Vertical Coupled Vibration Of Piles Embedded In Saturated Soil Layers Based On Boer's Theory Of Porous Media

Coupled vibrations of saturated soils and piles are always hot and tough issues in geotechnical and seismic engineering.So far,many scholars have presented various models for such problems with theoretical investigations.However,by the summary and comparison of the related reference,it is found that the reported studies have many limitations and deficiencies,and then there exsit many significant problems worth further consideration.To this end,in this paper,several corresponding models are presented to solve or improve the aforementioned limitations and deficiencies in the existing studies.The main work is as follows:1.With the consideration of the wave effect of the soil underneath piles,by employing Hankel's integral transformation and the decomposition theory of differential operator,the mathematical model for the vertical vibration of a pile embedded in a poro-visco-elastic half-space is built.Then,the analytical solution in frequency domain for the impedance function at the pile head is derived,as well as the semi-analytical velocity solution of the pile top in time domain corresponding to semi-sine loads.2.Based on the decomposition theory of differential operator and variables,the mathematical model for the vertical vibration of a floating pile embedded in a poro-visco-elastic soil layer underlain by bedrock is established,which can include the effect of bedrock depth.Then,the analytical solution in frequency domain for the impedance function at the pile head is derived,as well as the semi-analytical velocity solution of the pile top in time domain corresponding to semi-sine loads.3.First,based on the momentum balance equation established by de Boer,the equation of motion of saturated soil in the form of displacement and pore pressure is obtained by introducing the transversely isotropic and fraction derivative constitutive relationship.Secondly,the mathematical model for the vertical vibration of a large-diameter friction pile embedded in a transversely isotropic,poro-visco-elastic soil stratum resting on rigid bedrock is built,by employing the separation technique of variables to solve the equation of motion of the saturated soil.Then,the analytical solution in frequency domain for the impedance function at the pile head is derived,as well as the semi-analytical velocity solution of the pile top in time domain corresponding to semi-sine loads.4.On the basis of the separation technique of variables,the transfer-matrix method,and the principle of superposition,the mathematical model for the vertical vibration of viscoelastic pile groups partially embedded in a layered,transversely isotropic,liquid-saturated,viscoelastic soil medium described by the aforementioned equation of motion is established.Then,the analytical solution in frequency domain for the dynamic pile-pile interaction factor and the dynamic impedance of the pile group is derived.5.The simplified mathematical model for the dynamic response of a system consisting of saturated soil and pile group and superstructure under the vertical time-harmonic motion of bedrock is built,based on a method of continuum model,Helmhotz's decomposition of potential functions,and the principle of superposition.Then,the analytical solution in frequency domain for the displacement amplification factor of the system under the bedrock motion is gained.Finally,upon the foregoing proposed solutions,the effects of pile-soil parameters of interest on the vertical coupled vibration of saturated soils and piles are investigated.Some meaningful conclusions are also drawn.