This paper proposes a simple lattice model for collapse analysis of RC bridges subjected to earthquakesby using the extended distinct element method (EDEM). In the model, a concrete element consistsof lumped masses connected to one another by springs, and a reinforcement bar is represented by adiscrete model or an integrated model. The proposed lattice model is simple but its parameters arereasonably defined. It has fewer element nodes and connecting springs, which will be of benefit byshortening the CPU time. The processes to determine the initial stiffness of concrete and steel springs,the parameters of the constitutive model and the fracture criteria for springs are described. A re-contactspring model is also proposed to simulate the re-contact of the concrete after fracture of springs; anda general grid searching method is used to decrease the CPU time for judging re-contact after fracture.The lattice model is assessed by numerical simulations and experiments. As an application, a damagedsingle-column pier subjected to the Kobe Earthquake in 1995 is analysed by EDEM with the proposedmodel. The simulation results indicate that the proposed model predicts well qualitatively the collapseprocess of RC bridges. Copyright

A tuned liquid damper (TLD), which consists of rigid tanks partially filled by liquid, is a type of passive control devicerelying upon liquid sloshing forces or moments to change the dynamical properties and to dissipate vibrationalenergy of a structure. An analytical non-linear model is proposed for a TLD using rectangular tanks filled with shallowliquid under pitching vibration, utilizing a shallow water wave theory. The model includes the linear damping of thesloshing liquid, which is an important parameter in the study of a TLD as it affects the efficiency of the TLD. Shakingtable experiments were conducted for verification; good agreement between the analytical simulations and the experi-mental results was observed in a small excitation amplitude range. The simulations of TLD-structure interaction by usingthe proposed model show that the TLD can efficiently suppress resonant pitching vibration of a structure. It is also foundthat the effectiveness of a TLD for suppressing the pitching vibration depends not only on the mass of liquid in the TLDbut also on the configuration of the liquid as well as upon the position where the TLD is located. If the configuration ofthe liquid, i.e. the liquid depth and the TLD tank size, is designed suitably, the TLD can have a large suppressing momentand can be very effective even with a small mass of liquid.

Mechanical dampers are often installed near to anchorages of stay cables for mitigating vibrations due to wind or wind/rain. However, the optimal damping estimated by a linear theory is hard to be obtained and an efficiency factor between the designed damping and the practical one has to be considered for design. In this study, experiments of cable-damper system were conducted by using a 215 meters long full-scale stay cable. 7 types of mechanical dampers, including oil damper, viscous damper and MR damper, were adopted. The experimental results show that an inner type damper provided an additional damping (log decrement) 0.013, other outer type dampers provided additional damping larger than 0.030. Based on the experimental results, the authors suggest that the efficiency factor should be 0.3 for an inner type damper, and 0.5 for an outer type damper. The nonlinear design theory was also preliminarily studied.