Soil–Pile Interaction Analysis Using Multi-laminate Elasto-Plastic Modelling

Abstract

The safe and economical design of pile foundations are particularly important due to their usage in sensitive structures. This research aims to investigate soil–pile interaction using the numerical method and will provide greater familiarity with force distribution in deformation mechanisms in the soil as well as soil–pile interaction. Mohr–Coulomb model was used as the behavioral pattern. This model poorly applies the effects of soil anisotropy on mathematical relations. Therefore, this constitutive model was formulated within the multi-laminate framework which is of the great importance and value among different methods for material behavior modeling. This model can predict complex behavioral features, the effect of the principal stress axes rotation during plastic deformations, and prediction capability of the failure mechanism direction. The model is capable of predicting softening behavior of the soil in a reasonable manner due to using unconventional plasticity. The influences of induced anisotropy are included in a rational way without any additional hypotheses owing to natural properties of the multi-laminate framework. Results of this model were compared with test data and reasonable agreement was found. In this research, a pile sample was considered with its characteristics examined using a computer program within the framework of non-linear finite element method and multi-laminate theory. Calibrating the appropriate parameters of contact surfaces, the soil–pile interaction was estimated. Finally using the presented curves for planes, soil deformation, strain and tension controlling mechanism were identified to determine the shear failure route and critical areas with the risk of slip occurring at the pile shaft–soil interface.

Appendices

Appendix 1

The behavioral coefficient matrix is calculated at each integration point through numerical solutions. Since the objective of this study is to explain elastoplastic model based on multi-laminate theory to study the interaction between pile and soil, it is required to develop MULTI-LAMINATE formulation theory in FORTRAN programming framework. This code is introduced in following flowchart.

Appendix 2

The multi-laminate subroutine (written based on the mentioned theory in FORTRAN programming framework) have been implemented into finite element code employed to solve the non-linear equation system. This code is introduced in following flowcharts 1–12 which are included 12 subroutines.

Subroutines definition

INPMD:

Input data

COPRL:

Calculating cosines and weighted coefficient of the 13 planes

ISTRMD:

Converting stresses into node forces

LOAD:

Converting surface pressures and body forces into node forces

WPLDNL:

Applying water pore pressure to system

RESTSE:

Displacement and load increment

ALGOR:

Solving step control

STANMD:

Calculating required parameters to generate stiffness matrix

GAUSS:

Defining point’s location and weight coefficient in local coordinate

SFR:

Defining shape function and applying coordinate in Gaussian points

JACOB:

Defining Jacobean matrix

BMAT:

Calculating B matrix

FRONT:

Solving equation system

RESMD:

Calculating strain increments

OUTPMD:

Output data

DDATA and SDATA:

Calculating stress and strain components for each increment