Abstract
The Kaiyuan Pagoda in Dingzhou has a pagoda height of 83.7 m and a perimeter of 128 meters.It was established in Song Dynasty and was the highest brick pagoda in the same period.As shown in Figure 1,the pagoda consists of a pagoda base,a pagoda body and a pagoda brake.It has eleven floor and is shrunk from bottom to top.In the tenth year of Guangxu reign(AD 1884),the northeast side of the pagoda collapsed(Figure 2(a)).In 2001,the collapsed part was repaired(Figure 2(b)),while the first floor and the pagoda base were reinforced.Today,the Kaiyuan Pagoda stands on the land of China with its majestic style.
Figure 1 Plan of the top floor
Figure 2 Photos of Kaiyuan pagoda before and after restoration
The existing masonry pagoda reflects the essence of Chinese architectural art and is quite ingenious.It is not only an outstanding representative of ancient high-rise buildings,but also an important basis for studying ancient Chinese politics,religion and culture.However,due to earthquakes,winds,water disasters and man-made damage,a large number of masonry pagodas are seriously damaged over time.When the Pagoda is subjected to traffic vibration or earthquake,it is prone to damage or even collapse.Studying the damage of the existing masonry pagoda and assessing its safety limit is an urgent problem to be solved.The dynamic characteristics of the structure can effectively reflect the structural mechanical properties and can be also an important indicator to assess its health.In general,the dynamic characteristics of a structure can be obtained from established theoretical mechanical models or on-site measurements of structures.Yuan Jianli et al.[1]analyzed the dynamic characteristics of Suzhou Huqiu Pagoda under environmental excitation,and proposed a modeling method based on classical theory,test data and numerical simulation.Chen Ping[2,3]conducted an analysis of the dynamic characteristics of Xi'an Da and Xiaoyan Pagoda,and conducted an analysis and evaluation of seismic capacity.Yang Qingshan[4],Li Tieying[5]and others researched the dynamic performance of the Yingxian wooden pagoda in Shanxi,and obtained the modal parameters of the wooden pagoda.Gao Yanan et al.[6]analyzed the dynamic response data of Feiyun Building using random subspace method improved by random decrement technique.Qin Shujie et al.[7]conducted a dynamic test on the Jingting wood structure with the characteristics of ancient Ming and Qing Dynasties in the Forbidden City in Beijing.The study also determined the type of damage of the structure and analyzed the cause of the damage[7].
Based on the ambient vibration test method,this paper proposes a new spatial test method for the ancient pagoda structure—the parallel test method.With this method,we can(1)obtain the spatial vibration mode and corresponding frequency of the Kaiyuansi pagoda.The vibration of each position of the structure is evaluated to discuss the application of the test scheme on similar ancient pagodas.(2)Based on the measured analysis results and structural dynamics theory,the inter-layer stiffness of the two orthogonal directions of the northeast and southeast sides of the ancient pagoda is reversed.The stiffness distribution of the structure is evaluated.(3)The finite element model of the ancient pagoda ABAQUS is established,and compared with the measured results,the numerical calculation model of the subsequent dynamic response analysis of the ancient pagoda is obtained.
The main results are shown in Table 1,Figure 3 and Figure 4.
Table 1 Dynamic characteristics of Kaiyuan Pagoda
Figure 3 Three order mode shape in south-east direction
Figure 4 Finite element model of the Pagoda