| The design of tower structures foundation is more complicated than common structures, and it is difficult to study tower structure mechanical durability and diagnose its defects. The foundation stiffness or its load bearing capacity is not only the major index for design, but also the main goal to diagnose a tower's defects. In order to acquaint the behavior of a tower foundation, it is important to identify the restraints stiffness of a tower foundation. Over a long period of time, approximate method of soil mechanics has been used as the main way to design and analyze dynamic behavior of a foundation. But it is difficult to determine statistical parameters in this approximate method for they distribute complex, and would change with time and geological condition in various areas.Basic theory of tower was investigated thoroughly in this paper. Then approximate formulas to calculate fundamental frequency of tower structures were obtained by combining Rayleigh and Southwell's methods. Fundamental frequency of tower structure was presented as a composition of frequencies of several subsystems, which consisted of a deformation component and an inertia component. Deformation components include deformation, flexural deformation and shear deformation of upper structure, while inertia components include distributed mass of a tower and concentrated mass on its top. Influence of factors on fundamental frequency such as tapering coefficient, counterweight on tower top and elastic support were discussed. According to approximate formulas of fundamental frequency, a method was put forward to estimate preliminary the lowest of foundation restraints stiffness, and the relationship of translational restraint and rotational restraint was found. Based on the above theories, counterweight character method was built. The relationship between fundamental frequency of a tower structure and its foundation stiffness was used to identify the foundation restraints stiffness by measuring different kinds of fundamental frequencies changed with counterweights on tower's top. Standard experiment has been carried out to demonstrate the accuracy of the present approach.The methods presented in this paper are adaptable to identify various kinds of restraints stiffness of tower foundations, such as high-rise structures, bridge towers, chimneys and antenna towers, as well as the condition of foundation soil and stiffness of covered structure underground. In the end, virtual testing technique and system for tower structure was studied in order to apply aforementioned methods directly to practical engineering. |