Transfer matrix solutions for lateral behavior of pile foundation considering the skin and end resistance effect

To investigate the contributions of vertical skin friction, vertical end resistance and horizontal shear stress of pile tip to the lateral bearing capacity of a pile foundation, this work firstly deduces analytical expression of a linear constitutive model characterizing the relationship between additional moment and slope based on the trilinear τ-s curve model of pile shafts. Furthermore, combining the four-type spring model with the presented constitutive relations for additional moment of pile shafts and pile ends, as well as the shear force of pile tip, the differential equations for a pile section is established and the corresponding transfer matrix coefficients for piles in elastic and plastic stage are derived analytically by means of Laplace transformation. Finally, transfer matrix solutions for the lateral behavior of a pile foundation is obtained on the basis of a proposed iterative methodology. The agreement between test data and the calculated results by the proposed method is quite good, which verifies the correctness of the derivation and confirms the rationality of the produced constitutive relations for additional moment of pile shafts, as well as additional moment and shear force of pile tip. Moreover, the comparison also implies that the values of additional moment M_s of pile shafts, additional moment M_b and shear force F_b of pile ends have a significant influence on the lateral load-bearing capacity of piles when large-diameter piles are embedded in stiff materials.