Y M Cheng

The use of infinite element

Abstract In most practical geotechnical problems, the actual domain of soil and rock extends to infinity. For numerical analysis, a finite domain is however commonly used for preparation of finite element mesh which may, however, introduce end effects in computation. Problems involving infinite domain is best modelled with infinite element. The inclusion of body forces (gravity) in the gravity turn-on process with the use of infinite element, however, requires special care and this is considered in the present paper.

Problems with Some Common Plate Bending Elements and the Development of a Pseudo-higher Order Plate Bending Element

Anomalous results from a number of raft foundation and pile cap designs in Hong Kong employing the finite element analytical method have revealed the shortcomings of some popular plate elements. For simple cases with these problematic plate elements, this paper proposes to use simple interpolation functions to overcome the abnormalities. For more general cases, an improved pseudo-higher order rectangular plate element has been developed in this paper. The element possesses nine number of nodes which include the four corner nodes, four midside nodes and one centre node in the formulation of its shape functions. Such high order polynomials can simulate the structural behaviour much better than the classical plate element for both thin and thick plate configurations. In the formulation, the four mid-side nodes and the centre node are turned ‘pseudo’ by having their displacements incorporated into that of the four corner nodes. Such static condensation can reduce the required computer capacities as well as provide greater convenience for simulation of the structure and the boundary conditions. Comparisons with the former eight node plate element by the authors and the analytical solution by series have shown that this nine node element can perform well even when the mesh is coarse. The merits of the proposed nine node element over other popular plate elements are further illustrated by cross-comparison on a simple cantilever slab problem.

Parametric studies on the lateral restraints of pile caps in soil

The general behaviours of pile caps with vertical rectangular faces embedded in soil mass idealised as a semi-infinite elastic continuum under lateral shears and on-plan torsions are discussed in this paper. Approaches based on the elastic continuum theory with consideration of the soil pressure limited to the passive pressure values have been formulated for the estimation of lateral displacements and on-plan rotations of the pile cap. Based on the findings, parametric studies are then conducted with the production of tables for users to estimate the lateral translational and torsional resistances of pile caps and subsequently, their displacements and rotations under lateral shears and/or on-plan torsions. These tables, though not exactly reflecting the true elasto-plastic behaviour, give conservative results which are also fairly accurate as compared with that yielded by the elasto-plastic theory. The tables can therefore serve as a quick check for users without going into more sophisticated analyses such as the tedious finite element analysis by computer software. As a demonstration of the use of the tables, the method for determination of the combined actions of the pile cap and the pile group under lateral loads is also included, with the illustration of a worked example. Finally, the applicability and limitations of the approach in real cases including underground obstructions and non-homogeneity of soil properties are discussed.

Analysis of piled foundations with piles rigidly jointed to pile caps under coupled support stiffness

ABSTRACT A discussion is presented on analyses of piled foundations with the pile caps simulated as beam or slab structures supported on piles simulated as elastic springs carrying support stiffnesses with various degrees of freedom. In this paper, the shortcoming of applying only settlement, translational and rotational stiffnesses to the elastic springs for piles rigidly jointed to the pile cap in an integrated analysis of the lateral shears and out-of-plane loads for a piled foundation are explained. These shortcomings lie in the failure of this approach to account for the effects on the out-of-plane actions in the pile cap and the subsequent axial loads on the piles due to lateral translations, which can create moments at the pile heads. However, with the insertion of “coupled support stiffnesses” which relates the pile head translations to moments into the stiffness matrix of the pile cap, accurate analytical results can be obtained. As most commercial software does not allow for the input of such stiffnesses, the paper also discusses an approach that can arrive at the close analytical results and yet remain on the conservative side of estimation.

Studies on the P-delta effects of piles embedded in cohesionless soil

In this paper, an approach is formulated for analysing a pile embedded in soil in terms of the combined action of axial load and lateral shear with the inclusion of the “P-δ effect” by solving the fundamental differential equation governing the behaviour of an elastic strut supported by elastic springs by the finite difference method. As noted during the formulation of the approach, the lateral deflection and subsequently the internal force in the pile (the elastic strut) are controlled by the applied lateral shear at the pile head only under constant axial load. This phenomenon enables parametric studies to be conducted for piles so as to arrive at charts for quick determination of the lateral deflections and moments for pile heads and tips under different restraints. The approach is then used to analyse piled foundations against horizontal shears with the inclusion of the P-δ effect for piles being hinged and rigidly jointed on the underside of the pile caps with demonstration through the use of worked examples. As an alternative, another approach formulated by the finite element method is outlined and compared. Finally, the applications of the approaches for non-linear soil response, together with the tracing of load-displacement relation, are discussed.