This paper presents a theoretical evaluation of the axial stiffness characteristics of elastic rods partially embedded in elastic media. The novel analytical - numerical technique is based on an energy or variational scheme in which the deformation of the bar is specified by a function, which is indeterminate to within a set of unknown constants. A minimization of the potential energy of the bar - elastic medium system is used to determine these arbitrary constants. The numerical results presented illustrate the influence of the relative flexibility of the bar, its length-to-radius aspect ratio, etc. on its axial stiffness.

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Journal Canadian Journal of Civil Engineering
Selvadurai, A.P.S., & Rajapakse, N. (1990). Axial stiffness of anchoring rods embedded in elastic media. Canadian Journal of Civil Engineering, 17(3), 321–328.