Numerical Simulation Of Shaking Table Model Test Of Seismic Hydrodynamic Pressure On Bridge Piers

With the rapid development of bridge construction in China,a lot of long-span bridges,with new structure and complicated technology,have been built over the past 30 years,there are numerous highway bridges building in water depth of tens of meters or even more than 100 meters.However,the bridge pier in the water area will subject to seismic hydrodynamic pressure,which are superimposed with other seismic effects,as the loads acting on the piers,in the seismic design and bearing capacity checking calculation.While in the Guidelines for Seismic Design of Highway Bridges(JTC/TB02-01-2008),its hydrodynamic pressure calculation formula mainly standards for the bridge piers submerged within 15 meters water depth.Thus,whether the guideline is still applicable to high pier bridges and whether it needs to be modified that inspires the engineering discussions and concerns these years.This paper based on a series of shaking table tests of pier models in water tank,which were carried out by the Chongqing Transportation Research and Design Institute,in their bridge dynamics and earthquake resistance key laboratory.Under two kinds of input motions,we obtained 280 time-history test records of hydrodynamic pressure on five kinds of bridge pier models,submerged in four water depths.In addition,the corresponding fluid-structure coupling numerical simulation was adopted to obtain the hydrodynamic pressure as well.Three important basic problems were mainly studied in this paper: 1)the distribution of seismic hydrodynamic pressure along submerged depth;2)the difference and source between the test results and the numerical results;3)the limitations of the test scheme and its reasonable solutions;the applicability of the hydrodynamic force formula in codes.Firstly,based on classic researches into hydrodynamic pressure,this paper expounds the necessity of shaking table test.According to the observation quantities and experimental ways,13 experimental references are classified.In addition,about 60 numerical simulation references are summarized by the numerical methods of seismic hydrodynamic pressure,especially its variation along submerged depth.The results show that the experimental studies on seismic hydrodynamic pressure are not much,and the experimental study on its variation are rare.This paper also expounds the importance of shaking table test and numerical simulation.The pier model of shaking table test scheme is briefly introduced,especially the performance index of hydrodynamic pressure sensors and the arrangement of measuring points.From the observed hydrodynamic pressure time history records of each submerged depth,this paper reads the maximum unit-height hydrodynamic pressure as the representative value,and draws its distribution curve along submerged depth.The results show that the seismic hydrodynamic pressure increases with submerged depth deeper,and the increase rate is faster than the Goto-Toki simplified formula,which is the basic formula for guidelines of seismic design for highway bridges,and slower than the Westergaard simplified formula for vertical dam surface.Based on the model test scheme,the corresponding finite element model of fluidpier coupling system are established,with the same input motions.The basic physical quantities of potential fluid elements are firstly extracted,and calculated the time histories of seismic hydrodynamic pressure,and further read the corresponding representative values,and draws its distribution curve.The distribution curves of numerical simulation are similar with the experimental curves.The numerical results are slightly smaller than the experimental results,and the error from the bottom measuring point is slightly large.In general,the relative error of the two methods is less than 15%,it provides verification and explanation for the model test,and verifies the availability of the fluid-pier coupling numerical method in this paper.Accordingly,the test results are further discussed:(1)the hydrodynamic pressure on numerical bridge pier with rigid boundary is compared with that with infinite boundary in water domain,and the influence of boundary wave effect on hydrodynamic pressure is discussed.The results show that the wave absorbing material in the test program cannot significantly reduce the boundary wave,which can be solved by expanding the size of water domain along the direction of input motion.When,there is no significant difference between the calculation results of the 15 m length of water tank and that of the infinite boundary,which can provide a reference for the model shaking table test on hydrodynamic pressure in the future.(2)The number of numerical simulation and the scale of model are further expanded and supplemented to study the characteristics of hydrodynamic pressure increasing with the submerged depth.The results show that the hydrodynamic pressure always increases as the submerged depth deeper,with seismic intensity and total water depth become larger,the increase rate of hydrodynamic pressure slows slightly down,and gradually closes to the increase rate in classical formula.(3)The difference of hydrodynamic pressure on different cross-section shapes piers is preliminarily compared.The results show that hydrodynamic pressure on pier models with different sections is no obvious when obtaining data on the center line of the upstream surface.To study the effect of section shape,it is suggested to install pressure sensors on the edge line,and output more results from the section center to the edge in numerical results.(4)The differences in hydrodynamic pressure,internal force and deformation of piers with different materials are studied.The results show that the horizontal acceleration,velocity,displacement of pier top and shear stress of pier bottom are obviously different for different material pier models,but the hydrodynamic pressure is not obvious.Finally,according to the similarity ratio,the prototype piers are established.The hydrodynamic pressures on the prototype pier are analyzed,and compared with the revised Chinese guideline 2008 edition and Japanese guideline 2002 edition.This paper expounds the calculation formula of seismic hydrodynamic pressure on bridge pier in the two guidelines,and mainly discusses the calculation method of the hydrodynamic force,the position of its action point and the section shape coefficient in the formula.The results show that the total hydrodynamic forces are generally less than the standard value,with the ratio of 0.9-1.9.In shallow water,hydrodynamic forces calculated by the standard formula are more conservative.The action points of force are slightly lower than that of Chinese or Japanese guidelines;the shape coefficient of the circular-end section in numerical simulation are about 1.22 times than that in guideline,and it is also related to the ratio of the width of the adjacent side of the section.