction problem which is treated in a subsequent paper. The approach also applies for rigid deeply embedded footings.
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