Dynamic Interaction Of Pile Foundation And Transversely Isotropic Multilayered Saturated Soil

Because the natural soilis usually formed via a long-period deposit process,it thus often exhibits stratified property and the mechanical properties of the soil in the horizontal direction are often different from those of the vertical direction considerably.In eastern coastal areas of China,soils are often saturated,so to treat the soil as the transversely isotropic saturated medium is of practical engineering significance.Based on Biot's theory for the transversely isotropic saturated soil(TISS)under the axisymmetric deformation,this paper studied the dynamic response of the layered TISS,and the dynamic response of a single pile embedded in the layered TISS to a vertical harmonic load.The main contents of this paperare as follows:(1)Based on the Biot's theory for the TISS,the reflection-transmission matrix(RTM)method for the dynamic response of the layered TISS under axisymmetric deformation is established in this paper and then,the fundamental solution of the layered TISS under the axisymmetric vertical harmonic load was obtained by the proposed RTM method.Applying the Fourier and Hankel transforms to the partial differential equations satisfied by the state vector of the TISS furnishes the corresponding ordinary differential equations for the state vector.Solving the ordinary differential equations gives the general solutions for the state vector of the TISS.Based on the aforementioned general solutions,the transfer matrices of the state vector and wave vector as well as the transform matrices between the two vectors are obtained.The RTMs of the layered TISS are derived by means of the transfer matrices of the wave vector.By using the obtained RTMs,and the boundary conditions as well as the continuity conditions at the interfaces of the soil layers,the dynamic response of the layered TISS subjected to a vertical force is obtained in the transformed domain.Applying the inverse Hankel transform to the transformed domain response of the soil yields the frequency domain response of the soil.(2)By using the fundamental solution of the layered TISS subjected to the axisymmetric vertical harmonic load,the second kind of Fredholm integral equation for a single pile buried in the layered TISS is established in this paper.Firstly,on the basis of Muki's fictitious pile method,the layered TISS-pile system is decomposed into two parts: the layered TISS and a fictitious pile.Then,by using the identity of the vertical strain of the layered TISS at the original place of the pile with the axial strain of fictitious pile as the pile-soil compatibility condition and choosing the axial force and top displacement of the fictitious pile as the unknowns,the second kind of Fredholm integral equation for the single pile buried in the layered TISS is established.The axial force and top displacement of the fictitious pile can be determined by solving the obtained integral equation.Finally,the quantities of the real pile,such as the axial force,displacement and the porepressure of the TISS surrounding the pile can all be obtained with the axial force and top displacement of the fictitious pile.(3)Based on the RTM method for the dynamic response of the layered TISS,numerical simulations of the dynamic responses of the layered TISS subjected to a vertical harmonic load are conducted.Firstly,the comparison of the results obtained by RTM method with existing results validates the proposed RTM method.Then,parametric studies are carried out to investigate the influences of some factors on the dynamic response of the layered TISS under the vertical harmonic load.Numerical results suggest that the modulus of the TISS have a significant influence on the dynamic response of the TISS,while the permeability of the TISS only have a slight influence on the response of the TISS.Besides,the transverse isotropic property of the of soil also shows a significant influence on the dynamic response of the TISS.Further,the dynamic response of the TISS displays a significant frequencydependent nature.(4)Based on the second Fredholm integral equation of the pile,numerical simulations for the dynamic response of the single pile buried in the TISS are conducted.First,comparing results obtained by the integral equation for the pile with existing results verifies the proposed integral equation method.Then,factors affecting the dynamic response of the pile subjected the vertical harmonic load are studied by numerical simulations.Numerical results show that the pile impedance,the axial force and the pore pressure of the soil surrounding the pile are enhanced in the presence of a harder middle layer,while the pile impedance,the axial force and the pore pressur eof the soil surrounding the pile are decreased with the presence of a softer middle soil layer;in addition,the length and the stiffness of the pile also have a noticeable impact on the impedance of the pile: when the pile is longer or rigid,the impedance of the pile is larger,and vice versa;the transverse isotropic property of the soil also has a significant influence on the dynamic response of the pile.