Abstract

Abstract

Abstract

Beams on elastic foundation are basic elements within structural analysis, which are used to model foundation beams, foundation piles, retaining walls, and more complex structures that include some of these elements. For their analysis, the finite element method is usually used [1], which produces an approximate solution of the problem; and the Green’s function stiffness method [2], which produces an exact solution. This article presents a methodology 100 % based on the use of Green function’s (response to a unit point force), to obtain the exact response of beams on elastic foundation. The main advantage of this formulation is its computational low cost compared to the aforementioned alternatives, and even for a large number of problems, it can be expressed only by means of sums and integrals, which can be easily performed numerically.

Also, a great variety of Green function’s for finite and infinite beams on elastic foundations with different boundary conditions are also presented, as well as some examples with the implementation of the proposed methodology.

Abstract

In recent years, significant advancements in computational efficiency have enabled the application of advanced numerical models to solve boundary value problems (BVPs) in geotechnics, including those related to large-displacement problems. However, challenging problems, such as those involving open-ended piles (OEs) in soft rocks, require specialized approaches due to material and geometrical non linearities combined to the large deformation soil-structure interaction. This paper presents a comparison of two approaches for modeling OE pile installation in soft rocks. The first approach employs the Discrete Element Method (DEM), which represents the rock as separate particles bonded together, and introduces a new contact model for highly porous rocks. The second approach uses the Geotechnical Particle Finite Element Method (GPFEM) and investigates the coupled hydromechanical effects during pile installation using a robust and mesh-independent implementation of an elastic-plastic constitutive model at large strains. The DEM approach explores the micromechanical features of pile plugging and unveils the mechanisms behind radial stress distributions inside and outside the plug. The study highlights the strengths and limitations of each modeling approach, providing insights into the behavior of OE piles in soft rocks.