The Research Of Wave Characteristic In High-rise Building Under Seismic Effect

A large number of shaking table test and seismic field monitoring data show that the building exhibits significant wave effects under the seismic ground motion.First,there is a significant time lag between the seismic response of each floor as the height of the building increases.Second,the seismic response of the building has a prominent standing wave phenomenon along the height of the building.These features cannot be properly evaluated under the framework of traditional structural dynamic theory based on the lumped mass model in a closed system.Given this,the wave response of typical medium models,including one-dimensional（1D）homogenous rod,1D series particle system and shaking table test models,under a base excitation is studied using theoretical,numerical and experimental methods in this paper.The main research contents and results are as follows:1.The progress of research and application of modern seismic theory of buildings was comprehensively elaborated.Combined with the development of high-rise buildings and their significant wave effects,the limitations of traditional structural dynamic theory were analyzed and discussed,and the theoretical route and logical framework on seismic response of high-rise buildings were further proposed.2.According to the elastic theory and the classical calculation models such as structural layer model,plane rod model and plane shear beam model,the seismic wave response of the building was theoretical investigated.The results show that the continuum-based wave mechanics is more suitable for seismic response analysis of buildings compared with the discrete particle-based structural vibration mechanics.However,the comprehensive wave analysis of buildings is not feasible for practical engineering due to the complexity of wave analysis and the discontinuity of buildings.3.Aiming at the dynamic response of a typical 1D uniform shear rod in a closed system,three methods,including the continuum-based mode superposition method,the continuum based-analytical wave method and the lumped mass-based mode superposition method,were established.Then these models were compared by parametric analysis.The results show that（1）the continuum based-analytical wave method can truly reflect the wave effect of the medium model;（2）the accuracy of the continuum-based mode superposition method depends on the number of the superposed mode.The results of the mode superposition method are basically consistent with that of the wave method when the number of the modes is sufficient large;（3）the lumped mass-based mode superposition method cannot reflect the wave characteristics of the input excitation propagating in the rod.The error of the response peak at each particle increases with the degree of dispersion,which is far from reality.4.The experimental study on five medium model with different lumped mass under pulse excitation was carried out,and the experiment data was statistical analyzed according to different parameter indicators.The results show that（1）The acceleration response profile of each model gradually increases from the bottom upwards,then a necked phenomenon appears near the top,and it increases again at the top,showing the shape of a vase as a whole;（2）the acceleration profiles of each model at different times generally cross the zero baseline,and the acceleration response of each model under pulse excitation has a significant time lag from the bottom to the top;（3）the shear force profiles of each model do not change much from the bottom to the top,and a waist phenomenon appears in the middle.The bending moment profiles of each model belong to the anti-parabolic type;（4）the deformation response of each model is fairly strong in the middle and upper part,and response in the top and the bottom are obviously opposite;（5）the measured wave velocity and empirically estimated wave velocity of each model and the theoretical equivalent wave velocity considering the actual stress state of the building are consistent in value.The empirical estimation equation of equivalent wave velocity can be applied to the uniform cantilever beam model of lateral bending deformation;（6）based on the principle of a consistent equivalent shear wave velocity,a method for determining the equivalent uniform mass and equivalent shear stiffness of a simplified shear rod model was given;（7）according to the wavelength and fluctuation images of each model during the excitation period and the steady period,the mechanism of the standing wave phenomenon under a single frequency pulse excitation and the necking phenomenon under a composite frequency excitation is revealed,and applicable range of the classical vibration theory is that the total length of the building,H,does not exceed 1/4 of the wavelength,λ.5.The shaking table test data of the three high-rise buildings of China World Trade Center Phase Ⅲ,Shanghai Center and Shenzhen Ping An Finance Center were analyzed.The results show that（1）the response law of the shaking table test of the super high-rise buildings under the input excitation is highly consistent with that of the aforementioned 1D series particle medium model.That is,the acceleration response profile or envelope of each model exhibits prominent phenomena of alternating antinodes and nodes,and the acceleration profile has multiple anisotropies along the height direction;（2）the measured value of the equivalent wave velocity of each model is basically consistent with the estimated value according to the empirical equation of c=4Hf₁;（3）according to the results of the measured wave velocity and the spectrum analysis of the input excitation,the estimated wavelength under a forced excitation of each model are given,which is basically consistent with the experimental results.Based on the results of the shaking table test data and the aforementioned theoretical and experimental analyses,the flow chart and recommended schemes for value of key parameters of the seismic response analysis of high-rise buildings is further present.6.Based on the analysis of the data of the shaking table model test of the super high-rise building and the aforementioned theoretical and experimental research results,further research is conducted on the error between the recommended equivalent wave velocity calculation formula and the measured wave velocity of the shaking table test of the three super high-rise building.The calculation method of modified equivalent shear wave velocity considering the influence of the second natural vibration frequency f₂ of the structure is given,and the equivalent shear wave velocity adjustment coefficient b is also determined.By referring to the value of the characteristic period T_g in different ground categories in"Code for Seismic Design of Buildings"GB50011-2010（2016）,the value of the effective wavelength during the actual seismic response of the building structure is preliminary presented.Combined with the method of using 1/4 wavelength l to estimate the suitable height of the classical vibration theory in Chapter 4,the building height corresponding to 1/4 wavelength l in different ground categories are given.7.On the basis of the aforementioned work,a simplified and practical analysis method for seismic wave response of building structures is proposed.Based on the principle that the equivalent wave velocity and equivalent wavelength are invariable,the building structure is reduced to the equivalent straight rod medium.The seismic response is solved using the classical wave theory.Then the obtained acceleration,displacement,interlayer deformation and other response results with wave effect characteristics are applied as external loads to the structure.The internal force response of the structure is further solved to conduct the subsequent structure design.8.An exploratory theoretical analysis of the effect of several key factors on the displacement transfer parameter was conducted according to a numerical example.The results show that（1）the displacement transfer parameter decreases with increasing input excitation frequency;（2）the greater the lumped mass,the greater the displacement transfer parameter;（3）the damping of the building reduces the node displacement transfer parameter,but the reduction effect is not significant.