In Japan, to prevent the collapse of and power loss in lighthouses due to natural disasters such as earthquakes and typhoons and to ensure safe maritime traffic movement in disaster areas even after a disaster strikes, disaster-related measures including the reinforcement of lighthouses against earthquakes are implemented (Reference 5)). In the Building Standard Law, the design seismic force is calculated using the fundamental natural period of the structure. Therefore, it is important to accurately estimate the fundamental natural period in the seismic design of the structure.
The purpose of this paper is to propose an equation that can be used to accurately estimate the fundamental natural period of lighthouses. Regression analysis was used to determine the fundamental natural period estimation equation.
First, to clarify the accuracy of the estimated fundamental natural period from the existing equations, a comparison between the measured fundamental natural period from vibration tests and the value estimated using existing equations is presented. Vibration tests were conducted on four brick lighthouses, seven stone lighthouses, and fourteen reinforced concrete lighthouses (Tables 1 and 2).
Equations (1) and (2) are the existing equations. Equation (1) is given by the Building Standard Law, while equation (2) is based on the results of vibration tests conducted on eight lighthouses (Reference 8)). The fundamental natural period of chimneys is estimated using equation (3); chimneys are similar to lighthouses. However, chimneys do not have a heavy object at the top. The periods estimated using equation (1) were longer than those obtained from measurements (Fig. 4 (a)). The periods estimated using equation (2) were almost the same as those obtained from measurements (Fig. 4 (b)). The periods estimated using equation (3) were shorter than the periods obtained from measurements (Fig. 4 (c)). However, the corrected measured periods derived using equations (4) and (5) by considering the weight at the top were found to be relatively consistent with the estimated periods using equation (3) (Fig. 4 (d)).
Next, the relationship between the structural specifications and the fundamental natural period was examined. There are eight structural specifications (Fig. 5 and Equation (6)). The structural specifications that correlate with the fundamental natural period are obtained from the correlation matrix (Tables 3 and 5), and these are correlated to each other. To avoid problems due to multicollinearity in regression analysis, only the height of the structure (H) was used as an explanatory variable. The reason is that H has the strongest correlation with the fundamental natural period (the correlation coefficient was the largest). From the regression analysis, the following equations were obtained as the fundamental natural period estimation equations of lighthouses.
Brick lighthouse : T = 0.019H + 0.007
Stone lighthouse : T = 0.014H + 0.015
Reinforced concrete lighthouse : T = 0.013H
Among the reinforced concrete lighthouses, the Ujina lighthouse was excluded from the regression analysis. This is because the fundamental natural period of the Ujina lighthouse are outside the 95% prediction interval of equation (13) (Fig. 8 (c)). It appears that the fundamental natural period is increased because of damage to the foundation or structure, and because of the dynamic soil-structure interactions.
