Sensitivity analysis of short piles embedded in homogeneous soil. Part I (theoretical formulation)

Abstract

Abstract The general formulation of the sensitivity analysis of laterally loaded piles embedded in a homogeneous soil medium is presented. The described approach is based on the principles of variational calculus. The central point of analysis is connected with the concept of functional with constraints, which is then transformed into augmented functional without constraints, however dependent on the Lagrange multipliers vector. It is postulated that the functional depends on the generalized state variables and the design variables vector. The sought variation of the augmented functional due to variation of the design variables vector resulted in determination of the differential equation with respect to Lagrange multipliers vector. The solution of this equation is employed in determination of the sought variation of the initial functional. Application of the Dirac delta function to definition of functionals of kinematic and static field components of laterally loaded piles in conjunction with the Lagrange multipliers vector resulted in determination of the conjugated loads/distortions that are required to be imposed on the adjoint structure.