Analytical solution for laterally loaded non-uniform circular piles in multi-layered inhomogeneous soil

ABSTRACTNon-prismatic piles are typically used in cases where large lateral loads must be resisted. In many applications, piles are partially or fully embedded in multi-layered non-homogeneous soil, with each layer having its own set of properties. Analytical, simple solutions to study this problem are more limited and complex than that of prismatic ones. The analysis becomes even more complicated when both the variation of the cross-sectional area of the element and the soil inhomogeneity are included in the formulation. This work presents the derivation of the stiffness matrix and load vector of a non-uniform section of pile partially or fully embedded in non-homogeneous soil. The analysis of non-uniform piles in multi-layered soil is carried out by dividing the pile into multiple sub-elements and then assembling them using conventional matrix methods. Four examples, encompassing partially and fully embedded piles, are presented to validate the simplicity and accuracy of the proposed solution.KEYWORDS: Non-prismatic pilemulti-layered soilnon-homogeneous soilpartially embedded piledifferential transformation method Disclosure statementNo potential conflict of interest was reported by the author(s).List of Symbols A(x)=Area of the element at a depth xB(x)=Diameter of the element at a depth xE=Young’s modulus of the elementGp=Shear modulus of the pileI(x)=Second moment of inertia of the element at a depth xKL=First-parameter of the Pasternak foundationKo=Modulus of subgrade reactionLe=Embedded length of the pileLp=Total length of the pileLu=Unembedded length of the pileM=Bending momentm=Taper ratiomh=Variation of the modulus of subgrade reaction with depthPo=Axial loadq(x)=Applied transverse loadrb=Radius at the bottom of the elementreq=Equivalent radius at half of the length of the elementrt=Radius at the top of the elementSa, Sb=Shear stiffness of the linear transverse springs at ends A and B, respectively.V=Shear forcex=Coordinate along the longitudinal axisy=Transverse deflectionY=Non-dimensional term for the transverse deflectionkg=Second-parameter of elastic foundationκa, κb=Flexural stiffness of the flexural springs at ends A and B, respectively.ξ=Non-dimensional term for the length