Vibration Attenuation Of Plane Waves By Periodic Pile Barriers In Saturated Soil

Pile barriers have been widely used for ambient vibration mitigation in civil and traffic engineering.While,it has become a new research subject to analyze the dynamic characteristics and to design rationally for pile barriers with periodic theory in recent years.The published studies have shown that,by proper design,the periodic pile barriers in single-phased soil yield attenuation zones(AZs),within which the wave propagation is prohibited.However,in many cases,the foundation soil is located below the surface of the water table,thus it should be considered as saturated soil.Therefore,the study of vibration isolation of periodic pile barriers in saturated soil is of fundamental interest and has important values for engineering applications.In this paper,based on periodic theory,the numerical simulation is conducted and the results are compared with others’ experimental results.The AZs and vibration isolation characteristics of periodic pile barriers in saturated soil are analyzed.The main works are as follows:The first chapter is the introduction.First,the background and significance of this study are introduced.Next,the works about vibration mitigation by pile barriers,the theory of periodic structures,vibration mitigation by periodic pile barriers,etc.are reviewed,especially for the research progress.Finally,the main works and key points of this paper are briefly introduced.The second chapter presents the fundamental theory.First,several forms of Biot’s wave equation of saturated soil are introduced.Next,the basic theory of periodic structures especially the boundary conditions are introduced.Finally,the fundamentals of COMSOL PDE finite element method are introduced,which make preparations for the research of this paper.The third chapter investigates vibration attenuation of plane waves by periodic pile barriers in single-phased soil.In order to explore the COMSOL PDE method in studying the dynamic characteristics of periodic pile barriers in saturated soil,the COMSOL PDE method is first used to study the vibration reduction of periodic pile barriers in single-phased soil,a special case of saturated soil.The Eigenvalue equation,frequency domain and time domain equation of periodic pile and single-phased soil systems are written into PDE module,and a new module that can be used to solve the AZs of the ideal periodic pile barriers and the dynamic responses of the finite rows of pile barriers is developped.In addition to the AZs and parametric investigation,responses of finite rows of pile barriers in frequency domain and time domain are conducted in terms of two-(2D)and three-dimensional(3D)models.These results lay a foundation for COMSOL PDE method to study the vibration attenuation of periodic pile barriers in saturated soil.The fourth chapter presents vibration attenuation of plane waves by periodic solid pile barriers in saturated soil.At the beginning,the Eigenvalue equation and frequency domain equation of periodic pile and saturated soil systems are written into PDE module,and a new module that can be used to solve the AZs of the ideal periodic pile barriers and the dynamic responses of the finite rows of pile barriers is developped.Then the AZs and parametric investigation are studied by the aids of the new module.On this basis,2D and 3D finite periodic pile models are built,and the numerical simulations for the solid pile barriers are conducted.Moreover,the influence of pile location,the rows of piles and pile length on vibration reduction effects are revealed.The fifth chapter presents vibration attenuation of plane waves by periodic pipe pile barriers in saturated soil.First,the new module is developped and the AZs of the ideal periodic pipe pile,filling pile barriers in saturated soil are calculated by using the COMSOL PDE method.Then,the effects of filling ratio on AZs are discussed according to Bragg scattering and locally resonant mechanisms.Based on the above discussion,2D and 3D finite periodic pipe pile models are built and the influence of pile rows and pile length on vibration reduction effects are investigated.The sixth chapter presents vibration attenuation of plane waves by periodic pile barriers in saturated layered soils.First,based on the homogenization theory of composite materials,a simplified model to calculate the AZs of periodic pile barriers in saturated layered soils is proposed.Then a new module is developped and the AZs are calculated by COMSOL PDE method.Next,vibration isolation of finite rows of pile barriers in saturated layered soils is studied in 3D contexts.The main factors governing vibration isolation behavior of periodic pile barriers are discussed,including the thickness,density and shear wave velocity of saturated layered soils.Results not only verify the proposed simplified model,but also provide guidelines for the design of periodic pile barriers.The seventh chapter summarizes conclusions and prospects.First,the main conclusions of this study are given.Then,the inadequacy of this work is pointed out,and the prospect of the following research is put forward.Some conclusions are obtained:(1)By proper design,the periodic pile barriers in single-phased soil and saturated soil can form AZs.The filling ratio of periodic pile barriers is a main factor affecting AZ.With the increase of the filling ratio the lower bound frequency(LBF),the upper bound frequency(UBF)and the width of the attenuation zone(WAZ)increase.Keeping the same filling fraction,the periodic pile barriers with square configuration have lower LBF and UBF as well as narrow WAZ than those with triangular configuration.(2)The AZ of periodic solid pile barriers in saturated soil is formed by the Bragg scattering mode.With the increase of filling fraction for flexible material,the mechanism forming the AZ for periodic filling pipe pile barriers changes from Bragg scattering mode to locally resonant mode.The properly designed periodic filling pipe pile barriers can be used to isolate vibrations with lower frequencies in engineering.(3)In both single-phased soil and saturated soils,the elastic waves with the frequency within the AZ of ideal periodic structures are effectively attenuated in both 2D and 3D finite periodic pile barrier models.The frequency response curves of 3D models converge to those of the 2D models.The 2D model can be used to predict the AZ of the 3D model.(3)With the increase of pile rows,the attenuation amplitudes increase gradually.Three rows of piles are sufficient for practical applications.When the height of the periodic pile barriers is set to be equal to the depth of the incident body waves,the body wave with the frequency in the AZ can be effectively isolated.(5)Based on the homogenization theory of composite materials,the proposed simplified model of the periodic pile barriers in saturated layered soil for calculation of the AZ can be used to predict the AZ reasonably,and the result is good agreement with the vibration isolation zone of the 3D model for the finite periodic pile barriers.For the periodic pile barriers in saturated layered soil,the thickness and hardness or softness of the first layer soil is a main factor affecting AZ.With the increase of the thickness for the softer soil,the AZ moves toward the lower frequencies.The shear wave velocity of the first layer soil has a great influence on the AZ.With the increase of the shear wave velocity,the AZ moves to the upper frequencies,and the vibration isolation turn to be more effectively.(6)By the aid of the new module developped in this paper,the COMSOL PDE method can be used to calculate the AZ of infinite periodic pile barriers and responses of finite periodic pile barriers in single-phased soil and saturated soilThe present work provides a new method for the design of periodic pile barriers in single-phased soil,saturated soil and saturated layered soil to mitigate the ambient vibration,which has theoretical significance and engineering application values.