Research On Shear Wave Velocity In Sand Considering The Effects Of Frequency Based On The Spherical Particle Contact Theory

Sand medium,essentially heterogeneous,is three-phase assemblage of randomly piled tiny sand particles,liquid phase and gas phase filled between particles.When elastic wave transmits in sand media,different from compression wave,shear wave can only transmit through structure composed of sand particles,instead of liquid phase and gas phase.Therefore,shear wave is considered as a key dynamic parameter to clearly exhibit sand structure,arranging and contacting features of sand particles.Meanwhile,the study on shear wave velocity in sand has important engineering significance.In earthquake engineering,shear wave velocity in sand is an important indicator of its anti-liquefaction performance,which can be applied in determining the dynamic response and anti-vibration liquefaction capacity of the site.Previously,the research on the shear wave velocity in sand has focused on the macroscopic scale.In recent years,the research on micro-scale has paid more attention to the nature of the sand particle itself,without involving the nature of the shear wave.Based on the spherical particle contact theory,and considering the effects of the frequency,this paper focuses on the rotation of the sand particles caused by the shear wave propagation process,and makes a theoretical study on the shear wave velocity in the sand medium in a microscopic scale.The main work and research results of this paper are as follows:(1)The three basic assumptions of this paper are given,and the sandy media studied is modeled.According to the spherical particle contact theory under microcosmic scale,the formula for shear wave velocity in granular medium is deduced considering the rotation of the particles caused by the shear wave propagation process;furthermore,the relevant parameters which are not easily measured directly are re-parameterized;finally,the formula of shear wave velocity in sand involving frequency parameter is introduced.When the parameters change in the common range of actual engineering sand medium,the quantitative parameter analysis is made using the deduced formula of shear wave velocity in sand.Through parameter analysis,the effects of eight factors on the shear wave velocity of sand are studied,including the elastic modulus of sand particles,Poisson's ratio of sand particles,sand particle density,sand particle radius,porosity of sand media,effective angle of internal friction of the sand media,vertical effective stress on sand body unit,and frequency.And the effect result of each factor on the shear wave velocity in sand is analyzed.(2)According to the formula of the shear wave velocity in sand,the dispersion curve of the shear wave propagating in the sand medium is obtained by using the parameter calculation method.The dispersion characteristics of the shear wave propagating in the sand medium are analyzed.It is considered that the shear wave velocity starts to increase significantly with the increase of the frequency when the shear wavelength is 12 times of the sand particle radius.According to the dispersion characteristics,the critical frequency of shear wave in sand medium is defined.After the mathematical derivation,the exact expression of the critical frequency is provided,and the influence factors,along with each of their effect,of the critical frequency in the sand medium are determined.In order to facilitate the engineering application,on the basis of the exact expression of the critical frequency,a reasonable mathematical treatment is carried out,and a simplified expression of the critical frequency in the sand medium is obtained.(3)Using the equivalent medium theory,the modified coefficient of particle shape is introduced to derive the equivalent shear modulus of the particle medium without considering the particle rotation,and the theoretical maximum shear wave velocity formula in the sand medium based on the equivalent medium theory is obtained.Meanwhile,the simplified formula of shear wave velocity in sand is obtained by reasonable mathematical simplification to facilitate the engineering application.On the basis of the comparison between the two shear wave velocity formulas deduced respectively based on the two theories mentioned above,the formula of shear wave velocity in sand which is deduced based on the equivalent medium theory is corrected.(4)The theory and formulas proposed in this paper are validated by conducting the indoor bending element test and using the down-hole method to measure on-site shear wave velocity.The calculation results of this method are compared with 12 sets of indoor bending element test data and 50 sets of on-site shear wave velocity measurement data respectively.The rationality,correctness and applicability of the theory and the derived formulas in this paper are verified.