Bearing Capacity Factors for Eccentrically Loaded Strip Footings Using Variational Analysis

Xinggao Li

doi:10.1155/2013/640273

Abstract

Bearing capacity factors for eccentrically loaded strip smooth footings on homogenous cohesive frictional material are deduced by the variational limit equilibrium method and by assuming general shear failure along continuous curved slip surface. From the calculated results, the effective width rule suggested by Meyerhof for bearing capacity factors due to cohesion of soil is justified, and the superposition principle of bearing capacity for eccentrically loaded strip smooth footings is derived together with the bearing capacity factors for cohesion and unit weight of soil. The two factors are represented by soil strength parameters and eccentricity of load. The bearing capacity factor related to unit weight for cohesionless soil is less than that for cohesive frictional soil. The reason for this discrepancy lies in the existence of the soil cohesion, for the shape of the critical rupture surface of footing soil depends on both soil strength parameters rather than on friction angle alone in the previous limit equilibrium solutions. The contact between footing and soil is decided by both the load and the mechanical properties of soil. Under conditions of higher eccentricity and less strength properties of soil, part of the footing will separate from the underlying soil.

Highlights

The ultimate bearing capacity of a surface strip footing, subjected to a vertical load and resting on a ponderable cohesive frictional soil, has been studied by numerous investigators
A useful hypothesis was suggested by Meyerhof [10] to account for eccentricity of load, in which the footing width is reduced by twice the eccentricity to its “effective” size. This hypothesis was examined by Michalowski and You [14] using the kinematic approach of limit analysis for associative materials, and it is found that the effective width rule yields a bearing capacity equivalent to that calculated based on the assumption that the footing is smooth
Different from the work by these authors, the bearing capacity factors with respect to eccentricities of load are calculated, and the discrepancy between the bearing capacity factor related to unit weight for cohesionless soil and that for cohesive frictional soil is analyzed as well as the contact between footing and soil with respect to strength parameters of soil and eccentricities of load

Summary

Introduction

The ultimate bearing capacity of a surface strip footing, subjected to a vertical load and resting on a ponderable cohesive frictional soil, has been studied by numerous investigators. Numerical methods, such as the finite element method [11, 12] and the finite difference method [13], have been widely used to compute the bearing capacity of strip footings Most of these studies assume that the load applied to the footing is symmetric, and a few investigators deal with solutions to eccentrically loaded strip footings. A useful hypothesis was suggested by Meyerhof [10] to account for eccentricity of load, in which the footing width is reduced by twice the eccentricity to its “effective” size This hypothesis was examined by Michalowski and You [14] using the kinematic approach of limit analysis for associative materials, and it is found that the effective width rule yields a bearing capacity equivalent to that calculated based on the assumption that the footing is smooth. The validity of the effective width rule is justified from another approach, and the bearing factors for eccentrically loaded strip smooth footings with respect to mechanical properties of footing soil and eccentricities of load are presented and analyzed

Methods

Results

Conclusion