Analytical solution for the soil-structure interaction of a non-uniform section pile on non-homogeneous soil conditions

Abstract

Non-prismatic piles are typically used in cases where large lateral loads must be resisted. In many applications, these elements are implemented in partially and fully-embedded layered soils to improve the load transfer to the soil with a more efficient strength distribution due to their larger cross-sectional area at the top of the element. However, they require complex and more comprehensive analysis and design than uniform elements. This investigation presents the derivation of the stiffness matrix and load vector of an analytical solution for non-uniform section piles fully and partially embedded on non-homogeneous soils. The methodology presented herein allows to i) perform static and stability analyses of non-prismatic circular piles (i.e., tapered piles, stepped-tapered piles, etc.), ii) consider soil variation along depth with a linear and trapezoidal distribution of the modulus of subgrade reaction, iii) evaluate fully and partially embedded piles in multilayered soils by just neglecting the soil contribution in the unembedded section, iv) consider partially and fully restricted connections, v) account for a Pasternak soil foundation. The Differential Transformation Method (DTM) was used to solve the governing differential equation and determine the polynomial terms that satisfy the boundary conditions. Then, compatibility conditions were applied at the bounds of each pile segment to derive the stiffness matrix and load vector. Four examples are presented to evaluate the lateral response of tapered, stepped and prismatic piles: 1) Fully-embedded tapered and prismatic pile in two homogeneous soil layers; 2) Influence a non-homogeneous layer in the lateral deformation on tapered and prismatic piles; 3) Deformation, rotation, moment, and shear profile of a tapered pile in a four layers soil; 4) Prismatic pile and non-prismatic piles partially embedded in a two-layered soil. The reliability of the proposed method is validated using finite element analysis in SAP2000 for the above-mentioned examples. The results show excellent agreement with the FE analyses at a lower computational cost, and it is observed that lateral deformations are mainly affected by the taper ratio of the pile and the thickness and stiffness relationship of the layers.

Las pilas no prismáticas suelen ser utilizadas para resistir grandes cargas laterales. En muchas de estas aplicaciones dichos elementos se implementan en suelos estratificados parcial o totalmente embebidos para mejorar la transferencia de carga al suelo con una distribución de la resistencia más eficiente, debido al incremento de la sección transversal en la parte superior del elemento. Sin embargo, requieren un análisis y diseño más complejo y exhaustivo que los elementos uniformes. Esta investigación presenta la derivación de la matriz de rigidez y el vector de carga de una solución analítica para pilotes de sección no uniforme total y parcialmente embebidos en un suelo no homogéneo. La metodología presentada permite, i) realizar análisis estáticos y de estabilidad de pilas no prismáticas circulares (i.e., pilas cónicas, pilas escalonadas, etc.), ii) considerar la variación del suelo en profundidad con distribuciones lineales y trapezoidales del módulo de reacción del suelo, iii) evaluar pilas completa y parcialmente embebidas en suelos multi capa, iv) considerar conexiones parcial y completamente restringidas, v) tener en cuenta un modelo de fundación Pasternak. (texto tomado de la fuente)