Conclusion
This paper presented a methodology to measure the natural frequency of monopiles in centrifuge tests for loose and dense sand in wellcontrolled conditions and compared the results with theoretical solutions. The experimental results show that the fixity provided by the pile has a large effect on the natural frequency of the system, although for many geometries tested here the length of the piles was sufficient that increasing pile length had only a modest effect on the natural frequency. The frequencies observed were, however, lower than those of the fixed base structure, a point of fixity existing beneath the soil surface leading to an increased cantilever length and thus a reduced natural frequency. The ratio of free length and embedded depth (LT/LP) was also investigated. Only two different free lengths were used, and it is clear that the natural frequency changes inversely to the free length. For the same free length (LP =10 m), the natural frequency and fn/fn-str increase when the embedded depth increases (or LT/LP decreases). Although the relative densities of the two sand samples are very different, the data show only small differences in the natural frequency obtained, possibly due to the conflicting effects of increased stiffness but also increased added mass from the participating soil. Small-scale tests under 1 g conditions were also performed using the same models, sand conditions, and other variables. When comparing the response, the low stress level of the 1 g tests reduced the soil stiffness while the pile stiffness was maintained. The experimentally observed dynamic response illustrates this difference with the fn measured in the centrifuge scale model being higher than that 1 g, the variation not being a constant or following a well-established correlation.