Seismic Response Analysis of Multi Span Hyperbolic Brick Arch Thin Shell Structure

The research objective is to investigate the multi-span hyperbolic brick arch thin-shell structure located in Changleyuan, Baoji City, Shaanxi Province. The study utilizes on-site dynamic testing and finite element numerical simulation methods to analyze the dynamic characteristics of the thin-shell structure and its seismic response under various seismic waves and directions. The simulation results indicate the following findings: Vertical earthquakes cause more severe damage to structures compared to horizontal earthquakes. Bidirectional seismic excitation has a greater impact on the structure than unidirectional and three-dimensional seismic excitation. The obtained results provide a scientific basis for the seismic protection, reinforcement, and repair of this multi-span double-curved brick arch thin-shell structure.


Introduction
Given that old industrial buildings serve as the birthplace of modern industry and hold immense historical, scientific, and social value, it becomes crucial to understand their seismic performance.Therefore, exploring the seismic response patterns of existing old industrial buildings holds great significance.
Jiang Shan et al. [1] employed a numerical analysis method to calculate the damage morphology and assess the damage of masonry guttae structures subjected to various seismic excitations.They presented displacement patterns of ancient towers under different seismic wave excitations, obtained seismic response values for acceleration, and discussed the distribution of earthquake-induced damage.Valente and Milani et al. [2] developed a 3D finite element model for two masonry buildings, analyzing their seismic response and strengthening.They obtained insights into the damage and displacement reduction of key elements within the masonry structure under seismic excitation.Shepherd R et al. [3] demonstrated that masonry structures exhibit significantly reduced seismic performance under bidirectional horizontal seismic excitation.They further highlighted the superior seismic performance of complex brick column thin-shell structures compared to ordinary brick column structures.Kato and Ishikawa [4][5] systematically investigated the seismic response laws of thin-shell structures.They extensively explored the overall stability and collapse mechanisms under seismic excitation, assessing the stress values within the structure.Their research provides a valuable basis for evaluating the seismic performance of thin-shell structures.
This paper aims to address this gap by examining the thin-shell structure of Changle Plateau in Baoji City.Furthermore, the research investigates the seismic response behavior of this thin-shell structure when subjected to ground shaking from different directions.The findings of this study serve as a reference for seismic protection, reinforcement, and repair measures applicable to thin-shell structures.

Project Overview
The old site of the Baoji Shenxin Cotton Mill's thin shell structure factory building holds tremendous historical significance as the most intact surviving industrial site from the Anti-Japanese War in China.It gained worldwide recognition during the war and is hailed as "one of the greatest miracles of China's Anti-Japanese War" [6].Preserving and utilizing this thin shell structure from a scientific perspective, this bidirectional arched thin shell structure is relatively rare in China and holds significant importance in studying the evolution of the construction industry during that era.
The thin shell structure factory comprises three sets of workshops, totaling six individual workshops.Each workshop measures 14.72m in depth, 20.48m in width, and occupies an area of approximately 300m² .The overall appearance is illustrated in Figure1.All the workshops are constructed using brick masonry.

Dynamic test and Dynamic characteristic analysis
In the field, the dynamic characteristics of the structure are obtained by collecting the vibration signals under random ground excitation using a dynamic test device.A total of 6 measurement points were strategically positioned for data collection.Three measurement points were located at the foot of the arch, designated as monitoring points P1, P2, and P3.Additionally, three measurement points were placed at the top of the arch, recorded as monitoring points P4, P5, and P6.The layout of the monitoring points is depicted in Figure 2.
To obtain the frequency domain waveforms of each measurement point with respect to velocity and acceleration, the first-order and second-order intrinsic frequencies of each measurement point are derived [7].The frequencies corresponding to the velocity and acceleration are separately averaged, and then the averaged velocity and acceleration values are further averaged to obtain the measured results of the intrinsic frequency, as presented in Table 1.
Table 1.Measured results of natural frequency /Hz.

Establishing a finite element model
To analyze the brick arch shell structure with its complex design, an accurate structural model is created using Abaqus finite element software based on the actual survey data.Since the three groups of workshops have a similar form, only one group of workshops is simulated during the modeling process to simplify calculations.A three-dimensional finite element model of the brick arch thin shell structure is established using shell elements.The model of the factory building is depicted in Figure 3,   The material performance parameters used in the model were determined based on sample data collected during previous field testing and by referencing relevant specifications.The physical parameters of the materials are presented in Table 2.

