Research Of Structural Vulnerability Theory In Probabilistic And Non-probabilistic Level

Due to unexpected events and our lack of recognitions to the load and resistances, some local failure may happen to structures, even leading to the whole or progressive collapse. Since the gas explosion of the 18th floor in London Ronan Point apartment leading to progressive collapse of the balcony, this disproportionate damage of cause and result has aroused the concern of many scholars, also namely structural vulnerability. According to the nature of the external disturbance, the paper has done research on the structural vulnerability in both probabilistic and non-probabilistic level.On one hand, to the non-probabilistic disturbance, the paper takes the H2 norm of the transfer function matrices as the structural performance measurements and the relative value of the strain energy as the measurements of the initial disturbance, respectively, then gives a quantitative description of the structural vulnerability with the two parameters. Moreover, a vulnerability analysis of 2-D and 3-D truss structures is presented to validate the effectiveness and feasibility. According to the definition of failure scenarios, the element important index is identified with the minimum failure scenarios; and the shortest failure path of the structure, also namely the key path, is identified with the maximum failure scenarios; and the vulnerable path, also namely the weakness of the structure, is identified with the most vulnerable failure scenarios. By employing finite element software ANSYS and mathematical tool MATLAB, the vulnerability index is calculated, based on it, the failure scenarios are ranked, then the key path and congenital weakness can be obtained by searching the collapse and highly vulnerable rank. In collusion, based on the vulnerability index and the search method of the shortest path, it has provided a new evaluation standard to recognize the failure of the structures.On the other hand, to the probabilistic disturbance such as beyond the design load, the paper takes the string-structure as an example, considering the uncertainty of both structures and external loads, the paper did fragility analysis under exceeding loads and rare earthquakes. Firstly, based on Monte Carlo method (MC) and Latin hypercube sampling method (LHS), considering the relationship between the amplitude of live load and the failure probability, the static fragility curve has been drawn; Secondly, based on increment dynamic time history analysis (IDA), considering the relationship of different seismic waves and the failure probability of collapse, the seismic fragility curve has been drawn. At last, it investigated the effect of different pre-stress level subjected to structural fragility. Studies have shown that: basing on the fragility curves, the failure probability can be predicted under exceeding loads or rare earthquakes; and the string-structures have a low fragility, as the pre-stress increased, the structural fragility improved. Through the above research, it can provide an evaluation of the damage state of the string-structures under different range beyond load or different seismic intensity, thus provide some reference for the seismic assessment.