Research On Pseudo-dynamic Method For Seismic Active Earth Pressure Of Retaining Wall Based On Curve Surface Sliding

China is located in the world's most active seismic belt,the Pacific Rim earthquake belt and the Mediterranean-Himalayan earthquake belt.It is one of the countries that suffered the most serious earthquake damage in the world.Retaining walls are the most common structures in engineering construction.They often cause deformation and damage in earthquakes due to excessive earthquake earth pressure.The main seismic earth pressure calculation methods are: pseudo-static method,pseudo-dynamic method,elastic wave method and numerical method.The pseudo-static method is widely used in engineering practice because it can formulate parameter expressions with clear forces and simple forms.However,the quasi-static method is derived from the Coulomb earth pressure theory under static force.It still belongs to the category of statics and does not reflect the dynamic characteristics of earthquakes.The elastic wave method mainly studies the interaction between walls and soils,and is mainly used for the seismic design of underground building structures.The calculation of the seismic earth pressure used for the back wall of a retaining wall will produce large errors.The numerical method can simulate the seismic earth pressure distribution on the back wall of the retaining wall under actual earthquakes.However,this method cannot provide the expression of seismic earth pressure parameters.The numerical method results are affected by the material characteristics and boundary conditions.they are applicable to "one case,one solution",that means a concrete example to simulate the specific results.On the other hand,the pseudo-dynamic method is proposed on the basis of quasi-static method.Simultaneously,two parameters of shear wave velocity and excellent frequency are introduced to reflect the dynamic characteristics of the fill and the interaction of seismic waves.Therefore,the pseudo-motive method not only proposes a parametric expression with universal applicability,but also reflects the dynamic effect of the earthquake.Compared to the pseudo-static method and numerical method,the pseudodynamic method has its natural superiority.Therefore,it is important to carry out further research on the pseudo-dynamic method,which has important theoretical significance and engineering practice value.At present,the seismic earth pressure theory under the pseudo-dynamic method is based on the assumption that the sliding surface of the wall is plane,and the actual sliding surface of the wall is in the form of a curved surface.At present,the theory of active earth pressure on surface sliding earthquake based on the pseudo-dynamic method has not yet been formed,and the relevant research results are lacking.Therefore,on the basis of the pseudo-dynamic method,this paper assumes that the sliding surface of the rear soil wedge is a logarithmic spiral plus a compound surface in the form of a straight line,and the formula for the calculation of seismic active earth pressure is deduced.The effects of the dip angle of the retaining wall,the soil vibration amplification factor,the internal friction angle,the contact friction angle,and the horizontal and vertical seismic acceleration coefficients on the active seismic earth pressure coefficient and the active seismic earth pressure distribution are analyzed and discussed.The obtained formula is further analyzed and compared with other pseudo-static and pseudo-dynamic formulas.Through the comparison of different seismic earth pressure calculation methods,it is found that under the same conditions,the seismic earth pressure results of the four methods are as follows: this method,C-N method,S-Z method,and M-O method.Based on the pseudo-dynamic method,this paper assumes that the seismic active earth pressure when the sliding surface is a curved surface is greater than the seismic active earth pressure when the sliding surface is assumed to be a plane in other methods.From the seismic wave theory,the pseudo-dynamic method still has limitations.In the far field of the earthquake,Rayleigh wave accounts for 67% of the total energy of the earthquake.Irrespective of the influence of Rayleigh waves,it is unreasonable to calculate the earthquake earth pressure.In view of this,this paper considers the seismic wave propagation equation in the far field of the earthquake.The influence of Rayleigh wave on the earthquake earth pressure behind the retaining wall,and assuming that the sliding surface of the soil behind the wall is a compound curved surface with a straight line and a logarithmic spiral line,the seismic active earth pressure calculation formula for the retaining wall under seismic action is derived.The effects of the dip angle of the retaining wall,internal friction angle,contact friction angle,horizontal seismic acceleration coefficient,and vertical earthquake acceleration coefficient on the seismic active earth pressure coefficient and active seismic earth pressure distribution were analyzed and discussed.The obtained formula is further analyzed and compared with other pseudo-static and pseudo-dynamic formulas.Through comparison,it is found that the seismic earth pressure obtained by considering Rayleigh wave's influence on seismic earth pressure behind the retaining wall in the far field is larger than the seismic earth pressure under pseudo-static method and pseudo-dynamic method considering only the influence of body waves.