Modal Calibration
The modal analysis of the brick arch thin shell structure is conducted using the Lanczos algorithm to calculate the self-oscillation frequencies and vibration modes of the structure.The calculated self-oscillation frequencies are compared with the results obtained from the field dynamic characteristics test,the maximum error rate between the numerical simulation and the test result is 4.14%.This indicates that the difference between the two is within an acceptable range, thus providing preliminary verification of the reliability of the finite element model.

Selection and adjustment of seismic waves
When seismic action is applied to the structure, the three factors affecting the magnitude of ground shaking, peak seismic acceleration, spectral characteristics of ground shaking and seismic time of the earthquake are considered comprehensively, and the seismic wave to be applied is appropriately adapted.The peak acceleration of ground shaking of two natural seismic waves EL Centro, TAFT and one artificial wave are all modulated to 70 Gal, and the first 15 seconds of seismic records of the three seismic waves are taken as the acceleration time range to be input, which is inputted horizontally, vertically, bidirectionally and three-way at the corresponding locations in the model.3 demonstrates that the pattern of peak relative displacement remains similar regardless of the ground shaking excitation.Notably, the TAFT wave generates the largest peak relative displacement for the structure.Under vertical seismic excitation, the peak relative displacement of the structure surpasses the corresponding values under horizontal excitation.This indicates that the structure is more influenced by vertical seismic excitation than horizontal excitation.Moreover, the peak relative displacement under bidirectional seismic excitation exceeds the corresponding values under any unidirectional excitation.This behavior can be attributed to the fact that, under larger magnitude excitation, the input vertical ground shaking reduces the restraining effect on the structure, thereby enhancing the relative motion of the thin-shell plant structure.It also suggests that the coupling of horizontal and vertical seismic excitations plays a role in increasing the relative displacement induced by unidirectional seismic excitation.4, it is evident that monitoring point P2 exhibits the largest peak acceleration response under vertical, bidirectional, and three-way excitation for all three seismic waves.This observation can be attributed to the fact that monitoring point P2 is located directly above the entrance of the east-west wall.Due to the presence of structural openings, there is a concentration of stress, leading to increased local stress.

Structural time
Regardless of what kind of ground vibration excitation, the acceleration response peak rule of change is similar, the acceleration peak of each monitoring point appears at basically close to the time point, in which the monitoring point at the foot of the arch is in the same cross-section, but the acceleration difference is larger, the monitoring point at the top of the arch acceleration difference is smaller, the structure of the acceleration response peak of the monitoring point at the top of the arch is smaller than the corresponding value at the foot of the arch.This indicates that the magnitude of the peak acceleration response decreases with increasing height of the structure.Table 4.The peak value of the acceleration response of the structure under seismic excitation/mm/s 2 .

Conclusion
The dynamic characteristic tests of the brick arch thin shell structure were simulated and verified after the structure was tested and modelled with finite element calculations.Subsequently, the displacement response law, maximum principal stress and acceleration response law of the structure under ground vibration excitation in different directions were investigated.The following conclusions were drawn: The peak relative displacements of the structure under vertical seismic waves are consistently larger than the corresponding values under horizontal excitation of the same seismic wave.Additionally, the peak relative displacements under bidirectional seismic waves exceed those under unidirectional seismic waves.Vertical earthquakes reduces the restraining effect on the structure, thereby enhancing the relative motion of the thin-shell plant structure.Horizontal directional seismic excitation and vertical seismic excitation can amplify the relative displacement caused by unidirectional seismic excitation to some extent.
Regardless of the type of earthquake excitation, the patterns of peak acceleration response are similar.The peak acceleration response at each monitoring point generally occurs around the same time.Furthermore, it is observed that the magnitude of the peak acceleration response decreases as the height of the structure increases.

Figure 3 .
Figure 3. Finite element model of workshop.Figure 4. Integral finite element model of structure.The material performance parameters used in the model were determined based on sample data collected during previous field testing and by referencing relevant specifications.The physical parameters of the materials are presented in Table2.Table2.Physical parameters of materials.

Figure 4 .
Figure 3. Finite element model of workshop.Figure 4. Integral finite element model of structure.The material performance parameters used in the model were determined based on sample data collected during previous field testing and by referencing relevant specifications.The physical parameters of the materials are presented in Table2.Table2.Physical parameters of materials.

-procedure analysis 5 . 2 . 1 .
Displacement response analysis.Figures 5,6,7, and 8 depict the displacement time history curves of the structure under various seismic excitations along different directions, providing insight into the relative displacement values of the structure under different seismic conditions.Table

Figure 5 . 6 .Figure 7 .
Figure 5. Displacement time history curve Figure 6.Displacement time history curve of the structure under horizontal wave of the structure under vertical waves

Table 2 .
Physical parameters of materials.

Table 3 .
The relative displacement value of the structure under seismic excitation/mm.