Probabilistic Seismic Fragility Analysis Of Step-terrace Frame Structures In Mountain Areas

Mountainous building structures are more and more widely used in many mountainous cities,among which step-terrace frame structure is the most common form of application.Due to the unequal grounding of the bottom columns,step-terrace frame structure has the inherent vertical and plane irregularities,which results in that the dynamic response characteristics and failure mode of step-terrace frame structure are very different from ordinary frame structure.In recent years,more and more attention and research have been paid to the problem of mountain building structures,and some achievements have been made.However,there are still many shortcomings in the depth and breadth of the research on mountain building structures.At present,scholars focus on the new generation of PBEE(Performance-Based Earthquake Engineering)with full probability.The core research problem is how to quantitatively describe the seismic and structural uncertainties and how to reflect the transmission process of these uncertainties.Therefore,probabilistic seismic fragility analysis,which can take into account both seismic uncertainty and structural uncertainty and reflect the process of uncertainty transmission,has become an important research content of the new generation of PBEE.Based on the above two points,this paper takes step-terrace frame structure as the research object,and carries out research on probabilistic seismic fragility analysis of step-terrace frame structure.The work of this paper has a supporting role in promoting the concept of total probability into the design of step-terrace frame structure in mountain areas.According to the existing codes in China,with seismic fortification intensity of 8degrees(0.2g),this paper designs the ordinary frame structure and the step-terrace frame structures with different number of floors dropped,a total of four prototype structures.Using the improved cloud method,this paper discusses how the correlation of structural uncertain random variables influences on the probabilistic seismic demand analysis,and the probabilistic seismic demand analysis of the step-terrace frame structures is carried out to obtain the probability seismic demand model,probabilistic seismic demand fragility curve and probabilistic seismic demand hazard curve of each structure.Then,stochastic IDA method is used to analyze the probabilistic seismic capacity of the step-terrace frame structures,and then the overall probabilistic seismic capacity model of each structure is established,and the fragility of probabilistic seismic capacity is further achieved.Finally,based on the results of the probabilistic seismic demand analysis and the probabilistic seismic capacity of the step-terrace frame structures,the probabilistic seismic fragility curve of each structure is obtained by using the analytical functions of fragility,and the probabilistic seismic fragility curves are used to evaluate the probabilistic safety of the step-terrace frame structures.The characteristics of this paper include: 1)The probabilistic seismic demand model,the probabilistic seismic demand fragility curve and the probabilistic seismic demand hazard curve are obtained by using the improved Latin hypercube sampling technique combined with the traditional cloud method;2)Using the stochastic IDA method,which combines incremental dynamic analysis(IDA)with mean value first order second moment method(MVFOSM),the overall probabilistic seismic capacity models of the step-terrace frame structures are established,and the fragility analysis of the probabilistic seismic capacity is completed;3)Based on analytic functions,the probabilistic seismic fragility analysis and the probabilistic safety assessment are carried out for the step-terrace frame structures.The main research conclusions are as follows:(1)In terms of probabilistic seismic demand analysis of step-terrace frame structures,if the correlation between random variables is not considered in probabilistic seismic demand analysis of structures,the fragility and risk of seismic demand of structures will be overestimated.The results of analysis for the four example structures show that the failure probability of the step-terrace frame structures designed in accordance with the design standard of structural design of mountain building is lower than that of the ordinary frame structure in each limit state.With the number of stories under upper embedding end increased,the failure probability of each limit state decreases further.Structural seismic hazard is the result of the multiplication of site seismic hazard and structural fragility.In this example,the two effects cancel each other out,which is reflected in the similar seismic risk curves of the step-terrace frame structures and the ordinary frame structure.(2)In terms of probabilistic seismic capacity analysis of step-terrace frame structures,the dispersion degree of seismic capacity of structures increases with the development of structural nonlinearity.The existence of structural uncertainty will increase the logarithmic standard deviation of probability seismic capacity of structures,especially for the logarithmic standard deviation of seismic capacity corresponding to Collapse Prevention CP.According to the probabilistic seismic capacity fragility curves of the four example structures,except the life safety LS limit state,the failure probability of the ordinary frame structure at different limit states is greater than that of each step-terrace frame structure.(3)In terms of probabilistic seismic fragility of step-terrace frame structures,according to the probabilistic seismic fragility curves of the four example structures obtained by using analytic functions,the failure probability of ordinary frame structure reaching each limit state is greater than that of each step-terrace frame structure.With the number of stories under upper embedding end increased,the failure probability reaching each limit state further decreases.The number of stories under upper embedding end has less influence on the probabilistic seismic fragility of Operational OP and Immediate Occupancy IO limit state,but more influence on the probabilistic seismic fragility of Life Safe LS and Collapse Prevention CP limit state.Under the action of rare earthquake,each structure presents the characteristic of multi-stage damage.The ordinary frame structure and the step-terrace frame structures designed according to the current codes of our country can achieve the fortification goal of "no collapse under strong earthquake ".