Torsional radiation damping of arbitrarily shaped embedded foundations

Radiation damping of torsionally oscillating, arbitrarily shaped rigid foundations embedded in linear hysteretic homogeneous soil is studied parametrically with a rigorous boundary element formulation. A simplified analytical model, based on sound physical approximations and calibrated against the numerical results, is also developed. The basemat shapes studied include rectangles of aspect ratios up to 6, circles, triangles, and T-shapes. Particular emphasis is placed on the effects of the depth of embedment and the extent of contact between sidewalls and surrounding soil. It is shown that even foundations placed in an open trench, without sidewall-soil contact, radiate energy more effectively than surface foundations with an identical basemat. Additional radiation damping is generated from vertical side-walls, even if they are in good contact with the soil only over a small height compared with the embedment depth; hence, separation or slippage between sidewalls and soil near the ground surface would not substantially affect the amount of torsional damping. Physical arguments are put forward to explain these findings and develop insight to the problem. The paper concludes with an illustrative numerical example.