An approximate method for soil‐structure interaction for sh‐waves—the born approximation

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Abstract
An approximate method is proposed for the scattering of SH‐waves by foundations of irregular shape and the resulting soil‐structure interaction problems. The scattering of elastic waves by the rigid foundation embedded in half‐space is solved approximately by using integral representation of the wave equation. The procedure is the Born approximation which has been widely used in quantum mechanics for collision and scattering theory though not well‐known in elastodynamics. This paper extends the previous work of the authors on the scattering of waves to account for soil‐structure interaction. The motion of the foundation is evaluated by the balance of momentum under stresses due to the incident waves as well as the waves generated by its own motion and the forces coming from the superstructure. The model investigated consists of an infinitely long elastic shear wall of height H and thickness h erected on a rigid infinitely long foundation. Results are presented for the cases with circular, elliptical and rectangular foundations. For a circular foundation, excellent agreement is found with the exact solutions for the foundation displacement and the relative displacement between the top and bottom of the structure for the entire range of wave numbers. For an elliptical foundation, accuracy decreases with increasing wave numbers. Foundation displacements are compared for foundation shapes that are shallow elliptical, deep elliptical, rectangular and circular. It is observed that foundation displacements are dependent on the angle of incidence except for a semi‐circle. The results on the details of the scattered field are, however, not as accurate.

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